Analytic Debye-Grüneisen equation of state for a generalized Lennard-Jones solids

The approximate method to treat the practical quantum anharmonic solids proposed by Hardy,Lacks and Shukla is reformulated with explicit physical meanings.It is shown that the quantum effect is important at low temperature,it can be treated in the harmonic framework.and the anharmonic effect is important at high temperature and tends to zero at low temperature,it can be treated by using a classical approximation.The alternative formulation is easier for various applications,and is applied to a Debye-Grueneisen solid with the generalized Lennard-Jones intermolecular interaction.The expressions for the Debys temperature and Grueneisen parameter as a function of volume are analytically derived.The analytic equation of state is applied to predict the thermodynamic properties of solid xenon at normal-pressure with the nearest-neighbour Lennard-Jones interaction,and is further applied to research the properties of solid xenon and krypton at high pressure by using an all-neighbour Lennard-Jones interaction.The theoretical results are in agreement with the experiments.     

ANALYTIC EQUATION OF STATE FOR GENERALIZED LENNARD-JONES SOLID INCLUDING LOWEST-ORDER ANHARMONIC AND CORRELATION CORRECTIONS

Based on the cell model, the general formula for the free energy of solids is derived analytically with the lowest order anharmonic modification and correlation effect taken into account. Combining a method of summing over lattice sites, the analytic equation of state for generalized Lennard-Jones solid is derived. The calculations show that the agreement between theory and computer simulation is quite good and is significantly improved as compared with the numerical results in literature. The comparison of different effects shows the theory including all neighbors but only considering the lowest anharmonic and correlation effects may be a good and convenient approximation for practical solids. The approximation can be easily extended to the quantum case and other generalized potentials.     

ANALYTIC EQUATION OF STATE FOR GENERALIZED LENNARD-JONES SOLID INCLUDING LOWEST-ORDER ANHARMONIC AND CORRELATION CORRECTIONS*

Based on the cell model, the general formula for the free energy of solids is derived analytically with the lowest order anharmonic modification and correlation effect taken into account. Combining a method of summing over lattice sites, the analytic equation of state for generalized Lennard-Jones solid is derived. The calculations show that the agreement between theory and computer simulation is quite good and is significantly improved as compared with the numerical results in literature. The comparison of different effects shows the theory including all neighbors but only considering the lowest anharmonic and correlation effects may be a good and convenient approximation for practical solids. The approximation can be easily extended to the quantum case and other generalized potentials.     

Equation of state for solids with considering cohesive energy and anharmonic effect and its application to MgO

A simple equation of state (EOS) in wide ranges of pressure and temperature is constructed within the Mie-Grüneisen-Debye framework. Instead of the popular Birch-Murnaghan and Vinet EOS, we employ a five-parameter cold energy expression to represent the static EOS term, which can correctly produce cohesive energy without any spurious oscillations in extreme compression and expansion region. We developed a Padé approximation-based analytic Debye quasiharmonic model with high accuracy which improves the performance of EOS in low temperature region. The anharmonic effect is taken into account by using a semi-empirical approach. Its reasonability is verified by the fact that the total thermal pressure tends to the lowest-order anharmonic expansion in the literature at low temperature, and tends to ideal-gas limitation at high temperature, which is physically correct. Besides, based on this approach, the anharmonic thermal pressure can be expressed in the Grüneisen form, which is convenient for applications. The proposed EOS is used to study the thermodynamic properties of MgO including static and shock compression conditions, and the results are very satisfactory as compared with the experimental data.     

Equation of state for solids considering cohesive energy and anharmonic effect and its application to MgO

A simple equation of state(EOS) in wide ranges of pressure and temperature is constructed within the MieGrneisen-Debye framework.Instead of the popular Birch-Murnaghan and Vinet EOS,we employ a five-parameter cold energy expression to represent the static EOS term,which can correctly produce cohesive energy without any spurious oscillations in the extreme compression and expansion regions.We developed a Pad’e approximation-based analytic Debye quasiharmonic model with high accuracy which improves the performance of EOS in the low temperature region.The anharmonic effect is taken into account by using a semi-empirical approach.Its reasonability is verified by the fact that the total thermal pressure tends to the lowest-order anharmonic expansion in the literature at low temperature,and tends to ideal-gas limitation at high temperature,which is physically correct.Besides,based on this approach,the anharmonic thermal pressure can be expressed in the Gru¨neisen form,which is convenient for applications.The proposed EOS is used to study the thermodynamic properties of MgO including static and shock compression conditions,and the results are very satisfactory as compared with the experimental data.     

