Heat Capacity Cv Research Articles

Phase Stability and Thermo-Physical Properties of Nickel-Aluminum Binary Chemically Disordered Systems via First-Principles Study

The effect of Al content and crystal structures on ground state, phase stability, elasticity and thermodynamics of Ni1−xAlx (x = 0.25, 0.50 and 0.75) binary chemically disordered systems are investigated using first-principles method in combination with quasi-harmonic Debye-Gruneisen model. The special quasirandom structures are applied to model disordered body-centered cubic (bcc) and face-centered cubic (fcc) phases. The Gibbs free energy of mixing of equiatomic Ni0.5Al0.5 is the lowest. The nonmagnetic fcc structure’ Ni1−xAlx are predicted to be more favorable phases. Disordered Ni1−xAlx are less stable than ordered L21 Ni3Al and B2 NiAl, and L21 phase is the most likely to form a nuclear growth. The somewhat different impact of Al content on elastic properties has been extracted that the resistance to volume change, shear deformation and elastic deformation of Ni1−xAlx decrease with increasing Al content. For bcc and fcc phases, Ni0.75Al0.25 and Ni0.25Al0.75 are predicted to be ductile behavior, while Ni0.5Al0.5 exhibit brittleness. The structural, vibrational and electronic contributions are taken into account to study the thermodynamic properties at finite temperature. The lattice constants a and volumetric thermal expansion coefficient α of Ni1−xAlx systems increase with the increase of Al content. Nevertheless, it is decreasing for heat capacity Cv and C. The vibrational entropy Svib of bcc Ni0.25Al0.75 is the largest in considered temperature. The α, C and Svib of disordered Ni1−xAlx are larger than that of ordered Ni3Al and NiAl. Vibrational and electronic entropy are the dominating at finite temperature stabilization mechanism.

The Thermodynamic Properties of CO2 up to 200 MPa Including the Critical Region, Calculated by a New Combined Equation of State with Few Parameters

Heat capacities Cv, Cp, and sound velocity W of carbon dioxide are calculated on the basis of a new thermal combined equation of state (EoS) with a low number of regulated constants. This equation includes a new regular EoS with 11 coefficients, a scaling EoS with six coefficients, and a regular transition function containing two adjustable parameters. Calculating results for thermodynamic properties of CO2 in the regular behavior range of up to 200 MPa correspond to the accuracy level of modern practical equations of state with large numbers of determined constants. This makes it possible to calculate the properties of CO2 in the critical region, taking into account the achievements of scaling theory. To determine the constants of the calculated equations, only p,ρ,T-data for CO2 were used. The experimental and tabular data on Cv, Cp, S, H, and W were not involved except isochoric heat capacity Cv in the ideal gas state. These data were used to compare the calculated results with the experimental and tabulated values. The universal critical exponents were taken in accordance with the three-dimensional Ising model. The average errors in describing the thermal properties of CO2 do not exceed errors: rms error is 0.93 % in pressure and max deviation in Cv is 10 %. Divergences in the critical region relate to application of the scaling equation of state, in contrast to the regular equations. The comparison was made with calculated Cv, Cp using the current crossover EoSs for CO2.

Evaluating stability, elastic and thermodynamic properties of AlTiNiCuCox (x = 0.5,0.75,1,1.25,1.5) high entropy alloys

Alloying effect of Cobalt on structural stability, elastic and thermodynamic properties of AlTiNiCuCox (x = 0.5,0.75,1,1.25,1.5) high entropy alloys are investigated via performing ab-initio calculations combined with quasi-harmonic Debye-Grüneisen model. The equilibrium lattice constants and density are evaluated by ab-initio calculations, third-order Birch-Murnaghan equation of state and Vegard’s law. The results of cohesive energy and obtained elastic constants screen out the mechanical stable AlTiNiCuCox alloys and also indicate that AlTiNiCuCo1.0 of BCC structure exhibits ductility unlike most HEAs. Besides, all the mechanical stable alloys show elastic anisotropy. The AlTiNiCuCo1.0 of BCC exhibits the maximum anisotropy among all the AlTiNiCuCox alloys. Then various of thermodynamic properties including vibrational entropy Svib, volumetric thermal expansion coefficient α, constant volume heat capacity Cv and Debye temperature ΘD are calculated by using quasi-harmonic Debye-Grüneisen model. The FCC AlTiNiCuCo0.5 alloy exhibits outstanding thermodynamic properties compared with other HEAs of AlTiNiCuCox system. Finally, electronic structures are studied by density of states, partial density of states and Fermi energy.

