Dr Claude Esling

Yudong Zhang

Dr Yuping Ren

Dr Song Li

Dr Na Xiao

Dr Jing Bai

Ms Nan Xu

Ms Shiying Wang

Dr Zhangzhi Shi

Mr Yan Haile

Ms Xiaorui Liu

Ms Jianshen

马氏体变体为复合孪生关系 。 在平直的低反差区域

, 复合孪生的

N M 马氏体变体关于板

条界面对称分布 。 然而在弯曲的高反差区域

N M 马氏体变体关于板条界面

不对称分布 。 对于七层调制马氏体

, 在平直的低反差区域

Nimnga 薄膜中存在

个 Nm

马氏体变体团 , 每个

N M 马氏体变体团有

种 Nm

马氏体变体 , 因此在整个

Nimnga 薄膜中

种不同 取向的

N M 马氏体变体

。 对于

7m 马氏体

, 同样存在

个变体团 , 不过每个变体团有

种取向的 7m

马氏体变体 , 总共有

马氏体变体 。 这说明

, Nimnga

N M 马氏体变体必须经过

7m 才能获得

个变体 。 每种

马氏体变体转变为两种 取向的

EBSD 获得马氏体变体的取向和晶体学计算可知,在一个板条内部的两个 NM

Keywords: ferromagnetic shape memory alloys (FSMAs), Ni-Mn-Ga thin films, martensitic transformation, EBSD, misorientation, Texture

Epitaxial Ni-Mn-Ga thin films have attracted considerable attention, since they are promising candidates for magnetic sensors and actuators in micro-electro-mechanical systems.

Comprehensive information on the microstructural and crystallographic features of the NiMnGa films and their relationship with the constraints of the substrate is essential for further property optimization. In the present work, epitaxial Ni-Mn-Ga thin films were produced by DC magnetron sputtering and then characterized by x-ray diffraction technique (XRD) and backscatter electron diffraction equipped in scanning electron microscope (SEM-EBSD).

Epitaxial NiMnGa thin films with nominal composition of Ni50Mn30Ga20 and thickness of 1.5 µm were successfully fabricated on MgO monocrystalline substrate by DC magnetron sputtering, after the optimization of sputtering parameters such as sputtering power, substrate temperature and seed layer by the present work. XRD diffraction measurements demonstrate that the epitaxial NiMnGa thin films are composed of three phases: austenite, NM martensite and 7M martensite. With the optimized measurement geometries, maximum number of diffraction peaks of the concerning phases, especially of the low symmetrical 7M martensite, are acquired and analyzed. The lattice constants of all the three phases under the constraints of the substrate in the films are fully determined. These serve as prerequisites for the subsequent EBSD crystallographic orientation characterizations. SEM-EBSD in film depth analyses further verified the co-existence situation of the three constituent phases: austenite, 7M martensite and NM martensite. NM martensite is located near the free surface of the film, austenite above the substrate surface, and 7M martensite in the intermediate layers between austenite and NM martensite. Microstructure characterization shows that both the 7M martensite and NM martensite are of plate morphology and organized into two characteristic zones featured with low and high relative second electron image contrast. Local martensite plates with similar plate morphology orientation are organized into plate groups or groups or variant colonies. Further EBSD characterization indicates that there are four distinct martensite plates in Abstract -IV-each variant groups for both NM and 7M martensite. Each NM martensite plate is composed of paired major and minor lamellar variants in terms of their thicknesses having a coherent interlamellar interface, whereas, each 7M martensite plate contains one orientation variant. Thus, there are four orientation 7M martensite variants and eight orientation NM martensite variants in one variant group. According to the crystallographic orientation of martensites and the crystallographic calculation, for NM martensite, the inter-plate interfaces are composed of compound twins in adjacent NM plates. The symmetrically distribution of compound twins results in the long and straight plate interfaces in the low relative contrast zone. The asymmetrically distribution leads to the change of inter-plate interface orientation in the high relative contrast zone.

For 7M martensite, both Type-I and Type-II twin interfaces are nearly perpendicular to the substrate surface in the low relative contrast zones. The Type-I twin pairs appear with much higher frequency, as compared with that of the Type-II twin pairs. However, there are two Type-II twin interface trace orientations and one Type-I twin interface trace orientation in the high relative contrast zones. The Type-II twin pairs are more frequent than the Type-I twin pairs. The inconsistent occurrences of the different types of twins in different zones are originated from the substrate constrain.

The crystallographic calculation also indicates that the martensitic transformation sequence is from Austenite to 7M martensite and then transform into NM martensite (A→7M→NM). The present study intends to offer deep insights into the crystallographic features and martensitic transformation of epitaxial NiMnGa thin films.

Des couches minces é pitaxiales avec NiMnGa de composition nominale Ni50Mn30Ga20 et d'é paisseur 1,5 µm ont é té fabriqué es avec succè s sur le substrat monocristallin de MgO par pulvé risation cathodique magné tron DC, aprè s l'optimisation des paramè tres tels que la puissance de pulvé risation cathodique, la tempé rature du substrat et de la couche d'ensemencement dans le cadre du pré sent travail.

Les mesures de diffraction DRX montrent que les couches minces é pitaxiales NiMnGa sont composé es de trois phases: austé nite, martensite NM et martensite modulé e 7M. Avec les gé omé tries de mesure optimisé es, le nombre maximum possible de pics de diffraction des phases relatives, en particulier compte tenu de la basse symé trie de la martensite 7M, sont acquis et analysé s. Les constantes de ré seau de l'ensemble des trois phases dans le cadre des contraintes du substrat dans les films sont entiè rement dé terminé es.

L'analyse SEM-EBSD en profondeur du film a permis en outre de vé rifier la situation de coexistence de trois phases constitutives: austé nite, 7M martensite et martensite NM. La martensite NM se trouve prè s de la surface libre du film, l'austé nite au-dessus de la surface du substrat, et la martensite 7M dans les couches intermé diaires entre l'austé nite et la martensite NM. La caracté risation de microstructure montre que la martensite 7M et la martensite NM ont une morphologie de plaque et sont organisé es en deux zones caracté ristiques dé crites avec des bas et haut contraste en images d'électrons secondaires. Des plaques de martensite locales similaire en orientation morphologique sont organisé es en groupes de plaques ou colonies ou variantes de colonies.

Une caracté risation plus poussé e en EBSD indique qu'il existe quatre plaques de martensite distinctes dans chaque colonie de variante à la fois pour la martensite NM et 7M.

Chaque plaque de martensite NM est composé e de variantes lamellaires majeures et mineures en termes d'épaisseurs appariées et ayant une interface interlamellaire cohé rente, alors que chaque plaque de martensite 7M contient une variante d'orientation. Ainsi, il existe quatre variantes d'orientation de martensite 7M et huit variantes d'orientation de martensite NM dans une colonie de variantes.

Selon l'orientation cristallographique des martensites et des calculs cristallographiques, pour la martensite NM, les interfaces inter-plaques sont constitué es de macles de type composé es dans des plaques adjacentes de martensite NM. La distribution symé trique des macles composé es ré sulte dans des interfaces de plaques longues et droites dans la zone de contraste relatif faible. La répartition asymétrique conduit à la modification de l'orientation d'interface entre les plaques de la zone de contraste relativement é levé .Pour la martensite 7M, à la fois les interfaces de type I et de type II sont à peu prè s perpendiculaires à la surface du substrat dans les zones à faible contraste relatif. Les paires de macles de type-I apparaissent avec une fré quence beaucoup plus é levé e, par comparaison avec celle des macles de type II.

Cependant, il ya deux traces d'interface de macles de type II et une trace d'interface de macles de type I dans les zones de contraste relatifs é levé s. Les paires de macles de type II sont plus fré quentes que les paires de macles de type-I. Les apparitions incohé rentes des diffé rents types de macles dans les diffé rentes zones sont dues à la contrainte du substrat.

Le calcul cristallographique montre é galement que la sé quence de la transformation martensitique est d'austé nite en martensite 7M qui est ensuite transformé e en martensite NM (A →7M→NM). La présente étude se propose d'offrir une étude approfondie des caractéristiques cristallographiques et de la transformation martensitique de films minces de NiMnGa pré paré s par é pitaxie.

Mots clé s:

Alliages ferromagné tique à mé moire de forme (FSMAs); Films minces de Ni-Mn-Ga; transformation martensitique; EPCA; dé sorientation; texture。

General introduction

The miniaturization of electronic systems and the increase of their functionality require the implementation of active and sensitive devices on a small scale [START_REF] Yang | Substrate constraint induced variant selection of 7M martensite in epitaxial NiMnGa thin films[END_REF].

Micro-electro-mechanical systems (MEMS) or nano-electro-mechanical systems (NEMS) are one of the potential technologies for decreasing size of these devices and have been established in wide domains such as information technology, automotive, aerospace and bio-medical applications [2,3]. Developing excellent active and sensitive materials are of technological interest and also represent dominating challenges for the design of MEMS and NEMS. In particular, active and sensitive materials that can exhibit large strains with rapid response (also referred to smart materials) are desirable [4,5].

A number of active materials such as magnetostrictive materials, piezoelectric ceramics and shape memory alloys that show a few percent strains under an applied external field have been proposed as these kinds of actuator and sensor materials [6][7][8][START_REF] Fukuda | Giant magnetostriction in Fe-based ferromagnetic shape memory alloys[END_REF][START_REF] Handley R C | Modern magnetic materials: principles and applications[END_REF][START_REF] Kohl | Ferromagnetic Shape Memory Microactuators[END_REF]. Among the numerous advanced materials, the ferromagnetic shape memory alloys (FSMAs), also referred to magnetic shape memory alloys (MSMAs), are a group of fascinating material, which can provide a significant and reversible strain at high frequency driven by external magnetic field [START_REF] Faehler | An Introduction to Actuation Mechanisms of Magnetic Shape Memory Alloys[END_REF][START_REF] Jani | A review of shape memory alloy research, applications and opportunities[END_REF][START_REF] Jiles | Recent advances and future directions in magnetic materials[END_REF][START_REF] Wilson | New materials for micro-scale sensors and actuators: An engineering review[END_REF][START_REF] Nespoli | The high potential of shape memory alloys in developing miniature mechanical devices: A review on shape memory alloy mini-actuators[END_REF][START_REF] Hauser | Chapter 8 -Thin magnetic films[END_REF][START_REF] Acet | Chapter Four -Magnetic-Field-Induced Effects in Martensitic Heusler-Based Magnetic Shape Memory Alloys[END_REF]. FSMAs not only overcome the low potential efficiency of thermally controlled shape memory actuators, but also exhibit much larger output strains than those of the magnetostrictive, the piezoelectric or the electrostrictive materials. The unique properties of FSMAs have attracted extensive research interest during the past few years.

The discovery of ferromagnetic Ni-Mn-based Heusler alloys quickly promoted a breakthrough in the application of ferromagnetic shape memory alloys [START_REF] Sozinov | 12% magnetic field-induced strain in Ni-Mn-Ga-based non-modulated martensite[END_REF][START_REF] Sozinov | Giant magnetic-field-induced strain in NiMnGa seven-layered martensitic phase[END_REF][START_REF] Kohl | Recent Progress in FSMA Microactuator Developments[END_REF]. To date, magnetic field induced strain as high as 12% has been achieved recently in the bulk NiMnGa single crystals. Whereas, although extensive research has been centered on bulk polycrystalline NiMnGa alloys to understand their mechanical, magnetic properties and phase transformation behaviors [START_REF] Xu | Ni-Mn-Ga shape memory alloys development in China[END_REF][START_REF] Cong | Crystal structures and textures in the hot-forged Ni-Mn-Ga shape memory alloys[END_REF][START_REF] Cong | Crystal structure and phase transformation in Ni53Mn25Ga22 shape memory alloy from 20 K to 473 K[END_REF][START_REF] Cong | Crystal structures and textures of hot forged Ni48Mn30Ga22 alloy investigated by neutron diffraction technique[END_REF][START_REF] Li | Composition-dependent ground state of martensite in Ni-Mn-Ga alloys[END_REF][START_REF] Li | Microstructure and magnetocaloric effect of melt-spun Ni52Mn26Ga22 ribbon[END_REF][START_REF] Li | Twin relationships of 5M modulated martensite in Ni-Mn-Ga alloy[END_REF][START_REF] Wang | Twinning stress in shape memory alloys: Theory and experiments[END_REF][START_REF] Pond R C | Deformation twinning in Ni2MnGa[END_REF][START_REF] Matsuda | Transmission Electron Microscopy of Twins in 10M Martensite in Ni-Mn-Ga Ferromagnetic Shape Memory Alloy[END_REF][START_REF] Murray | 6% magnetic-field-induced strain by twin-boundary motion in ferromagnetic Ni--Mn--Ga[END_REF], magnetic field induced strains in bulk NiMnGa polycrystals are still in the magnitude order of 1%, owing to the complex microstructure. In addition, bulk NiMnGa alloys are very brittle in polycrystalline state, making them difficult to deform into desirable shape.

Ductility can be improved in a single crystal or thin film form. NiMnGa thin films deposited with various physical vapor deposition methods have shown superior mechanical properties [3,[START_REF] Backen | Epitaxial Ni-Mn-Ga Films for Magnetic Shape Memory Alloy Microactuators[END_REF][START_REF] Eichhorn | Microstructure of freestanding single-crystalline Ni2MnGa thin films[END_REF][START_REF] Dunand | Size Effects on Magnetic Actuation in Ni-Mn-Ga Shape-Memory Alloys[END_REF][START_REF] Chernenko | Magnetic domains in Ni-Mn-Ga martensitic thin films[END_REF][START_REF] Hakola | Ni-Mn-Ga films on Si, GaAs and Ni-Mn-Ga single crystals by pulsed laser deposition[END_REF][START_REF] Dong | Shape memory and ferromagnetic shape memory effects in single-crystal Ni[sub 2]MnGa thin films[END_REF][START_REF] Castano | Structure and thermomagnetic properties of polycrystalline Ni--Mn--Ga thin films[END_REF][START_REF] Dong | Epitaxial growth of ferromagnetic Ni[sub 2]MnGa on GaAs(001) using NiGa interlayers[END_REF][START_REF] Dong | Molecular beam epitaxy growth of ferromagnetic single crystal (001) Ni[sub 2]MnGa on (001) GaAs[END_REF]. However, most of the as-deposited NiMnGa thin films are composed of complex microstructure and several phases, which are the main obstacles to achieve huge magnetic field induced strain [START_REF] Tillier | Tuning macro-twinned domain sizes and the b-variants content of the adaptive 14-modulated martensite in epitaxial Ni-Mn-Ga films by co-sputtering[END_REF][START_REF] Leicht | Microstructure and atomic configuration of the (001)-oriented surface of epitaxial Ni-Mn-Ga thin films[END_REF][START_REF] Kaufmann | Modulated martensite: why it forms and why it deforms easily[END_REF][START_REF] Tillier | Martensite structures and twinning in substrate-constrained epitaxial Ni-Mn-Ga films deposited by a magnetron co-sputtering process[END_REF][START_REF] Kallmayer | Compositional dependence of element-specific magnetic moments in Ni 2 MnGa films[END_REF][START_REF] Annadurai | Composition, structure and magnetic properties of sputter deposited Ni-Mn-Ga ferromagnetic shape memory thin films[END_REF]. Revelation of the local crystallographic orientation and interfaces between microstructural constituents in epitaxial NiMnGa thin films have been an essential issue, in order to provide useful guidance for post treatments to eliminate the undesired martensite variants [START_REF] Witherspoon | Texture and training of magnetic shape memory foam[END_REF][START_REF] Wang | A variational approach towards the modeling of magnetic field-induced strains in magnetic shape memory alloys[END_REF][START_REF] Gaitzsch | Magnetomechanical training of single crystalline Ni-Mn-Ga alloy[END_REF][START_REF] Chulist | Twin boundaries in trained 10M Ni-Mn-Ga single crystals[END_REF][START_REF] Chmielus | Training, constraints, and high-cycle magneto-mechanical properties of Ni-Mn-Ga magnetic shape-memory alloys[END_REF].

Ferromagnetic shape memory effect

Of all shape memory effects discovered, magnetic field induced shape memory effect is the most conducive to application, due to its high response frequency and giant actuation strain. The nature of giant magnetic-field-induced strain is due to either orientation rearrangements of martensite variants or the structural transition of these materials [START_REF] Acet | Chapter Four -Magnetic-Field-Induced Effects in Martensitic Heusler-Based Magnetic Shape Memory Alloys[END_REF][START_REF] Liu | Giant magnetocaloric effect driven by structural transitions[END_REF][START_REF] Kainuma | Magnetic-field-induced shape recovery by reverse phase transformation[END_REF]. Orientation rearrangements of martensite variants, also referred to magnetic field induced re-orientation, is based on magnetostructural coupling which takes advantage of the larger uniaxial magnetocrystalline anisotropy of the martensite phase [START_REF] Acet | Chapter Four -Magnetic-Field-Induced Effects in Martensitic Heusler-Based Magnetic Shape Memory Alloys[END_REF][START_REF] Thomas | Magnetically induced reorientation of martensite variants in constrained epitaxial Ni-Mn-Ga films grown on MgO(001)[END_REF]. Normally, the c-axis (short axis) is the easy axis in the modulated martensites, while it is the hard-axis in non-modulated martensite which displays easy magnetization planes perpendicular to the c-axis. As shown Fig. 1.1, in the practical materials, twin variants in martensite have magnetic moments in different directions. On the application of magnetic field, the variants that are not aligned with the applied field, will de-twin to align their moments with the external magnetic field. This movement results in a macroscopic change in length resulting in strain.

The unique mechanism of magnetic field induced reorientation has been observed in NiMnGa alloys [START_REF] Thomas | Magnetically induced reorientation of martensite variants in constrained epitaxial Ni-Mn-Ga films grown on MgO(001)[END_REF][START_REF] Tickle | Ferromagnetic Shape Memory Materials[END_REF]. The microstructure evolution due to magnetic field induced variant rearrangement [START_REF] Tickle | Ferromagnetic Shape Memory Materials[END_REF].

The other mechanism to achieve giant magnetic field induced strain is the structural transitions under external magnetic field. The structural transitions contains the transition from paramagnetic parent phase to ferromagnetic martensite observed in Fe-Mn-Ga alloys [START_REF] Zhu | Magnetic-field-induced transformation in FeMnGa alloys[END_REF] and the reverse transition from antiferromagnetic martensite to ferromagnetic parent phase observed in Ni-Mn-In(Sn) alloys [START_REF] Hernando | Thermal and magnetic field-induced martensite-austenite transition in Ni(50.3)Mn(35.3)Sn(14.4) ribbons[END_REF][START_REF] Krenke | Martensitic transitions and the nature of ferromagnetism in the austenitic and martensitic states of Ni-Mn-Sn alloys[END_REF]. Since the required external magnetic field to induce structural transition is much larger than that to induce the reorientation of martensite variants, the NiMnGa Heusler alloys are more preferable to be applied in the practical actuators and sensors.

