Thermal expansion and lattice dynamics under pressure of ZnS,ZnSe and ZnTe

The thermal expansion against temperature of ZnS, ZnSe and ZnTe is studied theoretically using the experimental pressure dependence of elastic stiffness constants and phonon frequencies. The mode Grüneisen parameters obtained from the high pressure effect on the one- and two- phonon Raman spectra at the metallic transition pressure by Weinstein are used originally, but do not reproduce the experimental linear expansion coefficient at high temperatures. The contributions from optical modes with large phonon frequency are important to the thermal expansion at high temperatures, and a set of mode Grüneisen parameters, which bring good agreement with the observed linear expansion coefficient not only at low temperatures, but also at high temperatures, are obtained. Then, the phonon dispersion curves of ZnS, ZnSe and ZnTe at their metallic transition pressures are quantitatively shown.     

Some anharmonic properties of Caesium halides

The second thermal Grüneisen parameter and isentropic Anderson-Grüneisen parameter for caesium halides are determined at different temperatures employing a pressure dependent shell model of lattice dynamics. A new thermodynamic relation is also proposed to calculate the second thermal Grüneisen parameter using experimentally measurable quantities. The agreement between experimentally estimated and theoretically calculated values is fairly good for the Anderson-Grüneisen parameter while it is very poor for the second thermal Grüneisen parameter.     

Origin of negative thermal expansion in cubic ZrW2O8 revealed by high pressure inelastic neutron scattering

Isotropic negative thermal expansion has been reported in cubic ZrW2O8 over a wide range of temperatures (0-1050 K). Here we report the direct experimental determination of the Grüneisen parameters of phonon modes as a function of their energy, averaged over the whole Brillouin zone, by means of high pressure inelastic neutron scattering measurements. We observe a pronounced softening of the phonon spectrum at P = 1.7 kbar compared to that at ambient pressure by about 0.1-0.2 meV for phonons of energy below 8 meV. This unusual phonon softening on compression, corresponding to large negative Grüneisen parameters, is able to account for the observed large negative thermal expansion.     

Theoretical study of thermal properties for SiGe system

Using our presented treatment with the volume effect on the force constants of the pure constituent, we study the thermal properties of Si-Ge solid solution from first principle in the electronic theory of solids. The specific heat at constant volume of Si_1−xGe_x solid solution is monotonous function of the concentration x and is approximately given by the linear interpolation of atomic fraction. The Grüneisen constant and the thermal expansion coefficient of Si_1−xGe_x system have the characteristic concentration dependence. The almost constant value at high temperatures and the negative minimum at low temperature of the Grüneisen constant are not monotonous as function of x, and show a maximum near x = 0.7 and a minimum near x = 0.2, respectively. Then, the linear thermal expansion coefficient at low and high temperatures deviate largely from the linear interpolation of the atomic fraction.     

Equations of state of MgO,Au, Pt,NaCl-B1, and NaCl-B2: Internally consistent high-temperature pressure scales

Semiempirical equations of state (EoS) of Au, Pt, MgO, NaCl-B1, and NaCl-B2 based on expanded Mie–Grüneisen–Debye approach, which are consistent both with the Mie–Grüneisen–Bose–Einstein approach and the thermochemical, X-ray, ultrasonic and shock-wave data in a wide pressure-temperature range, have been constructed. It is shown that to determine the volume dependence of the Grüneisen parameter, not only shock-wave and static compression data, but also experimental information on heat capacity, bulk moduli, volume, and thermal expansion coefficient at zero pressure need to be taken into account. Intrinsic anharmonicity is of great importance at construction of EoS at high temperatures and x=V/V ₀>1. Cross-comparison of the current equations of state with independent measurements shows that these EoS may be used as the internally consistent and independent pressure scales in a wide range of temperatures and pressures.     

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     

Theoretical study of the thermodynamic properties of lithium, sodium, and potassium nitrates

The thermal properties of lithium, sodium, and potassium nitrates have been studied in a gradient approximation of the density functional theory using the method of linear combination of atomic orbitals of the CRYSTAL09 program package. The long-wave frequencies and corresponding mode Grüneisen parameters are calculated. The quasi-harmonic Debye-Einstein model is used to calculate the parameters of the equation of states and also the dependences of the thermodynamic potentials, the entropy, the heat capacity, the thermal expansion coefficient, and the Grüneisen parameter on pressure and temperature. The role of external and intramolecular vibrations in the interpretation of thermodynamic properties is determined. The obtained results agree well with the available experimental data.     

