Document [original]

Small-scale mechanical properties and functional fatigue of

Ni-Mn-Ga

Small-scale mechanical properties

and functional fatigue of Ni-Mn-Ga

Adnan Fareed - Dissertation

Small-scale mechanical properties and functional fatigue of

Ni-Mn-Ga

vorgelegt von

Adnan Fareed, M.Sc.

ORCID: 0009-0001-9212-1269

an der Fakultät III - Prozesswissenschaften

der Technischen Universität Berlin

zur Erlangung des akademischen Grades

Doktor der Ingenieurwissenschaften

- Dr.-Ing. -

genehmigte Dissertation

Promotionsausschuss:

Vorsitzender: Dr.-Ing. Sören Müller

Gutachterin: Prof. Dr. Isabella Gallino

Gutachter: Prof. Dr. Robert Maaß

Tag der wissenschaftlichen Aussprache: 26. Juni 2024

Berlin 2024

Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga Adnan Fareed

Abstract

The phenomenon of shape-memory response due to stress has been extensively studied at the bulk

scale for a wide variety of conventional shape-memory alloys, as well as their magnetic counterparts.

With the exception of NiTi and CuAlNi, the response is still largely unexplored at relevant scales for

applications in micro- and nanomechanical systems (MEMS and NEMS, respectively). A size effect

is expected when the surface-to-volume ratio approaches a critical threshold since the functional

characteristics of the Ni-Mn-Ga alloys are heavily dependent upon twin dynamics and martensitic

phase transformations. Given the enormous potential for small-scale actuators in the Ni-Mn-Ga

system under investigation, this work aims to provide an understanding of the stress-induced

martensitic phase transformation when probing small-scale volume, and to use this material in small-

scale applications, how this material responds under stress during cyclic loading (functional fatigue)

for long-term reliability.

First, employing the nanomechanical technique, we examine the temperature-dependent stress-

induced martensitic phase transformation in single-crystalline austenitic thin films. During

nanoindentation of 0.5 µm thin films, a distinct incipient phase transformation to martensite occurs,

leaving regions of residual martensite upon the removal of the load. These pop-ins occur regardless

of deformation rate or temperature, are Weibull-distributed, and show significant spatial variations in

transformation stress. On the contrary, completely reversible transformations occur at a film

thickness of 2 μm, and mechanical loading remains completely smooth. Ab-initio simulations explain

the thickness-dependent nanomechanical behavior by demonstrating how in-plane limitations could

significantly elevate the martensitic phase transformation stress.

For functional fatigue investigation, we employed micro-compression testing on cylindrical

microcrystals of austenitic thin films with a nominal radius of 2 μm. Ni-Mn-Ga exhibits its ability to

withstand up to a million superelastic cycles without any significant reduction (~ 2–3%) in its initial

switching strain. A similar response is also observed even when dislocation and slip bands are

introduced. This increase in plastic strain eventually leads to lower phase transformation stress.

There is no presence of residual martensite, which can be identified through STEM either for 106

cycles microcrystal or pre-deformed microcrystal. The hysteresis response of the microcrystal is five

times smaller compared to its bulk counterpart. The transformation stress is roughly twice compared

to the bulk value, and it deforms in the range of 1-1.4 GPa, which results in a significant size-affected

stress range for mechanical switching.

For tensile testing, we used the free-standing film, demonstrating 30% engineering strain. However,

due to contaminating nano-scale surface layers arising either during film fabrication or during tensile-

sample preparation, detailed quantitative testing could not be carried out meaningfully.

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

Table of Contents

Abstract .................................................................................................................................I

Table of Contents .................................................................................................................2

LIST OF ABBREVIATIONS ...................................................................................................5

Chapter 1: INTRODUCTION AND SCIENTIFIC BACKGROUND .........................................7

1.1 Shape memory alloys .................................................................................................8

1.2 Magnetic shape memory alloys ................................................................................ 11

1.3 Ni-Mn-Ga microstructure and thin films growth challenges .................................. 15

1.4 Adaptive martensite concept.................................................................................... 17

1.5 Thin film fabrication challenges ............................................................................... 19

1.6 Objectives of this thesis ........................................................................................... 20

CHAPTER 2: EXPERIMENTAL METHODS ........................................................................ 24

2.1 Samples material and characterization ................................................................... 24

2.2 AFM analysis ............................................................................................................. 29

2.3 FIB milling .................................................................................................................. 30

2.4 TEM analysis ............................................................................................................. 31

2.5 Nanoindentation and associated data analysis ...................................................... 34

2.5.1 Deformation modes .............................................................................................. 35

2.5.2 Data processing ................................................................................................... 38

2.5.3 Maximum Likelihood Estimation (MLE) .............................................................. 40

2.6 Microcompression and micro-tensile testing .......................................................... 43

2.6.1 Microcompression testing ................................................................................... 43

2.6.2 Temperature dependent nanoindentation and compression testing ............... 46

2.7 Tensile testing and analysis ..................................................................................... 48

CHAPTER 3: RESULTS AND DISCUSSION ....................................................................... 52

3.1 Constrained incipient phase transformation in Ni-Mn-Ga films: A small-scale

design challenge ....................................................................................................... 52

3.2 Small-scale functional fatigue of a Ni-Mn-Ga Heusler alloy ................................... 68

3.3 Ni-Mn-Ga free-standing film behavior in Tension ................................................... 89

SUMMARY AND OUTLOOK ............................................................................................... 96

LIST OF PUBLICATIONS .................................................................................................... 96

Reference List .................................................................................................................. 101

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

Acknowledgments

I want to express my heartfelt thanks to everyone who joined me on this journey, beginning

with my supervisor, Professor Robert Maaß. His support, invaluable guidance, and exceptional

mentorship throughout my doctoral research have been instrumental in shaping this

dissertation. Your expertise, encouragement, and unwavering commitment to excellence have

been the driving force behind my success. I am grateful for the opportunity to be your first

graduate at BAM and for your continued encouragement and support.

I extend my appreciation to Prof. Isabella Gallino for her supervision at TU Berlin and to Dr.-

Ing. Sören Müller for graciously accepting the role of committee chair on short notice. I am

thankful to our project collaborator colleagues, PD Dr. Sebastian Fähler, Dr. Heiko Reith, and

Satyakam Kar, for providing us with the samples and working with us on the papers. I am also

thankful to Dr. Tilmann Hickel and Dr. Sourabh Kumar for collaborating with us on the first

paper and providing us with simulation data. I want to express my gratitude to Dr. Julian M.

Rosalie for his support with TEM data and input on the work throughout my time at BAM.

Thanks to all the group members, especially Birte, for always helping with small tasks, either

work-related or German bureaucracy. Thanks to Reza, Sydney, Vara, Yuki, and Zengquan for

everything, giving your nanoindenter slot, and supporting me in many other ways. Thank you

for all the science group discussions, the monthly dinners, and the weekly lunch gatherings.

You guys are all fantastic colleagues and good friends. I would also like to thank our former

department assistant, Ms. Wiedmann, and our current department assistant Catherine for

helping with department affairs and handling all the matters regarding inventory orders and

business travel. Thanks to all the department colleagues who assisted and supported me

during my work. I am thankful to René Hesse for his help with TEM sample preparation and

FIB training and his willingness to assist with minor issues in the laboratory. I also want to

thank Dorothee Silbernagl for providing AFM training and measurements. Thank you to

Leonardo and Anna for their insightful scientific discussion. Additionally, I would like to express

my appreciation to M. Griepentrog for Nanoindentation training and to Oliver Schwarz for his

support at the nanoindenter lab throughout my work. I am also grateful for the financial support

provided by the BAM-IFW (Grant No. MIT1-2063-IFW) funding scheme and for the institutional

support from BAM.

I want to express my gratitude to my parents, Fareed Ullah and Shahjeera Bibi, for their

unwavering support and encouragement throughout my educational journey. I dedicate this

degree to them for their emotional and financial assistance, which helped me attain this

milestone. I would also like to thank my siblings for their constant support and inspiration during

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

challenging times. Thanks to all my friends for their support and encouraging words during

tough times. Thanks to my friend Faizan for his support and encouragement.

Finally, I would like to express my heartfelt gratitude to my wife, Zubeena, for the unwavering

support and encouragement she provided me throughout this journey. We got married two and

half years ago, and this was the beginning of my Ph.D., and I could not have imagined going

through this without you. Although you were in Pakistan, you still greatly helped with your kind

words, support, and encouragement. Now that you are here with me in Germany, I feel more

confident and prepared to embark on the next chapter of our lives together.

Thank you.

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

LIST OF ABBREVIATIONS

AFM

ATOMIC FORCE MICROSCOPY

BCC

BODY-CENTERED CUBIC

BCT

BODY-CENTERED TETRAGONAL

CCDF

COMPLEMENTARY CUMULATIVE DISTRIBUTION FUNCTION

DFT

DENSITY FUNCTIONAL THEORY

EDX

ENERGY DISPERSIVE X-RAY SPECTROSCOPY

FCC

FACE-CENTERED-CUBIC

FIB

FOCUS ION BEAM

FSMA

FERROMAGNETIC SHAPE MEMORY ALLOY

MFIS

MAGNETIC FIELD INDUCED STRAIN

MLE

MAXIMUM LIKELIHOOD ESTIMATION

MEMS/NEMS

MICRO- AND NANOMECHANICAL SYSTEMS

NM MARTENSITE

NON-MODULATED MARTENSITE

PSPD

POSITION-SENSITIVE PHOTODIODE

PVD

PHYSICAL VAPOR DEPOSITION

PAV

PLANE-AUGMENTED WAVE

PES

POTENTIAL ENERGY SURFACE

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

PDS

PROBABILITY DENSITY DISTRIBUTION

PID

PROPORTIONAL-INTEGRAL-DERIVATIVE

P2P

PUSH TO PULL

SEM

SCANNING ELECTRON MICROSCOPE

STEM

SCANNING TRANSMISSION ELECTRON MICROSCOPY

SADP

SELECTED AREA DIFFRACTION PATTERN

SMA

SHAPE MEMORY ALLOY

TDNC

TEMPERATURE-DEPENDENT NANOINDENTATION /

COMPRESSION

TOV

TRANSDUCER OUTPUT VOLTAGE

TEM

TRANSMISSION ELECTRON MICROSCOPY

VSM

VIBRATING SAMPLE MAGNETOMETER

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

Chapter 1: INTRODUCTION AND SCIENTIFIC

BACKGROUND

Ni-Mn-Ga alloys have been extensively investigated because of their promising outstanding

actuation characteristics by magnetically induced reorientation and magnetocaloric properties.

Most of the work has been focused on either bulk alloys or alloys in martensitic phases

(Chernenko et al., 2004a; Chernenko et al., 2005; Chmielus et al., 2009; Reinhold et al., 2009).

The underlying martensitic transformation is the critical factor determining these functional

properties. However, at relevant scales for applications in micro- and nanomechanical systems

(MEMS and NEMS, respectively), the response remains largely unexplored, with the exception

of NiTi (Frick et al., 2007) and CuAlNi (San Juan et al., 2007). Given the tremendous potential

for small-scale actuators in the Ni-Mn-Ga system under consideration, an effort is therefore

required to understand its cycling behavior under stress. It has been proposed that size effects

may occur when the characteristic length of the phenomenon interacts with a characteristic

size parameter, and different behavior can be expected from the constrained and free

surfaces. These hypotheses were based on polycrystalline material (bulk, wires, foam), as

experiments on well-defined geometries and orientations were missing. This is partly because

earlier work concentrated on martensitic material (Satapathy and Aich, 2019) or because of

high-indentation forces utilized for studying phase transformations through imaging post-

deformation (Ghahfarokhi et al., 2023; Niemann et al., 2016). Although, this is very much

reminiscent of known size effects in the NiTi system, for which some works suggest a functional

loss at or below physical sizes of ca. 60–50 nm (Fu et al., 2006; Waitz et al., 2004). This project

aims to use small-scale volume probing techniques to understand martensitic phase

transformation in thin films, microfabricated columns, and free-standing samples to identify

critical sample sizes at which true plastic deformation leads to a loss of the pseudoplastic

shape-memory effect. Microcrystals microfabricated using a focus ion beam are compressed

for up to a million cycles for size effect and functional fatigue study. This small-scale

mechanical test will be complemented with post-deformation structural characterization using

transmission electron microscopy to analyze any change in the structure of the microcrystals.

We will furthermore identify the plastic mechanisms that promote the loss of pseudoplasticity

via careful transmission electron microscopy analysis. Our experiments will address switching

due to quasi-static loading in both tension and compression, as well as cyclic dynamic loading.

Commercially available push-to-pull (P2P) devices will be used for tensile testing. In concert,

these efforts will not only quantify the small length scale at which reliable Ni-Mn-Ga shape-

memory actuators can be used, but we anticipate that this work will serve as a standard for

future identification of size-dependent shape-memory behavior in other Heusler alloys.

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

1.1 Shape memory alloys

When stress is applied to a material, it may undergo deformation. If the deformation is elastic,

the material will regain its initial shape once the applied stress is removed. However, if the

material undergoes plastic deformation, it may retain some or all of the deformation even after

the stress is removed. Some materials can recover their shape when the applied stress is

removed upon an application of heat or through phase transformation; materials with such

properties are known as shape memory alloys (SMAs). SMAs have two phases: high-

temperature austenite (Xu et al., 2013) and low-temperature martensite, which is further

characterized as modulated and non-modulated martensite (Pagounis et al., 2014; Sozinov et

al., 2013; Sozinov et al., 2002a). SMAs exhibit unique properties known as pseudoplasticity,

shape memory effect (SME), and superelasticity.

These properties are associated with the de-twinning of martensite, the change from de-

twinned martensite to austenite under temperature stimuli, and the direct transformation of

austenite into the martensite phase under stress stimuli. We can expect different properties

from these materials depending on what kind of phase is probed. Figure 1.1 represents the

schematics of different properties of SMAs as a stress-strain-temperature diagram. In this

figure, Ms and Mf are martensite start and finish temperatures, whereas As and Af are the start

and finish temperatures of the austenite phase. The SME is observed in the martensitic phase,

whereas superelasticity is observed in the austenite phase. To explain these two properties,

first, we need to understand the twinned and de-twinned martensite and its transformation to

austenite.

Fig. 1.1: Shape memory effect, and superelasticity behavior exhibited by SMAs. (Adapted

from (Seo et al., 2015))

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

Figure 1.2 further illustrates the formation of different variants, twin boundaries, and lattice

constants in the austenite and martensite phases. The planes of the martensitic structure can

move plastically, forming a collection of twin domains interconnected by dynamic twin

boundaries. This is a martensitic phase with a tetragonal structure, where lattice constants are

different and oriented in various directions. As a result, martensite regions with varying

orientations become distorted in relation to their surrounding lattice. As a result, local strain

can cause expansion or shrinkage along the preferred crystallographic direction. In the

martensitic phase, the applied stress deforms the material, and for shape recovery, the

material is heated from its martensitic phases until it is above the austenite finish temperature.

In this way, the material recovers its original shape, and after the removal of temperature, it

transforms back to the martensite phase. On the other hand, when stress is applied to the

austenite phase, it transforms directly into the martensitic phase. In this case, we do not require

any temperature element, and once the applied stress is removed, it is transformed back to

the austenitic phase. Shape memory effect and Superelasticity are further explained below.

Fig. 1.2: (a) Lattice constant of austenite, (b), (c) lattice constant for tetragonal structure, (d)

martensite variants separated by twin boundaries. (This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

Figure 1.3 illustrates the diagram of the thermal shape memory effect, depicting the

progression from twinned martensite to de-twinned martensite, austenite, and the subsequent

transformation back to de-twinned martensite. In the initial stage, we have twinned martensitic

phase material where we have regions with different crystal orientations separated by twin

boundaries. The movement of these twin boundaries occurs by external stress, leading to the

introduction of extra energy into the system. Since we have different orientations in the

martensite phase, the applied stress favors the orientation perpendicular to the applied

compressive force. This way, the system required the least energy to move the twin boundaries

in a particular direction, thus producing a single orientation de-twinned martensite. Once

twinned, martensite is transformed into de-twinned martensite; it does not return to its initial

stage after removing the applied stress. For the shape memory effect to happen, we have to

increase the temperature of the material to austenite start temperature. This rise in

temperature supplies the material with thermal energy, enabling it to overcome the energy

barrier required for the phase transformation from de-twinned martensite to austenite. Once

the temperature exceeds the As, the austenite phase is initiated by nucleation and forms small

regions within the de-twinned martensite. Austenite transformation is completed by further

increasing the temperature over Af, and the material is now fully austenite. This process

enables the material to return to its original form, called the shape memory effect. Since the

austenite phase is unstable at this high temperature, once we cool the sample, it recovers back

Fig. 1.3: Thermal shape memory effect, also known as two-way memory effect (a) twinned

martensite (b) twinned martensite is deformed to de-twinned martensite by stress (c) de-

twinned martensite transformed to austenite by heating above austenite temperature (d)

austenite transformed back to twinned martensite by cooling below martensite temperature.

(Adapted from (Stachiv et al., 2021))

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

to the same martensitic phase structure where we began the deformation. This phase

transformation is a diffusionless mechanism, which means it does not involve any change in

the chemical composition. Rather, the recovery process is associated with structure

rearrangement in the crystal lattice.

On the other hand, when austenite is subjected to stress instead of undergoing elastic

deformation, it can transform into martensite, which is energetically favorable since it can

accommodate the applied stress by variant redistribution without the need for elastic

deformation of its unit cell (L'vov and Chernenko, 1999). In Fig 1.1, a transition point can be

observed, where the phase changes from austenite-martensite under stress. Subsequent

compression causes a plateau in the stress-strain curve with very low yield stress, as observed

during martensite variant redistributions with low stress < 1 MPa. If further stress is applied

beyond the plateau regime, the stress rises significantly with very little strain. Thus, the

martensitic transformation is almost complete, and additional stress is mainly accommodated

elastically. Upon removal of applied stress, it will follow an unloading curve a path parallel to

the loading curve, and the strain is largely recovered.

NiTi, also known as nitinol, is the most well-known shape memory alloy, first discovered by

Buehler in 1963 (Buehler et al., 1963) while investigating material for heat protection. Although

similar behavior was observed in several other alloys, Au–47.5at.%Cd, In–Tl (Basinski. and

Cwristian., 1954; Burkart and Read, 1953; Chang and Read, 2017), prior to NiTi, these alloys

were unable to attract as much attraction as NiTi. Its properties which are common in many

other shape memory alloys, it also possesses some unique properties like low elastic

anisotropy, high ductility, corrosion, and abrasion resistance, which make it suitable for many

commercial applications, including bio-medical applications, aviation field, and small scale

sensors and actuators (Choudhary and Kaur, 2016; Duerig et al., 1999; Niinomi., 2016; Quan

and Hai, 2015) contrary to any other shape memory alloys.

1.2 Magnetic shape memory alloys

Magnetic shape memory alloys (MSMAs), often referred to as ferromagnetic shape memory

alloys (FMSMAs), have emerged as a novel category of materials that have received a lot of

attention owing to their distinctive characteristics. MSMAs are exceptional compared to other

ordinary-shaped memory alloys because they can achieve large strains in the martensitic

phase using a magnetic field. These alloys possess unique properties known as the magnetic

shape memory effect (MSME) (Sozinov et al., 2013; Sozinov et al., 2002a), magnetic field

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

induced strain (MFIS) also known as Magnetic induced reorientation (MIR), Magnetic induced

martensite (MIM), and ferromagnetic shape memory (FMSM) effect (Murray et al., 2000).

Figure 1.4 demonstrates the MFIS, whereby applying a magnetic field to the unit cell causes

a transition from one variant to another variant. This is achieved by matching the magnetically

easy axis with the magnetic field vector (Mauch et al., 2023).

Contrary to the MFIS effect, these alloys also go into switching behavior by the application of

stress or change in temperature, as observed in conventional shape memory alloys.

Nevertheless, a phase transition is not necessary for the MSME effect, which takes place in

the martensitic phase. Thus, MSME is much faster in comparison to the thermal SME. MFIS

was initially identified in Ni2MnGa single crystal where 0.2% strain was observed along [001].

Since then, extensive research has been conducted to achieve larger and larger strains, with

up to 12% of strains achieved in Ni-Mn-Ga (Sozinov et al., 2013). Although many other MSMAs

possess magnetic shape memory effect e.g. Fe-Ni-Co-Ti (Murray et al., 1999), Fe-Pt

(Kakeshita and Ullakko, 2002), Co-Ni-Ga (Singh et al., 2011), Ni-Mn-Ga-Fe (Koho et al., 2004),

Ni-Mn-Al (Acet et al., 2002), Co-Ni-Al alloys (Murakami et al., 2002), Fe-Pd (Sánchez-Alarcos

et al., 2008), Ni-Mn-Ga has received so much attention because of its unique magneto-

mechanical properties.

