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.     

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     

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.     

Four constant potential function of amorphous selenium and evaluation of its thermodynamic and acoustic properties

Litov and Anderson after various considerations suggested a four constant potential function for a-Se as well as a-As₂S₃. Hence we also used a four constant potential function with the sole purpose of applying this potential function to obtain several acoustic, thermodynamic and other properties. We calculated several acoustic properties of a-Se like second order elastic constants (SOECs), their pressure derivatives, the longitudinal and transverse Grüneisen constant by two different methods, phonon frequencies, absorption band position through the use of Nath-Smith-Delaunay’s equation, and the thermodynamic properties like heat capacity, bulk modulus, thermal Grüneisen constant, the pressure derivative of the bulk modulus (dK _T/dP=C ₁), the pressure derivative ofC ₁ which is related to Anderson-Grüneisen parameter, pressure derivative of Grüneisen constant namelyγ′ _g which is related to second Grüneisen constant, characteristics of phonon frequencies, potential energy function through the use of fitted parameters and third order elastic constants. Finally we calculatedK _T at the reduced density ofρ/ρ ₀=1.1.K _T is obtained from the potential function with the fitted parameters. In all the above cases the calculated values are found to be in good agreement with experiment wherever available. In this connection it is important to point out that we eliminated ‘C’ a constant in the potential function using the equilibrium condition as was done by Litovet al in a-Se and Gerlichet al in the case of a-As₂S₃ as all amorphous substances are isotropic as mentioned by several authors. We contemplate to calculate several other properties for a-Se and a-As₂S₃ and present them at a later stage.     

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.     

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.     

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     

KH2PO4和(CH3NHCH2COOH)CaCl2在高压下的状态方程与相变

 在活塞圆筒式p-V关系测量装置上，研究了KH₂PO₄（KDP）和(CH₃NHCH₂COOH)CaCl₂［Tris-sarcosine calcium chloride（TSCC）］在室温下、4.5 GPa内的p-V关系。实验结果表明：KDP在2.1 GPa左右有一个相变；TSCC在0.8 GPa和3.2 GPa左右各有一个相变。本工作还给出了它们在相变前后的状态方程，以及它们的格临爱森参数γ₀、体积模量B₀和B₀的压力导数B₀'。     

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.     

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.     

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.     

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.     

The thermodynamics of elastic deformation—I: Equation of state for solids

The isobaric and isothermal volume derivatives of In B, In μ and In μ' are investigated, where B, μ and μ' are the isothermal bulk modulus and the two shear moduli, respectively, of a cubic crystal. In the case of the bulk modulus, the temperature independence of αB (where α is the volume thermal expansion) for a large number of materials, ensures that the derivatives are constant and approximately equal, while for the shear moduli, evidence is advanced that the isothermal derivatives are constant along an isotherm, but not along an isobar except at high temperatures near the melting point. The relationships satisfied by the bulk modulus enable the explicit temperature and pressure dependence of the molar volume, V, thermal expansion, and bulk modulus to be determined. The most adequate representation of the volume dependence of the Grüneisen parameter, γ, appears to be that γ/V is independent of volume between the Debye and melting temperatures.     

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)。     

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。