Constant Volume Heat Capacity Research Articles

Thermophysical properties of the SPC/E model of water between 250 and 400 K at pressures up to 1000 MPa

This work explores the thermophysical properties of the SPC/E model of water at temperatures between 250 and 400 K and at pressure from 0.1 to 1000 MPa. From a series of Molecular Dynamics simulations (in the NPT ensemble and also in the NVT ensemble), the constant pressure and constant volume heat capacity, the isobaric expansion coefficient, the isothermal compressibility, and the speed of sound are obtained from fluctuation formulas and thermodynamic numerical derivatives and compared with available experimental data.

Surface phase diagrams from nested sampling.

Studies in atomic-scale modeling of surface phase equilibria often focus on temperatures near zero Kelvin due to the challenges in calculating the free energy of surfaces at finite temperatures. The Bayesian-inference-based nested sampling (NS) algorithm allows for modeling phase equilibria at arbitrary temperatures by directly and efficiently calculating the partition function, whose relationship with free energy is well known. This work extends NS to calculate adsorbate phase diagrams, incorporating all relevant configurational contributions to the free energy. We apply NS to the adsorption of Lennard-Jones (LJ) gas particles on low-index and vicinal LJ solid surfaces and construct the canonical partition function from these recorded energies to calculate ensemble averages of thermodynamic properties, such as the constant-volume heat capacity and order parameters that characterize the structure of adsorbate phases. Key results include determining the nature of phase transitions of adsorbed LJ particles on flat and stepped LJ surfaces, which typically feature an enthalpy-driven condensation at higher temperatures and an entropy-driven reordering process at lower temperatures, and the effect of surface geometry on the presence of triple points in the phase diagrams. Overall, we demonstrate the ability and potential of NS for surface modeling.

Mechanical, electronic and dynamical properties of T2-Al2MgC2 under pressure

The presence of T2-Al2MgC2 compound has significant influence on the mechanical properties of magnesium alloys. The mechanical, electronic and dynamical properties of T2-Al2MgC2 under high pressure are investigated by plane wave pseudopotential method based on the first-principles calculation. The results show that T2-Al2MgC2 is mechanically stable under high pressure, the elastic constants except [Formula: see text] increase with the increase of pressure. This compound presents brittleness and the brittleness decreases with increasing pressure when [Formula: see text][Formula: see text]GPa, but it displays ductility when [Formula: see text][Formula: see text]GPa. T2-Al2MgC2 has strong anisotropy, and the anisotropy decreases with increasing pressure. T2-Al2MgC2 is an indirect bandgap semiconductor material. Our calculated bandgap is 1.893[Formula: see text]eV at ambient pressure, the bandgap first increases and then decreases with increasing pressure. The phonon band structure as well as the total and partial phonon density of the state under different pressures had been analyzed. The constant volume heat capacity [Formula: see text] and entropy S of T2-Al2MgC2 increase with increasing pressure.

Structural and Thermodynamic Properties of Cu2ZnSnS4 Material: Theoretical Prediction

Abstract The present work aims to investigate the structural and thermodynamic properties of homogenous tetragonal Cu2ZnSnS4 (CZTS) absorber material in Kesterite phase using first-principle calculations based on density functional theory (DFT). This approach requires only knowledge of the atomic species and crystal structure to predict several physical properties of materials. The Quantum Espresso code within the Ultra Soft pseudopotentials (USPP) and the local density approximation (LDA) were used in the calculations. Equilibrium unit cell volumes, bulk modulus, as well as the pressure derivative of the bulk modulus are predicted. In addition, several thermodynamic properties, especially: the Debye’s vibrational energy, the vibrational free energy, the vibrational entropy, and the constant volume heat capacity at different temperatures T of Cu2ZnSnS4 material are calculated and discussed. Our study shows that the vibrational energy, the entropy and the constant volume heat capacity increase with increasing temperature, while the vibrational free energy decreases monotonously with the increase of temperature.

Control of thermodynamic liquid-liquid phase transition in a fragility-tunable glassy model.

We propose a distinguishable-particle glassy model suitable for the molecular dynamics simulation of structural glasses. This model can sensitively tune the kinetic fragility of supercooled liquids in a wide range by simply changing the distribution of particle interactions. In the model liquid, we observe the occurrence of thermodynamic liquid-liquid phase transitions above glass transition. The phase transition is facilitated by lowering fragility. Prior to the liquid-liquid phase transition, our simulations verify the existence of a constant-volume heat capacity maximum varying with fragility. We reveal the characteristics of the equilibrium potential energy landscape in liquids with different fragility. Within the Gaussian excitation model, the liquid-liquid transition as well as the response to fragility is reasonably interpreted in configuration space.

