Constant-volume Specific Heat Research Articles

THE AB INITIO CALCULATION OF THE DYNAMICAL AND THE THERMODYNAMIC PROPERTIES OF THE ZINC-BLENDE GaX (X=N, P, As AND Sb)

By this work, we aim to study the dynamical and the thermodynamic properties of the zinc-blende GaX ( X = N , P , As and Sb ) using the Ab initio simulation method. Indeed, we studied the lattice dynamics, the constant-volume specific heat (Cv), the internal energy (U), the entropy (S) and the free energy (F). The observed differences between the properties of GaX elements were discussed. Our results and the available literature data (theoretical and experimental) seems to be in good agreement. Moreover, Cv, U, F and S were calculated by using the harmonic approximation in the calculation of the dynamic lattice vibration. The good agreement between our results of both the phonon frequency, the constant-volume specific heat and the experimental data allows us to conclude that our results of S, U and F of GaX were well predicted.

Prediction of specific heat and thermal conductivity of nanofluids by a combined equilibrium and non-equilibrium molecular dynamics simulation

Abstract Nanofluids, a new thermal fluids, have scientific challenges because the existing theories underpredict their thermal conductivity. One way to calculate this parameter is equilibrium molecular dynamics (EMD). In the previous studies of EMD, the thermal conductivity of nanofluids was calculated by the autocorrelation function of the heat current through the Green-Kubo formula. The convergence of this function requires a large time, nevertheless convergence of integral may still be slow or not well behaved. In this study, a new method based on combination of equilibrium and non-equilibrium molecular dynamics simulation in a non-periodic boundary conditions was used to calculate the thermal conductivity. In this method, first the specific heat and the thermal diffusivity of a nanofluid were determined by EMD and non-equilibrium (NEMD) respectively. Then the thermal conductivity was calculated from the relation of thermal diffusivity with the constant volume specific heat. This approach was tested by the nanofluid of silicon nitride nanoparticles in a liquid argon. The CHARMM22 force field and the force field of silicon nitride were combined to perform the simulation. The nanoparticle was generated according to the data of X-ray crystallography. The results of simulation for the base fluid at different temperatures were compared with experimental data to check the accuracy of the MD modeling. The effects of temperature and nanoparticle loadings on the thermal conductivity were investigated. The results showed that the thermal conductivity increases with increasing the loadings and decreasing the temperature. The calculation of root mean square displacements for liquid argon showed that the thermal transport enhancement of the nanofluid was mostly due to the increased movement of liquid phase atoms in the presence of non-metallic nanoparticle. This finding was also confirmed by the analysis of the density profile of liquid atoms near the interface. Finally, the comparison of the results of this study with other researchers showed the kind of nanoparticle could not significant to increase the thermal conductivity of nanofluids.

Thermal Properties of Magnesium Hydroxide Using First-Principles Method

The thermal properties of the magnesium hydroxide crystalline powder samples, which were prepared by us, were investigated by first-principles method. The calculated results show that the forbidden band of phonon appears in both 14～19 THz and 33～102 THz. There are 3 acoustic lattice wave branches and 12 optical ones, where two horizontal acoustic branches are degeneracy and two horizontal optical ones are degeneracyhe. Moreover, The constant-volume specific heat quickly increases at low temperature; but it tends to be flat at high temperature. Besides, the Debye temperature quickly increases to 483K from temperature 0K to 10K; but from temperature 100K to 1000K, it is linear with temperature approximately, whose increasing rate is about 1.333; at temperature of 1000K, the Debye temperature is 1930K, reaching its maximum.

Thermodynamic Derivation in Magneto-Electro-Elasticity

Magneto-electro-elastic materials constitute important elements of smart structures. Based on thermodynamics within isothermal linear process and isentropic linear process, the mathematical derivation of magneto-electro-elasticity is established in this work. The Helmholtz free energy density, internal energy density and enthalpy density are applied to solve the problem. It is important to mention that constant pressure specific heat and constant volume specific heat play a remarkable role in thermodynamic analysis of magneto-electro-elasticity. Overall, this study has successfully derived a theoretical framework in solving basic problems of thermodynamics and magneto-electro-elasticity.

