Crystallographic Characterization on Polycrystalline Ni-Mn-Ga Alloys with Strong Preferred Orientation

Heusler type Ni-Mn-Ga ferromagnetic shape memory alloys can demonstrate excellent magnetic shape memory effect in single crystals. However, such effect in polycrystalline alloys is greatly weakened due to the random distribution of crystallographic orientation. Microstructure optimization and texture control are of great significance and challenge to improve the functional behaviors of polycrystalline alloys. In this paper, we summarize our recent progress on the microstructure control in polycrystalline Ni-Mn-Ga alloys in the form of bulk alloys, melt-spun ribbons and thin films, based on the detailed crystallographic characterizations through neutron diffraction, X-ray diffraction and electron backscatter diffraction. The presented results are expected to offer some guidelines for the microstructure modification and functional performance control of ferromagnetic shape memory alloys.


Introduction
Conventional shape memory alloys (SMAs) can generate large output strains as a result of reversible martensitic transformation. However, a major inconvenience for the practical application of SMAs is their low working frequency (less than 1 Hz), since thermal activation is necessary. Recently, a significant breakthrough in the research of high performance SMAs came about with the discovery of ferromagnetic shape memory alloys (FSMAs) [1], where the magnitude of output strain is comparative to that in conventional shape memory alloys [2][3][4][5][6][7][8]. Moreover, the possibility of controlling the shape change by the application of magnetic field enables relatively higher working frequency (KHz) than that of conventional shape memory alloys. With the integration of large output and fast dynamic response under the external magnetic field, FSMAs are conceived as the promising candidates for a new class of actuation and sensing applications.
During the last two decades, numerous experimental studies have been conducted on the composition-dependent magnetic shape memory behavior in Ni-Mn-Ga alloys. Thus far, the field induced output strains have almost reached the theoretical limit in single crystals, i.e.,~7%,~11% and 12% in single crystals with 5M, 7M and NM martensite [6][7][8], respectively. It should be noted that the high-cost for the fabrication of single crystals represents a severe obstacle for practical applications. In contrast, the preparation of polycrystalline alloys are much simpler and of lower cost. However, a more or less random distribution of crystallographic orientation in polycrystalline alloys greatly weakens the field controlled functional behavior. To improve the functional properties in polycrystalline alloys, microstructure optimization and texture control are of great significance and challenge. In this paper, we present our recent progress on the microstructure control in polycrystalline Ni-Mn-Ga alloys in the form of bulk alloys, melt-spun ribbons and thin films, based on the detailed crystallographic characterizations through neutron diffraction, X-ray diffraction and electron backscatter diffraction (EBSD). For the bulk alloys, which were prepared by directional solidification, the thermo-mechanical treatment (compressive load applied during the martensitic transformation) was introduced in order to redistribute the variants. For the melt-spun ribbons with strong preferential orientation, the orientation inheritance between austenite and 7M martensite was analyzed. For the thin films deposited on MgO(1 0 0) substrate, the preferential orientation and variant distribution were illustrated.

Experimental
Bulk polycrystalline alloys with the nominal composition of Ni 50 Mn 30 Ga 20 (at. %) and Ni 50 Mn 28.5 Ga 21.5 (at. %) were prepared by directional solidification. In order to obtain a composition homogenization, the directionally solidified Ni 50 Mn 30 Ga 20 and Ni 50 Mn 28.5 Ga 21.5 bulk alloys were homogenized at 1173 K for 24 h in a sealed vacuum quartz tube, followed by the quenching into water. A part of homogenized alloy was ground into powder and then the powder was annealed at 873 K for 5 h in vacuum to release the internal stress for the subsequent powder X-ray diffraction (XRD) measurements.
Ribbons with the nominal composition of Ni 53  The room-temperature crystal structure was determined by X-ray diffraction (XRD) with Cu-Kα radiation. The martensitic transformation temperatures were measured by differential scanning calorimetry (DSC, TA Q100) with a heating and cooling rate of 10 K/min. The microstructural characterization was performed in a field emission gun scanning electron microscope (SEM, Jeol JSM 6500 F) with an EBSD acquisition camera and Channel 5 software.
The neutron diffraction measurements were performed using the materials science diffractometer STRESS-SPEC operated by FRM II and HZG at the Heinz Maier-Leibnitz Zentrum (MLZ), Garching, Germany, with a monochromatic wavelength of 2.1 Å [32]. The uniaxial compressive load

Thermo-Mechanical Treatment of Directionally Solidified Alloys
In general, the martensitic transformation is deformation-dominant diffusionless phase transformation with symmetry break. The lower symmetry of the product martensitic phase may result in the formation of self-accommodated multi-variants to compensate the elastic strains associated with the phase transformation. However, such self-accommodated microstructure is not favorable for the achievement of magnetic shape memory effect in Ni-Mn-Ga alloys, since the co-existence of multi-variants would greatly enhance the resistance for the variant reorientation. As the deformation accompanying the martensitic transformation is anisotropic, unidirectional constraint (tension or compression) during the martensitic transformation could promote the formation of certain favorable variants but eliminate some other unfavorable ones [34]. Therefore, strong preferential orientation of martensite can be achieved through the selective formation of favorable variants with the application of an external field during the martensitic transformation, thus to realize the optimization of crystallographic anisotropy and magnetic shape memory effect [2,4,13,14,35]. In this section, thermo-mechanical treatments (compressive load applied during the martensitic transformation) were introduced in order to reformulate the variant distribution. Through in-situ neutron diffraction, the martensitic transformation process under uniaxial compressive load was traced and the direct evidence on the variant redistribution induced by thermo-mechanical treatments was followed.

