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We have presented ab initio study, based on density functional theory methods, of full-core edge dislocation impact on basic properties of 4H-SiC semiconductor. To enable calculations in periodic boundary conditions, we have proposed geometry with two dislocations with opposite Burgers vectors. For this geometry, which determines the distance between dislocations, we have estimated the creation energy per unit length of a single-edge dislocation. The radial distribution function has been used to assess the effect of the dislocations on the local crystal structure. The analysis of the electronic structure reveals mid-gap p states induced by broken atomic bonds in the dislocation core. The maps of charge distribution and electrostatic potential have been calculated, and the significant decrease in the electrostatic barriers in the vicinity of the dislocation cores has been quantified. The obtained results have been discussed in the light of previous findings and calculations based mainly on phenomenological models.

Using density functional theory, we study the lattice dynamical properties of magnetite (Fe$_3$O$_4$) in the high-temperature cubic and low-temperature monoclinic phases. The calculated phonon dispersion curves and phonon density of states are compared with the available experimental data obtained by inelastic neutron, inelastic x-ray, and nuclear inelastic scattering. We find a very good agreement between the theoretical and experimental results for the monoclinic $Cc$ structure revealing the strong coupling between charge-orbital (trimeron) order and specific phonon modes. For the cubic phase, clear discrepancies arise which, remarkably, can be understood assuming that the strong trimeron-phonon coupling can be extended above the Verwey transition, with lattice dynamics influenced by the short-range trimeron order instead of the average cubic structure. Our results establish the validity of trimerons (and trimeron-phonon coupling) in explaining the physics of magnetite much beyond their original formulation., Comment: 11 pages, 9 figures, 1 table

Physical review / B 102(19), 195414 (1-9) (2020). doi:10.1103/PhysRevB.102.195414, Self-organized silicide nanowires are considered as building blocks of future nanoelectronics and have been intensively investigated. In nanostructures, the lattice vibrational waves (phonons) deviate drastically from those in bulk crystals, which gives rise to anomalies in thermodynamic, elastic, electronic, and magnetic properties. Hence a thorough understanding of the physical properties of these materials requires a comprehensive investigation of the lattice dynamics as a function of the nanowire size. We performed a systematic lattice dynamics study of endotaxial FeSi$_2$ nanowires, forming the metastable, surface-stabilized $\alpha$ phase, which are in-plane embedded into the Si(110) surface. The average widths of the nanowires ranged from 24 to 3 nm, and their lengths ranged from several micrometers to about 100 nm. The Fe-partial phonon density of states, obtained by nuclear inelastic scattering, exhibits a broadening of the spectral features with decreasing nanowire width. The experimental data obtained along and across the nanowires unveiled a pronounced vibrational anisotropy that originates from the specific orientation of the tetragonal $\alpha$−FeSi$_2$ unit cell on the Si(110) surface. The results from first-principles calculations are fully consistent with the experimental observations and allow for a comprehensive understanding of the lattice dynamics of endotaxial silicide nanowires., Published by Inst., Woodbury, NY

The Verwey transition in magnetite (Fe$_3$O$_4$) is the first metal-insulator transition ever observed and involves a concomitant structural rearrangement and charge-orbital ordering. Due to the complex interplay of these intertwined degrees of freedom, a complete characterization of the low-temperature phase of magnetite and the mechanism driving the transition have long remained elusive. It was demonstrated in recent years that the fundamental building blocks of the charge-ordered structure are three-site small polarons called trimerons. However, electronic collective modes of this trimeron order have not been detected to date, and thus an understanding of the dynamics of the Verwey transition from an electronic point of view is still lacking. Here, we discover spectroscopic signatures of the low-energy electronic excitations of the trimeron network using terahertz light. By driving these modes coherently with an ultrashort laser pulse, we reveal their critical softening and hence demonstrate their direct involvement in the Verwey transition. These findings represent the first observation of soft modes in magnetite and shed new light on the cooperative mechanism at the origin of its exotic ground state., Comment: 20 pages, 18 figures

