Anomalous Small Angle X-ray Scattering (ASAXS)
analysis of nanocrystals in glass ceramics:
structure and composition
vorgelegt von
Vikram Singh Raghuwanshi
aus Bhopal (Indien)
der Fakultät III-Prozesswissenschaften
der Technischen Universität Berlin
zur Erlangung des akademischen Grades
Doktor der Naturwissenschaften
-Dr. rer. nat.-
genehmigte Dissertation
Promotionsausschuss:
Vorsitzender: Prof. Dr. Walter Reimers
Gutachter: Prof. Dr. John Banhart
Gutachter: Prof. Dr. Klaus Rademann
Gutachter: Prof. Dr. Christian Rüssel
Tag der wissenschaftlichen Aussprache: 31.5.2012
Berlin 2012
D 83
Dedicated to:
All the relations to whom I am connected
I
ABSTRACT
The aim of the present work is a quantitative analysis of nanocrystallites with respect to their
structures and compositions. This analysis will be done for all involved phases (crystalline
and amorphous) of two different nanoglass ceramics by using anomalous small angle X-ray
scattering (ASAXS) as a main method. Properties of glass ceramics depend on size, size
distribution, volume fraction and on the composition of the formed nanocrystals and the
remaining glass matrix.
Glass ceramics that contain nano-scale magnetic crystals showing special magnetic
properties have many future applications. ASAXS investigations on these glass ceramics
containing magnetic nanoparticles show the formation of a MnxFe3-xO4 crystalline phase
during heat treatment. The nanoparticles are surrounded by a thin layer enriched with SiO2.
Furthermore, the ratio of Fe and Mn atoms in the nanosized crystals is determined by
ASAXS. The investigations show that the crystal composition changes from magnetite
(Fe3O4) towards the Jacobsite phase (MnFe2O4) with increasing annealing time. SANS
investigations with polarized neutrons prove the existence of spherical core-shell like
structures. SANS also demonstrates that the nanoparticles are magnetic and the surface near
region is magnetically disturbed. A so called magnetic dead layer is formed. Such a
nanocrystal is surrounded by a nonmagnetic shell region.
Barium fluoride (BaF2) based nanocrystals doped with rare earth elements in silicate
glasses are potential materials for various photonic applications such as optical amplifiers or
fiber lasers. Energy filtering TEM studies imply that in glass ceramic containing nanosized
crystals of BaF2 a shell like region surrounding the crystals exists that is enriched with SiO2.
ASAXS investigations on these samples confirm the formation of such layers enriched with
SiO2. Furthermore, these investigations provide quantitative information about the
composition of the layer and the residual glass matrix and their temperature dependent
composition changes.
In the present work, it will be shown how ASAXS combined with other investigation
methods is able to provide quantitative information on structure and compositions of
nanoparticles in multiphase systems. The two investigated glass ceramics belong to this group
of multiphase systems.
III
ZUSAMMENFASSUNG
Das Ziel der vorliegenden Arbeit ist eine quantitative Analyse von Nanokristallen in Bezug
auf deren Struktur und Zusammensetzung. Diese Analyse wird von allen beteiligten Phasen
(kristallin und amorph) von zwei verschiedenen Nano-Glaskeramiken mit Hilfe der anomalen
Röntgenkleinwinkelstreuung (ASAXS) als wichtigste Methode durchgeführt. Die
Eigenschaften der Glaskeramiken sind von der Größe, der Größenverteilung, der
Volumenverteilung und der Zusammensetzung der gebildeten Nanokristalle sowie der
restlichen Glasmatrix abhängig.
Glaskeramiken, die magnetische Kristalle im Nanometerbereich enthalten, und damit
spezielle magnetische Eigenschaften haben, versprechen viele zukünftige Anwendungen. Die
ASAXS-Untersuchungen dieser Glaskeramiken mit magnetischen Nanopartikeln weisen die
Bildung einer kristallinen Phase (MnxFe3-XO4) bei der Wärmebehandlung nach. Diese
Nanopartikel sind durch eine dünne Schicht die mit SiO2 angereichert ist umgeben. Ferner
wird das Verhältnis von Fe- zu Mn-Atomen in den nanometergroßen Kristallen durch ASAXS
bestimmt. Die Untersuchungen zeigen, dass sich die Kristallstruktur ändert und die
Zusammensetzung sich von Magnetit (Fe3O4) in Richtung der Jacobsite Phase (MnFe2O4) mit
zunehmender Wärmebehandlungszeit ändert. SANS Untersuchungen mit polarisierten
Neutronen weisen nach, dass sich eine Kern-Schale-Struktur gebildet hat, Weiterhin weist
SANS nach, dass die Nanopartikel magnetisch sind sowie deren oberflächennahe Schicht
magnetisch gestört ist, d.h. eine sogenannte dünne magnetische Totschicht wird ausgebildet.
Umgeben ist solch ein Nanokristall von einer nichtmagnetischen Hüllenregion.
Nanokristalle, wie BaF2 in Silikat-Gläsern in Anwesenheit von seltenen Erden, sind
potenzielle Materialien für verschiedene photonische Anwendungen wie optische Verstärker
oder Faserlaser. TEM-Studien mit Energie-Filterung implizieren, dass in einer Glaskeramik,
die nanometergroße Kristalle aus BaF2 enthält, sich eine Region rund um die Kristalle bildet,
die mit SiO2 angereichert ist. ASAXS Untersuchungen an diesen Proben bestätigen die
Bildung einer solchen Schicht, die mit SiO2 angereichert ist. Darüber hinaus bieten diese
Untersuchungen quantitative Informationen über die Zusammensetzung der Hüllen-Schicht
und der Restglasmatrix sowie deren temperaturabhängigen Zusammensetzungsänderungen.
In dieser Arbeit wird gezeigt wie ASAXS in Kombination mit anderen hier verwendeten
Untersuchungsmethoden in der Lage ist, quantitative Informationen über Struktur und
Zusammensetzung von Nanopartikeln in mehrphasigen Systemen zu liefern. Die beiden hier
untersuchten Glaskeramiken gehören zu diesen mehrphasigen Systemen.
V
TABLE OF CONTENTS
Abstract ___________________________________________________________________I
Zusammenfassung __________________________________________________________III
1. Introduction ___________________________________________________________ 1
1.1 Motivation _________________________________________________________ 1
1.2 Objective __________________________________________________________ 3
2. Glass and Ceramics_____________________________________________________ 5
2.1 Introduction to glass-ceramics _________________________________________ 5
2.2 Importance of glass-ceramics __________________________________________ 5
2.3 Properties of glass-ceramics ___________________________________________ 6
2.4 Preparation of inorganic glass __________________________________________ 9
2.5 Thermodynamics of glass ____________________________________________ 11
2.6 Nucleation of glass _________________________________________________ 13
3. Small Angle Scattering _________________________________________________ 17
3.1 Scattering_________________________________________________________ 17
3.2 Small Angle X-ray Scattering (SAXS) __________________________________ 20
3.3 Anomalous Small Angle X-ray Scattering (ASAXS)_______________________ 25
3.4 Energy dependent scattering contrast ___________________________________ 27
3.5 Small Angle Neutron Scattering (SANS) ________________________________ 29
3.6 Polarized Small Angle Neutron Scattering (polarized SANS) ________________ 32
4. Experimental _________________________________________________________ 35
4.1 SAXS and ASAXS at BESSY II_______________________________________ 35
4.1.1 Beamline description______________________________________________ 35
4.1.2 Data reduction/SASREDTOOL _____________________________________ 38
4.2 SANS at ILL ______________________________________________________ 41
4.2.1 Description of the beamline D22 ____________________________________ 41
4.2.2 Data reduction/GRASP ____________________________________________ 42
5. Crystallization of magnetic MnxFe3-xO4 nanocrystals in silicate glasses _________ 43
5.1 Motivation ________________________________________________________ 43
5.2 Glass preparation___________________________________________________ 44
5.3 Sample characterization using electron microscopy and X-ray diffraction ______ 45
5.4 SAXS study of heat treated sample series________________________________ 50
5.5 Investigation of magnetic nanostructure using polarized SANS ______________ 56
Table of contents
VI
5.6 ASAXS study at the absorption edge of Fe and Mn ________________________ 64
5.7 Kinetics of phase formation as studied in situ_____________________________ 70
5.8 Discussion of the formation of magnetic nanoparticles _____________________ 75
6. BaF2 nanocrystals formation in transparent glass ceramics ___________________ 77
6.1 Motivation ________________________________________________________ 77
6.2 Glass preparation___________________________________________________ 78
6.3 Sample Characterization _____________________________________________ 79
6.4 SAXS Results _____________________________________________________ 83
6.5 ASAXS studies ____________________________________________________ 86
6.6 Discussion of the structure model of BaF2_______________________________ 92
7. Summary and Outlook _________________________________________________ 95
Appendix _________________________________________________________________ 97
References ________________________________________________________________ 99
Abbreviations ____________________________________________________________ 107
Publications______________________________________________________________ 109
Acknowledgement _________________________________________________________ 111
Declaration ______________________________________________________________ 113
1
1. Introduction
1.1 Motivation
Glasses play a vital role in the progress of society. They are used in various fields of daily life
and play an important role for the industry. Applications of glasses are very wide and
different. Therefore, different glasses have to fulfil a variety of different properties. As an
example, window glasses should be transparent and thermal isolating. Glass is defined as an
amorphous solid lacking of long range periodic atomic structure. A glass has a region of glass
transformation behaviour and gradually softens to a molten state on heating [1]. The
properties of glasses and glass ceramics are determined by their chemical composition and
also by nanophases that could be formed. The development of such nanosized heterogeneities
is influenced by the tendency of glasses to undergo a crystallization or segregation process.
Such processes can often be influenced by definite temperature treatments. The phase
separated glasses will be named as glass ceramics if at least the separated phase is crystalline.
Nanoglass ceramics can have superior properties such as high mechanical strength and impact
resistance but they can have also outstanding functionality. In particular, so called
ultratransparent glass-ceramics containing metal fluoride nanocrystals sized between 5 and
100nm possess a huge application potential since rare-earth-doped metal fluoride nanocrystals
feature significantly enhanced optical fluorescence, luminescence and upconversion [2-6].
Nanoglass ceramics containing nanosized magnetite or bariumhexaferrite crystals feature
interesting magnetic properties because the crystals are well dispersed in the glass matrix and
the magnetism (superparamagnetic or ferrimagnetic) depends on their sizes and on the
application temperature.
Nowadays, strong research efforts are going on to develop new glass ceramics featuring
new properties. Therefore methods to investigate such nanostructures are necessary. The
electron microscopy method is an often used direct method that gives local pictures out of
small volumes. Moreover, small angle scattering methods (SAS) allow analysing particle
sizes, size distributions and volume fractions. This method is a non-destructive integral
averaging analytical method that gives averaged structural parameters out of the whole
sample volume the beam penetrates. Therefore the method gives structural parameters with a
high statistical significance because the method averages usually over more than 1014
nanosized objects.
1. Introduction
2
The properties of nanostructured materials are depending on the chemical composition of
the components and not only on their size shape and distribution. The compositions of
nanophases can be determined with local non-destructive methods like energy dispersive X-
ray spectroscopy (EDX) or with energy filtering TEM. An advantage of these methods is that
the data evaluation and interpretation is relative fast and easy. But it can happen in case of
nanosized objects that the signal contains in parts the environment so that the composition
analyses are often cannot be quantitative.
The only method that allows obtaining an integral averaged composition analysis of
nanosized structures is the anomalous small angle X-ray scattering (ASAXS) method. The
method employs the anomalous dispersions of the atomic scattering amplitude near the
absorption edge of an element containing in the sample. This anomalous dispersion effect
results in a definite variation of the scattering contrasts and allows analysing composition
fluctuations between nanosized structures.
Small angle neutron scattering with polarized neutrons (SANS) is an outstanding method
that allows characterizing and distinguishing magnetic nanostructures from nonmagnetic
structures [7, 8]. SANS with polarized neutrons is a method of choice if the nanostructure of
magnetic nanoparticles have to be analysed. Their composition analysis requires the
application of ASAXS.
In the frame of this work the structure and chemical composition of two glass ceramics
will be analysed quantitatively. First a nanosized magnetic phase containing glass ceramics
will be investigated. It is known up to now by using microscopic methods (SEM, TEM) and
by diffraction (XRD) that the particles are spherical in shape and they contain of a mixed
phase of Iron and Manganese oxides [9]. It is up to now not clarified, which are the ratio of Fe
and Mn in the magnetic crystal. Will be this Fe to Mn ratio changes during the growth
process? Furthermore, it is not clear whether a shell like region will be formed surrounding
the particle or not?
Second a transparent silicate glass ceramic system containing the BaF2 nanoparticle is
chosen [10]. This transparent glass ceramic is usable for photonic application. It was observed
that the nanocrystal growth inhibited by a mechanism that could not explained by the known
theories of growth and ripening [11]. Energy filtering TEM investigations revealed a SiO2
enriched shell is formed that surrounds the particles and acts as barrier for further crystal
growth [12]. It is not quantitative known how the shell is composed and also the size
distribution of the formed BaF2 crystals has to be investigated.
1. Introduction
3
1.2 Objective
In the frame of this work the structural parameters (shape, size and volume fraction) of the
nanoparticles and its compositions of two different glass ceramics should be determined
quantitatively by anomalous small angle X-ray scattering.
Firstly, magnetic nanoparticles embedded in a glass ceramic of composition 13.6Na2O-
62.9SiO2-8.5MnO-15.0Fe2O3-x and secondly, a BaF2 nanoparticle containing transparent glass
ceramic of composition 69.6SiO2-15.0K2O-7.5Al2O3-1.9Na2O-4BaF2-2BaO have been chosen
for this purpose. In both glass ceramics, the formation of nanocrystals will take place during
annealing.
The main objective in case of the magnetic glass ceramic is to clarify, whether a core
shell like structure is formed. ASAXS combined with SANS (polarized neutrons) can help to
decide the structural model and to determine the structure of magnetic nanoparticles. The
objective also includes obtaining quantitatively the composition of other existing amorphous
phases (shell regions) and the residual glass matrix. In case of the BaF2 crystal forming glass
ceramic the growth stop and its structural reason will be studied by ASAXS. The common
aim in both materials is to analyze the nanostructures in multiphase systems.
5
2. Glass and Ceramics
2.1 Introduction to glass-ceramics
Glass-ceramics have a huge contribution in the growth of civilization, because of its
properties like transparency, lustre (or shine), and durability [1]. They are hard, brittle, and
stand up against the environment conditions such as effects of wind, rain or sun. Glass and
ceramics are widely used for making household utensils and also having other industrial
applications. The origin of the word glass is the Latin term glasum used to refer to a lustrous
and transparent or translucent body. Glassy substances are also called vitreous, originating
from the word vitrum, again denoting a clear, transparent body. Glass is known to be a non-
crystalline material, has no long-range order of positioning of its molecules and they exhibits
glass transition when heated towards the liquid state [13-16]. Glass-ceramics are materials
formed by crystallization of base glass. Glass does not have a sharp melting point like a
crystal and they soften and flow at higher temperatures. Any material, like inorganic, organic
or metallic formed by any technique and which exhibits glass transformation behaviour is
termed as a glass.
2.2 Importance of glass-ceramics
Most of the glass-ceramics are hard, chemically inert, transparent, refractory and poor
conductors of heat and electricity, which makes them suitable for many applications [17,18].
Nowadays, glass-ceramics can be tailored to meet an exact need of applications. Machinery
has been developed for precise, continuous manufacture of glass sheet, tubing, containers, and
a host of other products [13]. Glass and ceramics are used in beverage containers, window
panes, automobile, windshields, pipelines, cookware, building blocks, heat insulation,
telephone poles, electronic devices, and the nose cones of spacecraft [19,20]. The major
disadvantage of glass-ceramics is there brittle nature, which acquire tiny cracks and results in
breakage of materials. Glass-ceramics materials such as barium ferrite or nickel zinc ferrites
are used in manufacturing stronger magnetic field magnets, which are less weighted and cost
efficient. Some glass-ceramics such as lanthanum zirconate titanate have electro-optic
properties, which mean variation in transmitting light by applying variable voltages, which is
useful for memory-storage devices [17,18].
2. Glass and Ceramics
6
In the 1970's, optical fibers were developed for use as "light pipes" in laser
communication systems [21]. These pipes maintain the brightness and intensity of light being
transmitted over long distances. Glass fibers are the extremely fine fibers, which are made up
of glass materials. The glass fibers are so small (typically diameter 100µm) that more of them
fit into a cable of a given sizes. The glass fibers are not susceptible to electromagnetic
interference, so the signal is clearer [16,22]. Finally, the information carried on optical fibers
can be modulated at very high frequencies, so many more simultaneous transmissions, e.g.
telephone conversations are possible. Communication by light rather than electricity required
the development of suitable light sources as well as extremely pure, ultra transparent glass
fibers.
Glass-ceramics also have importance in field of medicine, e.g. used in fabricating
artificial bones and crowns for the damaged teeth and many other medical applications [23-
26]. Glass-ceramics of certain kinds are also used as materials for storing radioactive wastes
for long times [27].
2.3 Properties of glass-ceramics
Applications of glass-ceramics in different fields, depends on various properties of glasses
such as mechanical, chemical, optical, thermal, electrical and magnetic properties. The
properties of glass-ceramics can be tailored by modifying the compositions and fabrication
techniques. Some of the important properties of glass-ceramics are discussed below.
Mechanical Properties
In glass-ceramics, the atomic arrangements are more or less random. Hence, the physical
properties of glass-ceramics are, in general, isotropic like those of liquids. Like glass and
ceramics, glass-ceramics are brittle materials that exhibit elastic behaviour up to the strain that
causes fracture [28]. Due to the formations of crystalline microstructures in glass-ceramics,
they have higher strength, toughness, abrasion and elasticity. Plastic deformation may occur at
extremely high-point loading and involves a considerable amount of bond bending rather than
the large-scale dislocation motion or grain boundary sliding.
Viscosity
Viscosity is a property of the liquid state, which describe its flow due to externally applied
stresses. Viscosity is the reciprocal of fluidity and it is inversely proportional to the
2. Glass and Ceramics
7
temperature. Viscosity of glass-ceramics increases with network connectivity. Dependence of
the viscosity on temperature plays an important role in determining, how easily a product is
formed for any melt. When the viscosity is high at the melting temperature of crystalline
phase and increases rapidly with decreasing temperature, in both cases glasses are formed
easily. Determination of viscosity helps in forming bubble-free, homogenous, stress free
glass-ceramic used to form commercial applications.
Thermal properties
Many commercial glass-ceramics have importance due to their thermal properties such as low
thermal expansion coupled with high thermal stability and thermal shock resistance. When
heat is given to a body, thermal expansion shows the relative change in a given dimensions of
body. Thermal expansion is important in determining the suitability of using a variety of
materials particularly involving a glass-ceramic in a restrained condition. When glass-ceramic
components are suddenly goes to a rapid temperature change, due to there low thermal
conductivity tensile stress leads to glass fracture. The resistance to sudden temperature change
is called thermal shock resistance or thermal endurance. This property is determined
primarily by the thermal expansion coefficient and the thickness dimension of the product in
the direction of the heat flow. The expansion and the contraction due to thermal energy is an
important consideration for product design [29,31].