Impact of Point Defects and V Doping on the Thermodynamic Properties of TiB: First‐Principles Calculations

In this work, the thermodynamic properties of TiB with B‐vacancy, Ti‐vacancy, V‐substitutional doping, and V‐interstitial doping under high temperature and high pressure are systematically analyzed using first‐principles calculations. The presence of both types of vacancies leads to a decreasing trend for the volume, whereas the different forms of V doping could cause lattice distortion and affect supercell volume. In addition, regardless of the vacancy or doping‐based modification of TiB, its constant volume heat capacity increases with the temperature and approaches the Dulong–Petit limit, while the constant pressure heat capacity slowly decreases by increasing the pressure. The presence of vacancies also affects the thermal expansion coefficient of TiB, thereby regulating its high‐temperature ductility, and the V interstitial doping approach is beneficial for improving the high‐temperature ductility of TiB. The Debye temperature of TiB with vacancies is proven more sensitive to pressure changes than the temperature, where the V doping has a significant impact on the Debye temperature of TiB. And the Debye temperature of TiB with interstitial V atoms is lower than that of TiB with substitutional V atoms, indicating that the interaction force is higher than that of the interstitial sites.

Thermodynamics of static and stationary black holes in Einstein–Gauss–Bonnet gravity with dark matter

This paper studies Einstein–Gauss–Bonnet (EGB) black holes surrounded by three phenomenological distributions of dark matter halos. The main result is obtaining the analytical solutions for the metric and all thermodynamic quantities, such as Hawking temperature, entropy, constant-volume heat capacity, and Gibbs free energy for static and stationary black hole solutions. Consequently, we determine a non-null horizon radius at which the black hole halts its evaporation by vanishing the temperature, indicating the emergence of remnants. In the stationary case, we also obtain the ergosphere regions for the found solutions and compare them. Finally, we find local and global phase transitions by studying the behavior of the heat capacity and Gibbs free energy.

Density functional theory (DFT) calculations of structural, elastic, and thermal properties of Zn3P2 compound

In this paper, theoretical investigations of structural, elastic and thermal properties of Zn3P2 material were done using Quantum ESPRESSO code based on density functional theory. The generalized gradient approximation (GGA) exchange correlation-functional helped to model the atomic interaction. First, the structural optimization procedure was carried out, and hence, the optimized structural parameters were utilized to obtain six independent elastic constants [Formula: see text], and [Formula: see text] for the Zn3P2 tetragonal structure. Accordingly, these elastic constants were used to determine the elastic moduli such as the Bulk modulus, Young’s modulus, and shear modulus, as well as other mechanical parameters such as Pugh’s ratio, Poisson’s ratio, anisotropic ratio, sound velocities and Debye temperature. Calculations of thermodynamic properties such as vibrational energies, vibrational free energies, and fixed volume heat capacities, were performed within the implementation of the Thermo_pw code. Elastic calculations confirmed that this compound is characterized by mechanical stability at zero pressure and 0K temperature, ionic bonding, a high degree of anisotropy, and typical ductility. An observable increase in Debye vibrational energies, entropies and constant volume heat capacities of this compound with increasing temperature was detected throughout the thermodynamic calculations, unlike vibrational free energy which revealed a pronounced decrease as temperature increased.

Volumetric and Energetic Properties of Polystyrene and Polyethylene Oxide Affected by Thermal Cycling

AbstractPolymers are known to exhibit hysteresis in their thermal and volumetric properties between cooling and heating at the glass transition. A thorough investigation of this hysteresis using atomistic simulation is not proposed until now. In this work, therefore, the glass transition is studied through heating and cooling protocols at constant rate for two polymers, polystyrene (PS) and polyethylene oxide (PEO), with different molecular weights. To achieve this objective, the analysis is carried out by plotting against temperature, specific volume, coefficient of thermal expansion, total energy, and constant volume heat capacity. The calculated properties for PS and PEO are found to be in good agreement with experimental data, confirming the accuracy of the TraPPE force field for these polymers. The glass transition temperature (Tg) range remains the same regardless of the properties. Moreover, the difference in properties between heating and cooling processes systematically leads to a peak at the same temperature, associated with Tg. Finally, starting from a low temperature, the polymer chains remain mainly in a potential well as the temperature rises, while during cooling the exploration of the configuration space continues up to the temperature where no torsional changes are observed.

