Generalized Grüneisen parameters and low temperature limit of lattice thermal expansion of cadmium and zirconium

The generalized Grüneisen parameters (γ′ _j ) and (γ″ _j ) for cadmium and zirconium were calculated from the second- and third-order elastic constants to determine the low temperature limit of the volume thermal expansion of these metals of hexagonal symmetry. The low temperature limit of cadmium and zirconium was calculated to be positive values indicating a positive volume expansion down to 0 K even though many Grüneisen gammas were found to be negative.     

Grüneisen系数与铝的高温高压状态方程

基于Gray金属三相状态方程模型,分别采用ργ=常数,Gray,GRIZZLY的Grüneisen系数模型和从头算给出的Grüneisen系数,系统计算了铝的熔化曲线、等熵压缩线、等温压缩线和等熵卸载线,计算结果与实验数据比较表明;在冲击压力约为500GPa的宽广压力范围,GRIZZLY Grüneisen系数模型是最适合描述铝的热力学特性的形式,ργ=常数模型次之,在高压区,Gray和从头算的Grüneisen系数的计算结果与实验值差距较大. 关键词： Grneisen系数 状态方程 铝     

室温下金属中电子格林艾森常数的测量

在室温条件下用自己研制的超快电子衍射实验设备精确测量了金属铝的电子格林艾森常数(γ_e).当飞秒脉冲激光瞬间加热铝膜时,电子和晶格对固体热膨胀的作用在时间域上是不同步的,借助于超快电子衍射实验设备的高时间分辨能力,可以摆脱以往测量非磁性金属材料时低温的限制,在室温条件下,实验通过直接观测瞬间加热的铝膜中电子和晶格对热膨胀的不同贡献得到电子的格林艾森常数. 关键词： 格林艾森常数 超快电子衍射 晶格热运动 电子热运动     

New constraints on gruneisen parameters applications to equations of state for pressure markers

Abstract

“Regular” linear relations between shock and particle velocities, u_s = u_s0, + c · u_p, imply a divergence of the Hugoniot pressure p_H at a critical compression V _c/V _o = (c-1)/c, where the thermal pressure Δp _th = (γ/V)· ΔU _th = p _H-p _T becomes very large with respect to the cold (isothermal) pressure p _T at this compression. The Hugoniot relation for the total internal energy U _H results in this case in the relation γ_c = 2(c- 1) for the Grüneisen parameter in this region. Experimental data for the zero pressure value Γ_o and its derivative Γ_o together with theoretical data for the limiting value γ_∞ = 2/3, and the additional expenmental value γ_c are then used to determine the thermal (phonon) pressure with the common Mie-Grüneisen assumption.     

Interatomic forces,Grüneisen and Anderson-Grüneisen parameters of ionic crystals

The general expression for the Anderson-Grüneisen parameterδ recently derived by Gupta and others, has been used to study the variation ofδ with the Grüneisen parameterγ employing the interaction approach. For this purpose four potential energy functions have been selected. It is found thatδ values evaluated by the modified Varshni-Shukla potential are better than other forms of overlap repulsive interaction. The variation ofδ withγ is also studied by plotting curves betweenδ andγ. The method of least-squares has been employed to yield the best fitted equation.     

X-ray determination of thermal expansion of cadmium fluoride and lead fluoride

The lattice parameters of CdF₂ andβ-PbF₂ have been determined over the temperature range 300–670 K. The coefficient of expansion at room temperature is 21·3 × 10⁻⁶ K⁻¹ and 25·4 × 10⁻⁶ K⁻¹ for CdF₂ and PbF₂ respectively and it increases linearly with temperature over the range of temperature covered. The Grüneisen parameter decreases with temperature in both the crystals.     

Anderson–Grüneisen parameter for lower mantle region of the Earth under adiabatic condition

A revised model of volume dependence of Anderson–Grüneisen parameter for lower mantle under adiabatic condition is presented in this study, and the volume dependence of (α T/C _P =α ′) is then discussed. It is shown that the results are in good agreement with seismic data of the Earth.     

