Variant organization and mechanical detwinning of modulated martensite in Ni–Mn–In metamagnetic shape-memory alloys

Acta Materialia 111 (2016) 75e84

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Variant organization and mechanical detwinning of modulated martensite in NieMneIn metamagnetic shape-memory alloys Haile Yan a, b, c, Bo Yang a, Yudong Zhang b, c, Zongbin Li a, Claude Esling b, c, Xiang Zhao a, **, Liang Zuo a, d, * a

Key Laboratory for Anisotropy and Texture of Materials (Ministry of Education), Northeastern University, Shenyang 110819, China
Laboratoire d'Etude des Microstructures et de M
ecanique des Mat
eriaux (LEM3), CNRS UMR 7239, Universit
e de Lorraine, 57045 Metz, France Laboratory of Excellence on Design of Alloy Metals for low-mAss Structures (DAMAS), Universit
e de Lorraine, 57045 Metz, France d Taiyuan University of Science and Technology, Taiyuan 030024, China b c

a r t i c l e i n f o

a b s t r a c t

Article history: Received 6 February 2016 Received in revised form 13 March 2016 Accepted 15 March 2016

Based upon microstructural and crystallographic characterizations, the variant organization and mechanical detwinning of 6M modulated martensite in NieMneIn alloys have been studied. In the stressfree circumstance, each martensite colony is composed of four distinct orientation variants that are related to one another in three twin relations. Adjacent variants with type-I twin relation possess straight interfaces, whereas those with type-II or compound twin relation have stepped interfaces at atomic scale. Schmid factor (SF) calculations show that under uniaxial compression condition, the loading orientation zones with high SFs for the type-I and type-II detwinning systems are close to each other, being at about 90
away from those of the compound detwinning system. The detwinning resistances of the different types of twins are considered to be associated with their twinning shears and twin boundary structures. Type-I twin possesses much larger detwinning resistance than that of type-II twin, though they have the same amount of twinning shear (0.2392). Compound twin has the smallest detwinning resistance, which is benefited from its tiny twinning shear (0.0277) and stepped twin interface. Under external loading, martensite variants react locally within colonies through detwinning if the loading orientation is favorable. It is possible to obtain single variant state in some colonies when the loading orientation is located in the common positive SF zone of the three detwinning systems. This study is expected to provide fundamental information on local variant reorientation of 6M NieMneIn martensite during deformation. © 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: NieMneIn Modulated martensite Twin relationship Detwinning Schmid factor

1. Introduction Over the last two decades, NieMn-based magnetic shapememory alloys have attracted considerable attention due to their large magnetic-field-induced strains [1e14]. Two different mechanisms have been discovered to account for the magnetic shape memory effect (MSME) in these alloys. The first mechanism, as typically observed in NieMneGa alloys, involves the rearrangement of martensite variants through interface movement driven by magnetic field [2,15,16]. When the magnetocrystalline anisotropy

* Corresponding author. Key Laboratory for Anisotropy and Texture of Materials (Ministry of Education), Northeastern University, Shenyang 110819, China. ** Corresponding author. E-mail addresses: [email protected] (X. Zhao), [email protected] (L. Zuo). http://dx.doi.org/10.1016/j.actamat.2016.03.049 1359-6454/© 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

energies (MAEs) of some favored variants are larger than their interface movement resistances, they will grow at the expense of other unfavored variants and thus generate giant macroscopic strain. However, due to the quick saturation of magnetization, the output magnetostress is restricted to only a few MPa [10,17]. Thus, the applications are limited to the low environment resistant conditions. The second mechanism, as typically found in NieMneIn alloys, refers to the magnetic-field-induced inverse martensitic transformation (MIMT) [4,18]. Due to the giant difference in magnetization between the parent and product phase, the Zeeman energy (ZE) could significantly influence the phase stability and result in a structural change under external magnetic field. As the ZE continuously increases with magnetic field, a large output magnetostress may be achieved [10,15]. Moreover, unlike the MAE, the ZE does not strongly depend on crystal orientation. This character would allow utilizing polycrystalline NieMneIn

