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Piezoelectric materials, which convert mechanical to electrical energy (and vice versa), are crucial in medical imaging, telecommunication and ultrasonic devices. A new generation of single-crystal materials, such as Pb(Zn1/3Nb2/3)O3-PbTiO3 (PZN-PT) and Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT), exhibit a piezoelectric effect that is ten times larger than conventional ceramics, and may revolutionize these applications. However, the mechanism underlying the ultrahigh performance of these new materials-and consequently the possibilities for further improvements-are not at present clear. Here we report a first-principles study of the ferroelectric perovskite, BaTiO3, which is similar to single-crystal PZN-PT but is a simpler system to analyse. We show that a large piezoelectric response can be driven by polarization rotation induced by an external electric field. Our computations suggest how to design materials with better performance, and may stimulate further interest in the fundamental theory of dielectric systems in finite electric fields.

We present a new nonempirical density functional generalized gradient approximation (GGA) that gives significant improvements for lattice constants, crystal structures, and metal surface energies over the most popular Perdew-Burke-Ernzerhof (PBE) GGA. The new functional is based on a diffuse radial cutoff for the exchange-hole in real space, and the analytic gradient expansion of the exchange energy for small gradients. There are no adjustable parameters, the constraining conditions of PBE are maintained, and the functional is easily implemented in existing codes. PACS numbers: 71.15.Mb, 71.45.Gm, Kohn-Sham density functional theory (DFT) [1,2] makes it possible to solve many-electron ground-state problems efficiently and accurately. The DFT is exact if the exchange-correlation (XC) energy E XC were known exactly, but there is no tractable exact expressions of E XC in terms of electron density. Numerous attempts have been made to approximate E XC , starting with the local (spin) density (LSD) approximation (LDA), which is still widely used. The generalized gradient approximations (GGAs) [3,4,5] are semilocal, seeking to improve upon LSD. Other more complicated approximations are often orbital-dependent or/and nonlocal. They suffer from computational inefficiency; it is much harder to treat them self-consistently and to calculate energy derivative quantities.The XC energy of LSD and GGAs areandrespectively. Here the electron density n = n ↑ + n ↓ , and ǫ unif XC is the XC energy density for the uniform electron gas. LSD is the simplest approximation, constructed from uniform electron gas, and very successful for solids, where the valence electron densities vary relatively more slowly than in molecules and atoms, for which GGAs [5, 6] achieved a great improvement over LSD. It is well known that LSD underestimates the equilibrium lattice constant a 0 by 1-3%, and some properties such as ferroelectricity are extremely sensitive to volume. When calculated at the LSD volume, the ferroelectric instability is severely underestimated [7,8,9]. On the other hand, GGAs tend to expand lattice constants. They well predict correct a 0 for simple metals, such as Na and K [6], however for other materials they often overcorrect LSD by predicting a 0 1-2% bigger [10] than experiment. Predicting lattice constants more accurately than LSD remains a tough issue, even for state-of-the-art meta-GGAs; nonempirical TPSS [11] only achieves moderate TABLE I: Calculated equilibrium volume V0 (Å 3 ) and strain (%) of tetragonal PbTiO3 for various GGAs comparing with experimental data at low temperature [24]. PW91 PBE revPBE RPBE Expt. V0 70.78 70.54 74.01 75.47 63.09 strain 24.2 23.9 28.6 30.1 7.1 improvement over PBE, while empirical PKZB [12] is worse than PBE. GGAs are especially poor for ferroelectrics, e.g., PBE [5] predicts the volume and strain of relaxed tetragonal PbTiO 3 more than 10% and 200% too large, respectively [13], and other GGAs [ 4,14,15] are even worse, as seen in Table I. Another more complicated functional, the nonlocal...

A piezoelectric material is one that generates a voltage in response to a mechanical strain (and vice versa). The most useful piezoelectric materials display a transition region in their composition phase diagrams, known as a morphotropic phase boundary, where the crystal structure changes abruptly and the electromechanical properties are maximal. As a result, modern piezoelectric materials for technological applications are usually complex, engineered, solid solutions, which complicates their manufacture as well as introducing complexity in the study of the microscopic origins of their properties. Here we show that even a pure compound, in this case lead titanate, can display a morphotropic phase boundary under pressure. The results are consistent with first-principles theoretical predictions, but show a richer phase diagram than anticipated; moreover, the predicted electromechanical coupling at the transition is larger than any known. Our results show that the high electromechanical coupling in solid solutions with lead titanate is due to tuning of the high-pressure morphotropic phase boundary in pure lead titanate to ambient pressure. We also find that complex microstructures or compositions are not necessary to obtain strong piezoelectricity. This opens the door to the possible discovery of high-performance, pure-compound electromechanical materials, which could greatly decrease costs and expand the utility of piezoelectric materials.