Bulk NiMnGa Heusler alloys

NiMnGa alloys are one of the typical Heusler alloys and exhibit magnetic field induced strain as large as 6%~12% in the order of kHz [START_REF] Sozinov | 12% magnetic field-induced strain in Ni-Mn-Ga-based non-modulated martensite[END_REF][START_REF] Murray | 6% magnetic-field-induced strain by twin-boundary motion in ferromagnetic Ni--Mn--Ga[END_REF], even under relatively low bias magnetic fields. However, the phase constituents, crystal structure of various phases, crystallographic features and mechanical properties of the Ni-Mn-Ga alloys are highly sensitive to the chemical composition and temperature. A deep and complete understanding of NiMnGa alloys is crucial to deal with the magnetic field induced reorientation of NiMnGa martensite variants. Their crystal structures, and crystallographic features and some specific properties are introduced here. NiMnGa alloys have an L21 structure in the austenite state, which is based on the bcc structure and consists of four interpenetrating face centered cubic (FCC) sublattices as shown for Ni2MnGa in Fig. 1.3(a). When the temperature is decreased, Ni2MnGa and off-stoichiometric Ni-Mn-Ga Heusler alloys undergoes martensitic transformations and transforms to the L10 tetragonal structure at low-enough Ga concentrations, as shown in Fig. 1.3(b) [START_REF] Pons | Structure of the layered martensitic phases of Ni-Mn-Ga alloys[END_REF][START_REF] Pons | Crystal structure of martensitic phases in Ni-Mn-Ga shape memory alloys[END_REF][START_REF] Banik | Structural studies of Ni_{2+x}Mn_{1-x}Ga by powder x-ray diffraction and total energy calculations[END_REF]. Modulated structures other than the tetragonal structure can also be found in the martensite state especially at higher Ga concentrations. The most common crystal structure of modulated martensites are the 5M and 7M modulated structures (also denoted as 10M and 14M), as shown Fig. 1.3(c) and Fig. 1.3(d) [START_REF] Righi | Crystal structure of 7M modulated Ni-Mn-Ga martensitic phase[END_REF][START_REF] Righi | Commensurate and incommensurate "5M" modulated crystal structures in Ni-Mn-Ga martensitic phases[END_REF][START_REF] Righi | Incommensurate modulated structure of the ferromagnetic shape-memory Ni2MnGa martensite[END_REF].

Phase constituents and their crystal structures of NiMnGa alloys

From Fig. 1.3(c) and Fig. 1.3(d), the generated modulations can be seen for the 5M and 7M cases. The letter 'M' refers to the monoclinic resulting from the distortion associated with the modulation. Although this particular example is given for Ni2MnGa, similar modulated states are observed in off-stoichiometric martensitic Heusler alloys incorporating other Z(Z=Ga, In, Sn) elements as well. The crystal structures of martensite given here are only typical examples, as for the individual alloys, the structure parameters of martensite depends on their particular composition.

Twin boundaries of martensites in NiMnGa alloys

For the shape memory performances, low twinning stress is the key property of the ferromagnetic shape memory alloys, since magnetically induced rearrangement is mediated by twin boundary motion. In the 5M and 7M modulated NiMnGa martensite, magnetically induced rearrangement can be realized by the motion of type I or type II twin boundaries.

However, Type I twin boundaries exhibits a strong temperature-dependent twinning stress typically of about 1 MPa at room temperature. Type II twin boundaries exhibit a much lower and almost temperature independent twinning stress of 0.05-0.3 MPa [START_REF] Wang | Twinning stress in shape memory alloys: Theory and experiments[END_REF][START_REF] Chulist | Diffraction study of bending-induced polysynthetic twins in 10M modulated Ni-Mn-Ga martensite[END_REF][START_REF] Heczko | Different microstructures of mobile twin boundaries in 10M modulated Ni-Mn-Ga martensite[END_REF][START_REF] Chulist | Characterization of mobile type I and type II twin boundaries in 10M modulated Ni-Mn-Ga martensite by electron backscatter diffraction[END_REF]. Therefore, the Type II twin boundaries are preferred to achieve giant magnetic field induced strain at lower external magnetic field.

Orientation relationship between martensite variants in NiMnGa alloys

Clarification of the orientation relationship between the martensitic variants is quite helpful to understand the rearrangement of martensitic variants and to find a training process or loading scheme which will eliminate or control the twin boundaries. To date, both the orientation relationships between martensite variants of non-modulated and modulated martensite were successfully determined, based on electron backscatter diffraction (EBSD) [START_REF] Cong | Microstructural and crystallographic characteristics of interpenetrating and non-interpenetrating multiply twinned nanostructure in a Ni-Mn-Ga ferromagnetic shape memory alloy[END_REF][START_REF] Cong | Experiment and theoretical prediction of martensitic transformation crystallography in a Ni-Mn-Ga ferromagnetic shape memory alloy[END_REF] orientation determination, using the accurate crystal structure information.

For NM martensite, it is shown that there are two martensite variants with compound twin

Orientation relationship of martensitic transformation in NiMnGa alloys

The martensitic transformation is a diffusionless, displacive phase transformation under a specific orientation relationship between the parent phases and the product phase.

Determination of the orientation relationship during martensitic transformation enables us to not only predict the microstructural configuration of martensite variants and their crystallographic correlation, but also control the microstructure of martensite via thermal treatment. Dependent on the chemical composition, there are three possible transformation sequences for NiMnGa alloys, which are A-5M-7M-NM, A-7M-NM and A-NM. Thus, the martensitic transformation may result in three different types of martensite (i.e. 5M, 7M, and NM martensites), which also depends on the chemical composition.

Up to now, Li et.al [START_REF] Li | Determination of the orientation relationship between austenite and incommensurate 7M modulated martensite in Ni-Mn-Ga alloys[END_REF]

NiMnGa thin films

Shape memory material in thin films appears with the advancement of fabrication technology, where shape memory alloys are deposited directly onto micromachined materials or as stand-alone thin films. Micro-actuation models taking advantage of magnetic field induced reorientation have been proposed in NiMnGa thin films. Magnetically induced re-orientation in constrained NiMnGa film has been reported by Thomas et al. [START_REF] Thomas | Magnetically induced reorientation of martensite variants in constrained epitaxial Ni-Mn-Ga films grown on MgO(001)[END_REF][START_REF] Thomas | Stress induced martensite in epitaxial Ni-Mn-Ga films deposited on MgO(001)[END_REF]. With magnetic field operation, they are bound to have the advantage of fast response and high frequency operation. To date, since Ni-Mn-Ga thin films are promising candidates for magnetic sensors and actuators in MEMS, they have attracted considerable attention that focused on fabrication and freestanding, characterization of crystallographic features and microstructure, as well as martensitic transformation of NiMnGa thin films.

Fabrication process

The fabrication method needs to tune both microstructure and composition well, since microstructure and chemistry of NiMnGa films affects the phase constituent, the mobility of martensite variants and the critical stress. To date, a variety of techniques like sputtering, melt-spinning, pulsed laser deposition, molecular beam epitaxial and flash evaporation, have been used to deposit NiMnGa thin films [START_REF] Dong | Shape memory and ferromagnetic shape memory effects in single-crystal Ni[sub 2]MnGa thin films[END_REF][START_REF] Castano | Structure and thermomagnetic properties of polycrystalline Ni--Mn--Ga thin films[END_REF][START_REF] Dong | Epitaxial growth of ferromagnetic Ni[sub 2]MnGa on GaAs(001) using NiGa interlayers[END_REF][START_REF] Dong | Molecular beam epitaxy growth of ferromagnetic single crystal (001) Ni[sub 2]MnGa on (001) GaAs[END_REF][START_REF] Hakola | Pulsed laser deposition of NiMnGa thin films on silicon[END_REF].

Via the sputtering, it is easy to tailor the composition which is a critical parameter for many desired properties related to actuation and shape memory effect. For instance, using co-sputtering, the composition of NiMnGa can be finely tuned by adding Ni or Mn to vary the overall composition. Because the NiMnGa thin film is found to have ~ 3-5% increase in Ni with respect to that in the targets and a corresponding decrease in Mn and Ga depending upon the deposition parameters, desired thin film composition can also be obtained by appropriate adjustment of target alloy composition.

As significant texturation through reducing the number of variant colonies or groups in the film could be realized by epitaxial growth. Preparation of Epitaxial NiMnGa thin films on single crystal substrates such as MgO , Al2O3 , GaAs [START_REF] Hakola | Ni-Mn-Ga films on Si, GaAs and Ni-Mn-Ga single crystals by pulsed laser deposition[END_REF][START_REF] Dong | Epitaxial growth of ferromagnetic Ni[sub 2]MnGa on GaAs(001) using NiGa interlayers[END_REF] by magnetron sputtering has been performed. To date, the procedure to fabricate continuous films with homogeneous chemical composition and controllable thicknesses has been parameterized [START_REF] Tillier | Tuning macro-twinned domain sizes and the b-variants content of the adaptive 14-modulated martensite in epitaxial Ni-Mn-Ga films by co-sputtering[END_REF][START_REF] Kaufmann | Modulated martensite: why it forms and why it deforms easily[END_REF][START_REF] Tillier | Martensite structures and twinning in substrate-constrained epitaxial Ni-Mn-Ga films deposited by a magnetron co-sputtering process[END_REF][START_REF] Thomas | Magnetically induced reorientation of martensite variants in constrained epitaxial Ni-Mn-Ga films grown on MgO(001)[END_REF][START_REF] Yeduru S R, Backen | Microstructure of free-standing epitaxial Ni-Mn-Ga films before and after variant reorientation[END_REF][START_REF] Jetta | Phase transformations in sputtered Ni-Mn-Ga magnetic shape memory alloy thin films[END_REF]. For instance, Heczko et al. [START_REF] Heczko | Epitaxial Ni-Mn-Ga films deposited on SrTiO[sub 3] and evidence of magnetically induced reorientation of martensitic variants at room temperature[END_REF] showed that thin films deposited on SrTiO3 substrate showed epitaxial structure with a twinned orthorhombic martensite. Khelfaoui et al. [START_REF] Khelfaoui | A fabrication technology for epitaxial Ni-Mn-Ga microactuators[END_REF] reported epitaxial thin film deposition on MgO (100) substrate using DC magnetron sputtering at substrate temperature of 350 °C.

Phase constituent, microstructural and crystallographic features

In spite of the progress made in studying epitaxial NiMnGa alloys, the microstructural and crystallographic characterization of the produced films has been challenging due to the specific constrains from the substrate, the specific geometry of the film, and the ultra fineness of the microstructural constituents. Many pioneer efforts [34, 42-44, 55, 77, 81-88] have been made to characterize the phase constituent, microstructural and crystallographic features to advance the understanding of their physical and mechanical behaviors. The significant scientific and technical challenges remain.

Crystal structure of phases in epitaxial NiMnGa thin films

X-ray diffraction (XRD) [START_REF] Tillier | Tuning macro-twinned domain sizes and the b-variants content of the adaptive 14-modulated martensite in epitaxial Ni-Mn-Ga films by co-sputtering[END_REF][START_REF] Tillier | Martensite structures and twinning in substrate-constrained epitaxial Ni-Mn-Ga films deposited by a magnetron co-sputtering process[END_REF][START_REF] Thomas | Magnetically induced reorientation of martensite variants in constrained epitaxial Ni-Mn-Ga films grown on MgO(001)[END_REF][START_REF] Thomas | Stray-Field-Induced Actuation of Free-Standing Magnetic Shape-Memory Films[END_REF] was first used to analyze phase constituents and texture components of epitaxial NiMnGa films. Multiphase (austenite, modulated martensite and non-modulated martensite) have been identified in most of the epitaxial NiMnGa films and strong textures of each phase have been revealed. For austenite and the non-modulated martensite that have relative simple crystal structure, the lattice constants have been unambiguously determined from the limited XRD reflection peaks [START_REF] Tillier | Martensite structures and twinning in substrate-constrained epitaxial Ni-Mn-Ga films deposited by a magnetron co-sputtering process[END_REF][START_REF] Thomas | Magnetically induced reorientation of martensite variants in constrained epitaxial Ni-Mn-Ga films grown on MgO(001)[END_REF][START_REF] Kauffmann-Weiss | Magnetic Nanostructures by Adaptive Twinning in Strained Epitaxial Films[END_REF][START_REF] Buschbeck | In situ studies of the martensitic transformation in epitaxial Ni-Mn-Ga films[END_REF]. For the modulated martensite (7M or 14M), the maximum attainable number of observed reflection peaks in most cases has not been sufficient [START_REF] Tillier | Tuning macro-twinned domain sizes and the b-variants content of the adaptive 14-modulated martensite in epitaxial Ni-Mn-Ga films by co-sputtering[END_REF][START_REF] Kaufmann | Modulated martensite: why it forms and why it deforms easily[END_REF][START_REF] Tillier | Martensite structures and twinning in substrate-constrained epitaxial Ni-Mn-Ga films deposited by a magnetron co-sputtering process[END_REF][START_REF] Thomas | Magnetically induced reorientation of martensite variants in constrained epitaxial Ni-Mn-Ga films grown on MgO(001)[END_REF][START_REF] Kaufmann | Adaptive Modulations of Martensites[END_REF], thus the complete lattice constant determination is not possible. Without information on the monoclinic angle, the modulated martensite has to be simplified as pseudo-orthorhombic other than the monoclinic structure that has been identified in the bulk materials [START_REF] Tillier | Tuning macro-twinned domain sizes and the b-variants content of the adaptive 14-modulated martensite in epitaxial Ni-Mn-Ga films by co-sputtering[END_REF][START_REF] Kaufmann | Modulated martensite: why it forms and why it deforms easily[END_REF][START_REF] Tillier | Martensite structures and twinning in substrate-constrained epitaxial Ni-Mn-Ga films deposited by a magnetron co-sputtering process[END_REF][START_REF] Thomas | Magnetically induced reorientation of martensite variants in constrained epitaxial Ni-Mn-Ga films grown on MgO(001)[END_REF][START_REF] Kaufmann | Adaptive Modulations of Martensites[END_REF]. However, it is commonly accepted that 7M (or 14M) modulated NiMnGa martensite are of monoclinic crystal structure as in bulk NiMnGa materials [START_REF] Righi | Crystal structure of 7M modulated Ni-Mn-Ga martensitic phase[END_REF][START_REF] Righi | Commensurate and incommensurate "5M" modulated crystal structures in Ni-Mn-Ga martensitic phases[END_REF][START_REF] Righi | Incommensurate modulated structure of the ferromagnetic shape-memory Ni2MnGa martensite[END_REF]. Generally, to describe the lattice parameters of 7M martensite, two different coordinate reference systems are frequently used in the literature, i.e. an orthogonal coordinate system attached to the original cubic austenite lattice and a non-orthogonal coordinate system attached to the conventional monoclinic Bravais lattice [27, 28, 63-65, 72, 73]. Since the monoclinic angle is very close to 90°, the modulated structure may be approximated as a pseudo-orthorhombic structure under the former scheme [START_REF] Thomas | Magnetically induced reorientation of martensite variants in constrained epitaxial Ni-Mn-Ga films grown on MgO(001)[END_REF][START_REF] Müller | Nanoscale mechanical surface properties of single crystalline martensitic Ni-Mn-Ga ferromagnetic shape memory alloys[END_REF][START_REF] Kaufmann | Adaptive Modulations of Martensites[END_REF]. Fig. 1.4(a) illustrates the settings of the cubic coordinate system for austenite, the pseudo-orthorhombic coordinate system [START_REF] Kaufmann | Modulated martensite: why it forms and why it deforms easily[END_REF][START_REF] Kaufmann | Adaptive Modulations of Martensites[END_REF] for 14M modulated martensite under the adaptive phase model [START_REF] Kaufmann | Adaptive Modulations of Martensites[END_REF], and the monoclinic coordinate system for 7M modulated martensite [START_REF] Li | Twin relationships of 5M modulated martensite in Ni-Mn-Ga alloy[END_REF][START_REF] Li | Evidence for a monoclinic incommensurate superstructure in modulated martensite[END_REF][START_REF] Li | Determination of the orientation relationship between austenite and incommensurate 7M modulated martensite in Ni-Mn-Ga alloys[END_REF][START_REF] Li | New approach to twin interfaces of modulated martensite[END_REF]. It is seen from Fig. 1.4(b) that the deviations of the respective monoclinic basis vectors (amono, bmono and cmono) from the corresponding directions in the cubic coordinate system ) are very small (ranging from 1° to 3°), depending on the lattice constants of materials with different chemical compositions. The two settings have their own disadvantages. Apparently, a direct atomic or lattice correspondence between the austenite structure and the martensite structure is not so conveniently accessible under the monoclinic coordinate system. However, in the pseudo-orthorhombic setting, the basis vectors shown in Fig. 1.4(a) are not true lattice vectors, because the basis vectors of the original cubic cell become irrational in the newly formed structure after the martensitic transformation. This makes the precise description of the twin relationships of martensitic variants using well-defined twinning elements (such as twinning plane, twinning direction, and etc.) particularly difficult, especially when there are irrational twinning elements, as presented in table 1.2, the description of twinning elements in both 14M-adaptive and 7M monoclinic crystal reference system. It can be clearly seen that the precise twinning elements of Type II twin and compound twin have not been determined in the 14M-adaptive crystal system. Moreover, the pseudo-orthorhombic cell does not possess the same symmetry group as that of the monoclinic Bravais lattice. This affects the determination of the number of martensitic variants and the orientation relationships between adjacent variants.

Microstructure and crystallographic features of epitaxial NiMnGa thin films

For epitaxial NiMnGa thin films, so far microstructure examinations have been made mainly using scanning electron microscopy (SEM), atomic force microscopy (AFM) and high resolution scanning tunneling microscopy (STM). The crystallographic aspects have been deduced by examining the surface corrugations of the films.

Microstructure analyses by scanning electron microscopy (SEM) revealed that martensite is in plate shaped and organized in groups as is the case in bulk material but much finer. The important feature found is that there are two kinds of martensite groups in terms of secondary electron (SE) image contrast. One is with relative homogeneous contrast that consists of long strips running parallel to the two edge directions ( MgO [START_REF] Pitsch | Der Orientierungszusammenhang zwischen Zementit und Austenit[END_REF] and

MgO [ 010]
) of the substrate.

The other is with relatively high contrast that contains plates with their length direction running roughly in 45° with respect to the substrate edges [START_REF] Kaufmann | Modulated martensite: why it forms and why it deforms easily[END_REF]. Close observations using atomic force microscopy [START_REF] Leicht | Microstructure and atomic configuration of the (001)-oriented surface of epitaxial Ni-Mn-Ga thin films[END_REF][START_REF] Kaufmann | Modulated martensite: why it forms and why it deforms easily[END_REF][START_REF] Müller | Nanoscale mechanical surface properties of single crystalline martensitic Ni-Mn-Ga ferromagnetic shape memory alloys[END_REF] revealed that the different SE contrasts correspond to different surface corrugations of the films: the low SE relative contrast zones to low surface corrugation, whereas the high SE contrast zones to high surface relief.

According to the height profile of the surface relief in the high surface corrugation zones that are considered to be of 7M martensite, twin relationship between the adjacent martensite plates has been deducedthe so-called a-c twin relationship [START_REF] Kaufmann | Modulated martensite: why it forms and why it deforms easily[END_REF][START_REF] Thomas | Magnetically induced reorientation of martensite variants in constrained epitaxial Ni-Mn-Ga films grown on MgO(001)[END_REF]. It means that the pseudo-orthorhombic unit cells from the neighboring plates share a common b axis. The plate boundaries correspond to the (101)orth and they are inclined roughly 45° to the substrate surface.

Later high resolution scanning tunneling microscopy (STM) examination indicated that within the 7M martensite plates, there are still fine periodic corrugations [START_REF] Leicht | Microstructure and atomic configuration of the (001)-oriented surface of epitaxial Ni-Mn-Ga thin films[END_REF]. The fine corrugations have been considered to be related to the structure modulation of the 7M martensite [START_REF] Leicht | Microstructure and atomic configuration of the (001)-oriented surface of epitaxial Ni-Mn-Ga thin films[END_REF] and preferentially, the 7M modulated martensite was considered to be composed of nano-twinned NM martensite (the so-called adaptive phase), as the lattice constants of the three phases fulfill the relation proposed by the adaptive phase theory (a14M=cNM+aNM-aA, aA=b14M, c14M=aNM [START_REF] Kaufmann | Adaptive Modulations of Martensites[END_REF]). For the low contrast zones (composed of strips running parallel to the edges of the substrate ( MgO [START_REF] Pitsch | Der Orientierungszusammenhang zwischen Zementit und Austenit[END_REF] and the

MgO

[010]

)), the nature of the martensite has not been clearly revealed. Some consider that they are of NM tetragonal martensite [START_REF] Kaufmann | Modulated martensite: why it forms and why it deforms easily[END_REF] but others thought that they are of 7M martensite [START_REF] Tillier | Tuning macro-twinned domain sizes and the b-variants content of the adaptive 14-modulated martensite in epitaxial Ni-Mn-Ga films by co-sputtering[END_REF][START_REF] Müller | Nanoscale mechanical surface properties of single crystalline martensitic Ni-Mn-Ga ferromagnetic shape memory alloys[END_REF]. The neighboring plates were deduced to also be a-c twin related with the plate interfaces ((101)orth) perpendicular to the substrate surface, according to the epitaxial relationship between the substrate MgO and the austenite and the Bain relationship between the austenite and the NM martensite. For the substructure within the NM plate, as there are no significant corrugations detected, the microstructure and crystallographic features in the NM plates remains unclear.

