On the effective Debye temperatures of the C60 fullerite

The effective Debye temperatures Θ_eff determined for solids by different physical methods have been analyzed and compared. Attention has been focused on the original parameter of the Debye theory of heat capacity, i.e., the translational calorimetric Debye temperature Θ _c ^t (0), and the X-ray Debye temperature Θ _x in the framework of the Debye-Waller theory for the C₆₀ fullerite. It has been established that the true Debye law T ³ is satisfied for the C₆₀ fullerite over a very narrow range of temperatures: 0.4 K ≤ T ≤ 1.8 K. For this reason, the experimental Debye temperatures Θ _c ^t (0) obtained for the C₆₀ fullerite by different authors in the range T > 4.2 K are characterized by a large scatter (by a factor of ∼5). It has been revealed that the value Θ _c ^t (0) = 77.12 K calculated in this paper with the use of the six-term Betts formula from the harmonic elastic constants $ \tilde C_{ijkl} $ \tilde C_{ijkl} of the C₆₀ single crystal in the limit T = 0 K is closest to the true Debye temperature. It has been demonstrated using the method of equivalent moments that the real spectral frequency distribution of translational lattice vibrations g(ω) for the C₆₀ fullerite deviates from a parabolic distribution. The effective Debye temperatures Θ_eff involved in applied problems of thermodynamics of crystals and elastic scattering of different radiations from lattice vibrations have been determined. The quantitative measure of anharmonicity of translational and librational lattice vibrations of the C₆₀ fullerite has been determined. This has made it possible to empirically evaluate the lattice thermal conductivity κ of the C₆₀ fullerite at T ≈ 300 K: κ(300) = 0.80 W (m/K), which is in good agreement with the experimental thermal conductivity κ_exp = 0.78 W (m/K) at T ≈ 250 K.     

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.     

Equation of state for fullerite C60

A new equation of state for fullerite C₆₀ is derived in the framework of the quantum-statistical method. This equation includes two Grüneisen parameters responsible for vibration–rotational and intramolecular contributions of fullerene molecules, which are represented in the form of isotropic quantum oscillators. The intramolecular vibrations of carbon atoms are described by the Debye heat capacity theory, and the cold contribution to the free energy is calculated using the Lennard–Jones pair potential for fullerene molecules. The theory is in a very good agreement with the experiment.

     

Mechanical properties,lattice thermal conductivity,infrared and Raman spectrum of the fullerite C24

Lightweight carbon materials with excellent thermal and mechanical properties have important applications in aerospace industry. In this study, the stability, mechanical properties, lattice thermal conductivity, electronic structure, infrared and Raman spectrum of sp³ hybridized low-density fullerite C₂₄ were investigated according to density functional theory (DFT) calculations. It was found that the fullerite C₂₄ was both thermodynamic and dynamic stable. Quasi-harmonic approximation and Grüneisen parameter calculations clarified why the fullerite C₂₄ had a positive thermal expansion coefficient at low temperature. The fullerite C₂₄ also exhibited excellent mechanical properties. Interestingly, the Vickers hardness of carbon allotropes was found to almost be linear proportional to the density of a carbon material. HSE06 electronic structure calculations showed that it was a semiconductor with direct bandgap of 2.56 eV. Anharmonic lattice dynamic calculations showed that its thermal conductivity was higher than semiconductor silicon. Besides, Raman and infrared active modes as well as the corresponding spectra were presented.     

Relation between the Grüneisen constant and Poisson’s ratio of vitreous systems

The lattice Grüneisen constant is calculated for amorphous polymers and glasses by using the data on Poisson’s ratio. While the thermodynamic Grüneisen constant of vitreous polymers characterizes the anharmonicity averaged over intrachain and other vibration modes, the lattice Grüneisen constant describes the anharmonicity of interchain vibrations associated with intermolecular interaction. For alkali-silicate glasses, the lattice Grüneisen constant characterizes the anharmonicity of vibrations of the ionic sublattice, which is formed by alkali metal ions and nonbridge oxygen ions.     