Electrical Properties
Electrical properties of glass-ceramics are important for their applications in electrical and
electronic industries. A substance is electrically conducting when free electrons or ions within
it flow on applying electrical potential. Since the ionic motion is the dominant diffusion
phenomenon in glass-ceramics, ions are responsible for the charge carriers. Electronic
conduction is possible in the glass-ceramics, which contain transition metals such as Fe, Mn
and V displaying multivalency. Electronic conduction is predominant in elemental glasses,
such as silicon, germanium, and the chalcogenides, where it is responsible for the
semiconductor properties, and suitable for the modern electronic industries [32,33]. In
general, glass-ceramics have such a high resistivity that they are used as insulators. The
dielectric properties of glass-ceramics are depending on the nature of crystal phase and on the
amount and composition of the residual glass [28]. The homogeneous, grained character of
glass-ceramics leads high dielectric breakthrough strengths, and can be used as high voltage
insulators or condensers.
2. Glass and Ceramics
8
Chemical Properties
The chemical durability of glass-ceramics is depending on the crystals and the residual glass.
Due the chemical durability glass-ceramics are preferred materials in variety of applications
such as window glasses, in chemical laboratory etc. In spite of this, acids and alkali solution
attack glass in different way. Hydrofluoric acid affects any type of silicate glass, while other
acids attack only slightly. Water corrosion acts at slower rate in normal environment but at
high temperatures, water corrosion can be significant. Glass-ceramics having low alkali
residual glasses, such as b-quartz and b-spodumene, have excellent chemical durability and
corrosion resistance [28].
Magnetic Properties
There are wide ranges of magnetic glass-ceramic materials which exhibit ferromagnetism,
ferrimagnetism or superparamagnetism behaviour. Glass-ceramic magnets are usually
composed by transition metals doping, they have applications in making inductors, speaker
magnets, magnetic resonance imaging (MRI) etc. Ferrite is generally a used term for the
whole range of such magnetic materials. Many glass-ceramics compounds containing
transition metals are crystallize in spinel structure or inverse spinel structure, which are
associated with the magnetic behavior [34].
Optical Properties
Nowadays, optical properties of glass-ceramic are of interest in field of science and in the
industrial applications. The properties of glass-ceramic include refraction, reflection and
transmission of light and also the dependency of the wavelength to those properties.
Transparency (or absorption as its inverse) is one of the most important properties of glass for
its application. When light passes through the glass-ceramic (wide band gap) insulator, the
energy of light is not sufficient to excite the electronic energy states and not being absorbed
by them. Transparency of material depends on the crystal size, size distribution, refractive
index between crystals and glass matrix. Excellent transparency can be achieved, when the
size of the crystals are not of the order of the wavelength of the light. Dispersion characterizes
how the refractive index of a particular glass varies with wavelength. This is clearly an
important specification for optical glasses. When the wavelength of light is absorbs and
creates an electronic transition in the visible spectrum range in the electronic states, due to
which the glass appeared colored.
2. Glass and Ceramics
9
2.4 Preparation of inorganic glass
Inorganic glasses are the materials which are formed by fusion of inorganic compounds such
as silicates, potassium, sodium, calcium and other inorganic oxides. Manufacturing of
inorganic glass requires three major components; Network former, Intermediates and
Modifiers.
The major component in formation of any glass is the network former which serves as a
primary source for the glass structure. These components are generally termed as glass
formers, or glass forming oxides in many oxide glasses. Mainly, the network formers such as
Si, Ge have an ability to form a highly cross-linked network of chemical bonds. The network
former serves as the basis for the generic name used for the glass. For example in the glass
where the network former is silica is called as silicate glass, when boric oxide and silica are
acts a network former then glasses are termed as borosilicate glasses. The major glass former
are silica (SiO4), boric oxide (B2O3) and phosphoric oxide (P2O5) [1]. Intermediates are those
materials used in formation of glass which acts as both network formers and modifiers. For
example titanium, aluminium, zirconium, beryllium, magnesium, zinc etc are generally used
as an intermediate. Some compounds such as alumina, which acts a network former in
aluminates glasses and also it acts as a property modifiers in many silicate glasses [1].
Adding certain materials during glass formation which alter the network structure or the
properties of glasses are termed as glass modifiers or property modifiers. There are
compounds that have tendency to donate anions to the network, and the cations occupy
“holes” in the disordered structure. These conditions cause the formation of nonbridging
anions, or anions that are connected to only one network-forming cation [32]. Modifiers
generally have cations with low charge-to-radius ratios (Z/r), for example alkali or alkaline-
earth ions. Colorants and fining agents are used to control the color of the final glass and to
promote the removal of bubbles from the melt.
According to Zachariasen, [18] glass is a substance which can form extended three
dimensional networks lacking periodicity with an energy content comparable with that of the
corresponding crystal network. From these conditions, Zachariasen suggested four rules for
selecting the oxides AmOn, that tend to from glasses. The rules are follows as:
1. The oxygen is linked to no more than two atoms of A.
2. Coordination of the oxygen about A is small: 3 or 4.
3. Oxygen polyhedra share corners, and not edges or faces.
4. At least three corners are shared.
2. Glass and Ceramics
10
The main rule in formation of glasses is a distribution of M–A–M angles, where M is a
cation and A is an anion. Silicates are one of the most important constituents of glasses. Rigid
silicon oxygen tetrahedron structure is the main building blocks for both amorphous and
crystalline phase of silicates in glass-ceramics, where Si and O both are present in the three
dimensional tetrahedral network. Both crystalline and vitreous SiO2 are shown in Figure 2.1
[18,36] where Si is tetrahedraly bonded to oxygen, the fourth oxygen being out of the plane of
paper. Whereas the local oxygen coordination is almost the same as that in a corresponding
crystalline solid, the intermediate range order described by ring structures clearly differs
considerably between the crystalline and the glassy forms. The glass network consists of holes
that are larger than those in the crystal. Direct evidence of such kind of network of a thin
silicate glass is reported [37]. The structure of amorphous silica is quite uniform at atomic
distances, although there is no order beyond several layers of tetrahedral.
In silica glasses containing alkali and alkaline earth oxides, these cations apparently are not
randomly distributed throughout the glass; their average separation is less than from a
uniform distribution. It is possible that alkali ions form in sheets, as in certain crystalline
alkali silicates.
Figure 2.1: (a) Crystalline state of SiO2 (b) Amorphous state of SiO2 [18].
The network can be partially broken by other oxides like alkali and alkaline earth oxides,
termed as network modifiers. When a compound such as Na2O is introduced in silica, the
2. Glass and Ceramics
11
arrangement of atoms in a two-dimensional plane is shown in Figure 2.2. Those oxygen,
which connect two silicon tetrahedra at corners, are called bridging oxygens (BOs). Some
oxygen atoms are linked to only one silicon atom; which are called the nonbridging oxygen
(NBOs). Since oxygen is a bivalent ion, its connection to only one silicon ion leaves one
negative charge, which is satisfied by a univalent positive sodium ion in the interstitial spaces.
Figure 2.2: Na2O is introduced in silica, the arrangement of atoms in a two-dimensional
plane. The big gray filled circles are the Na atoms and the small black circles are the Si
atoms and the white circles are the oxygen atoms [18].
2.5 Thermodynamics of glass
Numerous investigations have been done to understand the basic thermodynamics and
kinetics of formation of glasses [38-40]. The thermodynamics of glass transformation
behavior can be understood on the basis of changing the volume with respect to temperature.
Figure 2.3 shows the curve for the change in the volume of a material with temperature.
In the Figure 2.3, point a is the small volume of a liquid at the temperature well above
the melting temperature of that substance. Atoms were arranged differently as the substance is
cooled differently below the melting temperature. When the substance is cooled below point a
then the volume shrinks along the line ab. The temperature at point b is the thermodynamic
melting point of crystals of same composition, slightly below this point there is high
probability of long range periodic arrangements of atoms to form crystalline structures.
Crystallization is possible only when there is a sufficient nucleation rate followed by
significant crystal growth.
2. Glass and Ceramics
12
Figure 2.3: The volume-temperature diagram [34].
Figure 2.4: Schematic of nucleation and crystal growth rates as a function of temperature.
Figure 2.4 shows the dependency of nucleation rate and crystal growth with temperature.
The shaded area in Figure 2.4 reveals the temperature range for the crystallization, which
resembles with the shaded line in Figure 2.3. Point c has the highest probability of crystal
formations. In this range of b-c the volume of the substance drop discontinuously without any
2. Glass and Ceramics
13
change in temperature is called as thermodynamically first order transition. For further
decrease of temperature, the volume decreases as followed by the slope d-e. In Figure 2.4,
when there is no overlap in nucleation rate with the crystal growth, then the volume of a
substance decreases by following the supercooled state and remain liquid below its melting
point because there are no nucleation sites to initiate the crystallization.
Further cooling leads to increase in viscosity of the substance. Below super cooled state
the volume decreases exponentially by following the slope c-g or c-h depending on the
cooling rate. In this range the substance now appears as a solid. In this region the molecules
have a disordered arrangement, but sufficient cohesion to maintain some rigidity. In this state
it is often called an amorphous solid or glass. There is a beginning of the glassy state below
the supercooled state. Volume is higher for the faster cooling and lower for the slow cooling
as shown in Figure 2.3.The transition between the supercooled and glassy state do not occur
rather at sharp temperature, but smoothly over a temperature range. Such type of continuous
transition is like a thermodynamic second order transition. This range of temperature is called
the glass transformation range. The glass transition temperature Tgin the transformation range
at the intersection of the glass line with a tangent to the steepest portion of the transition
curve. However, Tg is a useful indicator of the approximate temperature where the super
cooled liquid converts to a solid on cooling or conversely, of which the solid begins to behave
as a viscoelastic solid on heating. Thus, the glass transition range is characterized as the
region of temperatures where the structure of the mass is continuously relaxing to greater
equilibrium. The temperature Tf between the supercooled liquid and glass state is called as
fictive temperature. This temperature may be assumed as a point where the liquid is instantly
frozen into the solid glass. This approximity says that the structure of liquid relaxes rapidly at
first, and with increase of viscosity this relaxation rate slows down with the temperature.
2.6 Nucleation of glass
In glass, crystallization is a process of forming crystalline structures in glass matrix. For
crystallization process, it requires a crystal nucleation followed by the crystal growth as
discussed in section 2.5. Formation of nano or micro size crystalline phases in glass ceramics
may change drastically the properties of materials. Therefore in glass ceramics, many
properties can be optimizing by choosing base glass with suitable compositions and by
controlling crystal nucleation and growth process [41].
2. Glass and Ceramics
14
Formation of crystals in glasses primarily requires the formation of tiny nucleus or
embryo of the new phase which is termed as nucleation process and the specific temperature
at which the crystal nuclei are form is called as crystal nucleation temperature. Nucleation is
the important factor for controlling crystallization in glass ceramics. When the glass is held at
its crystal nucleation temperature, multiple crystal seeds are formed and starts to grow slowly.
For the better quality of material, requires crystals of small sizes and its uniform distribution
in the glass matrix. Classical nucleation theory can describe the nucleation and crystallization
in glass ceramics [42-44]. According to the classical theory, the difference between the free
energy of the crystal and the remaining glass G'acts as a driving force for the
transformation of glass to a crystal via nucleation and growth process. During the process of
nucleation and growth an interface between crystal and glass matrix and the energy associated
with the interface is termed as a surface free energy. As the crystal grows, the total surface
free energy increases. During the homogenous nucleation process the energy minimization
involves two terms: Volume transition and Surface formation.
The volume transition term for a spherical shape nucleation of radius r is given as:
vol
GrG ' ' 3
1
3
4
S (2.1)
where vol
G' is the change in free energy per unit volume. 1
G' is a negative term, which
provides a driving force for nucleation. The surface formation energy is given by:
JS
2
4rGsurf ' (2.2)
where the surface energy per unit area. The change in surface energy is always positive
when forming surfaces. So the total change in the energy is the sum of volume and surface
free energy term and given as:
JSS 23 4
3
4rGrG vol ' ' (2.3)
The variation of the above equation with the radius of the spherical particle is shown in
Figure 2.5. In the Figure, the different energy contribution yields an increase in the total free
energy up to a certain radius called as rc is the critical radius for the nuclei and after that, the
total free energy starts to decrease. The variation of total energy upto the critical radius is due
to decrease of surface to volume ratio with increasing radius. After reaching the critical
radius, the negative volume free energy dominates the positive surface free energy and the
total free energy starts to decrease.
2. Glass and Ceramics
15
Figure 2.5: Change in Gibbs free energy with radius of particles in nucleation and growth
process.
The value of critical radius can be calculated by taking the derivative of the total free
energy in equation (2.3) as 0
'
dr
Gd at r=r* and this evaluation gives the critical radius
values as:
vol
G
r'
J2
* (2.4)
By putting r* in equation (2.3) it is possible to evaluate the activation energy for
nucleation as:
2
3
*
3
16
vol
act G
G
'
' SJ (2.5)
As the nuclei grow larger, the free energy reaches a maximum and become negative and
leaving stable nuclei. Both nucleation and growth process dependent on viscosity and the free
energy change. At the initial process of nucleation, many small crystallites are form, but
slowly they disappear and remain only the big crystallites due to which the area around the
bigger crystal depleted of the smaller crystallites. The smaller crystallites have higher
solubility than the bigger crystallites, as results larger crystallites are more energetically
favorable than the smaller crystallites. This process is terms as Ostwald ripening. In this
process, the small crystallites are kinetically favored because they nucleate easily and the
larger crystals are thermodynamically favored.
17
3 Small Angle Scattering
3.1 Scattering
Scattering is a phenomenon that occurs when the trajectory of moving object or radiation
(light, sound) deviates from a straight line due to interaction with some other objects. In
science scattering theory is the study of the scattering of waves and particles. In any technique
that uses radiation, scattering and absorption are the first processes that take place while
interacting with matter. In microscopic techniques, a small part of the sample is illuminated
by electromagnetic radiation or particles beam, which interacts with the sample and the
consequent collection of scattered photons or particles and its phase relation are used to create
an image. In other scattering techniques such as XRD, SAXS, SANS etc. a whole illuminated
sample volume is investigated. Neutron and synchrotron X-rays has their wavelengths in
angstroms scale, which makes them a suitable tool for structure analysis, especially on
different length scales from the atomic scale to micron scale. Also due to the neutrality of
neutrons and the high energy of synchrotron X-rays, they can transmit through bulky
materials, enables to investigate the properties of the system as a bulk.
When an electromagnetic wave interacts with a matter, then depending on the energy of
wave, matter composition and thickness of the material, a fraction of photons will transmitted,
absorbed, scattered or transformed in other form of energies. Let us consider an
electromagnetic wave of intensity I0 is incident on the sample of thickness t, density ρ and the
linear absorption coefficient which combines with the density and makes mass absorption
coefficient (/ρ). Depending on the energy and material the values of mass absorption is
tabulated [45] and I is the resultant intensity of the wave after attenuation of incident wave I0.
Figure 3.1 shows the schematic profile of the propagation of electromagnetic wave through
matter. The formula that described the above attenuation of X-rays is defined as:
d
eII P
0 (3.1)
The number of photons transmitted through the matter depends on the thickness, density
and atomic number of the material and the energy of the individual photons. From the above
equation (3.1) transmission (T) or absorption (A) can be calculated, which is defined as a ratio
of transmitted wave over the incident wave as:
0
1
I
I
Absorption
onTransmissi (3.2)
3. Small Angle Scattering
18
Figure 3.1: Attenuation interaction of electromagnetic wave with matter.
Cross section is defined as an effective area for collision of photons with the matter. This
can also be defined as; it measures the effectiveness of the interaction between the incident
particle or wave with the target matter. A cross section depends on the type of the particles
and energy of the incoming beam. The amount of scattering from a medium is determined by
the product of the scattering cross sections and the number of scattering sites. Figure 3.2
shows the schematic of scattering of a wave with matter at a solid angle in three
dimensional spaces where the detector is located. The wave generated from the source
incident on the sample and after interacting with the sample scattered in all direction and
collected at the detector.
Figure 3.2: Scattering of wave by a medium.
3. Small Angle Scattering
19
The wave function for the incident electromagnetic or neutron wave as a plane wave is
defined as:
rki
inc eI 0
&
(3.3)
here O
S2
0 k is the momentum vector of the incident wave. After the interaction of the wave
with the sample, the wave scattered in all directions and the wave function for the scattered
wave is given by:
rki
scat AeI
&
(3.4)
where A is the scattering amplitude of the scattered outgoing wave. Since the electromagnetic
waves scattered by the electrons distributed in an atom, the scattering amplitude not only
depend on the distribution of electrons r
U
, but also on the scattering angle and wavelength
of the incident wave. The scattering amplitude for scattered wave is given by:
rderqA rqi
&
&
&
&
³
.
U (3.5)
where 0
kkq
&
&
&
is the momentum transfer vector. The scattering amplitude is proportional
to the differential scattering cross section of the scattered wave. The total scattered intensity
of the wave is evaluated from the differential scattering cross section, which is defined as a
number of particles which are scattered into a solid angle d per second divided by the
incident flux. The differential scattering cross section is given by:
2
.qA
dI
C
d
d
flux
&
:
:
V (3.6)
where Iflux is the incident flux, C is the count rate of the scattered flux and d is the solid
angle for the scattered wave at the detector. The above equation (3.6) reveals the probability
of finding a scattered particles or wave within a given solid angle. The total scattering cross
section which is proportional to the total scattered intensity is evaluated by the integral cross
section over the whole sphere of observation. The total scattering cross section is given by:
ITT
V
V
SS
dd
d
dsin
2
00
³³ :
(3.7)
Basically scattering cross sections are measured during the experiments. The total
scattering is the integral over all angles of the differential cross section.
3. Small Angle Scattering
20
3.2 Small Angle X-ray Scattering (SAXS)
Small angle scattering (SAS) techniques, including small angle X-ray scattering (SAXS) and
small angle neutron scattering (SANS), are capable to give information on the structural
features of particles of colloidal size as well as their spatial correlation. Both SAXS and
SANS are powerful techniques for determining size, shape and internal structure of particles
in the size range from few nanometers up to about hundred nanometers [46,47]. SAXS is an
elastic scattering of X-rays from the electrons in atoms and therefore it is sensitive to electron
density fluctuations in samples, whereas SANS is an elastic scattering of neutrons at the
atomic cores and sensitive to scattering length density differences.
Generally, when two or more parallel incoming waves as described by equation (3.3)
interact with the sample then the scattered waves of variable intensities are emitted in all
direction [48]. The scattered waves are spherically symmetric spherical waves. Figure 3.3
shows the schematic of interaction of the incident wave with two scattering centre 1 and 2
which are at r distance apart from each other. Due to different distance of the two volumes
from the wave front, the scattered momentum wave vector k undergoes different phase shift.
Figure 3.3: Scattering from nanoparticles.
The incident and scattered wave vector are described by 0
k
&
and k
&
, respectively. The
resultant intensity is the superposition of waves of different amplitudes and phases. The
intensity also depends on the scattering angle 2 and the momentum transfer
3. Small Angle Scattering
21
vector 0
kkq
&
&
&
. For the elastic scattering the scattering wave has the same energy as the
incident energy, therefore |k|=|k0| is valid for the elastic scattering.
