Gruneisen Coefficient Research Articles

Thermal expansion and evaluation of almandine heat capacity

The cell parameters of synthetic almandine were measured in the temperature range of 100–630 K by X-ray powder diffraction method. Interpolation and extrapolation of the experimental data from 50 to 1500 K were performed by the procedure based on the Debye model of solid body. Temperature dependencies of molar volumes and coefficients of volume thermal expansion were determined. The Gruneisen coefficient and Debye temperature were calculated. Heat capacity and its behavior in accordance with temperature were evaluated.

Angular dependent potential for α-boron and large-scale molecular dynamics simulations

Both quantum mechanical and molecular-dynamics (MD) simulations of α-boron are done at this work. Angular dependent interatomic potential (ADP) for boron is obtained using force-matching technique. Fitting data are based on ab initio results within −20..100 GPa pressure range and temperatures up to 2000 K. Characteristics of α-boron, obtained using ADP potential such as bond lengths at equilibrium condition, bulk modulus, pressure-volume relations, Gruneisen coefficient, thermal expansion coefficient are in good agreement with both ab initio data, obtained in this work and known experimental data. As an example of application, the propagation of shock waves through a single crystal of α-boron is also explored by large-scale MD simulations.

Model of the behavior of aluminum and aluminum-based mixtures under shock-wave loading

A thermodynamically equilibrium model is applied to describe the behavior of solid and porous materials. This model ensures good compliance with the experiment in a wide range of pressures. The gas in pores, which is a component of the medium, is taken into account in this model. The equation of state of the Mie-Gruneisen type with allowance for the dependence of the Gruneisen coefficient on temperature is used for condensed phases. The applied model allows the behavior of the aluminum with a porosity from 1 to 8 to be calculated under shock-wave loading at pressures above 5 GPa in the one-velocity and one-temperature approximations, as well as on the assumption of equal pressures for all the phases. Computational results are compared with the well-known experimental results obtained by different authors (shock adiabats, double compression by shock waves, and temperature estimation). The model permits the shock-wave loading of solid and porous mixtures with aluminum in their composition to be described reliably solely by using species parameters.

A Mie-Grüneisen EOS with non-constant specific heat

A complete and consistent equation of state based on Mie-Grüneisen assumptions was developed. This EOS assumes constant Gruneisen coefficient, but a variable specific heat that is modeled using Einstein's theory of heat capacities using two oscillators. The shock velocity particle velocity Hugoniot (Us-up) was derived from density functional theory molecular dynamics (DFT-MD). The EOS was formatted as a tabular EOS and checked for consistency using one-dimensional impact simulations in CTH.

Bifurcation Approach to Analysis of Travelling Waves in Nonlocal Hydrodynamic-Type Models

The paper considers the nonlocal hydrodynamic-type systems which are two-dimensional travelling wave systems with a five-parameter group. We apply the method of dynamical systems to investigate the bifurcations of phase portraits depending on the parameters of systems and analyze the dynamical behavior of the travelling wave solutions. The existence of peakons, compactons, and periodic cusp wave solutions is discussed. When the parameternequals 2, namely, let the isochoric Gruneisen coefficient equal 1, some exact analytical solutions such as smooth bright solitary wave solution, smooth and nonsmooth dark solitary wave solution, and periodic wave solutions, as well as uncountably infinitely many breaking wave solutions, are obtained.

Model of the behavior of the mixture with different properties of the species under high dynamic loads

Within the framework of a thermodynamically equilibrium model, dynamic loading of mixtures of two and more condensed phases with different properties within the experimental error is described by using species parameters only. The behavior of alloys considered as mixtures with the same volume fractions of the species is studied. The behavior of condensed phases for solid and porous materials is described with the use of the equation of state of the Mie-Gruneisen type and with allowance for the dependence of the Gruneisen coefficient on temperature. The calculated results are compared with experimental data and available calculated results in wide ranges of parameters.

The structure of shock and interphase layers for a heat conducting Maxwellian rate-type approach to solid–solid phase transitions

We consider a thermoelastic model for phase transforming materials which can adequately describe the evolution with respect to the temperature of the hysteresis loop both in compression and tension tests. The specificity of this model is that the Gruneisen coefficient changes its sign. The model is augmented by considering a dissipative mechanism governed by a Maxwellian rate-type constitutive equation that can describe stress relaxation phenomena toward equilibrium between phases. Existence and uniqueness of traveling wave solutions are investigated. One derives that the admissibility condition induced by the Maxwellian rate-type approach, coupled or not with Fourier heat conduction law is related to the chord criterion with respect to the Hugoniot locus. We investigate the structure of profile layers, and we focus on their thermodynamic properties. The influence of the exothermic or endothermic character of phase transitions on the inner structure of interphase layers is captured. A phenomenon of temperature overshoot/undershoot with respect to the front state temperature and Hugoniot back state temperature inside an interphase layer is revealed.

