Ab Initio Perturbed Ion Calculations Research Articles

Spinodal equation of state for rutileTiO2

We present a general computational scheme to extend the spinodal equation of state [Garcia Baonza et al., Phys. Rev. B 51, 28 (1995)] to the interpretation of the cell parameters response to hydrostatic pressure in orthogonal lattices. As an important example, we analyze the pressure (formula presented)–volume (formula presented)–temperature (T) data of the rutile phase of (formula presented) We show that results of ab initio perturbed ion calculations and very recent x-ray-diffraction experiments of isothermal compression on this system closely follow the spinodal conduct. The computational scheme permits the incorporation of temperature effects in the static calculation as well as in the room-temperature experimental data. Overall, we find highly consistent results and good theory-experiment agreement for a significant series of observables, including structural parameters, (formula presented) diagram, bulk modulus, linear compressibilities, and thermal-expansion coefficient. The observed discrepancies in the pressure first derivative of the bulk modulus can be traced back to the difference between the theoretical and the experimental spinodal pressure. © 2003 The American Physical Society.

The cohesive energetics of solid cesium chloride

The cohesive energetics of the sixfold and eightfold coordinated phases of solid cubic cesium chloride are studied using a nonempirical fully ionic description. The Oxford Dirac–Fock program is used to compute the ion wave functions and rearrangement energies needed to convert a free anion into the compressed yet still spherically symmetric anions optimally adapted to crystal. The Relativistic Integrals Program (RIP) is used to compute uncorrelated two-body interionic interaction potentials which take full account of relativity and are exact for given ion wave functions. These potentials and the further contributions arising from electron correlation are reported. The OEMFS model for describing the environment of the anion in-crystal yields lattice energies and equilibrium interionic separations in good agreement with experiment and correctly predicts the eight-fold coordinated structure to lie lowest in energy. The “optimal” anion–anion short-range potentials, computed by using at each geometry the wave function optimal for that geometry, are compared with the “frozen” potential in which the same anion wave function is used to compute the entire potential. The “frozen” anion–anion potential in solid sodium chloride is reported. The basic idea in the ab initio perturbed ion (AIPI) method, that the wave functions of anions in-crystal remain spherically symmetric yet as strongly orthogonal as possible to those of neighboring ions, cannot be justified. It differs from the standard view in the RIP computations that an ion wave function only remains spherically symmetric whilst overlapping with those of neighboring ions, such overlaps generating the short-range interionic repulsions. The RIP predictions of crystal cohesive energetics are preferable to those of the AIPI method. The correlation energy used in AIPI calculations is theoretically objectionable for crystals and is numerically poor. For CsCl, the anion wave function, rearrangement energy, and closest cation–anion repulsion optimal for the 8:8 structure at each geometry are all essentially identical to their counterparts in the 6:6 phase. The different coordination numbers in the two phases render unequal the effective cation–anion interactions given as the sum of the true cation–anion potentials and a fraction of the rearrangement energy. This inequality removes RIP computations from that class of theories which fail to predict the correct energy ordering of the phases through using the same effective potential in both structures.

An ab Initio Study of the Structures and Relative Stabilities of Doubly Charged [(NaCl)m(Na)2]2+ Cluster Ions

We present ab initio perturbed ion calculations on the structures and relative stabilities of doubly charged [(NaCl)m(Na)2]2+ cluster ions. The obtained stabilities show excellent agreement with ex...

Theoretical characterization of the high-pressure phases ofPbF2

Ab initio perturbed ion calculations were performed for the cubic, orthorhombic, hexagonal, and monoclinic phases of ${\mathrm{PbF}}_{2}.$ A complete characterization of these phases was achieved in terms of the potential energy surfaces, the equations of state, and the phase-transition pressures. Thermal effects were included via a quasiharmonic nonempirical Debye model. The internal parameters of the unit cell of each phase were reoptimized at each volume to generate the energy surface. The calculated results are in good agreement with the experimental data available for the cubic and orthorhombic phases. The results predict the hexagonal phase to be the high-pressure post-cotunnite structure for ${\mathrm{PbF}}_{2},$ since the monoclinic phase is seen to collapse into the hexagonal phase during the optimization at high pressures.

Experimental and theoretical study on the piezoelectric behavior of barium doped PZT

An experimental and theoretical study of the ferroelectric and piezoelectric behavior of PZT doped with barium is presented. Ab initio perturbed ion calculations was carried out. The properties, such as remnant polarization, coercive field and the coupling factor of the PZT at constant sintering temperature was compared with the Zr4+/Ti4+ ions dislocation energy and the lattice interaction energy. An agreement between the experimental and theoretical results, with a decrease of the interaction energy and an inversion of the energy stability from tetragonal to rhombohedral phase was observed.

Quantum-Mechanical Study of Thermodynamic and Bonding Properties of MgF2

The structural and thermodynamic properties of MgF2 have been investigated in a wide range of pressures (0−80 GPa) and temperatures (0−850 K) by coupling quantum-mechanical ab initio perturbed ion calculations with a quasi-harmonic Debye model. The room temperature, zero-pressure structural parameters and lattice energy are computed with errors smaller than 2% when correlation energy corrections are incorporated in the calculation. Our computed equation of state is compatible with direct measurements of the bulk modulus and obeys universal p−V relations. We have simulated the rutile-to-fluorite phase transition during the loading process and have found lower (≃4 GPa) and upper (≃45 GPa) bounds for the transition pressure by means of thermodynamic and mechanical criteria for phase stability. Bonding properties and their change with pressure have been derived through a topological analysis of the electron density using Bader's theory of atoms in molecules. This analysis reveals that MgF2 is a highly ionic compound. Its ionicity decreases linearly with increasing pressure and, as in other ionic compounds, the crystal shows anion−anion bonds.