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alloys for actuator/sensor applications. In order to obtain MSME in NieMneIn alloys, an appropriate predeformation at the martensite state is generally required, prior to applying an actuating magnetic field to induce the inverse martensitic transformation and realize the shape recovery. The aim of the predeformation process is to rearrange martensite variants by external loading [19e21]. Due to strong anisotropic mechanical response of martensite, the loading orientation should have significant impacts on the prestrain attainability and hence the resultant MSME triggered by magnetic field. In this context, it is essential to explore the mechanical behaviors of martensite variants during deformation. Apparently, in-depth knowledge on the martensite variant organization is a prerequisite to accomplish this task. It should be mentioned that various modulated martensite phases in NieMneGa alloys have been studied under different points of view [22e30]. As for NieMneIn alloys, the microstructural and crystallographic characteristics of modulated martensite have not been properly addressed, due to the lack of precise structure information such as modulation period and atomic coordinates. It is only very recently that the complete crystal structure of the 6M modulated NieMneIn martensite has been determined [31] in the frame of (3 þ 1)-dimensional superspace theory [32,33]. This serves as a basis for in-depth microstructural and crystallographic explorations of this family of alloys. In the present work, we selected one Mn-rich off-stoichiometric Ni2Mn1.44In0.56 polycrystalline alloy with incommensurate 6M modulated martensite at room temperature. The microstructural and crystallographic characteristics of the martensite phase, such as variant configurations, twin types, twinning elements and variant interfaces, were determined with the aids of electron backscatter diffraction (EBSD) and high-resolution transmission electron microscope (HRTEM). Guided by the obtained crystallographic parameters, the detwinning behaviors of martensite variants within chosen colonies were analyzed in detail under uniaxial compressive loading. As a first step, this work is expected to provide some fundamental information on how martensite variants react locally with external force through detwinning process in NieMneIn alloys.

microstructural examinations and crystallographic orientation investigations were performed in a field emission gun scanning electron microscope (SEM, Jeol JSM 6500F) with an EBSD acquisition camera and the Aztec online acquisition software package (Oxford Instruments). During the EBSD measurements, the “beamcontrol” mode was applied with a step size of 0.125 mm. A threefold layered superstructure model of the monoclinic incommensurate 6M modulated martensite, as illustrated in Fig. 1, was used to index the EBSD Kikuchi patterns. The details of this superstructure were described in Ref. [31]. The interfaces between adjacent martensite variants were examined using a high-resolution transmission electron microscope (HRTEM, JEM 2100F). In order to assess the crystalline perfectness of given martensite crystals, the orientation deviations from their mean orientations were calculated with individually measured EBSD orientation data, using a method described in Ref. [34]. The mean orientations were expressed in three Euler angles (41, f, 42) with respect to the macroscopic sample coordinate frame [35,36], and the mean and maximum orientation deviations were expressed in minimum rotation angles. The orientation relationships between adjacent martensite variants were determined from their mean orientations via misorientation calculations [37]. The twinning elements of different types of twins were derived on the basis of the minimum shear criterion and the Bilby-Crocker theory [38,39]. The detailed determination procedure is given in Appendix A. Moreover, the interfaces of twin-related martensite variants were determined by the indirect two-trace method [40]. The results are given in Appendix B. 3. Results and discussion 3.1. Characteristic temperatures of austenite-martensite transformation The heating and cooling DSC curves for the polycrystalline Ni2Mn1.44In0.56 bulk alloy are displayed in Fig. 2a. The start and finish temperatures of the martensitic and austenitic transformations are 339.7 K (Ms), 330.4 K (Mf), 339.4 K (As) and 349.2 K