Thermo-Mechanical Treatment of Directionally Solidified Alloys
In general, the martensitic transformation is deformation-dominant diffusionless phase transformation with symmetry break. The lower symmetry of the product martensitic phase may result in the formation of self-accommodated multi-variants to compensate the elastic strains associated with the phase transformation. However, such self-accommodated microstructure is not favorable for the achievement of magnetic shape memory effect in Ni-Mn-Ga alloys, since the co-existence of multi-variants would greatly enhance the resistance for the variant reorientation. As the deformation accompanying the martensitic transformation is anisotropic, unidirectional constraint (tension or compression) during the martensitic transformation could promote the formation of certain favorable variants but eliminate some other unfavorable ones [34]. Therefore, strong preferential orientation of martensite can be achieved through the selective formation of favorable variants with the application of an external field during the martensitic transformation, thus to realize the optimization of crystallographic anisotropy and magnetic shape memory effect [2,4,13,14,35]. In this section, thermo-mechanical treatments (compressive load applied during the martensitic transformation) were introduced in order to reformulate the variant distribution. Through in-situ neutron diffraction, the martensitic transformation process under uniaxial compressive load was traced and the direct evidence on the variant redistribution induced by thermo-mechanical treatments was followed.

Austenite to 7M Martensite Transformation
Polycrystalline Ni 50 Mn 30 Ga 20 alloy with 7M martensite at room temperature was prepared by directional solidification. The cylindrical-shaped (φ5 mm×10 mm) samples with the axial direction parallel to solidification direction were cut from the homogenized ingot for thermo-mechanic treatment and neutron diffraction. The actual composition was verified to be Ni 50.1 Mn 28.8 Ga 21.1 by energy dispersive spectroscopy (EDS). According to DSC measurements, the start and finish temperatures of the forward (M s , M f ) and inverse martensitic transformation (A s , A f ) were determined to be 347.8 K, 331.3 K, 336.8 K and 352.2 K, respectively. Powder XRD measurements reveal that the directionally solidified Ni 50 Mn 30 Ga 20 alloy consists of 7M martensite at room temperature with lattice parameters a 7M = 4.2651 Å, b 7M = 5.5114 Å, c 7M = 42.365 Å, and β = 93.27 • , where the crystal structure of 7M martensite is depicted as an incommensurate monoclinic superstructure consisting of ten unit cells [22]. Moreover, microstructural observations have shown that the original austenite of the directionally solidified alloy forms coarse columnar-shaped grains with the grain size of several hundreds of microns along the solidification direction (SD) [36].
To reveal the global texture of the directionally solidified Ni 50 Mn 30 Ga 20 alloy, the complete pole figures were measured by neutron diffraction. The high penetration capability of neutrons, which exceeds that of X-rays by about four orders of magnitude, is considered to allow more reliable analysis on the global orientation distribution of the studied samples. Figure 2  Polycrystalline Ni50Mn30Ga20 alloy with 7M martensite at room temperature was prepared by directional solidification. The cylindrical-shaped (φ5 mm×10 mm) samples with the axial direction parallel to solidification direction were cut from the homogenized ingot for thermo-mechanic treatment and neutron diffraction. The actual composition was verified to be Ni50.1Mn28.8Ga21.1 by energy dispersive spectroscopy (EDS). According to DSC measurements, the start and finish temperatures of the forward (Ms, Mf) and inverse martensitic transformation (As, Af) were determined to be 347.8 K, 331.3 K, 336.8 K and 352.2 K, respectively. Powder XRD measurements reveal that the directionally solidified Ni50Mn30Ga20 alloy consists of 7M martensite at room temperature with lattice parameters a7M = 4.2651 Å, b7M = 5.5114 Å, c7M = 42.365 Å, and β = 93.27°, where the crystal structure of 7M martensite is depicted as an incommensurate monoclinic superstructure consisting of ten unit cells [22]. Moreover, microstructural observations have shown that the original austenite of the directionally solidified alloy forms coarse columnar-shaped grains with the grain size of several hundreds of microns along the solidification direction (SD) [36].
