Fluctuating coulomb field near ionic dielectric surfaces

Analytical and numerical studies of the energy density spatial distribution of a fluctuating electric field near the model ionic crystal surface as a function of temperature are carried out. It is established that the fluctuating field energy density decreases as h ^−3.3 with increasing distance h from the crystal surface. The fluctuating field energy increases with temperature and differs from zero at −273°C due to quantum zero-point vibrations of ions in the lattice.     

Lattice dynamics of K2NaAlF6, K3AlF6, and Na3AlF6 crystals with the elpasolite structure

This paper presents the results of a nonempirical calculation of the static and dynamic properties of K₂NaAlF₆, K₃AlF₆, and Na₃AlF₆ crystals with the elpasolite structure. The calculation is based on a microscopic model of an ionic crystal that allows for the deformability and polarizability of the ions. The deformability parameters of the ions are determined by minimizing the total energy of the crystal. The total energy is regarded as a functional of the electron density, using the local Thomas-Fermi approximation and taking into account exchange (correlation) effects. The results of the calculations of the equilibrium lattice parameters and of the permittivities are in good agreement with the experimental data. Unstable vibrational modes are found in the spectrum of the lattice vibrations, with these modes occupying the phase space in the entire Brillouin zone. Zh. éksp. Teor. Fiz. 114, 1742–1756 (November 1998)     

Lattice dynamics of a Rb2KScF6 crystal in unstable cubic and tetragonal phases and in a stable monoclinic phase

The results of a nonempirical calculation of the static and dynamic properties of a Rb₂KScF₆ crystal with elpasolite structure in cubic, tetragonal, and monoclinic phases are presented. The calculation is performed on the basis of a microscopic model of an ionic crystal that takes account of the deformability and polarizability of the ions. The deformability parameters of the ions are determined from the condition that the total energy of the crystal is minimum. The computational results for the equilibrium lattice parameters are in satisfactory agreement with experimental data. Unstable vibrational modes are found in the vibrational spectrum of the lattice in the cubic and tetragonal phases. These modes occupy the phase space throughout the entire Brillouin zone. The characteristic vectors of the most unstable mode at the center of the Brillouin zone of the cubic phase are related to the displacements of the fluorine ions and correspond to rotation of ScF₆ octahedra. Condensation of this mode leads to a tetragonal distortion of the structure. In the tetragonal phase the most unstable mode belongs to the boundary point of the Brillouin zone and condensation of this mode leads to monoclinic distortion with doubling of the unit-cell volume. In the monoclinic phase unstable modes are absent in the vibrational spectrum of the lattice. Fiz. Tverd. Tela (St. Petersburg) 41, 1297–1305 (July 1999)     

Measured static hyperfine magnetic fields following implantation of Pt into Fe interpreted as evidence for pre-equilibrium effects

The static hyperfine magnetic field present at Pt nuclei implanted in ferromagnetic Fe has been measured using the ion-implantation perturbed angular correlation (IMPAC) technique following Coulomb excitation. The present measured precessions agree with earlier data, but more recent information on the transient field correction leads to an inferred static field strength that is 25% smaller than obtained previously. Comparisons are made between the static fields measured by various techniques for Pt and neighbouring ions in iron. From these comparisons, we show that the IMPAC data are consistent with a scenario in which (i) the static field takes about 10 ps to reach its equilibrium value, following recovery from dynamic structural damage caused by the ion-implantation process, and (ii) following equilibration, a large fraction ( 90%) of the implanted ions have final positions on lattice sites of the Fe host.     

Rearrangement of the Structure of Paratellurite Crystals in a Near-Surface Layer Caused by the Migration of Charge Carriers in an External Electric Field

The process of formation of surface structures in a paratellurite crystal (α-TeO₂) in an external electric field has been studied by in situ X-ray diffraction (XRD) measurements. This process is reversible and its dynamics (duration of tens of minutes) corresponds to the formation of a screening layer near the insulator–metal interface owing to the counter migration of oxygen ions and vacancies in the external electric field. The formation of domains has been observed in the experiment as the broadening and splitting of the XRD curve and is explained by mechanical stresses that appear in the high electric field near the surface in view of the piezoelectric effect and are responsible for a ferroelectric α–β phase transition. A change in the lattice parameter near the anode (surface of the crystal with a positive external charge) has been detected simultaneously. This change is due to the local rearrangement of the crystal structure because of the inflow of oxygen ions in this region and outflow of oxygen vacancies.     

Lattice dynamics and the ferroelectric and antiferrodistorsive instabilities in a bulk crystal and thin films of SrZrO3

The lattice dynamics and energies of phases related to antiferrodistorsive and ferroelectric distortions of bulk crystals and thin films of the SrZrO₃ crystal have been calculated within the framework of the ab initio model of an ionic crystal. In the case of a bulk crystal, it has been found that the most energetically favorable phases are related to antiferrodistorsive lattice distortions. Ferroelectricity in the SrZrO₃ crystal is suppressed by structural lattice distortions. In the case of thin films, it has been found that the ferroelectric instability is retained after the ??rotation?? of the oxygen octahedron and the film remains polar both in the case of a free surface and with the inclusion of the SrTiO₃ substrate in the calculation. The spontaneous polarization of thin films of different thicknesses in the ferroelectric phase has been calculated.     

