Ni<sub>2</sub>-based Heusler alloys have attracted increasing attention for the shape memory effects in them and the related application properties. It can be interesting to explore new Ni<sub>2</sub>-based shape memory alloys with novel properties. In this paper, the site preference, electronic structure, elastic parameters and martensitic transformation of new Ni<sub>2</sub>Cu-based Heusler alloys Ni<sub>2</sub>CuZ (Z = Al, Ga, In, Si, Ge, Sn and Sb) were investigated theoretically. Between the two highly-ordered structures of Heusler alloys, Ni<sub>2</sub>CuZ alloys tend to crystallize in the L2<sub>1</sub> structure with Cu atom entering the B site in the cubic lattice. In contrast, the XA structure is higher in energy and less stable. This is different from the usual rule that transition metal atoms with more valence electrons tend to occupy the A, C sites at first and can be related to the strong covalent hybridization between Ni and main group element Z in L2<sub>1</sub> type Ni<sub>2</sub>CuZ.<br>Ni<sub>2</sub>CuZ martensites are all lower in energy compared with the corresponding austenites, which makes them candidates as shape memory alloys. This can be explained by the Jahn‒Teller effect characterized by the reduced states near <i>E<sub>F</sub></i> in the DOS structure and the mechanical instability of the cubic austenite lattice. The martensite-austenite energy difference <i>ΔE<sub>M</sub></i> are strongly influenced by main group elements Z. When Z are in the same group, the <i>ΔE<sub>M</sub></i> increases with the increase of their atomic number, but when Z are in the same period, an opposite trend is observed. The <i>ΔE<sub>M</sub></i> can be looked on as the driving force for the martensitic transformation, a larger <i>ΔE<sub>M</sub></i> corresponds to a higher martensitic transformation <i>T<sub>M</sub></i>. InHeusler alloys, electron concentration <i>e/a</i> and electron density <i>n</i> are usually used to discuss the variation of <i>T<sub>M</sub></i>. An increase of<i> e/a</i> or n tends to leads to the increase of <i>T<sub>M</sub></i>. However, this is contrary to the results in Ni<sub>2</sub>CuZ. New factors, the negative shear modulus<i> C’</i> and softening of the elastic constant <i>C<sub>44</sub></i> and their variations with Z elements can be used to explain this. These results reveal the close relation between the martensitic transformation and mechanical parameters and suggest that they are important factors to predict new shape memory alloys and analyse their properties in Heusler alloys. It is also found that the Young’s modulus, shear modulus increase and Poisson’s ratio decreases after the martensitic transformation. Thus, the Ni<sub>2</sub>CuZ martensite has higher stiffness and rigidity but lower ductility compared with the austenite.
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