Recently, further attempts have been made in further revealing the characteristic microstructures of NiMnGa films [START_REF] Niemann | The Role of Adaptive Martensite in Magnetic Shape Memory Alloys[END_REF]. Two types of twins have been proposed, namely type I and type II twins, and build as paper models. Apparently, the type I twin is the so-called a-c twin with (101)A as twinning plane. However, it is not easy to correlate the proposed "type II twin" with yet published twin relationships in NiMnGa in literature, as there is no clear crystallographic description (such as twinning plane and twinning direction)) [START_REF] Niemann | The Role of Adaptive Martensite in Magnetic Shape Memory Alloys[END_REF]. It has been found that the type I twins are mainly in low surface corrugation zones (the so-called Y pattern) and the type II twins mainly in high surface corrugation zones (the so-called X pattern) [START_REF] Backen | Mesoscopic twin boundaries in epitaxial Ni-Mn-Ga films[END_REF]. Cross section observations [START_REF] Backen | Mesoscopic twin boundaries in epitaxial Ni-Mn-Ga films[END_REF] of the film have evidenced that in the low surface corrugation zones there are two interface orientations, one being perpendicular to the substrate surface and the other parallel to the substrate surface. In the high corrugation zones, there is only one interface orientation that is tilted to the substrate surface by roughly 45° [START_REF] Backen | Mesoscopic twin boundaries in epitaxial Ni-Mn-Ga films[END_REF].

The apparent different occurrences of different twins in the two different variants zones are due to the constraints of the substrate [START_REF] Kaufmann | Modulated martensite: why it forms and why it deforms easily[END_REF][START_REF] Backen | Mesoscopic twin boundaries in epitaxial Ni-Mn-Ga films[END_REF]. So far the short intra-plate interfaces in NiMnGa films have not been identified and the orientation relationship between the variants connected by such interfaces is not known.

Clearly, due to the lack of direct microstructure and crystallographic orientation correlation on the martensite variants (either 7M or NM martensite) and the inaccuracy of the orientation relationship between the parent austenite and the martensite, the precise information on the crystallographic configurations of the martensite lamellae inside each martensite plate and further the crystallographic organization of the martensite plates in each colony or group, especially the lamellar interfaces and plate interfaces, is still unavailable. In consequence, the possible number of variants in one variant group, their precise orientation relationships and interface planes stay unclear, which hinder the uncovering of microstructural singularities of NiMnGa films with respect to their counterparts in bulk materials.

Content of the present work

Based on the state of art mentioned above, epitaxial Ni-Mn-Ga thin films were produced by DC magnetron sputtering and then characterized by x-ray diffraction technique (XRD) and backscatter electron diffraction equipped in scanning electron microscope (SEM-EBSD). The scientific aim of the present work is first to produce qualified NiMnGa films with designed chemical compositions and film thicknesses and then to clarify the crystal structures of phase constituents, the configurations of martensite variants and their orientation correlations. The followings are the main content of the present work:

(1) Produce NiMnGa thin films with designed chemical composition and film thicknesses by magneto sputtering through optimizing the deposition parameters, such as sputtering power, substrate materials and seed layer materials..

Chapter Experimental and crystallographic calculation

In this chapter, the techniques used to prepare and characterize Ni-Mn-Ga thin films are summarized. The essential crystallographic calculation methods are also described in details.

Sample preparation

Preparation of sputtering target

In order to obtain NiMnGa thin films with different phases at ambient temperature, NiMnGa alloys with various nominal composition were dedicatedly prepared by arc melting using high purity elements Ni (99.97 wt. %), Mn (99.9 wt. %) and Ga (99.99 wt. %). The ingots with designed nominal composition were melted by arc-melting in water cooled copper crucible under argon atmosphere. In order to obtain ingots with homogenous composition, each ingot was re-melted for four times and electromagnetic stirring was applied during the melting process. For further reducing the composition inhomogeneity of the as-cast ingots, the ingots were homogenized at 900 o C for 12 h in a vacuum quartz tube, and then cooled within the furnace. Magnetron sputtering is a physical vapor deposition technique by which ions accelerated under certain high voltage bombard the target surface to eject atoms towards the substrate to be deposited, as illustrated in Fig. 2.2 (a). In a typical deposition, substrate with clean surface is attached to the substrate holder. Sputtering is done under high vacuum conditions to avoid contamination of the film. Base pressure is pumped down to 10 -6 -10 -9 Torr using turbo and molecular pumps. On realizing a very high negative potential to the cathode target, plasma is generated. The Argon atoms in the plasma are ionized and accelerated towards the target at very high velocities. Due to the collision cascade, sputtered atoms with enough velocity get deposited on the substrate surface. The residual kinetic energy in target atoms is converted to thermal energy which increases their mobility and facilitates surface diffusion. Hence a continuous chain of atoms are formed resulting in a high quality film. Magnetic field produced by a permanent magnet referred is used to increase the path of the electron and hence the number of ionized inert atoms. It also can change the path of accelerated ions, which results in ring-like ejection zones on the surface of target.

In the present thesis, a custom-built multi-source magnetron sputtering system (JZCK-400DJ) was used for thin film deposition. As illustrated in Fig. 2.2(b), the magnetron sputtering system has three sputtering sources arranged in confocal symmetry, which is capable of multilayer deposition, co-sputtering and deposition with a seed layer or cap layer.

The base pressure before depositing is pumped below 9.0×10 -5 Pa. In order to obtain a continuous NiMnGa thin film, the working Ar pressure is fixed at 0.15 Pa during the whole deposition process. The deposition parameters, such as sputtering power, substrate materials, substrate temperature, time and seedlayer have been optimized through examining their effects on film thickness, film composition, and phase constituents and their microstructures. (b) The x-ray diffractometer equipped with a curved position sensitive detector. Here,  is the angle between incidence beam and sample surface. is the angle between incidence beam and diffraction plane. 2is the angle of incidence beam and reflected beam.  is the tilting angle with respect to the substrate surface.isthe rotation angle along the film normal. represents that the sample is not rotated.

Characterization

X-ray diffraction

X-ray diffraction is well developed technique for determining the crystal structure and macroscopic crystallographic features of crystalline materials. In the present study, three X-ray diffractometers were employed to determine both the crystal structure and macroscopic crystallographic orientations. All the diffractometers are of four circle X-ray diffractometer with Cobalt cathode source (Co K= 0.178897 nm).

For the determination of the crystal structure of the phases in NiMnGa thin films, two X-ray diffractometers were employed. One is of conventional diffractometer with point detector (Fig. 2.3a) and the other is of X-ray diffractometer with curved position sensitive (CPS) detector (Fig. 2.3b). Compared with the conventional diffractometers, X-ray diffractometer with curved position-sensitive offers fast data collection over a wide 2 range.

As illustrated in Fig. 2.3(b), the reflection-mode Debye-Scherrer geometry for CPS detectors is unique in the sense that the angle for the incident X-ray beam is kept fixed with respect to the normal of a flat diffracting sample, while the reflected beams are measured at multiple angles with respect to the sample normal. Considering that the thin film possesses in-plane texture, X-ray diffractometer with curved position-sensitive detector was used to obtain maximum numbers of diffraction peaks from the NiMnGa film.

SEM and SEM-EBSD

The microstructure, composition and microscopic crystallographic features of NiMnGa thin films were investigated by the field emission gun scanning electron microscope (FEG-SEM, JEOL-6500F). The composition of the NiMnGa films were investigated by the energy dispersive X-ray spectrometry system (EDS, Bruker) attached this SEM. The morphology and microstructure of the NiMnGa thin films were characterized by the secondary electron image and backscattered electron image. The microstructure and the microscopic crystallographic orientations of the NiMnGa martensite variants were analyzed using the same SEM equipped with an EBSD acquisition camera (Oxford HKL) and acquisition software (Oxford Channel 5). The EBSD patterns from the martensite variants were manually acquired using Channel 5 Flamenco's interactive option.

The sample for SEM-EBSD analysis was electrolytically polished with the solution of 20%HNO3 in volume in CH3OH at room temperature.

TEM

Philips CM 200 TEM with 200 kV accelerating voltage and LaB6 filaments has been used to observe fine martensite variants in NiMnGa thin films. JEOL-2100F HR-TEM with field-emission gun was used to investigate the atomic-level stacking faults between variants within martensite plates.

Specimens for TEM investigation were cut off out the freestanding NiMnGa thin film and further thinned using twin-jet electrolytic polishing with an electrolyte of 20% HNO3 in volume in CH3OH at ambient temperature.

Crystallographic calculations

With the precise crystallographic orientations of martensite variants, the orientation relationships between the martensite variants and their interfaces, and orientation relationship between austenite and martensite can be calculated. In addition, the following presents the calculation methods used in the present work.

Fundaments and definitions

Reference systems

Considering the characteristics of the crystal structures of the phases concerned in the present study, austenite, modulated martensite and non modulated martensite, as given in Table 2. The lattice vector in reciprocal space can be expressed by the lattice vector in the direct space, as shown in Eq.(2-1)

) ( * c b a c b a     , ) ( * a c b a c b     , ) ( * b a c b a c     (2-1)
For the orthonormal crystal coordinate systems, the basis vectors are three orthogonal

Metric tensors

The metric tensor contains the same information as the set of crystal lattice parameters, but in a form that allows direct computation of the dot product between two vectors. The computational and algebraic aspects of these mutually reciprocal bases can be conveniently expressed in terms of the metric tensors of these bases. The matrix of the metric tensor of the direct basis G , or briefly the direct metric tensor, is The corresponding reciprocal metric tensor is

                              
                                                               2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 sin ) cos cos (cos ) cos cos (cos ) cos cos (cos sin ) cos cos (cos ) cos cos (cos ) cos cos (cos sin V b a V bc a V c ab V bc a V c a V abc V c ab V abc V c b                      c c b c a c c b b b a b c a b a a a G * (2-4) Where ) cos cos cos cos cos cos 2 1 ( 2 2 2 2 2 2 2            c b a V .
With the matrix tensor, the vectors of direct space and reciprocal space can be easily transformed between each other according to Eq.( 2

-5).   T w v u is a direction vector in direct space.   T l k h
is a miller index of a plane in direct space and also a direction vector in reciprocal space.

                      l k h w v u * G and                       w v u l k h G (2-5)
In the present study, for austenite, the matrix tensors in direct and reciprocal space are given in Eq.(2-6)

           2 2 2 0 0 0 0 0 0 A A A a a a A G and                    2 2 2 * 1 0 0 0 1 0 0 0 1 A A A a a a A G (2-6)
For NM martensite, the matrix tensors in direct and reciprocal space are given in Eq.(2-7)

           2

G

(2-9)

Coordinate transformation

As presented in Fig. 2.6, the sample coordinate system and the Bravais lattice cell are related by two coordinate transformations. The first transformation is from the sample coordinate system to the orthonormal crystal coordinate system. Normally, this transformation can be expressed by the Euler angles   [START_REF] Bunge | The role of the inversion centre in texture analysis[END_REF][START_REF] Bunge | Texture analysis in materials science-mathematical methods[END_REF], which can be directly determined by EBSD system. According to Eq.(2-10), the transformation matrix can be constructed with the acquired Euler angles. The second transformation is from the orthonormal crystal coordinate system to the bravais lattice cell. In general, let the vector ] [uvw be in the old coordinate system ) (abc and ] [UVW be the same vector expressed in the new coordinate system ) (ijk . Since, the coordinate transformation does not change the value of the vector, it follows that

2 1 , ,   Φ in Bunge notation
                          
2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1                     E M (2-10)
k j i c b a W V U w v u      (2-11)
The coordinate transformation can be made by:

                     w v u W V U C M (2-12)
If the transformation is from the orthonormal crystal coordinate system to a triclinic Bravais lattice unit cell,

                                  sin 0 sin / cos cos cos cos cos 0 0 sin / cos cos cos sin 2 2 c a c b a a C M (2-13)
In the present study, there are three phases: austenite, NM martensite and 7M martensite.

The transformation matrixes from the orthonormal coordinate system to their Bravais crystal basis are given in Eq. (2)(3)(4)(5)(6)(7)(8)[START_REF] Fukuda | Giant magnetostriction in Fe-based ferromagnetic shape memory alloys[END_REF][START_REF] Handley R C | Modern magnetic materials: principles and applications[END_REF][START_REF] Kohl | Ferromagnetic Shape Memory Microactuators[END_REF][START_REF] Faehler | An Introduction to Actuation Mechanisms of Magnetic Shape Memory Alloys[END_REF][START_REF] Jani | A review of shape memory alloy research, applications and opportunities[END_REF][START_REF] Jiles | Recent advances and future directions in magnetic materials[END_REF] to Eq. (2)(3)(4)(5)(6)(7)(8)[START_REF] Fukuda | Giant magnetostriction in Fe-based ferromagnetic shape memory alloys[END_REF][START_REF] Handley R C | Modern magnetic materials: principles and applications[END_REF][START_REF] Kohl | Ferromagnetic Shape Memory Microactuators[END_REF][START_REF] Faehler | An Introduction to Actuation Mechanisms of Magnetic Shape Memory Alloys[END_REF][START_REF] Jani | A review of shape memory alloy research, applications and opportunities[END_REF][START_REF] Jiles | Recent advances and future directions in magnetic materials[END_REF][START_REF] Wilson | New materials for micro-scale sensors and actuators: An engineering review[END_REF][START_REF] Nespoli | The high potential of shape memory alloys in developing miniature mechanical devices: A review on shape memory alloy mini-actuators[END_REF] . For austenite

A a c b a    , o 90      
, the coordinate transformation matrix crystal direction vector is

           A A A a a a 0 0 0 0 0 0 A C M (2-14)
For non modulated martensite, , ,    in Bunge's convention [START_REF] Bunge | The role of the inversion centre in texture analysis[END_REF]. The rotations are between the orthonormal sample coordinate system the the orthonormal crystal coordinate system, as described in the coordinate transformation part (2.3.1.3). In the present study, this method was employed to calculate the misorientation between two martensite variants.

If the orientations of variant A and variant B are specified in rotation matrices

Δg

going from variant A to variant B can be defined as follows:

j B 1 A 1 i B A S G G S Δg    (2-17)
where the term

Δg

(2-18)

The misorientation angle  and rotation

) d , d , (d 3 2 1 d
can be calculated: The misorientation relationship, expressed in rotation axis/angle pairs, can be used to determine twinning type and certain twin elements. According to the definition of twin orientation relationship, there is at least one 180° rotation for a twin. As shown in table 2.3, if there is one 180° rotation and the Miller indices of the plane normal to the rotation axis are rational, the crystal twin belongs to type-I and K1 is identified. If there is one 180° rotation and the Miller indices of the rotation axis are rational, the crystal twin belongs to type-II and η1 is identified. If there are two independent 180° rotations and the planes normal to the rotation axes are also rational, the twin is a compound twin, with one rotation axis being the twinning direction and the other being the normal to the twining plane [START_REF] Zhang | A general method to determine twinning elements[END_REF]. With the determined twin type and rotation axis, the other twinning elements can be calculated using the general method developed by our group [START_REF] Zhang | A general method to determine twinning elements[END_REF].

          2 1 arccos 33 22 11 g g g  (2-19) (1)  180                                  ) sgn(g ) sgn(d m, i convention by 0, d 1,2,3 i , d max d with 2 1 g , 2 1 g , 2 1 g ) d , d , (d im i m i m 33 22 11 3 2 1 d (2-20) (2)  0     0 0, 1, ) d , d , (d 3 2 1   d (2-21) (3)
 180   and  0                 sin 2 g , sin 2 g , sin 2
In addition, if the twin type and twinning elements are known, the rotation angle and rotation axis are also known. Thus, the misorientation matrix can be constructed by Eq. .

Suppose the rotation angle is  , the rotation axis is

  T 3 2 1 d , d , d  d
expressed in the orthonormal crystal coordinate system and must be a unit vector.

                             ) cos 1 ( cos sin ) cos 1 ( sin ) cos 1 ( sin ) cos 1 ( ) cos 1 ( cos sin ) cos 1 ( sin ) cos 1 ( sin ) cos 1 ( ) cos 1 ( cos 2 3 1 3 2 2 3 1 1 3 2 2 2 3 2 1 2 3 1 3 2 1 2 1                   d d d d d d d d d d d d d d d d d d d d d R M
(2-23)

Stereographic projection and traces determination

The stereographic projection is a particular mapping that projects a sphere onto a plane, which is one of the projection methods to calculate pole figures. To calculate the pole figure of crystal directions or plane normal vectors, the vectors have to be expressed in the macroscopic coordinate system set with respect to the equatorial plane (for example the sample coordinate system) t before the stereographic projection. For instance, when a plane normal vector is

 * hkl V P 
. The corresponding vector in the sample coordinate system S V can be calculated using Eq. .

P * i C E S V G S M M V  (2-24)
Here, E M is the Euler angle matrix, C M is the coordinate transformation matrix from the orthonormal crystal coordinate system to the Bravais lattice basis.

i S is the symmetric element of a crystal, * G is the metric tensor in reciprocal space. Then, the vector

T S t t t ] , , [ 3 2 1  V
should be normalized to unit vector.

As presented in Fig. 2.8a, vector OP represents the vector S V in the sphere S V OP  .

P is the intersection of vector OP with the sphere and is defined as the pole of plane ( hkl ). Let the line connect point P and the South Pole S. Line PS intersect the equatorial plane at point P'. P' is the stereographic projection of pole P. On the equatorial plane, P is expressed with the polar angle  and the azimuth angle  (  , ), where

           OP ON OP ON arccos  (2-25) and             ' ' arccos 2 OP OE OP OE   (2-26)
Line HK vertical to vector OP' in the equatorial plane represents the trace of plane ( hkl ). As shown in Fig. 2.9, the orthonormal reference frame is set such that the basis vector Known the orientation of the martensite variants, the orientation of the austenite with respect to the sample coordinate system expressed in matrix can be calculated with Eq. (2-28)

1 1 1 1 1 ) ( ) ( ) ( ) ( ) (         A C i A M j m C m E A C i A M j m C m E A E M S T S M M M S T T S M M M (2-28)
Where, For NiMnGa alloy, the possible orientation relationship between the austenite and martensite are shown in Table 2.4. If the orientation relationship between austenite and martensite is assumed to be the one between austenite and martensite, with Eq. (2-28), the orientation of the austenite from the measured orientations of the martensitic variants can be derived. The schematic illustration of the determination of the OR between austenite and martensite is shown in Fig. 2.10. As presented in Fig. 2.10, if the distinct austenite orientations calculated from the observed variants have at least one orientation in common, it can be deduced that the assumed orientation relationship indeed exists. The common orientation is the orientation of the austenite.

