High-throughput screening of perovskite alloys for piezoelectric performance and thermodynamic stability

We screen a large chemical space of perovskite alloys for systems with optimal properties to accommodate a morphotropic phase boundary (MPB) in their composition-temperature phase diagram, a crucial feature for high piezoelectric performance. We start from alloy end points previously identified in a high-throughput computational search. An interpolation scheme is used to estimate the relative energies between different perovskite distortions for alloy compositions with a minimum of computational effort. Suggested alloys are further screened for thermodynamic stability. The screening identifies alloy systems already known to host an MPB and suggests a few others that may be promising candidates for future experiments. Our method of investigation may be extended to other perovskite systems, e.g., (oxy-)nitrides, and provides a useful methodology for any application of high-throughput screening of isovalent alloy systems.

Figure 1

(a) The ideal perovskite crystal structure and (b)–(d) the three main distortions considered in our prior [47] and present work. The ideal perovskite structure $AB{\mathrm{O}}_3$ has a 12-coordinated $A$-site cation (big, black) and 6-coordinated $B$-site cations (big, pale shaded/blue) embedded in octahedra (blue) defined by oxygens (small, dark/red). The distorted phases are (b) tetragonal (TET), (c) rhombohedral (RHO), and (d) rotations along the (1,1,1) direction (ROT). For illustrative purposes, the magnitude of the distortions are exaggerated compared to typical values. The figures were created using vesta [48].

Figure 2

Stability (upper graph) and energy preference for TET distortion (lower graph) in eV/atom for the two-component alloy ${\mathrm{PbTiO}}_3$-${\mathrm{PbZrO}}_3$ (PZT). The upper graph shows the energy difference between TET-distorted PZT at a specific alloy ratio and the most stable linear combination of any of the possible competing phases we are aware of. This graph agrees with PZT being possible to synthesize over the whole range (since it stays below $50\mathrm{meV}$/atom; see text), and the lower graph indicates that the alloy prefers TET distortion over a significant range of alloy ratios (i.e., the lower graph is $>$0). The two graphs thus corroborate PZT as highly relevant for piezoelectrics due to the alloy being both possible to synthesize and having a phase boundary between TET and another distortion. The comparably low stability of pure PZ and the somewhat misplaced crossover between the TET to RHO distortions from what is known for PZT is discussed in the text.

Figure 3

Stability (upper graph) and energy preference for TET distortion (lower graph) in eV/atom for two-component alloys related to the $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$-$\mathrm{Ba}\mathrm{Zr}{\mathrm{O}}_3$-$\mathrm{Ca}\mathrm{Ti}{\mathrm{O}}_3$ system. The diagram suggests that BaTiO₃-CaTiO₃ is, possibly, a stable alloy that prefers TET distortion, as was reported by Liu and Ren [20].

Figure 4

Stability (upper graph) and energy preference for TET distortion (lower graph) in eV/atom for the $(\mathrm{K},\mathrm{Na})(\mathrm{Nb},\mathrm{Ta}){\mathrm{O}}_3$ system.

Figure 5

Stability (upper graph) and energy preference for TET distortion (lower graph) in eV/atom for relevant alloys with Li with the components of the $(\mathrm{K},\mathrm{Na})(\mathrm{Nb},\mathrm{Ta}){\mathrm{O}}_3$ system. The system becomes less stable the more $\mathrm{Li}$ is added, but it also more strongly prefers the TET distortion.

Figure 6

Stability (upper graph) and energy preference for TET distortion (lower graph) in eV/atom for all two-component alloys that remain after our initial screening which involve $\mathrm{Pb}$ (except for PZT, which is shown in Fig. 2). While individual alloys are not clearly discernible in the figure, it shows the general trend of these alloys as having small hull distances and TET distortions. For details on individual alloys, see the Supplemental Material [66].

Figure 7

Stability (upper graph) and energy preference for TET distortion (lower graph) in eV/atom when $\mathrm{Cu}$ is introduced into various perovskites. Small to moderate amounts of $\mathrm{Cu}$ appear to make the alloys more strongly prefer the TET distortion, and there may be a region of such substitution into $\mathrm{K}(\mathrm{Nb},\mathrm{Ta}){\mathrm{O}}_3$ with alloys that possibly can be stable in synthesis.

Figure 8

Stability (upper graph) and energy preference for TET distortion (lower graph) in eV/atom for two-component alloys involving $\mathrm{Si}$. The $\mathrm{Si}$-based end points are generally unstable. While individual alloys are not clearly discernible in the figure, the upper graph shows a general trend of these end points to not mix well. For details on individual alloys, see the Supplemental Material [66].

Figure 9

Stability (upper graph) and energy preference for TET distortion (lower graph) in eV/atom for two-component alloys involving $\mathrm{Sn}$. The alloy ${(\mathrm{Ba}}_x{\mathrm{Sn}}_{1-x}){\mathrm{TiO}}_3$ (column 2, row 3 in the legend) stands out as a tetragonal alloy of promising stability, indicating that synthesis may be possible. However, ${\mathrm{Ba}(\mathrm{Sn}}_x{\mathrm{Ti}}_{1-x}){\mathrm{O}}_3$ (column 2, row 4 in the legend) is even more stable and will generally be a readily accessible competing phase in a synthesis attempt of the former alloy.

Figure 10

Stability (upper graph) and energy preference for TET distortion (lower graph) in eV/atom for two-component alloys involving $\mathrm{Bi}$.