To reveal the global texture of the directionally solidified Ni50Mn30Ga20 alloy, the complete pole figures were measured by neutron diffraction. The high penetration capability of neutrons, which exceeds that of X-rays by about four orders of magnitude, is considered to allow more reliable analysis on the global orientation distribution of the studied samples.  In order to modify the variant distribution, cyclic thermo-mechanical treatments were performed on the directionally solidified Ni50Mn30Ga20 alloy, and the martensitic transformation process under external load was traced by in-situ neutron diffraction. The sample was first heated to 393 K to reach the fully austenite state, where the uniaxial compressive load was applied along the solidification direction (SD). Since the austenite of the directionally solidified Ni50Mn30Ga20 alloy possesses the strong <0 0 1>A preferential orientation in parallel to the solidification direction, the uniaxial compressive load was actually applied along the <0 0 1>A. Prior to thermo-mechanical treatment, the neutron diffraction patterns were collected at 393 K and 303 K in the 2θ range of ~36°-52° for the tested sample, as shown in Figure 3a. It is seen that within measured 2θ range, only In order to modify the variant distribution, cyclic thermo-mechanical treatments were performed on the directionally solidified Ni 50 Mn 30 Ga 20 alloy, and the martensitic transformation process under external load was traced by in-situ neutron diffraction. The sample was first heated to 393 K to reach the fully austenite state, where the uniaxial compressive load was applied along the solidification direction (SD). Since the austenite of the directionally solidified Ni 50 Mn 30 Ga 20 alloy possesses the strong <0 0 1> A preferential orientation in parallel to the solidification direction, the uniaxial compressive load was actually applied along the <0 0 1> A . Prior to thermo-mechanical treatment, the neutron diffraction patterns were collected at 393 K and 303 K in the 2θ range of~36 • -52 • for the tested sample, as shown in Figure 3a. It is seen that within measured 2θ range, only {2 0 0} A diffraction can be observed in the austenite (a A = 5.83 Å) temperature region. After martensitic transformation, {2 0 0} A evolves into {−1 0 10} 7M , {1 0 10} 7M and {0 2 0} 7M , where the {1 0 10} 7M diffraction possesses the strongest intensity. Figure 3b-d displays the serial patterns measured on cooling across the martensitic transformation under the compressive load of −10 MPa (Cycle 1), −25 MPa (Cycle 2) and −50 MPa (Cycle 3) applied along the solidification direction, respectively. With the increase of compressive load, the intensity of {0 2 0} 7M diffraction increases gradually. After three cycles of treatment, there remained almost only the {0 2 0} 7M diffraction in the measured 2θ range, as shown in Figure 3e. Apparently, the uniaxial compression has exerted significant influence on the variant distribution, creating a strong preferential orientation of the {0 2 0} 7M . Moreover, with increasing the compressive load, the macroscopic deformation amount accompanying the martensitic transformation increased gradually, i.e., −2.1%, −2.8% and −3.3% for Cycle 1, Cycle 2 and Cycle 3, respectively, which also indicates the increase in the degree of preferred variant orientation.   Figure 3e. Apparently, the uniaxial compression has exerted significant influence on the variant distribution, creating a strong preferential orientation of the {0 2 0}7M. Moreover, with increasing the compressive load, the macroscopic deformation amount accompanying the martensitic transformation increased gradually, i.e., −2.1%, −2.8% and −3.3% for Cycle 1, Cycle 2 and Cycle 3, respectively, which also indicates the increase in the degree of preferred variant orientation. The applied uniaxial compressive load can also result in the increase of martensitic transformation temperatures. Experimentally, the increases of Ms under −10 MPa, −25 MPa and −50 MPa applied during martensitic transformation were ~0.9 K, ~2.3 K and ~8.5 K, respectively [36]. The shifts of transformation temperatures under uniaxial load σ can be well explained by the Clausius-Clapeyron relation: dσ/dT = −∆S·ρ/ε, where ∆S and ε stand, respectively, for the entropy change and transformation strain, and ρ is the mass density. According to Clausius-Clapeyron relation, the increase of Ms under uniaxial load of −10 MPa, −25 MPa and −50 MPa was determined as 1.2 K, 4.1 K and 9.5 K, respectively, which is very close to the experimentally observed transformation temperature shifts [36].  The applied uniaxial compressive load can also result in the increase of martensitic transformation temperatures. Experimentally, the increases of M s under −10 MPa, −25 MPa and −50 MPa applied during martensitic transformation were~0.9 K,~2.3 K and~8.5 K, respectively [36]. The shifts of transformation temperatures under uniaxial load σ can be well explained by the Clausius-Clapeyron relation: dσ/dT = −∆S·ρ/ε, where ∆S and ε stand, respectively, for the entropy change and transformation strain, and ρ is the mass density. According to Clausius-Clapeyron relation, the increase of M s under uniaxial load of −10 MPa, −25 MPa and −50 MPa was determined as 1.2 K, 4.1 K and 9.5 K, respectively, which is very close to the experimentally observed transformation temperature shifts [36]. transformation. Under the compressive load applied during martensitic transformation, the variants with the reduction in the plane spacing should be more favorable. Thus, the formation of {0 2 0} 7M from {2 0 0} A is preferred under compressive load, leading to the large macroscopic strain and the formation of a strong <0 1 0> 7M preferred crystallographic orientation along the loading axis.