2. Experimental procedures and characterization methods A polycrystalline bulk alloy with nominal composition of Ni2Mn1.44In0.56 was prepared by arc-melting pure constituent elements Ni (99.97 wt.%), Mn (99.95 wt.%) and In (99.995 wt.%) under Ar atmosphere in a water-cooled copper crucible. The alloy was remelted for four times to ensure composition homogeneity. It was further remelted and injected into a copper mold to obtain a cylindrical rod of 8 mm in diameter and ~50 mm in length. The as-cast rod was annealed in a sealed quartz tube under Ar atmosphere at 1173 K for 24 h, followed by water quenching. Rectangular parallelepiped samples with dimension of 5.5  5.5  7.5 mm3 were cut out of the middle portion of the annealed rod for microstructural observations, crystallographic orientation measurements and mechanical compression tests. The sample surfaces were mechanically ground and further electrolytically polished at room temperature with a solution of 20% nitric acid in methanol at 8 V. The critical temperatures for the forward and backward martensitic transformation of the present alloy were measured by differential scanning calorimetry (DSC, TAQ100) in a temperature range from 183 K to 473 K at a heating and cooling rate of 5 K/min. The magnetic properties were examined by physical property measurement system (PPMS, Quantum Design) under a magnetic field of 1 T. The ex-situ uniaxial compression with a maximum strain of 5.44% along the length direction of the sample was carried out using a conventional uniaxial compression machine. The

Fig. 1. Illustration of monoclinic 6M modulated superstructure of Ni2Mn1.44In0.56 martensite.

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Fig. 2. (a) DSC curves and (b) thermoemagnetic curves at a magnetic field of 1 T for Ni2Mn1.44In0.56 alloy.

(Af), respectively. A small thermal hysteresis of about 9.5 K during the forward and backward martensitic transformation was detected. The magnetization variations of the alloy with temperature under a magnetic field of 1 T are shown in Fig. 2b. A magnetostructural transition - characterized by a drastic reduction in magnetization during the martensitic transformation - is observed. 3.2. Microstructural and crystallographic features of martensite variants 3.2.1. Microstructural features The band contrast and crystallographic orientation micrographs of the experimental sample - measured by EBSD at room temperature - are displayed in Fig. 3a and b, respectively. It can be seen that the martensite is in plate shape and organized in colonies or groups within initial austenite grains. In each colony, thin plates are alternately distributed with four different crystallographic orientations. As an example, Fig. 3c presents the zoomed orientation micrograph of the area outlined with the dashed white rectangle in Fig. 3b, where A, B, C and D denote four differently oriented martensite plates (variants). Adjacent martensite plates are separated by two kinds of interfaces in terms of the interface trace orientation. One refers to those interfaces with trace roughly paralleled to the plate length direction (termed interplate interfaces), i.e. the boundaries between variants A and B, A and C, B and D, and C and D. The other refers to those interfaces with trace across the plates (termed intraplate interfaces), i.e. the boundaries between variants A and D, and B and C. With the EBSD orientation data measured over the four martensite variants A, B, C and D in Fig. 3c, the mean and maximum deviations from their mean orientations were calculated, and the results are displayed in Table 1. It is seen that the mean and maximum angular deviations are respectively less than 0.3
and 1
, suggesting a homogeneous orientation for each variant. The small orientation deviations could be ascribed to the retained strains associated with the martensitic transformation as well as the EBSD imprecision in orientation measurements. Thus, each martensite variant is considered as a nearly perfect crystal with negligible lattice distortion. For the subsequent crystallographic calculations, the determined mean orientation data were used as the input to get better accuracy.