非简谐振动对石墨烯量子电容和热稳定性的影响

采用固体物理理论和方法,研究了单层石墨烯的量子电容和它的温度稳定性随温度和电压的变化规律,探讨原子非简谐振动对它的影响.结果表明:(1)当电压一定时,单层石墨烯的量子电容和温度稳定性系数均随温度升高发生非线性变化,电压小于2.3 V时,量子电容随温度升高而增大,温度稳定性系数随温度升高由缓慢变化到很快增大,电压高于2.3 V时,量子电容随温度升高先增大后减小,而其温度稳定性系数随温度升高由缓慢变化到很快减小.温度一定时,量子电容只在电压值为0.4～2.8 V范围内才变化较小,而电压值大于2.8 V时,量子电容迅速减小并趋于0;(2)与简谐近似相比,非简谐项会使石墨烯量子电容有所增大,且温度愈高,两者的差愈大,非简谐效应愈显著,温度为300 K时,非简谐的量子电容要比简谐近似的值大0.33%,而温度为1 000 K时,差值增大到1.47%;(3)电压在1.5～1.8 V之间,而温度低于800 K时,石墨烯量子电容的温度稳定性系数最小且不随温度而变,储能性能的温度稳定性最好;(4)非简谐项会使它的量子电容热稳定性系数比简谐近似的值增大,且增大的情况与温度有关,当温度为400 K时量子电容热...     

基于路径积分分子动力学与热力学积分方法的高压氢自由能计算

在相图研究中, 严格计算一个真实系统在特定温度、压强下的自由能是近年来该领域理论方法发展的前沿. 自Mermin提出有限温度密度泛函理论后, 在电子结构层面, 弱关联系统中人们就其在对自由能贡献的描述已相对完善, 但在原子核运动的描述上, 热运动与量子运动的非简谐项却总被忽视. 本文将路径积分分子动力学与热力学积分结合, 对300 GPa下氢晶体Cmca 结构中原子核热涨落与量子涨落对自由能的影响进行了分析. 发现在100 K核量子涨落非简谐项的贡献约为15 meV每原子, 远大于不同结构间静态焓的差别. 该研究提醒人们简谐近似在核量子效应描述中可能存在的不准确性(即使在低温下). 同时, 我们采取的方法 也为人们进行自由能的准确计算提供了一个简单有效的手段.     

Effects of intrinsic anharmonicity in the Mie–Grüneisen equation of state and higher order corrections

The usual quasiharmonic Mie–Grüneisen (MG) equation of state is modified by the inclusion of ‘intrinsic anharmonicities’, which have been considered up to now primarily in the high temperature limit. A comparison with experimental data for the rare gas solids, Ar, Kr and Xe and for MgO reveals that the anharmonic contributions cannot be represented perfectly within the MG approximation. A small but significant modification of the MG approach is presented to estimate intrinsic anharmonic contributions within a mean-field approximation for the thermal part of the internal energy. This estimate results in reasonable interpolations to low temperatures, where quantum effects are dominant. The present approach is also compared with more restricted recent theoretical results.     

Anharmonic stabilization of the high-pressure simple cubic phase of calcium

The phonon spectrum of the high-pressure simple cubic phase of calcium, in the harmonic approximation, shows imaginary branches that make it mechanically unstable. In this Letter, the phonon spectrum is recalculated by using density-functional theory ab initio methods fully including anharmonic effects up to fourth order at 50 GPa. Considering that the perturbation theory cannot be employed with imaginary harmonic frequencies, a variational procedure based on the Gibbs-Bogoliubov inequality is used to estimate the renormalized phonon frequencies. The results show that strong quantum anharmonic effects make the imaginary phonons become positive even at zero temperature so that the simple cubic phase becomes mechanically stable, as experiments suggest. Moreover, our calculations find a superconducting T(c) in agreement with experiments and predict an anomalous behavior of the specific heat.     