Two liquid states of matter: A dynamic line on a phase diagram

It is generally agreed that the supercritical region of a liquid consists of one single state (supercritical fluid). On the other hand, we show here that liquids in this region exist in two qualitatively different states: "rigid" and "nonrigid" liquids. Rigid to nonrigid transition corresponds to the condition τ≈τ(0), where τ is the liquid relaxation time and τ(0) is the minimal period of transverse quasiharmonic waves. This condition defines a new dynamic crossover line on the phase diagram and corresponds to the loss of shear stiffness of a liquid at all available frequencies and, consequently, to the qualitative change in many important liquid properties. We analyze this line theoretically as well as in real and model fluids and show that the transition corresponds to the disappearance of high-frequency sound, to the disappearance of roton minima, qualitative changes in the temperature dependencies of sound velocity, diffusion, viscous flow, and thermal conductivity, an increase in particle thermal speed to half the speed of sound, and a reduction in the constant volume specific heat to 2k(B) per particle. In contrast to the Widom line that exists near the critical point only, the new dynamic line is universal: It separates two liquid states at arbitrarily high pressure and temperature and exists in systems where liquid-gas transition and the critical point are absent altogether. We propose to call the new dynamic line on the phase diagram "Frenkel line".

Structural, vibrational and thermodynamic properties of Zirconium–cobalt: First-principles study

To evaluate ZrCo as a getter material for the storage of hydrogen and its isotopes, the structural, vibrational and thermodynamic properties of ZrCo are investigated by first-principles. The calculated phonon frequencies at the Γ point are assigned using density-functional perturbation theory (DFPT). The phonon dispersion curves along several high-symmetry lines at the Brillouin zone and the phonon density of states are also calculated. The thermodynamics properties including the phonon contribution to the Helmholtz free energy ΔF, the internal energy ΔE, the entropy S, and the constant-volume specific heat Cv are determined within the harmonic approximation based on the calculated phonon density of states.

Hydrated electron yields in liquid and supercritical water—a theory

Our theory, outlined earlier [Schiller, R., 1990. Ion-electron pairs in condensed polar media treated as H-like atoms. J. Chem. Phys. 92, 5527–5532.], is based on the idea that the electron and its geminate positive ion form a hydrogen-like atom, which can be ionized at the expense of the energy fluctuations in the medium. Temperature, T, static relative permittivity, εs, and constant-volume molar specific heat, Cvm, play here the decisive role; the combination Tεs2Cvm, is the variable by which the yield can be predicted. The calculations agree with the recent experimental results on the temperature dependent yields of hydrated electrons by Kratz et al. [Kratz, S., Torres-Alcan, J., Urbanek, J., Lindner, J., Vöhringer, P., 2010. Geminate recombination of hydrated electrons in liquid-to-supercritical water studied by ultrafast time-resolved spectroscopy. Phys. Chem. Chem. Phys. 12, 12169–12176.] reasonably well.

Thermal properties of BeX (X = S, Se and Te) compounds from ab initio quasi-harmonic method

We report ab initio calculations of the structure, elastic constants, lattice dynamics and thermodynamic properties of BeS, BeSe and BeTe compounds. The fully minimized structure parameters and elastic constants of BeS, BeSe and BeTe compounds are in good agreement with previous theoretical and experimental data. The density functional perturbations theory with quasi-harmonic approximation QHA methods are applied to determine the phonon dispersion relations, phonon density of states, phonon decomposition density of states, and thermal quantities. The computed thermodynamic properties such as Debye temperature is in agreement with the previous work. The vibrational entropy and constant-volume specific heat are shown for the first time.

Modified Nosé–Hoover thermostat for solid state for constant temperature molecular dynamics simulation

Nosé–Hoover (NH) thermostat methods incorporated with molecular dynamics (MD) simulation have been widely used to simulate the instantaneous system temperature and feedback energy in a canonical ensemble. The method simply relates the kinetic energy to the system temperature via the particles’ momenta based on the ideal gas law. However, when used in a tightly bound system such as solids, the method may suffer from deriving a lower system temperature and potentially inducing early breaking of atomic bonds at relatively high temperature due to the neglect of the effect of the potential energy of atoms based on solid state physics. In this paper, a modified NH thermostat method is proposed for solid system. The method takes into account the contribution of phonons by virtue of the vibrational energy of lattice and the zero-point energy, derived based on the Debye theory. Proof of the equivalence of the method and the canonical ensemble is first made. The modified NH thermostat is tested on different gold nanocrystals to characterize their melting point and constant volume specific heat, and also their size and temperature dependence. Results show that the modified NH method can give much more comparable results to both the literature experimental and theoretical data than the standard NH. Most importantly, the present model is the only one, among the six thermostat algorithms under comparison, that can accurately reproduce the experimental data and also the T 3-law at temperature below the Debye temperature, where the specific heat of a solid at constant volume is proportional to the cube of temperature.

Vibrational properties of graphene fluoride and graphane

The vibrational properties of graphene fluoride and graphane are studied using ab initio calculations. We find that both sp3 bonded derivatives of graphene have different phonon dispersion relations and phonon densities of states as expected from the different masses associated with the attached atoms of fluorine and hydrogen, respectively. These differences manifest themselves in the predicted temperature behavior of the constant-volume specific heat of both compounds.