Austenite to 5M Martensite Transformation
In order to figure out the effect of external loading direction applied during the martensitic transformation on the selection of preferential variants, a directionally solidified Ni50Mn28.5Ga21.5 alloy with two preferred orientations with <0 0 1>A and <1 1 0>A parallel to the solidification direction (SD) was used to perform thermo-mechanical treatments. The rectangular parallelepiped samples (10 mm × 6.5 mm × 6.5 mm) with their longitudinal direction parallel to the solidification direction were cut from the homogenized alloy for neutron diffraction testing.
According to the EDS, the actual composition was determined to be Ni49.6Mn28.4Ga22.0. Powder XRD measurement shows that the alloy composes of 5M martensite at room temperature and the lattice parameters were determined to be a5M = 4.226 Å, b5M = 5.581 Å, c5M = 21.052 Å and β = 90.3°. DSC measurements demonstrate that the martensitic transformation occurs above the room temperature. The start and finish temperatures of the forward and reverse martensitic transformation determined from DSC measurements are, respectively, 322.9 K (Ms), 318.4 K (Mf), 329.5 K (As) and 333.2 K (Af) [38].  [38].

Austenite to 5M Martensite Transformation
In order to figure out the effect of external loading direction applied during the martensitic transformation on the selection of preferential variants, a directionally solidified Ni 50 Mn 28.5 Ga 21.5 alloy with two preferred orientations with <0 0 1> A and <1 1 0> A parallel to the solidification direction (SD) was used to perform thermo-mechanical treatments. The rectangular parallelepiped samples (10 mm × 6.5 mm × 6.5 mm) with their longitudinal direction parallel to the solidification direction were cut from the homogenized alloy for neutron diffraction testing.
According to the EDS, the actual composition was determined to be Ni 49.6 Mn 28.4 Ga 22.0 . Powder XRD measurement shows that the alloy composes of 5M martensite at room temperature and the lattice parameters were determined to be a 5M = 4.226 Å, b 5M = 5.581 Å, c 5M = 21.052 Å and β = 90.3 • . DSC measurements demonstrate that the martensitic transformation occurs above the room temperature. The start and finish temperatures of the forward and reverse martensitic transformation determined from DSC measurements are, respectively, 322.9 K (M s ), 318.4 K (M f ), 329.5 K (A s ) and 333.2 K (A f ) [38].  [38].
It is seen in Figure 5 that both the {1 0 5} 5M /{−1 0 5} 5M and {0 2 0} 5M poles are roughly located at the tilt angle Psi =~0 • ,~40 • and~90 • in the corresponding pole figures. Since {1 0 5} 5M /{−1 0 5} 5M and {0 2 0} 5M of 5M martensite are originated from {2 0 0} A for the transformation from austenite to 5M martensite [39], it can be inferred that the initial austenite of directionally solidified Ni 50 Mn 28.5 Ga 21.5 alloy mainly possesses two preferred orientation components, i.e., <0 0 1> A //SD and <1 1 0> A //SD. Thus, during the subsequent thermo-mechanical treatment process, the compressive load applied along SD during the martensitic transformation can be viewed along <0 0 1> A and <1 1 0> A . For the initial austenite with the preferred orientation of <0 0 1> A //SD, the resultant {1 0 5} 5M /{−1 0 5} 5M and {0 2 0} 5M of martensite are either perpendicular or parallel to the SD. More specifically, for {1 0 5} 5M / {−1 0 5} 5M , the orientation component perpendicular to the SD possesses the much higher intensity, indicating that {1 0 5} 5M /{−1 0 5} 5M tends to be perpendicular to SD. On the other hand, for {0 2 0} 5M , the orientation component parallel to the SD has the higher intensity. For the initial austenite with the orientation of <1 1 0> A //SD, the resultant {2 0 0} 5M /{0 0 10} 5M tends to be perpendicular to SD and {1 2 5} 5M /{−1 2 5} 5M to be parallel to SD.     For each cycle of the thermo-mechanical treatment, there remained two diffractions of 5M martensite, i.e., {0 2 0} 5M and {1 0 5} 5M /{−1 0 5} 5M , in the measured 2θ range after the martensitic transformation. However, the intensity ratio between {0 2 0} 5M and {1 0 5} 5M /{−1 0 5} 5M increases with the increase of compressive load, suggesting a redistribution of martensitic variants induced by the compressive load applied during the martensitic transformation [38].  Figure 7 shows the corresponding pole figures measured by neutron diffraction after five cycles of thermo-mechanical treatment for directionally solidified Ni50Mn28.5Ga21.5 alloy. It should be mentioned that, although the pole figures presented in Figure 5 (without thermo-mechanical treatment) and Figure 7 (after thermo-mechanical) were obtained from two different samples, the initial texture of two samples should be very similar since they were cut from the same directionally solidified alloy rod and one sample was just adjacent to the other when cutting. It is seen that under the compressive load applied along <0 0 1>A during the martensitic transformation (Figure 7a 5}5M⊥SD from {2 2 0}A of austenite should be preferentially activated to accommodate the external constraint. Therefore, the coupling between anisotropic lattice distortion in martensitic transformation and the external constraint dominates the preferred orientation of the martensite variants formed under the external constraint applied during the martensitic transformation [38].   Figure 5 (without thermo-mechanical treatment) and Figure 7 (after thermo-mechanical) were obtained from two different samples, the initial texture of two samples should be very similar since they were cut from the same directionally solidified alloy rod and one sample was just adjacent to the other when cutting. It is seen that under the compressive load applied along <0 0 1> A during the martensitic transformation (Figure 7a [38]. Thus, the variant orientation distribution under the compressive load applied during the martensitic transformation is strongly dependent on the austenite orientation and the direction of the external load.
With of austenite should be preferentially activated to accommodate the external constraint. Therefore, the coupling between anisotropic lattice distortion in martensitic transformation and the external constraint dominates the preferred orientation of the martensite variants formed under the external constraint applied during the martensitic transformation [38].

Orientation Inheritance from Austenite to 7M Martensite in Melt-Spun Ribbons
The rapid solidification based on melt-spinning technique has been proven to be an effective processing route for the preparation of ribbon shaped ferromagnetic shape memory alloys [40][41][42][43][44][45][46][47][48][49][50]. This method can avoid long time post heat treatment to achieve the composition homogeneity. Moreover, melt-spun ribbons usually tend to form a highly textured microstructure [51]. In this section, Ni53Mn22Ga25 and Ni51Mn27Ga22 ribbons with austenite and 7M martensite at room temperature respectively, were prepared by melt-spinning. The preferred orientation of austenite and 7M martensite in ribbons was presented and their correlation was further analyzed.