In small angle scattering experiments one measures the spatial correlations in the
scattering density, averaged over the time scale of the measurement. The differential
scattering cross section q
d
d
:
V from a number distribution of scatters per unit volume N(r)
can be calculated by the following expression:
drrqSErqFrVrNq
d
d
p
³
f
'
:0
2
2
,,, K
V (3.8)
where matrixparticle
EKKK ' is the averaged electron density fluctuation between the
particle and remaining matrix. Vp(r) is the volume of the particle. Also q is momentum
transferred, which is related with the scattering angle 2θ and the wavelength of X-rays as:
O
T
S
sin4
qq
& (3.9)
The small angle scattering measurements are sensitive to the inhomogeneties of the
electron density of different nanosized phases in the sample, termed as contrast. The visibility
of detecting the particle in SAS measurement increases with enhancing the electron density
difference between the different phases in the sample. The electron density is evaluated by the
product of atom number density and the number of electrons of each atom is given by:
¦
¦
i
ii
i
ii
AMc
Zc
NUK (3.10)
where NA is the Avagodaro number, ρ is the mass density of the total phase and Z is the
atomic number of the i elements. ci is the atomic concentration and Mi is the atomic mass of
the particular element i present in the phase.
In equation (3.8), F (q,r,(E)) is the form factor which accounts for the shape and size
of particles. The form factor is the important factor while fitting the experimental data with
the theoretically assumed model except in the structural biology where the shape of the
particles is often the target of the study. For a homogenous sphere with the radius r, the form
factor is defined as [49,50]:
3
cossin
3,,
qr
qrqrqr
EErqF
' ' KK (3.11)
3. Small Angle Scattering
22
It depends on the scattering vector q, the radius of the particle r and the electron density
difference between the particles and remaining matrix represented by .
Figure 3.4: Sketch of an electron density profile of spherical model where the electron
density p of particle is larger than that of the matrix m.
The electron density difference profile with respect to the remaining matrix for a
spherical shape particle is shown in Figure 3.4. In equation (3.8) N(r) is the particle
distribution function which is used during the simulations of SAXS scattering curves. In our
investigations we have chosen two kinds of distribution functions, lognormal and Gauss
distribution. The lognormal distribution for particles is given as:
»
»
»
»
¼
º
«
«
«
«
¬
ª¸
¹
·
¨
©
§
2
2
22
ln
exp
2
1
V
P
VS
r
r
rN (3.12)
where r > 0.
22
2
exp)exp(1
2
exp
VVPV
V
PP
!
¸
¸
¹
·
¨
¨
©
§
!
The Gauss distribution of particles is given as:
»
¼
º
«
¬
ª
2
2
22
exp
2
1
V
P
SV
r
rN (3.13)
where is the mean and is the standard deviation of the particles.
3. Small Angle Scattering
23
In dense particular systems it is necessary to account for interparticle interaction
(structure factor). Such interactions will be calculated within approximations. Mainly, the
local monodisperse approximation and the decoupling approximation are used for dense
particulate system [51,52]. Complete randomness of size and position of particles is assumed
in decoupling approximation, while in local monodisperse approximation a particle of certain
size is surrounded by particles with the same size. The structure assuming a hard sphere
potential is given as [53,54]:
qR
qRfG
f
fRqS
HS
HSp
p
pHS
2
)2,(
241
1
,,
(3.14)
where
5
324
3
2
2
6sin6cos634cos
2cos2sin2cossin
,
A
AAAAAAA
A
AAAA
A
AAA
AqG
J
ED
4
2
1
21
p
p
f
f
D;
4
2
1
2
1
6
p
p
pf
f
f
¸
¹
·
¨
©
§
E;
2
D
Jp
f
A constant scattering background coming from fluorescence and resonant Raman
scattering is also added to equation (3.8).
Subtracting the form factor of the inner sphere from the outer sphere provides the case of
spherical core shell form factor.
P
K
Q
K
P
K
'
'
'
1,,,,,,, ErqFErqFErqF (3.15)
where is the electron density difference between shell and matrix and U is the
electron density difference between core and matrix. The total radius of the particles is
defined by r and the radius of the core rc =r.
There are different ways of variation of the electron density difference between the core,
shell and the remaining matrix. Figure 3.5 (a) and (b) shows the two main types of variation
of electron density profile for a spherical core shell type particles. In Figure 3.5 (a) a sink like
electron density profile is shown, while a stair like electron density profile in Figure 3.5 (b) is
shown.
3. Small Angle Scattering
24
Figure 3.5: Sketch of two main electron density profiles, shows how the electron density can
vary between core, shell and matrix. (a) Spherical core shell particle with an electron density
of the shell smaller than the matrix and one of the core is larger than that of the matrix. (b)
Spherical core shell particle with electron density of the core shell larger than the matrix.
Figure 3.5 (b) shows the steps like profile where the electron density of the core and shell
are greater than that of the matrix which represents the positive contrast for the core and shell.
While in the Figure 3.5 (a) shows the profile in which the electron density of core is greater
than the matrix, while the electron density of the shell is smaller than the matrix, which gives
a core contrast that is positive and a shell contrast that is negative.
Figure 3.6: Sketch of a small angle scattering setup.
3. Small Angle Scattering
25
Figure 3.6 shows the sketch of a small angle X-ray scattering setup. In the above sketch,
X-ray wave of certain energy interacts with the sample and scatters from the particles. The
scattered wave passes through a vacuum tube (to reduce the air scattering) and hits the
detector. The transmission, calibrating standard and background are measured with the
samples to correct and to calibrate the scattering images. Distance between the sample and
detector can vary in order to achieve the wide q range. A beam stop which is a good absorber
for X-rays is placed in the centre of the detector.
3.3 Anomalous Small Angle X-ray Scattering (ASAXS)
By SAXS investigation at different energies near the absorption edge of an element also
termed as ASAXS, enables to isolate the scattering from that particular element with respect
to rest of the surrounding matrix. ASAXS technique is applied to determine the spatial
distribution of a specific element on a nanometer scale. In ASAXS the anomalous properties
of the scattering amplitude is used. The atomic scattering amplitude f is the ratio of the wave
amplitude scattered by the actual electron distribution in an atom to that scattered by free
electron localized at a point [55]. Anomalous small angle X-ray scattering (ASAXS) refers to
variation in contrast of scatter in a system by using the physical phenomenon of anomalous
dispersion of X-rays near the absorption edge of an element. This phenomenon of dispersion
occurs when the X-ray photon energy reaches the binding energy of an electron in the sample
[56]. The atomic scattering amplitudes changes significantly near the energy absorption edge
of an element as shown in Figure 3.7. This drop is due to the resonance effect by the bound
electron. When the energy of X-rays increases beyond the binding energy, the X-rays are
absorbed and liberate the bound electron.
The scattering amplitude is given near to an edge of any element by:
EfiEffEf
c
c
c
0 (3.16)
where E is the X-ray energy and f0 = Z, where Z is the number of electron of the element.
The second and third terms are the complex anomalous dispersion corrections to the
scattering amplitude and depend on both atomic number of the elements in the sample and the
photon energy. Far from the absorption edge, SAXS intensities are proportional to the atomic
number of the element Z.
3. Small Angle Scattering
26
-10
-5
0
5
f'
f''
Energy (eV)
Figure 3.7: Typical atomic scattering amplitude variation near an X-ray absorption edge of
that element.
Optical theorem gives the relation between f’’ and the atomic absorption coefficient a
P
at an
incident photon energy E as:
!
e
Ecm
fae
P
H
0
cc (3.17)
where e is the classical radius of an electron, c is the velocity of light, h is Planck’s constant,
a is the attenuation coefficient per atom. Thus the increase in absorption is described in the
imaginary part, f’’(E). With further increases in the photon energy, the absorption decreases
smoothly. The real and imaginary parts of the scattering factors are connected to each other
by famous Kramers- Kronig relation defined as:
dE
EE
EfE
Ef ³
f
cc
c
0
2
2
0
0
2
S
(3.18)
Theoretically calculated scattering factors values have been used for the experiment,
which is tabulated by Cromer and Liberman [57]. Fluorescence, which is constant and occurs
when the incident photon energy is above the electron binding energy, leads to an increased
background in a small angle X-ray scattering experiment. Therefore it is appropriate to
perform ASAXS experiments below the absorption edge to avoid the fluorescence.
The small angle scattering from precipitates that are enriched with the anomalous element
may be isolated both qualitatively and quantitatively, even in the presence of other scatterers
which are not enriched with the anomalous element. SAXS is a contrast dependent technique
3. Small Angle Scattering
27
where the electron density fluctuation is proportional to the amplitude of atomic scattering
factors given as:
222 2)( EfEfffEfEfE oo cc
c
v'
K (3.19)
in ASAXS contribution of particular element (resonant atoms) in the scattering intensity is
separated from the total scattered intensity by calculating the resonant curve using the
Stuhrmann equation [58,59].
qFEfEfqFEfqFEqI RORO
22
,cc
c
c
(3.20)
where F0( q) -- Normal SAXS term
F0R( q) -- Scattering cross term
FR ( q) -- Resonant Scattering term
Solving the above equation (3.20) for three or more energies, allows us to separate the
resonant scattering term from the rest of the combined SAXS term. The resonant scattering
term contains the information about the spatial distribution of the resonant scattering atoms
only.
ASAXS not only gives a qualitative characterization of specific element, but also it
provides quantitative information about the distribution of the resonant atoms. The number
density of the resonant atoms can be calculated by using the following equation as reported
earlier by Goerigk et. al. [60,61]:
qdqF
r
V
V
NR
e
z
z
3
2
2
3
2)(
)2(
1
4
1
2
1³
r
S
(3.21)
where 3
3
4
ZZ RV S is the volume of the Z atoms with ionic radius RZ and re is the classical
electron radius. The integral represents the Q invariant of the resonant curve.
3.4 Energy dependent scattering contrast
The compositions were calculated by two different fitting routines. First, all ASAXS curves
were simultaneously fitted with the software SASfit [62] which used equation (3.8) in order to
obtain the nanostructure and the experimental contrast at a particular absorption edge. After
fitting we have different values of experimental contrast for different energies.
Second, after determining the relative experimental contrasts values from the first fitting
3. Small Angle Scattering
28
routine, these contrasts values were further fitted with the theoretically calculated contrasts in
a separate MATLAB routine. For calculating theoretical contrast, the total numbers of atoms
of each element were distributed into the nanoparticle (core), shell and in the remaining glass
matrix. The number of moles of each elements as well as the stoichiometry for the crystalline
phase is kept constant during fitting. For a crystalline phase PlQm in the core, the effective
electron density is calculated as follows:
»
¼
º
«
¬
ª ¦
i
i
i
p
C
tCA
core Ef
l
m
Ef
M
xPDN
EK (3.22)
where NA is the Avogadro number, DCis the mass density and MCis the total molar mass of
the crystalline phase. Pt is the total number of moles of an element P in the system before heat
treatment. x (0<x<1) is the fraction of moles out of total Pt moles used in the formation of
crystals after heat treatment. The number of moles for other elements (such as Q) in the
crystalline phase is evaluated by the stoichiometric ratio m/l. Theoretically calculated atomic
scattering amplitude for an element P is given by fp(E) and the atomic scattering amplitudes
for all the other elements present in the crystalline phase is given by fi(E), where the index of
summation i represents all the other elements present in the crystalline phase except P.
After the distribution of moles for a crystalline phase forming elements in the core, the
remaining moles of P and Q and the moles of all other elements present in the glass are
distributed into the shell and the remaining matrix. The effective electron density of the shell
is given by:
]1[ ¦
¸
¹
·
¨
©
§
i
iiiQttpt
S
SA
shell EfNuEfxP
l
m
QzEfPxy
M
DN
EK (3.23)
where DS is the mass density and MSis the total molar mass of the shell. In the first two terms,
y (0<y<1) and z (0<z<1) are the fractions of moles of element P and Q from the remaining
moles left in the system after the core formation. The last term ui (0<u<1) is the fraction of
moles for all the other elements Ni (except the elements in the core) present in the system and
the index of summation i represents the number of elements.
After the formation of a core and a shell, the remaining fraction of mole for each element
must be present in the matrix. The effective electron density of the matrix is given as:
]1
11[
¦
¸
¸
¹
·
¨
¨
©
§
¸
¸
¹
·
¨
¨
©
§
¸
¸
¹
·
¨
¨
©
§
i
iiiQ
t
t
tt
pt
M
MA
matrix
EfuNEfx
l
m
P
Q
z
l
m
xPQ
EfPxyx
M
DN
EK
(3.24)
3. Small Angle Scattering
29
where DM is the mass density and MM is the total molar mass of the remaining matrix. The
first two terms are the moles of the elements (P and Q) finally left in the matrix after the
formation of crystalline core and the shell. The last term represents the number of moles of all
the other elements Ni (except P and Q) left in the matrix after the formation of shell.
While fitting x, y, z, ui, DC, DSand DM were used as fitting variables to calculate the
theoretical contrast, which is the difference of the electron densities of core, shell and
remaining matrix, which is calculated as follows:
111 EE
EE
E
E
matrixcore
nmatrixncore
n
KK
KK
K
K
'
' (3.25)
By using the above equation for relative change in the energy dependent contrast enables
to evaluate the composition and density of the spherical core-shell particles in the studied
system.
Due to the anomalous dispersion of atomic scattering amplitudes f’ and f’’ near the
electron binding energy makes a variable photon energies as a basic requirement of ASAXS.
Such type of X-ray source with variable photon energy is available only at the synchrotrons.
Broad high-intensity spectrum, high intensity, good angular collimation makes synchrotron a
suitable tool for ASAXS. The energy resolution, defined as E/E, is also important for
diminishing the smearing effect near the absorption edge.
3.5 Small Angle Neutron Scattering (SANS)
Scattering of cold neutrons has become an elegant and powerful probe of both static and
dynamical properties of chemical and magnetic structure of solids. The power of the neutron
relies on a number of fortunate intrinsic properties such as electric neutrality, which makes it
penetrate easily into a bulky sample. By means of the strong nuclear forces, the neutron
interacts with the atomic nuclei of the sample. As the neutron possesses a magnetic moment,
it interacts also through magnetic dipole forces with the unpaired electrons of the sample. Due
to the actual value of the neutron mass, neutrons with energies of the order of meV have de
Broglie wavelengths of the order of Angstrom. In a scattering experiment, the detectable
momentum transfer is thus of the order of inverse atomic distance and at the same time, the
detectable energy transfer is comparable to the characteristic energies of structural and
magnetic excitations in solids.
3. Small Angle Scattering
30
The fundamental difference between the X-rays and neutron is the interaction with the
matter. X-rays scatter by an electron shell of the atom, while the neutrons interact with the
atomic nuclei called as neutron scattering. Due to the electric neutrality of neutrons, it
interacts weakly with the matter and penetrates deeply in the matter up to several millimeters.
Since the neutrons has a small magnetic moment, which interact with the spin and orbital
magnetic moment of atoms causing magnetic scattering. The other differences are the
scattering cross section for the electromagnetic wave varies with the square of the atomic
number of the element, while for neutrons the neutron-nucleus scattering cross section varies
randomly respective to the atom number and depends also on the isotopes of the elements.
The de Broglie and Schrödinger wave particle principle provides the relation between the
energy of the neutron with its respective wavelength as:
n
m
k
E
2
22
!
(3.26)
where k is the wave vector and n
m is the mass of the neutron 1.67 x 10-27 kg.
Small Angle Neutron Scattering (SANS) is a complementary method to SAXS and
analyses the same nanostructures, but having different contrasts. Additionally, scattering of
neutrons by the magnetic moments of atoms enable to determine both the chemical and
magnetic structure of materials. Also, the use of using polarized SANS permits to separate the
nuclear and magnetic scattering independently. The total scattering cross section of a system
is given similarly as we shown for the SAXS measurements in equation (3.8), only the
contrast has to be defined in terms of nuclear scattering length density which is given as [48]:
¦
N
i
ii b
V
1
K (3.27)
where V is the volume containing N atoms and bi is the (bound coherent) scattering length of
the ith atom in the volume. V is usually the molecular or molar volume for a homogenous
phase in the system of interest.
Nuclear Scattering
In SANS experiment neutrons are interacting with a complex array of spatially distributed
nuclei. When there are more than one phase is present in the studied sample, then the cross
section includes the different nuclear length densities and volumes for each phase in the
material. The scattering length density then modified as:
3. Small Angle Scattering
31
¦
¦
N
i
ii
N
i
ii
A
Mc
bc
N
1
1
UK (3.28)
where ci is the atomic part, bi is the nuclear scattering length of atoms of the ith element and
Miis the atomic weight of element i containing in the phase and is the mass density of the
phase. Then the scattering cross section is proportional to the square of the difference in
neutron scattering length density of different phases present in the sample also called as
nuclear contrast, 2
21
2KKK ' nucl and the nuclear scattering cross section is given as:
2
2
,rqFq
d
d
Nnucl
nuclear
K
V'v
¸
¹
·
¨
©
§
:
& (3.29)
where FN (q, r) is the nuclear form factor of the particles.
Magnetic Scattering
Neutrons have magnetic moment which interact with the magnetic moment of an atom with
unpaired electron spins and contributes as a magnetic scattering. The contrast for the magnetic
scattering comes from the moment of neutron n
P
and moment of electron e
P
. The unpaired
electron spins form the magnetic moment of the atom. Since SAS has no atomic resolution the
scattering is describe by the total magnetization M of a nanosized phase that appears. The
magnetic contrast is defined as the difference between the magnetizations of the phases in the
sample. For a two phase system (matrix and particles) it is given as:
matparnmagn MM
q
qMq v
»
¼
º
«
¬
ªuu
v' 2
&
&
&
PK (3.30)
where Mpar and Mmat are the magnetization of the crystalline phase and the remaining matrix
phase. The magnetic scattering measured at a 2D detector has an angular dependence by a
factor of sin2 where is the angle between the direction of external homogenous magnetic
field applied to the sample and the scattering vector q
&
. So from the above equation (3.30) it is
concluded that, when the direction of the vector q
&
is parallel (=0°) to the magnetization
direction, no magnetic scattering appears if all magnetic moments in the sample aligned by
the external field. While the case with q
&
perpendicular to the magnetization direction for
=90° results in mixture of magnetic and nuclear scattering. The magnetic scattering density
is defined as:
3. Small Angle Scattering
32
¦
N
i
ii
A
magn
Mc
mN
1
UP
K(3.31)
where ciis the atomic part of the element i, m is the magnetization of the phase in Bohr
magnetons per atoms perpendicular to momentum vector q
&
and Mi is the atomic weight of the
element i in the phase and =0.27 x 10-12 cm is an unit conversion multiplier. The magnetic
scattering cross section is given as:
2
22 ,sin rqFq
d
d
Mmagn
magnetic
\K
V'v
¸
¹
·
¨
©
§
:
& (3.32)
where FM (q, r) is the magnetic form factor.
3.6 Polarized Small Angle Neutron Scattering (polarized SANS)
When the incoming monochromatic neutron beam is unpolarized in nature such that the
neutron spin is randomly distributed, then the scattering cross section is the sum of the
scattering cross section of isotropic nuclear and anisotropic magnetic scattering given as [63]:
magneticnuclear
q
d
d
q
d
d
q
d
d¸
¹
·
¨
©
§
:
¸
¹
·
¨
©
§
:
:
&&& VVV
(3.33)
After putting the values from equation(3.29) and equation(3.32) in above equation we can
conclude that the scattering intensities measured perpendicular to the applied magnetic field
results the sum of nuclear and magnetic scattering, While the scattering intensities measured
parallel to magnetic field results only the nuclear scattering. When the magnetic contrast is
very small compared to the nuclear contrast then the magnetic caused anisotropic signal is
very weak and hard to measure precisely.