Piezoelectric behaviour of PZT doped with calcium: a combined experimental and theoretical study

An experimental and theoretical study on the piezoelectric behaviour of PZT doped with a range of calcium ion concentrations is presented. A systematic study of the effect on the piezoelectric properties of PZT doped with various concentrations of CaO at constant sintering temperature and sintering time was carried out. The remanent polarization, planar coupling factor and frequency–thickness constant increase with calcium concentration. Ab initio perturbed ion calculations show that the lattice energy decreases with calcium addition for both tetragonal and rhombohedral phases of PZT.

An ab initio perturbed ion study of structural properties of TiO2, SnO2 and GeO2 rutile lattices

This work describes a theoretical quantum mechanical study on TiO 2 , SnO 2 and GeO 2 rutile structures in order to characterize the geometric, mechanical, thermodynamic and electronic properties of these systems. The doping processes of V 4+ at the sixfold-coordinated site have been studied with the aim of determining the relative stability of pure and doped structures. Ab initio perturbed ion calculations with Slater-type orbitals for representing atomic centers and large cluster models have been used. Local geometry optimizations have been performed to determine the lattice energy, lattice parameters and bulk modulus, as well as the force constant and vibrational frequencies ( v ) of the breathing vibrational modes, a 1g , in the sixfold-coordinated site. Numerical results are analyzed and compared with experimental data, the geometrical distances obtained by computer simulation being in agreement with the reported experimental values. The difference in energy for the substitution of Ti 4+ , Sn 4+ and Ge 4+ for V 4+ in TiO 2 , SnO 2 and GeO 2 , respectively is very dependent on the method used to represent these doping processes. The TiO 2 , SnO 2 lattices show a decrease in the v value from the pure to the doped structure while a opposite trend is obtained for the GeO 2 structure. The validity of the methodology is discussed.

Theoretical study of the coordination of the Cr3+ ion in α-Al2O3

Abstract The local arrangement of a substitutional Cr3+ ion for an Al3+ ion in corundum is studied by means of first-principles pairwise simulations and quantum-mechanical ab initio Perturbed Ion calculations. Our investigation is organized in two steps. First, we determine the cohesive properties of the host lattice by calculating the set of four crystalline parameters that makes minimum the total energy of corundum. Secondly, we solve cluster models of increasing complexity centered at the Cr3+ site and embedded in the previously computed crystal potential. This is a consistent strategy that contributes to determine the local geometry of Cr3+ in α-Al2O3.

The High-Pressure Phase of Zincite

Synchrotron-radiation X-ray diffraction studies of ZnO have been performed with special emphasis on the rock-salt-type high-pressure phase. The wurtzite (B4) to rock salt (B1) phase transformation is accompanied by a volume collapse of 18%, which is a very large effect. The lattice constant of the B1 phase at ambient pressure is a(0) = 4.280 (4) A, and the bulk modulus is B(0) = 170 (10) GPa. Comparisons are made with a recently published theoretical equation of state obtained from ab initio perturbed-ion calculations.

Low- and high-pressure ab initio equations of state for the alkali chlorides.

We have carried out ab initio perturbed ion calculations in the rocksalt (B1) and cesium chloride (B2) phases of the alkali (A) chloride (ACl) crystals. Zero temperature (T), and pressure (P) lattice energies and equilibrium distances are computed with errors less than 5%. From static calculations, zero-T equations of state (EOS) are reported in the ranges 0\char21{}80 GPa for LiCl, 0\char21{}60 GPa for NaCl and KCl, 0\char21{}10 GPa for RbCl, and 0\char21{}5 GPa for CsCl. The experimental data enable us to perform a critical test of the performance of a theoretical methodology; we place particular emphasis on (a) the comparison between calculated and experimental trends and (b) the consistency with the behavior observed in real materials. We have found that our theoretically modeled solids obey the Vinet universal EOS and match the experimental behavior in temperature-scaled EOS diagrams. We have also analyzed the phase stability of the ACl crystals from a thermodynamic point of view. The hydrostatic pressure necessary to produce the B1-B2 phase transition is calculated to decrease with the cation size, in agreement with the experimental observation. Our predicted value of the (not yet measured) B1-B2 transition pressure for LiCl is close to 80 GPa. Finally, our calculations based on the combined kinetic-thermodynamic model proposed by Li and Jeanloz for the NaCl transition phase [Phys. Rev. B 36, 474 (1987)] predict that the hysteresis pressure range of the B1-B2 transition decreases from LiCl to RbCl.

Quantum-mechanical modeling of the high-pressure state equations of ZnO and ZnS.

Equations of state (EOS) for the high-pressure phases of ZnO and ZnS have been determined by carrying out ab initio perturbed-ion calculations. The results are used to examine different empirical EOS formalisms proposed for experimental P-V data. The generalized Vinet EOS is shown to be highly sensitive to the uncertainties in experimental data, thus providing a poor extrapolation for the properties at zero pressure. Contrarily, the modified Birch-Murnaghan EOS predicts zero-pressure properties that agree with ab initio calculations.