The pressure and temperature derivatives of the elastic moduli of lithium hydride

The pressure and temperature derivatives of the elastic moduli of single crystal LiH have been determined at room temperature, by the ultrasonic pulse echo method. From the pressure data, the mode Grüneisen parameters as well as the low and high temperature limiting values of the Grüneisen constant were computed; the latter were only slightly different. An equation of state has been constructed for LiH, and found to be in agreement with the experimental data. Based on a non-central force model, the values of the elastic moduli and their pressure derivatives have been calculated theoretically, and the latter values compared with the experimental data.     

The elastic constants and their temperature and pressure derivatives of AgBr-AgCl mixed crystals

The three independent second-order elastic constants and their temperature and pressure derivatives have been measured for four AgBr-AgCl mixed crystals, with 19.5, 39.1, 56.6 and 78.7 mole % AgCl, using the ultrasonic pulse-echo technique at room temperature. The explicit temperature dependence of the elastic constants is calculated and is found to be much larger than that of other NaCl structure crystals. The violation of the Cauchy relation C₁₂ = C₄₄ is found to be significant and increases between AgBr and AgCl. The high temperature limit of the Gruneisen parameter is calculated from the elastic data. A comparison is made between the elastic properties of the silver halides and the alkali halides.     

Second pressure derivatives of the elastic moduli of fused quartz

The first and second pressure derivatives of the elastic moduli of fused quartz have been determined by ultrasonic measurements of the sound velocity as a function of pressure. The second derivatives are positive in sign and are larger in magnitude than those in crystalline materials. The data are used to calculate the equation of state and the volume dependence of the Grüneisen constant.     

Hydrostatic pressure derivatives of the single crystal elastic moduli of Gd,Dy and Er

The hydrostatic pressure derivatives of the single crystal elastic moduli of Gd, Dy and Er have been measured at 298°K, to pressures near 5 Kbar. The very small pressure derivatives of the adiabatic bulk moduli indicate that a small ion core model should be appropriate for interpreting the data. The long-range electrostatic contributions to the shear moduli have a dominant influence on the pressure derivatives of the shear moduli of Er, whereas the Gd and Dy data evidently reflect band structure contributions. The values of the longitudinal stiffnesses correspond remarkably well with the Bohm-Staver model for velocity of waves in an ion plasma dispersed in a sea of electrons, where the ionic interaction is perely Coulombic. This model is extended to provide an interpretation of the volume derivatives of the longitudinal moduli in terms of the volume derivative of the density of electron states at the Fermi energy.The Grüneisen parameters calculated from averages of the acoustic model gammas are in relatively poor agreement with those determined from thermal expansion data. An explanation based on the changes in c/a ratio with volume change is tested quantitatively and found to be reasonably successful. The values of dK_T/dP, where K_T is the isothermal bulk modulus, are applied to the Murnaghan equation of state and give excelent agreement with Bridgman's direct compression data for Dy and Er to 40 Kbar. For Gd, Bridgman's data indicate either that (dK_T/dP)_p=0 should be considerably larger than deduced from the adiabatic dK_s/dP measurements or that a phase change occurs near 20 Kbar. The occurrence of a phase change in Er at ～90 Kbar is definitely indicated when comparing the Murnaghan equation with X-ray diffraction data.     

The wall theorem for elastic moduli

New expressions for the elastic moduli of a classical system are derived. They involve only the two-point correlation function and the derivative of the onepoint correlation function, both only on the boundary of the system. These expressions, valid for any interaction derivable from a potential, are proved from a mechanical point of view by generalizing the virial theorem of Clausius, and from a statistical point of view by a direct method that constitutes an alternative to Green's dilatation method.     

The temperature dependences of the elastic moduli of solid C60

This paper reports on the determination of the temperature dependences of the complete set of the elastic moduli of solid C₆₀ from sound-velocity measurements made along different crystallographic directions in single-crystal samples within the 100-to 300-K range. Substantial differences in their behavior were revealed, which are accounted for by different relative contributions from relaxation processes to various elastic moduli.     

