An ab initio study of electronic, mechanical, and piezoelectric properties of the trigonal, tetragonal and cubic phases of lead-free perovskite SnBO3 (B = Ti, Zr, Hf)

Abstract

(P4mm) and cubic (Pm̅3̅m) phases of SnBO3 (B Ti, Zr, Hf) oxide perovskite compounds using various functionals namely GGA-PBE, PBE0, HSE06, and B3LYP. From formation energy calculation, trigonal symmetry has been found to be the most stable phase. In the structure optimization, B3LYP estimates the largest volume under trigonal and tetragonal symmetry. However, for the cubic system of SnBO3, SnTiO3 possess the largest volume when using PBE-GGA, while B3LYP estimates the largest in SnZrO3 and both PBE-GGA and B3LYP estimates the same magnitude in SnHfO3. When Ti atom is replaced with either Zr or Hf, a notable shift in the second oxygen atomic coordinate was observed in the tetragonal phase along the z-direction, which impacts the lattice parameters leading to an expansion along the a-axis but with contraction along the c-axis. Structural changes have been found to correspond with electronic transitions. While the electronic transition in SnTiO3 takes place along �→Γ, the transitions in both SnZrO3 and SnHfO3 occurs along �→Z in k space. In the cubic system, SnTiO3 showed an indirect X→Z transition, whereas SnZrO3 and SnHfO3 demonstrated a direct X→X transition. Density of states calculations have revealed that contribution from the B-site atom in the energy states around the conduction band edge is reduced as Ti atom is substituted with Zr atom and subsequently with Hf atom for all the crystal phases. Mechanical stability was consistent across all the compounds in all the calculations with various exchange-correlation functionals considered. Analysis of the mechanical parameters of the trigonal phase of SnBO3 has deduced that only SnTiO3 using hybrid functionals shows brittleness. While only SnHfO3 consistently exhibited a ductile nature throughout the functionals considered in the tetragonal phase, all compounds in the cubic phase were ductile. Interestingly, while the bulk modulus increased sequentially from Ti to Zr and then to Hf when B site atom is substituted in tetragonal structures, SnTiO3 emerged as the most robust system in the cubic phase. In the tetragonal system, when Ti atom in SnBO3 is replaced with either Zr or Hf, the piezoelectric response exhibits massive increase associated with the change in atomic position of the second oxygen atom along the c-axis and the response is also predicted to be highest in SnHfO3.