Here we employ a novel method for preparing the homogeneous copper pyrophosphate nanocrystals inside silica mesopores. In order to characterize and identify synthesized nanocrystals we performed theab initiostudies of theαphase of Cu2P2O7. The electronic and crystal structure were optimized within the density functional theory with the strong electron interactions in the3dstates on copper atoms and van der Waals corrections included in calculations. The relaxed lattice parameters and atomic positions agree very well with the results of the diffraction measurements for nanocrystalline copper pyrophosphates embedded inside SBA-15 silica pores. The obtained Mott insulating state with the energy gap of 3.17 eV exhibits the antiferromagnetic order with magnetic moments on copper atoms (0.8μB) that is compatible with the experimental studies. The phonon dispersion relations were obtained to study the dynamical properties of the Cu2P2O7lattice and the element-specific atomic vibrations were analyzed using the partial phonon density of states. The calculated Raman spectrum revealed the consistency of typical bands of Cu2P2O7with the experimental data. The investigation that combines a new synthesis of nanomaterials with the first-principles calculations is important for better characterization and understanding of the physical properties relevant for nanotechnological applications.

The structure and dynamical properties of the ${\mathrm{Fe}}_{3}\mathrm{Si}/\mathrm{GaAs}(001)$ interface are investigated by density functional theory and nuclear inelastic scattering measurements. The stability of four different atomic configurations of the ${\mathrm{Fe}}_{3}\mathrm{Si}/\mathrm{GaAs}$ multilayers is analyzed by calculating the formation energies and phonon dispersion curves. The differences in charge density, magnetization, and electronic density of states between the configurations are examined. Our calculations unveil that magnetic moments of the Fe atoms tend to align in a plane parallel to the interface, along the [110] direction of the ${\mathrm{Fe}}_{3}\mathrm{Si}$ crystallographic unit cell. In some configurations, the spin polarization of interface layers is larger than that of bulk ${\mathrm{Fe}}_{3}\mathrm{Si}$. The effect of the interface on element-specific and layer-resolved phonon density of states is discussed. The Fe-partial phonon density of states measured for the ${\mathrm{Fe}}_{3}\mathrm{Si}$ layer thickness of three monolayers is compared with theoretical results obtained for each interface atomic configuration. The best agreement is found for one of the configurations with a mixed Fe-Si interface layer, which reproduces the anomalous enhancement of the phonon density of states below 10 meV.

The structure, magnetic properties, and lattice dynamics of ordered Fe–Pt alloys with three stoichiometric compositions, Fe 3 Pt, FePt and FePt 3 , have been investigated using the density functional theory. Additionally, the existing experimental data have been complemented by new measurements of the Fe projected phonon density of states performed for the Fe 3 Pt and FePt 3 thin films using the nuclear inelastic scattering technique. The calculated phonon dispersion relations and phonon density of states have been compared with the experimental data. The dispersion curves are very well reproduced by the calculations, although, the softening of the transversal acoustic mode TA 1 leads to some discrepancy between the theory and experiment in Fe 3 Pt. A very good agreement between the measured spectra and calculations performed for the tetragonal structure derived from the soft mode may signal that the tetragonal phase with the space group P 4/ mbm plays an important role in the martensitic transformation observed in Fe 3 Pt. For FePt 3 , the antiferromagnetic order appearing with decreasing temperature has been also investigated. The studies showed that the phonon density of states of FePt 3 very weakly depends on the magnetic configuration.

A method to compute anharmonic phonon peaks and anharmonic phonon-dispersion curves in crystals using ab initio calculated Hellmann-Feynman forces created from series of supercells is reported. The supercells are filled with atoms displaced from equilibrium positions in such a way that their configurations correspond to a given temperature. The obtained phonon-dispersion bands are able to represent the positions and shapes of the anharmonic peaks. As illustrations, the anharmonicity in cubic tungsten W, perovskite ${\mathrm{MgSiO}}_{3}$, and superconductor ${\text{MgB}}_{2}$ crystals is presented. The method can be applied to search for anharmonic potential-energy landscape of crystals. It includes electron-phonon coupling.

