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。     

Temperature dependence of elastic moduli of submicrocrystalline copper

The possibility of applying the two-component model of single-phase hybrid materials to the explanation of the anomalous temperature dependence of elastic moduli of copper with a submicrocrystalline structure has been discussed. An analysis has been performed based on new experimental data. A twin mechanism of changes in the crystallite orientation has been proposed. These changes cause the anomalous behavior of the elastic moduli of copper during deformation and subsequent heatings.     

Temperature dependence of elastic moduli for solid C60

The attenuation and velocity of ultrasonic waves (at a frequency of ～4 MHz) along the 〈111〉 and 〈100〉 directions in solid C₆₀ single-crystal samples are measured in the temperature range 100–300 K. The temperature dependences of the complete set of elastic constants for C₆₀ fullerite are determined from the experimental data. It is shown that the specific features in the behavior of the elastic moduli near the orientational phase transition temperature are associated with different contributions of the relaxation processes to the effective elastic moduli. The activation volume and deformation potentials for the ground and excited states of the C₆₀ low-temperature phase are evaluated from the results obtained in this work and the data available in the literature.     

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.     

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.     

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 moduli and their pressure and temperature derivatives for calcium oxide

The room temperature adiabatic elastic moduli of CaO were obtained using a pulse superposition technique to measure the ultrasonic velocities. The elastic moduli were found to be (in GPa) at 298 K.

     

11.

Second pressure derivatives of the elastic moduli of fused quartz     

D. Gerlich  George C. Kennedy 《Journal of Physics and Chemistry of Solids》1978,39(11):1189-1191

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.     

12.

On the volume dependence of superexchange in K2NiF4     

G. Gorodetsky  R.C. Leung  F.P. Missell  C.W. Garland 《Physics letters. A》1977,64(2):251-252

Ultrasonic velocity measurements in the two-dimensional antiferromagnet K₂NiF₄ as a function of temperature at several hydrostatic pressures show T_N to be very weakly pressure dependent. This result differs from previous estimates of the volume dependence of superexchange in similar compounds.     

13.

The wall theorem for elastic moduli     

F. Bavaud 《Journal of statistical physics》1986,45(1-2):171-181

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.     

14.

Low temperature dependence of elastic moduli and internal friction for the glassy alloy Zr55Cu30Al10Ni5     

Mikio Fukuhara  Xinmin Wang  Akihisa Inoue  Fuxing Yin 《固体物理学:研究快报》2007,1(5):220-222

Longitudinal and transverse wave velocities, eight kinds of elastic parameters, and dilational and shear internal frictions of Zr₅₅Cu₃₀Al₁₀Ni₅ glassy alloy were simultaneously measured as a function of temperature in the range from 77 to 373 K, using an ultrasonic pulse method. The inflections at around 150 K for wave velocities, anisotropy factor and Poisson's ratio, and the 150 K peak of shear friction seem to correspond to one topological change (pseudo‐transition) associated with an interatomic readjustment or vacancy rearrangements. The behaviors from 77 to 125 K and 125 to 373 K are due to thermal relaxation of squeezed free volumes and entropy elasticity associated with vibrational motions of clusters, respectively, accompanied by an increase in atomic distance. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

15.

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

Z. Zeng  L. Jin  Y. Huo 《The European physical journal. E, Soft matter》2010,32(1):71-79

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.     

16.

Statistical mechanics of elastic moduli     

F. Bavaud  Ph. Choquard  J. -R. Fontaine 《Journal of statistical physics》1986,42(3-4):621-646

We consider continuous systems of particles in the framework of classical statistical mechanics and derive a general expression for the static elastic moduli tensor in terms of correlation functions. We find sufficient conditions for the vanishing of the shear modulus. Relationships between these conditions and others insuring translational or rotational invariance are discussed.     

17.

Temperature dependence of light scattering by the one-magnon excitation in NiF2 crystals     

Dah-Min Hwang  T.T. Chen  Hua Chang 《Solid State Communications》1976,18(8):1099-1101

We have studied the one-magnon excitation in NiF₂ crystals by the method of right-angle light scattering from 1 to 73°K. The temperature dependence of frequency and line width agrees very well with previous far infrared absorption data. The temperature dependence of the integrated intensity follows the theoretical prediction but deviates from the previous far infrared data.     

18.

Third-order elastic moduli of single-layer graphene     

Davydov  S. Yu. 《Physics of the Solid State》2011,53(3):665-668

In the framework of the Keating model with allowance made for the anharmonic constant of the central interaction between the nearest neighbors μ, analytical expressions have been obtained for three third-order independent elastic constants c _ijk (μ, ζ) of single-layer graphene, where ζ = (2α − β)/(4α + β) is the Kleinman internal displacement parameter and α and β are the harmonic constants of the central interaction between the nearest neighbors and the noncentral interaction between the next-nearest neighbors, respectively. The dependences of the second-order elastic constants on the pressure p have been determined. It has been shown that the moduli c ₁₁ and c ₂₂ differently respond to the pressure. Therefore, graphene is isotropic in the harmonic approximation, whereas the inclusion of anharmonicity leads to the appearance of the anisotropy.     

19.