Structural phase transition, elastic constants and thermodynamic properties of TmAs: A DFT study

Employing the all-electron full-potential linearized augmented plane wave method and the local density approximation, we report on the results of the structural stability, phase transition pressure, thermodynamic, elastic, electronic and magnetic, properties of thulium arsenide (TmAs). The computed structural parameters, bulk modulus are compared with experimental and other theoretical values. It is found that TmAs undergoes a first-order phase transition from the NaCl-type structure to the CsCl-type structure at approximately 32.96 GPa, corresponding to a volume collapse of around 6.8% during this transition. We have also calculated some elastic properties such as Young modulus, anisotropy factor, and Poisson ratio. The Vickers hardness was predicted using two empirical expressions, which give the shame result ∼5.40 GPa. To gain further information, we used the quasi-harmonic approximation to calculate some thermodynamic properties such as the constant-volume specific heat capacity, the Debye temperature and the entropy of our material of interest. The authors’ results show a monotonous change of the thermodynamic properties of TmAs against temperature. These accords well with the general behavior commonly reported in the literature. The band structure and corresponding density of states have also been determined and analyzed using LSDA, LSDA + U and mBJ-LSDA + U approaches.

Ab Initio Study of Carrier Mobility, Thermodynamic and Thermoelectric Properties of Kesterite Cu2ZnGeS4.

The kesterite Cu2ZnGeS4 (CZGS) has recently gained significant interest in the scientific community. In this work, we investigated the thermodynamic and thermoelectric properties of CZGS by employing the first-principals calculation in association with the quasi-harmonic approximation, Boltzmann transport theory, deformation potential theory, and slack model. We obtained a bandgap of 2.05 eV and high carrier mobility. We found that CZGS exhibits adequate thermoelectric properties as a promising material for thermoelectric applications. The calculated Seebeck coefficient at room temperature is 149 µV·K-1. We also determined the thermal and electrical conductivity, the power factor, and the figure of merit. In addition, the thermodynamic properties such as Debye temperature, entropy, and constant volume heat capacity are estimated. According to our results, it is concluded that the Slack model fails to provide correct values for lattice thermal conductivity in this material.

Lattice dynamics, elastic, magnetic, thermodynamic and thermoelectric properties of the two-dimensional semiconductors MPSe3 (M = Cd, Fe and NI): a first-principles study

Adopting Density Functional Theory (DFT) with Hubbard U correction implemented in Quantum Espresso, we have performed a comprehensive first-principles study of MPSe3 (M = Cd. Fe and Ni) monolayers. The computed electronic properties revealed the semi-conductive nature of the monolayers with small indirect bandgaps. A free-standing single layer of MPSe3 can be exfoliated from the parent compound by virtue of its structural stability and high in-plane stiffness. Hence, the elastic and dynamical properties were computed to establish the mechanical and dynamical stability. The results showed that CdPSe3 and NiPSe3 are stable in the trigonal structure while a single negative frequency observed in the phonon dispersion of FePSe3 indicates the possibility to relax to another, less symmetric structure. In addition, these 2D systems showed relatively good response when subjected to strain hence, they can be said to be mechanically stable. The thermodynamic properties, such as internal energies, vibrational free energies, entropies and constant-volume heat capacities have been computed within the harmonic approximations using the phonon density of states. The computed thermoelectric properties show that CdPSe3 and FePSe3 have the peak figure of merit at low temperature of 50 K. This work predicts a thermoelectric performance with an electronic figure of merit of 0.28 for p-doped CdPSe3. Moreover, the DFT+U method predicts an electronic figure of merit of 0.39 and 0.2 for p-doped FePSe3 and NiPSe3, respectively.

Density functional theory studies on molecular geometry, spectroscopy, HOMO-LUMO and reactivity descriptors of titanium(IV) and oxidozirconium(IV) complexes of phenylacetohydroxamic acid.