Physical review / B covering condensed matter and materials physics 98(12), 121409 (2018). doi:10.1103/PhysRevB.98.121409, We report a systematic lattice dynamics study of the technologically important Fe$_3$Si/GaAs heterostructure for Fe$_3$Si layer thicknesses of 3, 6, 8, and 36 monolayers. The Fe-partial phonon density of states obtained by nuclear inelastic scattering exhibits up to a twofold enhancement of the low-energy phonon states compared to the bulk material for layer thicknesses of 8 monolayers and below. First-principles calculations explain the observed effect by interface-specific phonon states originating from the significantly reduced atomic force constants and allow for achieving a comprehensive understanding of the lattice dynamics of epitaxial strain-free interfaces., Published by APS, Woodbury, NY

The structural and dynamical properties of FePt nanoparticles were studied within the density functional theory. The effect of size and chemical composition on dynamical stability of nanoparticles was investigated for the cuboctahedral and icosahedral symmetries. In cuboctahedra, the structural distortion is observed, which for systems with odd number of Pt layers leads to lowering of the tetragonal symmetry. Significant differences between the vibrational properties of FePt particles and bulk crystal is observed, but similarly to the FePt crystal, cuboctahedral particles exhibit a strong anisotropy of atomic vibrations. The icosahedral particles with perfect shell geometry are unstable due to enlarged distances between Fe atoms. They can be stabilized by removing a central atom or replacing it by a smaller one. The heat capacity and entropy of nanoparticles show typical enhancement due to low-energy vibrations at the surface layers., Comment: 10 pages, 14 figures, 2 tables, accepted in Phys. Rev. B

Symmetry breaking across phase transitions often causes changes in selection rules and emergence of optical modes which can be detected via spectroscopic techniques or generated coherently in pump-probe experiments. In second-order or weakly first-order transitions, fluctuations of the ordering field are present above the ordering temperature, giving rise to intriguing precursor phenomena, such as critical opalescence. Here, we demonstrate that in magnetite $({\mathrm{Fe}}_{3}{\mathrm{O}}_{4})$ light excitation couples to the critical fluctuations of the charge order and coherently generates structural modes of the ordered phase above the critical temperature of the Verwey transition. Our findings are obtained by detecting coherent oscillations of the optical constants through ultrafast broadband spectroscopy and analyzing their dependence on temperature. To unveil the coupling between the structural modes and the electronic excitations, at the origin of the Verwey transition, we combine our results from pump-probe experiments with spontaneous Raman scattering data and theoretical calculations of both the phonon dispersion curves and the optical constants. Our methodology represents an effective tool to study the real-time dynamics of critical fluctuations across phase transitions.

We report a systematic lattice dynamics study of EuSi_{2} films and nanoislands by in situ nuclear inelastic scattering on ^{151}Eu and ab initio theory. The Eu-partial phonon density of states of the nanoislands exhibits anomalous excess of phonon states at low and high energies, not present in the bulk and at the EuSi_{2}(001) surface. We demonstrate that atomic vibrations along the island-substrate interface give rise to phonon states both at low and high energies, while atomic vibrations across the island-island interface result in localized high-energy phonon modes.

The phonon dispersion curves of the unconventional superconductor PuCoGa 5 were studied by inelastic X-ray scattering at room temperature. The experimental data agree well with ab initio lattice dynamics calculations. An accurate theoretical description of the phonon spectrum is obtained only when a local Coulomb repulsion U ≈ 3 eV among 5f electrons is taken into account. This implies partial localization of the 5f electrons in this compound. A comparison made with the phonon spectrum of UCoGa 5 suggests that the latter compound is better described with a fully itinerant f electrons model.

Comprehensive studies of lattice dynamics in the ferromagnetic semiconductor EuO have been performed by a combination of inelastic x-ray scattering, nuclear inelastic scattering, and ab initio calculations. A remarkably large broadening of the transverse acoustic phonons was discovered at temperatures above and below the Curie temperature ${T}_{C}=69\text{ }\text{ }\mathrm{K}$. This result indicates a surprisingly strong momentum-dependent spin-phonon coupling induced by the spin dynamics in EuO.

The structural and magnetic properties of ultrathin FeO(111) films on Pt(111) with thicknesses from 1 to 16 monolayers (ML) were studied using the nuclear inelastic scattering (NIS) of synchrotron radiation. Distinct evolution of vibrational characteristics with thickness that is revealed in the phonon density of states (PDOS) witnesses a textbook transition from 2D to 3D lattice dynamics. For the thinnest films of 1 and 2 ML, the low energy part of the PDOS followed a linear dependence in energy that is characteristic for 2-dimensional systems. This dependence gradually transforms with thickness to the bulk ~E-square relation. Density functional theory phonon calculations perfectly reproduced the measured 1 ML PDOS within a simple model of a pseudomorphic FeO/Pt(111) interface. The calculations show that the 2D PDOS character is due to a weak coupling of the FeO film to the Pt(111) substrate. The evolution of the vibrational properties with an increasing thickness is closely related to a transient long range magnetic order and stabilization of an unusual structural phase.