In order to further explain how MFIS is achieved, we first need to understand how magnetic

fields prefer specific crystallographic directions in tetragonal martensite. This preferred

Fig.1.4: Magnetic field induced strain (MFIS), also known as Magnetic induces reorientation

(MIR) concept. (a) Twinned martensite (b) Magnetic field is applied, (c) Redistribution of the

twin variations occurs in response to the applied magnetic field. (Adapted from (Milleret,

2022))

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

crystallographic direction is known as the short axis; it is the orientation in which the sample

needs the least energy in order to match the magnetic moment of the material to the applied

magnetic field. There are three possible variants (V1, V2, and V3) in low-temperature

martensite tetragonal structure illustrated in Fig.1.5. Transformation from austenite to

martensitic phase demonstrates extremely complex microstructure, which is a variety of

different twin variants (Niemann et al., 2017; Zhou et al., 2017). The twinning stress must be

smaller for twin boundary motion than the maximal magnetic stress. To ensure that twinning

stress is lower and to achieve large strain in the martensitic phase, we need a sample with a

single variant instead of a multivariant complex structure for the easy movement of twin

boundary motion in the sample under a magnetic field. Using suitable mechanical treatment,

multivariant complex martensite samples can be transformed into a single variant of the

Fig. 1.5: Cubic austenite to tetragonal martensite three variants transformation. Three

variants with easy axis magnetization direction marked with the green circle are shown for

martensite in the Mc axis. (Adapted from (Kiefer and Lagoudas, 2005))

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

martensitic phase, called the de-twinning process (Chmielus et al., 2008). The mobility of twin

boundaries in modulated martensite can be induced by mechanical stress below 0.1 MPa,

which makes these materials deform as easily as rubber (Straka et al., 2011; Straka et al.,

2010).

By achieving a single variant martensite sample using the de-twinning technique, which may

then be subjected to a magnetic field aligned with the easy axis. Figure 1.6 is an example of a

7M modulated martensite where the magnetic field is employed in [100], [010], and [001]

directions. We can observe that for [001], which is the hard axis, the magnetization curve

reaches its capacity at a very low magnetic field value and remains constant with an increasing

magnetic field. On the other hand, [100] is the easy axis where magnetization increases linearly

until it reaches saturation. On the contrary, we also have an intermediate axis [010] where the

magnetization increases with the magnetic field but as an intermediate stage to both the hard

and easy axes. In order to achieve a large strain, we need to apply a magnetic field along the

easy axis.

Fig.1.6: Magnetic field (T) plotted against normalized magnetization (M/Ms) along three axes

in a 7M modulated martensite sample. (This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

1.3 Ni-Mn-Ga microstructure and thin films growth challenges

Modulated and non-modulated martensite

Ni2MnGa in high-temperature austenite phase can be described by L21 structure. L21 is based

on a body-centered cubic (BCC) structure, where four face-centered cubic (f.c.c) sublattices

interpenetrating with each other with a lattice parameter of about a = 0.5825 nm at room

temperature (Brown et al., 2002), shown in Fig. 1.7a. The atomic positions of Ni, Mn, and Ga

according to space group Fm3m are as follows: Ni – 8c (14,14,14), Mn – 4a (0,0,0), Ga – 4b

(12,12,12) respectively. This L21 structure results from the B2 phase at about 750°C, which is

partially disordered; it can be obtained by keeping the Ni atoms fixed while interchanging half

of the positions of the Mn and Ga atoms (Overholser et al., 1999). Due to the complex interplay

of different factors such as composition, temperature, and external stimuli like stress and

magnetic field, Ni2MnGa can transform from high-temperature austenite to 7M (seven-layered

modulated also known as 14M), 5M (five-layered modulated, also known as 10M) or NM (non-

modulated, also known as 2M). The crystal configurations of martensite (10M and 14M) exhibit

unique lattice properties, and their schematic representation is shown in Fig.1.8. The 10M

martensite has a body-centered tetragonal arrangement with a c/a ratio of 0.93 (c/a < 1) and

dimensions of a = 0.59 nm and c = 0.54 nm (Pons et al., 2000). Webster first reported this in

a stoichiometric Ni2MnGa alloy (Webster et al., 2006). The tetragonality of the 10M lattice rises

as the temperature lowers, eventually stabilizing at extremely low temperatures.

Fig 1.7: (a) L21 structure for full Heusler alloys in austenite phase with four f.c.c interpenetrating

sublattices. (b) B2 structure. (Adapted from (Yamamoto et al., 2011))

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

In contrast to 10M, Martynov, and Kokorin (Martynov and Kokorin, 1992a) found that 14M

martensite has an orthorhombic structure with a c/a ratio of 0.89 and c/a less than 1, as well

as a monoclinic distortion of < 0.4° (Sozinov et al., 2002b). The lattice parameters are a =

0.614 Å, b = 0.578 Å, c = 0.551 Å, and γ = 90.5°. The 10M modulated martensite exhibits a

periodic rearrangement characterized by a long period arrangement of {110} closely packed

planes, with a stacking series of (32) atomic unit cells (AUC) yielding a recurrence of 10 layers.

Despite the 10M cell having complete symmetry, it is commonly abbreviated as 5M. Similar to

10M, the 14M martensite exhibits periodic shuffling with a long period arrangement of {110}

closely packed planes, with an alternating arrangement of (52) AUC yielding a recurrence of

14 layers. Despite having complete symmetry, it is typically known as 7M. Electron or X-ray

diffraction investigations can identify 5M and 7M modulations, showing four or six extra peaks

among the principal reflections along the [110] axis in reciprocal space (Pons et al., 2000; Zhou

et al., 2017).

The non-modulated martensite, also known as 2M, has a tetragonal structure with lattice

parameters a = 0.552 Å and c = 0.644 Å, also found by Martynov and Kokorin (Martynov and

Kokorin, 1992a) for the first time. As the name suggests, the non-modulated structure has no

periodicity as observed in the 5M and 7M in [110] direction. The non-modulated martensite c/a

ratio is larger than one (1.18 – 1.25) mostly depends on the composition of the system (Lanska

et al., 2004). The transition from c/a < 1 to c/a > 1 is observed when the valence electron to

Fig. 1.8: Crystal structure is shown schematically as follows: (a) long periodic arrangement

of 10 atomic layer structure in {110}, also known as 5M, (b) Periodic stacking of 14 atomic

layer structure, also known as 7M. (Adapted from (Liang et al., 2022))

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

atom ratio (e/a) > 7.7 which in the case of modulated martensite is smaller than 7.7 (Lanska et

al., 2004). Non-modulated martensite, along with pre-martensite, is represented schematically

in Fig. 1.9a,b. Apart from modulated and non-modulated martensite, pre-martensite is also

observed in one of our austenitic thin films. Pre-martensite does not affect the cubic symmetry

of the austenite phase due to its minor tetragonal distortion. In the TEM diffraction pattern,

streaks and satellite spots are the indication of the presence of the pre-martensite phase

(details explanation in section 3.2). This precursor state has already been observed in Ni-Al

(Robertson and Wayman, 2006; Shapiro et al., 1989), Ni-Ti (Salamon et al., 1985; Shapiro et

al., 1984), and Fe-Pd (Muto et al., 1990; Oshima et al., 1988) prior to martensitic

transformation.

1.4 Adaptive martensite concept

The first-order diffusionless phase transformation from high-symmetry austenite to low-

symmetry martensite (modulated and non-modulated) phase proceeds without plastic defect

in order to attain shape memory properties. Modulation in Ni-Mn-Ga plays an important role in

achieving large strain and entropy changes under mechanical stress and a moderate magnetic

field. The theory of adaptive martensite, as described by Khachaturan (Khachaturyan et al.,

1991) proposes that modulated and non-modulated martensite are not distinct equilibrium

Fig 1.9: Crystal structure is shown schematically as follows: (a) Non-modulated martensite

and (b) pre-martensite also observed in our film. (Adapted from (Liang et al., 2022))

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

phases. The modulated structure can be defined as a defective lattice with non-modulated

twins arranged at the unit cell level. Figure 1.10 schematically represents the concept of

adaptive martensite, where Fig. 1.10a shows that the austenitic unit cell can transform into

three different variants of the tetragonal martensite. During a symmetry break of the austenite,

the lattice unit cell undergoes a change in shape, causing the crystal structure to divide into

variously aligned twin variants of the low-symmetry phase (Niemann et al., 2012). For phase

Fig 1.10: Concept of adaptive martensite: (a) formation of the tetragonal unit cell with three

orientations of martensite from the parent phase austenite. (b) a schematic representation

of nanotwinned (adaptive) formation from austenite with a habit plane at the interface.

Twinned boundaries linking differently orientated martensite variants. (c) Formation of macro

twinned by the annihilation of twin boundaries to achieve energetically low favor state of the

system. (Adapted from (Kaufmann et al., 2011))

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

transformation, a boundary is formed between austenite and martensite for compatibility, also

known as habit plane, shown in Fig. 10b. In order to fulfill boundary conditions to austenite,

twin boundaries are introduced as c/a ratio > 1, a single variant of martensite is unable to

satisfy this criterion without causing severe deformation.

The formation of distinct martensite variants leads to twinned microstructure, which are the

interfaces oriented differently. These twin boundaries hold additional defect energy, implying

that these twin boundaries add energy to the system. However, the development of these twin

boundaries can also reduce the energy of the system through transformation strain. The

reduction in volume energy induced by the transformation strain can balance the excess

energy from the twin boundaries, resulting in the twinned microstructure (Niemann et al.,

2012). Figure 10b schematically represents the habit plane between the parent phase and the

transformed phase. Here we can observe differently oriented martensite variants with twin

boundaries forming a Nanotwinned structure. The formation of macro twinned by the

annihilation of twin boundaries leads to an energetically low favorable state of the system. A

macro-twinned martensite is characterized by twin boundaries that are macroscopically

spaced, in contrast to the atomic-scale separations observed in nano-twinned martensite

shown in Fig. 10c. This concept explains the transformation of the parent phase austenite from

the unit cell to the macroscopic (mesoscopic) scale, incorporating the formation of the habit

plane and various types of twin boundaries.

1.5 Thin film fabrication challenges

Bulk single crystals are frequently used as standard frameworks for investigating the

microstructure and their exceptional actuation characteristics established on the MSME

(Sozinov et al., 2013; Sozinov et al., 2002a). However, epitaxial films, which are thin film

counterparts of bulk single crystals, are becoming increasingly popular because they are an

exciting alternative and easier to fabricate. Various approaches, such as sputtering, melt-

spinning, pulsed laser deposition, molecular beam epitaxial, and flash evaporation, have been

employed to deposit Ni-Mn-Ga thin films (Castaño. et al., 2003; Dong et al., 1999; Dong et al.,

2000; Dong et al., 2004). Several single-crystal substrates like MgO, Al2O3, and GaAs have

been used to prepare thin films (Castaño. et al., 2003; Dong et al., 1999; Dong et al., 2000;

Dong et al., 2004; Kar et al., 2023b) by sputtering. So far, Ni-Mn-Ga has received significant

interest because of its potential use in magnetic sensors and actuators (Chmielus et al., 2009;

W.Huang., 2002).

The goal of using any material in any application, whether single crystal or epitaxially grown

thin film, is to produce defect-free material, which is only sometimes true, especially for

epitaxially grown thin films. Investigations have shown that defects in epitaxial films can be

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

caused by dewetting (Lünser et al., 2021) and deterioration of epitaxial growth exceeding a

certain limit of lattice misfit between film and substrate (Aseguinolaza et al., 2016). Upon

growth, lattice mismatch stress is released at the crucial film thickness, producing self-

patterned defects orientated onto the surface in the (1 1 0) direction. These defects, which

arise from a misfit between lattice and matrix, can alter the properties of the thin films, e.g.,

twinning stress for actuation. Twinnig stress also increases with cracks like defects in single

crystals (Musiienko et al., 2021). Moreover, local chemical variations impact the formation of

specific types of twin borders that form under mechanical stress. Hence, it is critical to grow

films free of defects to utilize epitaxial films for actuation purposes (Campanini et al., 2018;

Kohl et al., 2014b).

Recently, thin films with austenitic phase at room temperature for films above 4 µm thickness

have shown a precursor form known as pre-martensite. Other bulk alloy systems, such as Ni-

Al (Robertson and Wayman, 2006; Shapiro et al., 1989), Ni-Ti (Salamon et al., 1985; Shapiro

et al., 1984), and Fe-Pd (Muto et al., 1990; Oshima et al., 1988) have shown a similar pre-

martensite state prior to martensitic transformation. The pre-martensite displays distinctive

features, such as the emergence of streaks and satellite spots in the selected area diffraction

patterns. Additionally, a crosshatch tweed contrast is also noticeable in transmission electron

microscopy (TEM) images of the phase above (Chernenko et al., 2002; Fukuda et al., 2009;

Zhou et al., 2017). As discussed above, martensite and pre-martensite's modulated structure

of 5M and 7M (Kushida et al. 2008, Righi et al. 2007, Righi et al. 2008) can be expressed as

3M when ignoring chemical order. The diffraction patterns of the film show that this barely

affects the cubic symmetry of the austenitic phase because of its minor tetragonal distortion.

In order to get rid of this pre-martensitic state, Cr buffer with large thickness was used by which

up to 4 µm thick films were grown defects free. Cr buffer is epitaxially grown onto the substrate,

improving the film's adhesion. The substrate can be under-etched when needed to prepare

free-standing films. To date, with the improved fabrication techniques and all the microstructure

investigations, it is still not possible to produce fully austenitic thin films above 4 µm.

1.6 Objectives of this thesis

The shape-memory response due to stress is a well-studied phenomenon at the bulk scale for

many conventional shape-memory alloys and also their magnetic counterparts (Heusler

alloys). However, at relevant scales for applications in micro- and nanomechanical systems

(MEMS and NEMS, respectively), the response remains largely unexplored, with the exception

of NiTi (Frick et al., 2007) and CuAlNi (San Juan et al., 2007). Given the tremendous potential

for small-scale actuators in the Ni-Mn-Ga system under consideration, an effort is therefore

required to quantify and characterize both the materials incipient phase transformation in

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

reduced volumes and also its potential functional degradation during cyclic phase changes in

response to stress. Since the functional properties in the Ni-Mn-Ga alloys are strongly

dependent on martensitic phase transformations and twin dynamics (nucleation and growth),

a size effect is anticipated when the surface-to-volume ratio reaches a critical value. This

hypothesis is very much reminiscent of known size effects in the NiTi system, for which some

works suggest a functional loss at or below physical sizes of ca. 60-50 nm (Fu et al., 2006;

Waitz et al., 2004). Furthermore, in free-standing finite-size applications, as targeted in MEMS

or NEMS, a loss in recoverable strain was reported in the micron-regime, with a complete loss

of the switching behavior at 200 nm, which is at least four times larger than earlier suggested.

For the here considered Ni-Mn-Ga alloy, both finite size effects and also functional fatigue at

small scales remain essentially unassessed. This may on the one hand side be due to the

scarce availability of single crystalline small-scale structures with a stable room-temperature

austenite phase, or because earlier work pursued indentation to very high loads. The latter

obscures any initial response of the material, and post-imaging or structural characterization

of indentation sites reveals only high-load induced transformations that involve a significant

amount of plasticity. Indeed, earlier studies in such cases have focused on residual phase

transformations observed through microscopy imaging after deformation (Ghahfarokhi et al.,

2023; Niemann et al., 2016). In some cases, however, very shallow indentation and low-load

behavior of Ni-Mn-Ga have been assessed, but in these cases, room-temperature martensite

was the focus (Satapathy and Aich, 2019).

To address this general shortcoming, the present thesis aims at providing a first insight into

the small-scale mechanical response of Ni-Mn-Ga alloys at the micro and nanoscale. The

austenite-to-martensitic transformation, mechanical switching behavior, and functional fatigue

of pristine and pre-strain microcrystals will all be central. All done leveraging nanoindentation

or micro-compression, this thesis also aims at quantifying the tensile response of free-

standing, small-scale samples. This is motivated by the complex stress state and surface

sensitivity of nanoindentation, as well as the imperfect boundary conditions of micro-

compression (Kiener et al., 2009; Maaß and Uchic, 2012). Broken down into three main sub-

topics, the present thesis has the following objectives:

1) Quantifying the confined-volume effects of the austenite-to-martensite

phase transformation

A well-informed use of Ni-Mn-Ga as a small-scale actuator material in NEMS and

MEMS requires detailed knowledge of the phase-changing behavior of reduced

material volumes. Indeed, at the bulk scale and therefore sufficient volume, averaging

the transformation stress is a reproducible quantity. This might change upon a

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

significant volume reduction because of the statistical function of microstructural phase-

transformation initiation sites. To this end, this thesis begins with assessing the

temperature-dependent incipient austenite-to-martensite transformation using

nanoindentation. Specifically, spherical nanoindentation is used to probe phase

changes in single-crystalline austenitic Ni-Mn-Ga thin films. Through a large number of

tests at different temperatures, this thesis aims at quantifying the statistical spread of

critical phase-transformation stresses.

2) Determining mechanisms of functional fatigue during cyclic phase

changes

Any realistic application will rely on a large number of phase changes, and it is therefore

imperative to quantify potential dissipative processes that may lead to functional fatigue

as a function of cycles. In other SMAs, such as Ni-Ti, functional fatigue is a critical

issue, leading to several tens of percent of stain amplitude reduction after thousands

or tens of thousands of cycles, depending on whether a poly- or single crystal is

considered. In this thesis, functional fatigue at the micron scale will be pursued,

targeting small-scale actuation devices. Compressive fatigue with up to one million

superelastic cycles using a dynamic micro-compression at room temperature is applied

to columnar microcrystals. Combined with small-scale mechanical fatigue, TEM is used

to gain a microstructural picture of potentially underlying dissipative processes. Overall,

this second objective should be seen as a first step towards quantifying Ni-Mn-Ga as a

suitable material for reliable actuation.

3) Identifying the critical length scale below which a loss of superelasticity

is observed

Whilst experimentally less of a challenge, objective 2 above relies on examining

functional fatigue in a compressive dynamic loading scenario. A more robust

experimental approach to fatigue testing is in tensile geometry, which can be realized

by converting the compressive directional force applied with a nanoindenter into a

tensile force on the sample. This can be achieved with so-called push-to-pull devices

and will be leveraged as part of this third objective. With the combined interest in

identifying a critical length scale below which a superelastic response is lost and also

conducting complementary stress-driven cycling in tension, sub-micrometer dogbone

crystals shall be tested. Of primary interest is again Ni-Mi-Ga in its austenitic phase,

which is stable at room temperature, as such a challenging experiment cannot be

conducted as a function of temperature. Any successful cyclic push-to-pull tensile

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

testing would also provide insights into potential tensile-compression asymmetries that

might need to be considered in small-scale device design.

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

CHAPTER 2: EXPERIMENTAL METHODS

2.1 Samples material and characterization

In this work, thin films and free-standing samples are produced by DC magnetron sputtering

using Ni48Mn22Ga30 as the target material. Thin film thicknesses 0.5 μm and 2 μm with a

substrate of single-crystal MgO (001) substrates with a 20 nm epitaxial Cr-buffer layer are used

for nanoindentation studies. Whereas, for the compression study, films with thicknesses of 4

and 5 microns were used, and the Cr-buffer layer thickness of 150 nm was used instead of 20

nm to achieve larger thickness films to avoid nose-like structure defects. The advantages of

employing a Cr-buffer include enhanced adhesion of the film to the substrate (Diestel et al.,

2017) and the ability to under-etch this layer to produce a free-standing sample (Backen et al.,

2012; Kohl et al., 2014a). Different microfabrication techniques are used for the best possible

results to achieve a free-standing sample (FSS) for tensile testing from a thin film (Kar et al.,

2023b). A FSS with the best result is obtained by a two-step ion-beam etching process using

the Ar plasma technique compared to wet etching and reactive ion etching.

Although the same target Ni48Mn22Ga30 is used, the FSS transforms to a martensite phase at

room temperature. Despite further efforts to adjust different factors, e.g., e/a ratio and replacing

Ga for Mn and Ni, this also did not help in achieving the desired austenite phase at room

temperature. The thin films produced in this study are 10 mm * 10 mm, and the substrate

thickness is 1 mm thick for better handling. In the next sections, further experimental

techniques, e.g., DC Magnetron sputtering, X-ray diffraction (XRD), Vibrating sample

magnetometer (VSM), Atomic force microscopy (AFM), Nanoindentation, Focus ion beam

(FIB) milling, Transmission electron microscopy (TEM), and tensile testing will be discussed

briefly.

DC Magnetron sputtering

Sputtering is a physical vapor deposition (PVD) mechanism in which a target material deposits

atoms, molecules, or ions onto a substrate. Sputtering involves utilizing electrical means to

generate plasma between the target material, which is deposited onto the substrate. In this

process, high-energy ions are accelerated toward the target material by ejecting the atoms

from the material, which are later attracted toward the substrate. DC magnetron sputtering

differs from other methods because it uses magnets underneath the target material. The

purpose of using a magnet is to confine the electrons that are present in the plasma toward

the target, and it also enables an improved deposition rate. A Schematic of DC magnetron

sputtering is shown in Fig. 2.1a, which describes the basic mechanism of the process of how

thin films are produced. In this study, thin films with thicknesses of 0.5 μm, and 2 μm were

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

utilized for nanoindentation, films of 4, and 5 μm were used for compression testing, and free-

standing strips were employed for tensile testing.

Epitaxially grown Ni-Mn-Ga films were produced by direct current (DC) Magnetron sputtering.

