Dependence of elastic stiffness on electronic band structure of nanolaminateM2AlC(M=Ti,V,Nb, andCr) ceramics

Abstract

We investigate the elastic stiffness and electronic band structure of nanolaminate ${M}_{2}\mathrm{AlC}$ ($M=\mathrm{Ti},\mathrm{V},\mathrm{Nb}$, and $\mathrm{Cr}$) ceramics by using the ab initio pseudopotential total energy method. The relationship between elastic stiffness and valence electron concentration (VEC) is discussed. The results show that the bulk and shear moduli enhance monotonously as VEC increases in ${M}_{2}\mathrm{AlC}$. The shear modulus ${c}_{44}$, which by itself represents a pure shear shape change and is directly related to hardness, reaches its maximum when the VEC is in the range of $8.4--8.6$. This implies that the bulk modulus, shear modulus, and hardness vary in different trends when the VEC changes in ${M}_{2}\mathrm{AlC}$. Furthermore, trends in the elastic stiffness are well explained in terms of electronic band structure analysis, e.g., occupation of valence electrons in states near the Fermi level of ${M}_{2}\mathrm{AlC}$. We show that increments of bulk and shear moduli originate from additional valence electrons filling states involving $Md\text{\ensuremath{-}}\mathrm{Al}p$ covalent bonding and metal-to-metal ${t}_{2g}$ and ${e}_{g}$ orbitals. For the case of ${c}_{44}$, strengthening the $M\ensuremath{-}\mathrm{Al}$ $pd$ covalent bonds effectively enhances the shear resistance and excessive occupation of $dd$ orbitals gives rise to a negative contribution. The maximum of ${c}_{44}$ is attributed to the complete filling of the $Md\text{\ensuremath{-}}\mathrm{Al}p$ bonding states.