The molecular geometry of new titanium(IV) and oxidozirconium(IV) phenylacetohydroxamate complexes [TiCl2 (L1)2 ] (I) and [ZrO(L1)2 ] (II) (where L1=Potassium phenylacetohydroxamate=C6 H5 CH2 CONHOK) computed by B3LYP/6-311++G(d,p) method has shown these to be distorted octahedral and square pyramidal, respectively. A comparison of computed characteristic bond lengths (CO, CN, and NO) of complexes with that of free ligand has shown chelation through carbonyl and hydroxamic oxygen atoms (O, O coordination). The TiO/ZrO bond lengths in complexes are suggestive of weak coordination through (carbonyl CO) and strong covalent (hydroxamic NO) bonding of the ligand. The magnitude of ClTiCl bond angle involving two chloride atoms is suggestive of cis-conformation at titanium metal in (I). The thermodynamic parameters Gibbs free energy, enthalpy, entropy, nuclear internal energy, constant volume heat capacity, and internal energy of ligand and complexes have been computed. From the energies of highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), the global reactivity descriptors such as ionization potential (IP), electron affinity (EA), chemical potential (μ), hardness (η), softness (S), electronegativity (χ), electrophilicity index (ω), and dipole moment have been calculated. The computed vibrational frequencies, 1 H and 13 C NMR spectra have substantiated the molecular structure of complexes. The thermal behavior of complexes has been studied by thermogravimetric techniques (TGA, DTG, and DTA) in N2 atmosphere has shown complexes are thermally stable.

Automated high-temperature and high-pressure adiabatic calorimeter for measurements of the fundamental property ([formula omitted]) of fluids for scientific applications. Constant-volume heat capacity of compressed liquids and gases

Isochoric heat capacity is a well-recognized tool for the study of internal energy, UV,T, which is directly related with the intermolecular potential function. Therefore, reliable isochoric heat capacity data provides a sensitive test of proposed models for the potential energy function. This paper describes a new automated high-temperature and high-pressure vacuum –type adiabatic calorimeter to precisely measurements of the isochoric heat capacity and phase transitions properties of compressed liquids and gases. New experimental high-temperature and high-pressure CV-apparatus includes automatic control of adiabaticity condition, real-time display of all experimental data obtained on the monitor, storage and processing of experimental results in various text and graphic formats, etc. Automated experimental apparatus under a computer-assisted control system makes it possible to significantly simplify the problem of correcting the measurement process and obtaining experimental information in a processed final form. Developed high-temperature CVV T apparatus capable to measure of the isochoric heat capacity of liquid and gases in the two- and single –phases over a temperature range of 293–453 K and at pressures up to 50 MPa with combined expanded uncertainty of the temperature, pressure, and heat capacity measurements at 0.95 confidence level with a coverage factor of k = 2 of 15 mK, 0.05%, and 1.5 % in the liquid and 2.5% in the vapor phases, respectively. The capability (accuracy and reliability) of the new CVV T apparatus is demonstrated by measuring the isochoric heat capacity of several reference fluids (propanol-1, propanol-2, and water) in the single and two-phase regions.

Theoretical insights on structural, mechanical and thermodynamic properties of MCoB (M=Nb, Mo, and W) ternary borides under high pressure

In this work, the effects of the high pressure on the structural, mechanical and thermodynamic properties of MCoB (M = Nb, Mo, and W) ternary borides were calculated through the first-principles. The formation enthalpy and phonon dispersion results indicate that these ternary borides are thermodynamically and dynamically stable. In addition, the high pressure can enhance the thermodynamic stability of these ternary borides. The elastic constants and elastic modulus of these ternary borides increased with the pressure increase, and the elastic anisotropy sequence is NbCoB > MoCoB > WCoB. The states density proved that no phase transition occurs at pressures between of 0 and 50 GPa, and that the stability of these ternary borides also increased with the pressure increase. Furthermore, the influence of high pressure (0–50 GPa) and temperature (0–1500 K) on the thermodynamic properties of these ternary borides are systematically studied based on the Quasi-harmonic Debye model. The findings show that the isothermal bulk modulus and the Debye temperature of these ternary borides increase by increasing the pressure and decreasing the temperature, while the volume showed a reverse change trend. The constant volume heat capacity and the constant pressure heat capacity of these ternary borides slowly decrease with the pressure increase, while the thermal expansion coefficient of these ternary borides is more sensitive to the pressure than to the temperature.

The mechanical and thermodynamic properties of the tetragonal Mo5SiB2 and Mo5Si3 phase under high pressure: a first-principles study

The mechanical and thermodynamics properties of Mo5Si3 and Mo5SiB2 have been investigated by using the first-principle calculations. The cell structure parameters with pressure are briefly discussed. The values of micro-hardness and melting point of both Mo5SiB2 and Mo5Si3 are studied. In addition, both composite alloys’ elastic constants Cij and elastic modulus (B, G, E) are close to increase linearly with pressure. The B/G ratios and Cauchy pressure (C12–C44) were also investigated by this method, and the results suggest that pressure can improve the ductility properties of both alloys. The Poisson’s ratio indicates that the two alloys are bonded mainly metallic. Finally, the Debye temperature with pressure concluded from elastic constants was studied, and the temperature dependence of thermodynamic properties, including the entropy, constant volume heat capacity (CV), enthalpy, and Gibbs free energy, are also studied and discussed.