3.2.2. Crystallographic features The orientation relationships between two adjacent martensite variants of the same colony (group) are shown in Table 2. It is seen that all martensite variants are twin-related to one another, i.e. variant pair A:C (or B:D) is in type-I twin relation, A:B (or C:D) in type-II twin relation, and A:D (or B:C) in compound twin relation. The determined twinning elements (K1, the twinning plane; h1, the twinning direction; K2, the reciprocal or conjugate twinning plane; h2, the reciprocal or conjugate twinning direction; P, the plane of shear; s, the magnitude of shear) are summarized in Table 3. Notably, the twinning shears for type-I and type-II twins are exactly the same (0.2392), being almost one order of magnitude higher than that of compound twin (0.0277). Further calculations on the type-I, type-II and compound twins show that the twin interface planes coincide with their corresponding twinning planes K1 (Appendix B). Such twin interfaces should be considered as coherent boundaries. Fig. 4a presents the stereographic projections of interface planes in the macroscopic sample coordinate frame for the three twin types, where the overlapping poles are enlarged in the dashed line boxes. The poles of the interface planes of type-I twin pairs (A:C and B:D) are very close to each other, as represented by the filled circles in Fig. 4a. This means that the type-I twin interfaces are parallel. The poles of the interface planes of type-II twin pairs (A:B and C:D), as indicated by the filled diamonds in Fig. 4a, are distributed around those of type-I twin pairs (A:C and B:D) with a deviation of ~5
, suggesting that there is a small angular deviation between the interfaces of type-I and type-II twin. This is in accordance with that observed on the 5M and 7M modulated martensite in NieMneGa alloys [26,27,37,41,42]. As for the interfaces of compound twin pairs (A:D and B:C), they are also almost parallel. These compound twin interfaces are oriented roughly perpendicular to the type-I twin interfaces. To obtain an overview of variant organization in one martensite colony, the interface traces of the twin-related variants are illustrated in a two-dimensional sample section, as shown in Fig. 4b. According to the HRTEM observations, the three types of twins are associated with different interface characters at atomic scale, as shown in Fig. 5. More specifically, the type-I twin pair A:C possesses a straight interface (outlined with the dashed white horizontal line

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Fig. 3. (a) Band contrast micrograph and (b) crystallographic orientation micrograph of Ni2Mn1.44In0.56 alloy measured by EBSD at room temperature. Thick black lines in (a) and (b) outline original austenite grain boundaries. (c) Zoomed crystallographic orientation micrograph of the area enclosed with the dashed white rectangle in (b). Four differently oriented martensite plates (orientation variants) are labeled as A, B, C and D.

Table 1 Mean and maximum orientation deviations from mean orientations for four martensite variants A, B, C and D in Fig. 3c, represented in minimum rotation angle. Variant

Mean orientation (41, f, 42)

Mean deviation

Maximum deviation

A B C D

(167.4367
, 7.9514
, 246.3696
) (14.6294
, 107.6467
, 213.8242
) (90.2600
, 59.4931
, 21.9914
) (143.2065
, 100.2620
, 87.3843
)

0.2784
0.2792
0.2810
0.2997


0.9620
0.7975
0.7677
0.9955


Table 2 Orientation relationships between adjacent martensite variants of the same group in Ni2Mn1.44In0.56 alloy. The identified twinning planes and directions are referenced to the monoclinic 6M modulated superlattice. The subscript “M” denotes the 6M martensite. Variant pair

Twin type

Twinning plane

Twinning direction

A:C and B:D

Type-I Type-II

f1 2 3gM e

e

A:B and C:D A:D and B:C

Compound

{1 0 3}M

<3 0 1>M

<3 3 1>M

in Fig. 5a), whereas the type-II twin pair A:B has a stepped interface (outlined with the dashed white zigzag line in Fig. 5b). Thus, different stress-response behaviors could be expected for the type-I and type-II twins, although they have the same amount of twinning shear. The interface of the compound twin pair A:D also possesses step feature (Fig. 5c), just like that of the type-II twin pair but with larger step size.

Table 3 Twinning elements of type-I, type-II and compound twins identified for 6M modulated martensite in Ni2Mn1.44In0.56 alloy. The theoretical minimum rotation angles (u) and corresponding rotation axes (d) associated with the three twin types are also given. Twinning elements

Type-I twin

Type-II twin

Compound twin

K1

f1 2 3gM

f1:1240 2 2:6280gM

{1 0 3}M

K2

f1:1240 2 2:6280gM

f1 2 3gM

f1 0 3gM

< 3:3264 3 0:8912 > M

<3 3 1>M

<3 3 1>M

< 3:3264 3 0:8912 > M {1 0.1150 3.3451}M

<3 0 1>M <3 0 1>M

h1 h2 P s Theoretical u/d

f1 0:1150 3:3451gM 0.2392 83.20
/<3 0 1>M

0.2392 96.80
/normal to {1 0 3}M

{0 1 0}M 0.0277 180
= < 3 0 1 > M

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Fig. 4. (a) Stereographic projections of interface planes of various variant pairs (from one martensite colony) in the macroscopic sample coordinate frame. The overlapped poles are enlarged in the dashed line boxes. The interfaces associated with type-I, type-II and compound twins are denoted by filled circles, diamonds and stars, respectively. (b) Illustration of variant organization within one martensite colony. The interface traces associated with type-I, type-II and compound twins are highlighted in red solid, blue dashed and green solid lines, respectively. KI1 and K1 Compd. represent the twinning plane of type-I twin and that of compound twin. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