First-principles calculations to investigate structural and thermodynamic properties of Ni2LaZ (Z = As, Sb and Bi) Heusler alloys

Structural, electronic, elastic and thermodynamic properties of Ni2LaZ (Z = As, Sb and Bi) Heusler alloys based on rare earth element have been investigated using full-potential linear muffin-tin orbital (FP-LMTO) method within generalized gradient approximation (GGA) in the frame of density functional theory (DFT). By using total energy variations, the independent elastic constants and their pressure dependence have been determined. Also, anisotropic parameter (A), shear modulus (G), Young modulus (E), Poisson’s ratio (ν), ratio (B/G) are calculated. Using quasi-harmonic Debye model, thermodynamic properties of Ni2LaZ (Z = As, Sb and Bi) Heusler alloys are investigated in temperature range 0–1200 K and pressure range 0–50 GPa. The temperature and pressure effects on the unit cell volume, bulk modulus (B), heat capacities (Cv) at stable volume, (Cp), Debye temperatures (θD), Gibbs energies (G), thermal expansion coefficients (α) and entropies (S) are determined from non-equilibrium Gibbs functions. This study allows to understand deeply the structural and thermodynamic properties of Ni2LaZ (Z = As, Sb and Bi) Heusler alloys in shortest time and cost-effective.

First-principles study on the mechanical, vibrational and thermodynamic characteristics of intermetallic compound Ni2Ta

The mechanical, vibrational and thermodynamic characteristics of Ni2Ta were systematically investigated by means of density functional theory. The fully relaxed structure parameters were agreed well with the available experimental measured datas and published theoretical results. The single crystal elastic constants， polycrystalline modulus, Possion's ratio σ and Vickers hardness Hv were obtained. The anisotropic characters were studied by plotting the 3D surface contour of shear modulus and Young's modulus. Using the finite displacement method, the phonon dispersion curves and the phonon density of states were reported for the first time. The infrared-active and Raman phonon modes at the Г point were assigned and discussed. Finally, the thermodynamic characteristics such as isochoric specific heat capacities Cv and Debye temperature θD were predicted by the phonon density of states. Based on these exceptional properties, it was expected that Ni2Ta could be a promising intermetallic compound with high temperature and corrosion resistant performance.

Method for constructing fundamental equation of state that satisfies the scaling theory and applicable for substances insufficiently explored in the critical point vicinity

Here, the authors discuss the problem of describing the equilibrium properties of a substance in the vicinity of the critical point on the basis of the fundamental equation of state (FEoS) of a liquid and a gas in the absence of experimental information about the calorific properties of a given substance in this field of state parameters. FEoS has the following characteristics: in the region of low densities, FEoS transforms to the virial equation of state; in the asymptotic vicinity of the critical point, FEoS meets the requirements of the scaling theory of critical phenomena. The method is based on a new representation of the scaling hypothesis based on the Scofield–Litster–Ho linear model (LM), the Benedek hypothesis and the Lysenkov–Rykov ratio (LR) which establishes the relationship between LM parameters and the real liquid using the Pokrovsky transformations. Testing of the proposed method for constructing FEoS has been carried out using the example of describing the equilibrium properties of argon. It has been ascertained that the use of the LR ratio has allowed, firstly, reducing the number of individual FEoS parameters and, secondly, excluding the data about isochoric heat capacity CV related to the critical point wide vicinity from the calculation scheme.