The influence of intrinsic Fe defects in FeO (either single cation vacancies or prototypical 4:1 vacancy clusters) on the electronic and dielectric properties is studied within the density functional theory. The importance of local Coulomb interactions at Fe atoms is highlighted and shown to be responsible for the observed insulating Mott gap in FeO which is reduced by the presence of defects. We investigate nonstoichiometric configurations of Fe1-xO with x ranging from 3 to 9 % and find the aliovalent Fe cations in both the regular and interstitial lattice sites of the considered configurations. Furthermore, we show that the trivalent Fe ions are induced by both isolated and clustered Fe-vacancies and introduce the empty band states inside the insulating gap, which decreases monotonically with increasing cation vacancy concentration. The Fe1-xO systems with high defect content become metallic for small values of the Coulomb interaction U, yielding the increase in the dielectric functions and optical reflectivity at low energies in agreement with the experimental data. Due to the crystal defects, the infrared-active transverse optic phonons split and distribute over a wide range of frequencies clarifying the origin of the exceptionally large spectral linewidths of the dielectric loss functions observed for wustite in recent experiments., Comment: 11 page, 8 figures

The formation and site preference energies and volume changes of single and pair of defects of ternary alloying elements in γ-TiAl intermetallic compound were studied by the density functional theory. Slight tendency to clusterization of antisite defects has been found. This may lead to disorder in the system. The V and Cr atoms prefer to reside in the Ti sublattice. The formation energy for Cr–Cr, Cr–V and V–V nearest neighbour pairs are in the 1.3–2 eV range. The Al antisite in Ti sublattice requires much less energy than the Ti antisite in Al sublattice. The amorphisation process of TiAl alloy was studied by means of high energy ball milling of Ti and Al elemental powders, which produces amorphous structure after 40 h. The amorphous states were studied by the DFT calculations of many random atomic configurations and the results were compared with the NiAl compound. Possible explanation for the amorphisation of the TiAl compound is presented.

The vibrational spectrum for the type-III Si-clathrate Ba24Si100 has been computed from first principles electronic structure method. It is shown that the Ba vibrations are strongly hybridized with the host lattice in the cages formed by coordinately unsaturated Si. The electron-phonon coupling spectral function calculated from zone center phonons indicates that electron-phonon interaction is stronger for low-frequency Ba vibrations in the loosely enclathrated cages than those in the more tightly fitted cages. A similar trend was also observed in the related Ba8Si46 and Ba6Na2Si46 systems. The results show that low-frequency rattling vibrations of the Ba atoms are very efficient in mediating electron-phonon coupling in the superconductivity behaviour of these novel materials.

Using the first-principles computations we have calculated phonon-dispersion relations and the phonon density of states for perovskite and post-perovskite phases of MgSiO3. From them using the quasiharmonic approximation we have estimated the free energies, bulk modulus and volume expansion coefficients of both structures at various pressures and temperatures. Our calculations indicate that the thermal expansivity of MgSiO3 changes very little across the phase transition. We have determined the P–T coexisting line of perovskite and post-perovskite phases.

A complete elastic tensor of the low-pressure structure of the magnesium orthosilicate (Mg 2 SiO 4 , forsterite) is determined by an ab initio technique for the pressure range P =0–240 kB. The geologically important quantities: density, sound velocity, Young's modulus, Poisson's ratio, crystal anisotropy, are derived from the calculated data. A systematic increase of crystal's anisotropy with pressure has been noticed. The results agree well with the available experimental data.

The stability of SrBi2Ta2O9 has been studied by means of ab-initio calculations. The main instability of the tetragonal configuration concerns a non-polar mode at the Brillouin zone border. It can be related through Brillouin zone folding to the well-known soft rigid-unit mode R25 in perovskites. This implies a complex scenario for the whole Aurivillius family with two competing order parameters, which can result in a sequence of two continuous phase transitions or a single discontinuous one. A third hard-mode is shown to play an essential role in the stabilization of the ferroelectric phase.

A critical review of the experimental data of elastic stiffness constants of AgGaX2 and CuInX2 (X=S,Se) chalcopyrites is given. Using the ab initio pseudopotential method, their elastic constants have been calculated from strain–energy and from strain–stress relationships. On the basis of the linear elasticity approximation, axial and total compressibilities as well as elastic anisotropy factors have been derived. The calculated results are compared with available experimental data and previous calculations based on phenomenological models.