3.3. Martensite variant rearrangement under compressive loading Larger-scale microstructural and crystallographic examinations reveal that in the stress-free circumstance, at most 24 orientation variants of the 6M modulated martensite can form in one initial austenite grain. These 24 orientation variants are selfaccommodated into 6 distinct groups. Although the absolute crystallographic orientations of the 4 intra-grouped orientation variants vary from one group to another, their interrelationships (i.e. the three twin relations) and boundary characteristics keep constant over the entire martensite microstructure. In this sense, individual groups (colonies) are crystallographically equivalent and can be treated as mechanical units to an external load. Considering the fact that martensite variants within one colony are twin-related to one another, the variant rearrangement under external loading should be attributed to the so-called “detwinning” process [43]. Due to the specific variant organization illustrated in Fig. 4b, the loading orientations with respect to various variants would play an important role in deformation through detwinning. Here, an attempt was made to explore possible effective loading orientations for the detwinning of the three types of twins. First, we take one variant (variant A) as the host crystal of the other three variants (variants B, C and D). This implies that B, C and D could be regarded as the twins of A realized via the respective type-II, type-I and compound twinning, as summarized in Table 4. Fig. 6 presents the stereographic projections of the twinning planes K1 and twinning directions h1 of the three twinning systems in an orthonormal reference frame set to the crystal coordinate system of variant A. In view of the polarity of twinning process [44], we specially select the projection plane that allows the K1 and h1 of the three twinning systems to be stereographically projected from the same hemispheres. It is seen that for the type-I and type-II twins, the respective K1 and h1 are very close to each other. For the compound twin, its K1 is approximately perpendicular to the twinning planes of the type-I and type-II twins. With the specified twinning systems of one variant to produce the other three variants, it is possible to find out the optimum loading orientations for the reverse (detwinning) process to obtain single variant state. This can be done by applying a unit detwinning

force in all possible orientations with respect to the host crystal. In what follows, we shall consider only the uniaxial compression mode due to its convenience for practical operation. If one twinning system is denoted by K1 and h1, the detwinning system is thus K1 and h1. The Schmid factors (SFs) of the three detwinning systems were calculated as functions of loading orientation, as shown in stereographic projection in Fig. 7. For the case of variant A as the host crystal (Fig. 7a), the efficient SF zones for the type-I and type-II detwinning systems overlap to a large extent. It suggests that variant C (type-I twin) and variant B (type-II twin) could be simultaneously transformed into variant A under the same favorable loading orientation. Moreover, if choosing variant D as the host crystal of variants A, B and C (Fig. 7b), the efficient loading orientations to eliminate variants B and C are the same as the above case. This means that under a favorable loading orientation to obtain variant A, variant D could also become favorable. Interestingly, in either case, there are two common zones where the detwinning of three variants (variants B, C and D for host variant A or variants B, C and A for host variant D) has positive SF values. However, in the two cases, the common zones are not the same in terms of loading orientations. It should be noted that in the above analyses, the choice of variant A or D as the host crystal is arbitrary. The rest variants can also be taken as the host crystal, and the analysis procedures remain the same. Based on the above theoretical analyses, ex-situ uniaxial compression tests were performed on the polycrystalline Ni2Mn1.44In0.56 bulk samples. Two special martensite colonies with different variant orientations with respect to the compressive loading orientations, as shown in Fig. 8a and c, were presented to verify the above analyses. For the former (Fig. 8a), the uniaxial loading direction was along one orientation with high SF for both type-I and type-II detwinning systems (marked with rotated cross in Fig. 7). For the latter (Fig. 8c), the uniaxial loading direction was located within one common orientation zone with positive SF for all three detwinning systems (marked with cross in Fig. 7). In both cases, the area fractions of the four martensite variants A, B, C and D are comparable before compression but greatly changed after compression depending on the loading orientations. When the loading orientation is favored for only type-I and type-II detwinning

