Stability of incommensurately modulated Ni50Mn27Ga22Fe1 10M martensite under uniaxial tensile stress

Sc ip a Ma e ialia 247 (2024) 116096 A ailable online 30 Ma ch 2024 1359-6462/© 2024 The Au ho (s). Published by Else ie L d on behal o Ac a Ma e ialia Inc. This is an open access a icle unde he CC BY license (h p://c ea i ecommons.o g/licenses/by/4.0/). S abili y o incommensu a ely modula ed Ni 50 Mn 27 Ga 22 Fe 1 10M ma ensi e unde uniaxial ensile s ess M. Vinog ado a a , * , A. Sozino a , L. S aka b , P. Veˇ ´ a b , O. Heczko b , M. Zelený c , R. Chulis d , K. Ullakko a a Depa men o Physics, Ma e ials Science Labo a o y, LUT Uni e si y, Lappeen an a, Finland b FZU - Ins i u e o Physics o he Czech Academy o Sciences, P ague, Czech Republic c Ins i u e o Ma e ials Science and Enginee ing, Facul y o Mechanical Enginee ing, B no Uni e si y o Technology, B no, Czech Republic d Ins i u e o Me allu gy and Ma e ials Science, Polish Academy o Sciences, K akow, Poland ARTICLE INFO Keywo ds: Magne ic shape memo y Ni-Mn-Ga X- ay di ac ion Incommensu a ely modula ed c ys al s uc u e ABSTRACT We in es iga e he incommensu a ely modula ed c ys al s uc u e in he Ni 50 Mn 27 Ga 22 Fe 1 magne ic shape memo y alloy. We ocus on empe a u e- and s ess-induced changes, pa icula ly measu ing he a and b la ice pa ame e s and he monoclinic angle. The in-si u XRD expe imen shows ha he he mally-induced commen- su a e-incommensu a e (C-IC) ansi ion coincides wi h he change o he a e age la ice symme y om monoclinic o o ho hombic. The he mally-induced IC s uc u e is s able unde uniaxial ensile s ess along he a-axis o de o ma ion ε <0.8 %. A mix u e o he IC and C s uc u es appea s o ε >0.8 % and he changes become i e e sible. The olume ac ion o he C s uc u e u he inc eases wi h inc easing de o ma ion. These esul s p o ide i al ini ial insigh s in o he s uc u al e olu ion o Ni-Mn-Ga alloys and enable us o es ablish he ole o C and IC s uc u es in hei ex ao dina ily high mobili y o win bounda ies. Ni-Mn-Ga-based alloys a e p o o ype magne ic shape memo y ma- e ials wi h mul iple unique p ope ies and p omising applica ions [1–3]. Ex emely low winning s ess (TS) is one o he dis inc i e cha ac e is ics o he Ni-Mn-Ga-based ma ensi es [4–11]. Due o he low TS, e en mino magne ic o mechanical d i ing o ces p oduce gian de o ma ion ia win bounda y mo ion. The la ice o 10M ma ensi e can be modula ed ei he commensu a ely (C) o incommensu a ely (IC) [12–16]. The exac cha ac e o he modula ion can be c ucial gi en ha he win plane is he in e ace be ween wo modula ed win domains. The ole o C and IC modula ion in ex emely low winning s ess is a opic ye o be explo ed. P io o such an in es iga ion, i is essen ial o unde s and he ansi ion be ween C and IC s uc u es, especially in ela ion o he applied s ess. As sugges ed by p e ious in es iga ions [17–19], he IC s uc u e can be in e p e ed as composed o a/b nano wins. Howe e , he e ec o s ess on nano winned s uc u e has no ye been add essed. To e eal his e ec , we pe o med a ensile es o he nea ly single- a ian sample (wi h a/b wins) along he longes la ice di ec ion (a-axis). Such loading is no expec ed o c ea e and mo e ypical win in e aces, such as a/c and modula ion win bounda ies [10]. The ension along he a-axis p oduces he highes shea s ess in he (110) plane, which is a mi o plane o a/b winning and nano winning. We an icipa e ha su icien ly high s ess may induce he mo ion o he a/b nano win bounda ies and ul ima ely lead o he annihila ion o he IC s uc u e. The s ess-induced e ec s in Ni-Mn-Ga-based alloys we e s udied p e iously o easons such as he win a ian ea angemen [3,6,7, 20–22], and ma ensi ic and in e ma ensi ic ans o ma ions [23,24]. Cejpek e al. [25] s udied he in luence o he ensile s ess on he la ice pa ame e s and modula ion and poin ed ou he e y low Young modulus o he ma e ial. In his s udy, ou ini ial ocus is on he p e iously desc ibed he mally-induced ansi ions. Building on