Thin films are deposited after heating the single-crystal MgO (001) substrates to 673 K with a

20 nm epitaxial Cr-buffer layer for 0.5 μm and 2 μm thin films. In the case of 4 µm and 5 µm

thin films, the Cr-buffer layer thickness of 150 nm was used instead of 20 nm to achieve larger

thickness films to avoid nose-like structure defects as the thickness of the film increases (Kar

Fig. 2.1: Direct current (DC) magnetron sputtering setup schematics. Thin film (b) mounted

on SEM stub with graphite paste. A free-standing sample (c) etched using a two-step ion

beam can be observed in this figure. (This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

et al., 2023a). The Cr layer is deposited at 583 K with a sputtering power of 70 W and 0.8 Pa

working pressure of Ar + 5 vol.% H2 mixture. This Cr buffer layer grows epitaxially on the MgO

substrate and provides two benefits: one, it increases the adhesion of the film to the substrate

(Diestel et al., 2017), and second, the ability to under-etch this layer to produce free-standing

strips (Backen et al., 2012; Kohl et al., 2014a), which can be used for tensile tests. During the

film deposition, substrate temperatures were kept at 673K for all thin films used in this study.

To make sure that we achieve uniform thickness and composition across the thin film, the

substrate holder was rotated during the deposition process. Given that the temperature for the

martensitic phase transition can be adjusted by lowering the e/a ratio and replacing Mn and Ni

with Ga atoms, a Ni48Mn22Ga30 composition was used as the target material to achieve the

austenitic phase close to room temperature. Thin film and free-standing samples produced by

DC Magnetron sputtering are shown in Fig. 2.1b,c.

X-ray diffraction

X-ray diffraction (XRD) was conducted to ensure only single-phase thin films. The XRD

analysis was performed using a Bruker AXS D8 Advance X-ray diffractometer, with Co

radiation and a wavelength of λkα = 0.1788 nm. Since the martensite plane exhibits a slight tilt

in the epitaxial plane (Backen et al., 2010; Thomas et al., 2008), sample tilt ranging from 0˚ to

10˚ with incremental steps of 1˚ was also executed. For example, 5 µm thin film XRD data is

shown in Fig. 2.2, where cumulative intensity is plotted against 2θ. Using the equations for

different θ and miller indices h,k,l, we found that each peak belongs to the austenitic cubic

structure. Two clear peaks for austenite at (200) and (400) at 35.8˚ and 75.8˚and clear peaks

for MgO at (002) at 50˚ are observed. There is no presence of any modulated or non-modulated

martensite, confirming the presence of only single-phase austenitic thin film. Figure 2.2 also

Table 1: Displays the phase transition temperatures for both films and free-standing

samples (FSS). Ms denotes the temperature at which martensite begins to develop upon

cooling from austenite, while Mf signifies the completion of this transformation.

The austenite start and finish temperatures during heating are denoted as As and Af, re

spectively.

Thickness (μm)

Composition

At% (± 0.5)

(K)

Phase @

0.5

Ni55Mn18Ga27

280

268

278

288

Austenite

Ni54Mn20Ga26

274

257

270

285

Austenite

Ni52Mn21Ga27

205

187

202

218

Austenite

Ni51Mn22Ga27

207

176

180

210

Austenite

0.5 (FSS)

Ni55Mn19Ga26

333

317

324

343

Martensite

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

represents the lines at which all other phase peaks are expected, which is not the case for our

thin film. Energy dispersive x-ray spectroscopy (EDX) determined the sputtered thin film

compositions with 1 at. % accuracy using a Ni50Mn25Ga25 standard and are given in Table 1.

Vibrating sample magnetometer (VSM)

As we understand from Section 1, Heusler alloys can have different properties under stress

depending on their phase during the testing. The start and finish temperature of martensite

and austenite (Ms, Mf, As, Af) can be achieved using a vibrating sample magnetometer (VSM)

(Quantum Design-VERSALAB). VSM is calibrated using ferromagnetic material before

performing any measurement. A uniform magnetic field with a magnitude of 0.01 T was

applied, and the samples' behavior of transitioning between austenite and martensite phases

was analyzed within a temperature range of 100 K to 400 K, using a heating rate of 2 K/min.

The magnetic field was oriented parallel to the MgO [100] direction. For example, Fig. 2.3

illustrates the magnetization curves of two thin films. The red arrow represents the heating

Fig. 2.2: X-ray diffraction data for 5 µm thin film with Ni51.3Mn21.7Ga27 composition annealed

at 400 K. The corresponding austenite peaks, along with the MgO substrate peak, are

present in the film. Different corresponding dashed lines where we can expect martensite

are also drawn for reference. (This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

cycle, whereas the green curve represents the cooling cycle. Although the same magnetic field

is applied to both films, the slight difference in the magnetic moment is associated with the

composition and microstructure of the films. Austenitic start (As) and finish (Af) temperatures,

as well as martensitic start (Ms) and finish (Mf) temperatures, are calculated by drawing a

tangent at the point where a sudden shift in the magnetization curve is apparent as the material

undergoes a phase change. The solid pink lines are drawn to calculate all the phase

temperatures in the figure below.

Both films exhibit slight variations in the austenitic start (As) and finish (Af) temperatures, as

well as in the martensitic start (Ms) and finish (Mf) temperatures, depending on their

composition. All the phase temperature values and film thickness are provided in Table 1. The

value of the Ms reduces as we go from 0.5 – 5 µm films, but this drop is not associated with

the film thickness but rather the composition of the film. Generally, adding more Mn by

replacing Ni (reducing valence electron to atom ratio e/a) content tends to lower the martensitic

transformation temperature (Albertini. et al., 2002; Chernenko et al., 1995; Jin et al., 2002).

Since Mn are smaller-sized atoms, their presence introduces structural instabilities that favor

the formation of the martensite phase at lower temperatures. This way, we can ensure that the

final film will have an austenitic phase temperature, which is important for our mechanical

testing.

Fig. 2.3: VSM measurements with a magnitude of 0.01 T. The green arrows represent the

cooling cycles, whereas the red arrows indicate the heating cycle. The austenitic start and

finish temperature (As and Af) and martensitic start and finish temperature (Ms and Mf) are

calculated by drawing the tangent lines from the heating and cooling cycles, as shown in the

black curve. (This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

2.2 AFM analysis

Atomic force microscopy (AFM) is a remarkable technique for obtaining a precise topographic

map with surface features as small as fractions of a nanometer. To scan the sample's surface,

it uses a cantilever with a very sharp tip; the basic principle of AFM is based on the distance

between the cantilever tip and the material's surface, which is presented in Fig. 2.4 When the

distance between the cantilever tip and the sample surface is increased, then there would be

no deflection in the cantilever, as the distance gets smaller and smaller, the attractive force

between the cantilever and the surface leads the cantilever to bend towards the surface. On

the other hand, if the cantilever's tip connects with the sample surface, the repulsive force

comes into play, causing the cantilever to deflect away from the surface. To obtain the surface

feature of the sample, we bring the tip close to the surface, and a laser beam deviation allows

us to measure the profile. The deviation of the laser beam is collected at the position-sensitive

photodiode (PSPD) using a Z-scanner. The deviation of the laser beam is corrected at the

center of the PSPD. Using the position of the Z-scanner and PSPD signal, which is further

analyzed using detectors and electronic feedback provides us with a topographic image of the

surface in the nanometer range. Since AFM imaging depends on the force between the tip and

the sample, instead of measuring the force directly, it rather computed by measuring the

deflection of the lever since the stiffness of the cantilever can be found using

F = - kz

Fig. 2.4: The AFM mechanism: (a) where a cantilever with a very sharp tip is used to scan

the material's surface. (b) The potential-distance diagram is presented with three different

regions depending upon the distance of the cantilever tip to the sample. (This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

In this context, F represents the force, z denotes the amount of deflection or bending of the

lever, and k represents the stiffness of the lever. Most of the AFM uses tapping mode, which

produces accurate topographic imaging and protects the sample's surface because of periodic

oscillation detection and fewer contacts to the sample. For example, Fig. 2.5 displays the AFM

image of a Conospherical tip on Ni-Mn-Ga thin film studied in this work. The tip's indent also

shows an extra line feature around the indent, which is evidence of residual martensite when

an austenite film is deformed.

2.3 FIB milling

Focussed ion beam (FIB) milling can be employed to convert thin films into micrometre-scale

cylindrical volumes of small crystals. The FIB milling aims to generate a nominally 2 μm radius

microcrystal, effectively separating the microcrystal from the thin film bulk. The FIB milling

process is divided into four steps with varying currents, decreasing as the crystal radius

approaches 2 µm. Initially, a rectangular pattern is milled using the "Si application" to act as a

focus area and prevent damage to the target area at high currents. Next, a rough cut is made

using a circular pattern with an outer diameter of 20 µm and an inner diameter of 8 µm at 3 nA.

Subsequently, a circular pattern with an outer diameter of 8 µm and an inner diameter of 5 µm

is milled at 0.5 nA. It is crucial to precisely place the circular pattern at the microcrystal's edge

Fig. 2.5: An AFM image of a Berkovich tip indent reveals the line feature around the indent,

indicated by blue arrows. These nano-line features indicate the presence of residual

martensite after deformation when an austenite film is indented. (This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

as the radius decreases to control the column height. In step three, a circular pattern with an

outer diameter of 5 µm and an inner diameter of 3 µm is milled at 0.1 nA, and finally, an outer

diameter of 3 µm and an inner diameter of 2 µm is milled at 49 pA for precise milling. In the

final step, the outer diameter gradually decreases while keeping the inner diameter constant

to achieve a smooth surface and reduce the taper angle. The taper angle can be calculated

using θtapper=tan−1d1−d2

2h , here, d1 is the inner and d2 is the outer diameter, respectively, and

h is the height of the microcrystal. The taper angle in here studied microcrystal is < 1.5˚, which

is acceptable for compression testing. Figure 2.6 shows the microcrystal with two diameters,

starting with a rough cut and ending with a smooth surface with a diameter of 2 µm. To achieve

the best result possible, great care should be taken during the stage tilt, orientation, and ion

beam focus. Make sure you do not expose your region of interest (RIO) under the ion beam or

take images using the ion beam. To ensure a smooth, rough cut, allow the ion beam to stabilize

for 10-15 minutes prior to running the extended time pattern. During microcrystal preparation,

always use the milling direction from inner to outer when using a circular pattern; otherwise,

the milled material might be re-deposited onto the microcrystal if the milling direction is outer

to inner.

2.4 TEM analysis

Transmission Electron Microscopy (TEM) is an essential technique used to study materials at

Fig. 2.6: (a) Rough cut with an outer diameter of 20 µm and an inner diameter of 8 µm at 3

nA. (b) A precisely carved microcrystal with a diameter of a diameter of 2 µm and a minimum

taper angle. (This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

the nanoscale. It allows us to obtain information about the sample morphology, microstructure,

crystallography, and crystal defects, e.g., dislocations and planer defects. FIB Lamellae for

TEM analysis were prepared from thin films and strained and unstrained microcrystals using

standard methods. A protective layer of platinum was deposited so that the region of interest

(ROI) was protected from excessive ion milling. Each lamella was transferred to a Cu

Omniprobe lift-out grid using a FIB needle and given a final polish. The final thickness of the

lamella is usually between 50-100 nm, and the lamella dimensions are roughly 18 × 12 µm in

length and height, respectively.

In Fig.2.7, the FIB lamella of one of the microcrystals is shown, where the platinum is deposited

on the top and in the trench to protect the surface and support the column when the cross-

section is milled. The FIB lamella were examined using a JEOL 2200FS TEM operating at

200kV. In STEM mode, multiple detectors are used for different purposes, and depending on

the angle at which the electron is transmitted and collected plays a crucial role in the contrast

and information obtained in STEM imaging. In Bright-Field (BF) imaging, electrons are

transmitted at small angles (<0-10 rad), and the image obtained through this mode is similar

to BF-TEM. Since scattering is smaller in this mode, it provides overall information about the

sample. This mode is sensitive to defects but without the bend contours that appear in TEM

images. In AFD imaging (which we did not use in his study), electrons are transmitted at large

angles (10-50 mrad) means they are more likely to interact with light elements, providing

images with high contrast based on atomic number differences. In HAADF imaging, electrons

Fig. 2.7: FIB lamella preparation with thickness around 50-100 nm for TEM investigation.

(This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

are transmitted at an angle > 50 mrad, which is used for atomic contrast imaging. Utilizing

STEM allows for the acquisition of valuable information regarding sample composition,

variations in thickness, and other structural details. This study mainly utilized BF-STEM and

selected area electron diffraction (SAED) techniques for our TEM analysis. The BF-STEM

image of the microcrystal is displayed in Fig. 2.8a, revealing a wavy pattern and dislocation

within the microcrystal. On the other hand, the SAED technique is a well-known approach for

obtaining diffraction patterns from particular regions of a sample, allowing for the analysis of

the crystallographic structure of those regions. The TEM is first configured for the diffraction

mode to obtain a diffraction pattern, and a parallel electron beam is placed on the specific

region of interest in the sample.

The selected area aperture is then inserted to limit the portion of the electron beam interacting

with the sample and to collect only the diffraction pattern from the specific area of interest.

When an electron beam is directed onto the sample, the resulting image shows the interference

pattern caused by the diffraction of electrons through the crystal structure. The diffraction

patterns are captured by a detector situated behind the sample, such as a phosphorescent

screen or a digital camera. The diffraction pattern is shown in Fig. 2.8 (b), which can be

Fig. 2.8 (a) BF-STEM image of microcrystal, (b) Selected area diffraction (SAD) is later index

which provides the information about the crystal structure (Cubic). (This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

analyzed to determine the crystallographic orientation, phase identification, and crystal

structure. The CrysTBox software was used to index the SAED patterns, allowing us to identify

the material phases with precision.

Etching Protocol

According to the existing literature (Aseguinolaza et al., 2018; Maass et al., 2012; Maaß et al.,

2009; McCaffrey et al., 2001; Shim et al., 2009), the outer microcrystal layer can be damaged

for tens of nanometers during FIB milling and lower yield stresses relative to the non-FIBed

crystal. To ensure that this damage does not impact the mechanical response of the

microcrystals, a wet etching process was carried out to remove the outer layer of the column

gently. This allowed for comparing mechanical testing behavior both before and after etching.

The wet chemical etching process involved using a solution of 1.25% HCl, 37% HNO3, and

H2O, from which we removed approximately 70 nm of material from the microcrystal's outer

layer. Despite this etching process, the compression data showed no significant change in

mechanical response before and after the etching protocol. The mechanical testing of the

microcrystals was carried out immediately following FIB milling and without any subsequent

chemical etching.

2.5 Nanoindentation and associated data analysis

Nanoindentation, microcompression, and tensile testing have been performed using

TribonIndenter 980 (TI 980). Understanding the basic principle of Nanoindenter and how

transducers work during movement is very important for accurately evaluating the raw data. TI

Fig. 2.9: Schematic cross-sectional view of the 1D transducer with three capacitive plates—

two outer and center plates where the tip is mounted. (This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

980 is installed with 1D and 2D transducer heads for normal and lateral movement (scratch

testing), both are equipped with Piezo scanners. The Piezo scanner remains stationary during

the nanoindentation, compression, and tensile testing. The transducer performs the movement

of the tip during any testing. The TI 980 system has three plate capacitive displacement/force

transducer. Figure 2.9 represents the cross-sectional schematic of the 1D transducer, which

primarily facilitates the mechanical movement of the Indenter tip. The two outer plates of the

transducer are fixed, whereas the central plates move and are supported by springs. The

nanoindenter tip is rigidly mounted on the central plate, which causes the normal and lateral

movement of the tip. The 2D transducer is equipped with two extra transducer sensors that

are positioned on opposing sides at 90° angles, in addition to the 1D transducer. Since these

transducers have both force and displacement-controlled movement, let us see how both

mechanisms work during the testing.

2.5.1 Deformation modes

Displacement controlled mode

Fig. 2.10: The displacement mode of the transducer is plotted where voltage amplitude is

plotted against z-position with respect to the outer and center plate. Voltage amplitude is

converted to transducer output voltage using a drive circuit within the transducer. (This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

The displacement of the rigidly fixed tip to the center plate can be calculated by measuring the

voltage amplitude. A high-frequency oscillating voltage that varies linearly is applied to outer

plates picked up by the center plate. The voltage amplitude at the center plate with respect to

the outer plate can be converted to the transducer output voltage (TOV) using the drive circuit

installed within the transducer. The value of TOV should be zero when the center plate is

precisely positioned in the middle between the outer plates. The displacement mode of the

transducer is plotted in Fig. 2.10, where voltage amplitude is plotted against the z-position with

respect to the outer and center plates. During the testing (nanoindentation/compression), the

TOV values shift towards negative as the center plate (tip) moves further in the Z-direction. To

determine the displacement of the tip during a test, one can measure the voltage amplitude

and establish the calibration between the voltage amplitude and the location of the center plate.

Force controlled mode

To operate the transducer in force mode (electrostatic force), high DC voltage (up to 600 V)

is supplied to the lower capacitor plate. Figure 2.11 describes the schematic of the force-

controlled mode. Doing so creates an electrostatic attraction between the lower outer and

center plates. The force can be determined by subtracting a position-dependent value from the

magnitude of applied voltage, which mathematically can be written as

𝐹𝑜𝑢𝑡𝑝𝑢𝑡= 𝐹𝑣𝑜𝑙𝑡𝑎𝑔𝑒−kz

In the above equation, Fvoltage is the applied voltage, k is the spring constant of the central plate,

and z is the tip displacement. It is feasible to conduct micro-mechanical testing with a force-

controlled transducer at a predetermined displacement rate. To accomplish this, a feedback

control loop with a proportional-integral-derivative (PID) mechanism is employed to constantly

track the movement of the indenter tip. The applied load voltage is then modified in accordance

Fig. 2.11: Transducer force-controlled mode, where high voltage is applied to the lower

capacitor plate. (This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

with the prescribed displacement value(s) for the load function. This adjustment aids in

controlling the actual displacement and ensuring that it always remains at the desired value.

The given value rises linearly with time in an experiment with a constant drive rate. It is

important to note that if the tip displacement exceeds the specified displacement (e.g., phase

transformation/pop-in), the controller will decrease the applied force after the sudden jump. As

the force diminishes, the indenter tip will be unloaded elastically until the displacement

measurement reaches the initial nominal value again. Subsequently, the controller will

commence gradually augmenting the load onto the sample. If the increase in strain exceeds

the sample’s total elastic deformation, then unloading could persist until the indenter tip is no

longer in contact with the sample. Under such circumstances, the controller will guide the

indenter tip through the air until it reaches the sample, at which point the loading process will

resume according to the appropriate displacement-time profile. Before moving further we need

to discuss a very important aspect of nanoindenter which is machine compliance.

Machine compliance

The displacement recorded by a depth-sensing indentation instrument encapsulates both the

penetration depth into the specimen and the displacement arising from the instrument itself,

often attributed to machine compliance. Precise quantification of this machine compliance is

vital, especially under substantial force applications, as it substantially influences the total

displacement measured. Several factors impact the machine compliance of a system, with

primary influences including the transducer, the probe, the method of sample mounting, and

how the transducer is mounted. The compliance of the machine can be expressed

mathematically as the inverse of stiffness:

𝐶𝑐=𝑑ℎ

𝑑𝑃=√𝜋

2∗1

√𝐴∗1

𝐸𝑟

Here h denotes the displacement of the probe relative to the specimen, P represents the

applied load, A is the projected contact area, and Er is the reduced modulus. Here, the reduced

modulus is given by

Er=Ei

1−Vi2+ Es

1−Vs2

E and ν are the elastic modulus and Poisson ratio where subscripts i and s represent the

indenter and sample. To account for the elastic displacements attributed to machine

compliance, the contact compliance Cc must be incorporated alongside the intrinsic

compliance of the machine Cm, yielding the system's total compliance.

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

𝐶𝑡𝑜𝑡𝑎𝑙=𝐶𝑚+𝐶𝑐=√𝜋

2∗1

√𝐴∗1

𝐸𝑟

The hardness H of a sample is defined by the equation:

H=Pmax

where H is the hardness, Pmax is the maximum force applied, and A is the projected contact

area. Incorporating the earlier equations provides the total compliance:

𝐶𝑡𝑜𝑡𝑎𝑙=𝐶𝑚+√𝜋

2∗√𝐻

𝐸𝑟∗1

√𝑃𝑚𝑎𝑥

When utilizing a Berkovich probe without sample cracking, it is reasonable to consider that the

hardness and reduced modulus of fused quartz remain constant at higher displacements

(greater than one-third of the probe's radius). Although machine compliance may differ across

various transducer/probe/sample mounting configurations, it is generally acceptable to

assume that the machine compliance remains consistent for the majority of probes and sample

mounting techniques used with each specific type of transducer.

2.5.2 Data processing

Regardless of the mode of tip movement used in the indenter, the data output is the same in

both cases. The data we receive from the device is in a simple text file with six columns, namely

(‘Depth ’ ‘Load’ ‘Time ’ ‘Disp. Voltage’ ‘Raw Disp. Voltage’ ‘Force Voltage’). The total number

of data points in the text file depends on the data acquisition rate (points per second) and the

total number of seconds in the loading function. The Indenter software handles the conversion

from voltage to force and displacement. To further analyze the data, the depth column is

converted into Depth (nm), the load is converted into Load (µN) units, whereas time is in

seconds. Figure 2.12 represents the nanoindentation curve of the Ni-Mn-Ga thin film, depicting

the relationship between the load (µN) and the depth (nm). The nanoindentation

measurements at room temperature are performed using a cono-spherical tip. At 320 µN, there

is a clear jump of around 10 nm (called pop-in) at room temperature. The first pop-in is further

followed by a small pop-ins with 0.5 – 1 nm in size. This pop-in could be caused by plastic

dislocation or a phase transformation change from austenite to martensite. The Hertzian model

L= 43Er√Rh3/2 (Johnson., 1985) fits perfectly, indicating a purely elastic response before pop-

in occurs. L is the applied load, R is the indenter tip radius 890 nm, h is the penetration depth,

and Er (for our Ni-Mn-Ga thin film is 79 GPa) is the reduced modulus. There are similar events

at the higher force with smaller pop-ins, but we are only interested in the first event here.

