Confirmation of the orientation relationship between austenite and 7M martensite

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Ferromagnetism of Ni-Mn-Ga alloys

The ferromagnetism of Ni-Mn-Ga alloys is mainly from the contribution of the magnetic moment of Mn atoms. Ni atoms only carry a small magnetic moment and the magnetic moment of Ga is negligible [21]. From the magnetization measurements, Webster et al. [21] reported that the total magnetic moment of the cubic Heusler phase of Ni2MnGa is 4.17ȝB per formula unit. A more detailed magnetic analysis was performed by means of polarized neutron scattering measurements and 0.36ȝB for Ni, 2.80ȝB for Mn and -0.06ȝB for Ga at 100K at the martensite state of Ni2MnGa were reported [46]. By means of first principles calculations, Ayuela et al. reported that the magnetic moments for Ni, Mn and Ga were 0.36ȝB, 3.43ȝB and -0.04ȝB, respectively, in the parent phase and 0.40ȝB, 3.43ȝB and -0.04ȝB in the martensite of Ni2MnGa [82]. The ferromagnetism of Ni-Mn-Ga alloys is interesting because Mn is antiferromagnetic in its pure element state. The change from the antiferromagnetic behavior of pure Mn to the ferromagnetic behavior of Ni-Mn-Ga alloys is due to the increased distance between the Mn sites in the L21 structure compared with the distance between Mn atoms in pure Mn, which changes the Mn-Mn exchange interaction from antiferromagnetic to ferromagnetic [83].
Magnetocrystalline anisotropy is an intrinsic property of a material in which the magnetization favors preferred directions (easy directions). In Ni-Mn-Ga alloys, the easy axis of magnetization of the parent phase was reported to be <100>A [84]. The easy axis of magnetization of modulated martensites, i.e. 5M and 7M, correspond to the shortest axis of the distorted austenite, i.e. b-axis of the superlattice. NM martensite has the easy magnetization plane that perpendicular to the c-axis. Magnetocrystalline anisotropy energy, defined as the work necessary to rotate the magnetization from the easy axis to the hard axis with an applied magnetic field, is an important parameter for the achievement of giant magnetic-field-induced strain effects in Ni-Mn-Ga alloys. Magnetocrystalline anisotropy energy is usually expressed by the magnetocrystalline anisotropy constants, which can be acquired by measuring magnetization curves along different crystalline directions. It is reported that the magnetocrystalline anisotropy constant of the austenite for Ni-Mn-Ga alloys is relatively low, of the order of 103J/m3, whereas the anisotropy constant of the martensite is increased by two orders of magnitude [85]. Straka et al. systematically studied the magnetic anisotropy of the three types of martensites [85]. At room temperature, for Ni49.7Mn29.1Ga21.2 5M martensite, the anisotropy constant is K1=1.65×105 J/m3 (K2 is negligible); for Ni50.5Mn29.4Ga20.1 7M martensite K1=1.7×105 J/m3 and K2 =0.9×105 J/m3 referring to the hard and mid-hard axes; and for Ni50.5Mn30.4Ga19.1 NM martensite K1=-2.3×105 J/m3 and K2 =0.55×105 J/m3. It should be noted that the magnetic anisotropy constants are temperature and composition dependent [86, 87].

Mechanism of magnetic field-induced strain

The macroscopic shape memory effects induced by magnetic field in Ni-Mn-Ga alloys are the results of field-induced twin variants reorientation [10]. The twin boundary motion can occur when the difference in magnetization energy ( Emag) between different martensite variants exceeds the elastic energy needed for twin boundary motion [88]: Emag H0ıtw (1.3).
where H0 is the reorientation strain and ıtw is the twinning stress. If the material is magnetized to saturation perpendicularly to the easy axis of one variant and along the axis of the adjacent variant, the difference of the magnetic energy is equal to the difference of the magnetocrystalline anisotropy energy (Ku). The condition for twin boundary motion under magnetic field can be rewritten as [88]: Ku/H0 > ıtw + (ıext). (1.4).
The term in bracket, ıext, is the external applied stress applied in the direction perpendicular to the magnetic field direction. This equation describes the usual setup of an actuator.
When an external magnetic field is applied, the variants with their magnetization vectors aligning along the applied field are more energetically favorable and they will increase the volume fraction at the expense of the other variants through the twin boundary motion, leading to the macroscopic shape change of the sample, namely magnetic field induced strain [58]. The schematic illustration of the rearrangement of the martensite variants under a magnetic field is shown in Fig. 1.4. So far, large strains up to ~6% and ~10% have been reported in 5M [15] and 7M martensite [8], while the strain induced by magnetic field in NM martensite is negligible [89].