Extended data set for the equation of state of warm dense hydrogen isotopes

Laser-driven shock wave measurements on hydrogen and deuterium precompressed in diamond anvil cells from 0.16 to 1.6 GPa provide new shock Hugoniot data over a significantly broader range of density-temperature phase space than was previously achievable. Observations of shock velocity and thermal emission provide complete equation of state data (pressure, density, internal energy, and temperature) in the dense fluid regime up to 175 GPa. This data set is used to benchmark recent advanced ab initio calculations and is seen to be in good agreement with a maximum $8%$ density difference above 100 GPa. Thermodynamic quantities (specific heat and Gruneisen coefficient) are calculated directly from the data and compared to theory. Optical reflectivity data show a continuous transition from an electrically insulating to conducting fluid state and reveal that this transition is increasingly sensitive to temperature with increasing density. Ab initio calculations are observed to underestimate the temperature onset of metallization.

Derivation of equations of state for ideal crystals of simple structure

We consider an approach to the derivation of thermodynamic equations of state by averaging the dynamic equations of particles of the crystal lattice. Microscopic analogs of macroscopic variables such as pressure, volume, and thermal energy are introduced. An analysis of the introduced variables together with the equations of motion permits obtaining the equation of state. Earlier, this approach was used to obtain the equation of state in the Mie-Gruneisen form for a one-dimensional lattice. The aim of this paper is to develop and generalize this approach to the three-dimensional case. As a result, we obtain the dependence of the Gruneisen function on the volume, which is compared with the computations performed according to well-known models with experimental data taken into account. It is proved that the Gruneisen coefficient substantially depends on the form of the strain state. Moreover, we refine the equation of state; namely, we show that the Gruneisen coefficient depends on the thermal energy, but this dependence in the three-dimensional case is much weaker than in the one-dimensional case. A refined equation of state containing a nonlinear dependence on the thermal energy is obtained

On the force constants of graphene

It has been shown that the inclusion of an additional short-range potential in the repulsion energy of neighboring atoms allows one to satisfactorily describe the frequency of the phonon doublet at the Γ point for atomic vibrations in the plane of the graphene sheet and to calculate the corresponding Gruneisen coefficient. The results obtained are compared with those derived by other authors.

Review of Jones-Wilkins-Lee equation of state

The JWL EOS is widely used in different forms (two, three terms) accord- ing to the level of accuracy in the pressure-volume domain that applications need. The foundations of the relationship chosen to represent the reference curve, Chapman-Jouguet (CJ) isentrope, can be found assuming that the DP expansion isentrope issued from the CJ point is very nearly coincident with the Crussard curve in the pressure-material veloc- ity plane. Its mathematical expression, using an appropriate relationship between shock velocity and material velocity leads to the exponential terms of the JWL EOS. It well val- idates the pressure-volume relationship chosen to represent the reference curves for DP. Nevertheless, the assumption of constant Gruneisen coefficient and heat capacity in the EOS thermal part remains the more restrictive assumption. A new derivation of JWL EOS is proposed, using a less restrictive assumption for the Gruneisen coefficient suggested by W.C. Davis to represent both large expansions and near-CJ states.

Evaluation of Absorbing Chromophores Used in Tissue Phantoms for Quantitative Photoacoustic Spectroscopy and Imaging

In this paper, the optical properties of absorbing compounds that are often used to construct tissue phantoms for quantitative photoacoustic spectroscopy and imaging are investigated. The wavelength dependence of the optical absorption of inorganic chromophores, such as copper and nickel chloride, and organic chromophores, such as cyanine-based near infrared dyes, was measured using transmittance spectroscopy and compared with that determined using photoacoustic spectroscopy. In addition, the relative change in the Gruneisen coefficient of these solutions with concentration was determined. The sound speed of aqueous gels and lipid emulsions as a function of concentration was also measured. It was found that copper and nickel chloride are suitable chromophores for the construction of photoacoustic tissue phantoms due to their photostability. By contrast, organic dyes were found unsuitable for quantitative photoacoustic measurements due to optically induced transient changes to their absorption spectrum and permanent oxidative photobleaching.

A caloric equation of state of a condensed medium derived based on generalized Hugoniot curves

The caloric equation of state, which expresses the internal energy through the volume and pressure is required in analyzing and calculating shock-wave processes in reacting media. The present work develops a method for constructing such an equation for condensed media on the basis of generalized Hugoniot curves. Expressions approximating the dependence of the Gruneisen coefficient and pressure on the volume along the Hugoniot curve. Formulas for calculating detonation Hugoniot curves from the shock Hugoniot curve of the condensed reaction products. The expressions obtained can be applied to approximate calculations of shockwave processes (for example, gasless detonation) in reacting condensed media. If necessary, such calculations can be performed with the use of physical quantities from standard handbooks.