The formation and preference site energies and volume changes of single defects and pairs of defects of ternary alloying elements in NiAl intermetallic compound were studied by the density functional theory. Exceptionally, a small formation energy of Co defect in Ni sublattice was found. The Co, Cr, Fe atoms and vacancies prefer to reside in the Ni sublattice. The formation energy for Co–Co nearest neighbor pair is the smallest. The Ni antisite in Al sublattice requires less energy than the Al antisite in Ni sublattice.

First-principles density-functional approach was used to obtain the crystal parameters and phonon spectra of γ-Mg2SiO4 (spinel and ringwoodite) as functions of pressure. The Gruneisen parameters at the Γ point were obtained and compared with the experimental data. Using quasiharmonic approximation, the total free energy of the crystal was calculated as a function of volume for several temperatures, hence, the bulk modulus and thermal expansion were found as a function of temperature. A good agreement between calculated and experimental values was obtained in a wide temperature range.

The first principles plane-wave pseudopotential calculations based on density functional theory were used to determine structural and electronic properties of CuInS2 semiconducting chalcopyrite. The Born effective charges were obtained using Berry phase method. Phonon dispersion relations were evaluated from Hellmann–Feynman forces with the direct method. The elastic constants were derived from the stress–strain relationships. The calculated quantities agree well with available experimental data.

Inelastic neutron scattering experiments on powder samples of GeTe together with density functional theory investigations of the phonon dynamics in the low- and high-temperature phases of GeTe crystal are reported. The dispersion of phonons in the high-temperature rocksalt phase show soft branches with the lowest one at the $\ensuremath{\Gamma}$ high-symmetry point. The structural phase transition in GeTe is reconsidered and shown to be driven by the con-densation of exactly three components of the triply degenerate optical transverse soft-phonon mode at the Brillouin zone center. The mechanism proposed allows us to explain the formation of structural distortions in the low-temperature ferroelectric phase of GeTe revealed by various experiments. A displacive nature of the phase change in crystalline GeTe is supported by the results of the present theoretical studies.

The lattice dynamics of the antiferromagnetic FeBO3 crystal has been calculated by ab initio density-functional theory and measured by nuclear inelastic absorption spectroscopy. The calculations for the antiferromagnetic phase reproduce the experimental lattice parameters of the unit cell and provide phonon dispersion relations which agree well with the measured partial density of phonon states for the Fe atoms. Calculations for the nonmagnetic configuration lead to a smaller crystal volume and drastically higher phonon frequencies for the Fe atoms.

Total energy calculations within the density functional theory (DFT), generalized gradient approximation and ultrasoft pseudopotentials have been used to investigate structural, dynamical and thermodynamical properties of the high-pressure structure of the magnesium orthosilicate (Mg 2 SiO 4 , γ-spinel, ringwoodite). The phonon dispersion curves and phonon density of states have been calculated using the direct method. The results show agreement with the available experimental Raman data.

Using the local-density approximation, calculating the Hellmann-Feynman forces, applying the direct method and deriving the phonon dispersion relations, the stability of the perovskite-like structures of MgSiO3 at T =0 have been studied. The cubic Pm $$Pm\overline 3 m$$ m phase shows a dispersion-less soft phonon branch spreading from the R to M points of the cubic Brillouin zone. This soft branch persists up to high pressures of 150 GPa. The low-symmetry phases I4/mcm and Imma, P4/mbm can be considered as a result of the soft mode condensation at the M and R points, respectively. These phases prove to be unstable at T =0. The experimentally observed Pmnb phase is a consequence of the intersection of Imma and P4/mbm space groups. Thus, it can be regarded as a simultaneous condensation of two soft modes: one at the M and a second at the R high-symmetry points of the cubic Brillouin zone. The phonon dispersion relations of Pmnb show that this phase is stable and its optical phonons appear above 4.0 THz only.

