Modified grüneisen and anderson-grüneisen relations for quasispherical molecular liquids

The validity of the expression for the Grüneisen parameter of liquids has been tested by obtaining expressions for the heat capacity ratio, isothermal and adiabatic Anderson-Grüneisen parameters,C ₁-parameter, Rao’s acoustical parameter, Beyer’s non-linearity parameter, and relate them to the Grüneisen parameter. The calculated values for five liquefied gases comparising of quasi-spherical molecules are reasonably satisfactory and explain the experimental results for the variation of heat capacity ratio, Beyer’s nonlinearity parameter andC ₁-parameter with temperature for liquid state. It is shown that the isochoric temperature derivative of the sound speed, specified heat ratio and the compressibility are dominant factors with significant contribution for influencing the thermo-acoustic properties of liquids.     

On the spectral frequency distribution of translational vibrations in a face-centered cubic lattice of the C60 fullerite

The spectral frequency distribution g(ω) of translational lattice vibrations in the face-centered cubic phase of the C₆₀ fullerite at T = 300 K is calculated by the superposition method. The contribution from the translational vibrations to the heat capacity C _V of the C₆₀ fullerite and the x-ray characteristic temperature gJ_R entering into the exponent of the Debye-Waller factor are determined using the calculated frequency distribution g(ω). The results of the calculations are in good agreement with experimental data. It is noted that the librational and intramolecular lattice vibrations observed in the C₆₀ fullerite do not contribute significantly to the temperature-induced decrease in the x-ray diffraction intensity at T = 300 K. The Grüneisen parameters γ_mod calculated from the x-ray diffraction data are consistent with the thermodynamic Grüneisen parameters γ_lat at temperatures T ≤ 80 K but substantially exceed those at T ≈ 300 K. New x-ray diffraction experiments are proposed for independently determining the anomalously large negative values of the parameter γ₀, which is actually an orientational analog of the Grüneisen parameter.     

Thermal expansion and specific heat of Co-B-Si glasses

The thermal expansion coefficient α and specific heat C_p of Co-B-Si glasses are measured at temperatures from 20 to 295 K. Different types of structure, depending on composition, appear to be reflected in the temperature dependence of α. Negative values of α are found at temperatures below about 45 K. The specific heat displays some anomalies. The values of the Grüneisen parameter are quite different from those for crystalline metals.     

The hydrostatic pressure derivatives of the elastic constants of indium and an indium cadmium alloy

The hydrostatic pressure derivatives of the elastic stiffness constants of indium and indium-3.4 at.% cadmium alloy single crystals have been obtained from pulse echo overlap measurements of the dependence of ultrasonic wave velocities upon pressure. The softest zone centre acoustic phonon mode in indium is a shear mode propagating k along the [101] direction rather than that (k[110], e[11?0]) which drives the ferroelastic phase transition in the indium-cadmium alloys. The derivative δ((C₁₁ – C₁₂)/2)/δP is positive, accounting for the stability of the fct structure of indium under high pressure. Using the quasiharmonic, anisotropic continuum model the acoustic mode Grüneisen parameters have been calculated and are discussed in terms of mode softening. The high temperature limiting value$\text{\$}\text{?}$γ_H (= 2.56) of the mean acoustic mode Grüneisen parameter is found to be close to the thermodynamic Grüneisen parameter γ^th (=2.5).     

Volume dependence of the Grüneisen γ and other thermodynamic properties of NaCI

The quasi-harmonic approximation is used to calculate the Helmholtz free energy F of NaCl. The interionic forces are represented by a deformation-dipole model, which is parameterized self-consistently. We give a parameterized expression for F which can be used to predict the temperature and volume dependence of the thermodynamic properties. The expression for F is tested by comparing our predicted values for the heat capacity C_p, the thermal expansion α, and the bulk modulus B_s with experimental atmospheric-pressure values and by comparing predicted values for the Grüneisen γ at high pressures with the recent measurements of Boehler, Getting and Kennedy. Excellent agreement is obtained. Predictions for the volume dependence of C_p, α, and B_s and for the isothermal equation of state at room temperature are given. Values for the logarithmic derivative q_T = (?Inγ?? In V)_T and for the Anderson-Grüneisen parameters δ_S and δ_T are also given.     

Melting curve and Grüneisen coefficient for aluminum

The Lindeman law and a model for the volume dependence of the Grüneisen coefficient generalizing previous current theories are used to calculate the melting curve of aluminum at high pressure. In this model, the Grüneisen coefficient depends on a parameter p specific for the investigated material. Agreement between the calculated melting curve and experimental results involves a negative value of p for aluminum. This result confirms previous determinations of p from shock-wave data and also from the pressure dependance of the elastic moduli determined by ultrasonic measurements.     