hese obse a ions, we e alua e he e ec s o ensile de o ma ion on IC s uc u e, which has no been epo ed be o e. We selec ed he Ni 50 Mn 27 Ga 22 Fe 1 alloy o his s udy because i exhibi ed bo h 10M commensu a e and 10M incommensu a e ma ensi e s uc u es and i was possible o in es iga e bo h s uc u es a ambien empe a u es due o he he mal hys e esis [18,26]. The single c ys al ingo s we e g own by di ec ional solidi ica ion using [001] o ien ed seed c ys al in Adap aMa L d. Cu ie empe a u e was T C =380 K. The samples exhibi ed sha p ma ensi ic ans o ma ion a T M =(M s +M )/2 =330 K * Co esponding au ho . E-mail add ess: [email p o ec ed] (M. Vinog ado a). Con en s lis s a ailable a ScienceDi ec Sc ip a Ma e ialia jou nal homepage: www.jou nals.else ie .com/sc ip a-ma e ialia h ps://doi.o g/10.1016/j.sc ip ama .2024.116096 Recei ed 17 Janua y 2024; Recei ed in e ised o m 5 Ma ch 2024; Accep ed 22 Ma ch 2024 Sc ip a Ma e ialia 247 (2024) 116096 2 and e e se ans o ma ion a T A =(A s +A )/2 =335 K, whe e M s ≈M , A s ≈A a e ma ensi e and aus eni e s a and inish empe a u es, espec i ely. The nea ly single- a ian s a e o he sample wi h espec o he sho c-axis was achie ed by mul iple eo ien a ions o he c-axis in a sa u a ed magne ic ield ( μ 0 H ~ 1T). Finally, he sho c-axis was pe pendicula o he longes sample di ec ion. X- ay di ac ion p o ed ha a e such mul iple eo ien a ions, he sample had one modula ion di ec ion, i.e. he e a e no modula ion wins. Howe e , a/b wins s ill exis . The nea ly single- a ian s a e was achie ed wi hin he commensu a e s a e. To ob ain incommensu a e modula ion, he he mally-induced C-IC ansi ion and i s hys e esis we e employed [18]. The sample was cooled down o 233 K, c ossing he C-IC ansi ion, and hen hea ed back o oom empe a u e. The single- a ian s a e wi h espec o a/c and modula ion wins emained in he esul ing incommensu a e s a e a e his p ocedu e as p o en by X- ay di ac ion. A he same ime, X- ay di ac ion demons a es ha a =b making impossible mac o a/b wins in he IC s a e (see Re . [10] o he winning in cubic coo dina e sys em). In-si u X- ay di ac ion ensile expe imen s we e pe o med on a bone-shape sample wi h a leng h o 10 mm and a c oss-sec ion o 0.7 ×2 mm 2 . A cus om-made de o ma ion s age o in-si u measu emen s was Fig. 1. Di ac ion da a (Cu K α 1 adia ion) con i ming he exis ence and empe a u e hys e esis o ansi ion be ween commensu a e (C) and incommensu a e (IC) modula ion in Ni 50 Mn 27 Ga 22 Fe 1 alloy: (a) Q-scan along he [110]* di ec ion in ecip ocal space. Di ac ion da a we e eco ded a T =293 K a e cooling o 197 K and hea ing back o 293 K. Sa elli es ma ked as s -1 , s -2 , s -3 , s -4 , s -5 a e le g oup sa elli es belonging o he main peak (620). The dis ance be ween sa elli es q IC >0.4 con i ms IC modula ion. g 220 is he (2, 2, 0) ecip ocal la ice ec o . q IC is a modula ion ec o o incommensu a e modula ion. (b) Recip ocal space ul a- as scans a ound he (400) e lec ion in he (hk0) ecip ocal la ice plane showing he nea es s 5 sa elli es a di e en empe a u es. s -5 (620) and s 5 (220) belong o he le and igh sa elli es g oup co espondingly. The sa elli es a e obse ed in he IC s uc u e and disappea in he C s uc u e. Da a was ob ained du ing cooling om 328 K o 233 K and hea ing back. (c) Measu ed empe a u e dependence o he hal dis ance (δ) be ween he s -5 (620) and s 5 (220) sa elli es and calcula ed a io o modula ion ec o q o ecip ocal la ice ec o g 110 = 0.5g 220 using Eq. (1). (d) Tempe a u e dependences o a- and b- la ice pa ame e s. M. Vinog ado a e al. Sc ip a Ma e ialia 247 (2024) 116096 3 buil om a s anda d linea mo ion s age wi h a mic ome e . The ends o he sample we e a ached o he s age using s ong epoxy and de o - ma ion was quan i ied using a mic ome e . The wo king sample pa wi hou glue was 6.3 mm. The expe imen s employed wo PANaly ical Empy ean X- ay di ac ome e s, one equipped wi h a Cu and ano he wi h a Co ube. The Cu-based di ac ome e