Crystallographic orientation relationship of Ni-Mn-Ga alloys

As the field-induced effect originates from the reorientation of martensite variants through a detwinning and twinning process, the microstructural configuration and crystallographic correlation of constituent martensite variants have strong influence on the activation of the magnetic shape memory effect (output strain and dynamic response). Thus, comprehensive crystallographic knowledge on the microstructural features of martensite variants and variant boundaries is desired, from which a clear image of structure-property relation is built up and also necessary indications for further precise control and improvement of properties are presented.
So far, constant efforts have been devoted to the study of orientation relationships between martensite variants by means of X-ray diffraction (XRD) [97] and transmission electron microscopy (TEM) [98-100]. Mogylnyy et al. successfully determined the twinning mode in a Ni-Mn-Ga single crystal with 5M martensite by X-ray diffraction methods [97]. Han et al. [98, 99] investigated the orientation relationship between the martensite variants in 5M and 7M martensite by TEM. It was found that there exists a twin relationship between the variants in both 5M and 7M martensite. The twinning plane in 5M martensite is {1 2 5 }5M, while that in 7M twinning elements in 5M and 7M martensite were presented by Nishida et al. [100]. However, the XRD analysis suffers a limit on acquiring simultaneously the spatial microstructural information of the measured orientations, which prevents the identification of orientation-microstructure correlation. In contrast, the TEM analysis enables one to reveal the variant morphology and the inter-variant orientation relationships, but the exploitable area is too local. Hence, it is difficult to obtain a global orientation image of multi-variants. It has also been noted that for the incommensurate modulation, the number of the observed satellites plus the main reflection does not conform to the number of the subcells in the superstructure [75]. Apparently, the habitual interpretation of the structural modulation according to TEM observation is not suited for the determination of the lattice constants and hence the orientations of the martensite variants [100], and needs to be reconsidered. Moreover, due to the limitation of TEM observation, the crystallographic nature of inter-variant interfaces and their statistical distributions has also not been well addressed.
With the mature of SEM/EBSD technique, large-scale spatially resolved orientation examination has made the correlation between microstructure and crystallographic orientation possible, which overcomes the above mentioned limitations. The merits of EBSD measurements lie on that, firstly, it provides an alternative means for verifying the crystal structure information, as the EBSD-based orientation determination requires the complete crystal structure information including the lattice constants and the atomic position of each atom in the unit cell; secondly, it enables the automatic orientation mapping of individual martensite variants, which correlates the crystal structure and orientation information with the morphologic features on an individual variant basis; thirdly, it allows an unambiguous determination of the orientation relationships of adjacent variants and the twin interface planes, and thus a full crystallographic analysis on a bulk sample with statistical reliability.

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Scanning electron microscopy

For detailed microstructural analyses, the field emission gun scanning electron microscope (SEM) Jeol JSM 6500 F was used. Additionally to the ability of detecting secondary electrons, the SEM is also equipped with a backscattered electron detector, an energy dispersive X-ray spectrometry (EDS, BRUKER, Germany) and an electron backscatter diffraction camera.
The morphological features were characterized by secondary electron (SEI) imaging and backscattered electron (BSE) imaging. The composition of the alloy was verified by EDS. Electron backscatter diffraction (EBSD) was applied for the orientation acquisition. In the present work, the orientation measurements were performed in a field emission gun scanning electron microscope (Jeol JSM 6500 F) with EBSD acquisition camera and Channel 5 software. The working voltage was set at 15KV. The detailed crystal structure information was input into the Channel 5 software to construct the corresponding database for Kikuchi indexing. The orientation data were manually and automatically acquired. The beam control mode was applied for automatic orientation mapping. To ensure the indexation accuracy using the monoclinic superlattice for 7M and 5M martensite, the minimum number of detected bands is set to be 10 and 15, respectively. The maximum allowed MAD that represents the mean angular deviation between the calculated and the experimental EBSD pattern was set to be 1. For the case of 5M martensite, as the monoclinic angle is very close to 90°, it is unavoidable that there exist misindexations in the orientation map. For the determination of correct crystallographic orientation and variant number, we firstly judged and acquired the orientation data manually, then replaced the misindexations in the map by the post treatment.

