Simple calculation of the mean-square displacements of volume, (110) and (100) surface atoms of chromium

We use an analytic method based on the expansion of the dynamical matrix to determine the thermal dependence of the mean-square displacements 〈u²〉 of volume, and (100) and (110) surface atoms of Cr. For the volume and (110) surface the results are in satisfactory agreement with previous X-ray and low-energy electron diffraction data. In particular, the zero-point thermal motion of Cr-volume atoms is approximately reached at temperatures as high as 170°K in accordance with experiments.A discussion about the temperature at which the atomic vibrations are strongly frozen is carried out for b.c.c. crystals.     

Spin fluctuations and electronic semiconductor-metal transitions in iron monosilicide

This paper discusses the effect of dynamic zero-point and thermal spin-density fluctuations (SDF) on the electronic spectrum of the nearly-ferromagnetic semiconductor FeSi. It is shown that near T=0° zero-point SDF can lead to so much splitting of the electron states of the valence and conduction band that a “gapless” ground state arises. As the temperature increases, the forbidden gap in the spectrum of d electrons first reappears due to suppression of zero-point fluctuations and then disappears again, as the amplitude of thermal spin fluctuations increases. It is these transformations of the electronic spectrum that are the reason for the anomalous changes in the magnetic susceptibility with temperature observed experimentally. Fiz. Tverd. Tela (St. Petersburg) 40, 1437–1441 (August 1998)     

Effect of zero-point energy on the dielectric behavior of strontium titanate

Barrett formula has been obtained in the framework of the effective field approach by including the zero-point energy. By fitting with experimental data of dielectric constant of SrTiO₃, we find that they agree in the whole temperature range fairly well if the zero-point energy is assumed to change from a small value at low temperature to a large value at high temperature.     

基于第一性原理的固氦零点振动能的量子理论计算

基于第一性原理,运用原子团簇理论和Hartree-Fock Self-Consistent-Field从头算法计算了高压固氦hcp结构在平衡位置r=1.75-2.6附近的原子相互作用能,并使用1stOpt软件拟合出固氦的零点振动频率,得到零点振动能、Gruneisen系数及零点振动压强,最后与实验值做了比较.结果表明:固氦晶体在其各自平衡位置附近的运动可近似为简谐振动;固氦晶体的零点振动频率随着摩尔体积的增大而减小;零点振动能占多体相互总能的比例超过5%,已不可忽略,其比例随摩尔体积的增加而增大;零点振动能随原子间距和摩尔体积的增大而减小;Gruneisen系数随着摩尔体积的增大而增大,并始终处于1和2之间;零点振动引起的压强与实验值曲线趋势完全一致,但比实验值稍小,零点振动压强对总压强的贡献随着摩尔体积的增大由8%增大到50%左右,由此引起的零点振动压强值的贡献越来越大.     

基于第一性原理的固氦零点振动能的量子理论计算

基于第一性原理,运用原子团簇理论和Hartree-Fock Self-Consistent-Field从头算法计算了高压固氦hcp结构在平衡位置r=1.75-2.6Å附近的原子相互作用能,并使用1stOpt软件拟合出固氦的零点振动频率,得到零点振动能、Gruneisen系数及零点振动压强,最后与实验值做了比较.结果表明：固氦晶体在其各自平衡位置附近的运动可近似为简谐振动;固氦晶体的零点振动频率随着摩尔体积的增大而减小;零点振动能占多体相互总能的比例超过5%,已不可忽略,其比例随摩尔体积的增加而增大;零点振动能随原子间距和摩尔体积的增大而减小;Gruneisen系数随着摩尔体积的增大而增大,并始终处于1和2之间;零点振动引起的压强与实验值曲线趋势完全一致,但比实验值稍小,零点振动压强对总压强的贡献随着摩尔体积的增大由8%增大到50%左右,由此引起的零点振动压强值的贡献越来越大.     

