Shear modulus of shock-compressed LY12 aluminium up to melting point

Asymmetric plate impact experiments are conducted on LY12 aluminium alloy in a pressure range of 85--131\,GPa. The longitudinal sound speeds are obtained from the time-resolved particle speed profiles of the specimen measured with Velocity Interferometer System for Any Reflector (VISAR) technique, and they are shown to be good agreement with our previously reported data of this alloy in a pressure range of 20--70\,GPa, and also with those of 2024 aluminium reported by McQueen. Using all of the longitudinal speeds and the corresponding bulk speeds calculated from the Gruneisen equation of state (EOS), shear moduli of LY12 aluminium alloy are obtained. A comparison of the shear moduli in the solid phase region with those estimated from the Steinberg model demonstrate that the latter are systematically lower than the measurements. By re-analysing the pressure effect on the shear modulus, a modified equation is proposed, in which the pressure term of $P/\eta^{1/3}$ in the Steinberg model is replaced by a linear term. Good agreement between experiments and the modified equation is obtained, which implies that the shear modulus of LY12 aluminium varies linearly both with pressure and with temperature throughout the whole solid phase region. On the other hand, shear modulus of aluminium in a solid-liquid mixed phrase region decreases gradually and smoothly, a feature that is very different from the drastic dropping at the melting point under static conditions.     

静高压加载下LY12铝的超声测量与等温状态方程

 利用“脉冲回波重合法”测量了多晶LY12铝在流体静压加载下的纵波与横波声速随压力的变化。并根据较低压力（<0.5 GPa）下的超声测量数据所确定的零压弹性模量及其对压力的偏导数,导出了LY12铝的Murnaghan、Birch-Murnaghan、Vinet三种不同形式的等温状态方程,发现由超声测量数据导出的Vinet 状态方程能很好地描述面心立方（fcc）结构的铝与铝合金在较高压力（约200 GPa）下的压缩特性。此外,由超声数据计算了LY12铝在室温常压条件下的Debye温度为430.97 K、热力学Grüneisen系数为2.025、平均声模Grüneisen系数为2 379。     

Prediction of Pressure-Induced Structural Transition and Mechanical Properties of Mg Y from First-Principles Calculations

Using the particle swarm optimization algorithm on crystal structure prediction,we first predict that Mg Y alloy undergoes a first-order phase transition from Cs Cl phase to P4/NMM phase at about 55 GPa with a small volume collapse of 2.63%.The dynamical stability of P4/NMM phase at 55 GPa is evaluated by the phonon spectrum calculation and the electronic structure is discussed.The elastic constants are calculated,after which the bulk moduli,shear moduli,Young's modui,and Debye temperature are derived.The brittleness/ductile behavior,and anisotropy of two phases under pressure are discussed in details.Our results show that external pressure can change the brittle behavior to ductile at10 GPa for Cs Cl phase and improve the ductility of Mg Y alloy.As pressure increases,the elastic anisotropy in shear of Cs Cl phase decreases,while that of P4/NMM phase remains nearly constant.The elastic anisotropic constructions of the directional dependences of reciprocals of bulk modulus and Young's modulus are also calculated and discussed.     

Release Behaviour of Shock Loaded LY12 Aluminium Alloy

By making use of a light gas gun, a specially designed target is impacted by the LY12 flyer, and the pressure is taken in the range of 0.6-3 GPa. Based on the stress profiles measured in the buffer materials by manganese gauges, the Hugoniot curve and release curves of LY12 aluminium alloy are obtained. Meanwhile, the release curves from different initial shocked states are described in both the pressure-particle velocity plane and the pressure-specific volume plane.     

钨合金的超声测量及力学参量估算

 利用两面顶压机和六面顶压机作为压力装置，分别对93钨合金材料进行了高压超声测量。测得了93钨合金材料在常态下的横、纵波声速及在0~3 GPa压力范围内的纵波声速随压力的变化关系。测量结果为：在常温常压下，93钨合金的纵波声速为c_L＝5.135 km/s，横波声速为c_t＝2.987 km/s。纵波声速随压力变化的关系式为：c_L＝5.053+0.602p（GPa）。估算的93钨合金相关力学参量为：G＝157.4 GPa，E＝393.0 GPa，K＝260.2 GPa，λ＝155.3 GPa，μ＝157.4 GPa，ν＝0.248。经过对两种超声测量方法测量结果的比较及冲击波测量数据的验证，这些参数是可靠的。     