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

One of the key tasks is to identify what kind of mechanism is responsible for such an event. Is

it either phase transformation or dislocation plasticity? To proceed further with statistical

analysis of the first pop-in, we need to measure the threshold of the device where the

measured displacement rate is significantly larger than the nominal rate due to the phase

transformation. This step is very important so that the recorded jumps (pop-ins) in the

nanoindentation curves are real events and not random noise. Figure 2.13 represents the

histogram of point-to-point displacement and helps determine the noise threshold of the

device. The noise data follows a Gaussian distribution with a mean value μ = 8 x 10-5 nm

(approximated as zero) and a standard deviation of σ = 0.292 nm centered at zero as expected.

To ensure that we do not count the random noise as a pop-in event, we take the 2σ = 0.584

nm as the noise threshold. After this step, using Python, we can find the force where the first

pop-in event is larger than the noise threshold of 0.58 nm and the pop-in event's size. By

selecting the noise threshold, we can use Python code to find the force where the first pop-in

occurs for multiple indents, and by using this force and displacement value, we can calculate

shear stress via τmax = 0.31(6PLrEr2

π3R2)1/3 (Shim et al., 2008). Here, Er is the reduced modulus, Lr

is the load range between 100 to 600 μN, and R is the indentor radius. These stress values

Fig. 2.12: Load-depth data at room temperature measured with TI-980 Triboindenter. The

maximum force used during loading is 1 mN, and the sudden displacement jump (pop-in) is

observed at 300 μN. The orange line represents the Hertzian model, which fits perfectly

before a sudden jump in the displacement. (This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

are further analyzed by plotting the complement cumulative distribution function (CCDF),

discussed in the next section.

Fig. 2.13: This histogram represents the point-to-point displacement and helps determine

the noise threshold of the device. The distribution follows a Gaussian pattern with a standard

deviation of σ = 0.292 nm and 2σ = 0.584 nm, centered at zero as expected. The green

arrow represents the noise threshold above which an event is considered a pop-in. (This

work)

2.5.3 Maximum Likelihood Estimation (MLE)

The pop-in stresses are further plotted as a function of CCDF, which provides a straightforward

way to quantify the occurrence of pop-in events. Here

CCDF(x)=1−CDF(x)

CCDF(x) is a complementary cumulative distribution function at a value x, whereas CDF(x) is a

cumulative distribution function at the same value x. CCDF provides the probability of a pop-

in event occurring beyond a certain stress threshold. To understand the primary mechanism

that causes these pop-ins, different functions can precisely describe the distribution function

that fits CCDF. To achieve this, we employed a statistical technique called maximum likelihood

estimation (MLE). Although methods like Minimum mean square, least-square regression, and

Maximum a Posteriori estimation are frequently employed, more is needed to describe the

power law probability distributions fully. These methods rely on means or median, so the

distribution allows for low-probability tail events that could entirely skew the calculated

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

moments (means or radians). Since power law has no mean or standard deviation, it can be

fit to data regardless of the distribution. MLE provides an adaptable framework for evaluating

distribution parameters and estimating the goodness of a fit, which is important when

characterizing the pop-in stress data. The only condition for MLE to apply is that data should

be a set of random variables and that the mathematical equation for the distribution function

under test is relatively simple.

Let us discuss how MLE works mathematically by selecting a set of random data points [x₁,

x₂, x3..., xₙ]; the data follows a certain probability distribution that depends on an unknown

parameter. The primary objective of MLE is to determine the value of the unknown parameter

θ that maximizes the likelihood of observing our data. First, we need to define the likelihood

function L, denoted as L(θ), which describes the probability of observing our data providing a

precise value of unknown parameter θ. Mathematically we can define L(θ) as probability

density function of individual data points [x₁, x₂, ..., xₙ],

L(θ) = f(x₁|θ)* f(x₂|θ) *.........* f(xₙ|θ) =∏f(Xj|θ)

nj=1

To further simplify the math, the natural log of L(θ) is taken; since the logarithm is monotonic,

it does not change the location of the maximum point.

L(θ) = ln(L(θ)

We can determine the value of θ that maximizes the likelihood by calculating the difference of

ln(L(θ) w.r.t θ and then setting its value to zero. This will allow us to identify the optimal value

of θ. dL(θ)

dθ =0

To further ensure that we have found the maximum, second order derivate d2/dθ2 [L(θ)] can

also be taken; if its value is negative, we have the maximum for MLE. The probability

distribution function in our pop-in data is expected to be power law type 𝑃(𝑥) ∝ 𝑥−𝜏, which can

be written as (Clauset. et al., 2009)

f(x)=τ−1

xmin(x

xmin)−τ

In the above equation:

• x represents the size or duration of the event.

• xmin is the lowest value possible for power-law.

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

• τ is the exponent that defines the shape of the power-law distribution, with τ > 1.

lnL(τ)=ln∑τ−1

xmin(x

xmin)−τ

j=1

lnL(τxj

⁄)=∑ln(τ−1)−ln(xmin)−ln ( x

xmin)

j=1

lnL(τxj

⁄)=nln(τ−1)−nln(xmin)− τ ∑ ln(xj

xmin)

j=1

In the above equation, n represents the total number of data points, whereas ∑ denotes the

summation over all data points xj. In the next step, we need to take the derivate of the log-

likelihood function w.r.t τ and set it to 0 to get the maximum likelihood estimator τ.

∂ ln L(τ|Xi)

∂τ =0

τ= n

τ−1−∑ln xj

xmin

j=1 =1 + n ⌈∑ln xj

xmin

j=1 ⌉−1

There is a solution to τ, and it is the best estimate to the exponent 𝜏 for the function f(𝑥)

established above because the values of all 𝑥𝑖 random variables are known. Using α=τ− 1,

the exponent of the CCDF can be determined. This computation is carried out using Python

code and the power-law package (Alstott, Bullmore and Plenz 2014), which was developed

based on the work of (Clauset. et al., 2009). It is optional for the intermittent events to always

follow power law statistics; rather, they are occasionally associated with exponential (Stumpf

et al., 2005) or stretch exponential distributions (Vu. and Weiss., 2020).

The power-law package compares MLE results by introducing a likelihood ratio R to determine

the suitable fit for the current data. The ratio R provides us with the likelihood functions of two

alternative distributions applied to the current data depending upon the position of the

functions. A higher value of R means the function chosen in the numerator is most suitable for

the current data when R > 0; conversely, if R < 0, the function chosen in the denominator is

most suitable for the current data. In case the value of R is very near to zero (for 𝑛 → ∞ random

variables), the sign of likelihood ratio can be due to statistical fluctuation. To tackle this

problem, the Python code also provides a 𝑝-value indicative of the standard deviation of 𝑅

(Vuong, 1989). The 𝑝-value < 0.05 is the threshold; the lower the 𝑝-value, the better the

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

statistical signature for the likelihood ratio R (Andrade., 2019). So, for a function that fits very

close to the data, the R-value must be higher for the nominator and vice versa, whereas the

𝑝-value should be less than 0.05 to support the likelihood ratio. Figure 2.14 represents the

fitting comparison, where we can observe that the stretch exponential fit is perfect for our stress

data compared to any other fit.

2.6 Microcompression and micro-tensile testing

2.6.1 Microcompression testing

The micro-compression testing method tests small-scale volume structures where a

compressive force is applied to understand how the material responds to the applied force.

During microcompression testing, cylindrical or cuboidal crystals are compressed by

compressive force. Using such a technique, we can acquire properties like compressive

strength, yield strength, and deformation behavior of the material. This study focuses on

functional fatigue and dissipative processes by keeping the force under a pseudo-elastic

regime and compressing the microcrystal up to a million cycles. We also investigate the long-

term functional fatigue of Ni-Mn-Ga microcrystals when the samples are purposefully deformed

by 2-3%. The experimental method of microcompression testing is similar to that of

nanoindentation, except for the calibration process and indenter tip. Instead of using a cono-

spherical tip, we employ a flat punch with a 10 μm radius. To ensure precision in compression

Fig. 2.14: Most likelihood estimation (MLE) model used on our pop-in stress data, comparing

Power law, Exponential, stretch exponential fit, and Truncated power law. Stretch

exponential fits our stress data better than all other fitting functions. (This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

testing, we must calibrate the device with an optical microscope at a zoom factor of at least 6x

compared to 1x in nanoindentation, installed parallel to the indenter, allowing for calibration up

to ~ ± 1μm.

Fig. 2.15: 1x (left) vs. 6x (right) zoom calibration protocol to ensure that flat punch is

calibrated as good as possible for precise testing. (This work)

However, calibration of tip-to-optical at 1x zoom is sufficient for nanoindentation testing. Once

calibration is complete, we can switch between samples without further calibration. Figure 2.15

illustrates the difference between zoom factors one and six and how precise calibration allows

for accurate compression testing. During this study, we employed different loading functions

in both load-controlled and displacement-controlled modes to achieve our results for

nanoindentation. For fatigue studies, samples are taken out in between to take Scanning

electron microscope (SEM) images to observe any structural changes during the compression

testing. SEM images are also taken after the compression testing completion to compare the

microcrystals' initial and final stages. The nanoindenter data is analyzed using origin software,

where load-displacement data is further converted into stress-strain data using σ= L

πr2, and

strain ε =∆H

H, Where L is the applied load, r is the microcrystal radius, ∆H is the change in

height, and H is the total height of the microcrystal.

The typical compression behavior of nominally 2 μm radius microcrystal is shown in Fig. 2.16a.

This is a pseudoelastic behavior as the column fully recovers with an elastic strain of 4.2%

after unloading the applied stress of ~ 1 GPa. For the microcompression test, the linear

behavior of the column changes at 460 MPa, known as the martensitic transformation stress,

where austenite starts transforming into martensite. Since there is no clear transition point, the

exact value of this transition point can be obtained using a second derivative of the stress-

strain data for the microcrystal. Figure 2.14c represents the second derivate of displacement,

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

and at ~105 nm, we observe a large change in the slope, which belongs to 460 MPa in terms

of stress value. The original data is plotted against smooth data with polynomial fit for better

results. The bulk compression data for single crystal Ni52Mn24.4Ga23.6 is also plotted in Fig 2.16b

as a comparison, where a clear transition from linear behavior at ~ 125 MPa indicates the

starting pointing of stress-induced martensitic transformation. The hysteresis in bulk

compression is also larger than that of a single crystal. This indicated that micro-scale Ni-Mn-

Ga demonstrates a strong size effect in the austenite-martensite transformation compared to

bulk compression.

Fig. 2.16: (a) Stress-strain pseudoelastic behavior of nominally 2 μm radius microcrystal, (b)

bulk compression data of Ni-Mn-Ga single crystal, (c) The second derivative of the

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

compression data plotted against smooth data is used to obtain the value for martensitic

transformation stress. (This work)

2.6.2 Temperature dependent nanoindentation and compression testing

Temperature-dependent nanoindentation and compression (TDNC) testing were performed

using TI-980 Triboindenter. The experimental procedure is similar in both cases apart from

different tips (Xsol flat punch for compression testing and Xsol cono-spherical tip for

nanoindentation) and loading function parameters. The initial step involves replacing the

standard magnetic sample stage with the Xsol stage, which consists of the bottom heater,

thermocouple (Type-K thermocouple), and two connections to the water inlet/chiller. The mid-

stage is installed on top of the base stage, where the sample is mounted inside the chamber

with three screws to avoid any movement during the experiment. The mid-stage has a nitrogen

inflow and outflow connection and a connection to nitrogen gas (cover gas), which purges the

sample chamber (see Fig. 2.17). Its purpose is to prevent oxidation or condensation of the

probe and to push heated or humidified air away from the transducer sensor. The mid-stage

also has a thermocouple placed inside the sample chamber to precisely measure the sample

temperature with an accuracy of 0.5 ˚C.

Figure 2.17: Xsol is positioned on the middle stage on the left side, where the specimen is

held securely inside the chamber using three clamps. The whole low/high-temperature

arrangement is located on the right-hand side, where the center stage position is marked

with a red arrow to the right side figure. (This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

After installing the bottom and mid-stage, an environment shield is installed, which protects the

transducer, piezo scanner, probe, and other sensitive electronics. The environmental shield is

also connected to pressurized air, which prevents heat or humidity from entering into the

transducer, causing damage or excessive drift. During TDNC testing Xsol tip is used, which is

approximately 17 mm long compared to the 3mm long standard indentation tip. In the next

step, the polycarbonate (PC) sample is placed on the mid-stage, and tip-to-optics calibration

is performed in normal nanoindentation. In the case of compression testing, tip-to-optics is

done at a 6x zoom factor for better precision, similar to standard compression testing. After

calibration PC sample is removed from the stage, and the top stage is placed to complete the

setup. The top stage also has a top heating element, thermocouple, and two water connections

held down using four metal clamps. One of the connections is connected to the water outlet,

Fig. 2.18: Low-temperature nanoindentation/compression testing setup view of TI-980

Triboindenter. (Reproduced from TI-980 temperature-dependent testing module)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

whereas the second connection is attached to a bottom stage to complete the loop. Before we

start the TriboTc software (the program by which the temperature of the stage is controlled)

Lakeshore 336 control unit must be turned on. The Lakeshore control unit is connected to the

nanoindentation system by USB, and it manages the current magnitude that is applied to the

heating elements. In the last step, the copper coil is placed in the liquid nitrogen dewar, and

nitrogen gas is turned on, which circulates through the cooled tubing and out to the xSol stage

to cool the base. The enviro shield air flow (0.3l/min), chamber gas flow(0.6 l/min), and nitrogen

gas flow is maintained according to the temperature (12-20 l/min). The desired temperature

can be set in the TriboTc software; once the temperature is achieved, the heating elements

are turned on automatically to maintain the temperature. Once the desired temperature is

achieved, let it stabilize for a few minutes to achieve a minor drift, and after that,

nanoindentation/compression testing is performed. Figure 2.18 represents the labview visual

for low-temperature nanoindentation/compression testing. A few points should be kept in mind

to prevent system damage and personal safety and achieve the best results possible

• To prevent system damage, ensure you position the dovetail correctly when

using the xSol setup.

• Let the temperature of the sample stabilize for a few minutes before performing

the test.

• Be very careful with the xSol tip mounting step; you can damage the tip very

easily due to its large size compared to the standard tip.

• Do not touch the top and bottom stages immediately after completion of the

test; they could either be very cold/warm and damage the skin.

• Do not turn off the system abruptly after performing low/high-temperature

testing; let the system achieve the ambient temperature slowly and steadily to

prevent system damage.

2.7 Tensile testing and analysis

Tensile testing, unlike compression testing, utilizes an axial force to stretch the material along

its axis. The resulting deformation manifests primarily as axial elongation that coincides with

the direction of the applied force. This technique enables the acquisition of properties such as

ultimate tensile strength, yield strength, and reduction in material area. In our study, we will

employ free-standing Ni-Mn-Ga strips, as discussed in section 2.1 (Sample materials), to form

a dog-bone structure placed on a commercially available push-to-pull (P2P) device using a

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

focus ion beam. Bruker provides P2P devices with three different stiffness levels, including

150, 300, and 450 N/m. For our testing purposes, we will choose the P2P device with the

highest stiffness at 450 N/m. The process of tensile testing involves four distinct steps:

• Stiffness measurement of the P2P device

• Mounting of the free-standing strip onto the P2P device

• Converting the free-standing sample into a dog-bone structure

• The actual test

Let us discuss each step in detail,

The initial step involves mounting the P2P device onto a FIB lift-out grid holder, which offers

optimal handling due to the device's small size, as shown in Fig. 2. 19 a. The dimension of the

P2P device is 2 mm * 1.18 mm * 0.033 mm (L*H*W), whereas the actual size of the device

part where the sample is mounted and testing is performed is much smaller, 0.580 mm * 0.226

mm * 0.010 mm (L*H*W). Before further experiments, first stiffness measurements are

performed to make sure to take the device's compliance with our actual tests during data

analysis. Stiffness measurements are performed using a 10 μm flat punch and under

displacement control, subjecting the P2P device to strains of 100 nm and 1000 nm. The

stiffness value, calculated from both measurements, is ~ 460 N/m, which is very close to the

manufactured value of 450 N/m; the force-displacement data is shown in Fig. 2.19 b.

Fig. 2.19: Tensile testing experimental setup and sample preparation: (a) push to pull device

mounted on FIB lift-out grid holder for optimal handling due to device's smaller size, (b)

device stiffness is measured at 100 nm and 100 nm displacement. (This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

Mounting of the free-standing strip onto the P2P device and converting the free-standing

sample into a dog-bone shape is shown in Fig. 2.20. In step 1, the Ni-Mn-Ga free-standing

strip sample is inserted into the FIB without any stage tilt. In the subsequent step, the

Omniprobe is manipulated via an electron beam to position the desired free-standing strip, and

the Omniprobe's distance from the strip is monitored by scanning rotation of 180° in the ion

beam. Upon contact with the sample, platinum is applied on both ends to secure it in place,

and both sides of the strip are later cut by FIB milling. The strip size of approximately 35 μm is

then removed, and the Omniprobe is retracted to the highest possible point for sample safety

for the next step.

In the third step, the P2P device is mounted on a 45° Pin stub holder and placed inside the

FIB. The stage is tilted at 45˚ to perform eucentric height to prevent damage to the P2P device

and Omniprobe. The Omniprobe is then introduced, carrying the sample, and carefully

positioned in the center of the P2P. Once again, the probe is observed using an electron beam,

and an ion beam with a scan rotation of 180° is employed to place the sample precisely onto

the device. Platinum is deposited on both sample sides, and the Omniprobe is subsequently

separated and retracted. The third step is the most crucial part of the preparation, as the

chances of damaging the sample are very high due to misalignment between the P2P device

and Omniprobe. The fourth step involves placing the P2P device inside the FIB with only the

FIB lift-out grid holder (remove the 45° Pin stub holder). By tilting the stage at 7˚, which aligns

Fig. 2.20: Mounting of the free-standing strip onto the P2P device and converting the free-

standing sample into a dog-bone shape is shown in five steps. (This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

the sample to the ion beam, the sample is milled out as a dog bone by removing the sample

from both sides. The final prepared sample mounted on a P2P device is shown in Fig. 2.20

step 5. The dimensions of the sample are 2 μm * 0.5 μm * 05 μm (L*H*W). After successfully

preparing the sample, tensile testing is performed using Hysitron TI-98 Triboindenter.

Tensile testing data analysis

Tensile testing data is analyzed using a push-to-pull application developed by Bruker, which

can be integrated into OriginPro software. This application makes it very easy to obtain the

Engineering stress-strain data by analyzing the test data by providing the device's stiffness,

the system's compliance, and the sample's dimensions under testing. Here is an example

given of a stress-strain curve obtained for the 2 μm * 0.5 μm * 05 μm (L*H*W) Ni-Mn-Ga sample

Fig. 2.21: Engineering stress vs strain data obtained from a free-standing Ni-Mn-Ga sample.

(This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

CHAPTER 3: RESULTS AND DISCUSSION

3.1 Constrained incipient phase transformation in Ni-Mn-Ga films:

A small-scale design challenge

3.1.1 Author contribution statement

This work has been published in material and design journals and is available as open access

(Fareed et al., 2023).

J.M. Rosalie provided the scanning transmission electron microscopy (STEM) data. S. Kumar

and T. Hickel generated the simulation data using Ab initio calculation. S. Kar and S. Fähler

provided the thin films and vibrating sample magnetometer (VSM) data. A. Fareed performed

nanoindentation, atomic force microscopy, temperature-dependent experiments, statistical

calculations, and STEM data analysis and wrote the manuscript. R. Maaß supervised the

whole work.

3.1.2 Introduction

Materials with the remarkable ability to undergo reversible shape changes have found

extensive applications in various fields (Duerig et al., 1999; MohdJani et al., 2014; Niinomi.,

2016; Van Humbeeck, 2001). These applications span from traditional actuation mechanisms

that rely on reversible strains (Chmielus et al., 2009; W.Huang., 2002; Wilson et al., 2007) to

potential cooling mechanisms that exploit caloric effects (Fähler et al., 2011; Gottschall et al.,

2018). Among these, traditional shape-memory alloys like NiTi (Buehler et al., 1963; Hua et

al., 2020), CuAlNi (Gomez-Cortes et al., 2017), or CuAlBe (Fuster et al., 2019) have shown

significant strain recovery under thermal and/or mechanical stimuli. However, the potential of

ferromagnetic shape-memory alloys, which exhibit exceptionally large strains induced by

magnetic fields due to magnetically induced reorientations, is yet to be fully explored (Murray

et al., 2000; Sozinov et al., 2002a; Ullakko et al., 1996).

Ni-Mn-Ga ternary system is an attractive candidate for ferromagnetic shape memory materials.

In this system, L21-ordered compositions go through a first-order phase transition from a high-

temperature austenitic phase to a low-temperature martensite phase (Murray et al., 2000;

Sozinov et al., 2002a; Zhou et al., 2017). By changing the composition and microstructure, it

is possible to adjust the temperature at which phase transition occurs and the strain that may

be achieved by pseudoelastic switching. The strain range can vary from 6% to 24%, based on

the specific martensitic structure formed (Sozinov et al., 2013; Sozinov et al., 2002a).

