Isothermal Bulk Modulus BT Research Articles

Linear isotherm regularities of solid sodium under pressure

We propose several new regularities in solid sodium from the available experimental data and calculated thermodynamic properties along the isotherms with the equation of state (EOS) of the modified Holzapfel form. Z−1V2 is a linear function in terms of V2 with different intersection points for the isotherms at high temperatures within the considered pressure range, where Z and V are the compressibility factor and molar volume. The calculated isothermal bulk modulus BT and internal pressure Pint of solid sodium vary almost linearly with pressure. Both the calculated reduced isothermal bulk modulus B*=BTVRT and the parameter Zint=PintVRT from the modified Holzapfel EOS are observed to be linear with respect to V−2 with temperature T and gas constant R, which is verified by the derived analytical expression from the derived linear isothermal regularity EOS. In addition, analytical expressions of the thermodynamic properties of solid sodium are derived from the linear isothermal regularity EOS, such as internal energy, entropy, enthalpy, free energy, and heat capacity.

Temperature variation of the isothermal bulk modulus in solids: Thermo-elastic instability and melting

A new expression for the temperature dependence of the isothermal bulk modulus BT of solids is represented in terms of the Lambert function. The derived equation predicts a non-linear decrease in the bulk modulus over the entire temperature range of the solid phase, from a value of B0 at absolute zero to the nonzero value of B0e−1 at the melting point. The quasi-harmonic Debye-Gruneisen model is used to show that upon heating, the solid loses its elasticity and melts, when the thermal pressure exceeds a critical value B0(eδT)−1, with δT being the Anderson-Gruneisen parameter. The thermo-elastic instability criterion of melting and the Lindemann melting law are re-examined. The unspecified Lindemann scale factor is interpreted in terms of the Anderson and Anderson-Grüneisen parameters and the Poisson ratio.

Elastic Constants, Bulk Modulus, and Compressibility of H2O Ice Ih for the Temperature Range 50 K–273 K

Published elastic constant data for H2O ice in the Ih phase are compiled and evaluated. Fits of the five elastic constants for 50 ≤ T/K ≤ 273 are conducted to yield a reliable and convenient source for elastic constant values. Various elastic properties can be calculated from the elastic constants obtained herein. The elastic constants are used to determine the adiabatic bulk modulus BS for the same temperature range with an estimated uncertainty of less than 1.3%. Fitting those data yields an equation for BS that is extrapolated to provide values for 0 ≤ T/K < 50. The adiabatic compressibility KS, isothermal bulk modulus BT, and isothermal compressibility KT are calculated from BS. Comparisons are made to published data.

Change in the lattice properties and melting temperature of a face-centered cubic iron under compression

All four parameters of the Mie–Lennard-Jones pair interatomic potential have been determined, and the state equation (P) and baric dependences of the lattice properties of an fcc iron are calculated using a previously proposed method. The dependences have been studied for the following properties: Debye temperature; the first, second, and third Gruneisen parameters; isothermal bulk modulus B T and B′(P); isochoric specific heat C v and C v ′(P); isobaric specific heat C p ; coefficient of thermal expansion α p and α p ′(P); specific surface energy σ and σ′(P). Calculations performed along two isotherms (1500 and 3000 K) have shown good agreement with the experimental data. Analytical approximations of the baric dependences for B′(P), α p (P), C p (P), and σ′(P) have been obtained, and it is shown that at P → ∞ the functions B T (P) and σ(P) change linearly, while the functions α p′(P) and C p ′(P) tend to zero. The calculated baric dependence of the melting temperature shows good agreement with the experimental data.

Thermodynamic properties of liquid gallium from picosecond acoustic velocity measurements

Due to discrepancies in the literature data the thermodynamic properties of liquid gallium are still in debate. Accurate measurements of adiabatic sound velocities as a function of pressure and temperature have been obtained by the combination of laser picosecond acoustics and surface imaging on sample loaded in diamond anvil cell. From these results the thermodynamic parameters of gallium have been extracted by a numerical procedure up to 10 GPa and 570 K. It is demonstrated that a Murnaghan equation of state accounts well for the whole data set since the isothermal bulk modulus BT has been shown to vary linearly with pressure in the whole temperature range. No evidence for a previously reported liquid–liquid transition has been found in the whole pressure and temperature range explored.

First-principle calculations of the thermal properties of SrTiO3 and SrO(SrTiO3)n (n=1,2)

The thermal properties of SrTiO3 and SrO(SrTiO3)n (n=1,2) with layered perovskite structure are analyzed using the Debye–Grüneisen model combined with ab initio calculations. The thermal expansion coefficient, specific heat at constant pressure CP and specific heat at constant volume CV, adiabatic bulk modulus BS and isothermal bulk modulus BT, entropy, and Debye temperature are investigated. At temperatures higher than 550°C, the thermal expansion coefficient and the discrepancies between CP and CV, as well as that between BS and BT, of Sr3Ti2O7 increase the fastest as the temperature rises, followed by those of Sr2TiO4, and those of SrTiO3 increase the slowest. The bulk module and Debye temperature of Sr2TiO4, Sr3Ti2O7, and SrTiO3 increase with decreasing SrO/SrTiO3 ratio at 0K. With increasing temperature, however, the bulk modulus and Debye temperature of Sr3Ti2O7 both rapidly decrease and even fall below those of Sr2TiO4 when the temperature is higher than specific values. We also analyzed the thermal properties of these three compounds in the pressure range from 0GPa to 16GPa at 300K.