In order to extract the magnetic scattering, one possibility is to use the polarized neutron
beam, by using the specific spin orientation of the neutron either parallel or antiparallel to the
applied magnetic field [64]. In the polarized SANS experiment the constant magnetic field is
applied on the sample in such a way that the direction of the field is perpendicular to the
direction of the incident neutron beam. A polarizer is used to polarize the neutron beam
guided through the collimation tube. A spin flipper is used to flip the spins just before the
sample position. There are two possible situation for the flippers either it is ON or OFF and
3. Small Angle Scattering
33
depending on it the flipper flips the spin of the polarized neutron either parallel or antiparallel
to the applied magnetic field.
When the flipper is OFF then the state of polarized neutron (n+ or n-) is scattered through
the sample without change of the spin. In this situation we measured the scattering cross
section either
¸
¹
·
¨
©
§
:d
dV
or
¸
¹
·
¨
©
§
:d
dVcalled as non spin flip scattering (NSF). But when the
flipper is ON then the flippers flips the spin of the polarized neutrons and we measured the
scattering cross section either
¸
¹
·
¨
©
§
:d
dVor
¸
¹
·
¨
©
§
:d
dV
depending on the incident polarized
direction of the neutrons and called as spin flip scattering (SF). So we have four scattering
cross sections two for NSF and two for SF.
If the analyzer is not used then the scattered neutrons collected at the detector contains
the contribution from both the SF and NSF and depends on the polarization of the incident
neutron beam. When the neutron polarization and magnetic moments are directed along the
external applied magnetic field, then the cross sections are given by [7]:
\KKH
KK
VV
\
V
2
2222
sin),(),(212
),(),(,
rqFrqFP
rqFrqF
d
d
d
d
q
d
d
M
magn
N
nucl
MmagnNnucl
''
''
¸
¹
·
¨
©
§
:
¸
¹
·
¨
©
§
:
:
(3.34)
\KKH
KK
VV
\
V
2
2222
sin),(),(212
),(),(,
rqFrqFP
rqFrqF
d
d
d
d
q
d
d
M
magn
N
nucl
MmagnNnucl
''
''
¸
¹
·
¨
©
§
:
¸
¹
·
¨
©
§
:
:
(3.35)
where P is the polarization of the neutron and defined as:
N
N
NN
P (3.36)
where N+ is the number of neutron having spin anti-parallel and N-spin parallel to the applied
magnetic field direction H. The efficiency of the spin flipper is shown by . When the flipper
is ON efficiency is close to unity 1 and for OFF efficiency is zero ( = 0).
35
4 Experimental
4.1 SAXS and ASAXS at BESSY II
4.1.1 Beamline description
A system that delivers, chooses photons upon the requirements of the samples and shapes the
beam profile accordingly to the requirement of the experiment is denoted as a beamline. The
ASAXS beamline at BESSY II (HZB) uses a 7 Tesla multipole wiggler (7T-MPW) photon
source with a critical energy of 13.5keV for E=1.7GeV [65]. The wiggler allows a very high
photon flux with wide X-ray energy range from about 3.5keV to 28keV will be used in the
monochromatic branch for ASAXS. The beamline can be divided into four parts. These are
the optics (Figure 4.1) which contains slit system, beam forming and beam monitoring-
region, the sample environment and the detections system for the small angle scattering
signal. From the source to sample, the beam has to pass a collimating mirror for the white
beam, a Si (111) double crystal monochromator and a focusing mirror. A schematic sketch of
the beamline optics is shown in Figure 4.1.
Figure 4.1: Schematic view of the optics of the beamline from wiggler source.
4. Experimental
36
Figure 4.2: Schematic view of the SAXS-setup in the experimental hutch after the optical
hutch.
There are two main sections of the beamline:
(i) Optical Hutch (Figure 4.1)
(ii) Experimental Hutch (Figure 4.2)
Optical Hutch
The first section after the beam source is the optical hutch, which contains the X-ray optics
mainly consisting of 2 mirrors and a double crystal monochromator. From wiggler the beam
hits the aperture and the primary slit 1, which defines the horizontal and vertical cross section
of the beam hitting the first mirror. The slit one has usually size of 10mm by 3mm
(horizontal*vertical) depending on the mirror angle and defines mainly the divergence. The
first mirror is the collimating mirrors, with pitch angle variable between 0-5 milliradians. The
mirror provides a vertically parallel beam on the monochromator. The two mirrors have two
tracks from silicon and from rhodium to provide X-ray reflexion till high energies.The
function of the Double Crystal Monochromator (DCM) is to select and transmit X-ray
radiation of desired photon energy from an incident white synchrotron radiation beam. Our X-
ray monochromator is consists of two silicon crystals cuted to the Si (111) plane. The Si (111)
has a ‘d’ spacing of 1.135 Angstroms, which act as a diffraction grating to produce an angle
dependent monochromatic beam by following Bragg’s law:
d
n
2
sin O
T (4.1)
4. Experimental
37
where ‘d’ spacing is fixed and is the incidence angle and is the wavelength of energy. The
energy will be selected by rotating both the crystals and varying the Bragg angle whilst
keeping the crystals parallel to each other. A Si (111) crystal monochromator will produce a
monochromatic beam with an energy resolution, (E/E) = 1.2x10-4. After passing through
monochromator, the beam can be focused vertically by a second mirror.
The beamline has an option for tuning of energies higher then 15.2keV by removing the
mirrors. The beam forming and analysis region consists of the slit system, the absorbers to
vary the primary intensity, a fast shutter and the ionic chamber to monitor the incoming beam
that hits the sample. These parts are distributed in both the optical and experimental hutches.
Experimental Hutch
The small angle scattering process and the detection and data collection takes place in the
experimental hutch. A schematic view is show in Figure 4.2 and Figure 4.3 shows the SAXS
experimental setup in two geometric configurations from the sample chamber to the 2D
SAXS detector.
The sample environments are usually places in the center of a Huber diffractometer. The
main environment used in this thesis in a vacuum sample chamber in those a sample changer
is mounted (Figure 4.3 (b)). Additionally the chamber can be equipped with a furnace. The
advantage of the vacuum environment is the reduction of air scattering and no additional
windows are necessary.
4. Experimental
38
Figure 4.3: Experimental SAXS setup installed at BESSY II, Helmholtz-Zentrum Berlin: (a)
detector at long distance from the sample and (b) detector at short distance from the sample.
The SAXS instrument is show in Figures 4.3. The main part is an optical bench that can
be tilted for GISAXS. Different area detectors can be attached at the end of a vacuum
scattering part. This part is constructed by using an innovative solution of an edge welded
bellow system. Therefore, the sample detector distance, that means the q-range, can be varied
without breaking the vacuum between 80cm and 380cm.
Two different detectors are possible to be used. The standard detector in case of ASAXS is a
2D delayline gasfilled detector (MWPC) that can perform single photon counting while
having a low background. The second detector is a MAR CCD 165 that will be used in case
of very strong scattering samples and in case of GISAXS.
4.1.2 Data reduction / SASREDTOOL
During the SAXS measurement, photons scattered from the samples are collected at a two
dimensional detector in x-y plane. But these two-dimensional images have to be corrected for
various parameters and finally converted into one dimensional curve. The scattered intensity
from the particle at detector is corrected by the following formula:
4. Experimental
39
yx
obb
Db
oss
Ds
yxSI
tITzxI
I
tITzxI
yxI
,
,
1..,..,
,:
u
¸
¸
¹
·
¨
¨
©
§
WW
(4.2)
where Is(x, y) is the scattered intensity from the sample which is collected at the detector
during measurement.
Dead time correction
Dead time is the time interval, between a change in the input signal or event and response to
the signal. T is the dead time in equation (4.2). Dead time correction factor T is defined as:
yxI
T
s
yx ,
¦¦
D
(4.3)
where is the number of detected events at the anode of MWPC gas detector. Summations in
the above equation are sum over all the pixels of detector. The averaged factor is in our case
about 1.10. In case of the CCD detector is this effect not valid in first approximation.
Dark current correction
It is the small electric current that records when no photons are entering the detector. ID is the
dark current in equation (4.2), which has to be subtracted from the scattered intensity from
the sample. Various factors are responsible for the dark current, such as electromagnetic
interference from power lines, electronic noise, and cosmic radiation events in detector
trigger. The dark currents for gas detectors are much lower and have long term stability than
that of the CCD camera.
Normalization by primary intensity
Continuous decay of synchrotron current, leads to decay of X-ray photon flux with time.
Normalization with the primary beam intensity is necessary to omit the effect of continuous
decaying and potential fluctuations of photon flux with time. Ios is the primary intensity in
equation (4.2), which is measured simultaneously with the SAXS measurements.
Transmission correction
X-ray photons not only scatter from the sample, but also they absorbed by the samples. Ratio
of the transmitted photons over incident photons is termed as transmission of the sample. s is
the transmission from the sample, which is measured by the following formula:
11
00
00
11
De
De
Ds
Ds
sII
II
II
II
W (4.4)
4. Experimental
40
Where 1
s
I and 0
s
I are the intensity measured at diode after and before the samples. 1
e
I and
0
e
Iare the intensity measured at diode for the empty beam (no sample is present), after and
before the empty sample holder. In principle the ratio of 1
e
Iand 0
e
I must be equal to one.
0
D
I and 1
D
I are the intensities due to the inherent noise (dark current).b in equation (4.2) is
the transmission from the background respectively
Background correction
Backgrounds can arise from sample holders, slit scattering, primary beam absorber, beamline
flight tubes that means from all components in the beamline, are included in the measured
scattered curves. By measuring separately the scattering of an empty sample holder or
background samples (e.g. capillaries) and then subtracting it from the scattering of main
samples leads to correct the background for the measurements. Ib is the background scattering
from the sample holder.
Detector sensitivity
Sensitivity profile of detector is the important parameter, which has to be taken in account
while correcting the two-dimensional image of detector. The sensitivity relates all detector
pixels to each other in correction function. In equation (4.2), S(x, y) is the sensitivity profile
by which the scattered intensity is normalized. Sensitivity is also termed as flatfield. It is
mandatory to measure sensitivity for the 2D gas detector.
Solid Angle Correction
Since the detector has a flat surface while the wave reached the detector after scattering are
spherical in shape, which leads to the geometrical correction of the solid angle. In equation
(4.2), x, y is the solid angle correction for the measurement.
Calibration of q value
In order to calibrate the q values, Silver Behenate is used as a standard. Since the first peak
value for scattering vector q=1.067nm-1 for Silver Behenate is known, by using this value we
can calibrate the curves to the exact q values [66]. So the Silver Behenate standard is
measured in a sample sequence with the measuring samples.
4. Experimental
41
Normalization to Absolute value
To evaluate the quantitative measurement, it is necessary to get the corrected intensities in
differential scattering cross section per solid angle in units of cm-1. Normalizing the measured
sample curves with the standard sample of known scattering cross section, measured under
identical conditions allow to get the curves in absolute units of cross section. In SAXS
normally a glassy carbon sample of thickness 90µm or 1mm is used to normalize the curves.
This standard is also measured simultaneously with the measuring samples.
All the corrections mentioned above will be done during the primary data analysis by
using the software package “SASREDTOOL”.
4.2 SANS at ILL
4.2.1 Description of the beamline D22
The neutrons are coming from a cold source will be monochromatized by means of a velocity
selector. A 1.2m long permanent FeSi supermirror transmission polarizer is used after the
velocity selector. A schematic view of a beamline is shown in Figure 4.4. The polarizer is
used to select one of the neutron spin state. A radio frequency spin flipper is used to reverse
the spin state of polarized neutron and installed just before the sample [67].
Figure 4.4: Schematic of polarized SANS beamline.
Neutrons having wavelength of 6 Angstrom are incident on the sample. During
measurement magnetic field of 1.5 Tesla is applied perpendicular to the direction of the
incident neutron beam direction. Each sample is measured twice, once with the flipper ON
and once with the flipper OFF. The scattered neutrons were collected at a multi-tube detector,
which is consists of 128 x 128 pixels with a resolution of 8 x 8mm2. The samples were
4. Experimental
42
measured at three different detector positions, at 2m, 8m and 17.6m to achieve long q range.
The raw data was corrected for background, transmission, and calibrated to absolute value of
scattering cross sections. The scattered intensity contains the mixture of isotropic nuclear
scattering and anisotropic magnetic scattering from the magnetic moments. In the ideal case
all the magnetic moments in the sample has to be aligned with the field in the vertical
direction and there should be no magnetic scattering for q vector parallel to the magnetic
moments and a maximum magnetic scattered intensity for the q vector perpendicular to the
moment direction. Around a circle of constant momentum vector the magnetic scattered
intensity should vary as a cosine square with angle around the multi detector image. The
anisotropic averaged curve provides the separate curves for the nuclear and the magnetic
scattering. Measurement of the four partial neutron intensities I++, I−−, I+−, and I−+ became
possible by registering all scattered neutrons independently on their polarization state after the
scattering. That means no polarization analysis was done. Magnetic guide fields of the order
of 1mT serve to maintain the polarization between polarizer and RF flipper.
4.2.2 Data reduction / GRASP
Raw data treatment was carried out by means of the software named GRASP [68]. In GRASP
one has to load the scattering data, background and cadmium data sets (for dark current) into
the relevant workspace areas. For calculating transmission firstly load the transmission files
and the corresponding empty cell files into the worksheets then calculate the sample
transmission Ts using the graphical zoom and transmission calculator. Similarly, the empty
cell transmission will be calculated. GRASP software uses the 'Centre of Mass' calculator to
determine the beam centre coordinates from the zoomed area of the transmission or reference
beam measurement. In order to eliminate the bad data pixels software uses the masking of the
pixels which is combined with an instrumental mask that eliminates the inactive regions of the
detector. For calibration and scaling, software uses a water scattering measurement as a
differential scattering cross section standard. The detector efficiency calculator generates a
calibration scaling value and detector efficiency map. After all the corrections the image is
averaged isotropic or anisotropic depending on the scattering from the samples.
43
5 Crystallization of magnetic MnxFe3-xO4 nanocrystals in
silicate glasses
5.1 Motivation
Magnetic nanoparticles are abundant in nature and also present in some biological objects
[69]. The development of magnetic nanoparticles has been a source of invention of
spectacular new phenomena and increase the interest of the scientific community to study the
fundamental properties and enhance its potential applications in different fields mainly
information technology, telecommunication or medicine [70-75]. Magnetic nanocomposite
materials are generally composed of magnetic nanosized particles distributed either in a non-
magnetic or magnetic host matrix [76,77]. The transport and magnetic properties are
depending on the distribution of magnetic nanoparticles in the host matrix. Therefore,
understanding and controlling the nanostructures in materials is essential to obtain desired
physical properties.
The synthesis of nanosized magnetic crystals is usually achieved by using wet chemical
routes, i.e. by the precipitation of magnetite (Fe3O4) [34,78,79] but also of Co3O4 and
MnFe2O4 [80,81] from salt solutions. Magnetotactic bacteria (MTB) which has nanosized
magnetite crystals covered by protein and lipid membranes where produce by the biological
route [82-84]. These particles have often monodisperse size distributions and have sizes that
are difficult to prepare by other chemical methods. Precipitation of magnetic nanocrystals in
glass ceramics is another route to get well dispersed particles in glass matrix. The syntheses of
oxide glass-ceramics containing nanosized ferrimagnetic or superparamagnetic particles are
reported in the literature [85, 86]. The main problem associated with the synthesis of oxide
glasses with high concentrations of transition metals using standard melting techniques is that
the corresponding products may crystallize spontaneously [87-89]. This may result in
uncontrolled crystallite sizes and sometimes, phase compositions [90]. The spontaneous
crystallization during cooling can be avoided or reduced by adjusting the glass composition
accordingly and by increasing the cooling rate. Thermal annealing for variable time periods of
the obtained glasses can enable the precipitation of crystalline phases with tailored size-
distribution of the particles. Magnetic nanoparticles may lead to numerous applications
through variation of the matrix containing the nanoparticles. The magnetic nanoparticles in
glass ceramics can have different types of magnetism behaviour such as ferromagnetism,
ferrimagnetism or superparamagnetism.
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
44
The properties such as magnetic, electrical and optical of the magnetic nanoparticles are
depend on many factors, the key of these includes the chemical composition, the particle size,
its distribution, shape, volume fraction and on its morphology, also it depends on the
interaction of the particles with the surrounding matrix and with neighbouring particles [91,
92]. One can control the magnetic and electrical characteristic of the material by varying the
nanoparticle size, shape and composition. Broad variation of different properties of the
nanomagnetic particle provides possibility for a large variety of applications.
Transition metals (Fe, Mn) containing silicate glass ceramics can have a possibility of
precipitation of transition metal oxide nanocrystals during heat treatment. There is a
formation of spherical core shell kind of structure for these particles and it is difficult to
identify the complete structure and phase of particles by XRD and microscopic techniques.
We have implied the ASAXS technique to determine the Fe-Mn-O ratio in nanocrystals and
the composition of shell surrounds the crystalline phase.
5.2 Glass preparation
The base glass was produced by using reagent grade compounds of Na2CO3, MnCO3, SiO2
and FeC2O4.2H2O [93]. The batches (100g) were homogenized and melted in SiO2-crucibles
using a MoSi2-furnace with temperatures in the range from 1400 to 1450°С for 1.5h. After
that the melt is pouring into the pre-heated graphite mould, and after 3-5min when the surface
solidifies the resulting glasses were further transferred to a muffle furnace and kept at 480oС
for 10min, since the glass transition temperature is Tg=490°C. Then, the furnace was
switched off and the samples were cooled down with furnace velocity to room temperature.
The base glass used in our study has the composition as mixed 13.6Na2O-62.9SiO2-8.5MnO-
15.0Fe2O3-x (mol %). The measured density of the glass is 2.897g/cm3. The chemical
synthesis of the samples are shown in Table 6.1
Table 5.1: Chemical synthesis composition of the Fe-Mn-O containing glass ceramics.
Element Weight (%) Mol (%)
Na 7.91 8.46
Mn 6.17 2.65
Si 23.26 19.56
Fe 21.89 9.33
O 40.77 60.00
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
45
In order to get the iron and manganese containing crystals of composition MnxFe3-xO4 the
glass samples were heat treated at temperatures in the range from 500 to 700°C for different
times varying from 0-300min. The heating rate from room temperature to the preferred
annealing temperature was always 10K/min and the heat treatment temperature was always
above the glass transition temperature Tg = 490°C, for the studied samples. After annealing
the samples for desired time period, they are taken out from the furnace and cooled down in
air to room temperature. The samples are opaque and black in color as shown in Figure 5.1.
Figure 5.1: Picture of the glass ceramics samples containing magnetic Fe and Mn oxide
crystals.
Finally the samples were polished to about 150µm thicknesses both sides for the
SAXS and ASAXS experiments. A series of samples annealed at 540, 550 and 580°C for
different time periods varying from 0-180min were used for SAXS investigation. A list of
sample is given in the appendix A.1. Three samples annealed at 550°C for 40, 60 and 180
minutes have been selected for ASAXS measurement to study the nanostructure as well as
their averaged chemical compositions.
5.3 Sample characterization using electron microscopy and X-ray
diffraction
First, microscopic measurements were made to understand the morphology of the
nanoparticles. The microstructures were studied by using a scanning electron microscope
(SEM: JEOL 7001F). The samples surfaces have been polished to optical quality. Secondary
and back scattered electrons are used for the imaging. Figure 5.2 shows the SEM images of
the sample heat treated at 550°C for 180min [93]. The SEM shows nearly spherical particles
with an unimodal size distributions.
