Grüneisen parameter for HCP iron at extreme compression

The Thomas–Fermi approximation gives the Grüneisen parameter γ=γ_∞=1/2 for all materials at extreme compression (P→∞ or V→0). After re-analyzing the existing experimental data of volume dependence of Grüneisen parameter γ of hexagonal close-packed (HCP) iron, we find that γ=1/2+a(V/V ₀)^1/3+b(V/V ₀) ⁿ , where a, b and n are constants. Based on this new form of γ, the second Grüneisen parameter q, the Debye temperature θ_D and the shear sound velocity v _s of HCP iron are discussed in the present work. It is found that the zero pressure second Grüneisen parameter q ₀=0.654, which is consistent with the previously determined value of HCP iron for Earth's core physics from Dubrovinsky et al. The calculations for the Debye temperature and the shear sound velocity are also found to be in good agreement with the experimental data.     

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.     

An equation of state of a carbon-fibre epoxy composite under shock loading

An anisotropic equation of state (EOS) is proposed for the accurate extrapolation of high-pressure shock Hugoniot (anisotropic and isotropic) states to other thermodynamic (anisotropic and isotropic) states for a shocked carbon-fibre epoxy composite (CFC) of any symmetry. The proposed EOS, using a generalised decomposition of a stress tensor [A.A. Lukyanov, Int. J. Plasticity 24, 140 (2008)], represents a mathematical and physical generalisation of the Mie-Grüneisen EOS for isotropic material and reduces to this equation in the limit of isotropy. Although a linear relation between the generalised anisotropic bulk shock velocity U_s ^A and particle velocity u_p was adequate in the through-thickness orientation, damage softening process produces discontinuities both in value and slope in the U_s ^A-u_p relation. Therefore, the two-wave structure (non-linear anisotropic and isotropic elastic waves) that accompanies damage softening process was proposed for describing CFC behaviour under shock loading. The linear relationship U_s ^A-u_p over the range of measurements corresponding to non-linear anisotropic elastic wave shows a value of c₀ ^A (the intercept of the U_s ^A-u_p curve) that is in the range between first and second generalised anisotropic bulk speed of sound [A.A. Lukyanov, Eur. Phys. J. B 64, 159 (2008)]. An analytical calculation showed that Hugoniot Stress Levels (HSLs) in different directions for a CFC composite subject to the two-wave structure (non-linear anisotropic elastic and isotropic elastic waves) agree with experimental measurements at low and at high shock intensities. The results are presented, discussed and future studies are outlined.     

Pressure dependence of the superconducting transition temperature of T5T9 metallic glasses (T5Nb,Ta; T9Rh,Ir)

The pressure dependence of the superconducting transition temperature, T_c, is determined for eight metallic glasses in the series (Nb_1?xTa_x)₅₅T₄₅, where T Rh, Ir. From these data we estimate the Grüneisen parameter, γ_G, and the volume dependence of the electron-phonon coupling constant, λ. Pressure is observed to affect T_c through both γ_G and λ.     

Critical behaviour in the commensurate-incommensurate phase transition of pure and γ-irradiated LiRbSO4 crystals

The effect of γ-irradiation on the incommensurate phase of LiRbSO₄ crystals has been studied by measuring the specific heat C_p . As a result of γ-irradiation, the values of C_p decreased and the transition temperature T_c shifted to lower values. The values of ΔH and ΔS decreased with increasing dose rate. The results are explained on the basis of an energy change due to induced lattice defects.     

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.     

Relation between the critical magnetic field and energy gap of a superconductor

A dynamical model is used to derive a relationship between the slope of the reduced critical magnetic field for T = T_c and the energy gap Δ_o of a superconductor. Good agreement with the relation |dh/dt|_t=1 = Δ_o/ k T_c proposed by Toxen is found up to Δ_o/k T_c = 4.     

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.     

Raman analyses of co‐phasing and hysteresis behaviors in V2O3 thin film

We present the studies of the phase transition behaviors of V₂O₃ thin film using temperature‐dependent Raman scattering spectroscopy. Our results show that in both the cooling and heating processes of V₂O₃ thin film, the phase transition occurs gradually but not suddenly, contrary to that in single crystal. The coexistence of both the metal and insulator phases with co‐phasing ΔT_c larger than 30 K is observed in both the cooling and heating processes. We discuss that this large co‐phasing ΔT_c should be distinguished with the large hysteresis ΔT_h reported in nanostructures. In addition, our discussions indicate that co‐phasing ΔT_c and hysteresis ΔT_h would be mainly correlated with stress and defect states in sample, respectively. Furthermore, our Raman analyses suggest that stress would also induce phase transitions in V₂O₃, and the stress (pressure)‐induced phase transitions would behave differently comparing with the temperature‐induced transitions under normal pressure. Copyright © 2012 John Wiley & Sons, Ltd.     