Lattice dynamics and elastic properties of Mg 3As 2 and Mg 3Sb 2 compounds from first-principles calculations

We investigated the structure, elastic properties, lattice dynamics, and a few of the thermodynamic properties of β-Mg 3As 2 and α-Mg 3Sb 2 compounds with anti-La 2O 3 structure using first-principles calculations based on density-functional theory. The fully relaxed structure parameters of Mg 3As 2 and Mg 3Sb 2 compounds are in good agreement with previous experimental results. The linear response method is applied to determine the phonon dispersion relations, phonon density of states, Born effective charge, and optical phonon frequencies at the Γ point of the Brillouin zone. Thermodynamic quantities such as vibrational entropy, constant-volume specific heat, and Debye temperature are also presented.

Electronic and ionic contributions to the constant-volume specific heat of carbon tetrachloride shocked at pressures up to 23 GPa

For carbon tetrachloride, a temperature Hugoniot at 7–23 GPa and a distribution of the constant-volume specific heat on the Hugoniot CV(T) at 1057–3275 K are simultaneously estimated from the Walsh–Christian (WC) equation such that the Hugoniot fits well to the existing measured data. The estimated CV(T) distribution reveals the significance of the contribution of electrons and ions to the specific heat. That is, in contrast to the almost uniform distribution of the specific heat predicted from the Debye equation, the CV(T) distribution increases significantly with an increase in the Hugoniot temperature due to thermal excitation of electrons at 1057–1500 K (7–10.1 GPa), additional activation of the dimerization reaction at 1500–2350 K (10.1–16 GPa), and also additional activation of the polymerization reaction at 2350–3275 K (16–23 GPa). As an example, evidence is presented that carbon tetrachloride is a semiconductor at 1500 K. The CV(T) distribution in each temperature range is formulated and a temperature Hugoniot is reevaluated from the WC equation using the specific heat equations formulated. It is confirmed by a good fit of the reevaluated Hugoniot to the existing measured data that the specific heat equations express the CV(T) distribution appropriately.

Structural, vibrational and thermodynamics propertiesof Zn-based semiconductors

We have preformed first-principle calculations for the structural, vibrational and thermodynamic properties of the IIB–VIA Zn-based semiconductor compounds ZnX (X = O, S, Se, Te). The phonon dispersion curves along several high-symmetry lines at the Brillouin zone together with the corresponding phonon density of states are calculated using density-functional perturbation theory. The calculated phonon frequencies at the Γ, X, and L points of the Brillouin zone show good agreement with the experimental values and other calculations. The thermodynamics properties including the phonon contribution to the Helmholtz free energy Δ F, the phonon contribution to the internal energy Δ E, the entropy S, and the constant-volume specific heat C V are determined within the harmonic approximation based on the calculated phonon dispersion relations. If 298 K is taken as a reference temperature, the difference values of H − H 298 have been also calculated and compared with the available experimental data.

Liquid 4He: Contributions to First Principles Theory. II. Quantized Vortices and the λ Transition

Quantized vortices in liquid 4He at finite temperatures are treated by first principles theory that extends results presented in paper I of this two-part set. Then the possible role of thermally excited quantized vortices in accounting for the λ transition is studied. This study indicates that vortices are probably not the dominant mechanism responsible for the λ transition, but that they may account for some minor effects near Tλ. A model that identifies critical fluctuations with quantized isothermal fourth sound waves is developed and used to derive formulas for specific heat in He II and He I. Logarithmic divergence of the constant volume specific heat is found. Numerical calculations using those formulas produce close agreement with experimental data. A formula for the radial distribution function near Tλ in He II and He I is derived and numerically evaluated. A formula for the correlation length is derived and numerically evaluated and physical characteristics of the correlation length are discussed. Numerical calculations based on that formula for correlation length are compared with experimental results. Long-range order in the liquid exhibited in the radial distribution function and correlation length is shown not to involve a Bose-Einstein condensate in this theory. The isothermal compressibility is found by integration of the radial distribution function and the result shows that isothermal compressibility is unchanged by critical fluctuations of isothermal fourth sound.

The electronic structure and thermodynamic properties of Mg2Sn from first-principles calculations

Electronic structure, elastic constants and thermodynamic properties of Mg2Sn have been calculated by using the first-principles pseudopotential method. As shown by the calculated results, the band gap of Mg2Sn is 0.1198 eV. The linear response method is applied to determine the phonon dispersion relations and phonon density of states. The thermodynamic properties such as the constant-volume specific heat and Debye temperature are calculated. The calculated thermal conductivity is compared with the experimental data.