Complementary to our previous study [Wang et al., Phys. Rev. B $59,$ 12 672 (1999)], the intrinsic stability of the magic ${\mathrm{Fe}}_{13}{\mathrm{O}}_{8}$ cluster is confirmed by the calculations on the vibrational properties. For all the vibration modes, the frequency is positive, and therefore the structure is dynamically stable. ${A}_{1g},$ ${B}_{1g},$ and ${B}_{2g}$ modes are Raman active, ${A}_{2g},$ ${A}_{2u},$ and ${E}_{u}$ modes are infrared active, while the ${E}_{g}$ mode is active both in Raman and in infrared spectroscopy. The intrinsic stability combined with the relative stability make this cluster to be magic.

Using the local-density approximation, calculating the Hellmann-Feynman forces and applying the direct method, the phonon dispersion relations for the rutile-like structure of crystalline SnO2 have been derived for the first time. The phonon frequencies at the \(\) point agree very well with Raman and infrared data and other phenomenological model calculations. The LO/TO splitting is estimated by calculating phonons from an elongated supercell. The computations under pressure reveal a soft mode of B1g symmetry which leads to a ferroelastic phase transition. The pressure-dependence of the lattice constants and the Gruneisen parameters of the modes are calculated.

Using the ab initio method within the local-density approximation with ultrasoft pseudopotentials and plane-wave basis, calculating the Hellmann-Feynman forces and applying the direct method, the phonon-dispersion relations for ferroelectric and paraelectric rhombohedral phases of ${\mathrm{LiNbO}}_{3}$ crystal have been derived. The calculated phonon frequencies for the ferroelectric phase at the $\ensuremath{\Gamma}$ point are compared with Raman, infrared, and neutron-scattering measurements, and they agree very well. The phonon frequencies at the Z, L, and F high-symmetry points are also calculated. It is disclosed that the force constants involving lithium ions are an order of magnitude smaller than the force constants between niobium and oxygen ions. As a consequence, the lithium ions do not contribute to high-frequency optical vibrations. In the paraelectric phase the phonon-dispersion curves show a soft branch with the soft mode of symmetry ${A}_{2u}$ at the $\ensuremath{\Gamma}$ point. This soft mode leads to the observed paraelectric-ferroelectric phase transition. The LO/TO splitting is considered by assuming formal values of ionic charges, and by fitting the longitudinal infrared active modes to the experimental data.

The ab initio method within the local-density approximation is applied to calculate the Hellmann–Feynman forces for the cubic and elongated supercells of the polar MgO crystal. From these forces, using the direct method, the phonon dispersion relations and the phonon density of states are derived. The LO/TO splitting was extracted from phonon frequencies found within the elongated supercell.

Phonon dispersion relations for the hexagonal wurtzite phase of 2H-GaN are estimated using the local-density approximation with ultrasoft pseudopotentials and plane-wave basis, calculating the Hellmann-Feynman forces and applying the direct method. Ab initio calculations are performed on the rhombohedral supercell, which lowers the crystal space group. We propose a method to restore the proper symmetry. The calculated phonon frequencies at the $\ensuremath{\Gamma}$ point are compared with Raman and infrared measurements, phenomenological models and other ab initio calculations, and a very good agreement is obtained. Phonon frequencies at high-symmetry zone-boundary points and phonon density of states are deduced as well.

We present different approaches to computer simulations of the order-disorder phase transition in thiocyanate crystals. In these systems the order parameter is coupled to the strain by coupling of the type ŋ2e. This coupling plays the dominant role in the behavior of the system below T c. Molecular Dynamics and Monte Carlo techniques give the proper temperature dependence of the order parameter and the behavior of the fluctuations similar to that observed experimentally. The ab initio calculations allow us to render properly the structural properties of crystals like KSCN and additionally can become the basis for more realistic phenomenological models.

We have calculated the phonon dispersion and phonon density of states of superlattices of Ga1−xAlxAs for x=0.0, 0.25, 0.75 and 1.0 using the ab initio method within the supercell approach and calculating the Hellmann–Feynman forces. A noticeable difference of force constants between Ga–As and Al–As atomic pairs has been found. In any case, Al atoms vibrate in well-separated high-frequency optic modes.

We outline the procedure and approximations used to study the structural phase transition. The standard ab initio programs provide the Hellmann-Feynman forces, which allow, by the direct method, to describe the dispersion curves including the soft mode. The values of the anharmonic terms of the order parameter and order parameter-strain coupling terms, found from symmetry analysis, can be calculated within the ab initio total energy approach, by carring on the calculations for a variety of atom configurations. The method is used to describe the cubic-tetragonal phase transition in SrTiO3, for which a soft mode and anharmonic coefficients have been found.