冲击波作用下铝的等效剪切模量

提出了冲击波作用下通过测量沿着准弹性卸载过程纵波波速与体波波速得到等效剪切模量的方法,应用该方法对LY12铝在20—70 GPa冲击压力下的等效剪切模量进行了测量.实验结果表明,等效剪切模量随应力线性减少直至反向屈服时为零,而初始卸载时的等效剪切模量可以由修正的Steinberg-Cochran-Guinan模型进行描述.应用得到的等效剪切模量进行了初步数值模拟,计算结果与实验测量的粒子速度剖面符合很好,重现了准弹性卸载到塑性卸载的光滑过渡. 关键词： 等效剪切模量 波速 准弹性卸载 冲击波 铝     

动高压下拉格朗日声速的测定及其应用

 通过实时记录冲击加载—再加载和冲击加载—卸载波的粒子速度剖面,得到了再加载和卸载波在93W合金中传播的拉格朗日声速。通过拉格朗日声速从准弹性到纯塑性的转化,获得了材料在一次冲击终态时的剪应力、剪切模量以及考虑了剪应力修正后的93W合金的冲击绝热关系。     

Elasticity of BaFCl single crystal under hydrostatic pressure

The sound velocities for longitudinal and transverse waves have been measured in single crystalline BaFCl at room temperature using ultrasonic pulse echo and Brillouin scattering techniques. The complete set of elastic constants is deduced and lead to the bulk moduli values of BaFCl at ambiant conditions (, , ) which are compared with those obtained by a shell model. Moreover, using the ultrasonic technique under pressure, the pressure derivatives of the second order elastic constants at 298 K have been determined up to 0.3 GPa. All moduli increase linearly with pressure in this pressure range, allowing to determine directly and separately the first derivative of the bulk modulus B'₀ = 5.8. These data are used to calculate a Murnaghan equation of state. A detailed comparison is given between our results with those recently obtained by X-ray diffraction on powder or calculated using the local density approximation method. Finally, the anisotropy of BaFCl under pressure is discussed. Received: 19 March 1998 / Revised: 15 May 1998 / Accepted: 19 May 1998     

Mechanical anisotropy and thermoacoustic properties of SnO2 under high pressures: an ab initio approach

The effects of hydrostatic pressures on the electronic, thermoacoustic and elastic anisotropies of SnO₂ in the rutile structure is analyzed up to 18 GPa. It is found that the polycrystalline bulk modulus B increases from 227 to 312 GPa between 0 and 18 GPa while the Young and shear moduli slightly decrease with pressures. The resulting polycrystalline ductility increases with pressures. The speed of the sound for longitudinal waves increases with pressure, while the transverse polarizations and the Debye temperature decrease. Large crystal anisotropy for the shear planes {001} between ? 110? and ? 010? directions under pressures, associated with the phase transition to the Cl₂Ca, is found.     

High-pressure radial X-ray diffraction study of osmium to 58 GPa

Nonhydrostatic compression behavior of osmium (Os) was investigated up to 58.2 GPa using radial X-ray diffraction (RXRD) together with lattice strain theory in a diamond-anvil cell. The apparent bulk modulus of Os derived from RXRD data varies from 262 GPa to 413 GPa, depending on Ψ, the orientation of the diffraction planes with respect to the loading axis. Fitting to the third-order Birch-Murnaghan equation of state, the RXRD data obtained at Ψ = 54.7° yields a bulk modulus K₀ = 390 ± 6 GPa with pressure derivative K^′ ₀ fixed at 4. The ratio of differential stress to shear modulus t/G ranges from 0.024 to 0.029 at the pressures of 15.7–58.2 GPa. The yield strength was observed to increase with compression and reach the value of 11.7 GPa at the highest pressure. This confirms that Os is the strongest known pure metallic material compared with the reported stiff elemental metals such as W, Mo and Re. It was found that the apparent c/a ratio changed with the nonhydrostatic compression, as well as the orientation Ψ in our experiments. Moreover, the aggregate moduli of Os at high pressure were determined from the RXRD measurements.     