Experimental research of thermodynamic properties of water + aliphatic alcohol mixtures in the wide range of parameters of state

Experimental data of p, r, T, x - relations for water+aliphatic alcohol binary systems (methanol, ethanol, n-propanol) for values of composition x (0.2, 0.5, 0.8 mole fraction of alcohol) among the phase equilibrium line in one phase (liquid, vapor) and in supercritical regions are described by polynomial polynomial equation of state, represented by expansion of the compressibility factor Z = p/RTρ into a power series of density and temperature: , and , where ω = ρ/ρc and temperature τ = T/Tc – is reduced density and reduced temperature; ρc, Tc – critical density and critical temperature; R = 8.314 J/(mol⋅K) is the universal (molar) gas constant.The average relative deviation of calculated values of pressure from experimental ones is 1.1%. By using this equation and expressions thermodynamic properties: coefficient of isothermal compressibility KT, coefficient of volume thermal expansion, pressure coefficient, internal pressure pi, isochoric heat capacity Cv, isobaric heat capacity Cp, speed of sound, adiabatic index k, Helmholtz free energy F, Gibbs energy G, entropy S, enthalpy H, internal energy U, differential isothermal throttling effect dis, differential adiabatic throttling effect dad.

Quantitative modeling for prediction of thermodynamic properties of some pyridine derivatives using molecular descriptors and genetic algorithm‐multiple linear regressions

AbstractPyridines are compounds with a wide range of biological activities and they are the basis of several groups of drugs. In this study, the relationship between molecular descriptors and the thermal energy (Eth kJ/mol), heat capacity (C v J/molK), entropy (S J/mol K), enthalpy of formation (ΔH f kJ/mol), and Gibbs free energy (ΔG kJ/mol) of pyridine derivatives is studied. These properties were calculated at the Hartree–Fock level of theory and 6‐311G* G basis sets by Gaussian 09 software. The chemical structures of 171 pyridine derivatives were drawn by the Gauss View 05 program. The genetic algorithm‐multiple linear regression (GA‐MLR) and backward methods—were used to select the suitable descriptors and also for predicting the thermodynamic properties of pyridine derivatives. The correlations between the molecular descriptors in the best models were discussed by the Pearson coefficient correlation and collinearity statistics. The predictive powers of the GA‐MLR models are studied using leave‐one‐out (LOO) cross‐validation and external test set. The best quantitative structure–property relationship (QSPR) models are obtained based on the statistical parameters, such as R 2, Q 2 LOO, and RMSE values for the data sets. The predictive ability of the GA‐MLR models with two‐three selected molecular descriptors was found to be satisfactory and could be used for modeling and predicting of the mentioned properties of nontested pyridine derivatives.

Thermophysical Properties of the Lennard-Jones Fluid: Database and Data Assessment.

Literature data on the thermophysical properties of the Lennard-Jones fluid, which were sampled with molecular dynamics and Monte Carlo simulations, were reviewed and assessed. The literature data were complemented by simulation data from the present work that were taken in regions in which previously only sparse data were available. Data on homogeneous state points (for given temperature T and density ρ: pressure p, thermal expansion coefficient α, isothermal compressibility β, thermal pressure coefficient γ, internal energy u, isochoric heat capacity cv, isobaric heat capacity cp, Grüneisen parameter Γ, Joule-Thomson coefficient μJT, speed of sound w, Helmholtz energy a, and chemical potential) were considered, as well as data on the vapor-liquid equilibrium (for given T: vapor pressure ps, saturated liquid and vapor densities ρ' and ρ″, respectively, enthalpy of vaporization Δhv, and as well as surface tension γ). The entire set of available data, which contains about 35 000 data points, was digitalized and included in a database, which is made available in the Supporting Information of this paper. Different consistency tests were applied to assess the accuracy and precision of the data. The data on homogeneous states were evaluated pointwise using data from their respective vicinity and equations of state. Approximately 10% of all homogeneous bulk data were discarded as outliers. The vapor-liquid equilibrium data were assessed by tests based on the compressibility factor, the Clausius-Clapeyron equation, and by an outlier test. Seven particularly reliable vapor-liquid equilibrium data sets were identified. The mutual agreement of these data sets is approximately ±1% for the vapor pressure, ±0.2% for the saturated liquid density, ±1% for the saturated vapor density, and ±0.75% for the enthalpy of vaporization-excluding the region close to the critical point.

