Thermodynamic aspects of superionic conductivity

This article reviews the theoretical and experimental studies on a number of thermodynamic aspects of superionic conduction, the intensive study of which began in the past decades. We discuss the relation of superionic conductivity to the disordering of one of the sublattices of the crystal, disordering phase transitions caused by the interaction of point defects, and the mechanism of polymorphic transitions associated with partial disordering. We analyse the effect of jumpwise variation of the ionic conductivity induced by an external electric field, the thermodynamics of domain states in superionic conductors, and the effect of pressure on the phase transitions and the ionic conductivity.     

Phenomenological and microscopic models of sublattice disorder in ionic crystals—I: phenomenological models

The nature of phase transitions which arise from two classes of phenomenological models for the free energy of ionic crystals containing Prenkel disorder of one constitutent is examined. In one class of models, defect-produced energy and excess entropy vary quadratically with defect concentration, while in the second class the energy per added defect is damped by disorder more rapidly than in the first class. The order of phase transitions and their effect on the effective carrier concentration for electrical conductivity are discussed.     

Structure of electromagnetic fields near the surface of an ionic crystal

A NaCl ionic crystal whose (100) face is in contact with vacuum is used as an example to consider static and dynamic contributions to an electromagnetic field in close proximity to its surface. The expression for the potential of the electric field produced by a system of point charges in vacuum (derived by Lennard-Jones and Dent) is taken as the basis. The dynamic correction to the static field has been found. It appears as a result of thermal fluctuations of ions near equilibrium positions in the ionic lattice. Various contributions of the electrostatic field of the ionic lattice, the field of fluctuating ions of this lattice near their equilibrium positions, and of the dipole-type fluctuation field produced by spontaneous deformations of the crystal??s elementary cells to the energy density of the electromagnetic field near the surface of the ionic crystal have been calculated and compared. The periodic structuring of the electromagnetic field??s energy density caused by the presence of static and dynamic ionic lattices of the crystal at small distances from its surface is illustrated graphically. Fields generated by a film with a finite thickness containing an arbitrary number of ion monolayers have also been considered.     

Anisotropy of conductivity due to warm holes inp-type germanium andp-type silicon

The dependence of the electric conductivity on a d.c. electric field of medium intensity is measured for 3.5 ohm-cmp-type silicon and 0.9 ohm-cmp-type germanium. From these data and the symmetry properties of the cubic crystal lattice the dependence of the conductivity on crystal orientation is determined. Also, an analytical treatment is made for silicon by assuming a model of constant energy surfaces near momentum?k=0 which consists of spheroids of rotational symmetry penetrating each other. The usually accepted model of warped surfaces does not seem to be tractable. The ratio of effective masses parallel and perpendicular to the axis of rotation enters as a parameter which is determined by the experimental value of the conductivity anisotropy. This mass ratio for silicon at 275 °K is 3.25, at 193 °K 4.64 and at 77 °K 37. With germanium the observed anisotropy is stronger than the anisotropy calculated with any finite mass ratio which means that the model is not adequate.     

紫外激光诱导近化学计量比钽酸锂晶体铁电畴反转

对紫外激光诱导近化学计量比钽酸锂晶体铁电畴反转进行了实验研究。波长为351 nm的连续紫外激光被聚焦在近化学计量比钽酸锂晶体的-z表面,同时沿与晶体自发极化相反的方向施加均匀外电场。实验证实紫外激光辐照可以有效地降低晶体畴反转所需的矫顽电场,采用数字全息干涉测量技术检测证实在激光辐照区域实现局域畴反转。研究表明采用紫外激光诱导可以实现对近化学计量比钽酸锂晶体铁电畴反转的局域控制。提出了物理机理的理论分析,认为外电场和激光辐照场的共同作用在晶体内部产生高浓度、大尺寸的缺陷结构,缺陷一定程度上降低畴体成核和畴壁运动所需要克服的退极化能和畴壁能,实现激光诱导畴反转。     