Orientation Inheritance from Austenite to 7M Martensite in Melt-Spun Ribbons
The rapid solidification based on melt-spinning technique has been proven to be an effective processing route for the preparation of ribbon shaped ferromagnetic shape memory alloys [40][41][42][43][44][45][46][47][48][49][50]. This method can avoid long time post heat treatment to achieve the composition homogeneity. Moreover, melt-spun ribbons usually tend to form a highly textured microstructure [51]. In this section, Ni 53 Figure 8a shows the EBSD orientation map measured from ribbon plane for the Ni 53 Mn 22 Ga 25 ribbons. It is seen that the austenite grain appears in equiaxed shape in the ribbon plane with an averaged grain size of~10-20 µm. Figure 8b displays the corresponding {2 2 0} A , {4 0 0} A and {4 2 2} A pole figures recalculated from EBSD measurements. Obviously, the austenite in ribbons develops a strong preferred orientation with {4 0 0} A parallel to ribbon plane [52], which should be attributed to the thermal gradient during the melt-spinning process. Figure 9 shows 10 of 20 Figure 8a shows the EBSD orientation map measured from ribbon plane for the Ni53Mn22Ga25 ribbons. It is seen that the austenite grain appears in equiaxed shape in the ribbon plane with an averaged grain size of ~10-20 μm. Figure 8b displays the corresponding {2 2 0}A, {4 0 0}A and {4 2 2}A pole figures recalculated from EBSD measurements. Obviously, the austenite in ribbons develops a strong preferred orientation with {4 0 0}A parallel to ribbon plane [52], which should be attributed to the thermal gradient during the melt-spinning process. Figure 9 shows     Figure 8a shows the EBSD orientation map measured from ribbon plane for the Ni53Mn22Ga25 ribbons. It is seen that the austenite grain appears in equiaxed shape in the ribbon plane with an averaged grain size of ~10-20 μm. Figure 8b displays the corresponding {2 2 0}A, {4 0 0}A and {4 2 2}A pole figures recalculated from EBSD measurements. Obviously, the austenite in ribbons develops a strong preferred orientation with {4 0 0}A parallel to ribbon plane [52], which should be attributed to the thermal gradient during the melt-spinning process. Figure 9 shows     [52]. Based on the pole figures presented in Figure 8 (austenite) and Figure 9 (7M martensite) in ribbons, it can be inferred that the transformation from austenite to 7M martensite exhibits a strong orientation inheritance and such orientation inheritance should be attributed to the intrinsic orientation relationship between austenite and 7M martensite [52].

Preferential Orientation and Variant Distribution of Thin Film
The magnetron sputtering technique has been viewed as an effective method for the texturation of ferromagnetic Ni-Mn-Ga thin films epitaxially grown on a single crystal substrate [53][54][55][56][57][58][59][60][61]. In general, the epitaxial growth of Ni-Mn-Ga thin films on single crystal substrate may produce quite different microstructures compared to those of polycrystalline bulk alloys [18,20,27]. The microstructural and crystallographic characterizations of thin films remain challenging due to the local constraints from substrates, the specific geometry of thin films, and the ultrafine microstructures of constituent phases. Because of the lack of direct correlation of martensitic microstructures with crystallographic orientations, precise information on the configurations of variants in Ni-Mn-Ga thin films are still not available. In this section, based on XRD measurements and electron backscatter diffraction (EBSD) analyses, the crystal structures of constituent phases, the configurations of martensite variants and their orientation correlations are addressed.

Global Microstructure and Texture of Thin Film
Epitaxially grown thin films with nominal composition of Ni 50 Mn 30 Ga 20 were prepared on the MgO(1 0 0) substrate with a Cr buffer layer by DC magnetron sputtering [62,63]. Figure 10a shows the ψ-dependent XRD patterns of the thin films obtained by conventional θ-2θ coupled scanning at the room temperature. At each tilt angle ψ, there appear only a limited number of diffraction peaks. Figure 10b presents the XRD patterns measured using a large-angle position sensitive detector under two different incident beam conditions. Some extra diffraction peaks can be seen in the 2θ range of 48 • -55 • and~82 • . Based on the XRD patterns in Figure 10a,b, it can be inferred that austenite, 7M martensite and NM martensite co-exist in the as-deposited thin films at room temperature. The austenite phase has a cubic L2 1 crystal structure with lattice constant a A = 5.773 Å. The 7M martensite phase has a monoclinic crystal structure with lattice constants a 7M = 4.262 Å, b 7M = 5.442 Å, c 7M = 41.997 Å, and β = 93.7 • . The NM martensite phase is of tetragonal crystal structure with lattice constants a NM = 3.835 Å and c NM = 6.680 Å [62,63].  [52]. Based on the pole figures presented in Figure 8 (austenite) and Figure 9 (7M martensite) in ribbons, it can be inferred that the transformation from austenite to 7M martensite exhibits a strong orientation inheritance and such orientation inheritance should be attributed to the intrinsic orientation relationship between austenite and 7M martensite [52].

Preferential Orientation and Variant Distribution of Thin Film
The magnetron sputtering technique has been viewed as an effective method for the texturation of ferromagnetic Ni-Mn-Ga thin films epitaxially grown on a single crystal substrate [53][54][55][56][57][58][59][60][61]. In general, the epitaxial growth of Ni-Mn-Ga thin films on single crystal substrate may produce quite different microstructures compared to those of polycrystalline bulk alloys [18,20,27]. The microstructural and crystallographic characterizations of thin films remain challenging due to the local constraints from substrates, the specific geometry of thin films, and the ultrafine microstructures of constituent phases. Because of the lack of direct correlation of martensitic microstructures with crystallographic orientations, precise information on the configurations of variants in Ni-Mn-Ga thin films are still not available. In this section, based on XRD measurements and electron backscatter diffraction (EBSD) analyses, the crystal structures of constituent phases, the configurations of martensite variants and their orientation correlations are addressed.