The elastic constants of sodium from 20 to 95°C

We report ultrasonic pulse echo measurements of the elastic constants of sodium in the high temperature region. At room temperature the results agree with those of earlier work. No pronounced effects of anharmonicity are found contrary to theoretical predictions. The behaviour of the elastic constants is further analysed in terms of compressibilities, of Grüneisen parameters and of effects caused by lattice defects. The quantity[?lnω_i(q)/?T]_v is calculated from the temperature and pressure variation of the elastic constants.     

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).     

Anomalous thermal expansion in the paramagnetic phase of dysprosium and terbium-50% holmium

The c-axis thermal expansion and expansion coefficients have been measured over the temperature range T_N < T < 273 K in single crystal dysprosium and terbium-50% holmium. The data show abrupt changes in the expansion coefficients at approximately 226 K in dysprosium and 250 K, 212 K and 196 K in terbium-50% holmium. Departures from lattice Grüneisen behaviour occur at temperatures well in excess of the Néel temperatures.     

Thermal expansion of cadmium fluoride

The thermal expansion of CdF₂ single crystal has been measured over the temperature range 80–300°K. From the latter data, the thermal Grüneisen constant as a function of temperature has been evaluated, and compared with the elastic Grüneisen constant. The correlation between the two sets of data, and with possible lattice interactions is discussed.     

Vibrational modes and phase transition of Si-Ge solid solution

We present the simplified treatment where the lattice vibrations of Si or Ge atoms in the Si-Ge solid solution are replaced with that of pure Si or Ge crystal at lattice constants of the alloy. Considering the volume effect on the force constants of the pure constituent, we obtain the phonon dispersion curves of the local and band modes for Si_0.91Ge_0.09 and Si_0.11Ge_0.89 systems and the concentration x-dependence of the local and band modes frequencies in the Si_1?xGe_x solid solutions. Then, from the calculation of the effective mode Grüneisen parameter γ_i for the average phonon modes in the Si_1?xGe_x systems, we obtain the predominant correlation between TA mode Grüneisen parameter γ^X_TA at the point X and the phase transition pressure P_t, and the softening of TA modes is related to the pressure-induced phase transition of the Si-Ge solid solution.     

Heat capacity and lattice dynamics of yttrium diboride in the temperature range 5–300 K

This paper reports an experimental study of the heat capacity and crystal lattice parameters of a polycrystalline sample of yttrium diboride prepared by high-temperature synthesis from elements. The electronic and lattice contributions to the heat capacity are isolated. The temperature dependences of the characteristic temperature, the linear thermal expansion coefficients α_a(T) and α _c (T), the bulk thermal expansion coefficient β(T), and the Grüneisen coefficient are calculated. A region of negative values of α _c (T) and β(T) is revealed. Anharmonicity is found to exert only a minor effect on the YB₂ lattice dynamics over a larger part of the temperature range covered.     

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.     

Thermodynamic and dilatometric properties of the dimerized phase of a C<Subscript>60</Subscript> fullerene

This paper reports on the results of complex investigations into the structural, thermodynamic, and dilatometric properties of the C₆₀ dimerized phase prepared under compression of a C₆₀ fullerite at a pressure up to 8 GPa and a temperature of 290 K. It is demonstrated that the dimerized phase has a face-centered cubic structure with a lattice parameter a=14.02±0.05 Å. The dimeric structure of the studied sample is confirmed by x-ray diffraction analysis. According to the dilatometric data, the volume jump observed in the vicinity of the orientational transition for the dimerized phase is estimated to be approximately 30 times less than that for the C₆₀ fullerite. The temperature dependence of the heat capacity of the (C₆₀)₂ crystalline dimer is examined using precision adiabatic vacuum calorimetry under normal pressure in the temperature range from T → 0 K to 340 K. The results obtained are used in the calculations of thermodynamic functions, namely, the heat capacity C _p ⁰ (T), the enthalpy H⁰(T)-H⁰(0), the entropy S⁰(T), and the Gibbs function G⁰(T)-H⁰(0). The fractal dimension D is determined as a function of the heat capacity. The standard entropy of the formation of the (C₆₀)₂ crystalline dimer from a simple compound (graphite) at T=298.15 K and normal pressure is calculated.     