Differential elastic moduli of an anisotropic medium under pressure

Natural strain theory is used to determine the tensor of the differential elastic moduli for strains of arbitrary magnitude and its relationship is established with values measured in acoustic and mechanostatic experiments in which an additional small load is applied. For illustration purposes an expression for this tensor is given for an object which is isotropic before application of the load, and formulas to determine this tensor from the results of measurements are calculated for an anisotropic object under pressure to within the second order in terms of the shear produced as a result of its hydrostatic compression.     

Alpha-plutonium's polycrystalline elastic moduli over its full temperature range

alpha-plutonium's volume-corrected polycrystal elastic moduli were measured between 18 K and the upper limit of its occurrence, near 400 K. The two independent moduli for a polycrystal-bulk and shear-behave smoothly, indicating no phase transition. Both moduli show the same 50% increase on cooling, an order of magnitude larger than in other metals. The Debye temperature obtained from low-temperature elastic moduli, 207 K, significantly exceeds most previous estimates. The Gruneisen parameter gamma=5.3, obtained from the temperature dependence of the bulk modulus, is intermediate among previous estimates using other approaches, alpha-plutonium's Poisson ratio nu is low: 0.18, nearly temperature independent, and its small decrease on warming opposes usual behavior. The high gamma, large but equal bulk modulus and shear modulus fractional stiffening on cooling, and near-temperature-invariant nu are attributed to a single mechanism: 5-f electron localization-delocalization.     

The pressure dependence of elastic moduli of NiF2 to 10 kbar

At room temperature, the pressure dependence of the elastic stiffness moduli of NiF₂ have been measured by pulse superposition method to 10 kbar. The observed strong decreasing behavior in the modulus $\text{C}{}_{\mathrm{<mtext>s</mtext>}}\text{=}\text{1}\text{2}\text{(C}{}_{11}\text{? C}{}_{12}\text{)}$ is discussed.     

DSC and elastic moduli studies on tellurite-vanadate glasses containing antimony oxide

xSb₂O₃-40TeO₂-(60 − x) V₂O₅ glasses with 0 ≤ x ≤ 10 (in mol%) have been prepared by rapid- melt quenching method. DSC curves of these ternary glasses have been investigated. The glass transition properties that have been measured and reported in this paper, include the glass transition temperature (T _g ), glass transition width (ΔT _g ), heat capacity change at glass transition (ΔC _P ) and fragility (F). Thermal stability, Poisson’s ratio, fragility and glass forming tendency of these glasses have been estimated, to determine relationship between chemical composition and the thermal stability or to interpret the structure of glass. In addition, Makishima and Makenzie’s theory was applied for determination of Young’s modulus, bulk modulus and shear modulus, indicating a strong relation between elastic properties and structure of glass. Generally, results of this work show that glass with x = 0 has the highest shear, bulk and Young’s moduli which make it as suitable candidate for the manufacture of strong glass fibers in technological applications; but it should be mentioned that glass with x = 8 has higher handling temperature and super resistance against thermal attack.     

MgO和Cu的弹性常数随温度及压强变化关系的研究

从Anderson-Grüneisen参数定义式和热膨胀系数定义式出发,根据Tallon的普遍化理论,推导出了一个用于计算弹性常数的理论模型,用所得到的理论模型分别计算了MgO和Cu两种固体材料的弹性常数C_(11)、C_(12)和C_(44)随压强以及温度变化的理论数值,并将理论计算结果与Kumar模型计算结果以及相关实验数据进行了比较,对所得到的理论模型计算结果与Kumar模型计算结果之间的差异性进行了分析和探讨.研究结果表明:所推导的理论模型计算结果与实验数据更加符合,并且由于所用的推导方法不依赖于晶体的结构,因此该模型具有更好的合理性和普适性.     