Computation of phonon dynamics of Mg70Zn30 metallic glass

In the present paper, the computation of the phonon dynamics of binary Mg70Zn30 metallic glass is reported using the well-recognized model potential of Gajjar et al. The present study includes the phonon dispersion curves (PDC), elastic and thermodynamic properties such as longitudinal sound velocity υL, transverse sound velocity υT, Debye temperature θD, isothermal bulk modulus B T, modulus of rigidity G, Poisson’s ratio σ and Young’s modulus Y and specific heat capacity C V of the glass. Three theoretical models given by Hubbard–Beeby (HB), Takeno–Goda (TG) and Bhatia–Singh (BS) are used to compute the PDC. Five local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru–Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) are employed for the first time to study the effect of exchange and correlation in the aforesaid properties. The pseudo-alloy-atom (PAA) model is applied for the first time instead of Vegard’s Law.

On the Limit of the Thermodynamic Stability of Superheated Crystals and Mechanisms of Its Loss

Using the correlative method of unsymmetrized self-consistent field for strongly anharmonic crystals, the thermodynamic stability and the mechanism its loss is studied for crystals with various types of the chemical bond. The following interaction potentials are utilized: the Lennard-Jones pairwise potential together with Axilrod - Teller three-body one for simple van der Waals crystals (solid Ar), effective interionic pairwise potential proposed by Schiff for a metal (Na) and the Girifalco potential for fullerites (C60). In the first and third cases, the FCC lattice becomes unstable because the isothermal bulk modulus BT becomes zero. For fullerites, the shearing coefficient C44 goes to zero as well. Solid Na losses its stability when other shearing coefficient CT11 - CT12 becomes zero.

Thermomechanical model and temperature measurements for shocked ammonium perchlorate single crystals

A consistent thermomechanical material model was developed for unreacted ammonium perchlorate (AP) single crystals for shock compression normal to the (210) and (001) crystal planes. Building on previous work, the mechanical response for both orientations was described using a single isotropic elastic-plastic model and an overstress model to describe rate-dependent yielding. Velocity interferometer measurements to 12 GPa were performed to extend the AP Hugoniot curve to higher stresses. The specific heat cv, the coefficient of thermal pressure (∂P/∂T)V, and the isothermal bulk modulus BT were determined from Hugoniot and isothermal compression curves, along with available data at atmospheric pressure. Time-resolved Raman spectroscopy experiments were carried out under stepwise loading to obtain temperatures in the shocked state. Calculated temperatures using our material model are in good agreement with the temperatures obtained from our experiments, thus providing validation for our modeling approach.

Equation of state and temperature measurements for shocked nitromethane

A thermodynamically consistent equation of state (EOS) was developed for unreacted liquid nitromethane (NM). The specific heat cv, the coefficient of thermal pressure (∂P/∂T)v, and the isothermal bulk modulus BT, were modeled as functions of temperature and volume using existing experimental data. To test our EOS predictions, temperature measurements using time-resolved Raman spectroscopy were obtained from NM subjected to stepwise loading. In contrast to previous EOS developments, calculations using our EOS show good agreement with the measured temperatures. Comparison with previous EOS models shows that simplifying assumptions, such as holding (∂P/∂T)v or Γ/v constant, lead to significant inaccuracies in temperature predictions for shocked NM. The assumption that the Gruneisen parameter Γ is a function of volume only is not consistent with our EOS.

Temperature dependence of elastic constants and thermal expansion coefficient for NaCl crystals

AbstractThe second‐order elastic constants C11, C12, and C44, isothermal bulk modulus BT, and volume thermal expansion coefficient α are calculated for NaCl crystals in the temperature range (294 to 766 K) using Tallon's model based on the concept of modified Anderson‐Grüneisen parameters. The results obtained in the present study are compared with the experimental values reported in the literature. There is good agreement between calculated and experimental values for V/V0, C11, C44, BT, and α. It is found that C11, C44, and BT decrease whereas C12 and α increase with increase in temperature.

Bulk Modulus and Grüneisen Parameters for Linear Polymers

Expressions are derived for the isothermal bulk modulus BT and Anderson–Grüneisen parameter δ for a simple two-dimensional bundle-of-chains model where parallel nearest-neighbor chains are assumed to interact with a simple separation-dependent potential. Bulk modulus data for general linear polymers are examined and shown to be essentially temperature independent at constant volume in accord with the model. The theory is shown to predict quite accurately for reasonable assumed pair potentials both BT and δ of high-density polyethylene and n-paraffins with no adjustable parameters. The values of δ obtained for polyethylene from BT data are in excellent agreement with those reported from ultrasonic data. The analysis is also shown to provide a sensitive measure of the form of the effective chain pair potential near its minimum. Also, a close relationship between δ and the Grüneisen constant γ is derived for this model.