Global Microstructure and Texture of Thin Film
Epitaxially grown thin films with nominal composition of Ni50Mn30Ga20 were prepared on the MgO(1 0 0) substrate with a Cr buffer layer by DC magnetron sputtering [62,63]. Figure 10a shows the ψ-dependent XRD patterns of the thin films obtained by conventional θ-2θ coupled scanning at the room temperature. At each tilt angle ψ, there appear only a limited number of diffraction peaks. Figure 10b presents the XRD patterns measured using a large-angle position sensitive detector under two different incident beam conditions. Some extra diffraction peaks can be seen in the 2θ range of 48°-55°and ~82°. Based on the XRD patterns in Figure 10a,b, it can be inferred that austenite, 7M martensite and NM martensite co-exist in the as-deposited thin films at room temperature. The austenite phase has a cubic L21 crystal structure with lattice constant aA = 5.773 Å. The 7M martensite phase has a monoclinic crystal structure with lattice constants a7M = 4.262 Å, b7M = 5.442 Å, c7M = 41.997 Å, and β = 93.7°. The NM martensite phase is of tetragonal crystal structure with lattice constants aNM = 3.835 Å and cNM = 6.680 Å [62,63].   Figure 11b, the right side and the left side of the image represent the microstructure near the film surface and deep inside the film, respectively. Although the thin film has an overall plate-like microstructure, there exists certain plate thickening from its interior to its surface, which indicates a complete change of microstructural constituents or phases along the film thickness [28]. Based on EBSD measurements [62], it is revealed that the coarse plates in the top layer of the film are of the NM martensite, whereas the fine plates in the film interior are of the 7M martensite. Moreover, by combination of the XRD results, it is deduced that the NM martensite is located near the free surface of the film, the austenite above the substrate surface, and the 7M martensite in the intermediate layers between them.    Figure 11b, the right side and the left side of the image represent the microstructure near the film surface and deep inside the film, respectively. Although the thin film has an overall plate-like microstructure, there exists certain plate thickening from its interior to its surface, which indicates a complete change of microstructural constituents or phases along the film thickness [28]. Based on EBSD measurements [62], it is revealed that the coarse plates in the top layer of the film are of the NM martensite, whereas the fine plates in the film interior are of the 7M martensite. Moreover, by combination of the XRD results, it is deduced that the NM martensite is located near the free surface of the film, the austenite above the substrate surface, and the 7M martensite in the intermediate layers between them. Figure 11a presents a secondary electron (SE) image acquired from the top surface of an electrolytically polished sample with gradient thickness relative to the film surface. As schematically illustrated in Figure 11b, the right side and the left side of the image represent the microstructure near the film surface and deep inside the film, respectively. Although the thin film has an overall plate-like microstructure, there exists certain plate thickening from its interior to its surface, which indicates a complete change of microstructural constituents or phases along the film thickness [28]. Based on EBSD measurements [62], it is revealed that the coarse plates in the top layer of the film are of the NM martensite, whereas the fine plates in the film interior are of the 7M martensite. Moreover, by combination of the XRD results, it is deduced that the NM martensite is located near the free surface of the film, the austenite above the substrate surface, and the 7M martensite in the intermediate layers between them.    (Figure 12b), {0 0 4} NM and {2 2 0} NM tends to be close to the substrate surface. Although X-ray diffraction offers global texture information of the film, it is difficult to correlate the crystallographic features with those of the microstructure. Therefore, SEM/EBSD analysis is needed.  (Figure 12b), {0 0 4}NM and {2 2 0}NM tends to be close to the substrate surface. Although X-ray diffraction offers global texture information of the film, it is difficult to correlate the crystallographic features with those of the microstructure. Therefore, SEM/EBSD analysis is needed.  Figure 13 presents typical SE images of 7M martensite for Ni50Mn30Ga20 thin film. It is seen in Figure 13a that martensite plates are clustered in groups, exhibiting either low relative contrast (e.g., Group 1) with straight plates parallel to the substrate edges or high relative contrast (e.g., Group 2 and Group 3) with bent plates oriented at roughly 45° with respect to the substrate edges. In addition, the traces of inter-plate interfaces in high relative contrast zones have three distinct orientations, as indicated by the dotted yellow and green lines and the solid black lines in Figure 13b. In fact, the SE image contrast is related to the surface topography of an observed object. Thus, the low relative contrast zones and the high relative contrast zones are expected to have low and high surface reliefs, respectively. Here, the low relative contrast zone (Group 1) corresponds to the so-called Y pattern, and the high relative contrast zone (Group 2 or Group 3) to the X pattern [64].