MgO和Cu的弹性常数随温度及压强变化关系的研究

从Anderson-Grüneisen参数定义式和热膨胀系数定义式出发,根据Tallon的普遍化理论,推导出了一个用于计算弹性常数的理论模型,用所得到的理论模型分别计算了MgO和Cu两种固体材料的弹性常数 、 和 随压强以及温度变化的理论数值,并将理论计算结果与Kumar模型计算结果以及相关实验数据进行了比较,对所得到的理论模型计算结果与Kumar模型计算结果之间的差异性进行了分析和探讨。研究结果表明：所推导的理论模型计算结果与实验数据更加符合,并且由于所用的推导方法不依赖于晶体的结构,因此该模型具有更好的合理性和普适性。     

MgO和Cu的弹性常数随温度及压强变化关系的研究

从Anderson-Grüneisen参数定义式和热膨胀系数定义式出发,根据Tallon的普遍化理论,推导出了一个用于计算弹性常数的理论模型,用所得到的理论模型分别计算了MgO和Cu两种固体材料的弹性常数 、 和 随压强以及温度变化的理论数值,并将理论计算结果与Kumar模型计算结果以及相关实验数据进行了比较,对所得到的理论模型计算结果与Kumar模型计算结果之间的差异性进行了分析和探讨。研究结果表明：所推导的理论模型计算结果与实验数据更加符合,并且由于所用的推导方法不依赖于晶体的结构,因此该模型具有更好的合理性和普适性。     

Pressure derivatives of the elastic moduli of strontium,barium and lead nitrate

The pressure derivatives of the elastic moduli of Sr(NO₃)₂, Ba(NO₃)₂ and Pb(NO₃)₂ single crystal, have been measured by the ultrasonic pulse superposition method. The results for Sr(NO₃)₂ and Pb(NO₃)₂ are similar in magnitude and character, while the ones for Ba(NO₃)₂ differ strongly, $\text{?c}{}_{11}\text{?P}$ and $\text{?c}{}_{12}\text{?P}$ even From the measured pressure derivatives, the mode Grüneisen gammas and the Grüneisen constant as a function of temperature have been determined, and the latter is correlated with the experimental values, deduced from thermal expansion. The explicit temperature dependence of the elastic moduli is calculated, and found to be always negative, increasing in absolute value from Sr(NO₃)₂ to Pb(NO₃)₂.     

Hardness and elastic moduli of high pressure synthesized MoB2 and WB2 compacts

High pressure and high temperature synthesized MoB₂ and WB₂ compacts were investigated using X-ray diffraction, energy dispersive spectroscope, scanning electron microscope, Vickers indentation test and ultrasonic measurements. Experiments showed that both MoB₂ and WB₂ compacts are phase pure and with a grain size of 100–200 nm. Vickers indentation test under a large loading force of 49 N showed that the Vickers hardness of MoB₂ and WB₂ are about 21 and 22 GPa, respectively. The bulk modulus and shear modulus are about 296 GPa, and 190 GPa for MoB₂ and 349 and 200 GPa for WB₂ through ultrasonic measurements. Our results indicate that MoB₂ and WB₂ are both hard materials with a hardness similar to that of tungsten carbide, which is widely used in industry.     

Strongly anisotropic elastic moduli of nematic elastomers: Analytical expressions and nonlinear temperature dependence

Exact formulae for the elastic moduli of the nematic elastomers are obtained by the implicit function method based on somewhat general energy functions. The formulae indicate that both the moduli parallel and perpendicular to the director of the nematic elastomers are smaller than the modulus of the classical elastomers because of the mechanical-nematic coupling. Moreover, the moduli are generally anisotropic due to the biaxiality induced by stretching the nematic elastomers perpendicular to the director. Then we get the explicit analytical expressions of the parallel and perpendicular moduli by making use of the Landau-de Gennes free energy and the neo-classical elastic energy. Very different from the classical elastomers, they are both strongly nonlinear functions of the temperature in the nematic phase. Furthermore, their ratio, the degree of anisotropy, changes with the temperature as well. The results agree qualitatively with some experiments. Better quantitative agreement is obtained by some modifications of the constitutive relation of the elastic energy.     

Effect of thermal expansion on the elastic moduli and Debye temperature of paramagnetic lutetium

The temperature dependence of the Young’s modulus E of paramagnetic lutetium has been studied. It has been shown that an important reason for the dependence E(T) is thermal expansion of the crystal lattice, which also leads to a change in the Debye temperature Θ. The effect of this factor is also revealed in the thermodynamic properties of metals. In particular, we have shown that there is another contribution to variation of the total specific heat of lutetium, associated with the Θ(T) dependence and comparable with the electronic contribution. Fiz. Tverd. Tela (St. Petersburg) 40, 1581–1584 (September 1998)