Another sample was annealed at higher temperature and for higher times. The sample
annealed at 600°C for 16h shows the formation of two types of nanocrystalline phase as
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
46
shown in Figure 5.3 [93]. The images show that there is a formation of large ellipsoidal
crystals of a second phase NaFe(SiO3)2 having size in the range of 1 micrometer, along with a
population of smaller crystals with the mean size of 50nm as similar to those in Figure 6.2.
Figure 5.2: Scanning Electron Microscopy (SEM) image for the sample annealed at 550°C
for 180min (a) 0.5m (b) 200nm [93].
SEM revealed the formation and growth of nanoparticles in the glass ceramics. However,
SEM is not able to distinguish between amorphous or crystalline particles. Therefore, XRD
measurements were done on a series of samples. Moreover, it is assumed that MnxFe3-xO4
phase will crystallize, but the exact ratio of Fe and Mn is not known.
The XRD measurement was performed on the samples at 7T-MPW-SAXS beamline at
BESSY II. The glass samples were also examined by SAXS and ASAXS methods. The
measurement was done in the transmission geometry. During the measurement, X-ray of
energy 17keV (wavelength = 0.073nm) was used, which was appropriate for achieving
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
47
suitable transmission from the samples. The X-ray beam incident perpendicularly on the
sample and interacts with the distribution of electrons and scatters in all directions. The
scattered photons were collected at the MAR CCD 165 camera having pixel size of 79m x
79m. During measurement the sample was stationary and the detector was collecting the
photon at three different positions 15°, 35° and 55°. A gold foil was measured with the
samples was used to calibrate the XRD-2values in a range from 10° to 60° [94].
Figure 5.3: SEM image for the sample annealed at 600°C for 16h at different resolution
(a) 5m (b) 0.5m [93].
Figure 5.4 shows the XRD curves measured on an unannealed sample and on the samples
annealed at 550°C for 10, 40, 60 and 180min. XRD shows no peaks for unannealed and for
the sample annealed for 10min. While for the samples, which were annealed for more than
10min pronounced peaks at about 20°, 28.5° and 50° are clearly detectable.
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
48
10 20 30 40 50
0
100
200
300
2T(deg)
Unanneal
10 min
40 min
60 min
180 min
Figure 5.4: X-ray diffraction of the sample annealed at 550°C for unannealed, 10, 40, 60 and
180min.
For analyzing the phases, annealed samples were fitted with different standard phases of
iron and manganese oxide. XRD fit results shows the formation of particles having a mixed
phase of Fe and Mn oxides as MnxFe3-xO4 and it is difficult to distinguish between Fe3O4 and
MnFe2O4 (jacobsite) phases. However, in some cases e.g. of a solid solution containing two or
more transition metal are difficult to characterize by XRD. This is due to the insufficient
separation between the main diffraction peaks of two nanocrystalline phases due to relatively
low intensity of the peaks and by the nano dimension of the particles that broadens the peaks.
In such cases, XRD is not able to provide the precise phase of the nanocrystalline particles.
In XRD the broadening of peak decreases with the annealing time, which shows increase
in the particle size with time of heat treatment as evaluated by Debye Scherer equation.
TE
O
cos
K
T (5.1)
where T is the mean size of the crystalline domains, K is the shape factor, is the X-ray wave
length, is the line broadening at half the maximum intensity (FWHM) in radians and is
the Bragg angle. The shape factor K has a typical value of about 0.9, but varies with the actual
shape of the crystals. The FWHM was determined by fitting the peaks at 20°, 28.5° and 50°
by Gaussian fit, which fits well with the peaks. The fit for one of the sample annealed at
550°C for 40min and for the peak at 20° is shown in the Figure 5.5. The error for the particle
size is calculated by the equation (5.2):
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
49
2
2
2
tan TT
E
Ed
d
TTError
¸
¸
¹
·
¨
¨
©
§
(5.2)
where TError is the error for the particle size, d is an error in FWHM, and d is an error of
the Bragg angle. By using Scherer equation, particle size between 10-30nm was evaluated as
shown in Figure 5.6.
2 0 2 2
5 0
6 0
7 0
Data: A40m in _B
Mo del: G auss
Peak position 20.004r 0.002
FW H M 0.305r 0.009
T (deg)
Figure 5.5: Gaussian fit for the peak at 20° for the sample annealed at 550°C for 40min. The
inset shows the parameter after the fit.
40 80 120 160 200
10
15
20
25
30
t (min)
Particle Size
Figure 5.6: Size of the particles calculated by XRD using the Debye Scherer equation
Furthermore, in order to investigate the effect of heat treatment on the shape, size,
volume fraction and distribution of the particles in the glass matrix, the samples were studied
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
50
by SAXS and the composition is determined by analysing the ASAXS curves. The volume
studied in the SEM is much smaller (<1Pm3) than in the SAXS/ASAXS experiments
(>0.1mm3) and therefore a much better average and a more reliable statement for the
macroscopic sample is given in these experiments. XRD measurements delivers the average
sizes of the crystalline phases by Scherer equation, but it is not able to provide any
information about the amorphous phases present in the system. To get a comprehensive size
distribution we performed the SAXS investigations.
5.4 SAXS study of heat treated sample series
To investigate the nanostructure and its size distribution in the glass matrix, SAXS technique
was chosen. The SAXS measurement was performed at 7T-MPW SAXS beamline at BESSY
II. Since the X-ray K-absorption edges of Fe and Mn are at 7112eV and 6539eV, we have
chosen a X-ray energy of 6047eV for the SAXS measurement which is sufficiently below the
X-ray absorption edges of both the elements, so the fluorescence will be avoided. For
collecting the scattered photons a 2D delay-line gas detector with pixel size of 207m x
207m was used. The scattered photons were collected at two different distances, one far
form the sample at about 3800mm and other close to the sample at about 850mm to get the
whole reachable q range of the instrument. The glass-ceramic samples were measured in
transmission geometry. Samples were mounted on a sample changer together with a standard
samples. The sample chamber was under vacuum conditions (10-3mbar) to avoid air
scattering. All the samples were measured together with the background scattering, with a
glassy carbon standard for differential scattering calibration and with the silver behenate for
calibrating q values. The data reduction was done by using the software SASREDTOOL.
Figure 5.7 shows measured SAXS curves calibrated to differential scattering cross section
(cm-1 sr-1), as a function of magnitude of the scattering vector q. The SAXS Figure shows that
the intensity of the scattering curves increases with annealing time. The unannealed sample
shows the small hump at about q=0.8nm-1 which is shifted towards the lower q value for the
10min annealed sample. Both samples have a slope of about q-4 at smallest q values, which is
coming from nanosized surface structures. For longer time annealed samples for 40, 60 and
180min, the scattering intensities are increasing significantly and two humps can be seen in
the Figure, which gives a first hint for the presence of nanostructures of spherical core shell or
two different kinds of particles, also the shoulders are shifting towards lower q values with
annealing time, which implies the growth of the particles. In Figure 5.7 slope of the scattering
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
51
curves approached a q-4 behavior at higher q values larger than q=1nm-1. This implies for the
smooth surface of the particles.
0.1 1
1
10
100
1000
10000
q (nm-1)
Unanneal
10min
40 min
60 min
180 min
q-4
q-4
Figure 5.7: SAXS curves measured at 6047eV for the samples as prepared and annealed at
550°C for 10, 40, 60 and 180min. The slope of the scattering curves approached a q-4 at a
higher q values for annealing time larger than 10 minutes.
The SEM investigations gave a hint that the nanocrystals are almost spherical. Since the
SAXS curves show a pronounced shoulder, a spherical core shell structure seems to be
performed. Typically for particle growth process in an amorphous matrix, the particles will
have a lognormal size distribution. With these starting assumptions the SAXS scattering
curves in Figure 5.7 can be fitted well. To evaluate the structural information from the
scattering curves, they were fitted with equation (3.8) by assuming first a spherical core-shell
model by using program SASfit. The fitted SAXS curves annealed at 550°C for 40, 60 and
180min is shown in the Figure 5.8. Since the particles has higher volume fraction, structure
factor has to be considered by assuming local monodisperse approximation, which accounts
for the inter particle interaction. The lognormal size distributions are shown in the Figure 5.9
which reveals that the particle sizes are increasing with the annealing time and the sample
annealed for longer time has a broader size distribution than the sample annealed for shorter
times.
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
52
0.1 1
1
10
100
1000
10000
q (nm-1)
550°C_40min
550°C_60min
550°C_180min
Fit spherical core
-shell model
Figure 5.8: SAXS curves measured at 6047eV for three samples annealed at 550°C for 40, 60
and 180min. The fits using a spherical core shell model are shown by straight black line.
0 20 40 60
0
5000
10000
15000
20000
Core Radius (nm)
40 min
60 min
180 min
Figure 5.9: Volume weighted size distributions of the core radii for the particles in the
samples annealed at 550°C for 40, 60 and 180min.
The XRD results revealed the formation of MnxFe3-xO4, because of its high mass density
these particles must have the highest electron density as shown in Figure 5.10. Contrast
parameters from the SAXS curve fitting between core-shell and matrix, shows that electron
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
53
density of core has highest and the shell has the lowest electron density with respect to the
matrix as shown in Figure 5.10. Therefore, the electron density profile reveals that the
particles are surrounded by the layer dominated by elements whose electron density is smaller
than that of the remaining glass matrix. In our case, Si is the most prominent element
expected to be present in the layer and furthermore acts as a diffusion barrier for further
diffusion of the nanocrystals forming elements Fe and Mn. This layer grows with increasing
the annealing time and may slows down further crystal growth Table 5.2.
Figure 5.10: Sketch of variation of electron density for a spherical core shell model.
Table 5.2 shows the parameters obtained after the fitting of the three SAXS curves.
Parameters reveal an increase of particles diameter from 14nm up to 44nm after 180min of
annealing and also the thickness of shell increases with annealing time up to 2.2nm.
Table 5.2: Resulting parameters for the SAXS curves fitted by spherical core shell model for
the samples annealed at 550°C for 40, 60 and 180min.
Parameter 40min 60min 180min
Averaged
Core Radius (nm) 7.1 ± 0.5 11.9 ± 0.5 22.0 ± 1.0
Averaged
Shell Thickness (nm) 1.1 ± 0.2 1.7± 0.2 2.2± 0.2
On the other hand it turned out that the same SAXS curves can also be fitted with the two
size sorts of spheres model without any surrounding shell or diffusion region. The resulting fit
parameters are also nearly the same as for the spherical core shell model. Figure 5.11 shows
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
54
the curves fitted with the two sphere model. The deviation of the fitted lines are in the same
order as for the core shell model as shown in Figure 5.8 The size distributions of two sorts of
spheres are shown in the Figure 5.12, which shows the distribution of two types of particles.
Table 5.3 shows the averaged size parameters after fitting the scattering curves by two sphere
model.
0.1 1
1
10
100
1000
10000
550°C_40min
550°C_60min
550°C_180min
Fit Two
Sphere Model
q (nm-1)
Figure 5.11: SAXS curves measured at 6047eV for the sample annealed at 550°C for 40, 60
and 180min fitted with a model of bimodal distribution.
Table 5.3: Resulting parameters for the SAXS curves fitted by two sphere model for the
samples annealed at 550°C for 40, 60 and 180min.
Parameter 40min 60min 180min
Average Particle 1
Radius (nm) 6.8 ± 0.5 11.7 ± 0.5 22.2 ± 1.0
Average Particle 2
Radius (nm) 1.3 ± 0.2 1.8± 0.2 2.3± 0.2
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
55
0 10 20 30 40 50 60
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Radius (nm)
550°C_40min
550°C_60min
550°C_180min
(a) (b)
Figure 5.12: Bimodal size distributions for the samples annealed at 550°C for 40, 60 and
180min fitted with a model of two sorts of independent spherical particles. Enlarge image for
the distribution of the small sorts of particles are shown in fig (b).
The comparison of the sizes determined by XRD using the Debye Scherrer equation and
by SAXS (core shell model) shows that, both methods deliver similar averaged sizes upto
60min of annealing. At 180min the XRD diameter is much smaller, because XRD measures
correlation lengths, this is a direct hint that the crystals become polycrystalline for longer
annealing times (180min) as shown in Figure 5.13.
40 80 120 160 200
10
20
30
40
50
t (min)
XRD
SAXS
Figure 5.13: Comparison of the particle sizes as calculated by SAXS (spherical core-shell
model) and XRD.
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
56
The parameters shown in Table 5.2 for the spherical core shell model and in Table 5.3 for
the two sphere model are comparable to each other; also the fits are similar to each other.
Since both the spherical core shell and two sphere model fit to the curves; this makes it
difficult to distinguish between both the models. Such type of unsolved question remained as
already reported earlier for the SANS measurements [95].
5.5 Investigation of magnetic nanostructure using polarized SANS
Glasses that contain transition metals have the possibility to be magnetic in nature. The
sample studied contains a large amount of iron and manganese. This large amount of
transition elements makes this material to be magnetic. While SAXS resulted in two different
competiting structural models and one could not decide, which one is the appropriate model.
Here SANS was apply with polarized neutrons to overcome this contradiction. The reason to
choose this method is that XRD revealed the formation of crystalline particles of a mixed
composition of MnxFe3-xO4. Depending on the crystalline size they are superparamagnetic or
become ferromagnetic while growing.
The polarized SANS measurements were performed on the studied samples annealed at
different temperatures from 540-580°C for different times from 0-300min. The samples had
thicknesses between 800m to 2000m, which is roughly the optimal thickness for the SANS
measurement. A list of measured sample is given in appendix A.2. The SANS experiment was
performed at the D22 SANS beamline at the Institute Laue-Langevin (ILL), Grenoble France
[67]. In a polarized SANS experiments on magnetic materials one can observe a pronounced
anisotropic signal for I+ (ON) and I- (OFF) polarization states of neutrons as shown in Figure
5.14 (a) and (b) as an example for the sample annealed at 550°C for 60min.
The difference between both the states (I+ - I-) shows the cross terms and has a negligible
intensity along the direction of the magnetic field as shown in Figure 5.14 (c). This is an
evidence that the magnetic moments in the sample are very well oriented in magnetic field
direction. Therefore, it is not necessary to take a magnetization orientation distribution
(Langevin function) into account. The anisotropic average of the above images is shown in
the Figure 5.15, which shows only a small difference between the two polarization states,
while the interference term has an intensity that is about 10 times lower than both polarization
states. The cross term shows the interference between the nuclear and magnetic form factors.
The value of the cross term equals to zero, when the magnetic form factor of a given particles
will not interfere with the nuclear form factor of a particles [7].
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
57
Figure 5.14: 2D detector scattering images form the polarized SANS experiment after the
data correction for the sample annealed at 550°C for 60min. The applied magnetic field of
1.5Tesla is applied in the horizontal direction.
The images in Figure 5.14 reveal that by using polarized neutron scattering one can
separate the magnetic scattering from the nuclear scattering. The nuclear scattering A(q)= FN2
is extracted by analyzing the scattering intensity I+ and I- and the magnetic scattering is
determined by using the cross term represent as B(q) and the nuclear part as FM2 =
B(q)2/[A(q)24P2(1+e)2]. Figure 5.16 shows the separated magnetic and nuclear scattering for
one of the studied sample. The pronounced amount of magnetic scattering shows the magnetic
behavior of the sample.
Magnetic Field
direction
1.5 Tesla
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
58
0.1 1
0.01
0.1
1
10
100
1000
q (nm-1)
On
Off
Interference
Figure 5.15: Scattering curves for the ON, OFF and the cross term from the images for the
sample annealed at 550°C for 60min.
0.1 1
1E-3
0.01
0.1
1
10
100
1000 Nuclear
Magnetic
q (nm-1)
Figure 5.16: Separated nuclear and magnetic scattering curves for the sample annealed at
550°C for 60min.
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
59
Similarly the data reduction was performed on a series of samples annealed at the
temperature range from 550-580°C for 0-180 minutes (see the list in appendix A.2). Figure
5.17 shows the nuclear and magnetic scattering curves for the samples annealed at 550°C for
variable time periods from 10 to 180min. The scattering intensity increases with the annealing
time which reveals the growth of the particles. In order to evaluate the structural information
about the particles like size, shape and its distribution, the curves were further fitted with the
theoretically calculated intensity by using equation (3.8) and by the program SASfit [62]. On
the basis of structural information from SAXS in section 5.4, a spherical core shell model and
a model with two sorts of particles was taken into account. For such a glass system that under
goes a growth process of nanocrystals, it is known that a log normal distribution model is
appropriable.
0.1 1
0.1
1
10
100
1000
10 min
20 min
40 min
60 min
120 min
180 min
q (nm-1)
NUCLEAR SCATTERING
(a)
0.1 1
1E-3
0.01
0.1
1
10
100
1000
q (nm-1)
10 min
20 min
40 min
60 min
120 min
180 min
MAGNETIC SCATTERING
(b)
q-4
Figure 5.17: (a)Nuclear scattering (b) Magnetic scattering for the sample heat treated at
550°C for 10 to 180min. for the SANS measurement.
While fitting the nuclear scattering curves that fit well with the spherical core shell model
and the magnetic curves fits well with the normal sphere model. Table 5.4 shows the size
parameters obtained after the fitting of the respective SANS curves for the sample heat treated
at 550°C for different times from 10 to 180 minutes. Parameters reveal increase in the size of
particles as well as the thicknesses of the shell with annealing time. Distribution of particles is
also an important parameter while studying the kinetics of the crystal growth in this glass-
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
60
ceramic matrix. Figure 5.18 shows the volume weighted size distribution of particles
evaluated after fitting the scattering curves for the samples annealed for 550°C at different
time periods from 10min to 180min. The size distributions derived from magnetic scattering
curves revealed peaks at smaller radii in relation to those from nuclear scattering curves. The
smaller radii of magnetic nanocrystals indicate the presence of a magnetic surface dead layer
that surrounds the magnetically active core of the crystals [96]. The important result is (Table
5.4) that the magnetic scattering revealed only one sort of spherical particles. These magnetic
particles have a slightly smaller size as the core in case of the nuclear scattering, that could
modeled by spherical core shell model. While comparing the sizes given by the nuclear and
magnetic scattering in Table 5.4, one has to conclude that one sort of magnetic crystals are
formed having a non magnetic shell like region. These results provide a confirmation of
formations of a spherical core shell kind of magnetic nanoparticles in the glass matrix.
Table 5.4: Averaged size parameters calculated by polarized SANS form the nuclear and
magnetic scattering for the samples annealed at 550°C for 10 to 180min.
Nuclear Scattering Magnetic
Scattering
Sample
550°C Average Radius
Particle (nm)
Average
Thickness
Shell (nm)
Average
Radius
Particle (nm)
10 min 1.4 --- 1.3
20 min 2.8 0.4 2.7
40 min 10.0 1.0 9.8
60 min 11.5 1.5 11.4
120 min 16.2 1.8 16.2
180 min 22.0 2.2 22.0
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
61
0 10 20 30 40 50 60
0
2
4
6
8
10
Magnetic: ------
R (nm)
10min
20min
40min
60min
120min
180min
Nuclear:
Temperature: 550°C
Figure 5.18: Volume weighted size distribution curves for the samples annealed at 550°C for
a duration varying from 10 to 180min for nuclear and magnetic scattering. It can be seen that
the magnetic size distributions (dashed line) are smaller in comparison to the nuclear one
(solid line). The magnetic size distribution curves are scaled down for good visibility.