ea u ed a polycapilla y pa allel-beam lens, An on Paa domed cooling s age DCS 500, an Eule ian c adle, and a PIXcel3D de ec o . Co-based di ac ome e was equipped wi h a hyb id monoch oma o (pa abolic mi o +double bounce Ge(220) monoch oma o ). To mi iga e he e ec s o c ys al mosaici y o sligh miso ien a ion, ω −2θ scans we e conduc ed in scanning line de ec o mode. This app oach in eg a es con ibu ions om sligh ly miso ien ed c ys allog aphic domains wi hin he de ec o accep ance ange (3.35◦). Thus he measu emen is no a ec ed by he ypical 0.2–1◦c ys al miso ien a ions om mosaic, which a e common in Ni-Mn-Ga single c ys als [7]. Fig. 1a shows a q-scan in he [110]* di ec ion o he IC s uc u e a oom empe a u e. The scan e eals wo main peaks (400) and (620) as well as modula ion sa elli es. This obse a ion is consis en wi h he da a epo ed by Ve a e al. [18]. All sa elli e e lec ions can be indexed using a single modula ion ec o . Sa elli es o he 1s o 5 h o de s o he le om he (620) e lec ion a e deno ed as s -1 o s -5 . Sa elli es loca ed on he igh side o a main peak, in he di ec ion o he modula ion ec o [110]*, a e assigned posi i e indexes. The dis ance be ween he sa elli es is equal o q IC which exceeds he alue o g 220 /5, expec ed o a 10 M la ice wi h C modula ion and 5q IC = g 220 +δ, whe e g 220 is a ecip ocal la ice ec o illus a ed in Fig. 1a. Gi en ha g 220 =2g 110 , a ela ionship be ween dis ances can be exp essed as ollows: qIC =g110[0.4+δ/5g110],(1) which is equi alen o equa ions used in p e ious publica ions [12–16, 18]. Each main peak o he IC s uc u e is be ween he wo nea es sa - elli es belonging o he neighbo ing main peaks, e.g., he (400) peak has he nea es sa elli es s -5 (620) and s 5 (220). The dis ance be ween hese sa elli es is ma ked as 2δ in Fig. 1a. To e i y he empe a u e hys e esis o he q IC , as epo ed in [18], we measu ed he dis ance be ween he nea es sa elli es, 2δ. This was done by pe o ming na ow ecip ocal space scans o he (400) peak while cooling and hea ing. This me hod allows o obse e he ansi ions be ween he s uc u es (C o IC) as e and hus wi h ine empe a u e s eps du ing in-si u expe imen s han pe o ming ull q-scans o la ge ecip ocal space mapping. The in es- iga ed ange o q- ec o s is highligh ed in ed in Fig. 1a. The measu ed maps a e p esen ed in Fig. 1b. The igu es p o ide e idence o he empe a u e dependency o 2δ and, using Eq. (1), also o q IC . Fig. 1c shows he hys e e ic empe a u e dependency o he measu ed δ. The alues q IC /g 110 we e de e mined using Eq. (1), whe e g 110 was consid- e ed cons an and equal o g 110 (293 K), since he empe a u e depen- dence o g 110 was weak compa ed o he dependency o 2δ. Du ing cooling om 328 K o 293 K (Fig. 1b), he nea es sa elli es a e no de ec ed (δ =0), and q IC =0.4g 110 , indica ing a commensu a e modula ion. Upon u he cooling om 293 K o 283 K, he sa elli es appea and δ ises ab up ly om 0 o 0.11 nm −1 (Fig. 1c), indica ing a ansi ion o incommensu a e modula ion. Fu he cooling leads o a smoo h inc ease o he δ o 0.2 nm −1 a 233 K. Hea ing esul s in a dec ease o δ o 0.128 nm −1 a 313 K. Ra es o changing δ a e di e en du ing cooling and hea ing. Du ing hea ing om 313 K o 323 K he sa elli es disappea and δ changes ab up ly om 0.128 o 0 nm −1 , mani es ing ha modula ion became commensu a e again. The obse ed he mal hys e esis in he δ and co esponding q IC /g 110 is in co espondence wi h he da a p esen ed in [18]. To sum up, ou obse a ion con i ms he he mally-induced C-IC ansi ion wi h dec easing empe a u e and i s empe a u e hys e esis in 10 M Ni 50 Mn 27 Ga 22 Fe 1 ma ensi e. The magni ude o he modula ion ec o q IC inc eases wi h dec easing empe a u e. To de e mine he uni cell pa ame e s o he a e age la ice, he di ac ion pa e n’s modula ion sa elli es a e excluded, and only he p ima y e lec ions a e conside ed [27], as we p e iously used in [28]. Fo conduc ing he measu emen s a di e en empe a u es, we com- p essed and cons