Effect of covalency,zero-point energy and charge transfer on the phase-transition,elastic and thermophysical properties of Ca-chalcogenides under compression

The pressure induced phase-transition, elastic and thermophysical properties of Ca-chalcogenides have been investigated by means of many body potential. The modified charge transfer potential consists of long-range Coulomb and charge-transfer interactions modified by covalency and short-range overlap repulsion extended up to second neighbours and zero-point energy effects. Another charge-transfer model excludes covalency and zero-point energy effects. These chalcogenides undergo first-order phase-transition at P _T = 39.23, 36.30 and 31.20 GPa and their equation of state show volume collapse of 10.12, 7.61 and 4.55% for CaS, CaSe and CaTe, respectively, which are in good agreement with the experiments. The elastic and thermophysical properties of these compounds have also been computed at normal and high pressures. Both the models are capable of explaining the Cauchy-discrepancy (C₁₂ ≠ C₄₄), elastic, phase-transition and thermophysical properties successfully.     

Phase transition,structural, mechanical and thermal properties of erbium pnictides under pressure

In this article, we have investigated the high-pressure structural phase transition of erbium pnictides (ErX; X?=?N, P and As). An extended interaction potential model has been developed (including the zero-point energy effect in three-body interaction potential model). Phase transition pressures are associated with a sudden collapse in volume. The phase transition pressures and associated volume collapses have been predicted successfully. The elastic constants, their combinations and pressure derivatives are also reported. The pressure behaviour of elastic constants, bulk modulus and shear modulus have been presented and discussed. Moreover, the thermophysical properties such as molecular force constant (f), infrared absorption frequency (υ ₀), Debye temperature (θ _D) and Grunneisen parameter (γ) have also been predicted.     

Thermal Squeezed State Representation of Scalar Field and Energy Density in Semiclassical Theory of Gravity

The semiclassical theory of gravity is studied in terms of representation of scalar field in thermal coherent state and thermal squeezed state formalisms. For the FRW cosmological model with a minimal scalar field, the semiclassical Einstein equation reduces to zero-point energy term plus a finite temperature term and classical term in thermal coherent state. In thermal squeezed vacuum state it reduces to quantum term in addition to the finite temperature term and zero-point energy term. The present study can account for nonclassical state and finite temperature effect contributions to energy density in semiclassical theory of gravity.     

Investigation of the hyperfine interaction in the antiferromagnetic CsMnI3

The lower branch of the resonance spectrum of the quasi-one-dimensional triangular antiferromagnetic CsMnI₃ has been investigated experimentally. This branch possesses a gap due to the dynamic hyperfine interaction. The temperature dependence of the energy gap was studied in detail at several frequencies. A theoretical calculation of the corresponding spectrum of coupled electron-nuclear spin oscillations was performed in the “hydrodynamic approximation” with an empirical correction for thermal fluctuations of the antiferromagnetic system. The good agreement between the calculation and experimental data makes it possible to determine the zero-point spin reduction in the antiferromagnetic. Zh. éksp. Teor. Fiz. 112, 1893–1898 (November 1997)     

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.     

Temperature and size dependence of the optical response of small Ag clusters

The absorption spectra of small Ag ⁺ n clusters are calculated at finite vibrational temperature by using a microscopic tight-binding RPA method. We consider free clusters with sizes between n = 3 and n =13 and take into account explicitly the degrees of freedom corresponding to the 4 d-electrons. We analyze the optical absorption as a function of the cluster size. We show that the contribution of the d-electrons has an important influence on the size dependence of the energy of the Mie plasmon. We also perform ensemble averages to obtain the absorption spectra for different vibrational temperatures. We obtain relatively good agreement with experiment for a temperature . The dynamics of the 4 d-electrons, which shows in small clusters an incipient delocalized character for n >7, yields an important contribution to the absorption spectrum already for n =13. We find that the strength of this contribution can be controlled by varying the vibrational temperature. Received: 4 January 1999 / Received in final form: 12 May 1999     