Theoretical study of the surface structure and vibrations of solid argon

The influence of zero-point oscillations on the equilibrium structures and the vibrational modes for the (001), (110) and (111) surfaces of solid Ar is investigated at zero temperature. The surface structures are determined by minimizing the total energy, the static lattice energy plus zero-point energy, where the zero-point energy is evaluated from Einstein frequencies. It is found that the interlayer distances near the surface are larger than the values for bulk argon and are also larger than the distances predicted by minimizing only the static lattice energy. Based upon the surface structures determined by each of these two different minimization schemes, the phonon dispersion curves have been calculated for 21 layer slabs. The qualitative features of the dispersion curves in each case are very similar but there is a significant overall reduction in the frequencies calculated using the structures determined by minimizing the total energy, including the zero-point contribution. The rms vibrational amplitudes of atoms near the surface are calculated from the Einstein frequencies and their values relative to the bulk amplitude are the same as those evaluated by Allen and De Wette [Phys. Rev. 179 (1969) 873] from the lattice dynamics of slabs.     

Local deformation and the structure of the Stark splitting of rare-earth ions

A model for describing the relaxation of ligand ions close to a defect when impurity ions are introduced into a crystal is proposed and verified. The approach assumes that ionic displacements into new equilibrium positions can be regarded as fundamental parameters of impurity crystals that can be determined from experimental data concerning the energy structure of the impurity ion. Direct calculations for rare-earth impurity ions using crystal-field theory showed that the energy spectrum of these ions strongly depends on the equilibrium positions of the nearest matrix ions surrounding them. The results of the calculations are compared with the available experimental data. The parameters of the theory are determined. The possibility of applying this approach to the study of other systems is discussed. Fiz. Tverd. Tela (St. Petersburg) 41, 1194–1199 (July 1999)     

Mean-field kinetic theory of a classical electron gas in a periodic potential. I. Formal solution of the Vlasov equation

We study the static and dynamic behavior of a classical electron gas in the periodic potential created by an ionic lattice. Using the well-known Vlasov approximation, we derive a mean-field kinetic equation for the density-response function of the electrons. This equation is formally solved in terms of the trajectories of one electron in the mean-field equilibrium potential which determines the local electronic density. The mean-field expressions of the static and dynamic structure factors are then obtained through the fluctuation-dissipation theorem. These expressions are used to show that within the mean-field approximation the system is a conductor at all temperatures and for all dimensions.     

Surface electromagnetic waves in thin-layer biaxial structure in a magnetic field

The conditions for the existence of surface electromagnetic waves at the planar interface between a homogeneous medium (vacuum) and a thin-layer periodic structure consisting of alternating semiconductor and dielectric layers in an external magnetic field have been investigated. This structure represents an optically biaxial crystal with the effective permittivity tensor components dependent both on the geometric parameters of the structure and on the physical characteristics (magnetic field strength, frequency, and thicknesses of the layers). It has been shown that the propagation of surface electromagnetic waves localized near the interface can occur in the thin-layer biaxial structure within specific ranges of frequencies and external magnetic field strengths.     

Some dynamical properties of a two-dimensional Wigner crystal

Results for the static part of the ground state energy of the square and hexagonal two-dimensional Wigner lattices are given. The hexagonal lattice has the lower energy. Phonon dispersion curves and the vibrational zeropoint energy are calculated for the hexagonal lattice. The dielectric susceptibility tensor of a two-dimensional Wigner crystal χ_αβ(q) has been determined in the long wavelength limit in the presence of a static magnetic field perpendicular to the crystal, and explicit expressions have been obtained for the hexagonal lattice. Applying the analysis developed by Chiu and Quinn, the results for the susceptibility have been used to obtain the dispersion relation for the plasma oscillations in the electron crystal on the assumption that the crystal is embedded in a dielectric medium. The dispersion curves have been calculated for differing magnitudes of the applied magnetic field.     

Photon emission under bombardment of ruby by ions and electrons of medium energies

The characteristics of optical radiation produced under bombardment by ions (1–15 keV) and electrons (100–1000 eV) of a ruby surface are studied. Two broad bands with maxima at 330 and 450 nm attributed to defects of the crystal lattice are discovered in the spectral region of 200 to 800 nm. Characteristic radiation related to radiative relaxation of excited Cr³⁺ ions in the near-surface region of the crystal is observed. The dependence of the radiation intensity on the energy and current density of the bombarding particles is obtained experimentally. The degree of radiation polarization is determined.     

Optical phonons in ionic crystals with a diatomic unit cell

Optical phonons in an ionic crystal with two atoms per unit cell have been considered. The equation of relative motion of oppositely charged sublattices has been derived with the use of the concept of the self-consistent electromagnetic field. The frequency corresponding to transverse optical phonons and the expression for the frequency of the eigenmodes of the ionic crystal in terms of the physical characteristics of the crystal have been obtained from the condition of electrostatic equilibrium. The calculated values of the latter frequency agree with the experimental data.     