Phase relations for SrF2 TO 50 Kbars and 1900°C and its compression to 40Kbars at 25°C

The phase diagram of SrF₂ to 50 Kbars and 1900°C, obtained primarily by differential thermal analysis (d.t.a.), is presented. In analogy to the isostructural compound CaF₂, three solid phases, α, β, γ-SrF₂, as well as the liquid field, have been located. Thermochemical data (dT/dP, ΔV, ΔS) of the α-β and α-γ boundaries, and the melting curve are given. A tentative phase diagram for the isostructural compound BaF₂ is proposed. In addition, the first compression data for SrF₂ to 40 Kbars are reported. The bulk modulus, its pressure derivative, and the Grüneisen constant of SrF₂, CaF₂ and BaF₂ are compared.     

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).     

Thermodynamic characteristics of the thermal polymerization of perfluoropropylvinyl ether at high pressures

The limiting polymerization temperatures of PFPVE at pressures 5.28–10.56 kbar (T _c = 200°C at 7.04 kbar and T _c = 240°C at 10.56 kbar) are measured. The volume of reaction ΔV and enthalpy of polymerization ΔH are determined.     

Large-scale flow structures in a planar offset attaching jet with a co-flowing wall jet

Conditional averaging techniques were used to examine the periodic motions that were observed in flows consisting of an offset planar jet and a co-flowing planar wall jet. The offset jet is one jet height (H_j) away from the wall and has a Reynolds number of approximately 40, 000, based on H_j and flow-rate averaged velocity U_o; for the co-flowing jets, different heights (i.e., 0.18H_j and 0.5H_j) and velocities (i.e., 0.56U_o and 0.36U_o) were considered. The flows had periodic motions with frequencies fH_j/U_o = 0.28 and 0.49 or fH_c/U_o = 0.23 and 0.25, where H_c is the distance between the jets. The periodic motions were present in both the inner shear layer of the offset jet above the re-circulation region and the outer shear layer of the wall jet below the re-circulation region. The motions from the inner shear layer of the offset jet persisted in the shear layer that formed downstream of the re-circulating region. There were periodic motions in the outer shear layer of the offset jet particularly in the flow with the smaller wall jet. The relative contribution of the motions to the total fluctuations increased as the flow evolved downstream reaching a maximum approximately 4H_c downstream of the flow exit. The relative contribution of the periodic motions to the turbulent fluctuations was similar in the two flows but the periodic motions had a much larger impact on the near-wall velocity and pressure fluctuations in the flow with the smaller wall jet due to the trajectory of the periodic structures, the distance of the periodic structures to the wall and the size of these structures.     

Equation of state of fluid helium at high temperatures and densities

Hugoniot curves and shock temperatures of gas helium with initial temperature 293 K and three initial pressures 0.6, 1.2, and 5.0 MPa were measured up to 15000 K using a two-stage light-gas gun and transient radiation pyrometer. It was found that the calculated Hugoniot EOS of gas helium at the same initial pressure using Saha equation with Debye-Hückel correction was in good agreement with the experimental data. The curve of the calculated shock wave velocity with the particle velocity of gas helium which is shocked from the initial pressure 5 MPa and temperature 293 K, i.e., theD ≈u relation,D=C ₀+λu (u<10 km/s, λ=1.32) in a low pressure region, is approximately parallel with the fittedD ≈u (λ=1.36) of liquid helium from the experimental data of Nellis et al. Our calculations show that the Hugoniot parameter λ is independent of the initial density p{in0}. TheD≈u curves of gas helium will transfer to another one and approach a limiting value of compression when their temperature elevates to about 18000 K and the ionization degree of the shocked gas helium reaches 10⁻³.     