) M A 0] 1 [1 || [001] [96] Kurdjumov-Sachs (K-S) M A (101) || (111) M A ] 1 [11 || 0] 1 [1 [97] Nishiyama-Wassermann(N-W) M A (101) || (111) M A ] 1 [10 || 11] 2 [ [98, 99] Pitsch M A ) 2 1 (1 || (110) M A ] 1 1 1 [ || 0] 1 [1 [100]

Displacement gradient tensor

It is well known that martensitic transformation is a displacive transformation realized by coordinated atomic movements. As shown in Fig. 2.11, the transformation can be regarded as the deformation of an artificially set reference cell based on the orientation relationship plane and direction of austenite to the corresponding reference cell of martensite by certain lattice distortion. The reference cells of austenite and martensite can be built according to the orientation relationship

( M A ) ( || ) ( hkl hkl , M A ] [ || ] [ uvw uvw
). Normally, the reference cell of austenite is an orthogonal unit cell. To analysis the atomic displacement during martensitic transformation, the orthonormal coordinate systems are also helpful. As presented in Fig. 2.11, orthonormal coordinate systems ( k j i --) were fixed in both the austenite and martensite. The lattice vectors for both austenite and martensite can be expressed in the orthonormal coordinate system, as presented in Eq.(2-29) and Eq.(2-30)

                       k j i z k j i y k j i x A A A A A A 0 0 0 0 0 0 z y x (2-29)                        k j i z k j i y k j i x z y x z y x z y x z z z y y y x x x M M M M M M M M M M M M (2-30)
Then the displacement describing the lattice change from austenite to martensite can be obtained as

z y x D      
, where

k j i z k j i y k j i x                               ) ( ) 0 ( ) 0 ( ) 0 ( ) ( ) 0 ( ) 0 ( ) 0 ( ) ( M M M M M M M M M z z z z y y y y x x x x z y x z y x z y x (2-31)
Therefore, the displacement D can be rewritten as Eq. (2-32)

k j i k j i k j i z y x D                                                                               k j i z z z y y y x x x z z z y y y x x x D D D z z z z y y y x x x z z z y y y y x x x z z z y y y x x x x z z y x z y y x z y x x ) ( ) 0 ( ) 0 ( ) 0 ( ) ( ) 0 ( ) ) 0 ( ) 0 ( ) ( )) ( ) 0 ( ) 0 (( )) 0 ( ) ( ) 0 (( )) 0 ( ) 0 ( ) (( A A A M A A M A A M A A M A A A M A A M A A M A A M A A A M A M M M M A M M M M A M (2-32)
According to the definition, the displacement gradient tensor with respect to the

orthonormal coordinate system is                                                                       A A M A M A M A M A A M A M A M A M A A M

   

1 pitsch A A MgO pitsch A A MgO M S M M M S M M       i D i k (2-34)                       1,2,
 :                  1 0 0 0 ) 45 cos( ) 45 sin( 0 ) 45 sin( ) 45 cos( A MgO M ,                   2 2 2 2 0 0 0 1 2 2 2 2 0 pitsch A M . ( 2

Experimental procedure

In the present study, the films are produced with the base pressure higher than 9.0×10 -5 Pa and the working pressure fixed at a low argon pressure (0.15 Pa) in the DC magnetron sputtering machine (JZCK 400DJ), in order to obtain continuous film.

For Si substrates, the substrate temperature, the target composition, the sputtering power and deposition time to produce NiMnGa films are given in Fig. 3.1. The selection of the deposition time is under the consideration to ensure the same film thickness at all the sputtering powers used. The targeted film thickness is about 1 micrometer. The film deposited under 75W is further undergone annealing at 750°C, 800°C and 900°C.

Using the optimized sputtering power from the above tests, the other deposition parameters to produce the films are further refined on the MgO substrates without and with a NiMnGa thin films deposited on Si substrate with various sputtering power. As presented in Fig. 3.1, the concentration of Ni and Mn in NiMnGa thin films is slightly increased with the sputtering power, whereas the concentration of Ga is slightly decreased with the sputtering power. However, the changes are not linear with the sputtering power.

Influence of annealing

The film deposited under 75 W were further annealed at different temperature for 2 h.

Influence of seed layer

To obtain continuous film, a 100 nm seed layer of either Ag or Cr is deposited on the substrate. The misfit between the MgO and the austenite of NiMnGa is 2.42 %, whereas that between Cr and NiMnGa is 0.75%. It is easier to generate epitaxial thin films with small misfit.

Discussion

When the sputtered atoms arrive at the substrate, a thin film is formed. The morphology, the microstructure and the crystallographic orientation of the thin films depend on the sputtering conditions, which has been depicted in a so-called structure zone model [START_REF] Charpentier | X-Ray diffraction and Raman spectroscopy for a better understanding of ZnO:Al growth process[END_REF]. This model correlates the argon pressure and the substrate temperature to the morphological properties of the produced films. As shown in Fig. 3.12, low argon pressure produces films with microstructures that are smooth and featureless while high argon pressure produces films with microvoids surrounding the amorphous islands. In addition, the grain growth and

Summary

In summary, NiMnGa thin films with continuous microstructures were successfully produced by DC magnetron sputtering, after the optimization of sputtering parameters such as substrate temperature, sputtering power, substrate materials, seed-layer materials, film composition and thickness. Low argon pressure, high substrate temperature and seed layer are necessary to fabricate the epitaxial NiMnGa thin films with continuous microstructure.

The optimum fabrication parameters to produce NiMnGa films with continuous microstructure and with martensite phase at room temperature are:

 Target material: Ni46at.%-Mn32at.%-Ga22at.%;

 Substrate: MgO(100) substrate with 100 nm Cr seed layer.

 working pressure: 0.15Pa;

 sputtering power: 75 w;

 substrate temperature 500 ℃;

4 Chapter 4 Determination of crystal structure and crystallographic features by XRD

Introduction

A key requirement for considerable magnetic field-induced strains in ferromagnetic shape memory alloys, as reported for bulk NiMnGa samples, is the presence of modulated martensite. The precise knowledge of martensites in terms of crystal structure and crystallographic texture is of utmost importance. To conduct such characterizations, XRD techniques have been one of the privileged characterization techniques to analyze the phase constituents and texture components in many previous studies on NiMnGa epitaxial thin films [START_REF] Tillier | Tuning macro-twinned domain sizes and the b-variants content of the adaptive 14-modulated martensite in epitaxial Ni-Mn-Ga films by co-sputtering[END_REF][START_REF] Tillier | Martensite structures and twinning in substrate-constrained epitaxial Ni-Mn-Ga films deposited by a magnetron co-sputtering process[END_REF][START_REF] Thomas | Magnetically induced reorientation of martensite variants in constrained epitaxial Ni-Mn-Ga films grown on MgO(001)[END_REF][START_REF] Thomas | Stray-Field-Induced Actuation of Free-Standing Magnetic Shape-Memory Films[END_REF].

For crystal structure analyses of the constituent phases, the crystal structure of the cubic austenite and the tetragonal non-modulated (NM) martensite have been unambiguously determined from attainable XRD reflection peaks [START_REF] Tillier | Martensite structures and twinning in substrate-constrained epitaxial Ni-Mn-Ga films deposited by a magnetron co-sputtering process[END_REF][START_REF] Thomas | Magnetically induced reorientation of martensite variants in constrained epitaxial Ni-Mn-Ga films grown on MgO(001)[END_REF][START_REF] Kauffmann-Weiss | Magnetic Nanostructures by Adaptive Twinning in Strained Epitaxial Films[END_REF][START_REF] Buschbeck | In situ studies of the martensitic transformation in epitaxial Ni-Mn-Ga films[END_REF]. However, for the monoclinic modulated martensite (7M or 14M), the lattice constant determination have suffered from insufficient number of measured reflection peaks [START_REF] Tillier | Tuning macro-twinned domain sizes and the b-variants content of the adaptive 14-modulated martensite in epitaxial Ni-Mn-Ga films by co-sputtering[END_REF][START_REF] Kaufmann | Modulated martensite: why it forms and why it deforms easily[END_REF][START_REF] Tillier | Martensite structures and twinning in substrate-constrained epitaxial Ni-Mn-Ga films deposited by a magnetron co-sputtering process[END_REF][START_REF] Thomas | Magnetically induced reorientation of martensite variants in constrained epitaxial Ni-Mn-Ga films grown on MgO(001)[END_REF][START_REF] Kaufmann | Adaptive Modulations of Martensites[END_REF], which result in the monoclinic angle of the crystal unattainable. Without knowing precisely the monoclinic angle, the monoclinic modulated martensite has to be simplified to a pseudo-orthorhombic structure [START_REF] Tillier | Tuning macro-twinned domain sizes and the b-variants content of the adaptive 14-modulated martensite in epitaxial Ni-Mn-Ga films by co-sputtering[END_REF][START_REF] Kaufmann | Modulated martensite: why it forms and why it deforms easily[END_REF][START_REF] Tillier | Martensite structures and twinning in substrate-constrained epitaxial Ni-Mn-Ga films deposited by a magnetron co-sputtering process[END_REF][START_REF] Thomas | Magnetically induced reorientation of martensite variants in constrained epitaxial Ni-Mn-Ga films grown on MgO(001)[END_REF][START_REF] Kaufmann | Adaptive Modulations of Martensites[END_REF]. The simplification to pseudo-orthorhombic structure makes the precise description of the orientation relationships between martensitic variants using well-defined twinning elements (such as twinning plane, twinning direction, and etc.) particularly difficult, especially when there are irrationally indexed twinning elements.

For crystallographic texture analyses, several studies have been performed on the preferred orientations of the two kinds of martensite. Special attention has been paid to link the orientation relationship between the two martensites, and to provide experimental evidences for the "adaptive phase model".

In the chapter, the phase constituents and texture components of NiMnGa thin films were investigated by X-ray diffraction techniques. The crystal structure of modulated martensite and lattice constants expressed in monoclinic Bravais cell was fully determined and the texture characteristics were precisely detected.

Experimental

Ni-Mn-Ga thin films with nominal composition of Ni50Mn30Ga20 and nominal thickness of 1.5 m were deposited from a cathode target of Ni46Mn32Ga22 by DC magnetron sputtering. A Cr buffer layer of 100 nm thick was pre-coated on the MgO(100) monocrystal substrate.

The crystal structures of the as-deposited NiMnGa thin films were determined by X-ray diffraction using Co-Kradiation ( = 0.178897 nm). Considering that the thin films may possess in-plane texture, two four-circle X-ray diffractometers, one with a conventional 2 coupled scan and the other with a rotating anode generator (RIGAKU RU300) and a large-angle position sensitive detector (INEL CPS120), were used to collect a sufficient number of diffraction peaks. The geometrical configurations of the two X-ray diffractometers are schematically illustrated in Fig. 2.3. In the former case (Fig. 2.3a), the 2 coupled scans were performed between 45° and 90° at tilt angle  ranging from 0° to 10° with a step size of 1°.

In the latter case (Fig. 2.3b), the 2 scans were conducted at tilt angle  from 0.75° to 78.75° with a step size of 1.25°. At each tilt angle, the sample was rotated from 0° to 360° with a step size of 5°. Two incident angles  (27.9° and 40°) were selected in order to obtain possible diffraction peaks at the low 2 (48°-58°) and the high 2 (around 82.5°) regions. The final diffraction patterns were obtained by integrating all diffraction patterns acquired at different sample positions.

Results and discussion

Determination of crystal structure

Fig. 4.1a shows the -dependent XRD patterns of the as-deposited Ni-Mn-Ga thin films obtained by conventional -2 coupled scanning at ambient temperature. At each tilt angle , there are only a limited number of diffraction peaks. Besides, no diffraction peaks become visible over the 2 range of 48°-55°. This could be attributed to the texture effect of the as-deposited thin films, as several peaks at these positions were well observed in previous powder XRD measurements [START_REF] Righi | Crystal structure of 7M modulated Ni-Mn-Ga martensitic phase[END_REF][START_REF] Li | Determination of the orientation relationship between austenite and incommensurate 7M modulated martensite in Ni-Mn-Ga alloys[END_REF]. A close look at the measured and calculated peak positions, we found that fairly good matches can be found between the measured and recalculated ones for the two kinds of martensite, although a deviation of 0.2~2° exists. The good fits confirm that the modulated martensite and the NM martensite possess the same crystal structure as their counterparts in bulk materials, whereas the angular deviations indicates that the lattice constants of the 7M and NM martensite in the as-deposited thin films are not exactly the same as the ones derived from their powder counterparts, as the substrate imposes a constraint on the as-deposited thin films during the phase transitions. Using the measured peak positions of each phase, the lattice constants of the 7M and NM martensite were resolved. Table 4.1 summarizes the complete crystal structure information on the three different phases (austenite, 7M martensite, and NM martensite) involved in the as-deposited thin films. The unit cell of the 7M and NM martensite is shown in Fig. 4.2. This information is prerequisite for the subsequent EBSD orientation analyses. It should be noted that the macroscopic crystallographic features obtained in the present work are similar to those identified in the previous studies [START_REF] Tillier | Tuning macro-twinned domain sizes and the b-variants content of the adaptive 14-modulated martensite in epitaxial Ni-Mn-Ga films by co-sputtering[END_REF][START_REF] Kaufmann | Adaptive Modulations of Martensites[END_REF]. The only difference is that choice of the lattice cell for the two martensite is not the same. The (2 0 20)mono, (2 0 20 )mono and (0 4 0)mono planes in the present work refer to the respective (0 4 0)orth, (4 0 0)orth and (0 0 4)orth planes in the pseudo-orthorhombic coordinate system [START_REF] Tillier | Tuning macro-twinned domain sizes and the b-variants content of the adaptive 14-modulated martensite in epitaxial Ni-Mn-Ga films by co-sputtering[END_REF][START_REF] Kaufmann | Adaptive Modulations of Martensites[END_REF], whereas the (004)Tetr and (220)Tetr planes refer to the respective (004)NM and (400)NM in the previous studies [START_REF] Tillier | Tuning macro-twinned domain sizes and the b-variants content of the adaptive 14-modulated martensite in epitaxial Ni-Mn-Ga films by co-sputtering[END_REF][START_REF] Kaufmann | Adaptive Modulations of Martensites[END_REF].

Summary

X-ray crystal structural analysis shows that three different phases, i.e. austenite, 7M modulated martensite, and NM martensite, co-exist in the as-deposited Ni50Mn30Ga20 thin films.

The austenite phase has a cubic L21 crystal structure (Fm

Experimental procedure

The microstructures and crystallographic orientations of the thin films with nominal composition (at.%) of Ni50Mn30Ga20 and nominal thickness of 1.5 m were analyzed using the same SEM equipped with an EBSD system, where the EBSD patterns from martensitic variants were manually acquired using Channel 5 Flamenco's interactive option. Prior to the microstructural observations and orientation measurements, the thin film samples were subject to thickness-controlled electrolytic polishing with a solution of 20%HNO3 in CH3OH at 12 volts at room temperature.

NiMnGa thin films were also investigated by transmission electron microscope (TEM) with 200 kV accelerating voltage. Specimens for TEM investigation were cut off out the freestanding NiMnGa thin film and further thinned using twin-jet electrolytic polishing with an electrolyte of 20% HNO3 in volume in CH3OH at ambient temperature. ), the high relative contrast zones are of shorter and somewhat bent plates that orient roughly at 45° with respect to the substrate edges. 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. Further examination at a higher magnification in backscattered electron imaging (BSE) mode reveals that the fine lamellae having two different brightness levels are distributed alternately inside each plate, as highlighted with green and blue lines in Fig. 5.1(b). Of the two contrasted neighboring lamellae, one is thicker and the other is thinner. 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. The crystal structures of the coarse plates in the near surface layer of the film and fine plates well under the film surface were further verified by EBSD, using the determined crystal structure information for the 7M and NM martensite. In contrast, the pattern in Fig. 5.2(f) represents a single pattern and can be well indexed with the monoclinic superstructure of the 7M martensite (Fig. 5.2(g)). Large misfits between the acquired and calculated patterns are generated if using the tetragonal crystal structure of the NM martensite (Fig. 5.2(h)) to index this pattern. In this context, the coarse plates in the top layer of the film are composed of the NM martensite, whereas the fine plates in the film interior are of the 7M martensite. By taking into account of the X-ray measurement results, one may deduce 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. Using the determined lattice constants of the NM and 7M martensites and the published atomic position data [START_REF] Righi | Crystal structure of 7M modulated Ni-Mn-Ga martensitic phase[END_REF] as initial input, the constituent phases in the surface layers of the as-deposited thin films were verified by EBSD analysis. The Kikuchi line indexation has evidenced that both low and high relative contrast zones displayed in Fig. 5.3(a) can be identified as the tetragonal NM martensite other than the 7M martensite. Apparently, there is a difference in interpreting the microstructural features of Ni-Mn-Ga thin films between the present result and previous work by other groups [42-44, 55, 82, 85, 86, 88, 89]. This may be related to the different thickness of thin films used for microstructural characterizations. In the present study, the NM martensite was found at the surface of the produced thin films of about 1.5 µm thick, while the others reported the existence of the 7M martensite at the surface of the thin films with maximum thickness of about 0.5 µm. Indeed, the formation of different types of martensite is very sensitive to local constraints. It is obvious that at the film surface, the constraint from the substrate decreases with the increasing film thickness. Thus, the surface layers of thick films without much constraint from substrate would easily transform to the stable NM martensite, as demonstrated in the present case. the { 1 12}Tetr lamellar interfaces in P1 and P2 to be on edge, as shown in Fig. 5.7. The selected area diffraction patterns acquired from plate P1 and P3 in Fig. 5.6 and P1 and P2 in Fig. 5.7

Results

Microstructure of epitaxial NiMnGa thin films

Crystallographic features of NM martensite

well revealed that the adjacent fine lamellae in the same plate have their { 1 12}Tetr in parallel.

This further confirms the compound twin relationship between them.

Orientation correlation

Detailed EBSD orientation analyses were conducted on the NM martensite plates in the low and high relative contrast zones (Z1 and Z2 in Fig It is noted that the orientations of the major and minor variants in the low relative contrast zones are different from those in the high relative contrast zones. For the low relative contrast zones (Z1), the major and minor variants are oriented respectively with their (110)Tetr planes and (001)Tetr planes nearly parallel to the substrate surface (Fig. 5.8(c)). In the high relative contrast zones (Z2), 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 (110)Tetr planes nearly parallel to the substrate surface (Fig. 5.8(d)). In correlation with the microstructural observations, plates 2 and 4 are featured with higher brightness and plates 1 and 3 with lower brightness.

Misorientation relationships

Based on the misorientation calculations in part 2.3.2 and Eq. (2)(3)(4)(5)(6)(7)(8)[START_REF] Fukuda | Giant magnetostriction in Fe-based ferromagnetic shape memory alloys[END_REF][START_REF] Handley R C | Modern magnetic materials: principles and applications[END_REF][START_REF] Kohl | Ferromagnetic Shape Memory Microactuators[END_REF][START_REF] Faehler | An Introduction to Actuation Mechanisms of Magnetic Shape Memory Alloys[END_REF][START_REF] Jani | A review of shape memory alloy research, applications and opportunities[END_REF][START_REF] Jiles | Recent advances and future directions in magnetic materials[END_REF][START_REF] Wilson | New materials for micro-scale sensors and actuators: An engineering review[END_REF][START_REF] Nespoli | The high potential of shape memory alloys in developing miniature mechanical devices: A review on shape memory alloy mini-actuators[END_REF][START_REF] Hauser | Chapter 8 -Thin magnetic films[END_REF], the orientation relationships between adjacent lamellar variants were further determined from their orientation data manually acquired by EBSD. For both low and high relative contrast zones, the in-plate lamellar variants are found to have a compound twin relationship with the twinning elements

K1 = (112)Tetr, K2 = (11 2 )Tetr,  = ] 1 11 [ etr,  = ] 111 [
Tetr, P = (1 1 0)Tetr and s = 0.412. Here, all the crystallographic elements are expressed in the crystal basis of tetragonal Bravais lattice for the convenience in interpreting the EBSD orientation data and introducing the symmetry elements of the tetragonal structure to find proper misorientation axes and angles. The present twin relationship is the same as that reported for the bulk alloys [START_REF] Cong | Microstructural and crystallographic characteristics of interpenetrating and non-interpenetrating multiply twinned nanostructure in a Ni-Mn-Ga ferromagnetic shape memory alloy[END_REF][START_REF] Zhang | A general method to determine twinning elements[END_REF], and it is also consistent with the so-called a-c twin relationship found in the thin films [START_REF] Eichhorn | Microstructure of freestanding single-crystalline Ni2MnGa thin films[END_REF][START_REF] Leicht | Microstructure and atomic configuration of the (001)-oriented surface of epitaxial Ni-Mn-Ga thin films[END_REF][START_REF] Kaufmann | Modulated martensite: why it forms and why it deforms easily[END_REF][START_REF] Müller | Nanoscale mechanical surface properties of single crystalline martensitic Ni-Mn-Ga ferromagnetic shape memory alloys[END_REF][START_REF] Buschbeck | In situ studies of the martensitic transformation in epitaxial Ni-Mn-Ga films[END_REF][START_REF] Kaufmann | Adaptive Modulations of Martensites[END_REF].