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Fig. 6. Stereographic projections of twinning planes K1 and twinning directions h1 of type-I, type-II and compound twins of variant A. The orthonormal basis set to the monoclinic lattice basis of variant A under the Oxford Channel 5 convention is chosen as the projection reference. The poles of twinning planes (KI1, KII1 and KCompd. ) and twin1 ning directions (hI1, hII1 and hCompd. ) of type-I, type-II and compound twins are repre1 sented in filled and open circles, triangles and squares, respectively.

Fig. 5. HRTEM lattice images and corresponding diffraction patterns of (a) type-I, (b) type-II and (c) compound twins. The directions of incident electron beam are along [2 1 0] in (a), ~[2 1 0] in (b) and [0 1 0] in (c) with respect to the lattice reference of variant A, respectively. The type-I twin interface is indicated in dashed white straight line, and the type-II and compound twin interfaces in dashed white zigzag lines.

Table 4 Twinning systems and twin types required for the formation of variants B, C and D via twinning of variant A. The twinning planes K1 and twinning directions h1 are referenced to the lattice of 6M modulated superstructure. Twin variant

K1

h1

Twin type

B

f1:1240 2 2:6280gM

< 3:3264 3 0:8912 > M

Type-II

C

f1 2 3gM {1 0 3}M

<3 3 1>M

Type-I

<3 0 1>M

Compound

D

systems, variants B and C disappear while variants A and D are left with almost the same area fraction (Fig. 8b), as we predicted above. Such a loading orientation is not beneficial to eliminate variant D or A, since the SF value for the compound detwinning system is nearly zero. When the loading orientation falls into the common zone with positive SF for all three detwinning systems, the situation changes drastically. As evidenced in Fig. 8d, most part of the variant colony is occupied by variant A and only very small area fractions of variants B, C and D are present. Clearly, the most efficient loading orientation to obtain the single variant configuration is the one located in the common detwinning zone, although it does not provide the highest SF for any detwinning system. Taking into account the remaining variants B, C and D in Fig. 8d, one can further explore the detwinning behaviors of the three different types of twins. It is seen that variant B (in type-II twin relation with variant A) has a less remaining area fraction than variant C (in type-I twin relation with variant A), although the typeII detwinning system possesses a smaller SF value (0.31) than that of the type-I detwinning system (0.35). This suggests that type-I twin has a larger detwinning resistance, which is in good accordance with the results obtained in CueAleNi and NieMneGa alloys that the type-II twin requires a much smaller twinning stress [25,26,45e48]. This small twinning stress for type-II twin might be associated with the step feature of the twinning plane, as evidenced in Fig. 5b. Besides, most of variant D that is of compound twin relation with variant A has also been detwinned as shown in Fig. 8d, although the associated SF value is only 0.10. This implies that compound twin possesses very small detwinning resistance, which could be attributed to its tiny shear amount (0.0277) and highly stepped interface, as displayed in Fig. 5c. In addition, the shape of variant D becomes irregular after the uniaxial compression, as indicated in Fig. 8b and d. The heavily curved interfaces between variants A and D further confirm the high mobility of the compound twin interface. Thus, in addition to the loading orientation, the intrinsic resistance of detwinning system plays an important