Counting microstates via heat capacity and implications for the third law

Although supported by empirical data, two fundamental relations in thermodynamics are unproven. The current most authoritative statement of the third law contains an unproven assumption of the equivalency between entropy based on the distribution of energy and an entropy based on the distribution of matter at 0 K. The equality S0 + ∫(CV/T)dT = kBln(W/W0) where S0 is the zero point entropy, CV is the constant volume heat capacity, T is the absolute temperature, kB is Bolzmann’s constant, W is the number of microstates at T, and W0 is the number of microstates at 0 K has not previously been shown to be mathematically correct. This work offers a proof that positional and energy-based entropies are generally equal at 0 K, thus validating the assumption in the third law. But because positional entropy is not temperature dependent, any equality above 0 K is purely coincidental. This work also offers a mathematical proof of the equality between the entropy calculated from the temperature integral of (CV/T) and from kBln(W/W0) thus showing that heat capacity counts the number of energy microstates.

Thermodynamic functions of toroidal black holes

The thermodynamic functions of toroidal black holes are investigated in this paper by taking the cosmological constant as a dynamic variable equivalent to the pressure. The equation of state and the Smarr relation of a toroidal black hole are given. Then, the Gibbs function is obtained by calculating the Euclidian action. Further we study other thermodynamic functions of the toroidal black hole, such as, the free energy, internal energy and thermodynamic enthalpy. The heat capacities of the toroidal black hole at constant pressure and constant volume are obtained as well. The results show that toroidal black holes have no van der Waals type phase transition. Toroidal black hole is a stable thermodynamic system because its constant pressure heat capacity is greater than zero and constant volume heat capacity is equal to zero.

First-Order Phase Transformation at Constant Volume: A Continuous Transition?

We describe a first-order phase transition of a simple system in a process where the volume is kept constant. We show that, unlike what happens when the pressure is constant, (i) the transformation extends over a finite temperature (and pressure) range, (ii) each and every extensive potential (internal energy U, enthalpy H, Helmholtz energy F, and Gibbs energy G), and the entropy S is continuous across the transition, and (iii) the constant-volume heat capacity does not diverge during the transition and only exhibits discrete jumps. These non-intuitive results highlight the importance of controlling the correct variables in order to distinguish between continuous and discontinuous transitions. We apply our results to describe the transition between ice VI and liquid water using thermodynamic information available in the literature and also to show that a first-order phase transition driven in isochoric condition can be used as the operating principle of a mechanical actuator.

Electronic, mechanical, vibrational and thermodynamic properties of FeXSb (X = Hf and Nb) Half-Heusler alloys from first-principles approach

A comprehensive computational study of FeXSb (X = Hf and Nb) half-Heusler alloys have been performed by adopting ab initio density functional theory approach. Recent studies has shown that FeNbSb half-Heusler alloy is a potentially good and promising candidate for thermoelectric device when it is substitutionally doped with Hf. Therefore, the present study have investigated the electronic, elastic, mechanical, vibrational and thermodynamic properties of FeXSb (X = Hf and Nb) half-Heusler alloys for efficient and effective thermoelectric performance. The computed electronic properties affirmed the semiconductive nature of the FeNbSb alloy while FeHfSb alloy is predicted to be half metallic ferromagnetic compound with small magnetic moment of 0.9 μB. The contributions of the d-electrons of Fe Hf and Nb in the band structure is notable and significant as revealed in the projected density of states (PDOS). The mechanical stability of the two alloys was established when the computed elastic constants accurately satisfy the generalized mechanical stability conditions. Moreover, the mechanical properties revealed that our investigated materials are ductile and incompressible. Also, the alloys were predicted to be anisotropic in nature. The presence of positive frequencies obtained from the calculation of phonon dispersion throughout the Brillouin zone indicates that FeXSb alloys are dynamically stable. Moreso, LO-TO spliting is observed and reported in FeNbSb alloy. Various temperature dependent thermodynamic parameters such as debye temperature, sound velocity, internal energy, vibrational energy, entropy and constant volume heat capacity were computed within harmonic approximation. The obtained results pointed to the fact that the two alloys have impressive thermal response.