Isotope effects in Raman spectra of crystalline sulfur α-S8

The Raman spectra of ³²S, ³³S, and ³⁴S powders, as well as ^naturS powder with the natural isotopic composition, have been measured in the temperature range of 5–300 K. The isotope mass dependences of the vibrational frequencies have been obtained. It has been shown that such a dependence in the region of mixed translational-librational modes differs from the dependences known for monatomic inorganic crystals. The role of zero-point vibrations for low- and high-frequency modes has been revealed throughout the entire temperature range.     

NMR study of topological insulator Bi<Subscript>2</Subscript>Te<Subscript>3</Subscript> in a wide temperature range

NMR studies of ¹²⁵Te in the topological insulator bismuth telluride Bi₂Te₃ in a wide temperature range from room temperature to 12.5 K are performed. The pulsed NMR spectrometer Bruker Avance 400 is applied. The NMR spectra are obtained for the powder from Bi2Te3 single crystal and monocrystalline plates with the orientations c || B and c ⊥ B. At room temperature, the spectra consist of two lines related to two nonequivalent positions of tellurium nuclei Te1 and Te2. The parameters of the NMR frequency shift tensor are found from the powder spectrum. The temperature dependences of the spectra for the powder and plates with the orientation c ⊥ B agree with each other. The line shift with decreasing temperature is explained by the reduction of the Knight shift. The thermal activation energy of charge carriers is estimated. The spectra for the plates with the orientation c || B demonstrate peculiar behavior below 91 K. The spin-lattice relaxation time for the powder and monocrystalline plates with both orientations at room temperature is measured.     

Tl 0 and Tl 2+ centers as paramagnetic probes for the 74 K phase transition in Rb 2 ZnCl 4

Tl 0 (6 p 1 ) irradiation centers are proposed as new paramagnetic probes for structural phase transition investigations. The P2 1 cn M C1 c1 phase transition in Rb 2 ZnCl 4 single crystals is monitored using the Tl 0 and the well-known Tl 2+ (6 s 1 ) paramagnetic probes. The anomalous temperature dependence exhibited by the EPR spectra of both types of centers in the C1 c1 phase was analyzed considering a soft mode contribution.     

Quantum dynamics study of isotope effects of the OD/OH + CH3 reactions

ABSTRACT

A six-degrees-of-freedom, time-dependent quantum dynamics calculation is employed to study the integral cross sections, full-dimensional cumulative reaction probabilities and full-dimensional rate constants for the isotopic reactions of the OD and OH with CH₃ reactions. The full-dimensional cumulative reaction probabilities and full-dimensional rate constants are obtained using the energy and J-K shifting approaches based on the six-degrees-of-freedom calculations. The comparison of integral cross sections shows that the OD?+?CH₃ reaction has a larger energy threshold and a smaller tunnelling effect than the OH?+?CH₃ reaction. The corrected rate constants using the experimental zero-point energy have a very good agreement with the experimental results. The comparison of the rate constants shows that the OD?+?CH₃ has smaller rate constants than the OH?+?CH₃ reaction, which indicates a smaller reactivity due to the isotope substitution.     

Temperature dependence of Johnson noise

Johnson noise is usually considered to measure the absolute, thermodynamic temperature. A careful analysis of data on copper to 1.7 mK suggests that a kinetic temperature T_o coth T_o/T is measured, where T_o = 1.98 mK, and so reflects a zero-point energy.     