石墨烯低温热膨胀和声子弛豫时间随温度的变化规律

考虑到原子非简谐振动和电子-声子相互作用,用固体物理理论和方法研究了石墨烯格林艾森参量和低温热膨胀系数以及声子弛豫时间随温度的变化规律,探讨了原子非简谐振动项对它们的影响.结果表明:1)在低于室温的温度范围内,石墨烯的热膨胀系数为负值,随着温度的升高,其热膨胀系数的绝对值单调增加,室温热膨胀系数为-3.64×10~(-6)K~(-1);2)简谐近似下的格林艾森参量为零.考虑到非简谐项后,格林艾森参量在1.40-1.42之间并随温度升高而缓慢增大,几乎成线性关系,第二非简谐项对格林艾森参量的影响小于第一非简谐项;3)石墨烯声子弛豫时间随着温度的升高而减小,其中,温度很低(T10 K)时变化很快,此后变化很慢,当温度不太低(T300 K)时,声子弛豫时间与温度几乎成反比关系.     

An approximate scheme to determine the vibratory density of states in a quasi-harmonic solid

In a new and realistic conception of solids, an analytical approach is presented to find the phonon density of states in a quasi-harmonic one-dimensional solid by starting from the fact that a solid with strong interatomic forces can be regarded as an atomic array of quantum anharmonic oscillators under a Morse potential. In fact, our quasi-harmonic approximation is derived by assuming a large enough solid with an involved anharmonic parameter as a sufficiently small quantity. In this context, a mathematical relationship between the above parameter and the matrix element relative to oscillator’s strength is obtained.     

Anharmonic effects and the lattice dynamics of insulators

Anharmonic effects manifest themselves in everyday properties of solids. Two of the more obvious examples are thermal expansion and heat conductivity. More sophisticated examples anharmonicity are provided by the direct measurement of the lifetimes and of the pressure and temperature dependence of modes of vibration solids by infrared, Raman, Brillouin, or neutron spectroscopy. The present article reviews current status of the theory of anharmonic effects in insulators. We will draw our examples almost exclusively from the simplest insulators, namely the fcc rare gas solids (RGS) and alkali-halides (AH) mostly of the rocksalt structure. Much what we have to say is applicable to other kinds solids also, but we shall not dwell on this aspect. We shall arbitrarily exclude perhaps the two most interesting classes of anharmonic solids, that ferroelectrics and quantum solids. These subjects are sufficiently developed as to warrant reviews their own and it would be impossible to do them justice in the space avdable here. No mention will be made of the vast subject of impurity modes which especially in the case of alkali-halides has developed into an autonomous branch of solidstate physics. For similar reasons we have chosen to exclude thermal conductivity attenuation sound and second sound. We are then left with what we feel to be a more manageable task reviewing the basic anharmonic properties of the simplest classes of perfect insulators. Our selection of material reflects our own biased and peculiar interests. Examples wdl be illustrative rather than exhaustive. Previous reviews and basic articles dealing with anharmonic effects are listed separately in the references at the end of this article.     

Pinning mode resonances of new phases of 2D electron systems in high magnetic fields

A striking rf or microwave resonance is a generic feature of electron solid phases of two-dimensional electron systems. These resonances have served to identify and characterize such solids, in the insulator that terminates the series of fractional quantum Hall effects at high magnetic field, in the range of the integer quantum Hall effect, and in bubble phases in the first excited and higher Landau levels.     

The effect of 3-body forces and anharmonicity on the phonon spectrum of solid argon

The phonon spectra of solidified argon have been computed by a phenomenological rigid-atom-model. This model, which takes the constituent atoms as rigid-hard spheres, assumes that the potential energy of the solid is the sum of central and non-central interactions, and derives the same from the Buckingham-Corner potential function together with the Axilrod-Teller interaction term. The zero-point quantum and anharmonic effects, have been included. The effect of many-body forces as well as anharmonicity on the frequency spectrum and the lattice heat capacities of the solid is seen to be appreciable. The agreement between theoretical and the experimental results is not very satisfactory.     