Ab-initio study of electronic and phononic properties of bulk TiC and its narrow nanowires by density functional theory

In this article, electronic and phononic properties of TiC bulk and its narrow nanowires are calculated by using Quantum-Espresso/PWSCF computational package in the framework of density functional theory. According to the results, this compound shows a metallic behavior in the bulk structure, but for the smallest diameters of the nanowires, against the bulk, a semiconducting behavior was observed. This deviation becomes negligible at higher diameters. In the following, phonon calculations have been performed on bulk and the first diameter of nanowires with a square cross-section. By calculating the phonon modes of Brillouin zone, the thermodynamic properties of both mentioned structures such as vibrational free energy, the heat capacity Cv, Debye temperatureΘ, entropy and their variations against temperature T have been obtained through the quasi-harmonic Debye model. Calculations show that heat capacity behavior of the vibrational lattice is consistent with Debye model. Moreover, the temperature dependence of a Debye temperature indicates that the Debye stiffness in a bulk is greater than the nanowire structure.

On isochoric heat capacity of fluids at high temperatures

As known, the isochoric heat capacity Cv of many atomic and molecular substances in liquid and supercritical fluid states decreases with increasing temperature at high temperatures. It is shown that: such a behavior of Cv is related to a decrease of the contribution of interactions of atoms with each other to Cv with increasing temperature; such a behavior of Cv takes place for atomic substances when the fluctuations of the total kinetic energy increase with increasing temperature faster than that of the total potential energy; such a behavior of Cv can be described by the density independent radial distribution function of non-ideal dilute gas consisting of atoms interacting with each other via an additive potential which is equal to the sum of a spherically symmetrical pair interaction potentials over of all pairs of particles; the pair potential can be equal to: the potential of soft spheres, bounded potential, non-positive potential, the sum of the potential of hard spheres and bounded or non-positive or attractive potential, and the sum of the repulsive potential of soft spheres and attractive London potential; the above conclusions are valid for molecular substances if the isochoric heat capacity of the molecular ideal gas does not depend on temperature; the radial distribution function of non-ideal dilute gas can describe the above behavior of Cv for argon in liquid and supercritical states; the Carnahan–Starling equation of state for the hard spheres with temperature dependent diameter gives a good quantitative description of the isochoric heat capacity of argon if the diameter is defined using the Lennard-Jones potential. The equation to define the Frenkel line of molecular substances on the (temperature, density)-plane is established. The explicit expressions to define the Frenkel line are derived. It is shown that the existence of the Frenkel line established from the condition Cv−Cv,ig=k∕2, where Cv,ig is the isochoric heat capacity of an ideal gas, does not mean that the solid-like and liquid-like states exist in liquids, and the transition from Cv>2k to Cv<2k across the Frenkel line is the transition from the solid-like states to liquid-like ones.

Determination of heat capacity of pure metals, compounds and alloys by analytical and numerical methods

Phase diagrams are normally calculated from a combination of physical equations and experimental parameters. Gibbs free energy of mixing; thermodynamics activity and enthalpy of mixing; transformation temperatures and the concentration range of the alloys components are calculated to permit an alloy system database to be constructed. The molar specific heat capacity (cv) is normally obtained by numerical derivative of the enthalpy equation with respect to temperature and concentration. The experimental determinations of the topological parameters as a function of concentration and temperature is an enormous task. On the other hand, physical formulations such as Einstein’s and Debye’s equations are physically consistent models for the molar specific heat capacity of the solid, and they depend only on a set of basic physical parameters. Einstein’s formulation works very well for temperatures T > 102 K, however, as it varies in the form of 1/T2, it fails to conform to lower temperature experimental data. Debye assumed only three branches of the vibrational spectrum with the same linear dispersion relation, and derived an equation also consistent for lower temperatures, and as the temperature decreases to absolute zero, it varies as a function of 1/T3 thus permitting experimental scatters to be fitted. Another way for calculating cv is by carrying out polynomial functions [1], which are only recommended for temperatures above 298.15 K, because bellow this temperature, cv is strongly dependent on the quantization of thermal energy, which can be stored in different forms in the material, such as electronic, magnetic, vibrational, rotational and translational energies. In this paper corrections for Debye’s and Einstein’s equations for cv are derived to encompass its thermal history dependence, electronic and rotational energies for both lower and higher temperatures in order to permit the calculation of the molar specific heat capacity of pure metals, phases and single-phase alloys.