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Fig. 7. SF distributions of (a) variants B, C and D (host crystal A) and (b) variants A, B and C (host crystal D) under uniaxial compression. Contour lines for type-I, type-II and compound detwinning systems are plotted with gradient red, blue and green lines, respectively. The cross and rotated cross indicate two different loading orientations for the exsitu compression tests. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

role during detwinning. It is worth noting that under mechanical loading, martensite variants do react within colonies through detwinning of unfavorably oriented and less resistant variants. In some circumstances, it is possible to obtain single variant state in some colonies by one uniaxial compression. The efficient loading orientation is one located in the common zone where the SF values for the type-I, type-II and compound detwinning systems are all positive, profiting the different detwinning behaviors of different twins. If knowing the loading orientation with respect to a chosen colony, the detwinning process and the efficiency of variant reorientation can be deduced. For polycrystalline materials, the interactions between colonies should also be considered, and this will be the content of our subsequent work. Furthermore, it should be noted that a two-step

detwinning process has been effectuated to train 10M NieMneGa martensite [49], i.e. the first step by compression along the high SF orientations for both type-I and type-II detwinning systems and then the second step by compression along the high SF orientations for compound detwinning system. Under such a scheme, it allows one to obtain single crystals with only one martensite variant. 4. Conclusions The microstructural and crystallographic features of martensite variants in Ni2Mn1.44In0.56 alloy were characterized by EBSD and HRTEM analyses. With the obtained crystallographic parameters, the detwinning behaviors of differently oriented variants under uniaxial compression were explored theoretically and

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Fig. 8. (a and c) Initial configurations of martensite variants within one colony and (b and d) corresponding microstructures after uniaxial compression. The loading orientation in (b) is approximately along the optimum orientation with high SF for both type-I and type-II detwinning systems, and that in (d) is within the common zone with positive SF for type-I, type-II and compound detwinning systems.

experimentally. The main results are summarized as follows: The plate-like 6M martensite is organized in colonies within original austenite grains. Each colony consists of four orientation variants that are related to one another by either type-I, or type-II or compound twin relation. The complete twinning elements of the three types of twins are unambiguously determined. The twinning shear of compound twin (0.0277) is about one order of magnitude smaller than that of type-I and type-II twins (0.2392). Various twin interfaces are coincident with their corresponding twinning planes and thus should be coherent. In one colony, the interface planes of distinct type-I or compound twin pairs are parallel, whereas those of distinct type-II twin pairs are misoriented by about 10
. The highest SF loading orientations of type-I and type-II detwinning systems are almost common, being approximately perpendicular to that of compound detwinning system. Different twinning systems exhibit different detwinning resistances, depending on the magnitude of twinning shear and the structure of twin interface that determine twin interface mobility. Compound twin requires the least detwinning stress as it possesses tiny twinning shear and highly stepped twin interface. Although type-II twin has the same amount of twinning shear as type-I twin, it requires smaller detwinning stress than type-I twin as its boundary is stepped and thus more mobile. Under external loading, martensite variants react locally within

colonies. To obtain single variant state for one colony, the uniaxial compression (the simple and convenient deformation mode) should be applied along an orientation in which all the three detwinning systems possess positive SFs. Such information is essential for understanding the practical variant elimination operation through deformation. Acknowledgments This work is supported by the National Natural Science Foundation of China (Grant No. 51431005), the 863 Program of China (Grant No. 2015AA034101), the 111 Program of China (Grant No. B07015), the Program for Liaoning Innovative Research Team in University (Grant No. LT2013007), the Fundamental Research Funds for Central Universities of China (Grant No. N130110001), and the French State through the Program “Investment in the future” operated by the National Research Agency and referenced by ANR11-LABX-0008-01 (LabEx DAMAS). H.L. Yan is grateful to the China Scholarship Council (CSC) for providing a Ph.D. scholarship. Appendix A. Determination of twin types Let g1 and g2 be the respective orientations of two adjacent martensite variants 1 and 2 with respect to the sample coordinate frame. Each orientation can be specified with three successive

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elemental rotations (e.g. three Euler angles 41, f and 42 in Bunge notation) that transform the sample coordinate frame to the orthonormal coordinate frame set to the monoclinic martensite crystal system. In matrix notation, the misorientation between variants 1 and 2 is expressed as,

