Interionic potentials and force constant models for rocksalt structure crystals—II

A lattice dynamical model for rocksalt structure crystals is presented in which the interionic force constants are taken to be central and the departure from the Cauchy relations is accounted for by isotropic and anisotropic deformations of the anions. The model is applied to NaBr, NaI and KBr for which C₁₂ > C₄₄ and it is appropriate to consider only the anisotropic deformations. The model parameters are determined entirely from macroscopic data. By assuming an exponential form for the repulsive part of the interionic potential the cohesive energy of the crystals may be determined from the interionic force constants. The cohesive energies are in surprisingly good agreement with experiment although the potential parameters differ considerably from those of other workers. While the dispersion curves obtained from the model are in markedly worse agreement with experiment than those from the standard breathing shell model it is shown that the potentials(in addition to giving good cohesive energies) result in a reasonably consistent dynamical model.     

Lattice dynamics and ionic charge of VI2

We present an Extended Shell Model calculation of the phonon dispersion curves in VI₂. The dynamical matrix is derived from interionic potentials including Coulomb monopole and dipole, van der Waals, nearest-neighbor and next-nearest-neighbor Born-Mayer repulsive interactions. The potential parameters are either known in literature or derived from lattice constants and cohesive energy. A suitable choice of only three adjustable parameters (net charge Z, shell charge and shell-core displacement) yields an excellent fit of the five optical frequencies and of the anion static dipole. The resulting ionic charge Z = 0.75 is very well consistent with the recent neutron data on transferred hyperfine interaction.     

Third-order elastic constants for 2:2 chalcide crystals possessing the sodium chloride structure

Third-order elastic constants of 45 chalcide crystals having the sodium chloride structure are reported using Born-Mayer potential model. We have considered repulsive interaction up to second nearest neighbours. The temperature coefficients of the third-order elastic constants have also been computed for these crystals. As is the case for NaCl-type alkali halides we find that C₁₁₁, C₁₁₂, C₁₆₆ are negative and C₁₄₄ are positive for 2:2 chalcide crystals possessing the NaCl-type structure. We have found that a₁₂₃, a₄₅₆ and a₁₄₄ are negative whereas a₁₁₂ and a₁₆₆ are positive, once again in agreement with the situation found for the alkali halides a₁₁₁ values are positive for alkali halides whereas they are both positive and negative depending upon the interionic distance for the chalcide crystals. We have found that the nature of the variation of C⁰_αβγ with interionic separation is similar for alkali halides and for the 2:2 chalcides having the NaCl-structure. We have also computed the values of the pressure derivatives of second-order elastic constants for MgO, CaO, and SrO which agree well with the experimental values indicating the satisfactory nature of our computed data for C_αβγ.     

金红石结构TiO2晶体点缺陷形成能的经验途径计算

基于经验参数化途径,通过对晶体结构、晶格形成能、介电性质和弹性实验数据拟合确定金红石结构氧化物晶体TiO₂的电子壳模型参数和非Coulomb互作用势参数.计算点 缺陷形成能.论证Schottky缺陷是金红石结构TiO₂中的本征缺陷. 关键词： 2')" href="#">金红石TiO₂ 点缺陷形成能 电子壳模型 经验途径计算     

Structural stability of alkaline earth oxide crystals

Using recemtly developed interionic potentials we have studied the structural stability problem of MgO, CaO, SrO and BaO crystals. The observed crystal structure for the alkaline earth oxides viz. NaCl structure is found to be stable only when Lundqvist's three body potential is taken into account along with Madelung's potential, overlap repulsive potential and van der Waals potentials.     

The influence of covalency on anion-anion interionic potentials in NiO

Hartree-Fock self-consistent field cluster calculations were performed to investigate the short-range anion-anion interionic potential V₂₂ in NiO. The cluster consisted of two oxygen ions and ten surrounding Ni ions embedded in a matrix of point charges; the Ni²⁺ ions were represented by pseudopotentials. V₂₂ was extracted from calculations of the total cluster electronic energy as a function of the OO separation when one of the O ions is displaced from its lattice site towards the other O ion. The results indicate that covalency is mainly responsible for the anomalously large attractive terms in semiempirically derived OO interionic potentials.     