Various 10M and 14M martensitic structures, modulated and non-modulated (NM), have been

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

discovered (Schwabe et al., 2021; Zhou et al., 2017). The adaptive concept explains their

occurrence by identifying the NM structure as the ground state, which has the largest

tetragonal distortion (Kaufmann et al., 2010). Furthermore, there have been reports of intricate

intermediate pre-martensitic structural configurations, suggesting a wide range of unstable

structures leading to the creation of tetragonal martensite (Chernenko. et al., 2001), for which

we also recently observed a hierarchical pre-martensitic microstructure (Kar et al., 2023a).

Given the potential of the high-temperature austenite to undergo significant pseudoelastic

stresses when mechanically activated, it becomes crucial to understand the specific stage at

which losses occur due to structural deterioration. This understanding is key to preventing

incomplete phase changes and, ultimately, functional fatigue. However, at the macroscopic

level, this comprehension is challenging due to the microplastic processes that are often

unobservable in studies involving large-scale deformation (Maaß and Derlet, 2018). Therefore,

it is imperative to delve into the microscopic scale to gain a comprehensive understanding of

these processes. Nevertheless, performing small-scale mechanical evaluations provides a

highly precise approach that enables the examination of irreversible features of the underlying

first-order transition and the direct investigation of an incipient phase transformation.

Small-scale deformation of nickel-titanium (NiTi) could reveal regions of remnant martensite

during a single deformation cycle. These regions of remnant martensite would indicate the

beginning of mechanical dissipation in a shape-memory alloy (Laplanche et al., 2014).

However, the current understanding of functional fatigue and incipient phase changes in Ni-

Mn-Ga remains uncertain. This can be attributed, in part, to the fact that previous research in

nanomechanics mostly concentrated on as-prepared martensitic materials (Satapathy and

Aich, 2019) or utilized high indentation loads to investigate phase changes by imaging post-

deformation (Ghahfarokhi et al., 2023; Niemann et al., 2016). Due to a first-order transition,

where both phases can coexist, small-scale actuation can start at different critical stresses.

Consequently, a statistical evaluation is necessary at a smaller level rather than relying on the

overall average. In order to achieve this goal, we use automated nanoindentation on Ni-Mn-

Ga thin films to evaluate the beginning of the martensitic phase transition and any residual

martensite following deformation on microscopic scales.

In order to investigate small changes from the purely elastic response and to provide insight

into the incipient (pseudo) elastic as well as plastic behavior of Ni-Mn-Ga, we conducted

nanoindentation on single crystalline austenitic thin films at various temperatures, spanning

the austenite-martensite transition temperature. The 0.5 µm and 2 µm film thicknesses were

evaluated, and both exhibited an austenitic phase at room temperature. The austenite phase

was chosen as a very promising choice for the development of pseudoelastic and

electrocaloric microsystems (Bruederlin et al., 2018).

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

3.1.3 Experimental and Computational Details

DC Magnetron sputtering was used to produce epitaxial Ni-Mn-Ga-films with thicknesses of

0.5 µm and 2 µm on single-crystal MgO (001) substrates with a 20 nm epitaxial Cr-buffer layer,

as previously described (Thomas et al., 2008). The substrate temperatures during deposition

were 600˚C and 400˚C for the thinner and thicker films, respectively. The thin films that were

deposited using sputtering had compositions of Ni54.5Mn18.5Ga27 (thinner film) and

Ni53.5Mn20Ga26.5 (thicker film). The compositions were measured using energy dispersive x-ray

spectroscopy (EDX) with an accuracy of 1 atomic percent. A Ni50Mn25Ga25 reference was used

for comparison. The samples' phase-changing behavior was analyzed using a Quantum

Design VERSALAB vibrating sample magnetometer (VSM). A constant magnetic field of µ0H

= 0.01 T was applied during the examination. The temperature range of 200 K to 400 K with a

heating rate of 2 K/min, while the magnetic field was oriented along the [100] direction of the

MgO crystal. Figure 3.1a displays the magnetization curves for both films, with red and green

arrows representing the heating and cooling cycles. In contrast to low temperature, the high-

temperature austenite phase exhibits a predictable decrease in the magnetic moment above

the Curie temperature TC. The austenitic start (As) and finish (Af) temperatures, as well as the

Fig. 3.1: (a) Magnetization as a function of temperature under a constant magnetic field of

µ0H = 0.01 T. The red and green arrows correspondingly represent the heating and cooling

sequence. (b) Indicates the presence of the austenitic phase upon heating for 0.5 µm, as

seen by a smooth surface above Af. (c) Display the martensitic microstructure below the

martensite finish temperature (Mf) using an optical microscope during the cooling process of

the 2 µm film. (Adapted from (Fareed et al., 2023))

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

martensitic start (Ms) and finish (Mf) temperatures, show slight composition-dependent

variations in both films. The temperatures for the 0.5 µm and 2 µm thin films are presented in

Table 1. Figure 3.1b exhibits optical microscope images demonstrating the smooth and uniform

austenite condition, typically observed at temperatures above room temperature.

Additionally, Fig. 3.1c also shows the distinct patterns of martensite variations that are

observed below the Mf temperature. A Bruker-Hysitron TI980 instrument was used to perform

temperature- and rate-dependent nanoindentation. A cono-spherical diamond tip with a radius

of 890 nm was utilized only for experiments carried out at room temperature conditions.

Utilizing four distinct loading rates (1 mN/s, 0.1 mN/s, 0.01 mN/s, and 0.001 mN/s) at ambient

temperature, all tests were conducted in load-controlled mode with a maximum load of 1 mN.

A duration of 10 seconds at the highest load was maintained, and all unloading segments were

subjected to a loading rate of 0.1 mN/s. The spacing between all indents was precisely 4 μm,

and a minimum of 400 indents were performed at each rate or temperature. The temperature-

dependent nanoindentation investigations for both films followed the same testing technique,

but utilizing the instruments' Xsol-stage, another cono-spherical tip with a tip radius of 1 μm

was used.

The temperature range studied was from 242 K to 313 K, encompassing both the martensitic

phase at lower temperatures and the austenite phase at higher temperatures (Fig. 3.1a). Prior

to temperature-dependent testing, the thin films were introduced into their respective testing

environment, which included thermocouples, heaters, and liquid nitrogen coolers.

Subsequently, the sample was heated to a temperature of 313 K. A sequential cooling process

was employed to investigate the nanomechanical behavior at lower temperatures. The

environment was consistently purged with nitrogen gas to avoid water condensation on the

sample surface. We utilized atomic force microscopy (AFM, MFP-3D Asylum instrument) and

a dual beam scanning-electron (SEM) and focus ion beam (FIB) microscope (Quanta 3D FEG

from Thermo Fischer) to map specific indentation locations before and after nanomechanical

testing. Transmission electron microscopy (TEM, JEM-2200FS) samples were obtained from

indentation locations using normal FIB lift-out procedures to examine the microstructure

underneath the indents.

In addition to the experiment, ab-initio calculations were performed. Specifically, the study

utilized spin-polarized density functional theory (DFT) calculations using the Vienna ab initio

simulation program (VASP) (Kresse and Furthmuller, 1996a; Kresse and Furthmuller, 1996b;

Kresse and Hafner, 1993; Kresse and Hafner, 1994). The plane-augmented wave (PAW)

approach (Blöchl., 1994; Kresse. and Joubert., 1999) is used with GGA-PBE (generalized

gradient approximation as parametrized by Perdew-Burke-Enrzerhof) functionals (Perdew et

al., 1996) to describe the electron-ion interaction and exchange correlation. A Γ-centered k

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

point grid of 11×11×11 was used to sample the Brillouin zone. The energy and force

convergence criteria were set to 10−8 eV and 0.01 eV/Å. A conjugate-gradient algorithm was

used for relaxing and optimization of structural parameters. A conjugate-gradient technique

was employed to iteratively adjust and optimize the structural parameters. A 500 eV energy

cut-off was employed to represent the Kohn-Sham wavefunction and truncate the plane-wave

basis sets.

As stated in the introduction, the martensitic transformation in the Ni2+xMn1+y-xGa1-y system

involves a transition from a cubic unit cell to an orthorhombic one. Typically, the energy of the

crystal structure is analyzed in relation to the c/a ratio to describe the structural transition. In

order to assess the overall thermodynamics, it is common practice to do these calculations

with a constant volume equal to that of the austenite. This is because experimental

observations indicate that only minor changes in volume occur throughout the transformation

(Dutta et al., 2017; Uijttewaal et al., 2009). The constant volume assumption is no longer valid

when considering the shape changes caused by nanoindentation in this work. Conversely, we

are evaluating a uniaxial compression specifically along the c-axis. When considering the in-

plane lattice parameters, we only focus on the case when a = b. In this situation, several

possibilities may be evaluated. One possibility is that the parameters can be adjusted to a

value that minimizes the energy of the entire unit cell. This will be decided by the Poisson ratio,

provided that we are describing a single phase. However, they may be restricted by external

boundary conditions, such as the lattice constant of the substrate on which the thin films have

been deposited. Based on these two situations, the potential energy of the stoichiometric

Ni2MnGa alloy was computed for various c/a and a = b values. The findings will be analyzed

in relation to the resultant potential energy surface (PES). Currently, it is important to mention

that the PES only represents the NM variation of the martensite. However, martensite

structures like 10M and 14M, which have been discovered in experiments, need to be explicitly

computed to simplify the analysis. These variations are modified forms of the NM martensite

and have similar energy levels to NM due to the low energy of the twin boundaries involved

Table 1: Transition temperatures of phase transformation for both films. The

temperature at which martensite formation begins upon cooling from austenite is

referred to as Ms, whereas Mf represents the temperature at which this change is

completed. As and Af refer to the austenite start and finish temperatures that occur

throughout the heating process. Both thin films also provide the Curie temperature, Tc.

Film thickness

0.5 µm

268 K

256 K

268 K

281 K

312 K

2 µm

274 K

257 K

270 K

285 K

332 K

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

(Kaufmann et al., 2010). One crucial distinction for the forthcoming discussion is that the

modulated structures possess an effective c/a < 1.

Results and Discussion

3.1.4 Constraint-induced intermittent austenite to martensite phase

transformations

A distinct plastic instability, commonly referred to as a pop-in, is observed upon

nanoindentation of the 0.5 µm thin film at a rate of 0.1 mN/s, indicating a deviation from the

elastic contact. Figure 3.2a shows 70 nanoindentation curves on a 0.5 µm film together with

the elastic solution of a Hertzian contact model, which was fitted using the equation P=

43Er√Rh3/2 (Johnson., 1985). In this equation, P represents the applied load, R is the radius of

the indenter tip (890 nm), h is the penetration depth, and Er (79 GPa) is the reduced modulus.

The first pop-in has a displacement magnitude that is considerably larger compared with any

subsequent higher-order occurrences, much like indentation on single-crystalline single-

element metallic materials (Corcoran et al., 1997; Morris et al., 2011; Sato et al., 2020;

Shimanek et al., 2020). More precisely, the initial pop-in of the Ni54.5Mn18.5Ga27 thin film is

generally larger than 4 nm, while any subsequent pop-ins are generally between 0.6 and 1.5

nm in size. Figure 3.2a not only shows a distinct first pop-in signature but also demonstrates

Fig. 3.2: (a) Shows an accumulation of 70 load-displacement curves that were generated at

room temperature on the 0.5 µm thick film. Distinct pop-in behavior is seen following an

elastic loading segment that adheres to the Hertzian contact model. (b) The AFM figure

shows an indentation surrounded by line features, shown by arrows, which provide evidence

of residual martensite following deformation. (Adapted from (Fareed et al., 2023))

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

a notable overlap of the subsequent loading curves following the initial event. The initial pop-

in's magnitude is directly proportional to the applied load, a characteristic observed in various

metallic materials such as metallic glasses (Schuh et al., 2003), superalloys (Gan and Tin,

2012), and intermetallics (Ikeda et al., 2021). This behavior originates from the stressed-

volume indentation-depth scaling intrinsic to the experiment (Packard and Schuh, 2007).

Nevertheless, the infrequent and small size of subsequent pop-ins following the initial one

distinguishes the data in Fig. 3.2a from dislocation plasticity or shear-localization, which results

in indentation curves that closely overlap over one another.

Either a stress-induced phase transition from austenite to martensite or plastic deformation

such as dislocation activity can explain the observed distinct pop-in signature in the current

shape-memory alloy. Although there is less information available on the initial plastic behavior

of shape-memory alloys, previous research on NiTi has certainly shown such behavior

(Laplanche et al., 2014). In-situ SEM experiments conducted at significantly higher loads (50

mN) and corresponding displacements revealed that a transformation of the phase causes the

pop-in phenomenon observed in NiTi. If the same applies to Ni-Mn-Ga, the significant range

of pop-in stress shown in Fig. 3.2a suggests a substantial statistical variation in the local phase

transformation and associated critical stress in epitaxial films. This variation is notably distinct

from that observed in a bulk single crystal.

To provide a more precise measurement, the force required for pop-in, Pp, which varies

between about 100 and 600 μN for all curves, is translated into shear stress using the equation

τmax = 0.31(6PpEr2

π3R2)1/3 (Shim et al., 2008), with a value of 79 GPa used for Er. This method is

commonly employed to estimate the Poisson's ratio of the tested material as 0.3. It is frequently

utilized for statistically evaluating shear-stress statistics in metals (Morris et al., 2011;

Shimanek et al., 2020). Figure 3.3 presents a summary of the shear stresses derived using a

complementary cumulative distribution function (CCDF). A CCDF (1-CDF), which is the

complement of the cumulative distribution function (CDF), is favored over the commonly used

probability density distribution (PDF) because it eliminates the need for binning and so exposes

nuanced yet significant characteristics of the distribution. The CCDF focuses on occurrences

with lower probabilities, therefore highlighting the most extreme stress-scale values of the

examined mechanism. The data obtained at room temperature is uniformly distributed over all

applied loading rates, with little variation in the extreme values at low probability.

Following that, the method of the maximum likelihood estimator (MLE) (Alstott et al., 2014)

was utilized to quantitatively determine the distribution function that was suitable for the pop-

in stress data. This method enables the comparison of different distribution models, specifically

a truncated power law, a lognormal distribution, and a stretched exponential (Weibull)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

distribution. The comparison is carried out using a log-likelihood ratio, which falls within the

range of 1.4 to 2.9 and a significance value consistently < 0.05. These values are used to

determine which model best fits the actual data. The room temperature data may be accurately

characterized by a Weibull distribution, with the specific values for the shape and scale

parameters provided in Table 2. The selection of a Weibull distribution to represent the pop-

ins suggests a scenario where the weakest component is the determining factor. This is

commonly found in microstructural systems that are highly influenced by stress (Derlet and

Maass, 2016). Thus, we examine the statistical properties of the initial critical stress associated

with a certain fluctuation, displayed in Figure 3.3. This would be quite consistent with a

transformation from austenite to tetragonal martensite that is diffusionless and typically has a

weak dependence on the transformation rate. Prior to examining the microstructural change

that causes the plastic instability, we also analyze the pop-in response of the 0.5 µm film as it

is heated from the martensitic regime over the temperature range of the first-order transition

(Fig. 3.1).

Figure 3.4 illustrates the standard indentation curves obtained at temperatures ranging from

313 K to 243 K. Compared to the data collected at room temperature, the noise level has

Fig. 3.3: Displays the complementary cumulative distribution function (CCDF) of the first

pop-in stress for a 0.5 µm thick film. The CCDF is shown for various loading rates at ambient

temperature as well as at 243 K and 260 K with a loading rate of 0.1 mN/s. The Weibull

distribution is a comprehensive model that can accurately represent all data types. The

relevant fitting parameters are outlined in Table 2. (Reproduced from (Fareed et al., 2023))

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

increased from a standard deviation of 0.2 nm at 313 K to 0.6 nm at 243 K. This outcome is

anticipated

as a result of the gas flow of liquid nitrogen employed for the purpose of cooling. It is important

to point out that the low-temperature observations were performed with a larger tip radius,

resulting in lower-depth results at the same maximum force compared to the previously stated

room-temperature data. A very similar pop-in signal is observed despite the fact that the

magnetization curve (Fig. 3.1a) indicates that the lowest temperature in this series is probing

a pure martensitic phase.

Remarkably, the pop-in's statistical signature at 243 K is Weibull distributed as well, but it has

been noticeably moved to greater stress levels than it was at room temperature (Fig. 3.3). The

slightly larger tip radius, which actually decreases the stress under load conditions that are

Table 2: Weibull shape parameter (K) and scale parameter (λ) for different loading

rates at room temperature and 260 k. These parameters correspond to the

distributions shown in Fig. 3.3.

Loading rate (mN/s)

0.1

0.01

0.001

0.1 (260 K)

Shape parameter K

10.09

10.23

11.13

14.94

Scale parameter λ

0.47

0.49

0.48

0.39

Fig. 3.4: Nanoindentation measurements conducted at temperatures ranging from 313 K to

243 K, covering entirely the austenite and martensite phase regimes, for a 0.5 µm thin film.

Pop-ins are detected at all testing temperatures. (Reproduced from (Fareed et al., 2023))

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

otherwise similar, is not the cause of this phenomenon. Consequently, the shifted CCDF is a

clear indicator of increased activation stresses for the underlying stress-relaxation process that

enables rapid displacement increments. Based on the fact that Ni54.5Mn18.5Ga27 is martensitic

at 243 K, the shift in stress scale must be attributed to twin-variant reorientation (Niemann et

al., 2017) and twin-thickening (Laplanche et al., 2014), rather than an austenite-to-martensite

transition that could occur at higher temperatures. In order to provide additional proof for this

conclusion, it is important to carry out a series of nanomechanical tests at a temperature

slightly above 243 K when both martensite and austenite are present simultaneously. Thus,

one would anticipate a stress range of pop-ins with a certain probability when sampling the

material at many random sites, which now includes both the austenite and martensite ranges.

This is the case for the pop-in behavior at 260 K (Fig. 3.3), which now results in a CCDF

including plastic instabilities related to both the twin-variant formation and the austenite-to-

martensite transition across a stress range. Both structural processes adhere to Weibull

statistics and may be differentiated based on their respective stress scales.

Even though it is experimentally impossible to characterize the structural changes that occur

during low-temperature indentation directly, one can use AFM and TEM to evaluate the

residual imprint left behind after indentation at room temperature in order to determine whether

the pop-in is a sign of phase transformation or dislocation activity. Figure 3.2b displays an AFM

image of a 298 K-indentation imprint with line contrast characteristics corresponding to residual

martensite. A transmission electron microscopy (TEM) examination was conducted on the

pristine thin film and the underlying structure underneath the indents to obtain a deeper

understanding of potential microstructural changes related to the pop-in phenomenon. Figure

3.5a shows the as-deposited microstructure observed with bright-field scanning transmission

electron microscopy (BF-STEM). The selected area diffraction (SAD) technique confirms that

the microstructure consists entirely of the austenitic phase, with a film normal orientation of

[001], as shown in Fig. 3.5b. The cross-sectioned thin film showed no indication of martensite

pockets or pre-existing defect structures over several micrometers.

When examining the microstructure underneath a location with an indent, a distinct image

emerges. Figure 3.5c illustrates the presence of approximately 45° inclined lines that have a

repeat length scale of around 20 nm. These lines are indicative of martensite variants and

resemble the surface topography resolved by AFM. The indentation sites did not reveal any

dislocation features. SAD analysis of the microstructure beneath the indents revealed the

existence of austenite and a second phase. Indeed, the weaker austenite reflections (hkl) =

(200), (420), etc.) become indistinguishable, and the SAD of the austenite pattern (circles, Fig.

3.5d) is superpositioned with reflections (squares in Fig. 3.5d) that are in close proximity to the

positions of the austenite peaks. These extra reflections indicate the existence of a secondary

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

phase that possesses the following characteristics: i) a lattice parameter that closely resembles

the austenite phase in the direction of growth, ii) a shorter lattice parameter normal to this

direction, and iii) a counterclockwise rotation of approximately 6°. For a stoichiometric

Ni2MnGa-alloy or higher Mn-containing systems, modulated martensite (10 M or 14 M) is

expected to occur, which consists of a periodic stacking of the tetragonal unit cell disrupted by

twin boundaries to reduce the strain energy. The distinct crystallography of these modulated

structures includes a tetragonal unit cell with a > c for 10 M and an orthorhombic unit cell with

a > b > c for 14 M. The existence of 10 M or 14 M modulated martensite would result in weak

additional diffraction points along the <110> directions. However, these additional points are

not present in Fig. 3.5d. Alternatively, the SAD pattern seen in Fig. 3.5d may be classified as

a non-modulated (NM) martensite, which aligns well with the findings of Lanska et al. (Lanska

et al., 2004) when considering the alloy composition investigated in this study. This NM

martensite has a stronger tetragonal distortion, allowing it to withstand a higher level of strain

compared to modulated martensite (Chernenko et al., 2005) when subjected to high triaxial

stress under the indenter tip.

Fig. 3.5: (a) Bright field scanning transmission electron microscopy (BF-STEM) image of the as-

deposited austenite 0.5 µm thin film, exhibiting a pure single crystalline film with no impurities.

(b) The selected area diffraction pattern (SADP) of image (a), with beam direction B = [100],

demonstrates the austenetic film structure. (c) BF-STEM image underneath one of the indents.

