First Principles Theories of Piezoelectric Materials

Piezoelectrics have long been studied using parameterized models fit to experimental data, starting with the work of Devonshire in 1954. Much has been learned using such approaches, but they can also miss major phenomena if the materials properties are not well under-stood, as is exemplified by the realization that low-symmetry monoclinic phases are common around morphotropic phase boundaries, which was missed completed by low-order Devonshire models, and can only appear in higher order models. In the last 15 years, a new approach has developed using first-principles computations, based on fundamental physics, with no essential experimental input other than the desired chemistry (nuclear charges). First-principles theory laid the framework for a basic understanding of the origins of ferroelectric behavior and piezoelectric properties. The range of properties accessible to theory continues to expand as does the accuracy of the predictions. We are moving towards the ability to design materials of desired properties computationally. Here some of the fundamental developments of our understanding of piezoelectric material behavior and ability to predict a wide range of properties using theoretical methods are reviewed

Prediction of a new potential high-pressure structure of FeSiO3_3

We predict a new candidate high-temperature high-pressure structure of FeSiO$_3$ with space-group symmetry Cmmm by applying an evolutionary algorithm within DFT+U that we call post-perovskite II (PPv-II). An exhaustive search found no other competitive candidate structures with ABO$_3$ composition. We compared the X-ray diffraction (XRD) pattern of FeSiO$_3$ PPv-II with experimental results of the recently reported H-phase of (Fe,Mg)SiO$_3$. The intensities and positions of two main X-ray diffraction peaks of PPv-II FeSiO$_3$ compare well with those of the H-phase. We also calculated the static equation of state, the enthalpy and the bulk modulus of the PPv-II phase and compared it with those of perovskite (Pv) and post-perovskite (PPv) phases of FeSiO$_3$. According to the static DFT+U computations the PPv-II phase of FeSiO$_3$ is less stable than Pv and PPv phases under lower mantle pressure conditions at 0 K and has a higher volume. PPv-II may be entropically stabilized, and may be a stable phase in Earth$'$s lower mantle, coexisting with $\alpha$-PbO$_2$ (Columbite-structured) silica and perovskite, or with magnesiowustite or ferropericlase, depending on bulk composition

Thermal effects on lattice strain in hcp Fe under pressure

We compute the c/a lattice strain versus temperature for nonmagnetic hcp iron at high pressures using both first-principles linear response quasiharmonic calculations based on the full potential linear-muffin-tin-orbital (LMTO) method and the particle-in-cell (PIC) model for the vibrational partition function using a tight-binding total-energy method. The tight-binding model shows excellent agreement with the all-electron LMTO method. When hcp structure is stable, the calculated geometric mean frequency and Helmholtz free energy of hcp Fe from PIC and linear response lattice dynamics agree very well, as does the axial ratio as a function of temperature and pressure. On-site anharmonicity proves to be small up to the melting temperature, and PIC gives a good estimate of its sign and magnitude. At low pressures, hcp Fe becomes dynamically unstable at large c/a ratios, and the PIC model might fail where the structure approaches lattice instability. The PIC approximation describes well the vibrational behavior away from the instability, and thus is a reasonable approach to compute high temperature properties of materials. Our results show significant differences from earlier PIC studies, which gave much larger axial ratio increases with increasing temperature, or reported large differences between PIC and lattice dynamics results.Comment: 9 figure

Low-pressure phase diagram of crystalline benzene from quantum Monte Carlo

We study the low-pressure (0 to 10 GPa) phase diagram of crystalline benzene using quantum Monte Carlo (QMC) and density functional theory (DFT) methods. We consider the $Pbca$, $P4_32_12$, and $P2_1/c$ structures as the best candidates for phase I and phase II. We perform diffusion quantum Monte Carlo (DMC) calculations to obtain accurate static phase diagrams as benchmarks for modern van der Waals density functionals. We use density functional perturbation theory to compute phonon contribution in the free-energy calculations. Our DFT enthalpy-pressure phase diagram indicates that the $Pbca$ and $P2_1/c$ structures are the most stable phases within the studied pressure range. The DMC Gibbs free-energy calculations predict that the room temperature $Pbca$ to $P2_1/c$ phase transition occurs at 2.1(1) GPa. This prediction is consistent with available experimental results at room temperature. Our DMC calculations show an estimate of 50.6$\pm$0.5 kJ/mol for crystalline benzene lattice energy

Chemical accuracy from quantum Monte Carlo for the Benzene Dimer

We report an accurate study of interactions between Benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory (DFT) using different van der Waals (vdW) functionals. In our QMC calculations, we use accurate correlated trial wave functions including three-body Jastrow factors, and backflow transformations. We consider two benzene molecules in the parallel displaced (PD) geometry, and find that by highly optimizing the wave function and introducing more dynamical correlation into the wave function, we compute the weak chemical binding energy between aromatic rings accurately. We find optimal VMC and DMC binding energies of -2.3(4) and -2.7(3) kcal/mol, respectively. The best estimate of the CCSD(T)/CBS limit is -2.65(2) kcal/mol [E. Miliordos et al, J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate that QMC methods give chemical accuracy for weakly bound van der Waals molecular interactions, comparable to results from the best quantum chemistry methods.Comment: Accepted for publication in the Journal of Chemical Physics, Vol. 143, Issue 11, 201