Coupled temperature dependences of volume and compressibility

We present a new method for understanding the changes with temperature of the volume and compressibility of solids. These changes depend on five parameters: V ₀, B ₀, Θ, γ _G and δ _T. V ₀ and B ₀ are the atomic volume and bulk modulus at T?=?0?K, Θ is the Debye temperature, γ _G is the Grüneisen parameter, and δ _T is the Anderson–Grüneisen parameter. Equations for the temperature-dependent volume, bulk modulus and thermal expansion are given, and examples of the use of these equations are provided, with particular emphasis on the light actinides. For the elements, we examine the relationship between experimental values of γ _G and δ _T, and find no clear correlation. In particular, Swenson's rule, which states that the bulk modulus does not change with temperature if the volume is held constant, is a poor approximation to the data. We reveal a new useful approximate relationship between dB/dP and γ _G. We find that the thermodynamic quantity q, which describes the variation in γ _G with volume, distributes around 2, not around 1, as often assumed. We show that the thermal- expansion behavior of Si and Ge (including negative thermal expansion at low temperatures) are well described with the use of a two-level invar model.     

Grüneisen parameter for HCP iron at extreme compression

The Thomas–Fermi approximation gives the Grüneisen parameter γ=γ_∞=1/2 for all materials at extreme compression (P→∞ or V→0). After re-analyzing the existing experimental data of volume dependence of Grüneisen parameter γ of hexagonal close-packed (HCP) iron, we find that γ=1/2+a(V/V ₀)^1/3+b(V/V ₀) ⁿ , where a, b and n are constants. Based on this new form of γ, the second Grüneisen parameter q, the Debye temperature θ_D and the shear sound velocity v _s of HCP iron are discussed in the present work. It is found that the zero pressure second Grüneisen parameter q ₀=0.654, which is consistent with the previously determined value of HCP iron for Earth's core physics from Dubrovinsky et al. The calculations for the Debye temperature and the shear sound velocity are also found to be in good agreement with the experimental data.     

Equations of state of MgO,Au, Pt,NaCl-B1, and NaCl-B2: Internally consistent high-temperature pressure scales

Semiempirical equations of state (EoS) of Au, Pt, MgO, NaCl-B1, and NaCl-B2 based on expanded Mie–Grüneisen–Debye approach, which are consistent both with the Mie–Grüneisen–Bose–Einstein approach and the thermochemical, X-ray, ultrasonic and shock-wave data in a wide pressure-temperature range, have been constructed. It is shown that to determine the volume dependence of the Grüneisen parameter, not only shock-wave and static compression data, but also experimental information on heat capacity, bulk moduli, volume, and thermal expansion coefficient at zero pressure need to be taken into account. Intrinsic anharmonicity is of great importance at construction of EoS at high temperatures and x=V/V ₀>1. Cross-comparison of the current equations of state with independent measurements shows that these EoS may be used as the internally consistent and independent pressure scales in a wide range of temperatures and pressures.     

高压下铝的Grüneisen参数的实验测量

 采取突然加压的方法，测量在施压过程中产生的温度变化，从而直接决定物质的格留乃森（Grüneisen）参数。第一次在固体传压介质中进行该种实验，并在高达3.5 GPa的压力范围内，直接测量了铝的格留乃森参数随压力的变化。     

Relationship between the molecular constant,isothermal volume derivative of thermodynamic Grüneisen parameter,nonlinearity parameter and intermolecular forces in liquids

The isochoric temperature derivative of sound velocity, Beyer’s nonlinearity parameter, the isothermal volume derivatives of thermodynamic Grüneisen parameter and isochoric heat capacity and the repulsive exponent of intermolecular potential are shown to be related to the molecular constant representing the ratio of internal pressure to cohesive pressure of liquids. The calculated values are reasonably satisfactory and explain the experimental results on sound propagation data of liquids. The results have been used to develop further understanding of the significance of molecular constant, fractional free volume and repulsive exponent of intermolecular potential in describing various thermoacoustic and nonlinear properties and the anharmonic behaviour with regard to molecular order and intermolecular interactions in liquids.     

Liquid fluorine properties by the hardsphere model with attractive interactions

We test the validity of an approximate equation of state of real fluids and the expression for surface tension of hardsphere liquids with attractive interactions derived by Sharma and others by obtaining expressions for isothermal compressibility,C ₁-parameter and acoustical parameter and relate them to microscopic Grüneisen parameter. The calculated values for liquid fluorine show fair agreement with experimental values.     