Theoretical analysis of the influence of flexoelectric effect on the defect site in nematic inversion walls

Based on the experimental phenomena of flexoelectric response at defect sites in nematic inversion walls conducted by Kumar et al., we gave the theoretical analysis using the Frank elastic theory. When a direct-current electric field normal to the plane of the substrate is applied to the parallel aligned nematic liquid crystal cell with weak anchoring, the rotation of ± 1 defects in the narrow inversion walls can be exhibited. The free energy of liquid crystal molecules around the +1 and-1 defect sites in the nematic inversion walls under the electric field was formulated and the electric-field-driven structural changes at the defect site characterized by polar and azimuthal angles of the local director were simulated. The results reveal that the deviation of azimuthal angle induced by flexoelectric effect are consistent with the switching of extinction brushes at the +1 and-1 defects obtained in the experiment conducted by Kumar et al.     

Effect of dielectric properties of solvents on the quality factor for a beyond 900 MHz cryogenic probe model

A previous report by Kelly et al. [J. Am. Chem. Soc. 124 (2002) 12013] indicated that the ionic conductivity of aqueous solution produces a significant contribution to the sensitivity loss in high-resolution NMR equipped with a cryogenically cooled probe. The loss in a sample solution contains two contributions: one from the ionic conductivity and the other from the dielectric loss; the latter is especially important at high frequencies such as above 900 MHz. Here, we investigated the effect of the dielectric conductivity on the quality factor of a 930 MHz cryogenic probe model; in particular, it deals with the ionic aqueous solutions and organic solvents commonly used for NMR in biological research and the chemistry of natural compounds. The sample quality factor, Qs, at first increases with the real part of the relative dielectric permittivity epsilon' and then saturates. In the case of polar organic solvents, the transverse electric field on the sample decreases with epsilon', resulting in an increase of Qs. In the case of non-polar organic solvents, the dielectric conductivity is so small that the gradient of the increase is steep, resulting in much larger Qs though the epsilon' is small. The effect of the transverse electric field is negligible if the epsilon' becomes large, thus the loss for ionic aqueous solution is mainly governed by a loop current induced in the sample solution. As the induced electromotive force is independent of the epsilon', the Qs is saturated at high values of epsilon'. Based on the Qs obtained with the cryogenic probe model, the sensitivity for the cryogenic probe is expected to be as follows: the loss in sensitivity by loading water is more than 66%, i.e., the effect of the dielectric conductivity of water is remarkable at high frequencies; polar organic solvent suffers much larger losses, which is due to the enhancement of the effective sample resistance by the effect of epsilon'; a non-polar organic solvent is nearly free of the sensitivity loss as the dielectric conductivity is negligible; the reverse micelle behaves similarly.     

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.     

Chiral photonic crystals with an electrically tunable anisotropic defect. Experiment and theory

The possibility of inducing a planar defect in a plane structure of a cholesteric liquid crystal by an external electric field is demonstrated experimentally for the first time. The results of experimental and theoretical study of the behavior of the coefficient of reflection (transmission) of light from a layer of a cholesteric liquid crystal with a planar defect induced in it are considered. Possible applications of such a system are considered.     

Electric field of an isolated charged impurity in an ionic crystal

The character of the behavior of the electric field created by a charged impurity in an ionic crystal is studied on the basis of both cluster and analytical approaches. In the cluster approach about 30 000 ions surrounding the impurity are taken into account. These ions are described in a model of polarizable sites. A direct calculation shows that the asymptote of the electric field of a charged impurity at lattice points can differ strongly from the one given by the Coulomb equation written for a homogeneous polarizable medium. The behavior of the electric field at intermediate distances, where the asymptotic behavior cannot yet be used, is studied in detail. It is found that the electric field is increased significantly in comparison to the Coulomb field in the region near the defect. The size of this (strongly polarized) region increases as the dielectric constant increases. These data are in qualitative agreement with the results obtained by Vikhnin et al. and account for the results of recent experiments designed to investigate polarization in reduced virtual ferroelectrics. Fiz. Tverd. Tela (St. Petersburg) 40, 662–667 (April 1998)     