Similarly, polarized SANS measurements were performed on the samples heat treated at four
different temperature, but annealed always for 180 minutes. The nuclear and magnetic
scattering curves for the samples annealed at different temperature from 540°C to 580°C for
180min are shown in Figure 5.19.
The intensity of the scattering increases with the annealing temperature, which shows the
growth of the particles with the temperature. Structural information was evaluated by fitting
the nuclear scattering curves by spherical core shell model and the magnetic curves by simple
sphere model. The fit parameters are shown in Table 5.5 and the respective size distribution is
shown in Figure 5.20. Also this sample set; annealed at different temperature, prove the core
shell structures.
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
62
0.1 1
0.1
1
10
100
1000
540°C
550°C
560°C
580°C
q (nm-1)
NUCLEAR SCATTERING
(a)
0.1 1
1E-3
0.01
0.1
1
10
100
1000
540°C
550°C
560°C
580°C
q (nm
-1)
MAGNETIC SCATTERING
(b)
q-4
Figure 5.19: (a)Nuclear scattering (b) Magnetic scattering for the sample heat treated for
180min at different temperature for the SANS measurement.
Table 5.5: Parameters calculated by polarized SANS for nuclear and magnetic scattering for
the samples annealed for 180min at different temperatures.
Nuclear Scattering Magnetic
Scattering
Sample
180 minutes Average Radius
Particle (nm)
Average
Thickness Shell
(nm)
Average
Radius
Particle (nm)
540°C 16.5 2.5 16.2
550°C 22.0 2.2 22.0
560°C 25.9 1.9 25.5
580°C 30.4 1.4 30.4
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
63
0 20 40 60 80 100
0.0
0.2
0.4
0.6
0.8
1.0
1.2
R (nm)
Magnetic: ------
540°C
550°C
560°C
580°C
Annealing Time:180min
Nuclear:
Figure 5.20: Volume weighted size distribution curves for the sample annealed for 180min at
different temperatures from 540 to 580°C for nuclear and magnetic scattering represented by
the same color. The magnetic curves are scaled down for good visibility.
The size parameters reveal that the sizes of the particles are increases and the thickness of
layer decreases for the sample annealed at higher temperature for a particular time period.
Earlier, SAXS measurements were performed on these sample and the structural parameters
were evaluated by fitting the scattering curve by spherical core shell model. Figure 5.21
shows the comparison of the average size and thickness of the layer evaluated by SANS and
SAXS measurements.
30 60 90 120 150 180
0
5
10
15
20
25
SAXS
SANS
t (min)
(a)
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
64
30 60 90 120 150 180
1,0
1,5
2,0
2,5
SAXS_Shell
SANS_Shell
t (min)
(b)
Figure 5.21: Comparison of SAXS and SANS parameters for the sample annealed at 550°C
for 40, 60 and 180min (a) Particle Size (b) Shell Thickness.
5.6 ASAXS study at the absorption edge of Fe and Mn
ASAXS technique was applied to get additional information about the compositions of phases
and particular element distribution in the glass matrix, respectively. Figure 5.22 shows the
variation of effective atomic scattering amplitudes near the X-ray K absorption edges of Fe
and Mn. The equation for the effective atomic scattering amplitude is given by:
EfEffeff
(5.3)
where f(E) is the scattering factor defined in equation 3.16 (section 3.3).
4000 5000 6000 7000 8000 9000
10
15
20
25
Energy (eV)
Fe
Mn
7112 eV
6539 eV
Figure 5.22: Effective atomic scattering amplitudes for the elements Fe and Mn.
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
65
ASAXS measurements were performed on the samples that are already investigated by SAXS
by choosing five energies close to X-ray absorption edge of the elements iron and manganese
as shown in Figure 5.23.
6000 6500 7000 7500 8000
8
12
16
20
24
28
6000 6500 7000 7500
8
12
16
20
24
28 Fe
7112eV
7108eV
7100eV
7077eV
6998eV
Energy (eV)
6708eV
6539eV
6535eV
6528eV
6520eV
6497eV
6138eV
Energy (eV)
Mn
Figure 5.23: Effective atomic scattering amplitudes for the elements Fe and Mn. Arrows
indicate the energies used for ASAXS measurements.
Figure 5.24 (a) and (b) shows the ASAXS curves measured at the Fe and Mn edge for the
sample annealed at 550°C for 60min. It is seen from the Figure 5.24 (a) that for the iron edge
the ASAXS effect varies larger than the manganese edge in Figure 5.24 (b), which reveals the
fluctuation of higher concentration of Fe between the crystals, the shell region and the glass
matrix and is more pronounced than that in case of manganese.
0.1 1
1
10
100
1000
10000
q(nm-1)
6708eV
6998eV
7077eV
7100eV
7108eV
(a) Ek(Fe)=7112eV
0.1 1
0.1
1
10
100
1000
10000
6535eV
q (nm-1)
6138eV
6497eV
6520eV
6528eV
6535eV
6138eV
(b) Ek(Mn)=6539eV
Figure 5.24: ASAXS curve for sample annealed at 550C for 60min measured near but below
the X-ray absorption edges (a) Fe K-edge and (b) Mn K-edge.
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
66
On the basis of structural model informations from SANS investigations, the ASAXS
scattering curves were fitted by applying the spherical core-shell model and assuming a
lognormal size distribution. During fitting all the structure determining parameter such as
particle number, sizes, distribution function parameters (N, R,#) were fixed and only the
contrast for shell and core were used as a free variables [97]. Figure 5.25 (a) shows that the
fitted ASAXS scattering curves at two energies, (far and close) at the Fe absorption edge for
one of the sample annealed at 550°C for 60min. Similarly for the same sample, fitted ASAXS
scattering curves at Mn absorption edge is shown in Figure 5.25 (b).
0.1 1
1
10
100
1000
10000
6708eV
6708eV
7108eV
Fit
q (nm-1)
7108eV
(a)
0.1 1
0.1
1
10
100
1000
10000
6535eV
6138eV
6138eV
6535eV
Fit
q (nm-1)
(b)
Figure 5.25: ASAXS curves for the sample annealed at 550°C for 60min near the K
absorption edges (a) Fe (7112eV) (b) Mn (6539eV).
The experimental contrasts values obtained after fitting ASAXS scattering curves, were
further used for evaluating composition, density and volume fraction of the respective phases
(core, shell and matrix) present in the glass sample after heat treatment. The experimentally
evaluated contrasts were fitted with the theoretically calculated contrasts for core, shell and
remaining matrix by using equations (3.22-3.25) as discussed in section 3.4. During fitting
MnxFe3-xO4 phase was assumed as a phase formed in core, where x is a fitting variable along
with the density of the core, shell and matrix. During fitting the numbers of atoms were
distributed in core, shell and matrix in such a way that the total number of atoms for each
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
67
element must be conserved. Figure 5.26 shows the comparison of the relative contrasts
calculated theoretically with the experimentally evaluated contrasts for both Fe and Mn edges.
6000 6300 6600 6900 7200
0.7
0.8
0.9
1.0
Energy (eV)
ExpCore
TheoCore
(a)
6000 6300 6600 6900 7200
0.7
0.8
0.9
1.0
ExpShell
TheoShell
Energy (eV)
(b)
Figure 5.26: Comparison of the relative contrast calculated theoretically with the
experimentally evaluated contrast for both Fe and Mn edges (a) Core (b) Shell.
Table 5.6 shows the resulting parameters obtain after fitting routines for all the three
annealed samples. The respective parameters shows that the density of core is about
4.9 ± 0.1g/cm3 and for shell around 2.2 ± 0.05g/cm3 and for remaining matrix is 2.39 ±
0.02g/cm3. Also the parameters reveal increase in value of volume fraction for particles form
6 % to 9% during the heat treatment for long time periods. Variation of volume fraction
evaluated by composition with the annealing time is shown in Figure 5.27.
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
68
Table 5.6: Resulting parameters for the ASAXS for the samples annealed at 550°C for 40, 60
and 180min.
Parameter 550°C_40min 550°C_60min 550°C_180min
Averaged
Core Radius (nm)
7.1 ± 0.5 11.9 ± 0.5 22.0 ± 1.0
Averaged
shell thickness (nm)
1.1 ± 0.2 1.7± 0.2 2.2± 0.2
Density Core (g/cm3) 4.91 4.91 5.0
Density Shell (g/cm3) 2.22 2.24 2.26
Density Matrix (g/cm3) 2.38 2.40 2.40
Density System (g/cm3) 2.89 2.89 2.89
Volume Fraction Particle ~ 6 ± 0.5 ~7 ± 0.5 ~9.5 ± 0.5
Fe atoms in particle (%)
(Composition) ~ 55 ~ 62% ~ 80%
Fe atoms in particle (%)
(Resonant curve) -- ~ 60% ~ 82%
30 60 90 120 150 180
6
7
8
9
10
11
Volume Fraction (ASAXS)
t (min)
Figure 5.27: Volume fraction variation with the annealing time for the samples annealed at
550°C as calculated from ASAXS.
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
69
Evaluated density of shell from fitting is close to the bulk density of SiO2 (2.2g/cm3)
which provides direct hint of presence of SiO2 in shell. Table 5.7 shows the phases formed at
core, amount of SiO2 in shell and the remaining composition left as a glass matrix.
Quantitative information evaluated from the compositions shown in Table 5.6 and Table 5.7
reveals increase in the amount of Fe atoms along with the Mn atoms and the amount of SiO2
in shell with the annealing time.
Table 5.7: Composition calculated from ASAXS for the samples annealed at 550°C for 40, 60
and 180min.
Sample
(550°C) Core Shell
(SiO2)Matrix
40 min Mn0.2Fe2.8O436% 69.19SiO2-15.28Na2O-7.49Fe2O3-8.04MnO
60 min Mn0.35Fe2.65O455% 70.86SiO2-15.88Na2O-6.81Fe2O3-6.45MnO
180 min Mn0.5Fe2.5O465% 75.97SiO2-17.08Na2O-2.82Fe2O3-4.13MnO
Pure resonant scattering contribution of the Fe atoms in the particles has been separated
from the total scattering SAXS curves by using the Stuhrmann equation (3.20) [98]. Figure
5.28 shows the resonant curves calculated by the Stuhrmann equation at the Fe edge for the
samples annealed at 550°C for 60 and 180min fitted with spherical core shell model, resonant
curve for sample treated for 40min was very noisy, so it was excluded. Spherical core shell fit
reveals the presence of iron in both in the particle and the surrounding shell. From these
resonant curves, by evaluating the resonant invariant, the number density of Fe atoms in the
respective formed particles was calculated by using equation (3.21) [99]. ASAXS data
analysis in Table 5.6 reveals that concentration of Fe atoms in core increases up to 80% with
the annealing time, which is comparable to the concentration of Fe atoms calculated by
resonant curves.
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
70
0.1 1
0.01
0.1
1
10
100
1000
q (nm-1)
60min
180min
Fit
Spherical
core shell model
Figure 5.28: Resonant curves for the Fe edge ASAXS calculated by Stuhrmann method and
fitted with spherical core shell model
5.7 Kinetics of phase formation as studied in situ
Up to now all investigations to resolve the core-shell like structure of the magnetic
nanocrystals as well as their compositions were done at three samples annealed at 550°C for
40, 60 and 180min. In this chapter the kinetics of phase formation and its growth should be
investigated in more detail by using in situ SAXS measurements.
The experiments were done under vacuum conditions (10-3mbar) using a small furnace on
top of a sample changer with the reference samples (Figure 5.29). The ceramics samples are
mounted in a metal frame (Figure 5.29) that is fixed in a copper frame direct attached to the
ceramic heater for a good thermal contact and for fast temperature setup times. Moreover, at
least three thermocouples are used to control the temperatures.
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
71
Figure5 29: Picture of the furnace used for the insitu SAXS measurements installed on top of
a sample changer with the reference samples. During the experiment the chamber is under
vacuum conditions.
SAXS measurements were done at 12keV at the longest sample to detector distance
possible for the instrument at 3850mm, to measure the low q range. A single exposure took
two minutes. Empty beam and standard samples were measured in between the sample
measurements for subtracting the background from the measured curves and for calibrating
them to differential scattering cross sections.
0.1 1
10
100
1000
q (nm-1)
(a)
600°C (580min)
Start
0.1 1
10
100
1000
Start
q (nm-1)
640°C (210min)
(b)
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
72
0.1 1
10
100
1000
q (nm-1)
680°C (160min)
(c)
Start
Figure 5.30: In situ SAXS curves measured at different temperatures (a) 600°C, (b) 640°C,
(c) 680°C. Just after reaching the final temperature the first measurement was done and
marked with “start”. While annealing the scattering cross section increases at all q-values
and the final annealing time is marked.
Three in situ experiments at temperatures of 600°C, 640°C and 680°C were done. All
scattering curves at all three temperatures are increasing monotonically during annealing, as
shown in Figures 5.30 (a-c). Because the curves are measured equidistantly in time it can be
seen that the intensity increase slows down after a certain annealing time. That means a
growth stop or slowing down appears. The time after that the last curve is measured is
indicated in the Figures 5.30. From that it is also evident that the growth rate increases with
the annealing temperature. The observed growth stop appears earlier in case of higher
temperatures. Furthermore, if one compares the shape, especially of the long annealed
scattering curves, between the different temperatures, than it can be seen that these curves are
more straight at higher temperature. This reveals larger particles at higher temperature are
appearing. These qualitative findings can be summarized as follows: The higher the
temperature the faster is the nanoparticle growth process, the earlier the growth stops and the
particles are larger.
To determine the structural information from the curves, out of all the three measured
temperature curves, the sample measured at 640°C was chosen, and further fitted with the
SASfit software. Following the results from SANS and ASAXS it is evident that particles
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
73
with a shell region must be formed. This could be proved. Therefore, all curves could be fitted
by exact this structural model. The quality of the resulting fit can be seen in Figure 5.31 at
scattering curves chosen with an annealing time difference of ten minutes.
0,1 1
10
100
1000
10000
180 min
150 min
120 min
100 min
80 min
70 min
60min
50 min
40 min
30 min
20 min
10 min
Fit
q (nm-1)
Temperature = 640°C
Figure 5.31: Fitted insitu SAXS measurement at 640°C for variable time period from 0-180
minutes.
From the fit, one can determine the structural parameters as, size of the particles (core),
thicknesses of the shell region and the particle number. Figure 5.32 (a) shows the variation of
the particle (core) radius with the annealing time from 10 to 180min at the annealing
temperature of 640°C. It can be identified an increasing sizes with time. From about 30 to 100
minutes, the sizes are increase with about (t1/2) and after that with about (t1/3).
The variation of the shell thickness with the annealing time is shown in the Figure 5.32
(b). The Figure shows a growth of the shell thickness with the annealing time. Figure 5.32 (c)
shows the variation of the particle number with the annealing time, which shows that the
number of particles decreases with the annealing time. These findings are not typical for a
diffusion limited growth process or for an Ostwald ripening process. And will give raise for
further studies.
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
74
10 100
1
10 m=0.27
radius of particles (core)
linear Fit
t (min)
(a)
m=0.53
10 100
1
t (min)
shell thickness
linear fit
(b)
10 100
0.1
1
particle number
linear fit
t (min)
(c)
Figure 5.32: Fitted parameters for the insitu SAXS measurement at 640°C for
variable time period from 0-180 minutes (a) Particle (b) Shell (c) Number of particles.
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
75
5.8 Discussion of the formation of magnetic nanoparticles
The task is to clarify the structure of the formed magnetic nanocrystals in glass ceramics.
Previous studies resulted that a mixed phase containing Fe-Mn oxide is formed [9].
Microscopy results show the formation of spherical particles of sizes between 10-50nm. But
to clarify the whole structure and composition we applied XRD, SAXS, SANS with polarized
neutrons and ASAXS techniques.
XRD investigation reveals the formation of a MnxFe3-xO4 phase, which is a mixed phase
of Fe and Mn oxide. Particle sizes about 10-30nm are evaluated by XRD peaks analysis. But
XRD investigation unsolved the exact crystals compositions and it is not clear if the crystals
compositions will change with annealing time. SAXS investigation reveals that there is
already a presence of very small particles in the as prepared state and with the annealing time,
the size of the particle increases. Since the SAXS scattering curves for annealed sample were
fitted with both spherical core shell and two sphere models, it is not possible to distinguish
between both the models.
SANS investigations with polarized neutrons on the studied samples, show that the
particles are magnetic and surrounded by a nonmagnetic shell like region. This result proved
the formation of spherical core shell type on nanoparticles. Furthermore, the radii of the
magnetic nanoparticles are smaller than the actual radii of nanoparticles as evaluated by
nuclear scattering data; this reveals the presence of a small magnetic deadlayer in all the
annealed samples. The existence of such kind of nonmagnetic layer was already observed in
other glass ceramics [96]. Also the particles are growing with the annealing time for a
particular temperature as shown in Table 5.4. Particle sizes and shell thickness evaluated for
samples annealed at 550°C from SANS are comparable with the sizes calculated by SAXS
investigations.
ASAXS measurements show a larger anomalous effect at the Fe edge than the Mn, which
reveals the amount of Fe atoms in the particles are higher than the Mn atoms. For ASAXS
data analysis a spherical core shell model was taken from SANS investigation. Quantitative
information evaluated by ASAXS investigation reveals that the particles contain excessive
amount of Fe atoms (up to 80%) for the sample annealed for longer time. The amount of Fe
atoms in the particle computed from the resonant curves (at Fe edge) and by fitting the
ASAXS curves are comparable to each other. Evaluated density 2.22 0.05g/cm3 of shell
reveals that the particles are surrounded by a thin layer, which is dominated by lighter
elements of the glass composition. The evaluated density of shell is close to the bulk density
5. Crystallization of magnetic MnxFe3xO4 nanocrystals in silicate glass
76
of SiO2 (2.2g/cm3) which provide a direct hint for the enrichment of shell with SiO2. The
particles also have a high volume fraction and it is increases with the annealing time.
Furthermore, ASAXS data analysis results in Table 5.7 shows the phase (MnxFe3-xO4) formed
at core, amount of SiO2 in shell and the remaining composition left as a glass matrix. The
evaluated composition reveals increase in the amount of Fe atoms along with the Mn atoms
and the amount of SiO2 in shell with the annealing time.
It has previously been shown that different preparation conditions of MnFe2O4 may lead
to partial oxidation of manganese or iron ions which can lead to a different distribution of Mn
and Fe cations in the crystalline structure. In silicate glasses, ionic motion is the dominant
diffusion phenomenon. During the crystallization of MnxFe3-xO4 particles and subsequent
crystal growth, the melt near the core is depleted in Fe and Mn, hence formed a shell enriched
in Si and other glass components. This may leads to an increase in viscosity near the core and
to the formation of a diffusion barrier, which can hinders further diffusion of Fe and Mn to
core. With increasing annealing time, this layer becomes thicker (see Table 5.2) and the
growth process is decelerated. Such type of growth has already been reported earlier during
the precipitation of fluorides [100] or quartz from silicate glass [101,102]. As seen from the
evaluated composition, with increasing annealing time, i.e. with the growth of the core, Fe is
replaced by Mn. Presumably; pure Jacobsite (MnFe2O4) will be obtained at longer annealing.
This means that the particles are nucleate more like magnetite and then with annealing time
Fe atoms are replaced by Mn and the growth continues with larger flux of Mn atoms. It can be
associated with the smaller size of the Mn atoms, so that they go easier through the diffusion
barrier of SiO2 like shell.