ained he sample along he c-axis a oom empe a u e Fig. 2. Di ac ion expe imen s on he IC sample unde ensile s ess. (a) Schema ic ep esen a ion o he sample (001) o a-b plane in wo condi ions. Le , is an ini ial o ho hombic IC c ys al s uc u e, a =b, γ c >90◦, γ d =90◦Fo compa ison, he igh shows he C c ys al s uc u e wi h monoclinic symme y. In his s uc u e a >b, γ c >90◦, γ d <90◦(see [19,28]). D1 and D2 a e hal o he diagonals in a pa allelog am buil on a- and b-axes o modula ed la ices in cubic coo dina es. (b) Schema ic ep esen a ions o he sample o ien a ion in di ac ion expe imen unde ensile s ess σ . (c) In luence o applied ensile de o ma ion on (062) peak. Spli ing o he peak unde ensile de o ma ion abo e 0.8 % ela es o he appea ance and changing o olume ac ions o wo-s a e s uc u es: he pa en IC wi h a =b and he new C wi h a >b. In he C s uc u e, only peak (062) is obse ed om he wo possible (602) and (062), as he long a-axis is p e e ed along he ensile s ess and hus only he b-axis is p esen in he di ac ion plane. M. Vinog ado a e al. Sc ip a Ma e ialia 247 (2024) 116096 4 o simpli y a ian mic os uc u e (see de ail in [28]). Ne e heless, he sample s ill con ained a/b wins in he C s a e. Thus, he di ec de e - mina ion o he a- and b-la ice pa ame e s using 2θ angles o (400) and (040) in 10 M ma ensi e could be p oblema ic due o he peak o e lap o igina ing om his a/b- winning [17]. To imp o e he accu acy, we de i ed he la ice pa ame e s om 2θ o (602), (062) and (004) peaks, whe e he 2θ angle o he o me wo is signi ican ly highe and he e a e no o e laps. The used peaks, simila ly o (400) and (040), do no depend on la ice monoclinic dis o ion, hus he la ice pa ame e calcula ion is s aigh o wa d. Tempe a u e dependences o la ice pa ame e s a and b a e shown in Fig. 1d. A 328 K, he leng hs o la ice pa ame e s a and b di e , a >b. Du ing cooling he di e ence be ween a- and b- pa ame e s u he in- c eases. A hi d peak, eme ging be ween he o iginal (602) and (062) a 288 K, g ows in in ensi y wi hin he ange 288–268 K. Simul aneously, in ensi ies o he o iginal peaks dec ease, and hey anish a 258 K. In he nano winning model, he concu en p esence o hese h ee di ac ion peaks was a ibu ed o an in e media e s a e, cha ac e ized by a mix u e o coa se mic o wins and nano wins [17,19]. Using a mo e con en ional app oach, he beha io o he in ensi ies o he peaks can be in e p e ed as he ansi ion be ween wo s a es C (a >b) and IC (a = b) wi h a egion o coexis ence (C +IC) [29,30]. Upon hea ing om 218 K, a single peak pe sis s up o 323 K, implying ha he alloy has equal la ice pa ame e s a and b a e cooling o e a wide empe a u e ange. Addi ionally, we measu ed he empe a u e dependencies o he sho c-axis and 2θ angles o (444) and (444) peaks, whose di e ence di ec ly ela es o he la ice monoclinic angle γ c as p esen ed in Re . [28]. The c-axis leng h inc eases wi h inc easing empe a u e. The cooling and hea ing cu es ma ch in all empe a u e ange, wi h no hys e esis. The 2θ di e ence o he (444) and (444) peaks posi ions and co esponding monoclinic dis o ion dec eases wi h inc easing empe a u e. Tempe a- u e dependences a e again smoo h and show no hys e esis. Thus, he e is no hys e esis in he he mal e olu ion o he c-axis and he la ice monoclinici y γ c . In con as , he leng hs o he a- and b-axis exhibi he mal hys e esis, which co ela es wi h he he mal hys e esis obse ed in modula ion ec o magni ude q IC , Fig. 1c. This di e ence can be explained by he di e en symme ies o he a e age la ices o he C and IC s uc u es [12], see Fig. 2a. Symme y o C s uc u e is monoclinic wi h a >b, γ c >90◦, and γ d ∕= 90◦, whe e γ d is an angle be ween diagonals in he pa allelog am build using he la ice pa ame- e s a and b, Fig. 2a, also see Re . [28]. The IC s uc u e is o ho hombic and – despi e ha angle γ c ∕= 90◦is he same as in he C s uc u e – he a =b (Fig. 1d) implies γ d =90◦[17,19,28]. The di e en la ice symme- ies enable he simul