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The impact of shear deformation in $(1\,0\,1)[1\,0\,\bar{1}]$ system of non-modulated (NM) martensite in Ni$_2$MnGa ferromagnetic shape memory alloy is investigated by means of ab initio atomistic simulations. The shear system is associated with twinning of NM lattice and intermatensitic transformation to modulated structures. The stability of the NM lattice increases with increasing content of Mn. The most realistic shear mechanism for twin reorientation can be approximated by the simple shear mechanism, although the lowest barriers were calculated for pure shear mechanism. The energy barrier between twin variants further reduces due to spontaneous appearance of lattice modulation or, in other words, the nanotwins with thickness of two atomic planes. Such nanotwins appear also on the generalized planar fault energy (GPFE) curve calculated using a newly developed advanced procedure and exhibits even lower energy than the defect free NM structure. These nanotwin doublelayers are also basic building blocks of modulated structures and play an important role in intermartensitic transformation., Comment: Manuscript accepted to Shape Memory and Superelasticity

High mobility of twin boundaries in modulated martensites of Ni-Mn-Ga-based ferromagnetic shape memory alloys holds a promise for unique magnetomechanical applications. This feature has not been fully understood so far, and in particular it has yet not been unveiled what makes the lattice mechanics of modulated Ni-Mn-Ga specifically different from other martensitic alloys. Here, results of dedicated laser-ultrasonic measurements on hierarchically twinned five-layer modulated (10 M) crystals fill this gap. Using a combination of transient grating spectroscopy and laser-baser resonant ultrasound spectroscopy, it is confirmed that there is a shear elastic instability in the lattice, being significantly stronger than in any other martensitic material and also than what the first-principles calculations for Ni-Mn-Ga predict. The experimental results reveal that the instability is directly related to the lattice modulations. A lattice-scale mechanism of dynamic faulting of the modulation sequence that explains this behavior is proposed; this mechanism can explain the extraordinary mobility of twin boundaries in 10 M., Comment: Manuscript accepted to Advanced Materials. Supplementary material (text and figures) is available as ancillary file

The effect of non-planar substrate surface on homogeneity and quality of cold sprayed (CS) deposits was studied by scanning acoustic microscopy (SAM). Fe coatings were cold sprayed onto Al substrates containing artificially introduced grooves of square- and trapezoid-shaped geometries, with flat or cylindrical bottoms. The Al substrates were either wrought or cold sprayed, to comprehend their prospective influence on the Fe coatings build-up. SAM was then used to assess morphological properties of the materials from the cross-view and top-view directions. The microstructure below the surface of the studied samples was visualized by measuring the amplitudes of the reflection echoes and the velocity of the ultrasonic waves. The SAM analysis revealed that the regions of coating imperfections around the grooves are larger than what is suggested by standard scanning electron microscopy (SEM) observations. Furthermore, we found that the seemingly non-influenced coating regions that appear perfectly homogeneous and dense in SEM do, in fact, possess heterogeneous microstructure associated with the individual CS nozzle passes., Comment: Manuscript accepted to the Journal of Thermal Spray Technology (JTST)

Irreversible plastic forming of B19$^\prime$ martensite of the NiTi shape memory alloy is discussed within the framework of continuum mechanics. It is suggested that the main mechanism arises from coupling between martensite reorientation and coordinated $[100](001)_{\rm M}$ dislocation slip. A heuristic model is proposed, showing that the ${(20\bar{1})_{\rm M}}$ deformation-twin bands, commonly observed in experiments, can be interpreted as a combination of dislocation-mediated kink bands, appearing due to strong plastic anisotropy, and reversible twinning of martensite. We introduce a term 'kwinking' for this combination of reversible twinning and irreversible plastic kinking. The model is subsequently formulated using the tools of nonlinear elasticity theory of martensite and crystal plasticity, introducing 'kwink interfaces' as planar, kinematically compatible interfaces between two differently plastically slipped variants of martensite. It is shown that the ${(20\bar{1})_{\rm M}}$ kwink bands may be understood as resultsing from energy minimization, and that their nucleation and growth and their pairing with $(100)_{\rm M}$ twins into specific patterns enables low-energy plastic forming of NiTi martensite. We conclude that kwinking makes plastic deformation of B19$^\prime$ martensite in polycrystalline NiTi possible despite only one slip system being available., Comment: Manuscript accepted to International Journal of Plasticity

Martensitic materials show a complex, hierarchical microstructure containing structural domains separated by various types of twin boundaries. Several concepts exist to describe this microstructure on each length scale, however, there is no comprehensive approach bridging the whole range from the nano- up to the macroscopic scale. Here, we describe for a Ni-Mn-based Heusler alloy how this hierarchical microstructure is built from scratch with just one key parameter: the tetragonal distortion of the basic building block at the atomic level. Based on this initial block, we introduce five successive levels of nested building blocks. At each level, a larger building block is formed by twinning the preceding one to minimise the relevant energy contributions locally. This naturally explains the occurrence of different types of twin boundaries. We compare this scale-bridging approach of nested building blocks with experiments in real and reciprocal space. Our approach of nested building blocks is versatile as it can be applied to the broad class of functional materials exhibiting diffusionless transformations., Comment: 25 pages, including supplementary

We study the branching of twins appearing in shape memory alloys at the interface between austenite and martensite. In the framework of three-dimensional non-linear elasticity theory, we propose an explicit, low-energy construction of the branched microstructure, generally applicable to any shape memory material without restrictions on the symmetry class of martensite or on the geometric parameters of the interface. We show that the suggested construction follows the expected energy scaling law, i.e., that (for the surface energy of the twins being sufficiently small) the branching leads to energy reduction. Furthermore, the construction can be modified to capture different features of experimentally observed microstructures without violating this scaling law. By using a numerical procedure, we demonstrate that the proposed construction is able to predict realistically the twin width and the number of branching generations in a Cu-Al-Ni single crystal.

Shape memory alloys often show a complex hierarchical morphology in the martensitic state. To understand the formation of this twin-within-twins microstructure, we examine epitaxial Ni-Mn-Ga films as a model system. In-situ scanning electron microscopy experiments show beautiful complex twinning patterns with a number of different mesoscopic twin boundaries and macroscopic twin boundaries between already twinned regions. We explain the appearance and geometry of these patterns by constructing an internally twinned martensitic nucleus, which can take the shape of a diamond or a parallelogram, within the basic phenomenological theory of martensite. These nucleus contains already the seeds of different possible mesoscopic twin boundaries. Nucleation and growth of these nuclei determines the creation of the hierarchical space-filling martensitic microstructure. This is in contrast to previous approaches to explain a hierarchical martensitic microstructure. This new picture of creation and anisotropic, well-oriented growth of twinned martensitic nuclei explains the morphology and exact geometrical features of our experimentally observed twins-within-twins microstructure on the meso- and macroscopic scale., Comment: 17 pages, 6 figures

The nucleation of bcc austenite in a single crystal of a mechanically stabilized 2H-martensite of Cu-Al-Ni shape-memory alloy is studied. The nucleation process is induced by localized heating and observed by optical microscopy. It is observed that nucleation occurs after a time delay and that the nucleation points are always located at one of the corners of the sample (a rectangular bar in the austenite), regardless of where the localized heating is applied. Using a simplified nonlinear elasticity model, we propose an explanation for the location of the nucleation points, by showing that the martensite is a local minimizer of the energy with respect to localized variations in the interior, on faces and edges of the sample, but not at some corners, where a localized microstructure can lower the energy., Comment: Proceedings, ICOMAT 2011, Journal of Alloys and Compounds, in press