液晶在电场和剪切耦合作用下的流变学行为

本文通过理论和实验对液晶 5CB在剪切和电场耦合作用下流变行为进行了研究. 采用液晶连续理论, 建立了包括界面锚定能, 弹性自由能, 介电自由能和流动能在内的系统 Gibbs自由能公式, 通过最小化系统自由能的方法求解液晶在剪切和电场耦合作用下的取向分布及其黏度变化, 从分子基础模型上揭示了液晶在耦合作用下的流变行为、微观机理及其影响规律, 并通过流变测试对此进行验证. 对比分析了理论和试验结果的误差和原因, 发现界面锚定效应对于液晶分子的取向和黏度具有重要影响. 理论和试验结果均表明, 液晶在电场作用下具有明显的电黏效应, 表现出非牛顿流变行为, 其黏度值由剪切和电场的竞争和耦合作用共同决定. 在外电场作用下液晶的黏度可以增加到初始值的 4倍左右, 液晶这种其自身黏度可随着外场 (例如运动速度) 改变的特性在一定的条件下可以自适应地满足不同工况对黏度的要求, 这对实现智能摩擦润滑具有重要的意义. 关键词： 液晶 流变行为 电黏效应 耦合作用     

Field-theoretic approach to the properties of the solid state

The techniques of quantum field theory are used to investigate the thermodynamic ion displacement correlation function—or Green's function of the phonon field—in a crystal and especially in a metal. The structure of thermodynamic Green's functions is outlined and the method for solving for them at finite temperature is fully discussed.The analytic structure of the phonon Green's function is then considered. This function is shown to be bounded and invertible everywhere off the real axis; a spectral form is derived for its inverse. The symmetries imposed by the point group of the crystal are then discussed.Assuming small ionic oscillations, we find the inverse of the phonon Green's function as a linear function of the electronic contribution to the dielectric response function of the metal. This dielectric function is shown to be simply related to the longitudinal part of the conductivity tensor that gives the response of the electrons to the effective electric field in the metal. The assumption of translational invariance then leads to an explicit expression for the phonon Green's function in terms of this conductivity.The deformations in the lattice induced by an arbitrarily time varying external force are calculated in terms of the retarded phonon Green's function. In the static long wavelength limit the phonon Green's function yields the macroscopic elastic constants of the crystal. Their relation to the conductivity is exhibited, and several elastic constants are estimated. We also see that the complete phonon spectrum and the lifetimes of the phonon states may be calculated from this Green's function. A relation between the long wavelength acoustic attenuation in metals and the de conductivity is derived, which is in good agreement with recent experiments. Furthermore, the ions in a metal are shown to have a high-frequency oscillation along with the electrons, at essentially the electron plasma frequency.     

Fluctuation model of the high-frequency hopping electrical conductivity of moderately compensated semiconductors with hydrogenic impurities

A model is developed according to which a hop of an electron (or hole) between two hydrogenic donors (or acceptors) occurs only when their energy levels become equal due to thermal and/or electrostatic fluctuations in a doped crystal. The main contribution to the real part of the high-frequency hopping electrical conductivity is assumed to come from acceptor pairs in which the time of hole tunneling is equal to the half-period of the external electric field and the phase of tunneling coincides with that of the field. In this case, the imaginary and real parts of the hopping conductivity are approximately equal. The results of calculations based on this model are compared to the experimental data for p-Ge: Ga with an intermediate degree of compensation of the main doping impurity.     

