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.     

Anharmonic effects in crystals with vacancies

On the basis of the dynamic model proposed in [1] for a crystal with vacancies, the following are calculated: the contribution of anharmonic lattice oscillations at high temperatures, the elastic modulus and the thermal expansion coefficient as functions of the temperature and the vacancy concentration.     

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。     

纤锌矿GaN外延层薄膜热膨胀行为的变温Raman散射研究

本文对纤锌矿结构GaN外延层薄膜的热膨胀行为进行了研究,结合热膨胀系数的物理意义与变温Raman散射时声子频移的变化规律,研究了热膨胀系数与变温Raman散射之间的关系.结果表明:通过测量Raman声子E_2(high),A_1(TO)和E_1(TO)频移与温度之间的线性关系,结合相应声子Gruneisen参数的涵义,可对纤锌矿结构GaN外延层薄膜在一定温度范围内的热膨胀系数进行测量.本文提供了一种表征纤锌矿结构GaN外延层薄膜热膨胀行为的有效方法,为进一步研究III族氮化物外延层薄膜在生长过程中热膨胀系数的匹配、降低外延层薄膜中的位错密度并提高发光二极管的发光效率提供了理论依据.     

High-temperature thermodynamics of silver:Semi-empirical approach

We report high-temperature thermodynamics for fcc silver by combining ab initio phonon dynamics to empirical quadratic temperature-dependent term for anharmonic part of Helmholtz free energy. The electronic free energy is added through an interpolation scheme, which connects ambient condition free electron gas model to Thomas-Fermi results.The present study shows good agreement with experimental and reported findings for several thermal properties, and the discrepancy observed in some caloric properties is addressed. The decreases in the product of volume thermal expansion coefficient and isothermal bulk modulus and in the constant volume anharmonic lattice specific heat at high temperature are the clear evidences of proper account of anharmonicity. The present study also reveals that T~2-dependent anharmonic free energy is sufficient for correct evaluation of thermal pressure and conventional Grüneisen parameter. We observe that the intrinsic phonon anharmonicity starts dominating above characteristic temperature, which is attributed to higher order anharmonicity and can be related to higher order potential derivatives. We conclude that the uncorrelated and largeamplitude lattice vibrations at high temperature raise dominating intrinsic thermal stress mechanism, which surpasses the phonon-anharmonism and requires future consideration.     

Energy of the elastic loading of anharmonic solids

This paper reports on the results of measurements of changes in the temperature of a solid under the adiabatic elastic loading (thermoelastic effect), the coefficient of thermal expansion, and the Young’s modulus of a rigid-chain vitrified polymer, namely, polyimide. It has been found that there are differences in the sign and magnitude of the changes in the energy of thermal origin in samples and the work of the external force. The energy of the thermoelastic effect has been explained in terms of the influence exerted by the anharmonic expansion of a solid, with the separation of the quasi-static potential and dynamic components of the thermal energy of the solid. The loading with an external force causes a redistribution of the thermal energy. A change in the temperature of the solid corresponds to a change in the dynamic component. An energy analysis of the adiabatically loaded anharmonic oscillator has confirmed the conclusion regarding the mechanism of energy transfer and revealed that, under loading, there is a redistribution of the kinetic and potential components of the internal energy of the oscillator.     

Temperature and layer number dependence of the G and 2D phonon energy and damping in graphene

We have studied the temperature and size dependence of the G and 2D phonon modes in graphene. It is shown that in a graphene monolayer the phonon energy decreases whereas the phonon damping increases with increasing temperature. The electron-phonon interaction leads to hardening whereas the fourth-order anharmonic phonon-phonon processes lead to softening of the phonon energy with increasing temperature. We have shown that the electron-phonon interaction plays an important role also by the dispersion dependence of the phonon G mode, by the observation of the Kohn anomaly. The G mode frequency decreases and damping increases, whereas the 2D phonon frequency and damping increase with increasing layer number. The temperature and size effects of the 2D mode are much stronger than those of the G mode.     

Thermal expansion and lattice dynamics under pressure of ZnS,ZnSe and ZnTe

The thermal expansion against temperature of ZnS, ZnSe and ZnTe is studied theoretically using the experimental pressure dependence of elastic stiffness constants and phonon frequencies. The mode Grüneisen parameters obtained from the high pressure effect on the one- and two- phonon Raman spectra at the metallic transition pressure by Weinstein are used originally, but do not reproduce the experimental linear expansion coefficient at high temperatures. The contributions from optical modes with large phonon frequency are important to the thermal expansion at high temperatures, and a set of mode Grüneisen parameters, which bring good agreement with the observed linear expansion coefficient not only at low temperatures, but also at high temperatures, are obtained. Then, the phonon dispersion curves of ZnS, ZnSe and ZnTe at their metallic transition pressures are quantitatively shown.     