aneous exis ence o he mal hys e esis in he a- and b- axes oge he wi h no he mal hys e esis o he c-axis and monoclinici y γ c upon C-IC-C ansi ion. Summa izing he he mally induced e ec s, we obse e a C-IC-C ansi ion wi h a la ge he mal hys e esis. The la ice pa ame e s o bo h s uc u es a e p esen ed in Table 1. While he C s uc u e exhibi s a monoclinic symme y, he IC s uc u e is o ho hombic. Consequen ly, he C-IC ansi ion esul s no only in he change o modula ion ec o bu simul aneously also in he appa en me ging o di e en a and b axes ((602) and (062) peaks) in o a single uni ied leng h a =b, e idenced by he single cen al peak. P e iously, he e olu ion o he peaks was explained by he nano winning o he la ice bu i can also be in e - p e ed as a ansi ion be ween C and IC s uc u es, wi h a egion o coexis ence C +IC. Fu he ensile expe imen s exploi he ac ha he s uc u e can be ei he commensu a e o incommensu a e a he ambien empe a u e. To assess he s abili y o he IC s uc u e, we conduc ed a ensile es in ol ing load-unload cycles on a single- a ian IC sample, applying s ess along he longes la ice di ec ion, he a-axis. Such loading is no expec ed o esul in he a/c o modula ion win bounda y mo ion [10] bu can s imula e he mo ion o he a/b nano win bounda ies wi h he winning plane (110) and ul ima ely lead o he disappea ance o he IC s uc u e. As he applied s ess was no measu ed in ou expe imen no s ess-s ain cu e is a ailable. Howe e , he s ess-s ain cu e o simila ma e ial wi h commensu a e modula ion was published by Cejpek e al. [25], which indica es he excep ionally small Young’s modulus o 10M ma ensi e along he a-axis. We u ilized changes in he di ac ion line posi ion, speci ically he 2θ angle, unde ension, o p obe de o ma ion in se e al di ec ions app ox- ima ely pe pendicula o he a-axis. We ound ha he di ec ion o no mal o he plane (062) was sui able o such in es iga ion o bulk single c ys al. I was less han 20◦away om he di ec ion o he "b"-axis bu had a highe 2θ angle han he o he planes used o he measu emen s (044) and (060). Plane (060) also had a high 2θ angle, bu i s in ensi y was much smalle compa ed o he (062) line. Fig. 2b shows schema ically he sample o ien a ion in ou di ac ion expe imen unde ensile s ess. Pa allel beam X- ay op ics wi h a monoch oma ic Co K α 1 adia ion we e Table 1 La ice pa ame e s o C and IC c ys al s uc u es in Ni 50 Mn 27 Ga 22 Fe 1 alloy a 293 K, gi en in cubic (L2 1 -de i ed) and diagonal coo dina es (see Re . [28] o de ails). Coo dina e sys em Cubic Diagonal Commensu a e s uc u e a =5.979 Å D1 =4.229 Å b =5.942 Å D2 =4.200 Å c =5.572 Å c =5.572 Å γ c =90.39◦γ d =89.64◦ Incommensu a e s uc u e a =b =5.963 Å D1 =4.231 Å c =5.572 Å D2 =4.202 Å γ c =90.39◦c =5.572 Å γ d =90◦ Fig. 3. Recip ocal space map a ound he (040) e lec ion in he (hk0) ecip- ocal la ice plane. Da a a e ob ained wi h Cu adia ion and a polycapilla y X- ay lens in he inciden beam op ics (wi hou a monoch oma o ). (a) Sample in ini ial s a e wi hou de o ma ion, ε =0 %. The s 1 (040), s -1 (040), s -5 (260), and s 5 (220)sa elli es a e isible, indica ing he IC modula ion s a e. O he less in ensi e peaks (no ma ked) a e ela ed o he absence o a mono- ch oma o and a small olume ac ion o he second modula ion domain in he sample. (b) Sample unde ensile ε =1.43 %. The s -5 (260) and s 5 (220) sa elli es anish, p o iding e idence o he ansi ion om he IC o he C modula ion s a e du ing he ensile de o ma ion. M. Vinog ado a e al. Sc ip a Ma e ialia 247 (2024) 116096 5 u ilized o dec ease he sensi i i y o 2θ angle on he sample displacemen and o inc ease he 2θ angle in compa ison o Cu adia ion. As shown in Fig. 2c, he (062) 2θ angle is g ea e han 145◦, allowing us o de ec e y small changes in la ice spacing and he peak spli ing is co espondingly be e esol ed. Recip ocal space mapping was pe o med o p obe di ec ly which s uc u e (C o IC) is in he sample unde ensile s ess. Fig. 3 shows he (040) peak wi h he nea es