1 Dg ¼ S1  g2  Sj i  g1

(A1)

where Si (or Sj) represents the ith (or jth) rotational symmetry element of the monoclinic crystal system. Such a misorientation can also be represented in terms of a set of equivalent rotation angles (u) and the corresponding rotation axes (d). For the present Ni2Mn1.44In0.56 alloy, each colony of martensite plates consists of four variants (denoted as A, B, C and D in Fig. 3c). With Eq. (A1), the misorientations among various variants were calculated from their mean orientations, and the results are summarized in Table A1. It can be seen that there exists at least one misorientation angle of 180
(with a small deviation) for each variant pair. According to the classical definition of twin [38,50,51], all these martensite variants are twin-related to one another. More specifically, variant pairs A:C and B:D belong to type-I twin with the ð1 2 3ÞM plane as the twinning plane K1, A:B and C:D to type-II twin with the ½3 3 1M direction as the twinning direction h1, and A:D and B:C to compound twin with the (1 0 3)M plane as the twinning plane K1 and the ½3 0 1M direction as the twinning direction h1. Table A1 Misorientation angles and corresponding rotation axes between four martensite variants A, B, C and D. The subscripts “Ortho” and “M” represent the orthonormal coordinate frame and the lattice frame of the monoclinic superstructure, respectively. The geometric relationship between the two coordinate frames is consistent with the notation defined in Oxford Channel 5. Variant Misorientation Rotation axis pair angle u Rotation axis d A:C

83.4766
179.7258


B:D

83.1465
179.8741


A:B

179.9569
96.5670


C:D

96.8185


179.9123
A:D

179.7104


179.3718


B:C

179.9587


179.3070


83

Appendix B. Determination of twin interfaces Based on the indirect two-trace method [40], the interface planes connecting the twin-related martensite variants of the same group and their deviations from the corresponding twinning plane K1 were calculated, and the results are summarized in Table B1. It is seen that all the interface planes are well consistent with their respective K1. Thus, they could be considered as coherent boundaries. The angular deviations of compound twin interface planes from K1 are relatively larger than those of type-I and type-II twin interface planes. This is ascribed to the relative short length and “stepped” feature of compound twin interfaces.

Table B1 Interface planes across various martensite variants of the same colony and their deviations from the corresponding twinning planes K1. Twin type

K1

Variant pair

Interface plane

Type-I

f1 2 3gM

A:C


ð1:3051 2:5541 3:9843ÞM 0.9432
0.3838 ð1:2739 2:5556 3:7714ÞM

B:D Type-II

f1:1240 2 2:6280gM A:B C:D

Compound {1 0 3}M

A:D B:C

Deviation from K1


ð1:2452 2:5852 3:8277ÞM 0.8556
0.5571 ð1:3119 2:5617 3:8681ÞM
ð1:5576 2:7012 3:6795ÞM 0.8684
0.7186 ð1:4967 2:7387 3:5321ÞM
ð1:1677 2:0000 2:6877ÞM 0.9707
0.8395 ð1:1276 2:0000 2:5333ÞM
ð1:0000 0:0025 3:0540ÞM 0.4901
1.4353 ð1:0000 0:0225 2:8650ÞM

(1.0000 0.0369 2.9088)M 1.4206

ð1:0000 0:0094 2:9984ÞM 0.2875

References

Twin type Deviation angle


½0:7288 0:0036 0:6847Ortho 0.1730 from Type-I ½3 0 1M
½0:4559 0:7462 0:4852Ortho 0.2200 from normal to

ð1 2 3ÞM
½0:7300 0:0017 0:6835Ortho 0.0790 from ½3 0 1M
½0:4535 0:7481 0:4844Ortho 0.0094 from normal to ð1 2 3ÞM
½0:5157 0:6654 0:5397Ortho 0.1945 from Type-II ½3 3 1M [0.7230 0.0005 0.6908]Ortho 0.0411
from normal to (1 0 3)M [0.7198 0.0010 0.6942]Ortho 0.0543
from normal to (1 0 3)M
½0:5192 0:6638 0:5383Ortho 0.0667 from

½3 3 1M
½0:7253 0:0055 0:6884Ortho 0.2709 from Compound normal to (1 0 3)M
½0:6884 0:0025 0:7254Ortho 0.1531 from normal to ½3 0 1M [0.7245 0.0060 0.6893]Ortho 0.2938
from normal to (1 0 3)M
½0:6893 0:0004 0:7245Ortho 0.0696 from ½3 0 1M

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