Pressure and volume dependence of thelo-to phonons in InAs

The pressure dependence of thelo-to phonons in InAs has been investigated by Raman scattering using the diamond anvil cell. Indium arsenide transforms, presumably to the rock-salt structure at 70±1 kbar. The mode Grüneisen parameters for thelo-to phonons are γ _lo =0.99±0.03, γ _to =1.2±0.03 respectively. The effective charge,e* _T , for InAs decreases slightly with pressure and this trend is in accordance with the behaviour of other III–V zinc blende structured semiconductors: The structural phase transition is discussed in the light of theoretical calculations for phase stability of III–V compounds, as well as recent high pressure x-ray diffraction studies.     

高压熔化曲线的实验标定

 利用Al、Cu、Pb的冲击熔化实验结果,并考虑到材料的Grüneisen系数γ(ρ)从固态值向液态值过渡,通过Lindemann熔化定律标定了熔化曲线T_m(ρ)。由于Lindemann定律与Grüneisen系数γ(ρ)密切相关,因此用冲击熔化实验标定T_m(ρ),也间接标定了γ(ρ)。     

无氧铜等熵卸载路径的实验研究

 采用化爆加载,以黄铜为飞片、无氧铜为靶板,测量了以抗氢钢（HR2）、重玻璃（SiO₂）、铝合金（LY12/LF6）、镁铝合金（MB2）、有机玻璃（PMMA）和空气（Air）为垫块（Anvil）材料中的冲击波速度（上述材料的Hugoniot状态参数C₀、λ均为已知）,由此确定了无氧铜的等熵卸载路径。结果表明：在冲击态（即初始卸载态）高达219 GPa的压力范围内,无氧铜的等熵卸载过程可用Grüneisen状态方程在ργ=ρ₀γ₀近似下作很好的描述;各条卸载路径到一个大气压的终态粒子速度U_S与镜像反演的粒子速度2u的偏差(U_S-2u)/(2u),随冲击波压力的增加而增大。     

Mechanical properties,lattice thermal conductivity,infrared and Raman spectrum of the fullerite C24

Lightweight carbon materials with excellent thermal and mechanical properties have important applications in aerospace industry. In this study, the stability, mechanical properties, lattice thermal conductivity, electronic structure, infrared and Raman spectrum of sp³ hybridized low-density fullerite C₂₄ were investigated according to density functional theory (DFT) calculations. It was found that the fullerite C₂₄ was both thermodynamic and dynamic stable. Quasi-harmonic approximation and Grüneisen parameter calculations clarified why the fullerite C₂₄ had a positive thermal expansion coefficient at low temperature. The fullerite C₂₄ also exhibited excellent mechanical properties. Interestingly, the Vickers hardness of carbon allotropes was found to almost be linear proportional to the density of a carbon material. HSE06 electronic structure calculations showed that it was a semiconductor with direct bandgap of 2.56 eV. Anharmonic lattice dynamic calculations showed that its thermal conductivity was higher than semiconductor silicon. Besides, Raman and infrared active modes as well as the corresponding spectra were presented.     

KBrO3在高压下拉曼光谱和结构的研究

利用原位高压拉曼散射和X射线衍射技术,研究了KBrO3在高压下晶格振动和晶体结构演化行为.最高压力达30.9 GPa.通过拉曼光谱发现,在高压下拉曼峰位除了单调移动,没有其它变化,表明KBrO3在研究的压力范围没有发生相变.原位高压X射线衍射实验数据显示,其在高压下依然保持常压的六方结构.通过进一步分析,分别得到了体弹模量B0=25.9(2) GPa(B′0=5.68(0.38))和部分拉曼峰的Grüneisen参数.     

Volume variation of nuclear Grüneisen parameter for equation of state studies

The method of first principle pseudopotential is used to simulate the volume variation of nuclear Grüneisen parameter. The elements Al and Be, for which Neal’s experimental data exist are investigated. The nuclear Grüneisen obtained from the details of phonon frequencies are in better agreement with the experimental data as compared to those obtained from approximate Slater and Dugdale-MacDonald methods, often used in shock wave studies.