sa elli es a di e en de o ma ions. A he ini ial s a e ( ε =0 %), he e a e wo s -5 (620) and s 5 (220) sa elli es nea he (040) peak, con i ming he p esence o he IC s uc u e. When he sample is de o med o ε =1.43 %, hese sa elli es disappea (Fig. 3b). Only he s -1 (040) and s 1 (220) sa elli es emain, ma king he p og essing ansi ion o he C s uc u e. Fig. 4 displays how he 2θ posi ion o (060) and (062) peaks a y as a unc ion o de o ma ion along he a-axis, and alongside he calcula ed b- axis leng h is shown. De o ma ion ε along a-axis was de e mined om mic ome e eading and sample leng h. Loading abo e ε >0.8 % leads o he eme gence o a new peak loca ed a a highe 2θ-angle ( o bo h (060) and (062) peaks). We conclude ha his peak is ela ed o he b-axis o he eme ging C monoclinic s a e (Fig. 1d). Leng h o he b-axis in he C monoclinic s a e is sho e han he b =a axis in he IC o ho hombic s uc u e. The new peak, oge he wi h he ini ial peak, con inues o shi o a highe 2θ-angle wi h inc easing de o ma ion. Figs. 2c, 4a, b, c illus- a e ha he wo-s a e s uc u e (C +IC) exis s in he b oad ange o de o ma ion abo e ε >0.8 %. The olume ac ion o he monoclinic C s a e inc eases wi h de o ma ion on accoun o he IC o ho hombic s a e, as demons a ed by he peak in ensi y edis ibu ion in Fig. 2c. The loading-unloading cycles up o de o ma ion ε =0.8 % a e e e sible and esul in he same 2θ peak posi ions a ε =0 p io o and a e loading (Fig. 4d). The o ho hombic symme y emains, hus he s ain le el o modi y he IC s uc u e is abo e 0.8 % de o ma ion. Unloading om he de o ma ion exceeding ε =0.8 % is no e e sible (Fig. 4d). The unloaded s a e consis s o a mix u e o bo h C and IC domains. Du ing he unloading om he de o ma ion abo e ε =0.8 % he spli peaks ound a high le els o de o ma ion (Fig. 2c) shi o smalle 2θ angles. A an almos unloaded s a e, he hi d peak eme ges om he le side o he ini ial peaks (Fig. 4d). These h ee peaks co espond o di e en a- and b-axes in he C s a e and one (cen al) peak in he IC s a e due o a =b. The indexa ion and posi ions o he peaks a e shown in Fig. 4d. The calcula ed a- and b-axis leng hs co e- spond o he la ice pa ame e s o he C and IC s uc u es gi en in Table 1, wi h small de ia ions caused by he incomple e unloading. Two peaks in he C s uc u e indica e he appea ance o usual a/b win do- mains in he unloaded s a e. In summa y, we explo ed he s abili y o he incommensu a ely modula ed c ys al s uc u e in he Ni 50 Mn 27 Ga 22 Fe 1 magne ic shape memo y alloy unde uniaxial ensile s ess. Emphasizing he empe a- u e- and s ess-induced changes, he in es iga ion ocused on measu ing he a and b la ice pa ame e s and he monoclinic angle. Key indings a e: I. The he mally-induced commensu a e-incommensu a e (C-IC) an- si ion coincides wi h a ans o ma ion om monoclinic o o ho- hombic la ice symme y. Fig. 4. (a)-(b) 2θ-angle s. s ain o (060) and (062) peaks. (c) Leng h o b-axis s. s ain. (d) Di ac ion pa e ns nea he (062) peak a di e en sample condi ions (1) 0 % o de o ma ion; (2) a e loading o 0.48 % de o ma ion and unloading o almos 0 %; (3) a e loading up o 1.43 % de o ma ion and unloading o almos 0 %. The peak posi ions o C and IC s uc u es co espond o he ollowing la ice pa ame e s: a C =5.981 Å, b C =5.946 Å, a IC =b IC =5.962 Å. These pa ame e s a e close o he da a p esen ed in Table 1. (4) upon loading o 1.43 % de o ma ion. M. Vinog ado a e al. Sc ip a Ma e ialia 247 (2024) 116096 6 II. The IC s uc u e main ains s abili y unde uniaxial ensile s ess along he a-axis un il de o ma ion o ε =0.8 %. Beyond his h eshold, a mix u e o IC and C s uc u es eme ges, wi h he C s uc u e becoming mo e p edominan as de o ma ion inc eases. This s udy p o ides signi ican insigh s in o he s uc u al e olu ion o Ni-Mn-Ga alloys, pa icula ly in ela ion o ensile de o ma ion. I es ablishes he ole o C and IC s uc u es in he ma e ial’s esponse o mechanical o ces. Based on ou esul s and phase diag am p esen ed in Re . [17] we sugges ha