Study of static and thermophysical properties of alkaline earth fluoride crystals

An analysis for cohesive energy, bulk modulus and its pressure derivatives in BaF₂, SrF₂ and CaF₂ crystals has been carried out by means of interionic potential model. Interionic potential consist of long range coulomb and three-body interactions along with short-range attractive van der Waals and repulsive Hafemeister-Zarht type interactions. The three body force parameter $\text{?(r)}$ and vdWI coefficients C and D are determined using the Cochran's formula and Slater-Kirkwood variational (SKV) integrals. The calculated values of cohesive energy, bulk modulus and its pressure derivatives for solids under study are found generally in good agreement with available experimental data. The results achieved by other investigations [13, 14] have also been compared with results calculated in the present study.     

Molecular dynamics simulation of P-V-T relationship of ZnO with rock-salt structure using pair-wise interactions

Molecular dynamics (MD) method is used to investigate the behavior of the pressure-volume-temperature (P-V-T) relationship, lattice constant and thermal expansivity for ZnO with rock-salt structure at high pressures and temperatures. The interionic potential is taken to be the sum of pair-wise additive Coulomb, van der Waals attraction, and repulsive interactions. The isothermal and isobaric properties are discussed from the corresponding P-V-T relationship, and it is shown that the MD simulation is successful in reproducing the measured volumes of ZnO over a wide range of temperature and pressure. Meanwhile, the equations of state parameters including lattice constant, linear thermal expansion coefficient, and isothermal bulk modulus are calculated and compared with the available experimental data and the latest theoretical results. At an extended pressure and temperature range, P-V-T relationship, lattice constant, and linear thermal expansion coefficient have been predicted. The structural and thermodynamic properties of ZnO with rock-salt structure are summarized in the pressure 0-100 GPa ranges and the temperature up to 3100 K.     

Lattice mechanical properties of alkaline earth metals in bcc and fcc phases

A model pseudopotential depending on an effective core radius treated as a parameter is used for alkaline earth metals in bcc and fcc phases to study the Binding energy, Interatomic interactions, phonon dispersion curves, Phonon density of states, Debye-Waller factor, mean square displacement, Debye-Waller temperature parameters, dynamical elastic constants (C₁₁, C₁₂ and C₄₄), bulk modulus (B), shear modulus (C′), deviation from Cauchy relation (C₁₂−C₄₄), Poisson's ratio (σ), Young's modulus (Y), behavior of phonon frequencies in the elastic limit independent of the direction (Y₁), limiting value in the [1 1 0] direction (Y₂), degree of elastic anisotropy (A) and propagation velocities of the elastic waves. The contribution of s-like electrons is incorporated through the second-order perturbation theory due to model potential. The theoretical results are compared with the existing experimental data. A good agreement between theoretical investigations and experimental findings has confirmed the ability of our potential to yield large numbers of lattice mechanical properties of certain alkaline earth metals.     

Construction of a dynamical matrix for an HCP crystal using phonon data at the symmetry points of the Brillouin zone and elastic constants

General analytical expressions are obtained for the dynamical matrix D(k) and the elastic constants C _ik in an HCP crystal in terms of the Born-von Karman (BvK) parameters. An analytical method is proposed for constructing D(k) on the basis of data about the phonon frequencies ω _i (N) at the symmetry points of the Brillouin zone and the elastic constants C _ik . A number of relations between the values of ω _i (N) and C _ik are presented for conventional interaction models. It is shown that the standard method for determining BvK parameters by fitting them to experimental phonon spectra in HCP lattices is, as a rule, ambiguous, whereas the analytical method proposed allows one to find all the solutions of the problem. The methods developed are illustrated by the construction of dynamical matrices for Tb, Sc, Ti, and Co.     

