Ab initio study of $A{\mathrm{BiO}}_3$ ($A=\mathrm{Ba}$, Sr, Ca) under high pressure

Using ab initio crystal structure prediction we study the high-pressure phase diagram of $A{\mathrm{BiO}}_3$ bismuthates ($A=\mathrm{Ba}$, Sr, Ca) in a pressure range up to 100 GPa. All compounds show a transition from the low-pressure perovskite structure to highly distorted, low-symmetry phases at high pressures (PD transition), and remain charge-disproportionated and insulating up to the highest pressure studied. The PD transition at high pressures in bismuthates can be understood as a combined effect of steric arguments and of the strong tendency of bismuth to charge-disproportionation. In fact, distorted structures permit to achieve a very efficient atomic packing, and at the same time, to have Bi-O bonds of different lengths. The shift of the PD transition to higher pressures with increasing cation size within the $A{\mathrm{BiO}}_3$ series can be explained in terms of chemical pressure.

Figure 1

Phase diagram of the structural phase transitions in $A{\mathrm{BiO}}_3$ compounds. Each transition is labeled by a symbol which represents the rank of the structure in the sequence of transitions: filled circle for Structure I, square for Structure II, diamond for Structure III, and pentagon for Structure IV. “Dark-gray” (“blue”) region contains perovskite-like ($P$) structures, “light-gray” (“red”) distorted ($D$) structures, and “stroked” (“green”) nonperovskite (NP) structures. The thick dashed line indicates the transition line for the perovskite-to-distorted transition (PD transition) estimated from chemical pressure considerations, as explained in Sec. 3.

Figure 2

Structures of $A{\mathrm{BiO}}_3$ compounds used in this work: (a) nonperovskite ${\mathrm{CaBiO}}_3$, (b) perovskite ${\mathrm{SrBiO}}_3$, (c) ${\mathrm{BaBiO}}_3$, and distorted (d) ${\mathrm{CaBiO}}_3$, (e) ${\mathrm{SrBiO}}_3$, and (f) ${\mathrm{BaBiO}}_3$. $A$ cations (Ba, Sr, Ca) are shown as light-gray (light-green) spheres, Bi – gray (purple) spheres inside dark-gray (purple) polyhedron, O – small gray (red) spheres.

Figure 3

Total and atom-projected DOS for $A{\mathrm{BiO}}_3$ compounds before and after the PD transition: 22 GPa for ${\mathrm{CaBiO}}_3$, 25 GPa for ${\mathrm{SrBiO}}_3$, and 45 GPa for ${\mathrm{BaBiO}}_3$, calculated with the HSE functional; the structures were optimized at the PBE level. Bi atoms are divided into formal ${\mathrm{Bi}}^{3+}$ and ${\mathrm{Bi}}^5+$ valences. For the sake of clarity the Bi-DOS is multiplied by a factor of 15.

Figure 4

Band gaps for the most stable structures of $A{\mathrm{BiO}}_3$ compounds as a function of pressure [33]. Each symbol represents a specific structure, as defined in the caption of Fig. 1; the filling indicates whether the structure is perovskite-like (filled symbol) or distorted (empty symbol). Lines are meant as a guide to the eye.

Figure 5

Difference between maximum and minimum charge ($\mathrm{\Delta }\rho$) located on bismuth atoms w.r.t pressure, obtained using Bader analysis. Note that the Bader charge analysis yields sensibly higher values than the estimate based on the partial DOS estimate used in our previous paper [12]. The meaning of the symbols is the same as in Fig. 4.

Figure 6

Average number of Bi nearest neighbors as a function of pressure. The meaning of the symbols is the same as in Fig. 4.

Figure 7

Average BiO bond length as a function of pressure. The meaning of the symbols is the same as in Fig. 4.

Figure 8

Equation of state for $A{\mathrm{BiO}}_3$ compounds in the ideal cubic perovskite structure, used as a model to estimate the shift of the PD transition line due to the chemical pressure, showed by dashed lines in Fig. 1. The PD transition at 22 GPa for ${\mathrm{CaBiO}}_3$ is taken as a reference point to estimate a common volume for the transition (see text). Lines are meant as a guide for the eye.