The elastic properties of Mn3(Cu1−xGex)N compounds

We present an ab initio study of the elastic properties of the negative thermal expansion (NTE) compound Mn3(Cu1−xGex)N. The calculated energies show that the Ge atoms can be easily doped into the compound and, the distribution of the Ge atoms in the compound is very uniform. The elastic moduli of the compound in the form of polycrystalline are evaluated according to the Voigt-Reuss-Hill approximation, which show that the doped Ge enhances the ductile character of the compound, with fairly high elastic anisotropy. Furthermore, it is found that the bulk modulus and the Young's modulus of the compound increase as the Ge content increases from 12.5 % to 50 %, being in agreement with experiments. Through analyzing the electronic structures, we propose that these elastic features are essentially stemmed from the valence states and the valence electrons of the doped Ge.