Equation of state of fluid helium at high temperatures and densities

Helium, hydrogen, and their isotopes are the simplest monoatomic and diatomic molecules. It is relatively easy to describe their properties using the basic principles of quantum mechanics. In condensed matter physics, hydrogen and helium serve as the models for the condensed matter properties at extreme conditions so that both experi- mental and theoretical physicists pay much attention to the study of their properties[1], especially the insulator-metal transition of hydrogen[2]. The aim to st…     

Theory of Gravitational-Inertial Field of Universe. IV. The Universe and the Microcosm

On basis of principle of discreteness of the space and time the following relations are obtained Λ_oM_oc = 2π?, τ_oE_o = 2π? and c² = 2GM_o/Λ_o giving the values of fundamental elements of length Λ_o ≈ (?G/c³)^1/2, mass M_o ≈ (?c/G)^1/2, time τ_o ≈ (?G/c⁵)^1/2 and energy E_o ≈ (?c⁵/G)^1/2. The geon crown of any critical system and the crown of the Universe must have a thickness equal to the fundamental length Λ_o = 2(π?G/c³)^1/2 = 5.74. 10^?33 cm. Each critical system has its specific (most probable) quantum with an average invariant mass which in the case of the Universe is equal to (2π²?H_u/Gc)^1/3 ≈ 300 m_e where H_u is Hubble's constant. There are all reasons to consider the universal virtual quanta of an invariant mass m_u ≈ 300 m_e as carriers of gravitational, electromagnetic and nuclear fields in the Universe.     

The pressure dependence of superconducting energy gaps from high pressure critical field measurements

It is shown that the Toxen relationship Δ/kT_c = T_c/H_c(0) (dH_c/dT)_Tc can be used to obtain Δ/kT_c as a function of pressure from critical field curves taken at high pressures. Data for Sn, In, Zn, Al, Cd, Ga, and Th are analyzed and Δ(p)/kT_c are tabulated. For Sn and In a comparison was made of energy gaps so determined with those measured directly by tunnelling.     

Generalized Linear Mixing Rule for Classical Coulomb Mixtures

It is shown that the Coulomb energy U of fully ionized ionic mixture can be written as a sum over partial contributions of ion species j: U = T Σ_j N_ju (Γ_j, y_j) (generalized linear mixing rule). In contrast to the traditional linear mixing rule U_LM = T Σ_j N_ju_OCP(Γ_j), applicable for strong coupling, the partial contribution function u depends not only on Γ_j, but on an additional parameter y_j = (r_D/r_D^OCP)² also. Here r_D and r_DOCP are Debye radiuses in the mixture and in the one component plasma at coupling parameter Γ_j, correspondingly. The parameter y_j does not depend on a specific composition of the mixture, but on the Debye radius r_D only, making function u (Γ_j, y_j) universal. The generalized linear mixing rule can be applied at any coupling parameter, if ionic mixture is not crystallized. It reproduces results of the Debye‐Hückel theory at weak coupling and traditional linear mixing rule at strong coupling. It can be easily applied to the complicated mixtures, composed of a large number of ion species. Since y_j is temperature independent, the Coulomb contribution to Helmholtz free energy of the mixture can also be presented in a form of generalized linear mixing rule (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The instability point H s of the Meissner state for large-κ superconductors

The critical field H _s corresponding to the emergence of vortices in a superconductor without a threshold is found near the transition temperature and in the limit as T→0 for an arbitrary value of the depairing factor Γ. In superconductors of the second kind, this field value coincides with the absolute instability point of the Meissner state. In large-κ superconductors, the order parameter tends to zero on the surface of the super-conductor if the external magnetic field reaches the value H _s. We obtain that H _s=H _cm (where H _cm is the thermodynamic critical field) for an arbitrary value of the depairing factor Γin the temperature region near T _c and at T=0.     

On the Debye temperature and Grüneisen parameters for hexagonal close-packed crystals consisting of p-H2 and o-D2 molecules

The expressions for the Debye temperature Θ as well as for the first (γ = ?[?ln(Θ)/?ln(V)] _T ) and second (q = [?ln(γ)/?ln(V)] _T ) Grüneisen parameters are derived based on the Mie-Lennard-Jones pair atomic interaction potential. The conditions imposed on the Θ(V/V ₀), γ(V/V ₀), and q(V/V ₀) dependences for V/V ₀ → 0 and for V/V ₀ → ∞ are analyzed. Here, V/V ₀ is the ratio of the molar volumes for pressure P at temperature T and for P = 0 at T = 0 K. Calculations are performed for crystals of parahydrogen and orthodeuterium at T = 0 K for V/V ₀ ranging from 1.30 to 0.01. Good agreement is reached between the calculated dependences and experimental data. The behavior of dependences Θ(V/V ₀), γ(V/V ₀), and q(V/V ₀) upon a variation of the isotopic composition of the crystal is analyzed.