Pressure-Induced Anomalous Phase Transitions and Colossal Enhancement of Piezoelectricity in ${\mathrm{PbTiO}}_3$

We find an unexpected tetragonal-to-monoclinic-to-rhombohedral-to-cubic phase transition sequence induced by pressure, and a morphotropic phase boundary in a pure compound using first-principles calculations. Huge dielectric and piezoelectric coupling constants occur in the transition regions, comparable to those observed in the new complex single-crystal solid-solution piezoelectrics such as $\mathrm{Pb}({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_3\mathrm{\text{−}}{\mathrm{PbTiO}}_3$, which are expected to revolutionize electromechanical applications. Our results show that morphotropic phase boundaries and giant piezoelectric effects do not require intrinsic disorder, and open the possibility of studying this effect in simple systems.

Figure 1

Stability of various phases as a function of pressure. (a) Enthalpy difference with respect to the $C$ phase for the $T$ and $R$ phases. (b) Enthalpy difference with respect to the $T$ phase for the $R$ and $M$ phases. (c) Elastic constant $c_{44}$ and $c_{11}-c_{12}$, respectively, for the $T$ and $R$ phases, and square of the lowest optical phonon frequencies ${\omega }^2$ for the $T[E(1\mathrm{TO})$, $A_1(1\mathrm{TO})]$, $R[E(1\mathrm{TO})$, $A_1(1\mathrm{TO})]$, and $C[F_{1u}(1\mathrm{TO})]$ phases. (d) Dielectric susceptibility $\chi$.

Figure 2

Proposed ($P$, $T$) phase diagram. It combines theoretical results (solid circles) at 0 K with experimental data (solid squares) at finite temperatures. In this figure, we rescaled the theoretical pressure for the experimental volume to be zero by shifting. The open circles are our guess for these two tricritical points, and an ab initio molecular dynamics simulation is needed to predict them accurately.

Figure 3

Pressure dependence on piezoelectricity. (a) Spontaneous polarization ${\mathbf{P}}^{\mathrm{s}}$. (b) Piezoelectric stress coefficients $e_{15}$ and $e_{33}$. (c) Piezoelectric strain coefficients $d_{15}$ and $d_{33}$.