Furthermore, in situ investigations showing growth process that cannot be explained by
classical growth theories and it will be a task for further investigations.
77
6. BaF2 nanocrystals formation in transparent glass ceramics
6.1 Motivation
Nanoglass ceramics composed of a glassy host matrix and optically active nanocrystals play a
growing role for various optical applications. In the past few decades, a revolution in optics
has been emerged by the invention of a wide variety of lasers, having broad range of power,
operating wavelength and beam characteristics [103,104]. These properties of lasers creates a
broad range of applications, including fiber optic communications, navigation, medicine,
nuclear waste fundamental studies of matter and many other fields [105,106]. Glass-ceramics
containing rare-earth-doped metal fluoride or alkaline earth fluorides (BaF2, CaF2, PbF2,
LaF2) nanocrystals of sizes from 5 and 100nm posses a huge potential application in fiber
optics and photonics, due to their significantly enhanced fluorescence, luminescence and
upconversion [107-111].
Mainly, metal fluoride nanocrystals containing glass ceramics are transparent and various
factors affect the transparency and other properties of the glass ceramics such as crystallite
sizes and their size distributions in the matrix and also the difference between the refractive
index of the crystals and the glassy phase. An overall explanation for the formation of nano
crystals is still difficult to evaluate [112]. Recently, narrower experimental size distributions
were observed in glasses with specific compositions containing BaF2 or CaF2 [10,113]. This
was explained by the formation of a diffusion barrier around the crystals during their growth
[11]. During nucleation and subsequent growth of the barium fluoride crystals a fluoride and
barium depleted, i.e. silica-enriched, layer is formed. This leads to an increased viscosity and
a core-shell like structure is developed which acts as a diffusion barrier and limiting further
crystal growth. A homogeneous dispersion of the crystals in the glassy matrix and a narrow
crystal size distribution is the consequence [10]. Previously, an experimental evidence of such
a silica enriched shell surrounding BaF2 nanocrystals in glass ceramics was shown by using
energy filtering transmission electron microscopy (EFTEM) and electron energy-loss
spectrometry (EELS) spot analysis [12]. This qualitative information needs to be quantified;
therefore the aim of work is to gain mechanistic insight. We apply ASAXS technique for
quantitative analysis of the shell (sizes and composition) and of the distribution of the
nanocrystals.
6. BaF2 nanocrystals formations in transparent glass ceramics
78
6.2 Glass preparation
Glass ceramic samples were prepared by using reagent grade raw materials Na2CO3, K2CO3,
BaF2, Al (OH)3 and SiO2 (quartz). The glass preparation was done by our cooperation
partners at the university Jena. Glass batches of 200g were prepared in a platinum crucible
which was covered in order to avoid strong fluoride evaporation. The crucible was placed in a
furnace and heated to 1590°C kept for 1.5h. Then the melt was cast on a copper block and
subsequently placed into a furnace at 450°C. The glass transition temperature Tg for these
glasses is 549°C. In order to relax thermal stresses, the cooling furnace was switched off and
the glasses were cooled down to room temperature. For a better homogeneity, the glasses
were re-melted in an inductive furnace at 1500°C and stirred for 20min. In a second step, the
glasses were crystallized in a one step annealing process at temperatures in the range from
500 to 700°C for 2 to 20h. The already crystallized glass samples are visually transparent as
shown in Figure 6.1.
Figure 6.1: Transparent BaF2 nanocrystal containing glass ceramics [10].
The remaining fluorine concentration in later glasses was determined by a wet-chemical
analysis method [114]. X-ray fluorescence and energy-dispersive X-ray spectrometry in a
scanning electron microscope results, a mean value of 66 ± 3% of the fluorine remains in the
glass which leads to a nominal mol% composition of sample 69.6SiO2-15.0K2O-7.5Al2O3-
1.9Na2O-4BaF2-2BaO. The composition for the samples as prepared and after analysis is
shown in Table 6.1. The density of the bulk glass samples are 2.603 ± 0.001g/cm3, which was
measured by a helium pycnometer (AccuPyc 1330). Structural behavior and composition of
nanoparticles in the glass samples were studied by SAXS and ASAXS. The thicknesses of the
samples are about 30-50µm, which is suitable to achieve optimal X-ray transmission for the
SAXS and ASAXS measurements.
6. BaF2 nanocrystals formations in transparent glass ceramics
79
Table 6.1 Composition of the glass ceramics as synthesis and as analyzed.
Element Weight (%)
Synthesis
Mol (%)
Synthesis
Weight (%)
Analyzed
Mol (%)
Analyzed
Al 5.4 4.8 5.4 4.8
K 15.6 9.5 15.6 9.5
Na 1.2 1.2 1.2 1.2
Si 26.0 22.1 26.0 22.0
Ba 10.9 1.9 10.9 1.9
F 3.0 3.8 2.0 2.5
O 37.9 56.7 39.0 58.1
6.3 Sample Characterization
To investigate the crystalline phase and structure of the nanoparticles in the glass matrix,
various characterizing techniques were already applied on the studied samples such as TEM
and XRD. It is already reported that definite annealing of these glasses leads to a formation of
BaF2 nano crystals which are dispersed very homogeneously in the glassy matrix with a
narrow crystallite size distribution [10]. These samples are pre-characterized by transmission
electron microscopy (TEM). Figure 6.2 shows the dark field TEM image of the glass ceramics
sample annealed at 540°C for 20h [10]. The contrast between the bright crystals and the light
gray background for the amorphous matrix is clearly visible in the image. The TEM image
shows the formation of almost spherical shaped particles. Further investigation of the image
reveals the presence of 252 crystallites with a mean crystallite size of 9 ± 2nm. The dark field
TEM image of a sample annealed at 600°C for 20h is shown in Figure 6.3. It is clearly seen
from the image that there is a formation of bigger crystals for the sample annealed at 600°C
than the sample annealed at 540°C. The size distribution analysis of that sample shows the
crystallites with the mean size of 15 ± 2nm.
6. BaF2 nanocrystals formations in transparent glass ceramics
80
Figure 6.2: Dark field TEM image of the sample annealed at 540°C for 20h [10].
Figure 6.3: Dark field TEM image of the sample annealed at 600°C for 20h [10].
For the sample annealed at 700°C, a TEM micrograph was obtained as shown in Figure
6.4. It shows dark appearing BaF2 crystals in a grey glassy matrix. Due to the low contrast, a
reliable size distribution was not computed. However, it can be seen from the image that most
crystals are in the range from 50 to 70nm in diameter with a few crystals larger than 100nm.
Microscopic measurements and investigations show the growth of the crystallites with the
6. BaF2 nanocrystals formations in transparent glass ceramics
81
annealing temperature. Such type of microscopic investigations provides information only
about the size, shape and distribution of particles in the host matrix, but they do not provide
any information about the phase (crystalline or amorphous) of the particles. However, in order
to determine the phases of the particles, one option is to use the TEM measurements in the
diffraction mode and other option is to perform X-ray diffraction measurements.
Figure 6.4 TEM image of BaF2 particles for the sample heat treated at 700°C for 2h.
To determine the phase of the crystalline particles, XRD experiments are performed on
the samples. For recording the X-ray diffraction patterns, diffractometer Siemens D 5000
using a CuK (wavelength = 0.154nm) radiation source and an energy-dispersive SolX
detector was used. Figure 6.5 shows the XRD measurement of the as prepared and heat
treated samples [10]. Figure shows that, for as prepared sample there are no visible peaks or
distinct maxima is observed except the broadness around 27° due to the silica. For the
samples heat treated at different temperatures clearly shows the visible peaks around 25°, 28°,
42° and 48° which attributed to the crystalline BaF2 (JCPDS Nr. 4-452) phase. The sample
heat treated at 540°C for 20h shows the broadened peaks and lower intensity as compare to
the sample heat treated for 600°C and 700°C. The full width at half maxima (FWHM) of the
peaks decreases with increasing annealing temperature, which reveals the growth of particles.
From the peak broadening, the mean crystallite size was evaluated by using Debye Scherrer
equations (6.1) by using the values for shape factor K= 0.89 for cubic crystals, and the X-ray
6. BaF2 nanocrystals formations in transparent glass ceramics
82
wavelength of 0.154nm (Cu K radiation). The mean crystallite sizes of samples as calculated
by Scherrer equation were 10.8 ± 1nm and 12.5 ± 1nm for the samples annealed at 540°C and
600°C for 20h, respectively. The sample annealed at 700°C for 2h showed a mean crystal size
of 37.6 ± 4nm. By XRD technique it is possible to determine the information about the
crystalline phase and mean crystallite sizes, but by XRD it is not possible to get any
information about possible amorphous phases in the studied glass ceramics. Since XRD and
microscopy measurements are not sufficient to provide the complete information about the
structure and composition, SAXS and anomalous SAXS (ASAXS) experiments will be
performed in the frame of this work.
Figure 6.5: XRD-patterns of sample annealed at various temperatures and times. The peaks
marked by blue line are all attributed to cubic BaF2 crystals (JCPDS Nr. 4-452) [10].
Earlier, by applying energy filtering transmission electron microscopy (EFTEM) and
electron energy-loss spectrometry (EELS) spot analysis techniques on these samples provide
evidence for the formation of core shell like nanostructures, where the shell region is enriched
with silica and the core region is of BaF2 nanocrystals [12]. In order to summarize these pre-
investigations, it has to be pointed out that a formation of BaF2 takes place and a SiO2
enriched shell region could be revealed. This shell region seems to hinder the diffusion and
increases the viscosity. The aim of my SAXS and ASAXS investigations is a direct structural
evidence of these findings of a core shell structure and a quantitative analysis of nanostructure
and compositions.
6. BaF2 nanocrystals formations in transparent glass ceramics
83
6.4 SAXS Results
In order to investigate the effect of heat treatment on the shape, size, volume fraction and
distribution of particles in the glass matrix, the samples were studied by SAXS and the
composition of the particles will be determine by analysing the ASAXS curves. For the SAXS
measurements at BESSY II, X-ray energy of 4900eV which is sufficiently below the Ba L3 X-
ray absorption edge (5247eV) was used. The samples were measured under vacuum
conditions (10-3mbar) conditions to reduce air scattering. The samples were measured at both
long and short distance of the detector, in order to achieve wide q range. Figure 6.6 show
SAXS curves calibrated to differential scattering cross sections for as prepared and annealed
samples at various temperatures and time scales. As seen from the Figure the as prepared
sample show a small hump at q=0.8nm-1, which refers to the presence of small particles. In
Figure 6.6 slope of the scattering curve for as prepared sample approached a q-4 behavior at
lower q values, which implies for the smooth surface of the particles.
0.01 0.1 1
0.1
1
10
100
1000
10000
q (nm-1)
As Prepared
540°C_20h
600°C_20h
700°C_2h
q-4
Figure 6.6: SAXS curves measured at 4900eV for the as prepared and annealed samples at
7TMPW SAXS beamline BESSY II.
The shoulder in the SAXS curves for the heat treated sample at 540°C and 600°C were
shifted towards the lower q values which indicates an increase in the size of particles with the
annealing temperature. The sample annealed for 700°C for 2h shows a higher intensity which
6. BaF2 nanocrystals formations in transparent glass ceramics
84
is due to the larger size of the particles as compared to the other three samples. In order to
extract the structural information from the scattering curves. The curves were further
processed by fitting them using the SASfit program [62]. On the basis of pre-investigations in
section 6.3 a core shell structure has to be assumed. For fitting, spherical core-shell model and
on the basis of TEM analysis a Gaussian distribution for the particles has to be taken into
account [10]. Table 6.2 shows the parameters obtained after fitting of the SAXS curves for the
annealed samples. Structural parameters reveal that the size of the particles increases with the
annealing temperature. Furthermore, the thickness of the layer decreases notably with
increasing temperature.
Table 6.2:.Parameters for the SAXS measurement assuming a Gauss distribution of particles
for the samples annealed at 540°C and 600°C for 20h and 700°C for 2h.
Parameters 540°C 20h 600°C 20h 700°C 2h
Radius Particle (nm) 4.75 ± 0.5 5.20 ± 0.5 24.2 ± 1.0
Shell Thickness (nm) 2.35 ± 0.1 2.13 ± 0.1 1.82 ± 0.1
Figure 6.7 shows the comparison of the size parameters evaluated by XRD and SAXS.
The mean crystallite sizes calculated by XRD are in good agreement with the mean sizes
calculated after fitting of SAXS curves for the samples annealed at 540 and 600°C, while the
sample annealed at 700°C shows the larger size as compare to XRD. As prepared glass
samples contains already particles of very small size of 3nm with a narrow size distribution.
This is a new result that could not be determined by XRD measurements.
540_20h 600_20h 700_2h
10
20
30
40
50
Samples
SAXS
XRD
Figure 6.7: Comparison of the average diameter from SAXS and the XRD size parameter
given by Scherrer equation.
6. BaF2 nanocrystals formations in transparent glass ceramics
85
The core structure for the samples annealed at 540°C and 600°C have nearly the same
shaped size distributions as shown in Figure 6.8 (a) with maxima at 4.7 and 5.5nm,
respectively. The sample treated at 700°C for 2h shows a remarkable larger size as shown in
Figure 6.8 (b). From the SAXS measurements alone it is not possible to evaluate the
composition of the shell surrounding the nanoparticles. ASAXS experiment in the next
section provides the possibility to validate the composition of the nanocrystals and to
investigate the composition of the shell surrounding the particles.
0 2 4 6 8
0.0
0.2
0.4
0.6
0.8
As prepared
540°C_20h
600°C_20h
Particle Radius (nm)
(a)
0 20 40 60
0.00
0.03
0.06
0.09
0.12
0.15
0.18
Gauss
Particle Radius (nm)
700°C_2h
(b)
Figure 6.8: Size distributions of the particles obtained after fitting of the SAXS curves.(a)
Gauss distribution for the as prepared and two heat treated sample at 540 and 600°C for 20h.
(b)Gauss distribution of the sample heat treated at 700°C for 2h.
6. BaF2 nanocrystals formations in transparent glass ceramics
86
6.5 ASAXS studies
Figure 6.9 shows the variation of the atomic scattering amplitude for the Ba L3 X-ray
absorption edge (5247eV). For ASAXS measurement four different energies were chosen
near L3 X-ray absorption edge of Barium. The arrows in Figure 6.9 shows the energies used
for the ASAXS measurement. The scattering curves were corrected and finally obtained the
differential scattering cross sections as a function of the magnitude of the scattering vector q.
4400 4600 4800 5000 5200 5400
-20
-15
-10
-5
0
5
10
Energy (eV)
f'
f''
4900eV
5177eV
5234eV
5244eV
Barium
Figure 6.9: Atomic scattering amplitude of Ba atoms at the Ba L3 absorption edge (5247eV)
and the X-ray energies used for the measurement.
Figure 6.10 shows the ASAXS curves measured at four energies for the sample annealed
at 600°C for 20h. A large variation (decrease) of the scattered intensity at the lower q values
while as moving towards the energy close to X-ray absorption edge, while for the higher q
region at the energy close to absorption edge varies in the upward direction, which is due to
the upcoming resonant Raman scattering. Also all the other samples show significant ASAXS
effects near the Ba absorption edge including the as prepared sample.
6. BaF2 nanocrystals formations in transparent glass ceramics
87
0.1 1
0.1
1
10
100
q (nm-1)
4900eV
5177eV
5234eV
5244eV
Figure 6.10: ASAXS curves measured at four different energies near the absorption edge of
Ba for the sample annealed at 600°C for 20h
In order to extract information from the ASAXS curves, each set of curves were fitted by
SASfit program. While fitting all the structural determining parameters such as particle
number, and the size distributions are kept constant and only the contrast between the
particles with respect to the matrix varies as a free variable. The three samples annealed at
different temperature and times were fitted by assuming the spherical core shell model with
the Gauss distribution of particles. Figure 6.11 (a) shows fitted curves of the sample heat
treated at 540°C for 20h that model the measurement in a very good quality. Form the fitting
procedure; one can obtain four different values of experimental contrasts for the core of
particles. To calculate the composition and density of the phases (shell and matrix), the
experimental contrasts values were further fitted with the theoretically calculated contrast as
discussed in section 3.4. During the distribution of atoms in core, shell and matrix, the total
number of atoms for each element was conserved. During fitting we had assumed the bulk
density of BaF2 (4.89g/cm3), since there is no shifting of the peaks positions in XRD
investigations.
6. BaF2 nanocrystals formations in transparent glass ceramics
88
0.1 1
0.1
1
10
100
q (nm-1)
4900eV
5177eV
5234eV
5244eV
Fit
(a)
4900 5000 5100 5200
0.4
0.6
0.8
1.0
Energy (eV)
Exp.Core
Theo. Core
(b)
Figure 6.11: (a)ASAXS fitted curves measured at four energies near the absorption edge of
the Ba (5247 eV) for the samples 550°C 20 h. (b) Comparison of the experimental and
theoretical relative contrast variation.
Figure 6.11(b) show the comparison of the theoretically calculated and experimentally
evaluated relative contrast of the sample annealed at 540°C for 20h. Table 6.3 shows the
parameters obtain after fitting routines for all the three samples. The respective parameters
lead to a density of layer and matrix of around 2.2 ± 0.1g/cm3 and 2.55 ± 0.03g/cm3,
6. BaF2 nanocrystals formations in transparent glass ceramics
89
respectively. Parameters show that the particle volume fraction increases from 0.025 to 0.044
with the annealing temperature.
Table 6.3:.Resulting parameters for a SAXS as well as ASAXS curves assuming the Gauss
distribution of particles for the samples annealed at 540 and 600°C for 20h and 700°C for 2h.
Parameters 540°C 20h 600°C 20h 700°C 2h
Radius Particle (nm) 4.75 ± 0.5 5.20 ± 0.5 24.18 ± 1.0
Shell Thickness (nm) 2.35 ± 0.1 2.13 ± 0.1 1.82 ± 0.1
Density Core (g/cm3) 4.89 4.89 4.89
Density Shell (g/cm3) 2.20 ± 0.1 2.35 ± 0.1 2.2 ± 0.1
Density Matrix (g/cm3) 2.55 ± 0.03 2.58 ± 0.03 2.50± 0.03
Volume fraction particle 0.025 0.032 0.044
Volume Fraction Shell 0.049 0.045 0.01
Volume Fraction Matrix 0.926 0.923 0.946
Table 6.3 shows the composition evaluated after fitting experimental contrast with the
theoretical contrast for all the annealed samples. Composition shows that the layer surround
the core (BaF2) is enriched with low density SiO2 and with other glass components in fewer
amounts. After the formation of core and shell, remaining glass components forms the matrix
composition.
Table 6.4: Composition calculated from ASAXS for the samples annealed at 540°C, 600°C for
20 h and 700°C for 2h.
Sample Particle Shella Remaining matrix Composition
540°C_20h BaF2 SiO2 (91%) 69.71SiO2-16.15K2O-7.99Al2O3-2.03Na2O-2.03BaF2-2.1BaO
600°C_20h BaF2 SiO2 (89%) 70.37SiO2-16.10K2O-7.93Al2O3-2.02Na2O-1.47BaF2-2.11BaO
700°C_2h BaF2 SiO2 (76%) 72.02SiO2-15.69K2O-7.84Al2O3-1.97Na2O- 0.40BaF2-2.08BaO
a SiO2+(Ba,Na,Al,O,K)
From the ASAXS curves one can also evaluate the distribution of particular element in
the system by Stuhrmann equation (3.20). By using this method pure resonant scattering
contribution due to the distribution of Ba atoms in the samples annealed at different time and
temperature has been separated from the total scattering SAXS curves.