Second Hugoniot relationship for solids

The term second Hugoniot is used to describe a locus of states directly attainable by shock compression beginning with an initial state that has itself been achieved by shock compression. For many materials the principal Hugoniot is linear in the shock velocity-particle velocity [U_s — u_p] representation. A second Hugoniot for such materials is not linear in this representation, but the nonlinear effects can often be neglected if the compressions are not too great. These results are based on the Mie-Grüneisen equation of state and are more or less independent of the explicit functional dependence of the Grüneisen parameter. A criterion to evaluate the magnitude of nonlinear effects is posed and Mg and Pb are treated as examples. Calculated second Hugoniots are compared with experimental results for regular reflection in Mg, Pb and U. For these materials nonlinear effects are not important from a practical standpoint for final volumetric compressions to roughly two-thirds of the initial volume. Some future experimental work is also suggested.     

Elastic constants,acoustic mode vibrational anharmonicity and Grüneisen parameters of hexahalometallate crystals

The room-temperature elastic constants of a number of hexahalometallate A₂MX₆ single crystals [K₂SnCl₆, K₂ReCl₆, (NH₄)₂SnCl₆, (NH₄)₂SnBr₆, (NH₄)₂SiF₆, Rb₂SnBr₆, K₂SeBr₆, (NH₄)₂TeBr₆, K₂PtBr₆ and (NH₄)2PtBr₆] have been measured either by Brillouin scattering or by the ultrasonic pulse echo overlap technique. Refractive indices have also been determined. These antifluorite structure compounds contain large MX^2?₆ ions and the interionic spacings are much greater than those of the alkaline-earth fluorite structure halides: their elastic stiffnesses are correspondingly smaller. Hydrostatic pressure derivatives of the elastic stiffness constants have been measured for K₂SnCl₆, (NH₄)₂SnBr₆ and (NH₄)₂SnCl₆ and are found to be positive; there is no marked softening of the long-wavelength acoustic-phonon modes at room temperature. The vibrational anharmonicities of these long-wavelength modes are discussed in terms of the acousticmode Grüneisen parameters, which are compared with the thermal Grüneisen parameters. For K₂SnCl₆ a mean of optic- and acoustic-mode Grüneisen parameters is shown to correlate well with the thermal Grüneisen parameter.     

Pressure dependence of phonon energies at critical points in the Brillouin zone in KTaO3 measured with differential second order raman scattering

Wavelength modulated Raman scattering was used to study the effects of pressure on the second order spectrum of KTaO₃. The pressure results lend support to previous identifications of structures in the second order differential Raman spectrum in terms of pairs of phonons from critical points in the Brillouin zone. Using these identification mode Grüneisen parameters are obtained for several vibrational modes. Strong anharmonic behavior of of the TA(X) mode is observed when we correlate the results from pressure measurements with previous studies of the effects of temperature.     

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.     

Structural, electronic, elastic and thermal properties of Mg2Si

First-principles calculations of the lattice parameter, electron density maps, density of states and elastic constants of Mg₂Si are reported. The lattice parameter is found to differ by less than 0.8% from the experimental data. Calculations of density of states and electron density maps are also performed to describe the orbital mixing and the nature of chemical bonding. Our results indicate that the bonding interactions in the Mg₂Si crystal are more covalent than ionic. The quasi-harmonic Debye model, by means of total energy versus volume calculations obtained with the plane-wave pseudopotential method, is applied to study the elastic, thermal and vibrational effects. The variations of bulk modulus, Grüneisen parameter, Debye temperature, heat capacity C_v, C_p and entropy with pressure P up to 7 GPa in the temperature interval 0-1300 K have been systemically investigated. Significant differences in properties are observed at high pressure and high temperature. When T<1300 K, the calculated entropy and heat capacity agree reasonably with available experimental data. Therefore, the present results indicate that the combination of first-principles and quasi-harmonic Debye model is an efficient approach to simulate the behavior of Mg₂Si.     

Experimental study of the Grüneisen parameter of a fullerite C60 single crystal near phase transitions at 90 and 260 K by the photoacoustic method

The behavior of the Grüneisen parameter of single-crystal fullerite C₆₀ has been studied experimentally near orientational phase transitions at 90 and 260 K. The measurements have been performed by the photoacoustic method using an automated photoacoustic device with laser excitation (the intensity was modulated by a harmonic law) and shadow piezoelectric detection. The temperature dependence of the relative change in the Grüneisen parameter in the fullerite C₆₀ single crystal has been measured near the phase transitions at 90 and 260 K. The results have been analyzed.     

Lattice model calculation of hugoniot curves and the grüneisen parameter at high pressure for the alkali halides

A seven parameter shell model of the interatomic forces in the NaCl lattice is used to make a detailed lattice dynamics calculation at arbitrary volume, for fourteen alkali halides. The calculated normal mode spectrum gives an explicit vibrational contribution to the pressure and the elastic constants in the quasiharmonic approximation. The seven parameters are chosen to fit low pressure ultrasonic data and the low and high frequency dielectric constants. Prediction of the Grüneisen parameter γ, (?lnγ/?lnV), and δ_s = (?1/βB_s)(dB_s/dT) are in reasonable agreement with experiment. The calculated γ decreases monotonically with volume. Calculated Hugoniots are in good agreement with experiment for NaCl, NaBr and NaI, and in fair agreement for LiBr, LiI and NaF.     