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

3.1.5 Unconstrained smooth phase transformations

In order to gain a more comprehensive understanding of the process by which the residual

NM-martensite formed underneath the indents in the 0.5 µm thick film, further experiments

were carried out on a 2 μm thick film using temperature-dependent nanoindentation

techniques. Figure 3.6 presents a summary of the indentation curves obtained from tests

performed at temperatures ranging from 243 K to 313 K after heating from below the

martensitic start temperature (Ms). No plastic instabilities or pop-ins were observed during the

tests, regardless of the temperature.

Fig. 3.6: Temperature-dependent nanoindentation measurements for a 2 μm thick film

covering the austenite and martensite phase regime. No plastic instabilities can be identified

across the entire temperature regime. (Reproduced from (Fareed et al., 2023))

Furthermore, the thicker film exhibits a noticeably softer response when directly compared to

the thinner 0.5 μm film. When subjected to a load, the thicker film shows a displacement of 40

nm and a resistance of around 200–250 μN, corresponding to a maximum shear stress of 1.83

GPa. The 0.5 µm film achieved the same force or stress level at a distance of only 15 nm.

Similarly, the measurable remaining depth upon unloading is nearly three times greater for the

The SADP shown in (d) exhibits both austenite and residual martensite. Circles and squares

represent the austenite and martensite reflections, respectively. (Reproduced from (Fareed et

al., 2023))

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

thicker film compared to the film that is 0.5 µm thick. All temperatures reveal these differences,

although probing martensite at 243 K yields the predicted hardest response from the thicker

film. A notably softer mechanical reaction implies microstructural events that allow for

displacement. Due to the absence of initial dislocations in the thin films, any accumulation of

displacement caused by line defects can be ruled out. This leaves us with two plausible

mechanisms: pseudoelasticity driven by the transformation from austenite to martensite above

the martensite finish temperature (Mf) and the motion of twin boundaries below Mf.

Fig. 3.7: Bright field STEM overview image of the top part of the 2 µm thick film, including

indented areas. No residual imprints from indentation are visible. (b) Zoom-in from (a),

highlighting FIB curtaining and isolated defects present in both indented areas and as-

deposited film regions. (c) SADP of a defect-free region with B = [100]. (d) SADP of a region

containing defects as depicted in (b). (Reproduced from (Fareed et al., 2023))

Figure 3.7 presents a summary of the TEM microstructure analyses conducted on the 2 μm

film. Figure 3.7a depicts a montage of the film BF-STEM images, including indented areas. We

can observe only a few vertical streaks caused by FIB curtaining. This is particularly noticeable

in images with higher magnification, as in Fig. 3.7b, along with planar defects superficially

identical to those in Fig. 3.5c. The SAD patterns from the non-indented areas only reveal

single-phase austenite, characterized by distinct weak and strong reflections that alternate

along the [010] directions (Fig. 3.7c). SAD exhibits some extra-low-intensity spots, displaced

in the [110] directions compared to the austenite reflections, within regions exhibiting the planar

defects seen in Fig. 3.7b. We conclude that these defects, appearing in both non-indented and

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

indented areas of the film, are not the result of any nanomechanical testing. Combining this

with the fact that these defects redirected the curtaining lines, we can conclude that these are

artificial features created in the thick films, either during or after lamella preparation. Although

the FIB-introduced curtaining is evident, there is no indication of any dislocations or phases

other than austenite in the thick film, both in non-indented locations as well as underneath the

indents. This implies that, within the experiment's resolution, all displacement that has

accumulated over the curves in Fig. 3.6 is reversible. This suggests that the previously

indicated scenario involving the 0.5 µm film is likely to exhibit a distinct first pop-in response

and the formation of NM martensite, which may be attributed to the influence of size and/or the

constraint effect.

3.1.6. Ab-initio calculation of stoichiometric Ni2MnGa

We employ ab-initio calculations for further analysis, as discussed in section 3.13. The change

in phase-transformation behavior in the 0.5 µm film is particularly interesting when lateral

constraints are introduced. Figure 3.8a illustrates the potential energy of the stoichiometric

material Ni2MnGa for different values of c/a and various a = b values. The red dashed line

represents transformation-energy minimization under relatively unconstrained conditions,

while the pink dashed line represents the case of constant in-plane lattice constants. For clarity,

Fig. 3.8b also highlights the energy profiles along the two highlighted lines.

This means that the 0.5 µm film results are best explained by the case where the in-plane

lattice parameters stay the same, a = b. As indicated by the pink line in Fig. 3.8b, this particular

scenario results in only one minimum, eliminating the possibility of a martensitic

transformation. This implies that a coherency constraint on the substrate will enforce that the

material remains austenitic for small indentations. The elastic energy will only surpass the

coherency condition when the activation stress is significantly higher than that of the

unconstrained case. This will cause a shift to the global minimum at the PES and the pop-in

event in the nanoindenter. Alternatively, if we consider the 2 μm thick film as representing the

situation where the lattice parameters a = b are fully adapted (as indicated by the red line in

Fig. 3.8b). In this case, we can observe a continuous energy profile that links the austenite and

the martensite phases. Therefore, the system can effortlessly undergo the martensitic

transformation when subjected to the mechanical load of the nanoindenter. The computational

insights confirm that a much higher transformation stress is required under constrained

conditions. The experiments observe a pop-in signature at a stress level between ~ 1.4 and

2.6 GPa, significantly higher than the expected stress level of a few hundred MPa for the phase

transformation of bulk crystals (Chernenko et al., 2005; Martynov and Kokorin, 1992a). It is

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

important to note that the Clausius-Clapeyron equation is unable to account for the significant

rise in transformation stress despite its ability to explain temperature-related changes in

transformation stress for alloys with varying Ms temperatures.

Fig. 3.8. (a) Ab-initio calculation of the potential energy surface (PES) as a function of the

lattice constants along the c-axis (parallel to the nano-indentation) and the a-axis (in the

surface plane). (b) Energy profile along the highlighted path where the lattice parameters

a=b are allowed to adapt for each indentation depth (red) and where the lattice parameters

a=b remain constant (pink). (Reproduced from (Fareed et al., 2023))

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

3.1.7 Summary

Here, we have investigated the first elastic-plastic response of austenitic thin films at room

temperature using nanomechanical techniques. At a film thickness of 0.5 µm, deviations from

fully elastic behavior occur as pop-ins at a stress scale approximately an order of magnitude

greater than the bulk counterpart. Weibull statistics describe the occurrence of these pop-ins

with shape and scale parameters that remain unaffected by loading rate and temperature. TEM

reveals that the observed pop-ins are caused by an austenite-martensite phase

transformation, leaving residual martensite underneath indentation sites. Recent findings

suggest that thermal cycling could likely transform this residual martensite back to austenite

(Ghahfarokhi et al., 2023). At 2 μm film thickness, there is no presence of pop-in during loading,

and the microstructure remains entirely austenitic after unloading. The ab-initio calculation

results reveal a substantial increase in potential energy for the martensitic phase transition

when in-plane lattice parameters are constrained. This provides a logical explanation for the

thickness-dependent initiation of the phase transformation. Our results demonstrate how

dimensional restrictions may substantially increase the stress associated with the austenite-

martensite transition and, therefore, the actuation behavior of Ni-Mn-Ga shape-memory alloys.

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

3.2 Small-scale functional fatigue of a Ni-Mn-Ga Heusler alloy

3.2.1 Author contribution statement

This work has been published in Acta Materialia journals and is available as open open-access

(Fareed et al., 2024).

J.M. Rosalie provided the scanning transmission electron microscopy (STEM) data. S. Kar and

S. Fähler: Provided the thin films and VSM data. A. Fareed performed microcrystal preparation,

compression testing, temperature-dependent experiments, statistical calculations, and STEM

data analysis and wrote the manuscript. R. Maaß supervised the whole work.

3.2.2 Introduction

Magnetic shape memory alloys (MSMAs) possess the unique ability to strain martensitic

microstructure under a magnetic field, in addition to the shape memory effect and

superelasticity. Since the discovery of 0.2% magnetic field-induced strain in Ni-Mn-Ga (Ullakko

et al., 1996), significant efforts have been made towards achieving the enormous magnetic

field-induced strain of almost 12% (Murray et al., 2000; Pagounis et al., 2014; Sozinov et al.,

2013; Sozinov et al., 2002a). This significant strain in Heusler alloys is achieved through the

rearrangement of martensitic twin variants under an external magnetic field, also known as the

magnetic shape memory effect. While the shape memory effect results from both martensite

de-twinning and the heating sequence, the high-temperature austenite phase with L21 crystal

structure (Xu et al., 2013) transforms to martensite. The crystal structure of martensite is

complex and varies depending on composition; it can form NM, 5M, and 7M structures. On the

other hand, the transformation of austenite to stress-induced martensite (known as

superelasticity) and its reversible characteristics make it suitable for micro- and

nanomechanical systems (MEMS/NEMS) (Kohl et al., 2006).

A significant amount of research has been conducted on single crystal bulk scale compression

testing (Uchic. and Dimiduk., 2005) of martensite and austenite phases, in addition to studies

on magneto-mechanical coupling (Arndt et al., 2006; Chen and Zhu, 2013; Chernenko et al.,

2005; Martynov and Kokorin, 1992b). When compression is applied during the martensite

phase, the de-twining of martensite is observed. Conversely, compression under the austenite

phase typically produces a pseudoelastic response characterized by low stress-induced

austenite to martensitic transformation. The shape memory effect at a critical scale length in

Ni-Mn-Ga is believed to lead to switching behavior under both temperature and thermal stimuli,

in contrast to bulk behavior (Dunand and Mullner, 2011). It is essential to thoroughly evaluate

this property to utilize Ni-Mn-Ga in small-scale applications such as MEMS and NEMS.

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

However, this has only been done for Ni-Mn-Ga in a 10 µm microcolumn with a single cycle

(Reinhold et al., 2009), NiTi (Frick et al., 2007), and Cu-Al-Ni (San Juan and Nó, 2013;

San Juan et al., 2007).

Ni-Ti is the only alloy that has been investigated not only at the bulk scale but also at the small-

scale length scale. The long-term cyclic behavior of nanocrystalline Ni-Ti (Hua et al., 2020)

has been investigated for millions of load-unload cycles, where it suffers from functional

degradation starting at 10,000 cycles, leading to lower strain and an increase in residual stress

for a large number of cycles. The functional fatigue in nanocrystalline Ni-Ti is attributed to

transformation-induced dislocations and the resulting residual martensite. These dislocations

form during the cyclic phase transformations and lead to residual martensite, dislocation,

residual stress, and a change in surface morphology. At the submicron scale, Ni-Ti

demonstrated a complete loss of superelasticity (Frick et al., 2007), pronounced orientation

effects, and the formation of residual martensite pockets even after a single stress-driven

transformation cycle (Frick et al., 2010). The absence of pseudoelasticity in Ti-Ni may be

attributed to the elevated critical stress in Ti-Ni as compared to Cu-Al-Ni. This greater critical

stress would facilitate localized plastic deformation of the pillars, such as at the contact site,

prior to reaching the stress threshold necessary to initiate the transformation. Alternatively, the

loss of superelasticity can be associated with a change in chemical ordering.

In recent years, thin films of Heusler alloys have been extensively studied because of their

unique applications in microdevices and actuators (Kohl et al., 2004; Liu et al., 2006; Moumni

et al., 2005; Yeduru et al., 2013). Phase transformation in thin films to produce the desired

phase at room temperature is a significant challenge because of their sensitivity to deposition

conditions and parameters that control the phase of the thin films. Even with extensive

knowledge of preparation processes and techniques, producing austenite films free of defects

and the desired thickness is still a significant challenge. As seen previously (Fareed et al.,

2023), we observe a significant increase in the stress scale and partial reversibility of the

austenitic-martensitic phase shift in sub-micrometer films on MgO substrates. This suggests

that dissipation may vary depending on the length scale. Additionally, recent findings suggest

that sputter-deposited Ni-Mn-Ga thin films may possess pre-martensitic domains, as

discovered by (Kar et al., 2023a). These films also exhibit a hierarchical microstructure

consisting of nano- and mesoscopic twin boundaries, as seen by (Schwabe et al., 2021). In

addition to assessing the changes in the switching behavior of the system, we also need to

evaluate the dissipation behavior of the system, as it will be used as an actuator and go through

hundreds of thousands of cycles. Investigating how often this system can go through such a

switching mechanism is crucial before experiencing sufficient losses that deteriorate the

switching behavior.

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

In order to achieve this objective, we conducted compressive fatigue tests on cylindrical

austenitic Ni-Mn-Ga microcrystals at room temperature, performing a total of 106 consecutive

load-unloading cycles.

3.2.3 Experimental Details

A single crystalline thin film of Ni-Mn-Ga with a thickness of 4.8 µm was fabricated using DC

magnetron sputtering on single-crystal MgO (001) substrates with a 150 nm epitaxial Cr-buffer

layer, as described in detail in Refs. (Backen et al., 2012; Kar et al., 2023a). The substrate

temperature during the deposition process was 300 °C, whereas thin film was deposited at

400 °C. The Cr buffer layer serves the purpose of improving the adhesion between the film

and substrate, achieving a smooth film surface by obscuring substrate imperfections, and

reducing stress relaxation at the interface (Kar et al., 2023a). The composition of the film was

found to be Ni51.3Mn21.7Ga27 as determined by energy dispersive x-ray spectroscopy (EDX) with

an accuracy of 1 at.% using a Ni50Mn25Ga25 standard. The phase-changing behavior of the

sample was examined using a vibrating sample magnetometer (Quantum Design-VERSALAB)

with a constant magnetic field of 0.01 T in the temperature range of 200 – 400 K and a 2 K/min

heating rate. The magnetic field was applied along the MgO [100] direction. The phase

transformation temperatures are As = 180 K, Af = 222 K, Ms = 214 K, and Mf = 175 K

(corresponding to austenite start and finish and martensite start and finish, respectively).

The compression experiments were performed at room temperature (298 K), where the thin

film is in the pre-martensite phase, also known as tweed austenite. Several free-standing

microcolumns with an [001] orientation were milled following the standard annular procedure

(Maaß et al., 2015) using a focused ion beam (FIB) technique. The FIB milling was performed

using a Quanta 3D FEG system integrated with a Ga ion beam and scanning electron

microscopy (SEM). The microcolumns have an approximate diameter of 2 µm and a height of

4.8 µm. The initial milling process involved creating a 20 µm trench with an inner diameter of

8 µm at 30 kV/3 nA. Further milling was followed by more precise milling, reducing the inner

diameter from 8 µm to 2 µm in three steps using 0.5 nA, 0.1 nA, and 49 pA. A final milling step

was performed at 30 kV/30 pA to minimize the taper angle. The taper angle was calculated

using θ=tan−1(0.5∗𝑇𝑎𝑝𝑒𝑟), where 𝑇𝑎𝑝𝑒𝑟=(𝑑𝑙−𝑑𝐿)

𝐿𝑒𝑛𝑔ℎ𝑡 , here dL is the larger and dl is the smaller

diameter, resulting in a value of less than 2˚ for all the studied microcolumns with an aspect

ratio close to three as recommended for micro-compression tests (Zhang et al., 2006).

Micro-compression tests were carried out using a flat punch with a 10 µm diameter, employing

a Bruker-Hysitron TI-980 instrument. During functional fatigue/cyclic testing, load control mode

was utilized with a maximum load of 2400 µN, a loading time of 1 second, a minimum holding

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

time of 0.1 seconds, and an unloading time of 1 second. Whereas for functional fatigue, with

the addition of plastic strain to the system, the same parameters were used again as in

functional fatigue. Displacement control mode was used with a strain rate of approximately

3*10-3 s-1 to study the behavior of pseudoelasticity with the addition of plastic deformation. SEM

images of microcolumns were taken before and after the test, and additional images were

captured every 200 thousand cycles during cyclic/fatigue testing for the million-cycle column.

In addition, the microstructure of the columns was analyzed using transmission electron

microscopy (TEM, JEOL 2200FS) to examine their as-prepared, quasi-statically deformed, and

fatigued states. In order to achieve this objective, a cross-sectional TEM foil of the full column

was created using the FIB-based lift-out approach. Scanning-transmission mode (STEM),

bright-field (BF) imaging, and selected-area diffraction (SAD) techniques were employed

during transmission electron microscopy (TEM) to accurately measure the defect structure

along the vertical axis of the microcrystal.

Results

3.2.4 Pristine microstructure and etching procedure

Before conducting micro-mechanical testing and quantifying any functional fatigue

resulting from multiple cycles, the microcrystal is examined using TEM. Figure 3.9a

displays the BF-STEM cross-section image of a prepared 4.8 µm thin film, where we

can see the presence of dislocation and wavey patterns in the whole cross-section of

the microcolumn. These dislocations are also present at the film-buffer interface, but

they are not visible in the cross-section due to their in-plane direction. Nevertheless,

these dislocations must end at a free surface or another dislocation. Consequently,

they migrate towards the closest available surface (often the surface of the film),

resulting in the formation of threading dislocations. These dislocations are present in

the film due to the misfit between Ni-Mn-Ga film and Cr buffer, also known as misfit

dislocations. The density of these dislocations decreases as we go away from the

substrate, which is in agreement with the dislocation gradient (Bennett, 2010; Hull. and

Bean., 1992) because of a minor misfit between the film and substrate. To calculate

the misfit, we required the lattice constants of film, buffer, and substrate. The reciprocal

space mapping of (206) Ni-Mn-Ga, (103) Cr, and (224) MgO substrate reflections was

performed using a Philips X’Pert four-cycle x-ray setup. The setup was equipped with

a Cu tube and a main Ge monochromator. The measured values are 0.5822 nm for

Ni-Mn-Ga, 0.22890 nm for Cr, and 0.4214 nm for MgO. By using the following formula

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

ϵ (%)=( lattice constant of film − lattice constant of buffer

lattice constatn of buffer ) ∗ 100, the misfit values are 3% and 0.7%

for misfit between film-buffer and buffer-substrate, respectively.

This wavy structure is a precursor state prior to martensitic transformation, which is commonly

referred to as premartensite. This microstructure has been extensively examined in our recent

work (Kar et al., 2023a) and has also been observed in various other shape memory alloys

(SMAs), such as Ni-Al (Robertson and Wayman, 2006; Shapiro et al., 1989), Ni-Ti (Salamon

et al., 1985; Shapiro et al., 1984), and Fe-Pd (Muto et al., 1990; Oshima et al., 1988). The pre-

martensite phase is distinguished by a minimal tetragonal distortion that only slightly differs

from the cubic structure of the austenitic phase. The SADP in Figs. 3.9b and 9c show that we

have an austenitic Ni-Mn-Ga thin film. The presence of streaks in the diffraction patterns of Ni-

Mn-Ga, which exhibits an austenite phase, can be attributed to minor distortions in the crystal

lattice. These additional spots have been investigated (Kar et al., 2023a) using dark field TEM,

which reveals the alternating bright and dark horizontal wavy band characteristics that are

approximately 100 nm wide. Therefore, the horizontal band features constitute the

premartensite microstructure of the film matrix.

Fig. 3.9: Electron micrographs of the column prior to mechanical cycling. (a) shows a BF-

STEM image of the column, embedded in the platinum support material. The horizontal wavy

lines are indicative of a pre-martensitic structure (Kar et al., 2023a). The presence of

threading dislocation due to misfit between film and substrate, which reduces in density as

we go away from the substrate. SADP is taken from two positions shown in (b) and (c),

respectively. Red arrows and squares in (b) and (c) represent the streak and satellite spots

around each high-intensity spot, respectively. The diffraction patterns are indexed to the

[110] zone axis, with the long axis of the pillar in the [001] direction. (Adapted from (Fareed

et al., 2024))

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

To make sure that focus ion beam milling does not affect the mechanical behavior of our

microcrystal, the wet etching procedure was performed to get rid of the outer layer of the crystal

which can be damaged by the milling procedure. FIB milling could cause ion implantation into

the crystal causing surface damage (Aseguinolaza et al., 2018; McCaffrey et al., 2001) and

leading to lower yield stresses in comparison to crystal mechanical behavior without any milling

process (Maass et al., 2012; Shim et al., 2009). For wet-chemical etching, we have taken

several microcrystals with larger diameters compared to those used in mechanical testing and

etched them at room temperature with 1.25%HCl + 37%HNO3 + H2O

Fig. 3.10: (a) SEM image of a microcrystal from the top with a diameter of 4.5 μm before

etching. (b) High-resolution microscopic image after wet chemical etching with a diameter of

4.05 μm. (c) The stress-strain behavior of a microcrystal that has undergone focused ion

beam (FIB) treatment and subsequent wet etching is being studied. Each example displays

twenty cycles of superelasticity. (Adapted from (Fareed et al., 2024))

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

solution. For measuring the change in the microcrystal diameter these crystals were imaged

after etching under a high-resolution microscope. Figures 3.10a and b are shown before and

after etching where we can see the change in the microcrystal diameter from 4.50 µm to 4.05

µm. This reduction in diameter was achieved with a further dilution of the solution to achieve a

smoother and slower etching rate of 10 nm/min (Kar et al., 2023b).