Dual mode ultrasonic interferometry in multi-anvil high pressure apparatus using single-crystal olivine as the pressure standard

Acoustic measurements of compressional (P) and shear (S) wave travel times were performed in a 1000-ton uniaxial split-cylinder apparatus (USCA-1000) of the Kawai-type up to 10?GPa at room temperature, using dual mode lithium niobate transducers and ultrasonic interferometry. The cell pressures were calibrated continuously by in-situ measurements of the travel times in a single crystal San-Carlos olivine buffer rod inside the cell assembly. Elastic compressional and shear wave velocities in a dense, fine-grained polycrystalline Al₂O₃ were measured simultaneously to 10?GPa; from these data, the elastic moduli and their pressure derivatives were obtained for the longitudinal modulus {L ₀?=?461(3)?GPa, L ₀′?=?7.0(1)}, the shear modulus {G ₀?=?162(2)?GPa, G ₀′?=?1.9(1)} and the bulk modulus {K ₀?=?245(3)?GPa, K ₀′?=?4.5(1)}.     

低孔隙度疏松锡的高压声速与相变

为研究微孔洞对锡的高压相变的影响, 对含亚微米孔洞的疏松锡(疏松度m=1.01)进行了冲击加载-卸载实验. 利用DPS(Doppler pins system)测得了31.8-66.1 GPa冲击压力下疏松锡/LiF界面粒子的速度剖面, 获得了各压力下的纵波声速与体波声速, 给出了该疏松锡的冲击熔化起始压力约为49.1 GPa, 获得了各压力下的剪切模量与泊松比. 结合密实锡与疏松锡的高压纵波声速、体波声速与剪切模量, 界定密实锡的冲击熔化压力在53.5-62.3 GPa之间, 高于疏松锡的值, 表明微孔洞明显降低了冲击熔化压力. 对密实锡准确的冲击熔化压力值还需要进一步的实验数据. 测试的固态压力范围内的声速数据没有明显奇异点, 表明疏松锡没有类似密实锡的固态bcc 相变发生.     

MgCNi3超导体在静水压下的弹性性质

 在0.1 MPa到0.5 GPa压力范围内，采用脉冲回波重合法（Pulse-Echo Overlap Method）测量了MgCNi₃超导体的横波及纵波声速，计算了体弹模量B、剪切模量G等弹性参数以及德拜温度、比热等热力学参数随压力的变化。常压下的θ_D与c_V的值分别为454.82 K和111.30 J/(mol·K)。对B-p曲线作线性拟合，得到体弹模量B₀在零压附近的导数B′₀，由此建立了MgCNi₃的状态方程。     

一种计算剪切模量温度系数的方法

采用理论计算与动高压实验相结合的方法，提出了一个计算剪切模量温度系数G′T的新方法.首先用理论方法计算一个中间数据G(PS)，然后再与动高压实验数据G(PH)结合在一起计算出G′T,并针对93钨合金材料进行了计算.计算结果表明剪切模量温度系数G′T开始是随温度和压力变化的，但在高温高压下，它趋近于一常数.对于93钨合金，这个常数约为-004GPa／℃.同时，这也是对Steinberg本构模型中的剪切模量温度系数为常数的一个证明.并且，当把这一常数代入剪切模量温度系数的计算式中，将重新计算出的剪切模量与实验测得的剪切模量结果进行了比较，结果表明二者符合得很好，从而证明了本计算的剪切模量温度系数的正确性. 关键词： 有限应变物态方程 剪切模量温度系数 Steinberg本构模型 动高压实验     

Theoretical Study of Elastic Properties of Tungsten Disilicide

The plane-wave pseudopotential method using the generalized gradient approximation within the framework of density functional theory is applied to analyse the lattice parameters, elastic constants, bulk moduli, shear moduli and Young's moduli of WSi₂. The quasi-harmonic Debye model, using a set of total energy versus cell volume obtained with the plane-wave pseudopotential method, is applied to the study of the elastic properties and vibrational effects. The athermal elastic constants of WSi₂ are calculated as a function of pressure up to 35GPa. The relationship between bulk modulus and temperature up to 1200K is also obtained. Moreover, the Debye temperature is determined from the non-equilibrium Gibbs function. The calculated results are in good agreement with the experimental data.     