Effects of pressure and temperature on thermodynamic properties of WB3 by first-principles predictions

In this work, the effects of temperature and pressure on thermodynamic properties of potential ultrahard hP4-, hP8-, hP16- and hR24-WB3 were predicted using first-principles calculations based on density functional theory and using quasi-harmonic Debye model within GIBBS program. Bulk modulus B, thermal expansion coefficient α, Debye temperature Θ, Grüneisen ratio γ and heat capacity Cv and Cp under pressure (P) of 0–30 GPa and temperature (T) of 0–1500 K were investigated. The phonon dispersions and the formation enthalpy in the ground state demonstrated that these WB3 are thermodynamically stable. The thermal expansion coefficient α is more sensitive at the low temperatures than that at high temperatures. Moreover, as the pressure increases, thermal expansion coefficient of each WB3 decreases. The pressure and temperature dependences of Debye temperature Θ are just the opposites of Grüneisen parameter γ.

Ab-initio simulations of MgTiO3 oxide at different pressure

We employ Wien2k code, an all-electron scheme based on density functional theory (DFT) to explore the structural, thermodynamic, mechanical and opto-electronic behavior of MgTiO3 (MTO) oxide in the pressure range 0–200 GPa. The structural, mechanical and thermodynamic stabilities of MTO are discussed in terms of Goldschmidt's tolerance factor, enthalpy of formation and Born stability criteria, respectively. Mechanical nature is further discussed by calculating the Debye temperature, wave velocity, Pugh's and Poisson's ratios. The electron density (n) and specific heat capacity (Cv) of electrons are explained in details. The pressure up to 200 GPa, with the step of 50 GPa, is implemented in order to tune the electronic properties where a direct to indirect band gap transition is observed. We further explored the refraction of light (ultraviolet region), dielectric constant and the optical behavior of MTO.

The isochoric specific heat capacity for R1234ze(E) at temperatures from (237 to 349) K and pressures up to 9.2 MPa

In this work, the isochoric specific heat capacity (cv) of trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) in the compressed liquid states were measured using an adiabatic batch calorimeter. The temperatures ranged from (237 to 349) K and pressures up to 9.2 MPa. Measurements were obtained for a total of 112 state conditions on 22 pseudo-isochores. The standard uncertainties of temperatures, pressures and isochoric specific heat capacities were estimated to be 12 mK, 5 kPa and 0.98%, respectively. The experimental cv values for R1234ze(E) are compared with three equations, including two Helmholtz equations of state (EOSs) and a generalized equation based on corresponding state principle. The data in this work show good agreement, and the average absolute relative deviations are 1.37%, 1.27% and 1.59% for the above three equations, respectively.

High Pressure Effects on Structural, Elastic and Thermodynamic Properties of Tantalum Mononitride

The pressure effects on the structural, elastic and thermodynamic properties of tantalum mononitride in WC-type phase (i.e. WC–TaN) are investigated by the first-principles plane wave pseudo-potential density functional theory method and the quasi-harmonic Debye model. The obtained equilibrium structure parameters and ground state properties are in excellent agreement with the experimental and other theoretical results. The calculations of the phonon dispersion curve and the density of phonon states verify that the WC–TaN is dynamically stable. A full elastic tensor and anisotropies behavior of the WC–TaN is also evaluated and discussed in the wide pressure range. The results show that WC–TaN is elastic anisotropy and mechanically stable up to 100 GPa, and the compression along c-axis direction is more difficult than along a-axis. The obtained superior mechanical properties show that WC–TaN is a promising candidate structure to be one of the ultra-incompressible and hard materials. Finally, by using the quasi-harmonic approximation model, we predicted the thermodynamic properties of WC–TaN under pressure and temperature. The heat capacity CV, Debye temperature θ, the thermal expansion α and the Gruneisen constant γ are obtained successfully in the ranges of 0–100 GPa and 0–2000 K.