After a successful etching protocol, a microcrystal of 2 µm diameter is prepared following

annular milling, Fig. 3.10c represents the mechanical response of the microcrystal before and

after etching for 20 cycles. We do not observe any major difference in the mechanical response

of the crystal with a maximum stress of up to 800 MPa. However, there are some variations in

the stress and maximum strain. The reported 0.3% strain difference is caused by the normal

errors in determining the length of the sample under tilted scanning electron microscope (SEM)

imaging settings. In this case, even small deviations of a few nm in measurements might result

in significant strain differences. Based on this evaluation, it can be stated that any surface

damage caused by Focused Ion Beam (FIB) does not impact the superelastic behavior of the

Ni-Mn-Ga alloy. Since the FIB milling does not affect the mechanical response of our material,

further mechanical work will be performed without wet chemical etching.

3.2.5 Temperature-dependent compression testing and yield strength of the

crystal

To understand if we have a size effect on the small-scale mechanical response of Ni-Mn-Ga

microcrystal in comparison to bulk single crystal, we need to realize that the martensitic

transformation stress is very dependent on the temperature difference between the martensitic

start temperature and the temperature where the experiment is carried out according to the

Clausius-Clapeyron equation:

dσ

dT=(dH∗ρ

Ms∗ ε)(Texp− Ms) (3.2.1)

Here dσ

dT is the change in martensitic transformation stress with temperature T, dH is the change

in enthalpy, ρ is the density, Ms is the martensitic start temperature, є is the value of strain,

and Texp is the temperature where an experiment is carried out. In the above equation, the term

(Texp− Ms) plays a significant role in determining the change in stress with temperature. In

Fig. 3.11b, microcrystal data is compared with the bulk single crystal Ni52Mn24.4Ga23.6

(Chernenko et al., 2005) at 349 K in the [100] direction. For bulk single crystal, the martensitic

start temperature Ms is 310 K giving the Texp− Ms=39 𝐾 whereas for our microcrystal, Ms =

210 K, giving us Texp− Ms=91 𝐾 when comparing the results at room temperature. To make

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

sure that we have the same temperature difference as a bulk single crystal, temperature-

dependent microcompression testing is performed as discussed in Chapter 2 of the

Fig. 3.11: (a) Temperature-dependent mechanical response of microcrystal (T = 298 K, 278

K, 253 K, and 223 K) with bulk compression test at 349 K (Chernenko et al., 2005). A clear

change in transformation is observed with a decrease in temperature for microcrystal tests.

(b) Single deformed cycle to determine the yield strength of the microcrystal. (Reproduced

from (Fareed et al., 2024))

experimental section. For bulk single crystal, we observe a clear transition at 110 MPa with

dσ

dT=3.5 MPa/K (Chernenko et al., 2005). By using the Clausius-Clapeyron equation, we can

calculate the theoretical value of the change in stress with temperature by using the known

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

parameters in the above equation. The value of dH is taken as 6.1 Jg-1 from Ref. (Kök and

Aydoğdu, 2012)), by putting in the rest of the values, the theoretical value of ∆σ〈100〉/∆T=

5.9 MPa/K is obtained. For the experimental value, we can take the second derivative of the

curve obtained at each temperature to obtain the point of deflection, which gives us the exact

value of the stress-induced martensitic transformation value. In our case, these values are 462

MPa (298 K), 340 MPa (278 K), 220 MPa (253 K), and 110 MPa (223 K). From this, we can

calculate that ∆σ〈100〉

∆T =5.7MPa

K, which is in very good agreement with the theoretical value,

keeping in mind the complexities of these experiments. This value is large compared to the

bulk crystal, and by taking the temperature difference, the microcrystal value (110 MPa) is

almost two times larger compared to the bulk value (60 MPa). These values suggest a clear

size effect of martensitic transformation stress.

Furthermore, it is useful to examine the hysteresis loss response of the materials during the

initial loading cycle, along with transformation stresses. The single crystal shows an energy

absorption of around 5 MJ/m3, in contrast to our 2 µm crystal, which absorbs around 0.45

MJ/m3 at ambient temperature and 0.5 MJ/m3, 0.55 MJ/m3, and 0.7 MJ/m3 as the temperature

decreases. To find the threshold of the TI-980 device, the mechanical response of the silicon

wafer was calculated, which is around 0.16 MJ/m3. This value is clearly around an order of

magnitude higher compared to the microcrystals, which indicates the validity of the data

obtained for our samples. The numbers are shown in summary form in Figure 3.12d.

To further determine the cyclic response and functional fatigue of the microcrystal, it is

important to know the yield strength of the material. To do so, one single loading-unloading

displacement control is performed beyond its elastic limit, as shown in Fig. 3.11b. We see a

linear behavior with a clear transition to martensitic transformation and then further detwinning

of martensite until we plastically deform the crystal. This graph shows that plastic deformation

starts at around 1.2 GPa, and clear plastic deformation starts at 1.5 GPa with a large strain.

Different microcrystals have been plastically deformed, and the average yield strength is

between 1.2 and 1.5 GPa. For long-term cyclic response and functional fatigue, we will stay

under the 80% limit of the material.

3.2.6 Switching response and cyclic loading-unloading (functional fatigue)

The compression response of Ni-Mn-Ga microcrystals is being studied at room temperature to

understand how it responds to repeated load-unloading cycles. Figure 3.12a illustrates the

load-unloading characteristics of several microcrystals subjected to 103, 105, and 106 total

cycles, respectively. To enhance understanding, the data from each crystal was horizontally

moved by 0.5 µm. The graph shows the first and last load-unloading cycle for each scenario,

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

illustrating the strong and elastic nature of the reversible strain magnitude, which is around

4.3% in all instances. However, there is a small drop in elastic strain for 106 cycles of

microcrystal. In order to provide a more detailed measurement of this loss, we will examine

both the amplitude of reversible strain and the hysteresis envelop that surrounds it, as they

relate to the number of cycles, N.

Fig. 3.12: (a) Stress-strain graphs illustrating the effects of cyclic loading at cycle numbers

103, 105, and 106. (b) shows a load-time trace example of a sample that has been cycled

over 103 times. (c) The graph depicts the relative elastic strain of microcrystals that have

undergone different numbers of super-elastic cycles (103, 105, and 106 cycles, respectively).

Inset in (c) shows SEM images before (N = 0) and after (N = 106) cyclic loading-unloading.

(d) The stress-strain hysteresis loss of the microcrystals (m-crystal) is compared to their bulk

equivalent (Chernenko et al., 2005) and to a silicon wafer (SW) material, which is the

benchmark for our TI-980 device. (Adapted from (Fareed et al., 2024))

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

The compression test involved subjecting the material to cyclic loading with a maximum stress

of σmax = 943 MPa, a minimum stress of σmin = 3 MPa, a stress amplitude of σa = 470 MPa,

and a stress ratio R of 0.003. Figure 3.12b exemplifies these cyclic loading conditions with

data for a sample cycled 103 times. These values are shown in Figure 3.12b, which illustrates

the cyclic loading circumstances using data from a sample that has undergone 103 cycles and

is identical to those reported in Ref. (Jang et al., 2013). Figure 3.12d demonstrates that none

of the microcrystals had a decrease in strain over the first 10,000 cycles, as indicated by the

relative strain magnitude. Nevertheless, there were minor reductions in strain, between 3%

and 4%, which appeared at 3 × 104 and 8 × 105 cycles. The hysteresis loss of the microcrystal

is also calculated, where we do not observe any major change when comparing with the initial

and last cycles, either for 1,000 cycles or a million-cycle crystal, which was assessed at

intervals of 1×105. These values do not change compared to pristine crystal, ranging from

around 0.85 - 0.9 MJ/m3 for all three crystals. These results show that hysteresis loss is much

higher in the compression testing of microcrystals than the experimental resolution, and it is at

least five times lower during repeated phase changes than in the bulk material and does not

depend on the number of cycles (N).

In addition to determining how the material behaves mechanically, a scanning electron

microscope was used to see how the sample's size and shape changed over time as it went

through cyclic loading. The SEM images were taken every couple of hundred thousand and

are shown in insets in Fig. 3.12c. Given the absence of significant changes in the elastic strain

and the lack of surface damage or evidence of plastic deformation in the crystal, we can

assume at this point that there is no presence of residual martensite over 106 cycles. Further

microstructure investigation will be discussed in a later section.

3.2.7 Superelastic response and functional fatigue after pre-deformation

In this section, our goal is to understand the superelasticity response and functional fatigue as

we introduce plastic deformation into the system.

Superelasticity in response to plastic deformation

In order to study the superelastic response while adding the plastic strain to the system, this

process involves applying compression in a single direction at a slow and steady pace until a

certain amount of plastic deformation is reached. Figure 3.13 provides a concise summary of

a series of four successive elastic and plastic strain cycles out of a total of ten cycles applied

to a single microcrystal. Due to the unpredictable nature of plastic strain introduction beyond

the elastic limit of the crystal, it is crucial to control the gradual buildup of plastic pre-strain. At

the material's yielding point and beyond it, sudden bursts of strain called dislocation

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

avalanches may occur, resulting in immediate plastic deformation, as already shown in the

literature (Sparks and Maass, 2018; Uchic et al., 2009). This is what we also observe for our

microcrystal as we go near the yielding point and beyond it. For introducing large strains in the

microcrystal in the range of 15–18%, the plastic cycle stress is increased with each addition of

plastic strain to the system. We can see an increase in stress from 0.9 GPa to 1.3 GPa from

cycle 1 to cycle 4, as shown here, whereas this value reaches 2 GPa when the plastic strain

reaches 17%. Contrary to the introduction of plastic strain, the elastic strain cycle is applied at

a constant force to determine if there is any change in the response with the introduction of

plastic strain. A recoverable cycle is applied after each plastic strain cycle, which does not

show any change for the four cycles shown in Fig. 3.13.

Fig. 3.13: A series of four successive elastic and plastic strain cycles out of a total of ten

cycles were applied to a single microcrystal. The elastic strain cycle was applied at a

constant force to determine if there was any change in the response to the introduction of

plastic strain. In the first four cycles, the figure shows a plastic strain of 5% out of a total of

17%. (Adapted from (Fareed et al., 2024))

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

Figure 3.14a summarizes the relative elastic strain recovery as a function of plastic pre-

straining for two microcrystals. Despite some scatter, both samples follow the same trend of a

gradual decay of the maximum strain recovery relative to the initial value of the undeformed

specimen. Notably, only plastic strains exceeding approximately 3% plastic pre-deformation

lead to a reduction in maximum switching strain. It is very remarkable to observe that even at

~3-5% plastic deformation, the change in the elastic behavior is very minimal, which informs

that the system is forgiving in the sense that it can even accommodate the deformation

mechanism to a certain extent without losing the recovery. The relative elastic strain drops

below 20% compared to the initial value after accommodation of ~ 17% plastic deformation.

This behavior can be accurately modeled using a basic exponential decay function with a

decay value of 4.3 ± 0.6.

Figure 3.14b demonstrates the anticipated reduction in recovery strain upon the introduction

of plastic strain. Each curve represents a gradual rise in plastic strain, similar to the example

seen in Figure 3.13. The accumulation of plastic deformation predominantly leads to the

decrease and ultimate elimination of the superelastic behavior prior to the point of change in

the stress-strain relationship. The legend provides information about the plastic pre-strain and

reversible strain magnitudes. Even though the shape of the curve is not a standard response

Fig. 3.14: (a) The elastic strain of microcolumns gradually decreases until reaching 5-6%

plastic deformation, after which there is an abrupt decrease in elastic recovery once the

plastic strain accumulation exceeds 9%. The arrow in the figure indicates the point where

TEM lamella is taken at 14% plastic strain from one of the crystals. (b) A set of ten fully

recoverable cycles is performed under force control, and four of these cycles are shown in

Fig. 3.13. In the figure legend 𝛆𝐩𝐥, 𝛆𝐞𝐥 are the values of plastic strain and the change in elastic

strain with each cycle, respectively. (Adapted from (Fareed et al., 2024))

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

after 13% plastic deformation, we still have a full recoverable response after experiencing 17%

plastic strain. The change in the initial concave is associated with the lack of austenite's

capability to react elastically before experiencing a phase transition. This leads to the important

fact that the stress-induced martensitic transformation decreases as the plastic strain

accumulation increases.

Fig. 3.15: (a) Comparison of first, and (b) last cycle second derivative, with clear transition

from high value to a low value as plastic strain increases. (b) Stress-induced martensitic

transformation against plastic strain accumulation. (This work)

To calculate quantitatively how the accumulation of plastic strain leads to progressively lower

stress at which the martensitic phase transformation is induced. Here instead of drawing the

tangent technique to find the stress-induced value, we will use the second derivated of the

loading part only as it will give us a deflection point more precisely since loading curves for the

first six cycles are almost on top of each other. In Fig. 3.15a, and b the second derivative of

the first and last cycle is shown as a reference where the minimum of the second derivative is

at 61 nm (206 MPa), whereas for cycle 10 this is lower down to 21 nm (36MPa). Figure 3.15c

summarizes the stress-induced martensitic transformation against plastic strain accumulation,

we observe a clear reduction in stress with an increase in plastic strain. Subsequent TEM

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

experiments confirmed the presence of an austenitic microstructure despite plastic pre-

straining. Based on this evidence, we can confidently assume that permanent deformation

reduces the nucleation stress required for the austenite-martensite transformation.

Functional fatigue with the addition of plastic response

Here we will focus on how the system's functional fatigue responds when plastic deformation

is introduced, as previously we have observed that elastic strain does not change drastically

with the addition of plastic strain. It involves performing a pre-deformed pseudoelastic cycle

using load control mode and a deformed cycle using displacement control mode to reach the

desired strain. The experimental procedure is displayed in Fig. 3.16a, where the sample is

subjected to a 2% plastic strain. After introducing the deformation, the system is subjected to

cyclic loading for 105 cycles using the same parameters as in Section 3.2.6. As expected, the

change in elastic strain response with the addition of 2.2% plastic deformation is minimal (less

than 5%) compared to its original value, as shown in cycle 1 in Fig. 3.16a. Four microcolumns

were tested with the addition of 2.1%, 2.2%, 2.6%, and 2.7% plastic deformation for 105 cycles.

Figure 3.16b represents the normalized elastic strain behavior for several columns, showing

that the system's response is very robust even after pre-deformation for 105 cycles. The elastic

strain of the system drops from its pre-deformed state to a maximum of 4% for the 2.7%

Fig. 3.16: (a) Pre-deformed cycle (black) with 2.2% plastic deformation cycles (red) and the

first cycle (green) of functional fatigue measurements. (b) Normalized elastic strain plotted

against 105 cycles for four microcolumns with plastic deformation ranging from 2.1% to 2.7%.

The change in relative elastic strain is less than 1% for 105 as observed for the as-prepared

crystal. (Reproduced from (Fareed et al., 2024))

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

deformed microcolumn. After this drop, the elastic strain remains constant throughout the

cyclic loading, similar to columns without pre-deformation for functional fatigue. The change in

elastic strain for 105 cycles changes < 1%, which agrees very well with our as-prepared

functional fatigue experiment. This indicates that the system is capable of long-term cyclic

loading even after introducing 2-3% plastic deformation.

Fig. 3.17: BF-TEM micrographs of the elastically cycled columns after (a-c) 105 and (d-f) 106

cycles. The wavy contrast in the BF-STEM images (a, d) demonstrates that the pre-

martensitic phase persists despite repeated cycles. This is also apparent from the position

of the spots close to 004-type reflections in the SADP obtained from the upper (b, e) and

lower (c, f) regions of the columns. (Adapted from (Fareed et al., 2024))

3.2.8 Microstructure of deformed and fatigued microcrystals

In order to gain further understanding of possible microstructural changes associated with

functional fatigue and deformed microcolumns, a TEM analysis of the 105, 106 cycles, and fully

deformed microcolumns was undertaken. Figure 3.17a demonstrates the cross-sectioned

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

microstructure view of microcrystal in BF-STEM mode, which has gone through a cyclic loading

of 105 cycles. SADP shown in Fig. 3.17b, and c taken from the top and bottom locations of the

column reveals an austenitic phase with an extra low-intensity spot with a microcolumn normal

of [001]. At the current resolution, the column displays no modulated or non-modulated

martensite, and the pre-martensitic structure is visibly similar to the as-prepared microcolumn

without any mechanical history (Fig. 3.9a). A very similar response is also observed for 106

cycles microcrystal with BF-STEM image shown in Fig. 3.17d. The SADPs taken at the bottom

Fig. 3.18: Transmission Electron Microscopy (TEM) images of a crystal post 15% plastic

deformation. The BF-STEM image reveals a slip band passing through the lower section of the

microcrystal. Furthermore, diffraction patterns from both the upper and lower regions of the

column are illustrated in (b, c) respectively. The evaluation of dislocation density as a function

of the distance from the substrate for all microcolumns examined is presented in (d).

(Reproduced from (Fareed et al., 2024))

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

and lower positions of the column also reveal no additional or residual martensite phase as

shown in Fig. 3.17e, and f.

Observing a 15% deformed microcolumn cross-section under TEM presents a different picture.

The microcolumn's deformed microstructure is visible in the bright BF-STEM in Fig. 3.18a.

After deformation, the dislocation network structure underwent a complete change, and

surprisingly, even at this stage of the microcolumn, no residual martensite was present. SADPs

at two different locations reveal an austenitic phase, featuring extra points with a low-intensity

spot normal of [001] as shown in Fig. 3.18b,c. This is typical for microcompression tests which

show a significant alteration in the dislocation structure of microcrystals toward the top surface.

Additionally, slip band development commonly occurs at the end of the crystal, where the most

prominent rotational gradients arise which frequently coincide with localized slip (Maaß and

Uchic, 2012; Maaß et al., 2009).

To accurately measure the change in the arrangement of dislocations caused by repeated

cyclic loading-unloading and plastic deformation, we assess the dislocation density every 0.5

µm distance from the substrate to the top of the microcrystal. Figure 3.18d represents the

summary of all microcrystal density dislocations, where overall the density dislocation

decreases from top to bottom as expected from the thread dislocation, as these are misfit

dislocations and their density decreases away from the interface of film and substrate. In the

microcrystal that has gone through 106, we see a certain increase compared to the as-prepared

microcrystal, which could explain the small drop in elastic strain after 8 * 105 cycles. For 15%

deformed crystal, we observe that dislocations are either displaced from the sample or have

become part of a dense area. When calculating dislocation density, it is not possible at high-

density dislocation points or close to the slip band for a 15% deformed microcrystal. Overall,

the dislocation density decreases as cyclic functional fatigue or deformation is introduced into

the system.

Discussion

3.2.9 Size-affected plastic shear deformation and microscopic slip

Both microcolumns show a large yield strength occurring at 1 GPa for 4 µm, whereas it occurs

at around 1.2–1.3 GPa for a 4.8 µm microcolumn. Both films have the same pre-martensitic

structure at room temperature, with the starting and finishing temperatures for both martensite

(Ms, Mf) and austenite (As, Af) phases being pretty similar to each other, and the mechanical

response of both films under the same stress level is quite different. If we compare the

mechanical behavior, we see that the 4 µm column shows a clear transition at around 200

MPa, but in the case of 5 µm, the transition point is not very clear. Although they have the

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

same structural properties, there appears to be a possible size effect, both mechanically and

in phase transformation. In our previous work (Fareed et al., 2023) we discussed how thickness

can influence stress-induced phase transformation using nanoindentation, which is also a

possible scenario. Conversely, when we conduct the compression testing at a distance from

the martensitic temperature Ms, we demonstrate through the Clausius-Clapeyron equation

that, near Ms, we achieve the same stress levels as those observed in bulk compression. This

tells us that, although the phase transformation occurs at stress following the bulk behavior,

yielding is size-affected. This means we can apply the Clausius-Clapeyron equation for phase

transformation stresses but not for yield strength.

Another important aspect we understand from the TEM investigation is that the dislocation

structure of the microcolumn is completely altered compared to elastic testing when it is

subjected to large plastic deformation. The L21 Heusler structure and associated chemical

ordering result in the formation of antiphase barriers when slip lengths are lower than a

complete translational lattice vector. Dislocation splitting is an energetically advantageous

process. It usually results in the formation of four paired 1/4 〈111〉 partial dislocations, also

known as partial superlattice dislocations, on {110}-planes. These dislocations are separated

by a particular antiphase boundary ribbon. For instance, this has been extensively examined

in Cu2MnAl or DO3-ordered Fe3Si (Green. et al., 1977; Lakso and Marcinkowski, 1969).

Although there are significant stresses for dislocation motion, slip in the microcrystals being

studied happens after the inflection point of the superelastic response. This means that the

martensitic phase deforms during plastic pre-yielding, as seen in Figures 3.13 and 3.16a. Upon

unloading and undergoing phase change back to austenite, slip lines occur on the {110}-

planes.

3.2.10 Loss-free phase transformations at the micron scale

The loading-unloading curve for the cyclic testing microcolumns shows a single-stage

superelastic behavior, with very small damping expected from this material, and has also been

observed in bulk cases (Arndt et al., 2006; Chernenko et al., 2004a; Chernenko et al., 2005;

Martynov and Kokorin, 1992b). Even though the transformation point is unclear, this could be

further explained by the fact that our testing temperature is further away from the martensitic

transformation temperature, and since the presence of dislocations makes it easier for the

system to deform through the transformation into the martensitic phase. The system prefers

this as it requires less energy to overcome the dislocation barrier than much more stress to

transform from austenite to the martensitic structure.