By means of the indirect two-trace method [START_REF] Zhang | Indirect two-trace method to determine a faceted low-energy interface between two crystallographically correlated crystals[END_REF], the in-plate interlamellar interface planes in the two relative contrast zones were further determined. They coincide well with the As for the high relative contrast zones (Fig. 5.8(d)), the interlamellar interfaces in one plate (e.g. plate 1) are roughly perpendicular (88.6°) to the substrate surface. Whereas, the interlamellar interfaces in its neighboring plates (e.g. plate 2) are inclined 44.4° toward the substrate surface.

Moreover, the orientation relationships between two lamellae connected by an inter-plate interface in the low and high relative contrast zones were calculated. The respective minimum rotation angles and the corresponding rotation axes are displayed in Table 5.1 and Table 5.2.

The counterpart major and minor variants in adjacent plates are related by a rotation of ~83° around the <110>Tetr axes and a rotation of ~11-14° around the <301>Tetr axes with certain degrees of deviation, respectively. For the low relative contrast zones, the closest atomic planes from the counterpart major variants are referred to the ( 2

)Tetr planes with an angular deviation of 1.9° and those from the counterpart minor variants to the {010}Tetr planes with an angluar deviation of 4.2°, as outlined with black dotted rectangles in the {010}Tetr and {112}Tetr pole figures in Fig. 5.8(c). These characteristic planes are all nearly perpendicular to the substrate surface and the corresponding planes of the counterpart major and minor variants are positioned symmetrically to the (010)MgO plane. As for the high relative contrast zones (Fig.

5.8(d))

, the closest atomic planes from the counterpart major and minor variants are respective of the ( 121 )Tetr and (010)Tetr, similar to the case in the low relative contrast zones. However, they are no longer perpendicular to the substrate surface. Detailed calculations on plates 1 and 2

show that their ( It should be noted that the present results on the orientation relationships between lamellar variants in two neighboring NM plates (e.g. plates A and B in the low relative contrast zones and plates 1 and 2 in the high relative contrast zones), the orientations of in-plate interlamellar interfaces and those of inter-plate interfaces with respect to the substrate are similar to those reported in literature [42-44, 82, 89]. However, our direct EBSD orientation measurements have clarified that plates C and D in the low relative contrast zones (or plates 3 and 4 in the high relative contrast zones) are not a repetition of plates A and B (or plates 1 and 2), in terms of the orientations of the lamellar variants, intra-plate interfaces and inter-plate interfaces.

Discussion

As demonstrated above, the morphology and the surface topology of the NM martensite plates in the low and high relative contrast zones are clearly different, although they appear to be composed of the same (112)Tetr compound twins that act as the primary microstructural elements. In essence, the crystallographic orientations of the in-plate martensitic variants with respect to the substrate surface are not the same. This may be the origin of the morphological and topological differences observed for the two relative contrast zones, as discussed below.

(1) Low relative contrast zone Fig. 5.9(a) illustrates the atomic correspondences of eight lamellar variants organized in four NM plates (representing one variant group) for the low relative contrast zones (Z1), viewed from the top of the as-deposited thin films. The atomic correspondences were constructed with the individually measured orientations of lamellar variants and the detemined intra-and inter-plate interface planes. The width ratio (expressed in the number ratio of atomic layers) between the minor and major variants is 0.492, being determined according to the phenomenological theory of martensitic transformation (known as WLR theory [START_REF] Wechsler | On the Theory of the Formation of Martensite[END_REF][START_REF] Wayman | The phenomenological theory of martensite crystallography: Interrelationships[END_REF]) under the assumption that the invariant plane is parallel to the MgO subtrate surface. This width ratio is very close to 2:4 (0.5), i.e. that of the ideal (5 2 ) stacking sequence. It should be noted that for the sake of saving article space, only two atomic layers for the minor variants and five atomic layers for the major variants were taken in Fig. 5.9(a) to illustrate the thickness ratio between the minor variants and the major variants, the structures of intra-and inter-plate interfaces and the orientations of lamellar variants with respect to the substrate. In reality, the lamellar variants are much thicker in nanometer range. One should not confuse this with the structure model from the "adaptive phase theory" [START_REF] Leicht | Microstructure and atomic configuration of the (001)-oriented surface of epitaxial Ni-Mn-Ga thin films[END_REF][START_REF] Kaufmann | Modulated martensite: why it forms and why it deforms easily[END_REF][START_REF] Kauffmann-Weiss | Magnetic Nanostructures by Adaptive Twinning in Strained Epitaxial Films[END_REF][START_REF] Kaufmann | Adaptive Modulations of Martensites[END_REF][START_REF] Niemann | The Role of Adaptive Martensite in Magnetic Shape Memory Alloys[END_REF],

where the unit cell of the monoclinic 7M martensite is built based on a fixed number of atomic layers in each tetragonal variant. Fig. 5.9(b) presents a 3D display of the atomic correspondences between two alternately distributed lamellar variants with the (112)Tetr compound twin relationship in one NM martensite plate. It is seen from Figs. 5.9(a) and 5.9(b) that the in-plate interlamellar interfaces are coherent with perfect atomic match.

To further reveal the inter-plate interface features, a 3D configuration of two adjacent NM plates was constructed using the twinned lamellar variants as blocks, as illustrated in Fig. 5.9(c).

From Figs. 5.9(a) and 5.9(c), it is seen that the inter-plate interfaces are incoherent with certain amout of atomic mismatch. These inter-plate interfaces correspond to the so-called a-c twin interfaces, as mentioned in literature [START_REF] Kaufmann | Modulated martensite: why it forms and why it deforms easily[END_REF][START_REF] Müller | Nanoscale mechanical surface properties of single crystalline martensitic Ni-Mn-Ga ferromagnetic shape memory alloys[END_REF]. Interestingly, the atoms from two adjacent NM plates are not totally disordered at the inter-plate interfaces but show some periodicity. For instance, each pair of major and minor lamellae constitutes one period, and two end atoms at one period possess perfect match at the inter-plate interface. If choosing those coherent atoms as reference, the atoms within one period experience an increased mismatch symmetrically to the plate interface when approching the interlamellar interface enclosed in the period. Both the periodic coherence and the symmetrical mismatch would define a straight inter-plate interface, which acts as another invariant plane for the NM martensite in the low relative contrast zones. Indeed, the width ratio required by this invariant plane is the same as that required by the invariant plane parallel to the MgO substrate surface. Due to such an atomic construction, inter-plate interface are always straight without need to bend to accommodate the unbalanced interfacial atomic misfits. This boundary character has been evidenced in the microstructural observation (Fig. 5.3(a)). As the combination of the lamellar variants ((112)Tetr compound twins) are the same in neigboring plates, the atomic structures of all inter-plate interfaces are the same. Therefore, all plate interfaces in the low relative contrast zones are parallel to one another, as demonstrated in Fig. 5

.3(b).

Moreover, as the major and the minor lamellar variants ((112)Tetr compound twins) have the same orientation combination for all NM plates and they are distributed symmetrically to the inter-plate interfaces (Fig. 5.9(c)), there appear no microscopic height misfits across the inter-plate interfaces in the film normal direction. The NM plates in these zones are relatively flat without prononced surface relief or corrugation. Therefore, no significant relative contrast is visible between adjacent NM plates in the SE image.

(2) High relative contrast zone Similarly to the above analyzing scheme, the atomic correspondences of eight lamellar variants in four NM plates, the 3D-atomic correspondences of twinned lamellar variants in one NM plate, and the 3D configuration of two adjacent NM plates were also constructed for the high relative contrast zone (Z2), as shown in Fig. 5.10. Note that each high relative contrast zone contains two distinct orientation plates (e.g. plates 1 and 2 or plates 3 and 4 in Fig. 5.10(a)) in terms of the orientations of paired lamellar variants (the (112)Tetr compound twins). Due to the orientation differences, the width ratios between the minor and major variants in plate 1 and plate 2 are respectively 0.47 and 0.48, compared with that (0.492) for the low relative contrast zones. Here, the ideal width ratio 0.5 was used to construct Fig. 5.10. For a real material, the deviations from the ideal width ratio may be accommodated by stacking faults. From Fig. 5.10(a), it is seen that both major and minor lamellar variants in plate 1 are with their (110)Tetr planes near-parallel to the substrate surface, whereas the major and minor lamellar variants in plate 2 are respectively with their (001)Tetr and (110)Tetr planes near-parallel to the substrate surface. If taking the coherent (112)Tetr compound twin interfaces in plate 2 as reference, the (112)Tetr compound twin interfaces in plate 1 can be generated by a rotation of about 90° around the MgO [110] . In this manner, the (112)Tetr compound twin interfaces become perpendicular to the substrate surface.

It is commonly considered that the (112)Tetr compound twinning may bring about the atomic corrugations in NM plates, as illustrated in Fig. 5.10(b). As the direction of the atomic corrugations in plate 1 lie in the film plane, no significant surface relief is created on the free surface of thin films. Scanning tunneling microscopy (STM) imaging has evidenced that the free surface of the NM platesbeing equivalent to plate 1 in the present work -stays smooth [START_REF] Leicht | Microstructure and atomic configuration of the (001)-oriented surface of epitaxial Ni-Mn-Ga thin films[END_REF]. )Tetr and (010)Tetr planes from the neighboring plates are not in mirror relation with respect to the inter-plate interface. As the lengths of one pair of major and minor variants (considered as one period) in two plates are not the same along the macroscopic plate interface (Fig. 5.10(c)), unbalanced atomic misfit can be expected. This misfit is accumulative and increases with the increased length (parallel to the film surface) and the height (normal to the film surface) of the plates. Therefore, the plate interface orientation could be dominated by the orientation of the ( 121 )Tetr of the major variant in either plate 1 or plate 2, depending on local constraints. This may be the reason why the inter-plate interfaces in the high relative contrast zones are bent after running in certain length.

As displayed in Figs. 5.10(b) and 5.10(c), the atomic misfit also arises in the film normal direction. For example, the planar spacing of the major and minor variants in the film normal direction is 0.272 nm in plate 1, but 0.334 (major) and 0.272 nm (minor) in plate 2. If assuming that the major variants in plate 2 make dominant contribution to the atomic misfit between the two plates at the plate interface, the region of plate 2 is elevated by 23% in height with respect to that of plate 1. In the present work, the as-deposited thin films were subject to electrolytic polishing before microstructural observation. The constraints induced by the atomic misfits in the height direction may be fully released at the free surface. Thus, significant height difference between plate 1 and plate 2 can be expected. In the high relative contrast zones of Fig. 5.3(a), the plates with higher brightness are those with larger planar spacing in the film normal direction (major variants in plate 2), whereas the plates with lower brightness are those with smaller planar spacing in the film normal direction. This could well account for the distinct levels of brightness between neighboring plates observed in the high relative contrast zones. the dotted yellow and green lines is about 15°, being bisected by one solid black line that is parallel to the [ 1 1 0]MgO direction. The observed microstructural features are similar to those reported in recent studies [42-44, 82, 86]. A low relative contrast zone (Group 1) corresponds to the so-called Type Y pattern, and a high relative contrast zone (Group 2 or Group 3) to the Type X pattern [START_REF] Backen | Mesoscopic twin boundaries in epitaxial Ni-Mn-Ga films[END_REF]. In most cases, the neighboring plates in both the low and high relative contrast zones have almost the same width. The microstructural-correlated characterizations of crystallographic orientations of 7M martensite plates were conducted by EBSD, where the macroscopic reference frame was set to the crystal basis of the MgO monocrystal substrate. It is found that each 7M martensite plate is specified by a single crystallographic orientation, being designated as one orientation variant.

Crystallographic features of 7M martensite

There are a total of four different orientation variants distributed in one plate group, as illustrated in Fig. 5.12(a) and Fig. 5.12(b). Here, the four orientation variants -representing one plate group with low or high relative contrast -are denoted by the symbols 7M-V1, V2, V3, V4 (Fig. 5.12(a)) and 7M-VA, VB, VC, VD (Fig. 5.12(b)), respectively. and Group 2 in the form of {2 0 20}mono, {2 0 20 }mono and {0 4 0}mono pole figures. The subscript "mono" stands for monoclinic, as the three indices of the crystallographic planes are defined in the monoclinic Bravais lattice frame. Clearly, in the low relative contrast zone (Group 1), the four variants 7M-V1, V2, V3, V4 are all with their (2 0 20)mono plane nearly parallel to the substrate surface (Fig. 5.12(c), left). These variants correspond to the a-c twins with their common b axis perpendicular to the substrate surface, the so-called b-variants in the literature [START_REF] Tillier | Tuning macro-twinned domain sizes and the b-variants content of the adaptive 14-modulated martensite in epitaxial Ni-Mn-Ga films by co-sputtering[END_REF][START_REF] Kaufmann | Modulated martensite: why it forms and why it deforms easily[END_REF][START_REF] Müller | Nanoscale mechanical surface properties of single crystalline martensitic Ni-Mn-Ga ferromagnetic shape memory alloys[END_REF]. However, in the high relative contrast zone (Group 2), the variants VA and VD (colored in yellow and green in Fig. 5.12(b)) are with their (2 0 20 )mono plane nearly parallel to the substrate surface (Fig. 5.12(c), middle), and the variants VB and VC (colored in blue and red in Fig. 5.12(b)) with their (0 4 0)mono plane nearly parallel to the substrate surface (Fig. 5.12(c), left). Furthermore, the variants VB and VC and the variants VA and VD are of low brightness and high brightness, respectively. They correspond to the a-c twins with their common b axis parallel to the substrate surface, the so-called a-variants for VA and VD and c-variants for VB and VC [START_REF] Kaufmann | Modulated martensite: why it forms and why it deforms easily[END_REF].

It should be noted that in the high relative contrast zones, one plate group is composed of two (2 0 20 )mono variants (VA and VD) and two (0 4 0)mono variants (VB and VC). But in the literature [START_REF] Tillier | Tuning macro-twinned domain sizes and the b-variants content of the adaptive 14-modulated martensite in epitaxial Ni-Mn-Ga films by co-sputtering[END_REF][START_REF] Kaufmann | Modulated martensite: why it forms and why it deforms easily[END_REF][START_REF] Müller | Nanoscale mechanical surface properties of single crystalline martensitic Ni-Mn-Ga ferromagnetic shape memory alloys[END_REF], a pair of the (2 0 20 )mono variants (VA and VD) was designated to be one 0)orth, (4 0 0)orth and (0 0 4)orth planes in the pseudo-orthorhombic coordinate system, respectively [START_REF] Tillier | Tuning macro-twinned domain sizes and the b-variants content of the adaptive 14-modulated martensite in epitaxial Ni-Mn-Ga films by co-sputtering[END_REF][START_REF] Kaufmann | Adaptive Modulations of Martensites[END_REF]). In consequence, only two variants were found in each plate group [START_REF] Kaufmann | Modulated martensite: why it forms and why it deforms easily[END_REF][START_REF] Müller | Nanoscale mechanical surface properties of single crystalline martensitic Ni-Mn-Ga ferromagnetic shape memory alloys[END_REF], instead of four variants as evidenced in the present work. From the calculated misorientation data, the complete twinning elements -K1, K2, , P and s -of the above three types of twins were derived using a general method developed by our group [START_REF] Li | New approach to twin interfaces of modulated martensite[END_REF][START_REF] Zhang | A general method to determine twinning elements[END_REF], as shown in Table 5.5. The twinning modes are exactly the same as those in bulk materials [START_REF] Li | Determination of the orientation relationship between austenite and incommensurate 7M modulated martensite in Ni-Mn-Ga alloys[END_REF][START_REF] Li | New approach to twin interfaces of modulated martensite[END_REF]. Here, an attempt is made to correlate the present twin relationships (identified by EBSD) under the monoclinic crystal system with the published ones (deduced from XRD) under the pseudo-orthorhombic crystal system. It is seen from Table 5.6 that the so-called a-c twins with the (1 0 1)A as the twin interface are the Type-I twins in the present work. Interestingly, the Type-II twins in the present work also belong to the so-called a-c twins.

Clearly the specification of twin relationships under the pseudo-orthorhombic crystal system has difficulty to distinguish the subtle differences between the two types of twins. Apart from this, the compound twins could not be differentiated due to the simplification of the 7M martensite with a pseudo-orthorhombic crystal structure. To have a general view on the configuration of the 7M variants, the occurrences of the three types of twins in the two relative contrast zones are further examined. In the low relative contrast zone (Fig. 5.12(a)), the Type-I twins (V1:V3 and V2:V4) and the Type-II twins (V1:V2 and V3:V4) are those with the interface traces marked by solid black lines and dotted white lines, respectively. In these zones, the traces of Type-I and Type-II interfaces are in parallel, and the majority of variants are Type-I twins. Moreover, no compound twin relationship (V1:V4 and V2:V3) can be observed between two adjacent variants. However, in the high relative contrast zone (Fig. 5.12(b)), the majority of variants are Type-II twins. The interface traces of Type-I twins have only one orientation (marked by the solid black lines), whereas those of Type-II twins have two orientations (marked by the dotted yellow and green lines).

  mono 1 10 2 1  K Type I twin   mono 1 1 2 1  K   A mono 1 M 14 1 1 0 1 || || K K a14M-c14M twin K1 close to (1 0 1)14M
The interfaces with compound twin relationship (VA:VD and VB:VC) are those intra-plate interfaces, occurred with the bending of martensite plates.

Using the indirect two-trace method [START_REF] Zhang | Indirect two-trace method to determine a faceted low-energy interface between two crystallographically correlated crystals[END_REF][START_REF] Cong | Determination of microstructure and twinning relationship between martensitic variants in 53 at.%Ni-25 at.%Mn-22 at.%Ga ferromagnetic shape memory alloy[END_REF], the planes of twin interfaces in the low and high relative contrast zones were calculated with the measured crystallographic orientations of individual variants and orientations of their interface traces on the film surface. Since the epitaxial NiMnGa thin films were prepared on the MgO monocrystal substrate at elevated temperature, the thin films were composed of monocrystalline austenite when the deposition process was finished. According to the scanning tunneling microscopy (STM) analysis [START_REF] Leicht | Microstructure and atomic configuration of the (001)-oriented surface of epitaxial Ni-Mn-Ga thin films[END_REF], the orientation relationship between the MgO substrate and the NiMnGa austenite refers to

A A MgO MgO ] 0 0 1 [ ) 1 0 0 ( ] 0 1 1 [ ) 1 0 0 (

||

, as illustrated in Fig. 5.14(a). Upon cooling, the cubic austenite transforms to the monoclinic 7M modulated martensite below the martensitic transformation start temperature. Due to the displacive nature of martensitic transformation, the phase transformation from austenite to 7M martensite in the present thin films is realized by coordinated lattice deformation of the parent phase following certain orientation relationship between the two phases. The Pitsch orientation relationship

( mono mono A A ] 1 1 1 [ ) 1 2 1 ( ] 0 1 1 [ ) 0 1 1 (

||

), previously revealed for the austenite to 7M martensite transformation in bulk NiMnGa [START_REF] Li | Determination of the orientation relationship between austenite and incommensurate 7M modulated martensite in Ni-Mn-Ga alloys[END_REF], is further confirmed in the present work, as illustrated in Fig. 5.14(b).