On the energy of formation of defects

We present a formulation of the Gibbs free energy of defect formation in crystals which is formally based on a quasi-classical thermodynamical cluster expansion of the Gibbs free energy of the defect crystal. Thus a microscopic formulation of the Gibbs free energy of formation is achieved. The related quantities like formation volume per defect and defect susceptibility functions are then derived from the formation energy. The resulting expressions depend only on the defect concentration and the bulk properties of the crystal. Finally we discuss an approximate form of the formation energy which was introduced intuitively by Varotsos and Alexopoulos. As an example for the applicability of this formulation we present an explanation of the anomaly in the conductivity and diffusion of AgBr.     

Nonlinear response from the perspective of energy landscapes and beyond

The paper discusses the nonlinear response of disordered systems. In particular we show how the nonlinear response can be interpreted in terms of properties of the potential energy landscape. It is shown why the use of relatively small systems is very helpful for this approach. For a standard model system we check which system sizes are particular suited. In case of the driving of a single particle via an external force the concept of an effective temperature helps to scale the force dependence for different temperature on a single master curve. In all cases the mobility increases with increasing external force. These results are compared with a stochastic process described by a 1d Langevin equation where a similar scaling is observed. Furthermore it is shown that for different classes of disordered systems the mobility can also decrease with increasing force. The results can be related to the properties of the chosen potential energy landscape. Finally, results for the crossover from the linear to the nonlinear conductivity of ionic liquids are presented, inspired by recent experimental results in the Roling group. Apart from a standard imidazolium-based ionic liquid we study a system which is characterized by a low conductivity as compared to other ionic liquids and very small nonlinear effects. We show via a real space structural analysis that for this system a particularly strong pair formation is observed and that the strength of the pair formation is insensitive to the application of strong electric fields. Consequences of this observation are discussed.     

Selective reflection of light from a layer of cholesteric liquid crystal with induced inhomogeneity of helix pitch

A possibility to induce a planar defect in a plane-layer structure of a cholesteric liquid crystal via an external electric field is shown experimentally. The results of studies of behavior of the selective reflection (transmission) coefficient of light for a layer of the cholesteric liquid crystal, where planar defects are induced, are presented     

Problems and perspectives in the investigation of the electron conductivity of ionic crystals

On the basis of a generalization- and a systematization of the few data on the fundamental parameters of electrons in ionic crystals, an analysis is carried out on the optimum concentration of nonequilibrium carriers, the magnitude of the applied electric field, and the excitation conditions when an object's electron conductivity is changed. Peculiarities, limitations, and some technical complications of the experimental investigation of electron conductivity of ionic crystals are described. It is demonstrated that, for crystals with a very wide gap (E_g > 10 eV), which are important in practical-terms., the most effective method for determining carrier parameters is to measure the conductivity induced by short x-ray pulses of low density.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 79–83, June, 1989.     

The elastic dielectric

Macroscopic field equations, boundary conditions and equations of state are derived for the non-linear, macroscopic elastic and dielectric response of an insulator. A centrosymmetric polynomial representation of order four is introduced for the energy density; the equations of state for the electric field and stress tensor are then deduced as polynomials of degree three in the displacement gradients and electric displacement field. The results are applied to the special case of m3m material symmetry.

A finite, point-charge model of a centrosymmetric ionic crystal is introduced and used to determine 0°K microscopic expressions for the electric field and stress tensor equation of state coefficients introduced in the macroscopic analysis. The results are used to calculate the full set of second and third-order non-linear coefficients for NaI, based on a Born-Mayer potential and the 4·2°K elastic stiffness data of Claytor and Marshall.     

Adsorption on the surface of ionic crystals and the effect of applied electric field

Adsorption of molecules on an ideal surface of ionic crystals and the effect of an external uniform electric field on this process have been investigated using a model Hamiltonian, which takes account of the Coulomb interaction between electrons and atomic cores of the system under consideration, all valence orbitals of the admolecule, as well as their nonorthogonality to the crystal wavefunctions, the substrate band structure. The binding energy as a function of the adsorbate-to-substrate distance is calculated for H₂O and CO on NaCl and MgO (001) surfaces. The main attention is focused on the contributions of admolecule-substrate interaction of various types to the binding energy.