First principles study of electronic structure, mechanical properties and possible martensitic transformation in Ni<sub>2</sub>Cu-based Heusler alloys

<sec>Ni<sub>2</sub>-based Heusler alloys have received increasing attention due to their shape memory effects and the relevant application properties. It is interesting to explore new Ni<sub>2</sub>-based shape memory alloys with novel properties. In this work, the site preference, electronic structure, elastic parameters and martensitic transformation of new Ni<sub>2</sub>Cu-based Heusler alloys Ni<sub>2</sub>Cu<i>Z</i> (<i>Z</i> = Al, Ga, In, Si, Ge, Sn and Sb) are investigated theoretically. Between the two highly-ordered structures of Heusler alloys, Ni<sub>2</sub>Cu<i>Z</i> alloy tends to crystallize in the <i>L</i>2<sub>1</sub> structure with Cu atom entering the <i>B</i> site in the cubic lattice. In contrast, the <i>XA</i> structure is higher in energy and lower in stability. This is different from the usual rule that transition metal atoms with more valence electrons tend to occupy the <i>A</i>, <i>C</i> sites at first and can be related to the strong covalent hybridization between Ni and main group elements <i>Z</i> in <i>L</i>2<sub>1</sub> type Ni<sub>2</sub>Cu<i>Z</i>.</sec><sec>Ni<sub>2</sub>Cu<i>Z</i> martensites are all lower in energy than the corresponding austenites, which makes them candidates for shape memory alloys. This can be explained by the Jahn-Teller effect characterized by the reduced states near <i>E</i><sub>F</sub> in the DOS structure and the mechanical instability of the cubic austenite lattice. The martensite-austenite energy difference Δ<i>E</i><sub>M</sub> is strongly influenced by main group elements <i>Z</i>. When <i>Z</i> are in the same group, the Δ<i>E</i><sub>M</sub> increases with their atomic number increasing, but when <i>Z</i> are in the same period, an opposite trend is observed. The Δ<i>E</i><sub>M</sub> can be regarded as a driving force for the martensitic transformation: a larger Δ<i>E</i><sub>M</sub> corresponds to a higher martensitic transformation <i>T</i><sub>M</sub>. In Heusler alloys, electron concentration <i>e/a</i> and electron density <i>n</i> are usually used to discuss the variation of <i>T</i><sub>M</sub>. An increase of <i>e/a</i> or <i>n</i> tends to increase <i>T</i><sub>M</sub>. However, this is in discrepancy with the results in Ni<sub>2</sub>Cu<i>Z</i>, which can be explained by using, the new factors, the negative shear modulus <inline-formula><tex-math id="M2">\begin{document}$ C' $\end{document}</tex-math></inline-formula> and softening of the elastic constant <i>C</i><sub>44</sub> and their variations with <i>Z</i> elements. These results reveal the close relation between the martensitic transformation and mechanical parameters and indicate 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 and shear modulus increase and Poisson’s ratio decreases after the martensitic transformation. Thus, the Ni<sub>2</sub>Cu<i>Z</i> martensite has higher stiffness and rigidity but lower ductility than the austenite.</sec>