Elasticity of SrTiO₃ perovskite under high pressure in cubic, tetragonal and orthorhombic phases

Abstract

We investigated the athermal high-pressure behavior of the elastic properties of SrTiO3 (STO) up to 26 GPa in cubic, tetragonal and orthorhombic phases using the ab initio pseudo-potential method. Our results for the cubic phase are in good agreement with experiment and previous pseudo-potential calculations. There are no studies for the tetragonal and orthorhombic phases under high pressure available for comparison. To date, there are no global data on elastic parameters under high pressure for STO. We establish data when we report the results of our structural and elastic study under high pressure in the three phases. Our calculations show that the cubic–tetragonal phase transition occurs at 6 GPa and the tetragonal–orthorhombic phase transition at 14 GPa. A third and unknown phase transition from orthorhombic Cmcm to monoclinic P21 /m was observed at 24 GPa, but no study has explored it. The orthorhombic phase is unstable and this instability may be due to ferroelectricity at high pressure. The elastic properties of STO are also strongly pressure dependent with instabilities near the phase transition pressure. STO is more resistant to plastic deformation and to fracture in the cubic phase than in the tetragonal and orthorhombic phases.

High‐throughput first‐principle calculations of the structural, mechanical, and electronic properties of cubic XTiO3 (X = Ca, Sr, Ba, Pb) ceramics under high pressure

“… is the equilibrium lattice constants, and is the primitive cell volumes of XTiO 3 crystal structures under the equilibrium ground state ( P = 0 and T = 0). By comparing the lattice constants , we obtain the fairly consistent results compared with the other theoretical and experimental data, as listed in Table .…”

“…Through adequate structural optimization, the fitting results in Figure 2 indicate that when the total energies of crystal structures reach equilibrium states, various the equilibrium ground state (P = 0 and T = 0). By comparing the lattice constants a 0− XTiO3 , we obtain the fairly consistent results compared with the other theoretical [26,29,34,[44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60] and experimental data, [61][62][63][64][65][66] as listed in Table 1.…”

“…In the process of investigating the structural stability of cubic crystals, the three elastic constants C 11 , C 12 , and C 44 are used to evaluate the capability to resist external forces. In accordance with the stability criterion of cubic crystals, [67,68] the crystal structures of cubic XTiO 3 (X = Ca, Sr, Ba, Pb) ceramics remain stable only if the following formulas are all satisfied: [29] 3.890, [34] 3.890, [44] 3.895 [61] 3.880, [45] 3.851, [46] 3.859 [47] SrTiO 3 3.947 3.940, [26] 3.930, [45] 3.850, [48] 3.901, [62] 3.910 [63] 3.920, [49] 3.905, [50] 3.912 [51] BaTiO 3 4.065 4.030, [26] 4.004, [52] 4.048, [53] 3.996 [64] 3.988, [54] 4.036, [55] 3.935 [56] PbTiO 3 3.962 3.960, [26] 3.983, [52] 3.970, [57] 3.970, [65] 3.969 [66] 3.887, [58] 3.980, [59] 3.883 [60] C 11 − C 12 ð Þ > 0,C 11 > 0,C 44 > 0,…”

“…Through comparison, the results of this work fit well with the other data. [26,34,44,47,49,55,[69][70][71][72][73] As the lattice constants from CaTiO 3 to BaTiO 3 increase at P = 0, the value of the bulk modulus decreases (Table 2), which implies that the resistance to bulk deformation is the weakest for BaTiO 3 compared with CaTiO 3 and SrTiO 3 ceramics. The results fit well with those in Figure 3.…”

“…However, the C 11 value decreases with the increase in atomic radius of X (X = Ca, Sr, Ba) atoms when comparing the results in Figure 4A-C. The C 11 value of [34] C 12 (GPa) 109.07 93.27 [34] C 44 (GPa) 98.47 94.47 [34] B (GPa) 198.00 176.20, [34] 185.20 [47] 171.00 [44] E (GPa) 281.02 263.80 [34] G (GPa) 111.21 105.50 [34] σ 0.26 0.25 [34] SrTiO 3 (cubic structure) C 11 (GPa) 359.34 319.30, [26] 366.10 [49] 317.20 [69] C 12 (GPa) 111.60 97.50, [26] 91.39 [49] 102.50 [69] C 44 (GPa) 115.32 113.00, [26] 102.20 [49] 122.35 [69] B (GPa) 194.18 171.00, [26] 182.96 [49] 174.00 [69] E (GPa) 295.76 285.36 [49] G (GPa) 118.67 115.06 [49] σ 0.25 0.24 [49] BaTiO 3 (cubic structure) C 11 (GPa) 300.42 310.40, [26] 300.70 [26] 173.00 [70] C 12 (GPa) 117.16 107.20, [26] 134.60 [26] 82.00 [70] C 44 (GPa) 122.80 139.80, [26] 173.40 [26] 108.00 [70] B (GPa) 178.25 175.00, [26] 166.00 [55] 139.40 [71] E (GPa) 272.07…”