Decay constants of pseudoscalar and vector mesons with improved holographic wavefunction

We calculate the decay constants of light and heavy-light pseudoscalar and vector mesons with improved soft-wall holographic wavefuntions,which take into account the effects of both quark masses and dynamical spins.We find that the predicted decay constants,especially for the ratio f V/f P,based on light-front holographic QCD,can be significantly improved,once the dynamical spin effects are taken into account by introducing the helicity-dependent wavefunctions.We also perform detailed χ~2 analyses for the holographic parameters(i.e.the mass-scale parameterκ and the quark masses),by confronting our predictions with the data for the charged-meson decay constants and the meson spectra.The fitted values for these parameters are generally in agreement with those obtained by fitting to the Regge trajectories.At the same time,most of our results for the decay constants and their ratios agree with the data as well as the predictions based on lattice QCD and QCD sum rule approaches,with only a few exceptions observed.     

Zn-Mg合金的长程Finnis-Sinclair势

通过拟合Mg的晶格能、晶格常数、弹性常数,并将其与前人的结果相比较后获得了描述Mg的最优长程Finnis-Sinclair(F-S)势函数参数,使用同样方法并引入修正因子后得到了Zn的长程F-S势参数.基于单质Zn,Mg的F-S势参数,进一步拟合合金Mg₂₁Zn₂₅,MgZn₂,Mg₂Zn₁₁的晶格常数、晶格能获得Zn-Mg原子对的F-S势参数,构建了整套描述Zn-Mg合金的长程F-S势参数.在此 关键词： 长程Finnis-Sinclair势 Zn-Mg合金 分子动力学模拟     

Static and vibrational properties of equiatomic Na-based binary alloys

The computations of the static and vibrational properties of four equiatomic Na-based binary alloys viz. Na_0.5Li_0.5, Na_0.5K_0.5, Na_0.5Rb_0.5 and Na_0.5Cs_0.5, to second order in local model potential is discussed in terms of real-space sum of Born von Karman central force constants. The local field correlation functions due to Hartree (H), Ichimaru-Utsumi (IU) and Sarkar et al. (S) are used to investigate the influence of the screening effects on the aforesaid properties. Results for the lattice constants C₁₁, C₁₂, C₄₄, C₁₂-C₄₄, C₁₂/C₄₄ and bulk modulus B obtained using the H-local field correction function have higher values in comparison with the results obtained for the same properties using IU- and S-local field correction functions. The results for the Shear modulus (C′), deviation from Cauchy's relation, Poisson's ratio σ, Young modulus Y, propagation velocity of elastic waves, phonon dispersion curves and degree of anisotropy A are highly appreciable for the four equiatomic Na-based binary alloys.     

Bulk properties of C76 and C84 fullerites studied by MD simulation based on a central two body intermolecular potential

Molecular dynamics simulations based on the Girifalco central two-body potential are performed in order to study bulk properties of solid C₇₆ and C₈₄. The fullerene cages are modelled as rigid sphere whose ‘effective’ diameter is first determined in such a way that NVT–NPT simulations of the model fullerite reproduce the experimental lattice constant at ambient pressure and at various temperatures. It turns out that the diameter so fixed depends only slightly on the temperature. A unique molecular size, yielding the fit of the lattice constant at a conveniently chosen temperature, is then adopted throughout the whole temperature ranges investigated; the lattice constants, and the internal potential energy of C₇₆ and C₈₄ thereby calculated at various T, turn out to be in qualitative agreement with the available experimental data. The equation of state at ambient temperature is then also calculated. Results for C₇₆ compare favorably with experiment only at low pressures; by converse, results for C₈₄ turn out to be qualitatively or semi-quantitatively accurate up to 9 GPa. Other possible applications of the model are discussed.     

The structure and properties of the stepped surfaces of MgO and NiO

The static lattice computer simulation method has been used to study the structure and properties of high index faces of MgO and NiO. The (10_n) series of faces can be considered as stepped (001) surfaces and have been studied for both materials. In addition, the (403) and (302) faces which can be considered as stepped (101) surfaces have been studied for NiO. The calculated energies for steps on the (001) face are 3.72×10^?10 and 3.62×10^?10 J m^?1 for MgO and NiO respectively. The NiO energy also requires correction for the crystal field splitting. The energy of steps on the (101) surface is at least an order of magnitude lower. The interaction between the steps is repulsive but of short range. The large variation of surface energy with angle indicates that torque terms cannot be neglected in the analysis of thermal grooving experiments. The step structure is modified by substantial ionic displacements leading to an obtuse step angle. The structure is qualitatively similar for both NiO and MgO. The large distortions are likely to modify the step properties from those deduced by consideration of only the ideal geometry.     