It has been demonstrated that the austenite to 7M martensite transformation should be self-accommodated to minimize the macroscopic strain by forming specific variant pairs or groups with specific variant volume fractions [START_REF] Hane | Microstructure in the cubic to monoclinic transition in titanium-nickel shape memory alloys[END_REF][START_REF] Yang | Self-accomodation and shape memory mechanism of ϵ-martensite -II. Theoretical considerations[END_REF][START_REF] Bhattacharya | Wedge-like microstructure in martensites[END_REF]. This self-accommodation character in accordance with the substrate constraint may be the origin of the characteristic organizations of 7M variants in different variant zones, notably the low and high relative contrast zones in the present work. With the aid of the Pitsch orientation relationship, the lattice deformation during the martensitic transformation can be described by the displacement gradient tensor (M) in the orthonormal basis referenced to the ) should be subject to different constraints from the MgO substrate. To quantify these differences and their influence on the occurrences of different variant pairs in different martensite groups, the displacement gradient tensor of each variant is calculated and presented in the macroscopic reference frame

A ] 0 1 [0 - A ] 1 0 [1 - A ] 1 0 [1 , i.e.                         0
( MgO ] 0 0 1 [ - MgO ] 0 1 0 [ - MgO ] 1 0 0 [ ).
For the low relative contrast zone (Group 1), the displacement gradient tensors of the four 7M variants (V1, V2, V3, V4) in the macroscopic reference frame are expressed as According to our experimental observations on the low relative contrast zones, the variant pair V1:V3 (or V2:V4) belongs to Type-I twins, and the variant pair V1:V2 (or V3:V4) to Type-II twins. To estimate the overall transformation deformations of the two types of twins, a mean tensor matrix is defined as

) 1 ( 1 3 or 2 1 1 d M d M M     
, where d1 represents the relative volume fraction of one variant. Fig. 5.15 plots the non-zero ij e components of the matrix M against d1 for the Type-I and Type-II twin variant pairs. In the case of the Type-I twins, the ii e components representing dilatation in the three principal directions (Fig. This may be the reason why in the low relative contrast zones, Type-I twins appear with much higher frequency compared to the Type-II twins. Moreover, the formation of the Type-I twins does not create any height difference between adjacent variants in the film normal direction

( 31 e and 32 e = 0, and 33 e is the same for the constituent variants). Thus, a homogenous SE image contrast should be obtained for all the variants. For the high relative contrast zone (Group 2), the displacement gradient tensors of the four 7M variants (VA, VB, VC, VD) in the macroscopic reference frame are:

( Following the above analysis scheme for the low relative contrast zones, the non-zero ij e components in the matrix M (

) (1 × + × = 1 or 1 d - M d M M C B A
) were calculated as a function of the volume fraction d1 of variant VA, as shown in Figs. 5.17 When the Type-II twin pair forms, the situation for the dilatation deformations is similar to that for the Type-I twin pair. Fig. 5.17(c) shows that the 22 e and 33 e terms are nearly cancelled at d1 = 0.4964, whereas the 11 e term at d1 = 0.6020. For the shear deformations, all the components converge towards zero around d1 = 0.5 (Fig. 5.17d). The j e 3 term can nearly be cancelled at two volume ratios that are very close, d1 = 0.5284 and d1 = 0.5364. When the 31 e equals to zero, the 32 e is -0.0006; when the 32 e equals to zero, the 31 e is 0.0008. This indicates that the formation of the Type-II twins in the high relative contrast zone could effectively eliminate the shear deformation along MgO 1] 0 [0 direction. Moreover, at these volume ratios, the other components have relatively small values as shown in the matrices in Fig. 5.17(d). These volume ratios are very close to the effectively observed thickness ratio and close to the values reported in the literature [START_REF] Leicht | Microstructure and atomic configuration of the (001)-oriented surface of epitaxial Ni-Mn-Ga thin films[END_REF][START_REF] Kaufmann | Modulated martensite: why it forms and why it deforms easily[END_REF]. In this connection, the formation of the twins should appear with higher frequency that is in accordance with our experimental observation. In addition, there exist height differences between adjacent variants, as presented by the 33 e component of the matrix in Eq. (5-3) for the four 7M variants. This accounts for the high relative contrast between the pairs of variants in the SE images.

Crystallography and sequence of martensitic transformation

As mentioned above, the local microscopic microstructural and local crystallographic features in specific martensite variant groups were correlated by EBSD. To obtain the macroscopic crystallographic features, several martensite variant groups in the present NiMnGa thin films were analyzed by EBSD. It is seen that macroscopically, martensite variants are organized in colonies or groups, demonstrated by different brightnesses in Fig. 5.18. There are two differently oriented bright long straight strips parallel to the substrate edges ( MgO [START_REF] Pitsch | Der Orientierungszusammenhang zwischen Zementit und Austenit[END_REF] or MgO [010] ) that correspond to the low relative contrast zones mentioned in section 5.

Summary

Microstructure characterization shows that both the 7M martensite and NM martensite the Type-II twin pairs. The rigid constraint from the substrate accounts for this preference. Due to the fact that the formation of Type-I twin pair can cancel the shear deformation in the film normal direction at macroscopic scale (this shear tends to "peel" the film off the substrate) and requires much lower effort.

In the high relative contrast zones, there exists one interface trace orientation for Type-I twins but two interface trace orientations for Type-II twins on the film surface. In contrast to the low relative contrast zones, the Type-II twin pairs are more frequent than the Type-I twin pairs, due to the constraint from the rigid substrate. The formation of Type-II twin pair allows cancelling the shear deformation in the film normal direction at macroscopic scale. Large relative height differences between adjacent variants account for the high relative contrast.

Crystallographic calculation indicates that the martensitic transformation sequence is from Austenite to 7M martensite and then to NM martensite (A→7M→NM). The present study intends to offer deep insights into the crystallographic features and martensitic transformation of epitaxial NiMnGa thin films.

  Les couches minces é pitaxiales de Ni-Mn-Ga ont attiré une attention considé rable, car ils sont des candidats prometteurs pour les capteurs et actionneurs magné tiques dans des microsystè mes é lectromé caniques. Des informations complè tes sur les caracté ristiques de la microstructure et de la cristallographie des films NiMnGa et leur relation avec les contraintes du substrat sont essentielles à l'optimisation des proprié té s. Dans le pré sent travail, les couches minces é pitaxiale de Ni-Mn-Ga ont é té produites par pulvé risation cathodique magné tron à courant continu et ensuite caracté risé es par la technique de diffraction des rayons X (XRD) et la diffraction d'é lectrons ré trodiffusé s dans un microscope é lectronique à balayage é quipé d'analyse EBSD (MEB-EBSD).

  ,目前制备出的 NiMnGa 薄膜中包含多种晶体结构的相、多种取 向的马氏体变体和复杂的微观组织, 导致其很难获得较大的磁场诱发应变。 揭示 NiMnGa 薄膜中微观组织与晶体学取向之间的内在联系、探究 NiMnGa 薄膜中马氏体相变过程, 是通过训练消除不利的马氏体变体,获得较大磁场诱发应变的前提。但是,NiMnGa 薄 膜中的马氏体板条尺寸远远小于块体材料的板条尺寸,使得马氏体相的晶体学取向表征 异常困难,因此在 NiMnGa 薄膜种,局部马氏体变体的详细取向信息尚未报道。本论文 针对这一科学难题,利用 X-射线衍射(XRD) ,扫描电镜,电子背散射衍射(EBSD) 和透射电镜(TEM) ,对外延生长 NiMnGa 薄膜进行了系统全面的晶体学分析和研究。 结果如下: 首先,通过调控磁控溅射的工艺参数(溅射功率、气压、基板温度) ,薄膜的成分、 厚度等,成功制备出柱状晶和强取向的外延生长 NiMnGa 薄膜。由于柱状晶薄膜的晶界 会限制磁诱导形状变化的效果,导致其磁场诱发应变受到限制,因此本论文重点研究外 延生长 NiMnGa 薄膜。 XRD 结果表明,外延生长 NiMnGa 薄膜由奥氏体、非调制马氏体(NM)和七层调 制马氏体(7M)三相组成。其中七层调制马氏体的晶体结构为单斜结构。在薄膜中, 。通过分析 EBSD 的 Kikuchi 花样,发现表 层粗大的马氏体板条为 NM 马氏体,底层细小的马氏体板条为 7 层调制马氏体结构。 每个马氏体变体团由 4 种不同取向的马氏体板条组成,且每个板条中由两种取向的

Fig. 1 . 1

 11 Fig.1.1 Schematic illustration of the magnetic field induced deformation due to the rearrangements of martensite variants.

Fig. 1 .

 1 2 shows magnetic field-induced variant rearrangement occurring in a rectangular bar specimen under the applied field along the ] 100 [ direction of the specimen. The twinned microstructure is visible using polarized microscopy on a polished (001) surface of the specimen.

Fig. 1 . 2

 12 Fig.1.2The microstructure evolution due to magnetic field induced variant rearrangement[START_REF] Tickle | Ferromagnetic Shape Memory Materials[END_REF].

Fig. 1 . 3

 13 Fig.1.3 The illustration of crystal structure of NiMnGa alloys in austensite(a), non modulated martensite (b) and modulated martensite (c,d)

  relationships existing in each martensite plate and in total eight martensite variants in each variant group. The twin related variants have a minimum misorientation angle of ~79° around the <110>Tetr axis [69, 70]. For modulated martensites (5M and 7M), four types of alternately distributed martensite variants (A, B, C, and D) in one martensite variant group were determined to be twin-related: A and C (or B and D) possess type I twin relation, A and B (or C and D) type II twin, and A and D (or B and C) compound twin. All the twin interfaces are in coincidence with the respective twinning plane (K1) [26-28, 71-74].

Fig. 1 . 4

 14 Fig.1.4 (a) the relationship of crystal coordinate systems of austenite, adaptive phase and monoclinic seven layer modulated martensite. (b) The pole figure presents the projection of monoclinic seven layer modulated martensite coordinate system along cA (

( 2 )( 4 )

 24 Determination of the phase constituents, their crystal structures and macroscopic crystallographic features of various types of martensite in NiMnGa thin films by X-ray diffraction technique. (3) Correlation the microstructure with local crystallographic orientation of NM martensite and 7M modulated martensite by means of EBSD. Investigation of the orientation relationships between martensite variants and the orientation relationship for martensitic transformation by determined local crystallographic orientations and crystallographic calculation. Examination of the influence of substrate constraint on martensitic transformation and preferential selection of martensite variants in NiMnGa thin films based on crystallographic analyses.

Fig. 2 . 1

 21 Fig. 2.1 the schematics of fabrication process for NiMnGa target

Fig. 2 . 2

 22 Fig.2.2 illustration of direct current magnetron sputtering process (a) and the confocal magnetron sputtering system (b).

Fig. 2 . 3

 23 Fig.2.3 schematic illustration of X-ray diffractometers. (a) the conventional four-circle x-ray diffractometer.

  2 and shown in Fig. 2.4, in connect with SEM/EBSD orientation definition (Convention Oxford-Channel 5), two crystal coordinate systems are selected by convenience.One is referred to the Bravais lattice cell of each phase and the other is a Cartesian coordinate system set to the lattice cell in the present work. The macroscopic sample coordinate system is referenced to the three edges of MgO substrate (

Fig. 2 . 4

 24 Fig. 2.4 Schematic representation of a general (triclinic or anorthic) unit cell.

  vectors i, j and k with j parallel to b (j//b) and i perpendicular to b-O-c plane ( bOc i  ) following Channel 5 convention, as shown in Fig.2.5 for the three phases in the present work.

Fig. 2 . 5

 25 Fig.2.5 The schematics of selection of orthonormal coordinate systems

  , the matrix tensors in direct and reciprocal space are given in Eq.(2

Fig. 2 . 6

 26 Fig.2.6 Illustration of coordinate transformation from sample coordinate system to Bravais lattice cell.

Fig. 2 . 7

 27 Fig.2.7 The schematics of misorientation between two martensite variants

M

  is the Euler angle matrix). Then the misorientation matrix B A

1 AG

 1  is the reverse matrix of A G , transforming from crystal frame A back to the sample frame.

S

  are the generic elements of the rotation symmetry group.This provides an alternate description of misorientation as the successive operation of transforming from the first variant frame (A) back to the sample frame and subsequently to the new variant frames (B). Various methods can be used to represent this transformation operation, such as: Euler angles, axis/angle (where the axis is specified as a crystallographic direction), or unit quaternion.Misorientation expressed in angle and rotation axis is of particular interest for the present work, as it brings first information about twin orientation relationship between martensite variants. The determination of the angle and axis is explained as follow[START_REF] Humbert | Determination of the Orientation of a Parent [beta] Grain from the Orientations of the Inherited [alpha] Plates in the Phase Transformation from Body-Centred Cubic to Hexagonal Close Packed[END_REF]. If we denote the misorientation matrix

Fig. 2 . 8

 28 Fig. 2.8 The stereographic projection of the normal on crystal

2 eFig. 2 . 9

 229 Fig.2.9 Schematic illustration of the determination of OR between austenite and martensite.

MM

  is the Euler angle matrix of martensite, which can be determined by SEM-EBSD. i S and j S are the symmetry elements of austenite and martensite, respectively.A M T  is the transformation matrix from martensite to austenite. A T and M T are the transformation matrix from the Bravais lattice cell of austenite and martensite to the orthonormal reference frame set with respect to the parallel plane and direction.. are the transformation matrix for the orthonormal crystal coordinate system to the respective Bravais lattice cell of austenite and martensite.

Fig. 2 .

 2 Fig. 2.10 Schematic illustration of the determination of orientation relationship between austenite and martensite. A 1n g and A n g 2 ( N n , , 2 , 1    ) represent possible distinct orientations of the austenite

Fig. 2 .

 2 Fig. 2.11 the schematics of martensitic transformation

  examining the change of the length of the basis vectors of the reference cell before and after the transformation, the displacement gradient tensor can be readily built.To clearly analysis the constraint from MgO substrate during martensitic transformation process, the deformation gradient tensors of variants transformed from the transformed to the basis coordinate system of MgO substrate, with the following equation.

  components of the displacement gradient tensor in the MgO substrate coordinate system represent the dilatation and shear. The components) ( j i e ij stand for the normal strain, which represent the dilatation along in the MgO are shear strains, which indicates the shear magnitude in j plane (the plane normal direction is the j axis) along i direction.

Fig. 2 .

 2 Fig.2.12 Illustration of coordinate transformation from the coordinates of MgO substrate to austenite and from the coordinates of austenite to Pitsch.

Fig. 3 . 1

 31 Fig. 3.1 Composition of NiMnGa thin films deposited on Si substrate with various sputtering power

Fig. 3 . 2

 32 Fig. 3.2 Microstructure of thin films deposited on Silicon substrate at various sputtering power (a) 30w, (b) 50w, (c) 75w, (d) 100w.

Fig. 3 .

 3 Fig. 3.3 shows the microstructures of the thin film annealed at different temperatures. It can be seen that the column thicknesses increase with the annealing temperatures. The film annealed at 900 ℃ for 2 h show a plate structure in each column with the plate width of about 200 nm. .

Fig. 3 . 3 Fig. 3 . 4 X 3 . 3 . 2 3 . 3 . 2 . 1 Fig. 3 . 5 Fig. 3 .

 33343323321353 Fig. 3.3 SEM microstructure of NiMnGa thin films deposited on Si annealed at different temperature for 2 h (a) As-deposited; (b) 750°C ; (c) 800°C ; (d) 900°C

Fig. 3 . 6

 36 Fig. 3.6 NiMnGa thin films deposited on MgO(100) at different substrate temperature(a)400℃, (b) 500 ℃.

Fig. 3 .

 3 Fig.3.6 shows the X-ray diffraction patterns of the NiMnGa thin film deposited on the MgO substrate. X-ray diffraction spectra show that the crystal structure of these thin films is of those of 7M martensite and austenite.

Figure 3 .

 3 7 shows the microstructures of the NiMnGa thin films deposited on MgO (100) and on MgO (100) with Ag or Cr seed layer. As can be seen in Fig. 3.7, only the NiMnGa thin films deposited on MgO\Cr show a continuous character. On one hand the Cr seed layer improves element diffusion on the substrate and on the other hand, the Cr seed layer decreases lattice misfit between the substrate and the NiMnGa thin films. Since the lattice parameter of Cr and NiMnGa austenite is 2.888 Å and 5.803 Å, respectively. The orientation relationship between MgO, Cr and NiMnGa is 10

Fig. 3 . 7 3 . 3 . 3 Influence of film composition and thickness 3 . 3 . 3 . 1

 373333331 Fig. 3.7 NiMnGa thin films deposited on MgO (100) with and without seed layer (a) MgO(100),(b) MgO\Ag(100 nm), (c) MgO\Cr(100 nm)3.3.3 Influence of film composition and thickness

Fig. 3 . 8 Fig. 3 . 9 Fig. 3 . 3 . 3 . 3 . 2 Fig. 3 .

 3839333323 Fig. 3.8 SEM image of MgO\Cr\NiMnGa thin films with different compositions (a-b) Ni51.42at.%-Mn29.25 at.%-Ga19.33 at.%, (c-d) Ni55.45 at.%-Mn26.62 at.%-Ga17.93 at.%

Figure 3 .Fig. 3 .

 33 Figure 3.10 presents the microstructure of MgO\Cr\NiMnGa thin film(composition?) withdifferent thickness prepared in the present work. It is seen from the figures that with the increase of the film thickness, the amount of terrace shape constituents is increased. SEM-EDX analyses show that the composition of the terraces it is the same as that of the matrix. This

Fig. 3 .

 3 Fig. 3.11 XRD patterns of MgO\Cr\NiMnGa thin films with two different thicknesses (a)1.5 m, (b) 3 m.

microstructure of deposited films is classified in different zones depending on the

  temperature, TS is the substrate temperature). High substrate temperature also produces films with continuous microstructure. However, in the present study, in order to fabricate NiMnGa thin films with continuous microstructure other than column microstructure, both the low argon pressure (0.15 Pa) and high substrate temperature (500 ℃) were employed. Maybe due to the limitations of the present depositing equipment, films with continuous microstructure were not attainable direct on the substrates without utilizing any seed layer. Introducing a seed layer proves to be an alternative. For the NiMnGa deposited on the MgO single crystal substrate, the Cr seed layer improves the element diffusion on the substrate, which results in the continuous microstructure.

Fig. 3 .

 3 Fig.3.12 Thornton structure zone model correlating the argon pressure and the substrate temperature to the morphological properties of the films [101].

Fig. 4 . 1

 41 Fig.4.1 XRD patterns of as-deposited Ni-Mn-Ga thin films with MgO/Cr substrate: (a) measured by conventional -2 coupled scanning at different tilt angles ; (b) measured by 2θ scanning at two incidence angles ω and integrated over the rotation angle φ.

Fig. 4 .