ma e ial wi h ex emely low winning s ess such as epo ed in [9] should ha e IC modula ion. This poin s ou ha he in es iga ion o he physical p ope ies o he IC s uc u e is p in- cipal o he MSM ield. Decla a ion o compe ing in e es The au ho s decla e ha hey ha e no known compe ing inancial in e es s o pe sonal ela ionships ha could ha e appea ed o in luence he wo k epo ed in his pape . Acknowledgmen s This wo k was inancially suppo ed by he Academy o Finland (g an numbe 325910). The au ho s om he Czech Republic acknowledge he unding om he Czech Science Founda ion g an no. 21-06613S and he assis ance p o ided by he Fe oic Mul i- unc ionali ies p ojec , suppo ed by heYou h, and Spo s o he Czech Republic, P ojec No. CZ.02.01.01/00/22_008/0004591, co- unded by he Eu opean Union. The in e na ional mobili y o Alexei Sozino was suppo ed by ESIF and MEYS p ojec MOBILITY FZU 2 – CZ.02.2.69/ 0.0/0.0/18_053/0016627. Robe Chulis acknowledges he p ojec s 2021/42/E/ST5/00367 o he Na ional Science Cen e o Poland. Re e ences [1] J.P. Liu, E. Fulle on, O. Gu leisch, D.J. Sellmye , Nanoscale Magne ic Ma e ials and Applica ions, Sp inge US, Bos on, MA, 2009, h ps://doi.o g/10.1007/978-0- 387-85600-1. [2] M. Ace , Ll. Ma˜ nosa, A. Planes, Magne ic- ield-induced e ec s in ma ensi ic Heusle -based magne ic shape memo y alloys, Handb. Magn. Ma e . (2011) 231–289, h ps://doi.o g/10.1016/B978-0-444-53780-5.00004-1. [3] I. Aal io, A. Sozino , Y. Ge, K. Ullakko, V.K. Lind oos, S.P. Hannula, Gian magne os ic i e ma e ials, in: S. Hashmi (Ed.), Re . Module Ma e . Sci. Ma e . Eng., Else ie , 2016, h ps://doi.o g/10.1016/B978-0-12-803581-8.01830-0. B9780128035818019000. [4] L. S aka, H. H¨ anninen, A. So oka, A. Sozino , Ni-Mn-Ga single c ys als wi h e y low winning s ess, J. Phys. Con . Se . 303 (2011) 012079, h ps://doi.o g/ 10.1088/1742-6596/303/1/012079. [5] O. Heczko, A. Sozino , K. Ullakko, Gian ield-induced e e sible s ain in magne ic shape memo y NiMnGa alloy, IEEE T ans. Magn. 36 (2000) 3266–3268, h ps:// doi.o g/10.1109/20.908764. [6] M. Chmielus, K. Rol s, R. Wimpo y, W. Reime s, P. Müllne , R. Schneide , E ec s o su ace oughness and aining on he winning s ess o Ni–Mn–Ga single c ys als, Ac a Ma e . 58 (2010) 3952–3962, h ps://doi.o g/10.1016/j. ac ama .2010.03.031. [7] D. Musiienko, F. Nils´ en, A. A ms ong, M. Rameˇ s, P. Veˇ ´ a , R.H. Colman, J. ˇ Capek, P. Müllne , O. Heczko, L. S aka, E ec o c ys al quali y on winning s ess in Ni–Mn–Ga magne ic shape memo y alloys, J. Ma e . Res. Technol. 14 (2021) 1934–1944, h ps://doi.o g/10.1016/j.jm .2021.07.081. [8] J. Wang, H. Sehi oglu, Twinning s ess in shape memo y alloys: heo y and expe imen s, Ac a Ma e . 61 (2013) 6790–6801, h ps://doi.o g/10.1016/j. ac ama .2013.07.053. [9] O. Heczko, V. Kopecký, A. Sozino , L. S aka, Magne ic shape memo y e ec a 1.7 K, Appl. Phys. Le . 103 (2013) 072405, h ps://doi.o g/10.1063/1.4817941. [10] L. S aka, O. Heczko, H. Seine , N. Lanska, J. D ahokoupil, A. So oka, S. F¨ ahle , H. H¨ anninen, A. Sozino , Highly mobile winned in e ace in 10 M modula ed Ni–Mn–Ga ma ensi e: analysis beyond he e agonal app oxima ion o la ice, Ac a Ma e . 59 (2011) 7450–7463, h ps://doi.o g/10.1016/j. ac ama .2011.09.020. [11] A. Sa en, A. Sozino , S. Kus o , K. Ullakko, S ess-induced a/b compound wins edis ibu ion in 10 M Ni-Mn-Ga ma ensi e, Sc . Ma e . 175 (2020) 11–15, h ps://doi.o g/10.1016/j.sc ip ama .2019.09.001. [12] L. Righi, F. Albe ini, L. Pa e i, A. Paoluzi, G. Cales ani, Commensu a e and incommensu a e “5M” modula ed c ys al s uc u es in Ni–Mn–Ga ma ensi ic phases, Ac a Ma e . 55 (2007) 5237–5245, h ps://doi.o g/10.1016/j. ac ama .2007.05.040. [13] L. Righi, F. Albe ini, A. Paoluzi, S. Fabb ici, E. Villa, G. Cales ani, S. Besseghini, Incommensu a e and commensu a e s uc u al modula ion in ma ensi ic phases o FSMA, Ma e . Sci. Fo um 635 (2009) 33–41, h ps://doi.o g/10.4028/www. scien i ic.ne /MSF.635.33. [14] A. Çakı , M. Ace , L. Righi, F. Albe ini, M. Fa le, Cha ac e is ics o 5 M modula ed ma ensi e in Ni-Mn-Ga magne ic shape memo y alloys, AIP Ad . 