First principles study of the vibrational,dielectric and thermal properties of SrClF

SrClF is an important optical crystal and has many technological applications. In this work, vibrational, dielectric and thermal properties of SrClF were investigated by density functional perturbation calculation. The calculated Born effective charges are close to their nominal ionic charges, revealing the ionic characteristic of SrClF. Group theory analysis indicates that there are two E _u and A _2u infrared modes at the Brillouin zone center of SrClF. The LO-TO splitting of these infrared modes were calculated and discussed and their vibrational modes were sketched. Static dielectric constants were studied, which show that SrClF has a larger ionic dielectric contribution than its electrons. Its birefringence was calculated and the infrared reflectance spectra were simulated, which can be used to explain the experimental findings. Based on the computed phonon dispersion curves, the lattice heat capacity, the Grüneisen parameter and the thermal expansion coefficient as functions of temperature were predicted.     

Acoustic mode vibrational anharmonicity of hexahelometallate crystals

The vibrational anharmonicity and Grüneisen parameters of hexahelometallate A₂MX₆ single crystals have been determined theoretically by making use of phonon lattice theory. The potential model employed to calculate these properties consists of long range coulomb, three body interactions, short range overlap repulsion effective upto the nearest neighbour ions and phonon-lattice interactions. These antifluorite structure compounds contain large MX²⁻₆- ions and as the interionic spacings are much greater than those of the alkaline-earth fluorite structure halides, their elastic constants are correspondingly smaller. The hydrostatic pressure derivatives of the second order elastic constants (SOEC) calculated for K₂SnCl₆, K₂ReCl₆, (NH₄)₂SnCl₆, (NH₄)₂TeCl₆, (NH₄)₂SnBr₆, and (NH₄)₂TeBr₆, are found to be positive and close to the experimental values. The vibrational anharmonicities of the long-wavelength modes are explained in terms of the acoustic mode Grüneisen parameters.     

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.     

高压下TiC的弹性、电子结构及热力学性质的第一性原理计算

利用基于密度泛函理论的第一性原理平面波赝势方法 并结合准谐徳拜模型研究了NaCl结构的TiC在高压下的弹性性质、电子结构和热力学性质. 计算所得零温零压下的晶格常数、体弹模量及弹性常数与实验值符合得很好. 零温下弹性常数和弹性模量随压强增大而增大. 通过态密度和电荷密度的分析, Ti-C键随压强增大而增强. 运用准谐德拜模型, 成功计算了TiC在高温高压下的体弹模量、熵、热膨胀系数、徳拜温度、 Grüneisen参数和比热容. 结果表明压强对体弹模量、热膨胀系数和徳拜温度的影响大于温度对其的影响. 热容随着压强升高而减小, 在高温高压下, 热容接近Dulong-Petit极限.     

Vibronic structure of the 3s Rydberg state of the 2-methylallyl radical

Resonance-enhanced multiphoton ionization combined with electronic ground state depletion spectroscopy of jet-cooled 2-methylallyl (C₄H₇) radicals provides vibronic spectra of the 3s and 3p Rydberg states. Analysis of the vibronic structure following one-photon and two-photon excitation of rovibronically cold 2-methylallyl radicals and its isotopologues C₄H₄D₃ and C₄D₇ reveals transitions to more than 30 vibrational levels in the 3s Rydberg state that are identified and reassigned on the basis of predictions from ab initio calculations and results from pulsed-field-ionization zero-kinetic-energy photoelectron spectra obtained with resonant multiphoton excitation via selected intermediate states. Depletion spectroscopy reveals transitions to short-lived 3p Rydberg states that have a large oscillator strength.     

Quantitative calculations of thermal-expansion coefficient in Fe–Ni alloys: First-principles approach

The thermal expansion coefficients (α) of Fe_1-xNi_x alloys are calculated by means of the Debye-Grüneisen model, which uses the input parameters calculated from density functional theory (DFT) with collinear spin alignments. The various atomic configurations of fcc and bcc supercells with x being 0–0.5 are calculated to conduct the composition-specific analysis. Thermodynamic analysis is employed to facilitate the evaluation of α in bulk alloys, where the calculated supercells are used as the canonical ensemble. Such calculated α exhibits very similar composition-dependency in comparison with the experimental data from literature, particularly providing the well-known Invar effect at 65 wt% of Fe. The calculations also demonstrated that the pressure-derived magnetic frustration, i.e. the magneto-volume effect, is strongly correlated with the Invar effect. The present approach combining the Debye-Grüneisen formalism and the collinear DFT calculation is shown to be a comprehensive theoretical framework for analysis on the thermal expansion properties in metal alloys.