 4 Fig. 4.1b presents the XRD patterns measured using a large-angle position sensitive detector under two different incident beam conditions. Compared with Fig. 4.1a, extradiffraction peaks are clearly seen in the 2range of 48°-55° and at the higher 2 positions (around 82°). These additional peaks in the 2range of 48°-55° were not detected in the previous studies on the Ni-Mn-Ga thin films[START_REF] Tillier | Tuning macro-twinned domain sizes and the b-variants content of the adaptive 14-modulated martensite in epitaxial Ni-Mn-Ga films by co-sputtering[END_REF][START_REF] Tillier | Martensite structures and twinning in substrate-constrained epitaxial Ni-Mn-Ga films deposited by a magnetron co-sputtering process[END_REF][START_REF] Thomas | Magnetically induced reorientation of martensite variants in constrained epitaxial Ni-Mn-Ga films grown on MgO(001)[END_REF][START_REF] Backen | Comparing properties of substrate-constrained and freestanding epitaxial Ni-Mn-Ga films[END_REF][START_REF] Buschbeck | In situ studies of the martensitic transformation in epitaxial Ni-Mn-Ga films[END_REF][START_REF] Kaufmann | Adaptive Modulations of Martensites[END_REF]. By combining all the characteristic diffraction peaks in Figs.4.1a and 4.1b, we are able to conduct more reliable phase identification and lattice constant determination on the constituent phases of the as-deposited thin films, especially for the modulated martensite.

Fig. 4 . 2

 42 Fig.4.2 the illustration of crystal structure of NM martensite and 7M martensite in NiMnGa thin films

Fig. 4 .

 4 Fig.4.3 presents the pole figures of NM martensite and 7M martensite. Let the edges of MgO substrate as the macroscopic sample coordinate system as shown in Fig.4.3(a) and the crystal direction of

Fig. 4 . 3

 43 Fig. 4.3 Pole figures of NM and 7M martensite in NiMnGa thin films (a) NM martensite, (b) 7M martensite

  figures and local surface morphologies. To determine the twin relationship and precise twinning elements, local crystallographic orientation correlated with microstructure is the prerequisite information. In this chapter, a spatially-resolved orientation analysis is conducted on martensites of NiMnGa thin films by means of electron backscatter diffraction (EBSD)a SEM based microstructural-crystallographic characterization technique. The microstructural features of both NM martensite and 7M modulated martensitic variants are directly correlated with their crystallographic orientations. The roles of substrate constraint in the preferential selection of martensitic variants are addressed. Based on the crystallographic calculation the martensitic transformation sequence in the present NiMnGa thin films was verified.

Fig. 5 . 1

 51 Fig.5.1 SE image of electrolytically polished Ni-Mn-Ga thin films, showing martensite plates that are clustered in groups with low and high relative contrasts. The sample coordinate system is set in accordance with the basis vectors of the MgO substrate. (b) High-magnification BSE image of the squared area Z1 in Fig. 5.1a, showing fine lamellae distributed alternately inside each plate. The inter-plate interfaces are marked with white dotted lines, and the intra-plate interfaces with blue and green solid lines.

Fig. 5 .

 5 Fig.5.1(a) shows a SE image of the as-deposited thin films after slight electrolytic polishing. It is clearly seen that the martensite appears in plate shape, and individual plates are clustered into groups that can be distinguished locally by the alignment of parallel or near-parallel inter-plate boundaries. According to the SE image contrast of neighboring martensite plates, the clustered groups are characteristic of two different relative contrasts -low relative contrast (Z1) or high relative contrast (Z2), as illustrated in Fig.5.1(a). Whereas 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.

Fig. 5 .

 5 Fig. 5.2(a) presents the secondary electron (SE) image acquired from the sample with gradient thickness film thickness. This sample was prepared by a controlled polishing to obtain an increased polishing depth from the left to the right, as schematically illustrated in Fig. 5.2(b). The right side and the left side of Fig. 5.2(a) represent the microstructure near the film surface and that deep inside the film, respectively. It can be seen from Fig. 5.2(a) that the thin film has an overall plate-like microstructure, with plate thickening from its interior to its surface. Although the polishing depth of the film changes smoothly, an abrupt change in the plate thickness occurs without any transition zone. This indicates a complete change of microstructural constituents or phases along the film thickness.

Fig. 5 .

 5 2(c) and Fig. 5.2(f) present the respective Kikuchi patterns, acquired from one coarse plate (with high brightness in the dotted blue square of Fig. 5.2(a)) and one thin plate (with high brightness in the dotted yellow square of Fig. 5.2(a)). Obviously, the measured patterns bear intrinsic differences, as arrowed in Fig. 5.2(c) and Fig. 5.2(f). Fig. 5.2(d) and Fig. 5.2(e) demonstrate that each of the two overlapping patterns appeared in Fig. 5.2(c) can be indexed with the tetragonal crystal structure of the NM martensite. It means that one coarse plate in the top surface layer of the film contains two NM martensitic variants. This is coherent with the BSE observations, shown in Fig. 5.1(b).

Fig. 5 . 2 .

 52 Fig.5.2. (a) SE image showing the plate-like microstructure of an electropolished sample with gradient film thickness. (b) Schematic illustration of the sample thickness change from the left side to the right side, produced by gradually electrolytic polishing. (c-e) Kikuchi patterns acquired from one coarse plate with high brightness in the dotted blue square of Fig. 5.2a. The mixed patterns in Fig. 1c are indexed as two NM variants (Fig. 5.2d and Fig. 5.2e) with Euler angles of (156.7 o , 175.2 o , 38.1 o ) and (163.8 o , 96.7 o , 44.7 o ), respectively. (f) Kikuchi pattern acquired from one fine plate with high brightness in the dotted yellow square of Fig. 5.2a.(g and h) Calculated Kikuchi patterns using the monoclinic superstructure of 7M martensite and the tetragonal structure of NM martensite, respectively. Note that in the latter case there appear large mismatches with the measured Kikuchi pattern.

Fig. 5 .

 5 Fig.5.3 (a) SE image of the as-deposited thin films after slight electrolytic polishing. (b) High-magnification BSE image of the squared area Z1 in Fig. 5.3(a). The insets represent the crystallographic orientation of the major and minor lamella variants. V1 and V2 are the major and minor variants in one martensite plate. V3 and V4 are the major and minor variants in the left adjacent martensite plate.

Fig. 5 .

 5 4 presents an example of the Kikuchi line pattern acquired from one martensite plate with high brightness in the high relative contrast zone and the calculated patterns using the tetragonal NM martensite structure. As the in-plate lamellar variants are too fine and beyond the resolution of the present EBSD analysis system, we could not obtain a single set of Kikuchi lines from one variant. For each acquisition, there are always mixed patterns from two neighboring variants in one image, as displayed in Fig.5.4(a). However, the high intensity reflection lines belonging to two different variants can be well separated in the image, as outlined by the green and red triangles in Fig. 5.4(b). By comparing Figs. 5.4(c) and 5.4(d) with Fig. 5.4(a), perfect matches between the acquired Kikuchi lines for the two variants and the calculated ones using the tetragonal NM martensite structure are evident.

Fig. 5 . 4 .

 54 Fig. 5.4. (a) Kikuchi line pattern acquired from one martensite plate in the high relative contrast zone (Z2) in Fig. 5.3a. (b) Indication of high intensity reflection lines from two adjacent variants 1 (the green triangle) and 2 (the red triangle). (c-d) Calculated Kikuchi line patterns using the tetragonal structure for variants 1 and 2, respectively.

Fig. 5 . 5

 55 Fig.5.5 The TEM bright field image of NiMnGa thin films (a) the low relative contrast zone, (b) the high relative contrast zone. The yellow dotted lines represent traces of the inter plate interfaces. The blue dashed lines represent traces of the intra plate interfaces.

Fig. 5 . 6

 56 Fig.5.6 The TEM bright field image in the high relative contrast zones of NiMnGa thin films (a-b) and the corresponding diffraction patterns of P1 and P3 (c-d). The yellow dotted lines represent traces of the inter plate interfaces. The blue dashed lines represent traces of the intra plate interfaces. Here the electron beam is parallel to the <110>Tetr zone axes of P1 and P3.

Fig. 5 . 7

 57 Fig.5.7 The TEM bright field image in the high relative contrast zones of NiMnGa thin films (a-b) and the corresponding diffraction patterns of P1 and P2 (c-d). Here the electron beam is parallel to the <201>Tetr zone axes of P1 and P2.

Fig. 5 .

 5 Fig. 5.6 and 5.7 show the TEM bright field images from the same area displayed in Fig.

  . 5.3(a)). Individual plates were identified to be composed of two alternately distributed orientation variants (lamellae) with different thicknesses, as schematically illustrated in Fig. 5.8(a) and 5.8(b). The clustered martensite plates running parallel to the substrate edges (Z1) represent one kind of variant group, whereas those running roughly at 45° to the substrate edges (Z2) represent another kind. According to the orientations of the thicker variants in plates, two sets of orientation plates can be distinguished, i.e. the set of plates A, B, C and D in the low relative contrast zones and the set of plates 1, 2, 3 and 4 in the high relative contrast zones. Thus, there are in total eight orientation variants of the NM martensite in one variant group. For easy visualization, they are denoted as V1, V2, …, V8 in Fig. 5.8(a) and SV1, SV2, …, SV8 in Fig. 5.8(b), where the symbols with odd subscripts correspond to the thicker (major) variants and those with even subscripts the thinner (minor) variants. Taking the basis vectors of the MgO(100) monocrystal substrate as the sample reference frame, as defined in the "Experimental" part, the measured orientations of the NM variants in the two relative contrast zones are presented in the form of {001}Tetr, {110}Tetr, {010}Tetr and {112}Tetr pole figures, as displayed in Figs. 5.8(c) and Fig. 5.8(d).

Fig. 5 . 5 .

 55 Fig. 5.5. (a-b) Schematic illustration of the geometrical configuration of NM plates. V1, V2, …, V8 and SV1, SV2, …, SV8 denote eight orientation variants in the low relative contrast zones (Z1) and in the high relative contrast zones (Z2), respectively. (c-d) Representation of measured orientations of in-plate lamellar variants in the form of {001}Tetr, {110}Tetr, {010}Tetr and {112}Tetr pole figures. The orientations of the intraand inter-plate interface planes are respectively indicated by light green solid squares and black dotted rectangles in the {010}Tetr and {112}Tetr pole figures.

( 112 )

 112 Tetr twining plane (roughly corresponding to the (101) planes of the austenite [44, 55, 88, 89]) and are perfectly coherent, as indicated by the light green solid squares in Figs. 5.8(c) and 5.8(d). According to the {112}Tetr pole figure of the low relative contrast zones shown in Fig. 5.8(c), the interlamellar interfaces in each plate are inclined roughly 47.5° toward the substrate surface, and two interlamellar interfaces from adjacent plates are positioned symmetrically either to the (010)MgO plane (e.g. plates A and B) or to the (100)MgO plane (e.g. plates B and C).

Fig. 5 . 9 .

 59 Fig. 5.9. (a) Atomic correspondences of eight lamellar variants in four NM plates for the low relative contrast zones (viewed from the top of as-deposited thin films). Only Mn and Ga atoms are displayed. (b) 3D-atomic correspondences of two alternately distributed lamellae with (112)Tetr compound twin relationship in one NM plate. The coherent twinning planes are outlined in green. is the dihedral angle between the (110)Tetr plane of the major variants and the MgO substrate, and is the dihedral angle between the (001)Tetr plane of the minor variants and the MgO substrate. (c) 3D configuration of two adjacent NM plates using in-plate lamellar variants as blocks to illustrate the plate interface misfits.

Fig. 5 .

 5 Fig. 5.10. (a) Atomic correspondences of eight lamellar variants in four NM plates for high relative contrast zones (viewed from the top of as-deposited thin films). Only Mn and Ga atoms are displayed. (b) 3D-atomic illustration of the combination of two lamellar variants ((112)Tetr compound twins) in plates 1 and 2. The twinning planes between lamellar variants are colored in green. is the dihedral angle between (001)Tetr plane of the major variants and the MgO substrate, and is the dihedral angle between the (110)Tetr plane of the minor variants and the MgO substrate. (c) 3D construction of two adjacent plates showing the plate interface misfits.

Fig. 5 .

 5 Fig. 5.11 presents a selected SE image of 7M martensite plates with full-featured microstructural constituents. It is evident that in Fig. 5.11(a) the individual martensite plates are clustered into groups, exhibiting either low relative contrast (Group 1) or high relative SE contrast (Group 2 and Group 3), as the case of NM martensite. The low relative contrast zones contain long straight plates parallel to one of the substrate edges, whereas the high relative

Fig. 5 .

 5 Fig. 5.11. (a) SE image of plate groups of 7M martensite with low relative contrast (Group 1) and high relative contrast (Group 2 and Group 3). (b) Magnified image of individual plates belonging to Group 2. Note that the traces of inter-plate interfaces have three distinct spatial orientations, as highlighted by the dotted yellow lines (Type-II twin interfaces), the dotted green lines (Type-II twin interfaces), and the solid black lines (Type-I twin interfaces).

Fig. 5 .

 5 Fig. 5.12. (a and b) Illustration of 7M martensite plates with four orientation variants in Group 1 (denoted by V1, V2, V3, V4) and Group 2 (denoted by VA, VB, VC, VD). The insets show the corresponding microstructures in the same zones. (c) Representation of individually measured orientations of 7M variants in Group 1 and Group 2 in the form of {2 0 20}mono, {2 0 20 }mono and {0 4 0}mono pole figures.

Fig. 5 .

 5 Fig. 5.12(c) presents the individually measured orientations of the 7M variants in Group 1

  single a-variant and a pair of the (0 4 0)mono variants (VB and VC) to one single c-variant. The same situation has also happened to the identification of constituent variants in the low relative contrast zones, e.g. a pair of the (2 0 20)mono variants (V1 and V4, or V2 and V3) was previously taken as one single b-variant. The appearance of such a discrepancy in specifying the number of variants in one plate group arises from the fact that in the other work, the crystallographic orientations of constituent variants in thin films were determined by conventional X-ray diffraction (XRD). The limited spatial resolution with this technique has prevented differentiating the corresponding (2 0 20)mono, (2 0 20 )mono, and (0 4 0)mono planes from variant pairs in pole figures. Here, the (2 0 20)mono, (2 0 20 )mono and (0 4 0)mono planes refer to the (0 4

5 .

 5 interface traces on the film surface are both in parallel to the cases can be found for the Type-II twin interfaces. As shown in the Fig.5.13(a), middle), the two Type-II twin interfaces that have parallel traces on the film surface intersect the substrate surface at +85° (V3 and V4) and -85° (V1 and V2), respectively. Apparently, the four Type-I and Type-II twin interfaces are oriented differently through the film thickness, but they have the same interface trace orientation on the film surface. As for the Compound twin interfaces, the interfaces between adjacent variants are all parallel to the film surface, as shown in the Fig.5.13(a), right). That is why no Compound twin interfaces could be observed by examining solely the film surface microstructure in the present work. Such Compound twin interfaces have been detected by cross section SEM observation[START_REF] Kaufmann | Modulated martensite: why it forms and why it deforms easily[END_REF].For the high relative contrast zone (Group 2), it is seen from the 13(b), left) that the Type-I twin interfaces between variants VA and VC and those between variants VB and VD possess roughly the same orientation in the film. They incline at about 45° to the substrate surface and their traces on the film surface are along the , for the Type-II twin interfaces as shown in the figure (Fig.5.13(b), middle), although the interface between VA and VB and that between VC and VD are inclined at about 45° to the substrate surface, their interface traces on the film surface do not possess the same orientation. One is 37.3° (VA and VB) away from the angle between two differently oriented Type-II twin interface traces on the film surface is 15° (as shown in Fig.5.11(b)), being in accordance with the results reported in the literature[START_REF] Backen | Mesoscopic twin boundaries in epitaxial Ni-Mn-Ga films[END_REF].As for the Compound twin interfaces, the interface between VA and VD and that between variant VB and VC possess roughly the same orientation (Fig.5.13(b), right). They are nearly perpendicular to the substrate surface and their traces on the film surface are nearly parallel to the is found that the bending of martensite plates in the high relative contrast zone is associated with the orientation change from VA to VD or from VB to VC, which results in an change of the plate interface from type I twin interface to type II twin interface or from type II twin interface to type I twin interface.

Fig. 5 .

 5 Fig. 5.14. (a) Illustration of the orientation relationship between NiMnGa austenite and MgO substrate. (b) Schematic of the Pitsch orientation relationship between the cubic austenite lattice and the monoclinic 7M martensite lattice. Note that only the average monoclinic unit cell [73] is used for describing the 7M structure.

  the diagonal term eii represents the dilatation in the i direction ( the off diagonal term eij represents the shear in the i direction on the plane normal and in the j direction. It is seen that the largest deformation during the transformation happens as a shear in the   , i.e. the twinning plane and the twinning direction of the 7M martensite. Here, for simplicity, we ignore the structural modulation of the 7M martensite and the 7M superstructure is reduced to an average monoclinic unit cell that corresponds to one cubic unit cell[START_REF] Li | Determination of the orientation relationship between austenite and incommensurate 7M modulated martensite in Ni-Mn-Ga alloys[END_REF].Due to the cubic crystal symmetry of the austenite phase, there are six distinct but equivalent confirmed that the four 7M variants in Group 1 in the low relative contrast zone are originated from the . Clearly, the 7M variants that originate from the two austenite planes (

(5- 2 )

 2 It is seen that the diagonal components of the four displacement gradient tensors are exactly the same, whereas the off diagonal components are of the same absolute value but sometimes with opposite signs. The maximum deformation appears as a shear 21 e in the (1 highlighted in bold in the matrices in Eq. (5-2).

5. 15 ( 31 e

 1531 a), as well as the 23 e component representing the shear in the (0 0 1)MgO plane along the . 5.15(b)), remain unchanged with the variation of d1. This means that these transformation deformations cannot be accommodated by forming twin variants. However, when the variant volume ratio d1 reaches 0.5, the largest shear 21 e and the shear are cancelled out. This volume ratio is very close to the thickness ration observed in the present work. For the case of the Type-II twins, the ii e and 31 e terms stay unchanged under the variant volume change. When the volume ratio reaches 0.5, the largest shear 21 e and the shear 23 e are both cancelled out.

Fig. 5 . 15 .

 515 Fig. 5.15. Displacement gradient tensor components of (a-b) Type-I twins and (c-d) Type-II twins in the low relative contrast zone, averaged with the volume fractions of two constituent variants.

Fig. 5 . 16 .

 516 Fig. 5.16. Illustration of the shear deformations from austenite to 7M martensite in the low relative contrast zone with respect to the substrate, viewed on (a) the (0 0 1)MgO plane and (b) the (0 1 0)MgO plane.

- 3 )

 3 Here, all the components in each displacement gradient tensor are not zero and their absolute values are in the same order of magnitude. The maximum deformation appears as a e ), as highlighted in bold in the matrices in Eq. (5-3).

and 22 e

 22 (a-b) (Type-I twin pair) and Figs.5.17(c-d) (Type-II twin pair). For the Type-I twin pair, it is seen from Fig.5.17(a) that the dilatation deformations can be accommodated to some extent through variant volume change, but they cannot be accommodated at one single volume ratio. Indeed, the 11 e terms are nearly cancelled out at d1 = 0.4876, but the 33 e term at d1 = 0.5935. Similarly, shear deformation accommodation exists but cannot be achieved at one single volume ratio, as shown in Fig.5.17(b). The 13 e , 21 e , 23 e and 31 e terms are roughly cancelled at d1 = 0.4698 but the 12 e and 32 e terms at d1 = 0.5940. If we consider that the j e 3 terms are the most important components to be accommodated due to the constraints from the rigid substrate, no volume ratio can be reached to cancel these components. When the 31 e component of the Type-I twin pair equals to zero, the 32 e component is -0.0111; when the 32 e component of the Type-I twin equals to zero, the component 31 e is 0.0111. Therefore, the formation of Type-I twins in the high relative contrast zone is energetically costly.

Fig. 5 . 17 .

 517 Fig. 5.17. Displacement gradient tensor components of (a-b) Type-I twins and (c-d) Type-II twins in the high relative contrast zone, averaged with the volume fractions of two constituent variants.

Fig. 5 .