Electron-phonon interaction in tetrahedral semiconductors

Considerable progress has been made in recent years in the field of ab initio calculations of electronic band structures of semiconductors and insulators. The one-electron states (and the concomitant two-particle excitations) have been obtained without adjustable parameters, with a high degree of reliability. Also, more recently, the electron-hole excitation frequencies responsible for optical spectra have been calculated. These calculations, however, are performed with the constituent atoms fixed in their crystallographic positions and thus neglect the effects of the lattice vibrations (i.e. electron-phonon interaction) which can be rather large, even larger than the error bars assumed for ab initio calculations.Effects of electron-phonon interactions on the band structure can be experimentally investigated in detail by measuring the temperature dependence of energy gaps or critical points (van Hove singularities) of the optical excitation spectra. These studies have been complemented in recent years by observing the dependence of such spectra on isotopic mass whenever different stable isotopes of a given atom are available at affordable prices. In crystals composed of different atoms, the effect of the vibration of each separate atom can thus be investigated by isotopic substitution. Because of the zero-point vibrations, such effects are present even at zero temperature (T=0).In this paper, we discuss state-of-the-art calculations of the dielectric function spectra and compare them with experimental results, with emphasis on the differences introduced by the electron-phonon interaction. The temperature dependence of various optical parameters will be described by means of one or two (in a few cases three) Einstein oscillators, except at the lowest temperatures where the T⁴ law (contrary to the Varshni T² result) will be shown to apply. Increasing an isotopic mass increases the energy gaps, except in the case of monovalent Cu (e.g. CuCl) and possibly Ag (e.g. AgGaS₂). It will be shown that the gaps of tetrahedral materials containing an element of the first row of the periodic table (C,N,O) are strongly affected by the electron-phonon interaction. It will be conjectured that this effect is related to the superconductivity recently observed in heavily boron-doped carbon.     

Phase transition in liquid 3He in an aerogel at zero temperature

An expansion of the thermodynamic potential in powers of the order parameter of the superfluid phase transition is found for liquid ³He in an aerogel at T=0. The discontinuity in the compressibility (sound velocity), which is the analog of the discontinuity in the specific heat for second-order temperature phase transitions, is calculated. The magnitude of the critical quantum fluctuations (zero-point vibrations) of the order parameter is estimated. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 10, 655–660 (25 November 1997)     

The effect of perturbedk-selection and gap shrinkage on the optical transitions in III–V semiconductors

Optical transitions in direct semiconductors are governed according to simple one-electron treatment by ak-selection rule, which in doped or mixed crystals is but lifted to some extent (k) caused by 1) shallow impurities, 2) isoelectronic impurities or 3) alloy scattering. Values of k for these mechanisms are given and the implications for line shapes of optical spectra are discussed.Furthermore, as to the position of lines in the optical spectra of highly doped or highly excited crystals, gap shrinkage effects have to be considered, three main mechanisms of which can be distinguished: 1) Quadratic response of the band edges with respect to the fluctuating potential of the (screened) impurities, 2) polaron effects and 3) carrier exchange and correlation effects. Results of theoretical calculation are compared with experimental findings for GaAs and GaP. The practical importance of gap shrinkage effects for gain measurements and for the operation of (Ga, Al) As laser diodes is pointed out.From the Coulomb interaction of the carriers an additional mechanism for the lifting of thek-selection rule (especially valid for pure, but excited semiconductors) can be derived (plasmon coupling): Estimations show that the simplek-selection rule is almost never fulfilled within the energy range of emission spectra and that these spectra can be well explained simply assuming no-k-selection even for pure direct material.     

金属铍热力学性质的理论研究

使用第一性原理方法结合平均场模型研究了压力从0到150GPa、温度从0到1500K，金属铍六角密排结构(hcp)的热力学性质，包括铍的常态性质，等温高压物态方程，以及常压下平衡体积、体弹模量随温度的变化，Hugoniot曲线等.0K物态方程由广义梯度近似下的密度泛函理论计算，粒子热运动的贡献由平均场模型计算.由于铍的Debye温度比较高，计算自由能时考虑了零点振动能修正.计算结果与已有的静力学和冲击波实验数据符合得非常好. 关键词： 热力学性质 物态方程 第一原理计算