A procedure to study structural phase transitions by calculating the data from an ab initio program is outlined. In particular, the soft mode can be found directly from the Hellman-Feynman force. The anharmonic part of the potential energy is inferred by tracing the total energy surface as a function of the order parameter.

A model of lanthanum orthoniobate which possesses a ferroelastic tetragonal-monoclinic phase transition is proposed. It contains only one particle per unit cell, but it is constructed consistently with symmetry changes at the phase transition. The model parameters are chosen to reproduce the bare soft mode, degree of deformation of the tetragonal unit cell to monoclinic one, and the phase transition temperature. The ferroelastic system with free boundary conditions was simulated by the molecular dynamics technique, and the second order phase transition was reproduced. The studied annealing process shows formation of the stripe lenticular domain pattern, which has been interrupted by appearance of a temporary band of perpendicularly oriented lenticular domains. The maps contain W{sup {prime}}-type domain walls whose orientations are fixed only by interplay of potential parameters and not by symmetry elements. The simulated domain pattern has the same features as those observed by transmission electron microscopy. {copyright} {ital 1997 Materials Research Society.}

A direct approach to calculate the phonon dispersion using an ab initio force constant method is introduced. The phonon dispersion and structural instability of cubic ${\mathrm{ZrO}}_{2}$ are found using a supercell method in the local-density approximation. The force constants are determined from the Hellmann-Feynman forces induced by the displacement of an atom in the $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2$ fcc supercell. This size of the supercell gives ``exact'' phonon frequencies at $\ensuremath{\gamma},X,L,W$ Brillouin zone points. The phonon dispersion curves show a pronounced soft mode at the $X$ point, in agreement with the experimentally observed cubic to tetragonal phase transition.

Silver halide crystals are of considerable interest, since they exhibit deviation from the ideal ionic character due to the presence of the d electrons in Ag 1 ions. Numerous studies of these crystals have been undertaken in the past years using various forms of interaction potentials including threebody interactions and van der Waals forces, 1,2 as well as the ab initio total energy pseudopotential calculations. 3 There are also many experimental works studying various aspects of these solids. 4‐1 3 The results of studies using phenomenological potentials generally show good agreement with experiment. 2 These studies use sophisticated schemes involving three body interactions and van der Waals potentials. The ab initio results for transition pressure seems to be less accurate. 3 There is one ab initio study of phase stability of silver bromide AgBr. 14 Nevertheless, the transition mechanism is still unclear for this compound. Several models have been proposed, 5‐7,14 ‐17 but the transition mechanism remains still an open problem. The ab initio study by Nunes, Allen, and Martins, 14 which investigated the energy of several can

Ab initio calculations and a direct method have been applied to derive the phonon dispersion curves and phonon density of states for the TiC crystal. The results are compared and found to be in a good agreement with the experimental neutron scattering data. The force constants have been determined from the Hellmann-Feynman forces induced by atomic displacements in the 2x2x2 supercell. The calculated phonon density of states suggests that vibrations of Ti atoms form acoustic branches, whereas the motion of C atoms is confined to optic branches. The elastic constants have been found using the deformation method and compared with the results obtained from acoustic phonon slopes.

Ab initio calculations and a direct method are applied to derive the phonon dispersion relations and phonon density of states for the ZrC crystal. The results are in good agreement with neutron scattering data. The force constants are determined from the Hellmann-Feynman forces induced by atomic displacements in a 2 2 2 supercell. The elastic constants are found using the deformation method and successfully compare with experimental data.

We report pronounced modifications of electronic and vibrational properties induced in FeO by cation vacancies, obtained within density functional theory incorporating strong local Coulomb interactions at Fe atoms. The insulating gap of FeO is reduced by about 50% due to unoccupied electronic bands introduced by trivalent Fe ions stabilized by cation vacancies. The changes in the electronic structure along with atomic displacements induced by cation vacancies affect strongly phonon dispersions via modified force constants, including those at atoms beyond nearest neighbors of defects. We demonstrate that theoretical phonon dispersions and their densities of states reproduce the results of inelastic neutron and nuclear resonant x-ray scattering experiments \emph{only} when Fe vacancies and Coulomb interaction $U$ are both included explicitly in \emph{ab initio} simulations, which also suggests that the electron-phonon coupling in FeO is strong., 5 pages, 4 figures