Dependence of limited radiative recombination rate of InGaN-based light-emitting diode on lattice temperature with high injection

It is observed that the radiative recombination rate in InGaN-based light-emitting diode decreases with lattice temperature increasing.The effect of lattice temperature on the radiative recombination rate tends to be stable at high injection.Thus,there should be an upper limit for the radiative recombination rate in the quantum well with the carrier concentration increasing,even under the same lattice temperature.A modified and easily used ABC-model is proposed.It describes that the slope of the radiative recombination rate gradually decreases to zero,and further reaches a negative value in a small range of lattice temperature increasing.These provide a new insight into understanding the dependence of the radiative recombination rate on lattice temperature and carrier concentration in InGaN-based light-emitting diode.     

传感器电解质材料热膨胀性能和热稳定性变化规律研究

以ZrO2固体电解质材料为例,研究氧传感器电解质材料原子振动特点和热膨胀系数及其热稳定性随温度和时间的变化规律,探讨原子非简谐振动的影响。结果表明：原子振动的频率、阻尼系数,在简谐近似下为常数,在考虑到非简谐效应后随温度升高而增大;原子平均位移和热膨胀系数在简谐近似下为零,在考虑到非简谐效应后随温度升高而增大,随的时间的增长而减小;热膨胀性能稳定性温度系数随温度的升高而减小,随时间的增长而增大,即使用时间越长,材料的热膨胀性能稳定性越低;温度越高,热膨胀性能越稳定;非简谐情况下的原子振动的频率、阻尼系数和热膨胀系数与简谐近似下的差值随温度的升高而增大,即温度越高,非简谐效应越显著。     

Inside a quantum solid

A quantum solid is intrinsically 'restless', in the sense that atoms continuously vibrate about their position and exchange places even at the absolute zero of temperature. The archetypal quantum solid is low density solid helium. This paper describes some recent experiments done on solid He which illuminate the distinction of a quantum solid from a classical one, and relate some of these properties to new theoretical predictions.     

Analytic study of a sequence of path integral approximations for simple quantum systems at low temperature

The sequence of Feynman-Trotter approximations to the thermal Feynman path integral for the simple harmonic oscillator is obtained in an easily analyzable closed form. While it converges pointwise at every non-zero temperature to the quantum thermal propagator, the sequence manifests a highly non-uniform behaviour in the zero temperature limit—every one of its elements tends toward theclassical ground state (static equilibrium). For high order elements of the sequence, there is an abrupt “collapse” from the quantum to the classical ground state with falling temperature, a phenomenon which bears a possibly misleading resemblance to a phase transition. It is shown that Feynman-Trotter sequences for many simple systems other than the harmonic oscillator also have all their elements tending to the classical static equilibrium state in the zero temperature limit.     

Possible manifestations of quantum effects in the boron microindentation kinetics

The kinetics of indentation of a solid (viz., the dependence of the indenter intrusion depth on the time, force, and temperature), is analyzed theoretically taking into account quantum effects in the atomic dynamics of solids. The experimental study of the temperature dependence of the boron microhardness reveals qualitative and quantitative agreement with calculated dependences. A possible manifestation of quantum (tunnel) effects in the boron microindentation kinetics is predicted.     

Time dependent local field distribution and metastable states in the SK-spin-glass

Different sets of metastable states can be reached in glassy systems below some transition temperature depending on initial conditions and details of the dynamics. This is investigated for the Sherrington-Kirkpatrick spin glass model with long ranged interactions. In particular, the time dependent local field distribution and energy are calculated for zero temperature. This is done for a system quenched to zero temperature, slow cooling or simulated annealing, a greedy algorithm and repeated tapping. Results are obtained from Monte-Carlo simulations and a Master-Fokker-Planck approach. A comparison with replica symmetry broken theory, evaluated in high orders, shows that the energies obtained via dynamics are higher than the ground state energy of replica theory. Tapping and simulated annealing yield on the other hand results which are very close to the ground state energy. The local field distribution tends to zero for small fields. This is in contrast to the Edwards flat measure hypothesis. The distribution of energies obtained for different tapping strengths does again not follow the canonical form proposed by Edwards.