Theoretical predictions of thermodynamic and electronic properties of TiM (M = Fe, Ru and Os)

In this work, thermodynamic and electronic properties of CsCl-type Intermetallics TiM (M = Fe, Ru and Os) were predicted by first-principles calculation. The bulk modulus B, the specific heat capacity Cv and Cp, Grüneisen parameter γ and Debye temperature Θ were investigated under temperature of 0–1200 K and pressure of 0–20 GPa. The calculated phonon dispersion and density of states verified that these compounds are thermodynamically stable. The thermal expansion coefficient α is sensitive to high temperature and high pressure. And as the pressure increases, thermal expansion coefficient of these compounds decreases. The pressure and temperature dependence of the Grüneisen parameter γ is exactly the opposite of Debye temperature. By analyzing the electron density distribution, we find the bonds formed between Ti and M atoms. The obtained results will provide guidance for future application and investigation.

First-Principle Computed Structural and Thermodynamic Properties of Cu2ZnSn(SxSe1−x)4 Pentanary Solid Solution

This paper is dedicated to the ab initio study of the structural and thermodynamic properties of Cu2ZnSn(SxSe1−x)4 bulk alloys. The calculations are conducted using full-potential linear-augmented-plane-wave plus local-orbital (FP-LAPW + lo) method within the revised generalized gradient approximation of Perdew–Burke–Ernzerhof (GGAPBEsol). This method is used to find more valuable equilibrium structural parameters than the simplest approximations of PBE and local density approximation (LDA). The obtained structural properties appear to be affected by the relaxation effect, and all alloys are thermodynamically favorable to the process according to the enthalpy of formation calculations. We find here a nonlinear dependence of lattice parameters a and c with respectively a small downward bowing parameter b of + 0.09 A and + 0.19 A for relaxed structures. The thermodynamic quantities, namely the entropy, the constant volume, the pressure heat capacity (Cv and Cp) and Debye temperature, are computed for different S/(S + Se) atomic ratios by varying temperature from 0 K to 1000 K. These quantities are successfully obtained by using the combined approach of FP-LAPW and a quasi-harmonic model. Overall, there is good agreement between our calculated quantities and other results.

Low-frequency phonon dynamics and related thermal properties of axially stressed single-walled carbon nanotubes

Synthesis temperatures of composite materials are usually far less than the ones of their use, thus carbon nanotubes (CNTs) embedded into a polymer matrix undergo significant axial stress. We develop a continuous theory, which describes the dynamics of stressed single-walled (SW-) CNTs and predicts their low-frequency phonon spectra. The changes in dispersion laws of SWCNT low-frequency phonon modes due to the axial stress of different signs are discussed. Then, the results obtained are used to analyze low-temperature (T < 70 K) heat capacity and thermal conductivity of individual nanotubes. We demonstrate that compressive stress leads to increase in heat capacity CV of an individual SWCNT, while tensile stress causes CV to decrease. In the latter case at T → 0 heat capacity diminishes according to a linear law ~T instead of a power one ~T1/2. Nevertheless, according to our results, axial stress hardly affects low-temperature thermal conductance of SWCNTs. Influence of investigated effects on the corresponding macroscopic properties of CNT-based composite materials are also discussed.

Bose Liquid Mean-Field Theory with Application to HeI

A mean-field theory is developed for a Bose liquid enclosed in a large vessel 𝒱. In accord with liquid structure concepts of Mitus et al., the liquid in 𝒱 is assumed to consist of adjacent macroscopic subregions Λk. In each subregion the bosons perform a locally ordered motion with prevailing orientation k + x, which varies randomly when passing from one subregion to another. |k| is constant, whereas temperature dependence of |x| is governed by a mean-field theory (MFT). The theory is applied to simulate HeI heat capacity CV (T) at T &gt; Tλ = 2.17 K and CV (T) singularity at [Formula: see text]. The MFT numerical heat capacity Cn(T) = ΔE/ΔT exhibits behaviour characteristic of a singularity at [Formula: see text]: rapid increase with decreasing ΔT. Apart from [Formula: see text], good agreement of Cn(T) with CV(T) experimental plot is also found above Tλ, at T ∊ (Tλ, 3K].