Zero-frequency elastic moduli of uniform fluids     

C. F. Tejero 《Journal of statistical physics》1989,57(1-2):393-398

A statistical mechanical treatment of equilibrium elasticity of a uniform fluid phase based on density functional theory is presented. Bulk expressions for the stress tensor and the zero-frequency elastic moduli tensor involving the direct correlation function are found.     

20.

Absorption measurements at high pressure (0–10kbar) on strained superlattices     

P. Garrilovic  K. Meehan  N. Holonyak  K. Hess  W.P. Zurawsky  H.G. Drickamer  M.J. Ludowise  W.T. Dietze  C.R. Lewis 《Solid State Communications》1983,45(9):803-806

Absorption data on strained GaAs_1?xP_x-GaAs superlattices (SL, 128-period, barrier size L_B≈75 Å, quantum-well size L_z≈75 Å, alloy composition x≈0.25) are presented in the range 0–10 kbars. The absorption curves obtained show no exciton show no exciton peaks such as seen in lattice- matched Al_xGa_1?xAs-GaAs SL's, and the pressure coefficient decreases from 11.5 meV/kbar to ≈ 10.5 meV/kbar in the wells and ≈6.5 meV/kbar at energies approaching and above the barrier energies. This behavior is attributed to the fluctuations in strain caused by the alloy disorder, and clustering, of the barriers.     

c11	c12	c44
226.2 ±0.9	62.4 ±0.9	80.6 ±0.3 The pressure derivatives of the elastic moduli, which were measured at and below room temperature, decrease with decreasing temperature. The temperature derivatives of the elastic moduli were also obtained for several temperatures below room temperature.

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.     

On the volume dependence of superexchange in K2NiF4

Ultrasonic velocity measurements in the two-dimensional antiferromagnet K₂NiF₄ as a function of temperature at several hydrostatic pressures show T_N to be very weakly pressure dependent. This result differs from previous estimates of the volume dependence of superexchange in similar compounds.     

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.     

Low temperature dependence of elastic moduli and internal friction for the glassy alloy Zr55Cu30Al10Ni5

Longitudinal and transverse wave velocities, eight kinds of elastic parameters, and dilational and shear internal frictions of Zr₅₅Cu₃₀Al₁₀Ni₅ glassy alloy were simultaneously measured as a function of temperature in the range from 77 to 373 K, using an ultrasonic pulse method. The inflections at around 150 K for wave velocities, anisotropy factor and Poisson's ratio, and the 150 K peak of shear friction seem to correspond to one topological change (pseudo‐transition) associated with an interatomic readjustment or vacancy rearrangements. The behaviors from 77 to 125 K and 125 to 373 K are due to thermal relaxation of squeezed free volumes and entropy elasticity associated with vibrational motions of clusters, respectively, accompanied by an increase in atomic distance. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Statistical mechanics of elastic moduli

We consider continuous systems of particles in the framework of classical statistical mechanics and derive a general expression for the static elastic moduli tensor in terms of correlation functions. We find sufficient conditions for the vanishing of the shear modulus. Relationships between these conditions and others insuring translational or rotational invariance are discussed.     

Temperature dependence of light scattering by the one-magnon excitation in NiF2 crystals

We have studied the one-magnon excitation in NiF₂ crystals by the method of right-angle light scattering from 1 to 73°K. The temperature dependence of frequency and line width agrees very well with previous far infrared absorption data. The temperature dependence of the integrated intensity follows the theoretical prediction but deviates from the previous far infrared data.     

Third-order elastic moduli of single-layer graphene

In the framework of the Keating model with allowance made for the anharmonic constant of the central interaction between the nearest neighbors μ, analytical expressions have been obtained for three third-order independent elastic constants c _ijk (μ, ζ) of single-layer graphene, where ζ = (2α − β)/(4α + β) is the Kleinman internal displacement parameter and α and β are the harmonic constants of the central interaction between the nearest neighbors and the noncentral interaction between the next-nearest neighbors, respectively. The dependences of the second-order elastic constants on the pressure p have been determined. It has been shown that the moduli c ₁₁ and c ₂₂ differently respond to the pressure. Therefore, graphene is isotropic in the harmonic approximation, whereas the inclusion of anharmonicity leads to the appearance of the anisotropy.     

Zero-frequency elastic moduli of uniform fluids

A statistical mechanical treatment of equilibrium elasticity of a uniform fluid phase based on density functional theory is presented. Bulk expressions for the stress tensor and the zero-frequency elastic moduli tensor involving the direct correlation function are found.     

Absorption measurements at high pressure (0–10kbar) on strained superlattices

Absorption data on strained GaAs_1?xP_x-GaAs superlattices (SL, 128-period, barrier size L_B≈75 Å, quantum-well size L_z≈75 Å, alloy composition x≈0.25) are presented in the range 0–10 kbars. The absorption curves obtained show no exciton show no exciton peaks such as seen in lattice- matched Al_xGa_1?xAs-GaAs SL's, and the pressure coefficient decreases from 11.5 meV/kbar to ≈ 10.5 meV/kbar in the wells and ≈6.5 meV/kbar at energies approaching and above the barrier energies. This behavior is attributed to the fluctuations in strain caused by the alloy disorder, and clustering, of the barriers.