7M Variants Distribution in the Thin Film
EBSD measurements show that one 7M martensite plate corresponds to one orientation variant. There are in total four different variants distributed in one plate group. Here, the four orientation variants, representing one plate group with low and high relative contrast, are denoted by the show that there exist three types of twinning relation between the adjacent variant, i.e., Type-I, or Type-II, or compound twinning relation, for the four variants in one plate group. The complete twinning elements were reported in elsewhere [62].  Figure 13a that martensite plates are clustered in groups, exhibiting either low relative contrast (e.g., Group 1) with straight plates parallel to the substrate edges or high relative contrast (e.g., Group 2 and Group 3) with bent plates oriented at roughly 45 • with respect to the substrate edges. In addition, the traces of inter-plate interfaces in high relative contrast zones have three distinct orientations, as indicated by the dotted yellow and green lines and the solid black lines in Figure 13b. In fact, the SE image contrast is related to the surface topography of an observed object. Thus, the low relative contrast zones and the high relative contrast zones are expected to have low and high surface reliefs, respectively. Here, the low relative contrast zone (Group 1) corresponds to the so-called Y pattern, and the high relative contrast zone (Group 2 or Group 3) to the X pattern [64].
EBSD measurements show that one 7M martensite plate corresponds to one orientation variant. There are in total four different variants distributed in one plate group. Here, the four orientation variants, representing one plate group with low and high relative contrast, are denoted by the symbols V L A , V L B , V L C , V L D and V H A , V H B , V H C , and V H D , respectively. Crystallographic calculations show that there exist three types of twinning relation between the adjacent variant, i.e., Type-I, or Type-II, or compound twinning relation, for the four variants in one plate group. The complete twinning elements were reported in elsewhere [62].   Analyses show that, in the low relative contrast zone, the majority of variants are in Type-I twin relation. Both Type-I and Type-II twin interfaces are nearly perpendicular to the substrate surface. For the high relative contrast zone, the majority of variants are in Type-II twin relation. The existence of height differences between adjacent variants accounts for the high relative contrast in this region. Further crystallographic calculations indicate that the preferential occurrence of different twinning type is a consequence of external constraint from the rigid substrate. The dominated twinning type allows effective cancellation of the shear deformation in the film normal direction [62]. Figure 15a shows an SE image of NM martensite for Ni50Mn30Ga20 thin film. Similar to 7M martensite, the clustered colonies can also be characterized by two different relative contrasts, i.e., low relative contrast (Z1) or high relative contrast (Z2), as illustrated in Figure 15a. The low relative contrast zones consist of long and straight plates running with their length direction parallel to one edge of the substrate (i.e., [1 0 0]MgO or [0 1 0]MgO). The high relative contrast zones are of shorter and somewhat bent plates that orient roughly at 45°with respect to the substrate edges.    Analyses show that, in the low relative contrast zone, the majority of variants are in Type-I twin relation. Both Type-I and Type-II twin interfaces are nearly perpendicular to the substrate surface. For the high relative contrast zone, the majority of variants are in Type-II twin relation. The existence of height differences between adjacent variants accounts for the high relative contrast in this region. Further crystallographic calculations indicate that the preferential occurrence of different twinning type is a consequence of external constraint from the rigid substrate. The dominated twinning type allows effective cancellation of the shear deformation in the film normal direction [62]. Figure 15a shows an SE image of NM martensite for Ni50Mn30Ga20 thin film. Similar to 7M martensite, the clustered colonies can also be characterized by two different relative contrasts, i.e., low relative contrast (Z1) or high relative contrast (Z2), as illustrated in Figure 15a. The low relative contrast zones consist of long and straight plates running with their length direction parallel to one edge of the substrate (i.e., [1 0 0]MgO or [0 1 0]MgO). The high relative contrast zones are of shorter and somewhat bent plates that orient roughly at 45°with respect to the substrate edges. Analyses show that, in the low relative contrast zone, the majority of variants are in Type-I twin relation. Both Type-I and Type-II twin interfaces are nearly perpendicular to the substrate surface. For the high relative contrast zone, the majority of variants are in Type-II twin relation. The existence of height differences between adjacent variants accounts for the high relative contrast in this region. Further crystallographic calculations indicate that the preferential occurrence of different twinning type is a consequence of external constraint from the rigid substrate. The dominated twinning type allows effective cancellation of the shear deformation in the film normal direction [62]. Figure 15a shows an SE image of NM martensite for Ni 50 Mn 30 Ga 20 thin film. Similar to 7M martensite, the clustered colonies can also be characterized by two different relative contrasts, i.e., low relative contrast (Z 1 ) or high relative contrast (Z 2 ), as illustrated in Figure 15a. The low relative contrast zones consist of long and straight plates running with their length direction parallel to one edge of the substrate (i.e., [1 0 0] MgO or [0 1 0] MgO ). The high relative contrast zones are of shorter and somewhat bent plates that orient roughly at 45 • with respect to the substrate edges.