Lattice dynamics,third order elastic constants and thermal expansion of Cadmium

The lattice dynamics, second and third order elastic constants, pressure derivatives of the second order elastic constants and the temperature variation of the lattice thermal expansion of Cadmium have been worked out utilising Keating's approach. The ten TOE constants are calculated using four anharmonic parameters. The model used here reproduces the measured pressure derivatives of the SOE constants of Cadmium extremely well. The low temperature limit of the volume Gruneisen function γ_L is found to be nearer to the value of Andres. The high temperature limit γ_v(T) is in good agreement with the value calculated by Gschneidner Jr. from the Cv data for Cadmium. The lattice dynamics of Cadmium is found to be essentially similar to that of Zinc.     

非简谐振动对石墨烯杨氏模量与声子频率的影响

在哈里森键联轨道法框架下, 考虑到原子的短程相互作用和原子的非简谐振动, 应用固体物理理论和方法, 得到了石墨烯的力常数、杨氏模量、扭曲模量、泊松系数以及声子频率随温度的变化关系, 探讨了非简谐振动对它们的影响. 结果表明: 1)杨氏模量与声子频率等随温度变化并遵从一定的规律, 其中力常数、杨氏模量、扭曲模量随温度升高而增大, 但变化较小; 声子频率随温度升高而增大但变化较快; 泊松系数随温度升高而较快地减小; 2)石墨烯原子具有沿键长方向的纵振动和垂直键长方向的横振动, 但以纵振动为主, 纵振动的非简谐效应远大于横振动, 横振动的简谐系数ε₀' 和第二非谐系数ε₂' 均小于纵振动的相应值ε₀,ε₂; 比值为ε₀/ε₀' ≈ 8.477,ε₂/ε₂' ≈ 156; 3)若不考虑非简谐振动项, 则石墨烯的力常数、杨氏模量和扭曲模量、泊松系数、声子频率均为常量, 与实验不符合; 同时考虑到原子的第一、二非简谐振动项后, 它们均随温度升高而变化, 而且温度愈高, 原子振动的非简谐效应愈显著. 本文的结果与文献的实验结果符合较好.     

The thermal expansion of GaP below room temperature

The thermal expansion of GaP is estimated theoretically as a function of temperature using the experimental pressure dependence of elastic stiffness constants and phonon frequencies. The numerical values of the linear expansion coefficient and the Grüneisen constant do not become negative at low temperatures, contrary to other tetrahedrally bonded covalent solids. This positive thermal expansion of GaP at low temperatures is closely connected with the small values of the transverse acoustical mode Grüneisen parameter and with the large value of the metallic phase transition pressure from the linear correlation obtained by Weinstein.     

硅纳米晶体薄膜热膨胀性质的分子动力学研究

基于Stillinger-Weber势对硅纳米晶体薄膜的热膨胀性质进行了分子动力学模拟。研究表明,硅纳米晶体薄膜表面层原子的二聚现象引起薄膜收缩,而原子之间的非和谐势能引起薄膜膨胀;在约400K以下的低温段,由于硅纳米晶体薄膜表面层原子发生二聚的原子数目随温度的升高而明显增多,而原子间非和谐势能很小,故此时二聚主导热膨胀性质,热膨胀系数为负;在高温段（约400K以上）,由于发生二聚的原子数目随温度升高不再显著地增加并渐趋于稳定,而原子间非和谐势能逐渐显著并主导热膨胀性质,故热膨胀系数为正。     

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...     