高功率微波沿面闪络击穿机制粒子模拟

针对高功率微波介质沿面闪络击穿物理过程,首先建立了理论模型,包括：动力学方程、粒子模拟算法、二次电子发射, 以及电子与气体分子蒙特卡罗碰撞模型、电子碰撞介质表面退吸附气体分子机制;其次,基于理论模型,编制了1D3V PIC-MCC程序,分别针对真空二次电子倍增、高气压体电离击穿和低气压面电离击穿过程,运用该程序仔细研究了电子和离子随时间演化关系、电子运动轨迹、电子及离子密度分布、空间电荷场时空分布、电子平均能量、碰撞电子平均能量、碰撞电子数目随时间演化关系、电子能量分布函数、平均二次电子发射率以及能量转换关系。研究结果表明：真空二次电子倍增引发的介质表面沉积功率只能达到入射微波功率1%左右的水平,不足以击穿;气体碰撞电离主导的高气压体电离击穿,是由低能电子（eV量级）数目指数增长到一定程度导致的,形成位置远离介质表面,形成时间为s量级;低气压下的介质沿面闪络击穿,是在二次电子倍增和气体碰撞电离共同作用下,由于数目持续增长的高能电子（keV量级）碰撞介质沿面导致沉积功率激增而引发的,形成位置贴近介质沿面,形成时间在ns量级。     

高功率微波沿面闪络击穿机制粒子模拟

针对高功率微波介质沿面闪络击穿物理过程,首先建立了理论模型,包括:动力学方程、粒子模拟算法、二次电子发射, 以及电子与气体分子蒙特卡罗碰撞模型、电子碰撞介质表面退吸附气体分子机制;其次,基于理论模型,编制了1D3V PIC-MCC程序,分别针对真空二次电子倍增、高气压体电离击穿和低气压面电离击穿过程,运用该程序仔细研究了电子和离子随时间演化关系、电子运动轨迹、电子及离子密度分布、空间电荷场时空分布、电子平均能量、碰撞电子平均能量、碰撞电子数目随时间演化关系、电子能量分布函数、平均二次电子发射率以及能量转换关系。研究结果表明:真空二次电子倍增引发的介质表面沉积功率只能达到入射微波功率1%左右的水平,不足以击穿;气体碰撞电离主导的高气压体电离击穿,是由低能电子（eV量级）数目指数增长到一定程度导致的,形成位置远离介质表面,形成时间为s量级;低气压下的介质沿面闪络击穿,是在二次电子倍增和气体碰撞电离共同作用下,由于数目持续增长的高能电子（keV量级）碰撞介质沿面导致沉积功率激增而引发的,形成位置贴近介质沿面,形成时间在ns量级。     

First-principles study of LiBaF3 crystals containing interstitial fluoride

The positions of the interstitial fluoride atoms in LiBaF₃ crystal are simulated by GULP. It is found that the formation energy is low when interstitial fluoride atoms at the center of the edge of the cube formed by Ba ions. The electronic structures and absorption bands for the perfect LiBaF₃ crystal and the LiBaF₃ crystal containing interstitial fluoride have been calculated using density functional theory code CASTEP. It is predicted that the interstitial fluoride atom combine with a formal lattice fluoride ion forming H center causes the 320 nm absorption band.     

A new approach to repulsion in ionic crystals

An empirical approach is attempted to make the repulsion potential of ions in an ionic crystal structure independent and crystal independent so that once the repulsion parameters for an ion are evaluated in one compound, in one structure, they could be used for that ion in any crystal. The repulsion between ions is postulated to be due to the increase in the internal energy of the ions arising from the distortion and the compression at the points of contact with their neighbours. Using an exponential form for the compression energy involving two parameters per ion, a repulsion potential for ionic crystals is proposed which includes the repulsion between nearest and next nearest neighbours. The repulsion parameters for the alkali and halogen ions have been determined to fit the behaviour of 20 alkali halides over the pressure range 0–45 kbars. The r.m.s. percentage deviations from experiment, of the calculated values of lattice spacing and compressibility are respectively 0.997% and 6.76%. The calculated radii of the ions in the various compounds compare well with the experimental values deduced from electron density maps. The advantages of the present form of the repulsion potential over earlier forms are discussed.     

SrTiO3薄膜氧缺陷的第一性原理研究

在广义梯度近似(GGA)下,利用超软赝势对真空条件下SrTiO3超晶胞的体系能量、原子间电子云重叠布局数和电子态密度等进行了自恰计算.结果显示,对有氧缺陷的超晶胞优化后,晶格参数的几何平均值增大了2.711%,这表明在高温条件下外延生长STO薄膜时,产生了氧缺陷,并且氧空位易处于薄膜表层;另外,表层氧缺陷使表层Ti原子明显的发生偏心位移,两个Ti原子的核间距由0.3905 nm增大至0.4234 nm,b轴上的氧原子则向中心靠近了0.0108 nm、并沿c轴方向上突了0.0027 nm,使STO晶体产生自发极化,氧缺陷还使STO的电子态密度的能隙增宽了1.75 eV,达到2.48 eV,从而使STO晶体由顺电相转向铁电相.