Transmission electron microscopy

TEM is capable of imaging at a significantly higher resolution than optical microscopy and SEM, which enables the research to examine fine detail of the microstructure. Here, a Philips CM 200 LaB6 cathode TEM was used to observe the stacking faults inside the martensite plates. A Gatan MSC 792 CCD camera was used to acquire the images. The working voltage was set at 200KV.

Table of contents :

Chapter 1 Literature Review
1.1 General introduction
1.2 Martensitic transformation and twin relationship between variants
1.3 Ni-Mn-Ga Ferromagnetic Shape Memory Alloys
1.3.1 Introduction
1.3.2 Magneto-structural transformation in Ni-Mn-Ga alloys
1.3.3 Crystal structure of martensite
1.3.4 Ferromagnetism of Ni-Mn-Ga alloys
1.3.5 Mechanism of magnetic field-induced strain
1.3.6 Crystallographic orientation relationship of Ni-Mn-Ga alloys
1.4 Content of the present work
Chapter 2 Experimental and calculation methods
2.1 Alloy preparation
2.2 Sample preparation
2.3 Characterization methods
2.3.1 Optical microscopy
2.3.2 Mechanical property testing
2.3.3 Differential scanning calorimetry
2.3.4 X-ray diffraction
2.3.5 Scanning electron microscopy
2.3.6 Transmission electron microscopy
2.4 Crystallographic calculation method
2.4.1 Coordinate transformation between orthonormal reference system and monoclinic system 30􀀃
2.4.2 Misorientation calculation
Chapter 3 Characterization of Ni-Mn-Ga martensites
3.1 5M martensite
3.1.1 Crystal structure of 5M martensite
3.1.2 Microstructural features of 5M martensite
3.1.3 Orientation identification of 5M martensite
3.1.4 Orientation relationships between martensite variants
3.1.5 Characters of twin interface planes
3.1.6 Orientation relationship between austenite and 5M martensite
3.1.7 Summary
3.2 7M Martensite
3.2.1 Phase transformation temperatures and mechanical property
3.2.2 Crystal structure of 7M martensite
3.2.3 Microstructure
3.2.4 Determination of twin relationships and twin interfaces of 7M martensite
3.2.5 Orientation relationship between austenite and 7M martensite
3.2.6 Summary
3.3 Non-modulated martensite
3.3.1 Phase transformation temperatures and crystal structure
3.3.2 Compressive properties
3.3.3 Microstructure
3.3.4 Determination of inter-plate and inter-lamellar interface
3.3.5 Summary
Chapter 4 Austenite-7M-NM transformation
4.1 Formation of self-accommodated 7M martensite
4.1.1 Martensitic transformation temperatures and crystal structure
4.1.2 Microstructure features of austenite to 7M transformation
4.1.3 Confirmation of the orientation relationship between austenite and 7M martensite
4.1.4 Experimental determination of habit plane
4.1.5 Calculation based on the crystallographic phenomenological theory
4.1.6 Summary
4.2 Clarification of structure and stability of long-period modulated martensite
4.2.1 Lattice modulation and nanotwin combination
4.2.2 EBSD measurements on the coexistence of three phases
4.2.3 Inter-plate interface
4.2.4 Summary
4.3 Role of 7M martensite in the transformation from austenite to NM martensite
4.3.1 EBSD measurements on the co-existing austenite, 7M martensite and NM martensite
4.3.2 Orientation relationship between 7M martensite and NM martensite
4.3.3 Transformation mechanism from 7M martensite to NM martensite
4.3.4 Summary
Chapter 5 Conclusion and perspective
Conclusion
Perspective
Appendix I: atomic coordinates of 5M superstructure
Appendix II: atomic coordinates of incommensurate 7M superstructure
Appendix III: atomic coordinates of nanotwinned 7M superstructure
References

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