Effects of surface charges on phonon properties and thermal conductivity in GaN nanofilms

Surface charges can modify the elastic modulus of nanostructure, leading to the change of the phonon and thermal properties in semiconductor nanostructure. In this work, the influence of surface charges on the phonon properties and phonon thermal conductivity of GaN nanofilm are quantitatively investigated. In the framework of continuum mechanics,the modified elastic modulus can be derived for the nanofilm with surface charges. The elastic model is presented to analyze the phonon properties such as the phonon dispersion relation, phonon group velocity, density of states of phonons in nanofilm with the surface charges. The phonon thermal conductivity of nanofilm can be obtained by considering surface charges. The simulation results demonstrate that surface charges can significantly change the phonon properties and thermal conductivity in a GaN nanofilm. Positive surface charges reduce the phonon energy and phonon group velocity but increase the density of states of phonons. The surface charges can change the size and temperature dependence of phonon thermal conductivity of GaN nanofilm. Based on these theoretical results, one can adjust the phonon properties and temperature/size dependent thermal conductivity in GaN nanofilm by changing the surface charges.     

Structural relationship between negative thermal expansion and quartic anharmonicity of cubic ScF3

Cubic scandium trifluoride (ScF3) has a large negative thermal expansion over a wide range of temperatures. Inelastic neutron scattering experiments were performed to study the temperature dependence of the lattice dynamics of ScF3 from 7 to 750 K. The measured phonon densities of states show a large anharmonic contribution with a thermal stiffening of modes around 25 meV. Phonon calculations with first-principles methods identified the individual modes in the densities of states, and frozen phonon calculations showed that some of the modes with motions of F atoms transverse to their bond direction behave as quantum quartic oscillators. The quartic potential originates from harmonic interatomic forces in the DO9 structure of ScF3, and accounts for phonon stiffening with the temperature and a significant part of the negative thermal expansion.     

CaS电子结构和热力学性质的第一性原理计算

根据密度泛函理论,采用平面波赝势和广义梯度方法,计算了Ca S的晶体结构和电子结构.通过准谐徳拜模型预测了硫化钙的体积变化率、体弹模量、热膨胀系数分别与温度和压强的变化关系,以及热容和温度的变化关系.     

功能化石墨烯改性聚乙烯热力学特性的分子动力学模拟

聚乙烯绝缘材料在我国高压电缆中有着广泛的应用,为了提高其耐热稳定性和力学性能,利用石墨烯对聚乙烯进行掺杂改性,并基于分子动力学模拟的研究方法分别建立了低密度聚乙烯（LDPE）、石墨烯和3种官能团接枝石墨烯掺杂聚乙烯的复合模型。研究表明,相比石墨烯直接掺杂聚乙烯,羧基（-COOH）、氨基(-NH2)和羟基(-OH)接枝石墨烯能够更加有效地提高聚乙烯的玻璃化温度（分别提高了16k、7k、5k）、减弱聚乙烯分子链的移动和降低聚乙烯的热膨胀系数、均方位移(MSD),从而使得聚乙烯复合体系的热学性能得到了有效增强;此外发现石墨烯的掺杂能够提高复合模型的力学模量,其中官能团接枝石墨烯改进效果更明显,室温下弹性模量和剪切模量的提升幅度由不接枝的33.98%、36.18%,提升到了44%和42.89%（羧基功能化体系）。研究结果可为聚乙烯绝缘材料的热老化抑制和力学性能的改善提供有益的参考。     

Thermodynamics and elastic properties of Ta from first-principles calculations

<正>Within the framework of the quasiharmonic approximation,the thermodynamics and elastic properties of Ta, including phonon density of states(DOS),equation of state,linear thermal expansion coefficient,entropy,enthalpy, heat capacity,elastic constants,bulk modulus,shear modulus,Young’s modulus,microhardness,and sound velocity, are studied using the first-principles projector-augmented wave method.The vibrational contribution to Helmholtz free energy is evaluated from the first-principles phonon DOS and the Debye model.The thermal electronic contribution to Helmholtz free energy is estimated from the integration over the electronic DOS.By comparing the experimental results with the calculation results from the first-principles and the Debye model,it is found that the thermodynamic properties of Ta are depicted well by the first-principles.The elastic properties of Ta from the first-principles are consistent with the available experimental data.     

First-principles calculations of elastic,phonon and thermodynamic properties of W

We investigate the elastic properties, lattice dynamical, thermal equation of state and thermodynamic properties of bcc phase W under high pressure using density functional theory. The calculated high-pressure elastic constants of bcc phase W agree well with experimental and theoretical data. Under compression, the phonon dispersion curves of bcc phase W do not show any anomaly or instability. Our calculated zero-pressure phonon dispersion curves are in excellent agreement with experiments. Within the quasiharmonic approximation, we predict the thermal equation of state and other properties including the thermal expansion coefficient, adiabatic bulk modulus, specific heat at constant volume and entropy.