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.     

Lattice-dynamical calculations of the thermodynamic properties of CsBr and CsI

Results of a quasi-harmonic calculation of the normal mode frequencies, mode-Grüneisen parameters, the coefficient of thermal expansion α, the heat capacity C_p, and the macroscopic Grüneisen function γ(itT) for CsBr and CsI are presented. Very good agreement with the experimental results for α and C_p is obtained. A self-consistent procedure is used to parametrize the models so that some often neglected vibrational and configuration-dependent effects can be accounted for. Predictions are made for the values that the potential energy derivatives and the elastic constants would have in the absence of vibrational motion.     

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.     

Anomalous low-frequency phonons in ZrB<Subscript>12</Subscript>

The influence of pressure and temperature on low-frequency lines (100–300 cm^–1) in Raman spectra of ZrB₁₂ and LuB₁₂ single crystals has been investigated. These spectral features have been identified as one-phonon and two-phonon excitations of the acoustic branches of the phonon spectrum. It has been found that the observed spectra of ZrB₁₂ single crystals are more structured and indicate the development of phonon anomalies with a decrease in the temperature. Despite the fact that the low-frequency features in the phonon spectrum of ZrB₁₂ are characterized by a high value of the isothermal Grüneisen parameter, their isobaric Grüneisen parameter has a negative value. This indicates large contributions from the fourth-order anharmonicity, which significantly exceed the volume effects. The appearance of narrow lines in the frequency range from 155 to 175 cm^–1 at temperatures T < 100 K suggests the possibility of a structural transition with an incomplete softening of the lattice.     

Grüneisen parameter of cerium compounds with unstable 4f shells

We give experimental results of magnetic susceptibility, thermal expansion and elastic constant measurements for CeSn₃ and CePd₃. We interpret these results with a phenomenological scaling function for the free energy and we include a brief discussion of CeAl₃. The coupling between the electronic system and the lattice can be described by an electronic Grüneisen parameter Ω_g associated with the unstable 4f system which turns out to become a system specific constant far below the fluctuation temperatureT ₀. The coupling parameter T₀Ω_g is an order of magnitude larger than the coupling constant for stable valentRE systems extracted from crystal field effects. A generalization to include magnetic field dependent effects is also given.     

Electroconductivity and pressure–temperature states of step shocked C60 fullerite

A study of electrophysical and thermodynamic properties of C₆₀ single crystals under step shock loading has been carried out. The increase and the following reduction in specific electroconductivity of C₆₀ fullerite single crystals at step shock compression up to pressure 30 GPa have been measured. The equations of state for face centred cubic (fcc) C₆₀ fullerite as well as for two-dimensional polymer C₆₀ and for three-dimensional polymer C₆₀ (3D-C₆₀) were constructed. The pressure–temperature states of C₆₀ fullerite were calculated at step shock compression up to pressure 30 GPa and temperature 550 K. The X-ray diffraction studies of shock-recovered samples reveal a mixture of fcc C₆₀ and a X-ray amorphous component of fullerite C₆₀. The start of the formation of the X-ray amorphous component occurs at a pressure P _m≈ 19.8 GPa and a temperature T _m≈ 520 K. At pressures exceeding P _m and temperatures exceeding T _m, the shock compressed fullerite consist of a two-phase mixture of fcc C₆₀ fullerite and an X-ray amorphous component presumably consisting of the nucleators of polymer 3D-C₆₀ fullerite. The decrease in electroconductivity of fullerite can be explained by the percolation effect caused by the change of pressure, size and number of polymeric phase nuclei.     

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