负膨胀材料Zn(CN)_2和Cd(CN)_2的晶格振动分析

运用群论理论对负膨胀系数材料Zn(CN)2和Cd(CN)2的晶格振动进行了对称性分类,利用第一性原理密度泛函理论计算了它们布里渊区中心点的声子频率和Grüneisen参数,根据计算得到的各个模式所对应的本征矢对各个振动模式进行了指认,根据各模式Grüneisen参数讨论了负膨胀机理。在11个光学振动模式中,一个属于Zn/Cd原子的晶格振动模,位于223 cm-1/154 cm-1;5个属于C≡N刚性单元平移振动模;3个属于C≡N刚性单元天平动;2个属于C≡N刚性单元内振动。有7个振动模为拉曼活性,4个振动模为红外活性,两个振动模红外和拉曼均为非活性。C≡N刚性单元的3个低频平移振动模和全部天平动模的Grüneisen参数为负,对负热膨胀的产生有贡献,振动频率为47 cm-1的平移振动模具有最大的负Grüneisen参数,对负膨胀贡献最大。     

Phonon dispersion of zinc chalcogenides under extreme pressure and the metallic transformation

The effect of high pressure on the one- and two-phonon Raman spectra of ZnTe, ZnSe, and ZnS has been measured up to their metallic phase transitions, at 95, 137, and 150 kbar respectively. Zone boundary transverse acoustic phonons “soften” with pressure in each case. For ZnTe, ZnSe, ZnS, Si, and GaP a linear correlation is found between the mode Grüneisen parameters for TA(X) and the transition pressures.     

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.     

Thermal expansion and mode Grüneisen parameters of LiH and LiD

The third order contribution of the shell-shell interaction between next nearest neighbours has been determined from a calculation of the coefficient of linear thermal expansion of LiH and ⁷LiD. The Coulomb anharmonicity is included. A shell model fitted to phonon energies from inelastic neutron scattering in ⁷LiD was used. From this model then averaged Grüneisen constants and individual mode Grüneisen parameters have been deduced.     

Theoretical study of elastic and thermodynamic properties of CuSc intermetallic compound under high pressure

The structural, mechanical and thermodynamic properties of copper scandium CuSc intermetallic compound under temperature and pressure have been investigated using the plane wave (PW) - pseudopotential (PP) approach in the framework of the density functional theory (DFT). The structural parameters at equilibrium, the elastic moduli, the mechanical stability criteria and the sound velocity are studied in the pressure range 0–12 GPa. In addition, the heat capacity, the Grüneisen parameter, the Debye temperature, the entropy, and the thermal expansion coefficient are studied for temperatures ranging from 0 up to 1000 K. The equilibrium lattice parameter found is around 3.261 Å. It is in good agreement with the experimental one of 3.25 Å reported in the literature. According to the generalized elastic stability criteria, we predict the occurrence of a phase transition of the B2-type structure at 25.5 GPa. At room temperature and zero-pressure, the isothermal bulk modulus and the Grüneisen parameter found were 80.86 GPa and 2.04 respectively.     

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.     

Generalized Grüneisen parameters and low temperature limit of lattice thermal expansion of cadmium and zirconium

The generalized Grüneisen parameters (γ′ _j ) and (γ″ _j ) for cadmium and zirconium were calculated from the second- and third-order elastic constants to determine the low temperature limit of the volume thermal expansion of these metals of hexagonal symmetry. The low temperature limit of cadmium and zirconium was calculated to be positive values indicating a positive volume expansion down to 0 K even though many Grüneisen gammas were found to be negative.     

Pressure–temperature dependence of thermodynamic properties of rutile (TiO2): A first-principles study

Ab-initio calculations of thermal properties of rutile (TiO₂) have been performed by using the projector augmented-wave (PAW) method within the generalized gradient approximation (GGA). Both pressure- and temperature-dependent thermodynamic properties such as the bulk modulus, thermal expansion, thermal expansion coefficient, heat capacity at constant volume and constant pressure were calculated using two different models based on the quasiharmonic approximation (QHA): the Debye–Slater and Debye–Grüneisen model with Dugdale–MacDonald (DM) approximation. Also, the empirical energy corrections were applied to the results to correct the systematic errors introduced by the functional. It is found that the Debye–Grüneisen model provides more accurate estimates than the Debye-Slater models, especially after empirical energy correction.     

Sur la dilatation des solides a haute temperature

It appears that at high temperature, experimental results for the thermal expansion of solids do not obey the Grüneisen law. Hence, we propose two expressions representing them correctly, one for temperatures between 0.2 and 2θ, and another for temperatures over 2θ (θ being the Debye temperature).     

Elastic Properties of Graphene-Like Compounds: the Keating’s and Harisson’s Models

Physics of the Solid State - The third-order elastic constants, the pressure dependences of the second-order elastic constants, the Kleinman and Grüneisen parameters, and the thermal expansion...     

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.     

Lattice-dynamical calculation of the thermodynamic properties of NaCl,KCl and RbCl

Results of a lattice-dynamical calculation of the coefficient of thermal expansion, the heat capacity, and the macroscopie Grüneisen ratlo for NaCl, KC1 and RbCl are presented. Good agreement with the experimentai results is obtained without adjustable parameters. The needed normal mode frequencies and mode-Grüneisen parameters were caiculated with a deformation dipole model with nearest- and next-nearest-neighbor central-force interactions. Predicted values for the static elastic constants, the strain derivatives of the static potential energy, the mechanical equilibrium value of the nearest-neighbor distance, and the mode-Grüneisen parameters are given.