NM Variants Distribution in the Thin Film
Microstructural observation reveals that there exist two variants distributed alternately in one martensite plate, as highlighted with yellow and blue lines in Figure 15b. Of the two contrasted neighboring lamellae, one is thicker and the other is thinner, which is different from the situation of 7M martensite. The two lamellar variants in one plate have a compound twin relationship with the {1 1 2} NM as twinning plane and <1 1 −1> NM as twinning direction. As the BSE image contrast for a monophase microstructure with homogenous chemical composition originates from the orientation differences of the microstructural components, the thicker and thinner lamellae distributed alternately in each plate should be correlated with two distinct orientations, which is also confirmed by the indexation of Kikuchi line patterns [63]. Microstructural observation reveals that there exist two variants distributed alternately in one martensite plate, as highlighted with yellow and blue lines in Figure 15b. Of the two contrasted neighboring lamellae, one is thicker and the other is thinner, which is different from the situation of 7M martensite. The two lamellar variants in one plate have a compound twin relationship with the {1 1 2}NM as twinning plane and <1 1 −1>NM as twinning direction. As the BSE image contrast for a monophase microstructure with homogenous chemical composition originates from the orientation differences of the microstructural components, the thicker and thinner lamellae distributed alternately in each plate should be correlated with two distinct orientations, which is also confirmed by the indexation of Kikuchi line patterns [63]. Detailed EBSD orientation analyses were conducted on the NM martensite plates in the low and high relative contrast zones (Z1 and Z2 in Figure15a). In each variant colony, there are four types of plates, i.e., A, B, C and D in the low relative contrast (Z1) zones and 1, 2, 3 and 4 in the high relative contrast (Z2) zones, as illustrated in Figure 15c,d. Since one NM plate contains two variants, there are in total eight NM variants in one variant colony. For easy visualization, they are denoted as V1, V2, …, V8 in Figure15c and SV1, SV2, …, SV8 in Figure 15d, where the symbols with odd subscripts correspond to the thicker (major) variants and those with even subscripts the thinner (minor) variants. The measured orientations of the NM variants in the two relative contrast zones are presented in the form of {0 0 1}NM and {1 1 0}NM pole figures, as displayed in Figure 16a,b [63].
For the low relative contrast zones (Z1), the major and minor variants are oriented respectively with their {1 1 0}NM planes and {0 0 1}NM planes nearly parallel to the substrate surface (Figure 16a). In the high relative contrast zones (Z2), such plane parallelisms hold for plates 2 and 4 but with an Detailed EBSD orientation analyses were conducted on the NM martensite plates in the low and high relative contrast zones (Z 1 and Z 2 in Figure 15a). In each variant colony, there are four types of plates, i.e., A, B, C and D in the low relative contrast (Z 1 ) zones and 1, 2, 3 and 4 in the high relative contrast (Z 2 ) zones, as illustrated in Figure 15c,d. Since one NM plate contains two variants, there are in total eight NM variants in one variant colony. For easy visualization, they are denoted as V 1 , V 2 , . . . , V 8 in Figure 15c and SV 1 , SV 2 , . . . , SV 8 in Figure 15d, where the symbols with odd subscripts correspond to the thicker (major) variants and those with even subscripts the thinner (minor) variants. The measured orientations of the NM variants in the two relative contrast zones are presented in the form of {0 0 1} NM and {1 1 0} NM pole figures, as displayed in Figure 16a,b [63].
For the low relative contrast zones (Z 1 ), the major and minor variants are oriented respectively with their {1 1 0} NM planes and {0 0 1} NM planes nearly parallel to the substrate surface (Figure 16a). In the high relative contrast zones (Z 2 ), such plane parallelisms hold for plates 2 and 4 but with an exchange of the planes between the major and minor variants, whereas both major and minor variants in plates 1 and 3 are oriented with their {1 1 0} NM planes nearly parallel to the substrate surface (Figure 16b). In correlation with the microstructural observations, plates 2 and 4 are featured with higher brightness and plates 1 and 3 with lower brightness [63].
Indeed, for the two distinct relative contrast zones, the crystallographic orientations of the in-plate martensitic variants with respect to the substrate surface are not the same, which should be the origin of the topological differences observed for the two relative contrast zones. In the low relative contrast zones, the in-plate major and minor variants have the same orientation combination for all NM plates and they are distributed symmetrically to the inter-plate interfaces. As no microscopic height misfits across inter-plate interfaces appear in the film normal direction, the relative contrast between adjacent NM plates is not pronounced in the SE images. However, in the high relative contrast zone, the asymmetrically distributed lamellar variants in adjacent NM plates lead to the pronounced height misfits across inter-plate interfaces in the film normal direction, which gives rise to surface reliefs, hence the high relative contrast between adjacent NM plates [63]. exchange of the planes between the major and minor variants, whereas both major and minor variants in plates 1 and 3 are oriented with their {1 1 0}NM planes nearly parallel to the substrate surface (Figure 16b). In correlation with the microstructural observations, plates 2 and 4 are featured with higher brightness and plates 1 and 3 with lower brightness [63]. Indeed, for the two distinct relative contrast zones, the crystallographic orientations of the in-plate martensitic variants with respect to the substrate surface are not the same, which should be the origin of the topological differences observed for the two relative contrast zones. In the low relative contrast zones, the in-plate major and minor variants have the same orientation combination for all NM plates and they are distributed symmetrically to the inter-plate interfaces. As no microscopic height misfits across inter-plate interfaces appear in the film normal direction, the relative contrast between adjacent NM plates is not pronounced in the SE images. However, in the high relative contrast zone, the asymmetrically distributed lamellar variants in adjacent NM plates lead to the pronounced height misfits across inter-plate interfaces in the film normal direction, which gives rise to surface reliefs, hence the high relative contrast between adjacent NM plates [63].

Conclusions
(1) The influence of uniaxial compression on martensitic transformation in directionally solidified Ni50Mn30Ga20 and Ni50Mn28.5Ga21.5 polycrystalline alloys was studied by neutron diffraction. It was shown that the distribution of martensite variants can be tuned through cyclic thermo-mechanical treatments. For the Ni50Mn30Ga20 alloy with <0 0 1>A preferential orientation parallel to the solidification direction, a strong <0 1 0>7M preferential orientation of 7M martensite along the loading direction (//solidification direction) was induced by the external compression during martensitic transformation. In addition, it was found that the selection of

Conclusions
(1) The influence of uniaxial compression on martensitic transformation in directionally solidified Ni 50 Mn 30 Ga 20 and Ni 50 Mn 28.5 Ga 21.5 polycrystalline alloys was studied by neutron diffraction. It was shown that the distribution of martensite variants can be tuned through cyclic thermo-mechanical treatments. For the Ni 50 Mn 30 Ga 20 alloy with <0 0 1> A preferential orientation parallel to the solidification direction, a strong <0 1 0> 7M preferential orientation of 7M martensite along the loading direction (//solidification direction) was induced by the external compression during martensitic transformation. In addition, it was found that the selection of preferential variants induced by thermo-mechanical treatments was strongly dependent on the austenite orientation and the direction of external load, which was evidenced in Ni 50 Mn 28.5 Ga 21.5 polycrystalline alloys with <0 0 1> A and <1 1 0> A parallel to the solidification direction. In the low relative contrast zone, the majority of variants are in Type-I twin relation, whereas for the high relative contrast zone, the majority of variants are in Type-II twin relation. The selection of twinning type is a consequence of external constraint from the rigid substrate and the twinning type with less shear deformation in the film normal direction is favored. For NM martensite, one plate group of NM martensite also consists of 4 martensite plates, but each plate is composed of two twin related variants with one thicker than the other. The in-plate major and minor variants are distributed symmetrically to the inter-plate interfaces in low relative contrast zones, but asymmetrically distributed in high relative contrast zones. The difference in the orientation combination of the in-plate variants accounts for the topological differences observed for the two relative contrast zones.
The presented investigations are expected to provide some fundamental information for the microstructure modification and functional performance control of ferromagnetic shape memory alloys.