6. BaF2 nanocrystals formations in transparent glass ceramics
90
Figure 6.12 shows the resonant curves fitted with the sphere model for the samples
annealed at 540 to 700°C evaluated by using equation (3.20). From the resonant curves, the
number density of the resonant atoms was calculated by equation (3.21). The number of Ba
atoms in the crystalline phase was found for the sample annealed at 600°C is about 48% of
the total Ba atoms in the system. The comparison of the atomic fraction of Ba atoms in
nanoparticles calculated by ASAXS and the resonant curves are shown in Figure 6.13.
0.1 1
1E-5
1E-4
1E-3
0.01
0.1
1
10
100
540°C_20h
600°C_20h
700°C_2h
fit
Sphere model
q (nm-1)
Figure 6.12: Resonant scattering curves for Barium calculated by the Stuhrmann method and
fitted with sphere model.
540°C_20h 600°C_20h 700°C_2h
0.0
0.2
0.4
0.6
0.8
Sample
Composition
Resonant Curve
Figure 6.13 Comparison of the atomic fraction of Ba atoms in nanoparticles calculated by
resonant curve and from the composition calculated from the ASAXS curves.
6. BaF2 nanocrystals formations in transparent glass ceramics
91
The scattering intensity of as prepared sample is rather small due to very small particle
size of 3nm as shown in Figure 6.6. Since both the sphere and spherical core shell model fits
to the scattering curves, it is not sure whether a shell region is formed around the particles
during glass preparations. ASAXS investigations on the sample shows noticeable contrast
variation near the Ba absorption edge, which give an evidence for the presence of particles
enriched with Barium. Figure 6.14 (a) and (b) show fitted ASAXS curves for both the
spherical and spherical core shell models for the as prepared sample. Furthermore, it is not
clear whether these particles are crystalline or amorphous, because these particles are not
observed by XRD and TEM investigations. The particles region might be formed due to
bonding between Ba and F atoms, but yet they are not crystalline as reported by NMR
investigations [115].
0.1 1
0.1
1
10 4900eV
5177eV
5234eV
5244eV
Fit
q (nm-1)
Sphere model
(a)
0.1 1
0.1
1
10 4900eV
5177eV
5234eV
5244eV
Fit
q (nm-1)
Spherical core shell
(b)
Figure 6.14: ASAXS fitted curves measured at four energies near the L3 absorption edge of
the Ba (5247eV) for the as prepared.(a) Fit the sphere model (b) Spherical Core shell model.
6. BaF2 nanocrystals formations in transparent glass ceramics
92
6.6 Discussion of the structure model of BaF2
It was reported in refs. [10,116,117] that in a silicate glass of composition 69.6SiO2-7.5Al2O3-
15.0K2O-1.9Na2O-4BaF2-2BaO containing BaF2 nanoparticles are growing and, a SiO2
enriched layer around the nanoparticles might be formed. This layer hinders further diffusion
of Ba ions towards the particles and hence acts as a diffusion barrier, which inhibits further
growth of crystals. Also an increase of the glass viscosity is reported.
ASAXS measurements at the Ba L3 absorption edge provide information on the
distribution of Ba atoms in the studied glass ceramics. The observed contrast variation is
caused only due to the resonant Ba atoms. ASAXS measurements on the as prepared glass
sample show already a prominent contrast variation close to the Ba edge, which provides a
direct evidence for the formation of very small (3nm) Ba enriched particles or regions during
melting and quenching the glasses. However, it cannot be said whether these particles are
crystalline or amorphous. According to the NMR results it is more likely that these “particles”
are due to regions where Ba is bonded with F but they are not yet crystalline [115]. As both
spherical and spherical core shell models fits to ASAXS curves, yet it is not confirmed
whether these particles were of spherical shape or the particles were already surrounded by a
layer enriched in other components. These particles also have a very low volume fraction
(<0.5 %).
The samples annealed at various temperatures and times, also show prominent ASAXS
effect close to the Ba absorption edge and their scattering intensity is dramatically increased
in comparison to the as prepared samples. Table 6.2 shows the parameters obtained after
fitting the ASAXS curves with spherical core shell model for all heat treated samples. The
parameters show that there is not much difference in the particle sizes (8-12nm) of samples
annealed at 540 and 600°C. The particles in these samples are surrounded by a rather thick
layer (2.35 - 2.13nm). Later on, for the sample annealed at 700°C, the crystals are larger
(44nm) and surrounded by a rather thin layer (1.8nm). The density of the shell calculated by
fitting the experimental contrasts is close to the density of amorphous SiO2 (between 2.0 to
2.2g/cm3) which provides a further hint of the presence of SiO2 enriched layer.
Table 6.3 shows the composition of the particles, the layer and the matrix evaluated after
fitting the experimental contrasts. The calculation reveals the formation of BaF2 particles and
the layer surrounds the particles is predominantly composed of SiO2. The formation of
particles surrounded by the layer (shell) revealed from the ASAXS curves analysis could be
explained as; during annealing, nuclei are formed and start to grow, but due to large
6. BaF2 nanocrystals formations in transparent glass ceramics
93
differences in the diffusion coefficients of Ba and F ions (approximately two orders of
magnitudes), the Ba ions diffuse slower than F ions [118,119]. Meanwhile, because of the
formation of the crystals, the other components of the glass are enriched near the crystals.
However, near the interface of crystal and matrix there will be a depletion layer of the crystal
forming components Ba and F which leads to a rise in viscosity. This layer acts as a barrier
for further diffusion of Ba and F ions towards the crystals. Due to this barrier, in the
temperature range of 540 to 600°C, the particles grow slowly and do not exceed a certain
sizes. But at higher temperatures (700°C) and increased diffusion rates this layer starts to
dissolve in the matrix and becomes less important for the hindrance of the diffusion of ions.
This results in a decrease of the shell thickness and in an increase in the size of particles. An
increase in the volume fraction of the crystals with temperature resembles the growth of the
particles. A Figure 6.13 show a bar chart of the percentage of Ba atoms presents in the core
region as a crystalline BaF2 phase and illustrates an increase of this percentage with the
annealing temperature.
ASAXS technique does not only provide qualitative information, but also it gives
quantitative information on the distribution of particular resonant atoms in the system. The
extraction of the resonant curve of particular atoms from the SAXS curves shows that the Ba
atoms are dominant in the particles. The atomic fraction of Ba atoms in the nanoparticles,
calculated by using equation (3.21), shows that 30-60% of the Ba atoms are incorporated into
the crystals, which is in agreement with the composition as calculated by ASAXS.
95
7. Summary and Outlook
In this work, the structure and averaged chemical composition of two different glass ceramic
materials containing spherical core shell type nanocrystals were analyzed quantitatively by
using small angle scattering methods: small angle neutron scattering (SANS) and especially
the method of anomalous small angle X-ray scattering (ASAXS). The nanocrystals are formed
during controlled heat treatments in two different types of silicate based glass ceramics. The
common aspect of both ceramics is that the formation of a three phase system is occurring (a
nanocrystalline core, a silica shell and the glass matrix).
First, I investigated the structure of magnetic nanocrystals ranging from magnetite to
Jacobsite phases (generally composed of MnxFe3-xO4) in a silicate glass ceramics. XRD
investigations could only show the formation of MnxFe3-xO4 phases which appeared as a
mixed phase of Fe and Mn oxides. XRD gave no information about the Fe to Mn ratio.
Composition and structural information evaluated by ASAXS analysis reveals that during
crystallization a layer around the nanoparticles is formed. This layer is depleted in Fe and Mn
and becomes enriched with other glass components, mainly with Si and O. Moreover, the
amount of SiO2 increases in the layer with the annealing time. Depending on the viscosity of
the layer, a SiO2 enriched layer may acts as a diffusion barrier for further diffusion of Fe and
Mn ions towards the nanoparticle core. Therefore, the further crystal growth is kinetically
slowed down. Furthermore, ASAXS results show that the particles start to nucleate like
magnetite (Fe3O4). With an ongoing annealing time, Fe atoms are replaced by Mn in the
crystal and the phase changes towards the pure Jacobsite (MnFe2O4) phase due to the higher
diffusion of Mn into the nanoparticles. SANS investigations with polarized neutrons clearly
show that the particles are magnetic. However, they are surrounded with a thin magnetic dead
layer followed by a nonmagnetic SiO2 enriched shell region.
Second, I studied BaF2 nanocrystals precipitated in an optically transparent silicate glass
ceramics. Already during the preparation of glasses small Ba enriched particles of about 3nm
in diameter are formed. These particles give a pronounced ASAXS effect for the as prepared
samples. During further annealing, BaF2 nanocrystals grow in the glass matrix and a silicate
enriched layer is formed. Previous investigations on these glasses by energy filtered TEM
showed the formation of a SiO2 layer, which hinders the further growth of the BaF2 particles.
Quantitative information about the structure and composition of the BaF2 nanoparticles
evaluated by ASAXS provides direct structural evidence for the formation of a SiO2 enriched
layer. This layer is formed during the crystallization of the particles and has a lower density
7. Summary and Outlook
96
(2.2g/cm3) than the host glass matrix (2.603g/cm3). Furthermore, for annealing temperatures
at 540°C and 600°C, a thick layer enriched with SiO2 is formed, which hinders the further
diffusion of Ba and F ions towards the particles. A further growth of these nanocrystals
(diameter about 12nm) is effectively inhibited. At a higher temperature of 700°C, the
diffusion rates increase and the layer begins to dissolve into the matrix. The layer becomes
less important for the hindrance of the diffusing ions (Ba and F). As a result, the shell
thickness decreases and the size of the BaF2 particles increase significantly (to about 50nm,
see Figure 6.7).
Outlook: kinetic studies
For both investigated systems, time and temperature dependent results on the growth of the
nanocrystals are derived in this thesis. It is known that a growth inhibition takes places in the
BaF2 crystallizing glass ceramics. In chapter 5.7, a similar process was found in case of the
magnetic glass ceramic. In situ SAXS and ASAXS investigations should be carried out in
order to study the crystallization kinetics in more detail and the role of structural development
of the diffusion barrier layers surrounding the nanocrystals. As known from in situ studies on
the immiscibility in oxide glasses the role of the atmosphere should also be studied.
Outlook: rare-earth-doped metal fluoride nanocrystals
It is known that rare-earth-doped metal fluoride nanocrystals feature enhanced fluorescence,
luminescence and up-conversion. Therefore, the formation of CaF2 nanocrystals should be
studied with respect to a formation of a SiO2 enriched diffusion barrier layer. This should be
compared to the results in this thesis. Moreover, the segregation process of the rare-earth
doped materials will be studied.
Outlook: theoretical studies: how ASAXS distinguishes between structural models
First theoretical calculations show that the SAXS method alone is not able to distinguish
between a mono-modal size distribution of core-shell structures and two different
distributions of spherical particles. This result is also revealed experimentally in my thesis.
The model calculations should be extended to the case of the contrast variation by ASAXS.
.
97
APPENDIX
A.1: List of samples of composition 13.6Na2O-62.9SiO2-8.5MnO-15.0Fe2O3-x (mol %). The
highlighted samples were used for the measurements using SAXS and ASAXS.
Serial No. Sample Name Thickness (m)
1 As prepared 210.2 0.9
2 540°C _180min 160.5 1.5
3 550°C _5min 184.4 4.5
4 550°C _10min 177.2 3.27
5 550°C _20min 142.75 0.24
6 550°C _40min 144.00 2.0
7 550°C _60min 123.00 1.87
8 550°C _120min 132.0 4.3
9 550°C _180min 138.00 8.15
11 560°C_20min 171.5 0.50
12 560°C_40min 163.25 5.36
13 560°C_60min 118.50 8.50
14 560°C_120min 170.50 9.39
15 560°C_180min 130.00 6.52
16 580°C_20min 157.00 1.73
17 580°C_40min 172.00 9.11
18 580°C_60min 170.00 10.56
19 580°C_180min 128.50 5.0
98
A.2: List of samples of composition 13.6Na2O-62.9SiO2-8.5MnO-15.0Fe2O3-x (mol %). The
highlighted samples were used for the measurements using SANS with polarized neutrons.
Serial No. Sample Name Thickness (m)
1 As prepared 827.8 5.31
2 540°C _180min 2175.2 15.97
3 550°C _5min 836.2 4.35
4 550°C _10min 843.6 4.08
5 550°C _20min 913.0 8.8
6 550°C _40min 803.8 8.13
7 550°C _60min 833.4 10
8 550°C _120min 2173.8 7.78
9 550°C _180min 861.8 4.49
11 560°C_20min 2225 11
12 560°C_40min 2076 23.26
13 560°C_60min 2106.2 23.68
14 560°C_120min 887 2.4
15 560°C_180min 2207.2 5.6
16 580°C_20min 2172.8 2.14
17 580°C_40min 2119.6 9.39
18 580°C_60min 2145.0 20.15
19 580°C_180min 756.4 26.3
99
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107
ABBREVIATIONS
ASAXS Anomalous Small Angle X-ray Scattering
BESSY II Berliner Elektronen Speichering für Synchrotronstrahlung II
CCD Charge Coupled Device
ILL Institute of Laue Langevin
7T-MPW-SAXS 7 Tesla Multipole Wiggler SAXS beamline
MWPC Multi Wire Proportional Counter
SANS Small Angle Neutron Scattering
SASREDTOOL Small Angle Scattering Reduction Tool
SAXS Small Angle X-ray scattering
TEM Transmission Electron Microscopy
WAXS Wide Angle X-ray Scattering
XAFS X-ray Absorption Fine Structure
XANES X-ray Absorption Near Edge Structure
XRD X-ray Diffraction
XRF X-ray Fluorescence analysis
109
PUBLICATIONS
1. Ruzha Harizanova, Ivailo Gugov, Christian Rüssel, Dragomir Tatchev, Vikram Singh
Raghuwanshi, Armin Hoell : Crystallization of (Fe, Mn) –based nanoparticles in
sodium –silicate glasses: Journal of Material Science 46 (2011) p 7169-7176. DOI:
10.1007/s10853-011-5840-x
2. Ruzha Harizanova Vikram Singh Raghuwanshi, Dragomir Tatchev, Ivailo Gugov,
Armin Hoell, Christian Rüssel: Synthesis and Phase composition of Fe/Mn containing
Nanocrystals in Glasses from the system Na2O/MnO/SiO22/Fe2O3: NATO Science for
peace and security series B: Physics and Biophysics, Nanotechnological Basis for
Advanced Sensors, Part 7 (2011),p 249-254. DOI: 10.1007/978-94-007-0903-4_28
3. Vikram Singh Raghuwanshi, Armin Hoell, Christian Bocker, Christian Rüssel:
Experimental evidence of a diffusion barrier around BaF2 nano crystals in a silicate
glass system by ASAXS: CrystEngComm (2012) (accepted). DOI: 10.1039/C2CE06544D
4. Vikram Singh Raghuwanshi, Dragomir Tatchev, Ruzha Harizanova , Sylvio Haas,
Armin Hoell, Ivailo Gugov, Christian Rüssel: Structural analysis of ferromagnetic
nanocrystals embedded in silicate glasses by ASAXS: Journal of Applied Crystallography
(2012) (accepted).
5. Vikram Singh Raghuwanshi, Dragomir Tatchev, Ruzha Harizanova , Sylvio Haas,
Armin Hoell, Ivailo Gugov, Christian Rüssel: Structural analysis of ferromagnetic
nanocrystals embedded in silicate glasses by SANS (in preparation)
6. Armin Hoell, Zoltan Varga, Vikram Singh Raghuwanshi, Christian Bocker, Christian
Rüssel: Characterization of CaF2 nanoparticles embedded in silicate glass matrix by
ASAXS. (in preparation)
111
ACKNOWLEDGEMENT
I am grateful to all peoples who help me in achieving my PhD work. I am grateful to my
supervisor Prof. Dr. John Banhart for his encouragement, guidance, and financial support
throughout this study.
I would like to express my great appreciation to my advisor Dr. Armin Hoell. I wish to
thank him for his valuable technical advice and supervision. His observations, comments and
incisive reviewing of my thesis helped me to establish the overall direction of the research and
to move forward with investigation in depth. I am grateful to him for always being kind and
patient with his suggestions and constantly forced me to remain focused on achieving my
goal. I also appreciated his open mind and confidence, allowing me to propose and develop
my own ideas.
I would like to express my deep sense of gratitude towards Prof. Dr. Christoph Genzel
for extending me the opportunity and for giving his precious time and continuous guidance to
accomplish the present work.
I am heartily thankful to Dr. Dragomir Tatchev, for providing advice, guidance and
encouragement, particularly during my work and his support from the initial to the final level
enabled me to develop an understanding of the subject. I am grateful to him for helping me
with the measurements and precious suggestions at crucial junctures during my thesis work.
I am heartily thankful to Dr. Sylvio Haas, whose encouragement, guidance and support
for the programming skills and helped me in doing the measurements. I am grateful to him for
always being kind and providing me valuable advice for improvement of my work.
Additionally, I am grateful to Dr. Ruzha Harizanova from Bulgaria and Dr. Christian
Bocker from Jena for their efforts in preparations of the samples and providing the sample at
the time of need. The valuable suggestions that I have received from them were indispensable
in the completion of the thesis.
I am heartily thankful to Dr. Rodrigo Coelho for helping me adjust to the life of a PhD
student in a new environment and atmosphere. The valuable suggestions that I have received
from him were indispensable in the completion of the thesis. Sincere thanks to him for his
encouraging remarks and positive attitude that always brought me back to a sensible mood
during hard times
Appreciation is extended to my colleagues at BESSY for sharing a stimulating and fun
environment in which to learn and grow was an unforgettable experience. Particular thanks go
to Dr. Manuela Klaus, Daniel Apel, Diana Thomas, Tillman Fuß, Matthias Meixner,
Acknowledgement
112
Shrawan and Tirupathai Setti. They were always available when I needed advice or just
someone to talk to, but most of all, I consider them cherished friends.
Special thanks to Klaus Efland for supporting me with the instrumentation of the
experimental ASAXS setup.
Also I would like to give thanks to the group from HMI (Wannse), mainly Manas,
Cynthia, Jatin, Amit, and Prashanth for providing me the friendly environment. I am
grateful to Dr. Pankaj & Archana Sagdeo, Ram Janay, Shilpa, Pravin Siwach, Parasmani,
Ram prakash, Sanjay, Sunil, Abhijeet, Anupam, Ashim, Kaustav, Tirtha, Swati, Trupti,
Zoltan, Karthick, Anil, Manoj for their moral support.
I would like to thank to my family supporting me spiritually throughout my life.
113
DECLARATION
I declare that, except where otherwise stated this PhD dissertation is the result of my own
work and includes nothing that is the outcome of others. No part of this dissertation has
submitted at Technical University Berlin or any other University for a degree or diploma or
other qualifications.
Ich erkläre an Eides Statt, dass die vorliegende Dissertation in allen Teilen von mir
selbständig angefertigt wurde und die benutzen Hilfsmittel vollständig angegeben worden
sind. Weiter erkläre ich, daß ich nicht schon anderweitig einmal die Promotionsabsicht
angemeldet oder ein Promotionser öffnungsverfahren beantragt habe.
Date: 29.02.2012
Place: Berlin, Germany (Vikram Singh Raghuwanshi)