Another way to explain this low hysteresis during cyclic loading is by using the theory of

reversibility of phase transformations (Chakravarty et al., 2004; Cui et al., 2006). This

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

mathematical model explains how the SME is tied to the crystalline symmetry and geometric

compatibilities and how the material with low hysteresis can be achieved using the geometric

compatibility of the martensite and the austenite. Using this model, two conditions should be

satisfied one determinant of the transformation tensor should be one (detU = 1) and the

eigenvalue should also be 1 (λ2 = 1 When a cubic material transforms into an orthorhombic

structure, six possible variants can occur through a face-diagonal stretch. The transformation

stretch tensor becomes U=f (a,b,c), where α=a

ao, β=b

ao, γ=c

ao , and a0 is the lattice

parameters of the cubic austenite and a, b, c are the lattice parameters of the orthorhombic

martensite. To satisfy both conditions, one of the variants U1 out of six for the austenite to

martensite transformation is given below:

U1 = [β 0 0

0α+γ

2α−γ

0α−γ

2α+γ

Using the lattice constants of martensite and austenite, both conditions satisfy and are enlisted

in Table 1. We observe that, generally, Ni-Mn-Ga shows good compatibility, and our studied

material shows the best result using this mathematical model compared to other compositions

and shape memory alloys. Fulfilling these conditions means the system has low hysteresis,

which means the transition from austenite to martensite is very compatible, resulting in small

dissipation work, further leading to longer fatigue life of the system.

3.2.11 Summary

Here, we focus on the functional fatigue and deception behavior of Ni-Mn-Ga Heusler alloys,

which could play an essential role in small-scale actuation applications. For small-scale

testing, microcolumns with a diameter of 2 µm were tested using a compression technique

Table 1: a, b, c, and a0 represent the lattice constants of martensite and austenite.

Both the first and second conditions are calculated using these lattice constants. To

compare Ni-Mn-Ga austenite-martensite compatibility, the data from the literature is

also taken for comparison. (Reproduced from (Fareed et al., 2024))

Det U1

λ2

References

0.618

0.578

0.562

0.578

1.044

1.099

(Kaufmann et al., 2010)

0.616

0.579

0.548

0.581

1.003

1.124

(Ge et al., 2010)

0.609

0.578

0.554

0.582

0.993

1.099

(Thomas et al., 2008)

0.380

0.320

0.286

2.004

1.187

(Chernenko et al., 2004b)

0.614

0.583

0.550

0.583

1.008

1.08

Present work

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

for long-term functional fatigue at room temperature in the austenite phase. We discuss our

findings in light of the microstructural evolution due to cyclic loading and, in comparison, the

material’s bulk behavior. From these results, the following conclusions can be drawn:

▪ The Ni-Mn-Ga system shows long-term switching behavior, even for a million cycles

without functional degradation.

▪ These microcolumns can also switch behavior even with a small amount of plastic

deformation (2–3%) in the system for hundreds of thousands of cycles.

▪ The STEM reveals no evidence of residual martensite at any stage in the system for

pseudoelastic behavior, but the microcolumn deforms plastically by shear formation

when the applied stress is beyond a specific yield limit.

▪ The system's dislocation density decreases compared to the prepared crystal as the

number of cycles increases.

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

3.3 Ni-Mn-Ga free-standing film behavior in Tension

Shape-memory alloys are known to exhibit a remarkable tension-compression asymmetry,

which originates from the fact that the stress-induced martensitic transformation is sensitive to

the direction of the resolved shear stress. This has a pronounced effect on the temperature

regime in which pseudoplasticity occurs, as well as the reversible strain values associated with

pseudoplasticity. As such, it is imperative to determine the small-scale mechanical response

in both deformation modes to understand how this bulk tension-compression asymmetry

manifests itself in changes in the critical dimensions and how dimensionality affects the

magnitude of the transformation strain. As we previously discussed the pseudoelastic

response in compression mode, here we will utilize the commercially available push-to-pull

(P2P) devices to understand how pseudoelasticity responds at the smaller length scale during

tensile testing.

3.3.1 Experimental details

The results presented here were obtained through experiments using the PI 89 in-situ SEM

PicoIndenter ( at the Nanobrucken facility in Berlin). This setup allows for direct observation of

sample displacement under tension. In Fig. 3.19a, we can see that the sample and

PicoIndenter are horizontally aligned, as opposed to the TI-980 Triboindenter, due to geometry

Fig. 3.19: In-situ testing setup: (a) On the left side, we have a Picoindentor with a sample

mounted on a FIB lift-out grid holder. On the right side (b), a flat punch with a diameter of 10

μm is carefully aligned at the center of the P2P Device. (This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

and movement axis differences. After placing the sample, the flat punch is carefully aligned at

the center and top of the P2P device, as shown in Fig. 3.19b. Since the flat punch diameter

and thickness of the actual P2P device are 10 μm, precise calibration is necessary. All the

results presented here were acquired in displacement control mode.

3.3.2 Results and Discussion

Fig 3.20: VSM measurements under a constant magnetic field of µ0H = 0.01 T. The green

line indicates the cooling cycle, whereas the red line indicates the heating cycle. The

austenitic start and finish temperature (As and Af) and martensitic start and finish

temperature are calculated by drawing the tangent lines from the heating and cooling

cycles. (This work)

The thin film was first produced as described elsewhere (Thomas et al., 2008) by DC

Magnetron sputtering to obtain a free-standing sample. Ni-Mn-Ga film was deposited on a

commercially available SOI substrate with a 4 nm-thick SrTiO3 (001) buffer and a 7 μm-thick

Si (001) device layer instead of the MgO (001) substrate. A two-step ion-beam etching

technique was used for a free-standing sample to achieve the best result (Kar et al., 2023b).

Figure 3.20 displays the magnetization curves for a free-standing sample, where green and

red lines indicate the heating and cooling cycles. The austenitic start (As) and finish (Af)

temperatures are 324 K and 343 K, whereas the martensitic start (Ms) and finish (Mf)

temperatures are 333 K and 317 K. Although the sample composition is Ni55Mn19Ga26, and the

same target material is used, it is fully martensite at room temperature. Despite various

attempts to obtain an austenite sample that is stable at room temperature, due to time

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

constraints and operational issues with the sputtering device, we had to proceed with tensile

tests using a martensite sample. The free-standing sample with a stripes-like formation at the

top surface is shown in inset Fig. 3.20. This free-standing sample in a dog bone shape is

mounted on a P2P device.

The sample has a stripes-like structure at the top surface, is much more complex than already

observed in the literature, and cannot be explained using the adaptive martensite concept. The

Fig. 3.21: The cross-section of the free-standing sample shows the unique structure of

the complex and periodic structure of triangle A exhibiting 14M modulation, whereas

rhombus B and C have an NM twinning plane. (This work)

Fig 3.22: (a) The engineering stress-strain behavior of a sample at 600 nm displacement

with 32% engineering strain exhibiting fully recoverable behavior, (b) multi-cycles (5) tests

at ~ 30% strain also remain fully recoverable. (This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

microstructure is under investigation, and a new approach is taken to describe this unique

structure. The cross-section of the sample is shown in Fig. 3.21, which looks like a very

complex but very periodic microstructure. Triangle A exhibits {110} twinning of orthorhombic

14M martensite with the presence of macroscopic, conjugation, and mesoscopic twin

boundaries. In contrast, rhombus B and C contain nano-twinned tetragonal non-modulated

martensite with different {110} twinning planes.

Since we have a martensite phase, we expect a completely different mechanism under

mechanical testing. Instead of phase transformation, we could anticipate the motion of

mesoscopic and conjugation twin boundaries. The results shown here were conducted in-situ

and under displacement control. Figure 3.22a displays the martensitic sample exhibiting

outstanding elastic behavior up to 32% engineering strain, demonstrating full recovery upon

unloading. A linear behavior of stress and strain is observed for 15% strain, then a clear

deviation, which could suggest the motion of mesoscopic and nano-twin boundaries, which are

aligned in the x direction, leading to a de-twinned structure of the sample. The exceptional

ability of the Ni-Mn-Ga free-standing sample to demonstrate reversible strains over 30%

engineering strain is mainly ascribed to the martensitic transformation and the distinctive

microstructure of the material. The martensite phase in Ni-Mn-Ga can experience a substantial

Fig. 3.23: SEM images of the tensile sample before testing and after testing at three different

strain values. Cracks start appearing, as shown for 40% strain, which widens further as

displacement increases. (This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

reorientation of its twin variations when subjected to external stress, which explains the

considerable and reversible stresses seen. This large strain can be associated with one or a

combination of the following mechanisms:

• Twin Boundary Motion: The martensitic phase is composed of many twin variants that

can move and change direction when exposed to mechanical stress. The motion of

twin boundaries enables the material to sustain substantial deformation without

experiencing irreversible plastic deformation.

• Transformation Strain: Significant reversible strains occur due to the stress-induced

martensitic transformation. Under the application of stress, the material undergoes a

transformation from one martensitic variation to another. This transformation results in

a change in shape without any volume change, allowing for significant strain.

• Reversible Transformation: When the applied stress is removed, the twin boundaries

return to their original positions, causing the material to return to its original shape. The

ability to undergo this reversible change is crucial for obtaining significant strains

without causing permanent deformation.

The reversible behavior of the Ni-Mn-Ga films is supported by their microstructure, which is

characterized by finely twinned martensite. Twin boundaries serve as internal planes that have

the ability to smoothly slide past one another, allowing for significant and reversible

deformations.

The measured reversible strains in the context of the tensile testing apparatus utilized (PI 89

in-situ SEM Picoindenter) are considered valid based on the direct assessments of sample

displacement and the consistent stress-strain responses. The experimental arrangement

guarantees meticulous control and quantification of strains, therefore confirming the

substantial reversible strains reported. Utilizing a commercially accessible push-to-pull (P2P)

device for conducting tensile tests at small scales offers accurate information on the

mechanical properties of the films. The experimental setup enables precise measurement of

displacement and stress, assuring that the reported strains are not influenced by the

experimental conditions but are inherent to the material's characteristics. The data analysis is

performed using the Hysitron built-in push-to-pull application, which takes into account the

stiffness of the P2P device and provides true stress-strain data.

The post-test analysis could reveal how the structure changes from macroscopic to nano-twin

boundaries under the tensile test. Apart from the single test, multi-cycles (5 cycles) were also

performed at 30% strain, where we observed a very robust behavior, and the sample remained

fully elastic during these tests.

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

Although the sample exhibits a very large strain, when the strain exceeds 30%, the material

undergoes plastic deformation, indicating permanent changes. Unfortunately, we observed

top-layer cracks start appearing as we went beyond 30% engineering strain. The SEM images

of the sample before and after tests are shown in Fig. 3.23. As can be seen, these cracks

appear on the sample's right and left sides, extending further as we increase the displacement.

However, no cracks appear until 600 nm (30% strain) is observed for both samples, whereas

one sample deformed above 30% engineering strain. There seems to be some layer that starts

deforming above 30% strain, and the results above this strain are different than what we

observed before. Although we tested two samples, both showed very similar results, up to 30%

strain, considering this large strain only associated with the free-standing sample would not be

accurate after observing this layer on the top of the sample.

Energy dispersive X-ray spectroscopy (EDS) was conducted to investigate this top layer at

three points of the sample where cracks appeared during testing. Figure 3.24 depicts the

atomic and weight percentage at various locations on the sample, as marked on the

accompanying SEM image. Point 1 was taken in the cracked region and showed Ni-Mn-Ga

predominantly with a very small amount of carbon (C), platinum (Pt), silicon (Si), and oxygen

Fig. 3.24: (a) EDS measurements at various locations on the sample, as marked on the

accompanying SEM images. Both atomic and weight % charts are shown in (b) and (c).

(This work)

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

(O). On the other hand, points 2 and 3 show low specimen elements (Ni-Mn-Ga), a higher

amount of C, and a few percent of Pt (colored violet-purple), with a fairly consistent ratio

between both points. The low presence of Pt indicates that this layer was not deposited during

the milling and mounting processes. Rather, a large amount of carbon suggests this could be

artifacts from photoresists during the etching process to obtain free-standing samples from a

thin film. Plasma cleaning was used to remove this layer, but since the thickness is quite large,

the layer thickness remains on the sample. Due to the project's time constraints, further testing

of the sample was not possible. We can conclude from the experiment that these materials

remain fully elastic up to 30% strain, as shown by two samples with identical results. However,

with the present state of the sample, it would be challenging to consider these results

completely associated with only Ni-Mn-Ga.

3.3.4 Summary

Ni-Mn-Ga free-standing films exhibit exceptional pseudoelastic behavior up to 30%

engineering strain with complete reversibility. The motion of mesoscopic and nano-twin

boundaries, aligned in the tensile direction, can be associated with this large strain, leading to

a de-twinned structure of the sample. Notably, the emergence of top-layer defects post 30%

strain creates a significant limitation for additional experimentation. EDX analysis concludes

the presence of a large amount of carbon content that contributed to the top layer. Future

investigations necessitate defect-free samples to precisely determine the material's

pseudoelastic response and microstructural evolution under tensile stress.

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

SUMMARY AND OUTLOOK

Conclusions drawn from this thesis’ work are categorized according to the three main

objectives outlined in Section 1.6:

1) Quantifying the confined-volume effects of the austenite-to-martensite phase

transformation

• Incipient phase transformation probed with nanoindentation revealed a significant

constraint effect, where a 0.5 µm Ni-Mn-Ga film reveals the formation of residual non-

modulated martensite, whereas a thicker 2 µm film does transform fully reversibly.

• This difference in transformation behavior is linked to a mechanical instability seen for

the thinner film, where distinct pop-ins characterize the initial loading. Such pop-ins are

present across the full temperature regime from austenite through the co-existing

domain and into the low temperature martensite phase.

• In contrast, the thicker Ni-Mn-Ga film does not exhibit any resolvable mechanical

instabilities that are associated with the mechanically-driven phase transformation. This

difference is attributed to the loading geometry and the substantially lower

transformation stress in the absence of a length-scale and substrate constraint. As

such, the phase transformation is expected to occur smoothly in the thick film geometry

and at very small contract depths and therefore lower shear stresses.

• For the thinner film geometry, pop-ins above the phase transformation temperature are

admitted by a stress-driven austenite-to-martensite phase transformation. In the lower-

temperature martensitic stability domain, pop-ins are linked to twin-variant reorientation

and twin-thickening.

• The shear-stress statistics of the incipient phase transformation arising due to length-

scale constraints in the thinner film follows a Weibull weakest-link model, with a

significantly higher stress scale than expected from bulk experiments. In fact, the critical

transformation stress is substantially higher, ranging from 1.4 – 2.9 GPa, compared to

the bulk scale.

As an outlook for future research, it would be important to gain a deeper understanding of the

size effect and constraint effect, as there are still open questions that need to be addressed.

Here are some of these questions:

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

• What is the critical thickness threshold below which the martensitic transformation

behavior significantly changes in Ni-Mn-Ga films?

• What is the influence of various geometric constraints, such as uniaxial and biaxial

constraints, on the transformation properties of Ni-Mn-Ga thin films?

• How do constraint-induced stresses interact with intrinsic microstructural defects such

as dislocations, grain boundaries, and precipitates?

• How do these interactions affect the nucleation and growth of martensitic variants?

2) Determining mechanisms of functional fatigue during cyclic phase changes

• Focussing on finite volume effects via compressive mechanical testing of focused-ion

beam prepared microcrystals with diameters of ~2 µm, a size effect in the austenite-to-

martensite transformation stress is observed. At this micron-scale, the transformation

stress is about twice as high as at the bulk scale.

• At the same time, the stress-strain area enclosed by the superelastic response is

approximately five times smaller at the micron-scale than at the bulk scale, which

indicates reduced mechanical dissipation during mechanical cycling.

• During superelastic cycling in compression, as-prepared Ni-Mn-Ga microcrystals

reveal at most a 2-3% reduction in the strain-reversibility for cycle numbers up to one

million. This remarkable robustness against functional fatigue remains true even when

the tested crystals have a mechanical deformation history of up to 3% plastic strain.

• Higher levels of plastic prestraining lead to a gradual deterioration of the reversible

superelastic strain magnitude. A simple exponential decay function captures this

behavior well.

• Following both superelastic cyclings up to one million cycles or plastic pre-straining,

scanning-transmission electron microscopy does not resolve any indications of residual

martensite. This is either due to a lack of high-resolution insights, or the slip must in

fact have been admitted by full dislocations, as expected partials lead to chemical

disordering and therefore a loss of the alloys shape-memory capacity.

As an outlook for future research, cyclic loading-unloading reveals that the introduction of

defect structures does not lead to the expected change in functional behavior or functional

properties. It would be interesting to understand the lattice defects in the system that

seemingly do not change the transformation behavior that is unexpected because, in

similar systems in Cu2MnAl or DO3-ordered Fe3Si, detailed dislocation analysis reveals that

these full dislocations split up in the partials, notably four partials leading to two complex

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

stacking fault ribbons. If that is the case, which we would expect in the system, we would

lose all functional behavior because the chemical ordering has been disrupted. This

fundamental question remains unresolved as the results seem to suggest no loss or

alteration in the system's functional ability, despite the clear introduction of deformation.

Furthermore as an outlook we need to understand how dislocations affect the phase

transformation. Dislocations in Ni-Mn-Ga can change the transformation stress required

for the martensitic phase change, thereby lowering the energy barrier and affecting phase

equilibrium. Dislocations may favor martensitic phase nucleation sites. The stress fields

around dislocations can locally enhance martensite nucleation, altering transformation

dynamics and potentially resulting in an uneven distribution of phases within the thin film.

Dislocations interact with other microstructural flaws, such as twin boundaries. These

interactions can disrupt the ordered transformation process, causing non-uniform

nucleation and the development of martensitic variations.

Overall, dislocations influence phase transformation in Ni-Mn-Ga thin films by changing the

stress state, providing nucleation sites, interacting with martensitic variants, and creating

mechanical instability. These effects are mostly due to concentrated stress, pinning effects,

interactions with other microstructural defects, and changes in thermodynamic stability

caused by dislocations. Understanding these impacts is critical for maximizing the

performance and dependability of Ni-Mn-Ga thin films in practical applications.

3) Identifying the critical length scale below which a loss of superelasticity is

observed

• Through the realization of free-standing Ni-Mn-Ga films, a micro-mechanical tensile

test was successfully designed.

• Tested free-standing martensitic Ni-Mn-Ga samples exhibit exceptional pseudoelastic

behavior with up to 30% engineering strain at complete reversibility.

• This large strain is ascribed to the movement of mesoscopic and nano-twin boundaries

present in the martensite and aligned in the tensile direction.

• However, due to contaminating nano-scale surface layers arising either during film

fabrication or during tensile-sample preparation, detailed quantitative testing could not

be carried out meaningfully.

As an outlook for future research, first, it would be important to further carry out these

tensile tests on a free-standing sample, ideally on an austenitic thin film free of any

residuals with a martensitic transformation temperature near room temperature. It would

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

be meaningful to further investigate the microcompression testing not only at the submicron

scale but also in different crystallographic orientations instead of (001). As we have seen,

the SME and SE responses are very dependent on the compression direction. It would

also be crucial to understand if this material can sustain its superelasticity response at the

submicron scale, as this is not the case for NiTi due to high critical stress and changes in

chemical ordering. The superelasticity response at the submicron scale for Ni-Mn-Ga

would also depend on the local stresses for plastic deformation and if we observe any

change in chemical ordering at this scale.

In concert, the three objectives of this thesis demonstrate the high potential that Ni-Mn-Ga has

as a functional actuator material in small-scale design. Whilst device design will need to

consider significantly offset transformation stresses at small length scales or under geometric

constraints, the material’s functional robustness is exceptional and clearly outperforms

traditional shape-memory alloys, as for example Ni-Ti. Having revealed how transformation

stresses may increase, a systematic assessment of free-standing crystals or a systematic

quantification of film thicknesses and in-plane lattice constraints remains to be done. Besides

cyclic superelasticity and functional fatigue of unconstrained finite volumes, these

microstructural and microplastic directions are the most promising emerging out of the present

thesis. The future of Ni-Mn-Ga in NEMS/MEMS applications and with respect to continued

fundamental research on functional fatigue and dissipation is bright.

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

100

LIST OF PUBLICATIONS

1. A. Fareed, J.M. Rosalie, S. Kumar, S. Kar, T. Hickel, S. Fähler, R. Maaß, Constrained

incipient phase transformation in Ni-Mn-Ga films: A small-scale design

challenge, Materials & Design, 233 (2023) 112259.

https://doi.org/10.1016/j.matdes.2023.112259

J.M. Rosalie provided the scanning transmission electron microscopy (STEM) data. S. Kumar

and T. Hickel generated the simulation data using Ab initio calculation. S. Kar and S. Fähler

provided the thin films and vibrating sample magnetometer (VSM) data. A. Fareed performed

nanoindentation, atomic force microscopy, temperature-dependent experiments, statistical

calculations, and STEM data analysis and wrote the manuscript. R. Maaß supervised the

whole work.

2. A. Fareed, J.M. Rosalie, S. Kar, S. Fähler, R. Maaß, Small-scale functional fatigue

of a Ni-Mn-Ga Heusler alloy, Acta Materialia, 274 (2024) 119988.

https://doi.org/10.1016/j.actamat.2024.119988

J.M. Rosalie provided the scanning transmission electron microscopy (STEM) data. S. Kar and

S. Fähler: Provided the thin films and VSM data. A. Fareed performed microcrystal preparation,

compression testing, temperature-dependent experiments, statistical calculations, and STEM

data analysis and wrote the manuscript. R. Maaß supervised the whole work.

Adnan Fareed Small-scale mechanical properties and functional fatigue of Ni-Mn-Ga

101

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