5 (2015) 097222, h ps://doi.o g/10.1063/1.4932233. [15] S.O. Ma iage , T. Hube , G. Ingold, The incommensu a e modula ions o s oichiome ic Ni2MnGa, Ac a Ma e . 66 (2014) 192–198, h ps://doi.o g/ 10.1016/j.ac ama .2013.11.077. [16] T. Fukuda, H. Kushida, M. Todai, T. Kakeshi a, H. Mo i, C ys al s uc u e o he ma ensi e phase in he e omagne ic shape memo y compound Ni2MnGa s udied by elec on di ac ion, Sc . Ma e . 61 (2009) 473–476, h ps://doi.o g/10.1016/j. sc ip ama .2009.04.046. [17] L. S aka, J. D ahokoupil, P. Veˇ ´ a , M. Zelený, J. Kopeˇ cek, A. Sozino , O. Heczko, Low empe a u e a/b nano wins in Ni50Mn25+xGa25−x Heusle alloys, Sci. Rep. 8 (2018) 11943, h ps://doi.o g/10.1038/s41598-018-30388-8. [18] P. Veˇ ´ a , H. Seine , L. S aka, M. Klicpe a, A. Sozino , O. Fabelo, O. Heczko, Hys e e ic s uc u al changes wi hin i e-laye ed modula ed 10 M ma ensi e o Ni–Mn–Ga(–Fe), J. Phys. Condens. Ma e 33 (2021) 265404, h ps://doi.o g/ 10.1088/1361-648X/ab b8 . [19] L. S aka, J. D ahokoupil, P. Veˇ ´ a , J. Kopeˇ cek, M. Zelený, H. Seine , O. Heczko, O ho hombic in e media e phase o igina ing om {110} nano winning in Ni50.0Mn28.7Ga21.3 modula ed ma ensi e, Ac a Ma e . 132 (2017) 335–344, h ps://doi.o g/10.1016/j.ac ama .2017.04.048. [20] J.M. Ball, C. Chu, R.D. James, Hys e esis du ing s ess-induced a ian ea angemen , J. Phys. IV 05 (1995), h ps://doi.o g/10.1051/jp4:1995834. C8- 245-C8-251. [21] P. Müllne , S ess-induced win ea angemen esul ing in change o magne iza ion in a Ni–Mn–Ga e omagne ic ma ensi e, Sc . Ma e . 49 (2003) 129–133, h ps://doi.o g/10.1016/S1359-6462(03)00219-7. [22] P. Molna , P. Si ne , P. Lukas, S.-P. Hannula, O. Heczko, S ess-induced ma ensi e a ian eo ien a ion in magne ic shape memo y Ni–Mn–Ga single c ys al s udied by neu on di ac ion, Sma Ma e . S uc . 17 (2008) 035014, h ps://doi.o g/ 10.1088/0964-1726/17/3/035014. [23] V.V. Ma yno , X- ay di ac ion s udy o he mally and s ess-induced phase ans o ma ions in single c ys alline Ni-Mn-Ga alloys, J. Phys. IV 05 (1995), h ps://doi.o g/10.1051/jp4:1995810. C8-91-C8-99. [24] V.A. Che nenko, E. Villa, D. Salaza , J.M. Ba andia an, La ge ensile supe elas ici y om in e ma ensi ic ans o ma ions in Ni49Mn28Ga23 single c ys al, Appl. Phys. Le . 108 (2016) 071903, h ps://doi.o g/10.1063/1.4942195. [25] P. Cejpek, D. D ozdenko, K. Ma his, R.H. Colman, M. Dopi a, L. S aka, O. Heczko, Excep ionally small Young modulus in 10 M ma ensi e o Ni-Mn-Ga exhibi ing magne ic shape memo y e ec , Ac a Ma e . 257 (2023) 119133, h ps://doi.o g/ 10.1016/j.ac ama .2023.119133. [26] M. Klicpe a, N. Biniskos, L. Ca˜ nadillas-Delgado, P. Cejpek, R. Chulis , O.R. Fabelo Rosa, P. Veˇ ´ a , Sol ing s uc u e o i e-laye ed modula ed ma ensi e o Ni-Mn- Ga(-Fe) using single-c ys al neu on di ac ion. (2023). h ps://doi.o g/10.52 91/ILL-DATA.DIR-299. [27] P.M. de Wol , The pseudo-symme y o modula ed c ys al s uc u es, Ac a C ys allog . Sec . A 30 (1974) 777–785, h ps://doi.o g/10.1107/ S0567739474010710. [28] M. Vinog ado a, A. Sozino , L. S aka, P. Veˇ ´ a , O. Heczko, M. Zelený, R. Chulis , E. L¨ ahde an a, K. Ullakko, Cons an plane shi model: s uc u e analysis o ma ensi ic phases in Ni50Mn27Ga22Fe1 beyond non-modula ed building blocks, Ac a Ma e . 255 (2023) 119042, h ps://doi.o g/10.1016/j.ac ama .2023.119042. [29] L. S aka, J. D ahokoupil, O. Pache o ´ a, K. Rich e o ´ a, V. Kopecký, H. H¨ anninen, O. Heczko, The mally induced changes o s uc u e in Ni50Mn25+xGa25−x magne ic shape memo y single c ys als wi h e y low winning s ess, (2014). h ps://doi.o g/10.48550/a Xi .1411.1550. [30] P. Veˇ ´ a , L. S aka, J. D ahokoupil, O. Heczko, S udy o 10M’ nano winned phase in he icini y o ma ensi ic ans o ma ion in Ni-Mn-Ga Magne ic shape memo y alloy, Ac a Phys. Pol. A 134 (2018) 859–862, h ps://doi.o g/10.12693/ APhysPolA.134.859. M. Vinog ado a e al.