Lattice dynamics of Mg 2Si and Mg 2Ge compounds from first-principles calculations

We report first-principles calculations of the structure, elastic properties, lattice dynamics and some thermodynamic properties of Mg 2Si and Mg 2Ge compounds. The fully relaxed structure parameters and elastic stiffness constants of Mg 2Si and Mg 2Ge compounds are in good agreement with previous experimental data. The linear response method is applied to determine the phonon dispersion relations, phonon density of states, and Born effective charge. The computed thermodynamic properties such as vibrational entropy, constant-volume specific heat, and Debye temperature coincide with previous experimental data.

First-principles study of lattice dynamics and thermodynamic properties ofLaCl3andLaBr3

We perform first-principles calculations of the lattice dynamics and the thermodynamic properties of $\mathrm{La}{\mathrm{Cl}}_{3}$ and $\mathrm{La}{\mathrm{Br}}_{3}$. Using density-functional perturbation theory, we obtain the Born effective charge tensors, the dielectric permittivity tensors, the phonon frequencies at the Brillouin zone center, and the phonon dispersion curves, as well as corresponding density of states. The Born effective charge and the dielectric permittivity tensors exhibit anisotropy, which are analyzed in detail. The calculated phonon frequencies at the $\ensuremath{\Gamma}$ point of the Brillouin zone show good agreement with the experimental values for most vibrational modes. The light yields of $\mathrm{La}{\mathrm{Cl}}_{3}:\mathrm{Ce}$ and $\mathrm{La}{\mathrm{Br}}_{3}:\mathrm{Ce}$ are theoretically estimated to be 62 400 and $71\phantom{\rule{0.2em}{0ex}}400\phantom{\rule{0.3em}{0ex}}\text{photons}∕\mathrm{MeV}$, respectively, on the basis of the calculated values of the dielectric constants and the highest longitudinal optical infrared phonon frequencies. The thermodynamics properties including the phonon contribution to the Helmholtz free energy $\ensuremath{\Delta}F$, the phonon contribution to the internal energy $\ensuremath{\Delta}E$, the entropy $S$, and the constant-volume specific heat ${C}_{v}$ are determined within the harmonic approximation based on the calculated phonon dispersion relations.

Forced convection gaseous slip flow in circular porous micro-channels

Laminar forced convection of gaseous slip flow in a circular micro-channel filled with porous media under local thermal equilibrium condition is studied numer- ically using the finite difference technique. Hydrodynamically fully developed flow is considered and the Darcy-Brinkman-Forchheimer model is used to model the flow inside the porous domain. The present study reports the effect of several operating parameters (Knudsen number (Kn), Darcy number (Da), Forchhiemer number (�) , and modified Reynolds number (Re ∗ )) on the velocity slip and temperature jump at the wall. Results are given in terms of the velocity distribution, temperature distri- bution, skin friction (CfRe ∗ ), and the Nusselt number (Nu). It is found that the skin friction is increased by (1) decreasing Knudsen number, (2) increasing Darcy number, and (3) decreasing Forchheimer number. Heat transfer is found to (1) decrease as the Knudsen number, or Forchheimer number increase, (2) increase as the Peclet number or Darcy number increase. Nomenclature C Coefficient in the Forchheimer term Cf Skin friction coefficient Cp Constant pressure specific heat Cv Constant volume specific heat D Diameter of the circular channel Da Darcy number (K/er 2 ) h Local heat transfer coefficient K Intrinsic permeability of the porous medium Kn Knudsen number (λ/r0)

Linear interaction analysis applied to a mixture of two perfect gases

The linear interaction analysis is applied to mixtures of two perfect gases. Differences of molar mass and constant volume specific heat between both gases are taken into account as two new wave families. Transfer functions across the shock wave from these waves to acoustic, shear or entropy waves are given. The approach is validated against numerical simulations of the interaction of concentration spots with a shock wave. The case of turbulence creation by a shock wave traveling in an inhomogeneous mixture is considered.

Finite temperature properties for zinc nanoclusters

The Gupta-type many-body potential was applied to describe the interactions between atoms in zinc nanoclusters. From the calculated ground state structures, obtained by Brownian-type molecular dynamic simulation, we investigated the temperature effect of zinc clusters. We studied in particular the constant volume specific heat CV which is a thermodynamic quantity and also the relative bond length Lindemann parameter δ which is a geometric quantity. Effort is devoted to revealing the anomalies observed in these quantities for Zn clusters and making a comparison with those of the typical sp-type metallic clusters. To this end, we have chosen to calculate the CV and δ of clusters Znn for 29, 33, and 53 which are judged to be less stable by the energy difference and the second energy difference as well as 6, 36, 42, and 49 which are judged by the same energy criteria to be relatively more stable. Our results of simulation show that the structures of CV and δ exhibit unusual phase transition behaviors which are drastically different from those of the usual metallic clusters. General scenarios observed in the simulation are the prevalence of the pre-melting phenomenon predicted in all of the clusters studied here.