High-temperature expansion for the Coulomb lattice

It is shown that the high-temperature expansion for the Coulomb lattice is Tr exp{−βH} = αβ^−3/2[1 − C₁β + C₂β² − C₃β^5/2 + O(β³logβ)]. C₁ and C₂ are the usual Korteweg-de Vries constants of motion. C₃ reflects the local singularity of the Coulomb potential and is absent for smooth periodic fields. C₃ turns out to be independent of the details of the potential.     

A15—A structure stabilized by crystal field distortion of “exotic” elements at chain sites

The repulsive component of a classical inverse power pair potential is modified to take into account the crystal field induced change in shape of the electron density distribution responsible for the repulsive interaction of a chain sited atom in the A15 structure with neighboring atoms. Minimization of the lattice energy with respect to this shape parameter and also with respect to the lattice parameter results in predictions in the absence of adjustable parameters of: (1) the lattice parameters (to within an RMS deviation of the observed values of 0.4%); (2) the nearly zero value for $\text{(C}{}_{11}\text{? C}{}_{12}\text{)}\text{2}$ (as observed for Nb₃Sn and V₃Si); (3) the correct ordering of relative stability for 98 out of 101 observed comparisons between 4 different crystal structures; (4) other effects which have been or can be observed. Implicit in the predictions is the assumption that the crystal field induced shape change encounters no intraatomic resistance for elements belonging to the Ti, V and Cr columns of the periodic table—denoted “exotic” elements. Some consequences of this assumption are found to be consistent with experiment.     

金红石结构TiO2晶体点缺陷形成能的经验途径计算

基于经验参数化途径 ,通过对晶体结构、晶格形成能、介电性质和弹性实验数据拟合确定金红石结构氧化物晶体TiO2 的电子壳模型参数和非Coulomb互作用势参数 .计算点缺陷形成能 .论证Schottky缺陷是金红石结构TiO2中的本征缺陷 .     

Structural,mechanical and thermal properties of some Holmium Pnictides under pressure: A theoretical approach

The high pressure structural, elastic and thermal properties of holmium pnictides HoX (X=N, P, As and Bi) were investigated theoretically by using an inter-ionic potential theory with modified ionic charge parameter. We have predicted a structural phase transition from NaCl (B₁) to CsCl (B₂)-type structure at pressure of 139 GPa for HoN, 52 GPa for HoP, 44 GPa for HoAs and 26 GPa for HoBi. Other properties, such as lattice constant, bulk modulus, cohesive energy, second and third-order elastic constants were calculated and compared with the available experimental and theoretical data. In order to gain further information the brittle behaviour of these compounds was observed. Some other properties like Shear modulus (G), Young's modulus (E), Poisson's ratio (ν), anisotropy factor (A), sound velocities, Debye temperature (θ_D) were calculated. The variation of elastic constants (C₁₁ and C₄₄) and Debye temperature (θ_D) with pressure was also presented.     

Defect modes due to substitutional impurities in FCC lattice: Green's function approach

Lattice dynamical study of monoatomic fcc crystals containing substitutional impurities has been made by the Green's function technique, using group theory. The impurity and its 12 nearest neighbors constitute an XY₁₂ impurity space having O_h symmetry. The phonon Green function matrix is analyzed according to the irreducible representations of the point group pertaining to the substitutional impurity in the fcc lattice. The effects due to change in mass at the impurity site and the change in nearest neighbor force constants for the impurity-host atom interactions are taken into account. Analytical expressions for the various modes of vibrations pertaining to the defect space have been obtained. Local mode frequencies due to various substitutional impurities, corresponding to F_1u mode (defect atom moving) have been computed. A special model is chosen for the defecthost force and it is assumed that there are no distortions of the lattice structure due to the defect. A Kihara hardcore potential with parameters fitted to neutron data has been used to compute lattice dynamics and Green functions of the host lattices. Our theoretical results have been compared with available experimental and theoretical results. Our results show reasonably good agreement with experimental results.