 5 Fig.5.18 the BSE image of the NiMnGa thin films (a), (b) is the magnification view of area A and (c) is the magnification view of area B. The dotted lines are the variant group boundaries.

Fig. 5 .

 5 Fig.5.18 presents the BSE images of NiMnGa thin films after slight electrolytic polishing.

3 . 2 .

 32 Adjacent to the long strips (G5 and G6), there are several either bright or dark polygonal zones, which are the corresponding high relative contrast zones. Fig.5.18(b) and Fig.5.18(c) are the magnified view that presents the martensite groups. As shown in Fig.5.18(c), although the traces of plate interface in G3 are close to those in G4, the image brightness of the two martensite variant groups (G3 and G4) are different, indicating that group G3 and G4 possess different crystallographic features. As the contrast of a BSE image for a monophase microstructure with homogenous chemical composition originates from the orientation differences of the microstructural components, the difference in contrast between two martensite variant groups indicates the difference in their crystallographic orientations.

Fig. 5 .Fig. 5 . 2

 552 Fig. 5.19 (004)Tetr pole figure of NM martensite from the six variant groups determined by EBSD

Fig. 5 .Fig. 5 .

 55 Fig.5.22 Pole figures of NM martensite variants in the six variant groups

  are of plate morphology and organized into two characteristic zones featured with low and high relative SEM second electron image contrast. Local martensite plates with similar plate morphology orientation are organized into variant groups or variant groups. Low relative contrast zones consists of long straight plates running with their length direction parallel to the substrate edges, whereas the high relative contrast zones consists of shorter and bent plates with the length direction roughly in 45° against the substrate edges. SEM-EBSD in film depth analyses further verified the co-existence of the three constituent phases: austenite, 7M martensite and NM martensite. NM martensite is located near the free surface of the film, austenite above the substrate surface, and 7M martensite in the intermediate layers between austenite and NM martensite.Further EBSD characterization indicates that there are four distinct martensite plates in each variant group for both NM and 7M martensite. Each NM plate is composed of paired major and minor lamellar variants (i.e. (112)Tetr compound twins) in terms of their thicknesses having a coherent interlamellar interface, whereas, each 7M martensite plate contains one orientation variant. Thus, there are four orientation 7M martensite variants and eight orientation NM martensite variants in one variant group.For NM martensite, in the low relative contrast zones, the long and straight inter-plate interfaces between adjacent NM plates result from the configuration of the counterpart (112)Tetr compound twins that have the same orientation combination and are distributed symmetrically to the macroscopic plate interfaces. As there are no microscopic height misfits across plate interfaces in the film normal direction, the relative contrasts of adjacent NM plates are not distinct in the SE image. However, in the high relative contrast zones, the asymmetrically distributed (112)Tetr compound twins in adjacent NM plates lead to the change of inter-plate interface orientation. The pronounced height misfits across inter-plate interfaces in the film normal direction give rise to the surface reliefs, hence high relative contrast between adjacent plates.For 7M martensite, both Type-I and Type-II twin interfaces are nearly perpendicular to the substrate surface in the low relative contrast zones. The Type-I twin pairs appear with much higher frequency, as compared with that of the Type-II twin pairs. However, there are two Type-II twin interface trace orientations and one Type-I twin interface trace orientation in the high relative contrast zones. The Type-II twin pairs are more frequent than the Type-I twin pairs. The inconsistent occurrences of the different types of twins in different zones are originated from the substrate constrain.The crystallographic calculation also indicates that the martensitic transformation sequence is from Austenite to 7M martensite and then to NM martensite (A→7M→NM). The present study intends to offer deep insights into the crystallographic features and martensitic transformation of epitaxial NiMnGa thin films.In conclusion, both NiMnGa thin films with column and continuous microstructures were successfully fabricated by DC magnetron sputtering, after the optimization of sputtering parameters such as substrate temperature, sputtering power, substrate, seed-layer, film composition and thickness.X-ray diffraction analysis demonstrates that three different phases, i.e. austenite, 7M modulated martensite, and NM martensite, co-exist in the as-deposited epitaxial Ni50Mn30Ga20 thin films. The austenite phase has a cubic L21 crystal structure (Fm 3 m, No. 225) with lattice constant aA = 0.5773 nm. The 7M martensite phase has an incommensurate monoclinic crystal structure (P2/m, No. 10) with lattice constants a7M = 0.4262 nm, b7M = 0.5442 nm, c7M = 4.1997 nm, and = 93.7  The NM martensite phase is of tetragonal crystal structure (I4/mmm, No. 139) with lattice constants aNM = 0.3835 nm and cNM =0.6680 nm.By the combined the XRD and EBSD orientation characterizations, it is revealed that the as-deposited microstructures is mainly composed of the tetragonal NM martensite at the film surface and the monoclinic 7M martensite beneath the surface layer. For the NM martensite, there are two characteristic zones featured respectively with low and high relative SE image contrast. The NM martensite in the low relative contrast zones consists of long straight plates running with their length direction parallel to the substrate edges, whereas the NM martensite in the high relative contrast zones consists of shorter and bent plates with the length direction roughly in 45° against the substrate edges.Each NM plate is composed of paired major and minor lamellar variants (i.e. (112)Tetr compound twins) having a coherent interlamellar interface. There are in total eight orientation variants in one variant group. Indeed, in the low relative contrast zones, the long and straight inter-plate interfaces between adjacent NM plates result from the configuration of the counterpart (112)Tetr compound twins that have the same orientation combination and are distributed symmetrically to the macroscopic plate interfaces. As there are no microscopic height misfits across plate interfaces in the film normal direction, the relative contrasts of adjacent NM plates are not distinct in the SE image. However, in the high relative contrast zones, the asymmetrically distributed (112)Tetr compound twins in adjacent NM plates lead to the change of inter-plate interface orientation. The pronounced height misfits across inter-plate interfaces in the film normal direction give rise to the surface reliefs, hence high relative contrast between adjacent plates.The plate-like microstructures of the 7M martensite are composed of two distinct kinds of plate groups too. Each 7M martensite plate contains one orientation variant. There are four orientation variants in one plate group. The inter-plate interfaces are either Type-I or Type-II twin interfaces. The Type-I twin pairs appear with much higher frequency, as compared with

Table 2 .1

 2 List of NiMnGa targets with various compositions for deposition

	No.	Nominal composition of	phase of	Targeted composition in	Targeted phase
		the targets	targets at	thin films	of thin film at
			room		room
			temperature		temperature
	A	Ni46at.%-Mn32at.%-Ga-22at.%	A	Ni50at.%-Mn30at.%-Ga-20at.%	7M
	B	Ni48at.%-Mn30at.%-Ga-22at.%	A	Ni50at.%-Mn28at.%-Ga-22at.%	5M
	C	Ni50at.%-Mn28at.%-Ga-22at.%	5M	Ni52at.%-Mn26at.%-Ga-22at.%	7M
	D	Ni50at.%-Mn30at.%-Ga-20at.%	7M	Ni52at.%-Mn28at.%-Ga-20at.%	NM
	2

.1.2 Thin film deposition

	sputtering technique also produces films with a better adhesion than films produced by
	evaporation techniques. Substrate heating can be done by attaching a heater to the sample
	holder for epitaxial depositions. Thermal energy imparted to the deposition atoms increases
	the mobility of atoms forming thin film that have a nearly perfect atomic stacking during
	deposition.
	Several deposition methods have been developed to deposit thin films with the thickness
	ranging from several nanometers to several microns. Comparing with other depositing
	techniques, magnetron sputtering process has a number of advantages. First of all, plasma can
	be sustained at lower Argon pressures and hence resulting in low level of impurities. In
	addition, since the sputtering mechanism is not a thermal evaporation process, even the
	material with highest melting point can be deposited at ambient temperature. Usually, the
	deposited alloy films have a composition close to their target composition. Moreover,

Table 2 . 2

 22 The selection of coordinate systems

	Phases	Crystal structure	Lattice parameters
	Austenite	Cubic (L21)
	Crystal coordinate
	system

Table 2 .

 2

	3 the characteristic features of different twinning types
		Type I twin	Type II twin	Compound twin
	Number of 180°Rotation axis	1	1	2
	Twinning plane K1	Rational		Rational
	Conjugate twinning plane K2		Rational	Rational
	Twinning shear direction 1		Rational	Rational
	Conjugate Twinning direction 2	Rational		Rational

Table 2 .

 2

		4 the relationships of martensitic transformation
	Relationship		Plane	Direction	Ref.
	Bain	(001	A (001) ||	M

3 Chapter 3 Fabrication of NiMnGa thin films 3.1 Introduction In

  -36) spite of the effort made recently to use sputtering technology for the preparation of thick Ni-Mn-Ga films (from sub-micron to micron range (<2µm)), there are still some open questions in scientific and technical aspects in producing NiMnGa thin films, such as the control of the film composition during sputtering, the attainability of ultra thick epitaxial films (in several microns thick). The present work is dedicated to tackle these issues by optimizing

the substrate parameters and the deposition parameters. Two substrate materials were used in the present work: one is thermal oxidization silicon and the other one is monocrystalline MgO

[START_REF] Pitsch | Der Orientierungszusammenhang zwischen Zementit und Austenit[END_REF]

. It is known that compared with MgO, Si substrate is not optimum for producing qualified epitaxial NiMnGa films in terms of mono-crystallinity of austenite at high temperature but it is of low cost. It allows to determinate the optimum depositing parameters that require large numbers of trial and errors with a relatively low cost. Thus in the present work, the Si substrate is used to optimize the primary deposition parameters and the MgO substrate is used to finally produced the qualified films with limited numbers of tests.

Table 3 .

 3 1 the corresponding parameters of NiMnGa thin films deposited on Si with various sputtering power

		Power	Time	Thickness	Sputtering	Film composition (at.%)
		(W)	(h)	(m)	rates(nm/s)	Ni	Mn	Ga
	Si 1	30	6	1.142	0.059	54.85	23.92	21.23
	Si 2	50	3.5	1.142	0.091	55.36	24.22	20.42
	Si 3	75	1.5	0.714	0.132	55.76	23.92	20.02
	Si 4	100	2	1.285	0.159	55.17	24.97	19.87

Table 4 . 1 .

 41 Calculated lattice constants of austenite, 7M martensite and NM martensite for as-deposited Ni-Mn-Ga thin films.

				Lattice constants
	Phase	Space group	Crystal system
				a (nm) b (nm) c (nm)	  
	7M	P2/m (No. 10)	Monoclinic	0.4262 0.5442 4.199 90°,  93.7°
	NM	I4/mmm (No. 139)	Tetragonal	0.3835 0.3835 0.6680	°
	Austenite	Fm 3 m (No.225)	Cubic L21	0.5773 0.5773 0.5773	°
	4.3

.2 Determination of crystallographic texture

  12 1 )Tetr planes are inclined to the substrate surface at 42.57° and 47.24°, and the (010)Tetr planes are at 48.29° and 41.68°, respectively.

	Neighboring plates	Variant pairs	Misorientation angle  ( o )	Rotation axis
	A/B	V1-V3 V2-V4	82.6518 13.6865	3.4 o from the <110>Tetr direction 5.4 o from the <031>Tetr direction
	C/D	V5-V7 V6-V8	83.0965 13.1146	3.7 o from the <110>Tetr direction 4.6 o from the <301>Tetr direction
	B/C	V3-V5 V4-V6	83.1537 14.4210	3.6 o from the <110>Tetr direction 4.0 o from the <301>Tetr direction
	D/A	V7-V1 V8-V2	83.0093 14.4189	3.7 o from the <110>Tetr direction 3.1 o from the <301>Tetr direction

Table5.1. Minimum rotation angle and rotation axis between two lamellar variants connected by an inter-plate interface in the low relative contrast zones.

Table 5 . 2 .

 52 Minimum rotation angle and rotation axis between two lamellar variants connected by an inter-plate interface in the high relative contrast zones.

	Neighboring plates	Variant pairs	Misorientation angle  ( o )	Rotation axis
	1/2	SV1-SV3 SV2-SV4	82.9699 14.1760	3.9 o from the <110>Tetr direction 2.1 o from the <301>Tetr direction
	3/4	SV5-SV7 SV6-SV8	82.7963 14.8473	3.4 o from the <110>Tetr direction 3.6 o from the <031>Tetr direction
	2/3	SV3-SV5 SV4-SV6	82.5782 12.2859	4.7 o from the <110>Tetr direction 3.5 o from the <031>Tetr direction
	4/1	SV7-SV1 SV8-SV2	82.8110 11.8090	5.0 o from the <110>Tetr direction 9.9 o from the <031>Tetr direction

Table 5 . 3 .

 53 Calculated misorientations between adjacent 7M variants in Group 1, expressed as rotation axis (d) and angle () in the orthonormal crystal reference frame. The Euler angles of four variants V1, V2, V3, and V4 are respectively (137.94°, 46.93°, 90.45°), (221.82°, 133.15°, 270.46°), (41.68° ,133.18°, 270.44°), and (318.32°, 46.80°, 90.50°).

	Variant pairs	Misorientation angle ()	d1	Rotation axis d d2	d3	Twin type
	V1:V3	83.1337 179.9229	-0.7342 0.4504	-0.0010 0.7482	-0.6789 -0.4871	Type I
	V2:V4	82.8455 179.9432	-0.7339 0.4493	-0.0007 0.7498	-0.6791 -0.4856	Type I
	V1:V2	96.7436 179.9519	0.7265 -0.5136	-0.0005 0.6643	0.6871 0.5430	Type II
	V3:V4	97.2851 179.9806	0.7254 0.5166	0.0002 -0.6607	0.6882 -0.5445	Type II
	V1:V4	179.3063 179.5858	0.6837 -0.7297	0.0036 -0.0060	-0.7297 -0.6837	Compound
	V2:V3	179.3435 179.8736	0.6841 0.7293	-0.0011 0.0057	-0.7293 0.6841	Compound

Table 5 . 4 .

 54 Calculated misorientations between adjacent 7M variants in Group 2, expressed as rotation axis (d) and angle () in the orthonormal crystal reference frame. The Euler angles of four variants VA, VB, VC, ) of the four 7M variants in each plate group, the orientation relationships between neighboring variants can be further calculated.Table 5.3 and Table 5.4 show the calculated misorientations of adjacent variants in the low and high relative contrast zones, expressed in terms of rotation axis and angle. Detailed analysis has revealed that each pair of adjacent variants can be identified as either Type-I or Type-II or Compound twins, depending on whether the rotation axis is close to the normal of a rational plane or/and a rational direction in the monoclinic crystal basis. It is seen from Table1that in the low relative

	and VD are respectively (48.43°, 136.75°, 95.28°), (178.19°, 92.35°, 2.78°), (271.81°, 87.65°, 182.78°), and
	(41.57°, 43.25°, 275.28°).
	Variant pairs	Misorientation angle ()	d1	Rotation axis d d2	d3	Twin type
	VA:VC	82.3098 178.5255	-0.7414 -0.4414	0.0195 -0.7529	-0.6707 0.4880	Type I
	VB:VD	82.2390 177.9083	-0.7476 0.4364	-0.0277 0.7534	-0.6635 -0.4917	Type I
	VA:VB	97.8691 179.5722	0.7295 -0.5156	0.0049 -0.6569	0.6839 0.5500	Type II
	VC:VD	97.6586 179.7170	0.7246 0.5187	-0.0032 0.6583	0.6891 -0.5454	Type II
	VA:VD	177.3972 179.9432	0.6871 0.7263	-0.0004 0.0227	-0.7265 0.6869	Compound
	VB:VC	179.6341 179.8470	0.6693 0.7429	-0.0013 0.0031	-0.7429 0.6693	Compound
	With the correctly determined crystallographic orientations (represented with three Euler
	angles in Bunge's notation [92]

Table 2 ,

 2 where VA:VC and VB:VD belong to Type I twins, VA:VB and VC:VD to Type II twins, and VA:VD and VB:VC to Compound twins.

Table 5 . 5 .

 55 Twinning elements of 7M variants represented in the monoclinic crystal coordinate frame. K1 is the twinning plane, K2 the reciprocal or conjugate twinning plane,  the twinning direction,  the conjugate twinning direction, P the shear plane, and s the magnitude of shear.

	Twin		Type I twin		Type II twin	Compound twin
	elements	(VA:VC, VB:VD; V1:V3, V2:V4)	(VA:VB, VC:VD; V1:V2, V3:V4)	(VA:VD, VB:VC; V1:V4, V2:V3)
	K1		(1	2	) 10	mono	(1.1240	2	) 8.7602	mono	(1	0	10)	mono
	K2	1.1240 (	2	mono 8.7602)		1 (	2	10)	mono	1 (	0	10)	mono
		[11.0973	10	mono ] 0.8903		10 [	10	mono 1]	10 [	0	mono 1]
			[10	10	mono ] 1	[11.0973	10	mono ] 0.8903	[10	0	mono 1]
	P	(1	0.1161	mono 11.1610)	(1	0.1161	mono 11.1610)	(0	1	0)	mono
	s			0.2537			0.2537	0.0295

Table 5 . 6 .

 56 Comparison of twin orientation relationships identified in the present work with those reported in the literature.

	14M-adaptive [44, 82, 91]	7M modulated super cell	7M-average unit cell	Notes
	a14M-c14M twin	Type I twin
	K1 = (1 0 1)14M

Table 5 . 8

 58 The published orientation relationships of martensitic and intermartensitic transformation in NiMnGa alloys

	Orientation relationship	Austenite	Martensite
		Plane	direction	Plane	direction
	Bain	(001)	A

A

[START_REF] Pitsch | Der Orientierungszusammenhang zwischen Zementit und Austenit[END_REF]

This work is supported by the Sino-French Cai Yuanpei Program (N°24013QG), the Northeastern University Research Foundation for Excellent Doctor of Philosophy Candidates (No. 200904), and the French State through the program "Investment in the future" operated by the National Research Agency (ANR) and referenced by ANR-11-LABX-0008-01 (LabEx DAMAS). The work presented in this thesis is completed at LEM3 (former LETAM, University of Lorraine, France) and the Key Laboratory for Anisotropy and Texture of Materials (Northeastern University, China).

seed layer (100 nm Cr or Ag). The corresponding parameters are displayed in Table 3.2. The film thickness was verified by stylus profiler (DEKTAK 150). SEM (JEOL 6500F) equipped with EDS were used to analyze the microstructure and composition of these films.

Home-made X-ray diffraction machine (FSM) with Cobalt cathode source (nm was used to determine the phase constituents of the produced films. for Compound twins, as in the case for bulk materials. For easy visualization of the through-film-thickness orientations of twin interfaces in two relative contrast zones, the With the crystallographic orientations of the NM martensite variants in the six variant groups, the crystallographic orientations of 7M martensite variants can be calculated based on the published orientation relationship between 7M and NM martensites [71]. Fig. 5.20 presents the (001)mono pole figures of the 7M martensite calculated based on the orientation of the NM martensite variants. As shown in Fig. 5.20, there are also six 7M martensite variant groups, each containing 4 distinct variants. Then in total twenty-four 7M martensite variants.

Results

Influence of sputtering parameters and post annealing

Influence of sputtering power

Crystallographic orientation of 7M martensite variant

The calculated crystallographic orientation of 7M martensite variants are consistent with that acquired by EBSD in part 5.3.3. It is indicated that the intermartensitic transformation from 7M martensite to NM martensite follows the orientation relationship determined by Li et.al [71]. In order to compare the pole figures obtained by EBSD with those by XRD (Fig. 4.3) in the present study and previous studies [START_REF] Tillier | Tuning macro-twinned domain sizes and the b-variants content of the adaptive 14-modulated martensite in epitaxial Ni-Mn-Ga films by co-sputtering[END_REF][START_REF] Kaufmann | Adaptive Modulations of Martensites[END_REF], the (2 0 20)mono , (2 0 20 ) mono, (0 4 0) mono (Invited lecture).

II. Contributions to