A first-principles study on the structural and elastic properties and the equation of state of wurtzite-type cadmium selenide under pressure

A first-principles investigation on the crystal structural and elastic properties and the equation of state of wurtzite-type cadmium selenide (w-CdSe) has been conducted using the plane-wave pseudo-potential density functional theory and the quasi-harmonic Debye model. The elastic constants, the aggregate elastic moduli, the elastic anisotropy, and Poisson's ratio under pressure have been investigated. Our calculated equilibrium lattice constants, the elastic constants, and the aggregate elastic moduli at zero pressure are in good agreement with the experimental data and other theoretical results. The variations in the compressional and shear elastic wave velocities with pressure at zero temperature up to pressure 2.7 GPa have been studied; the computed Debye temperature at zero pressure and zero temperature is in reasonable agreement with the result of Bonello et al., In addition, the equation of state of w-CdSe in the pressure range of 0–2.7 GPa and up to a temperature of 900 K has also been obtained.     

Boron–Carbon Nanocomposites Fabricated at High Pressures and Temperatures

Interaction of amorphous boron and C₆₀ fullerite is analyzed at pressures of 2.0 and 7.7. GPa and temperatures of 600–1800°C. Effect of pressure and temperature on the material structure is studied, temperatures for synthesis of boron carbide and diamond are found, and the sequence of transformations of the carbon component is determined. Ultrasonic method is used to measure elastic moduli of the samples, and the dependences of the moduli on the structure are analyzed. It is demonstrated that the boron–carbon nanocomposite synthesized at relatively low pressure (2.0 GPa) and temperature (about 1000°C) exhibits high elastic parameters (bulk modulus, B ≈ 75.3–84.0 GPa; Young modulus, E ≈ 108–119 GPa; and shear modulus, G ≈ 43–47 GPa at a density of about 2.2 g/cm³). The results can be used for development of novel nanocomposite materials.     

冲击加载下铝的剪切模量

分别用Steinberg-Cochran-Guinan (SCG)模型、修正的SCG模型和有限应变理论对材料的剪切模量做了数值计算，并与一维平面应变加载下铝的实验结果进行了比较.结果表明，修正的SCG模型与实验结果较为符合.在10—80GPa的压力范围下，剪切模量随冲击压力的增加而逐渐增大，这是由于压力的影响占主要地位，发生了加工硬化.在80—125GPa的压力范围下，剪切模量随冲击压力的增大快速减小，这是因为温度的影响比较严重，发生了高温软化现象.剪切模量最终在冲击压力为125GPa处趋于零，这是由于在该压力点冲击熔化发生，剪切强度消失. 关键词： 剪切模量 Steinberg-Cochran-Guinan模型 有限应变理论 铝     

Melting and isothermal bulk modulus of the rocksalt phase of ZnO with molecular dynamics simulation

The Buckingham potential has been employed to simulate the melting of the rocksalt phase of ZnO over a wide pressure–temperature range and isothermal bulk modulus with shell model molecular dynamics method. The melting curve from molecular dynamics simulations is in good agreement with the results obtained from Lindemann melting equation in the pressure below 7 GPa. The calculated null compression bulk modulus is compared with the available experimental data and other theoretical results. At extended temperature ranges, the isothermal bulk modulus has also been predicted up to 3000 K.     

First-principles study of elastic and electronic properties of layered ternary nitride SrZrN2 under pressure

The structural, elastic, and electronic properties of SrZrN₂ under pressure up to 100?GPa have been carried out with first-principles calculations based on density functional theory. The calculated lattice parameters at 0?GPa and 0?K by using the GGA-PW91-ultrasoft method are in good agreement with the available experimental data and other previous theoretical calculations. The pressure dependence of the elastic constants and the elastic-dependent properties of SrZrN₂, such as bulk modulus B, shear modulus G, Young's modulus E, Debye temperature Θ, shear and longitudinal wave velocity V_S and V_L, are also successfully obtained. It is found that all elastic constants increase monotonically with pressure. When the pressure increases up to 140?GPa, the obtained elastic constants do not satisfy the mechanical stability criteria and a phase transition might has occurred. Moreover, the anisotropy of the directional-dependent Young's modulus and the linear compressibility under different pressures are analysed for the first time. Finally, the pressure dependence of the total and partial densities of states and the bonding property of SrZrN₂ are also investigated.