Few-Parameter Equation of State of the Shock Adiabat with Allowance for Melting

The model equations for thermodynamic functions of liquid status based on volume and temperature dependence of Gruneisen coefficient are offered. Thermal components are described by the Debye’s model. Despite the perfect analogy to solid-state body the distinction in an elastic component of energy and pressures is taken into consideration when deriving the equations. The configuration entropy is embedded into thermodynamic functions of liquid. It describes a disorderliness measure of liquid and results in the final values of the entropy when temperature formally amounts to zero. The melting curve as the boundary between phases is constructed.

Formation of nanocavities in dielectrics: influence of equation of state

Tight focusing of a sub-picosecond laser pulse in a transparent dielectric provides a mean for localized deposition and plasma formation. A micro-explosion in a confined geometry results in a sub-micron cavity formation. Our numerical simulations show the cavity size is strongly dependent on the parameters of the equation of state such as the Gruneisen coefficient or the latent heat of sublimation. A comparison of numerical simulations with experimental data should allow a tuning of equations of state in the domain of extreme parameters

Heat capacity and lattice dynamics of yttrium diboride in the temperature range 5–300 K

This paper reports an experimental study of the heat capacity and crystal lattice parameters of a polycrystalline sample of yttrium diboride prepared by high-temperature synthesis from elements. The electronic and lattice contributions to the heat capacity are isolated. The temperature dependences of the characteristic temperature, the linear thermal expansion coefficients αa(T) and αc(T), the bulk thermal expansion coefficient β(T), and the Gruneisen coefficient are calculated. A region of negative values of αc(T) and β(T) is revealed. Anharmonicity is found to exert only a minor effect on the YB2 lattice dynamics over a larger part of the temperature range covered.

Residual temperature measurements of light flash under hypervelocity impact

Experimental and theoretical results for light flash temperatures are presented for impacts on soda-lime glass by iron projectiles. The experiments were performed with a 2 MV Van de Graaff, where iron dust particles (0.14–0.63 μm in diameter) impacted soda-lime glass at a velocity range of 5–20 km s −1. Theoretical calculations were based on the assumption of the Mie–Gruneisen equation of state (EoS) with different values for the Gruneisen coefficient and hydrodynamic behaviour (no strength effects were considered). Within the scatter of experimental data, results suggest a constant value for the average light flash temperature of approximately 2600 K independent of iron dust impact velocity. Although theoretical calculations are limited by the use of the Mie–Gruneisen EoS up to the point of incipient vaporisation of the target material, relatively good agreement with experiments is observed. This agreement suggests that the observed constant temperature may be due to material phase change from incipient to complete vaporisation over the range of velocities considered.

Molecular simulations of Hugoniots of detonation product mixtures at chemical equilibrium: Microscopic calculation of the Chapman-Jouguet state

In this work, we used simultaneously the reaction ensemble Monte Carlo (ReMC) method and the adaptive Erpenbeck equation of state (AE-EOS) method to directly calculate the thermodynamic and chemical equilibria of mixtures of detonation products on the Hugoniot curve. The ReMC method [W. R. Smith and B. Triska, J. Chem. Phys. 100, 3019 (1994)] allows us to reach the chemical equilibrium of a reacting mixture, and the AE-EOS method [J. J. Erpenbeck, Phys. Rev. A 46, 6406 (1992)] constrains the system to satisfy the Hugoniot relation. Once the Hugoniot curve of the detonation product mixture is established, the Chapman-Jouguet (CJ) state of the explosive can be determined. A NPT simulation at P(CJ) and T(CJ) is then performed in order to calculate direct thermodynamic properties and the following derivative properties of the system using a fluctuation method: calorific capacities, sound velocity, and Gruneisen coefficient. As the chemical composition fluctuates, and the number of particles is not necessarily constant in this ensemble, a fluctuation formula has been developed to take into account the fluctuations of mole number and composition. This type of calculation has been applied to several usual energetic materials: nitromethane, tetranitromethane, hexanitroethane, PETN, and RDX.

Equation of state for liquid water

The equation of state for water (EOSW) in Mi–Gruneisen form with Born–Mayer potential for densities less, than 1 g/cm^3 is developed. The equation is applicable to moderate and high pressures (up to 2·10^12 Pa), in particular, to explosive and static pressures in the range of densities from 0.7 to 3.8 g/cm^3 . The equation for the Gruneisen coefficient that depends not only on the specific volume but also on the temperature is received. The proposed method by the experimental data for dependencies on specific volume and temperature the heat capacity and isochoric temperature coefficient of pressure increase allows to calculate the Gruneisen coefficient and the internal heat energy.

Noninvasive optoacoustic online retinal temperature determination during continuous-wave laser irradiation

The therapeutic effect of most retinal laser treatments is initiated by a transient temperature increase. Although crucial to the effectiveness of the treatment, the temperature course is not exactly known due to individually different tissue properties. We develop an optoacoustic method to determine the retinal temperature increase in real time during continuous-wave (cw) laser irradiation, and perform temperature calculations to interpret the results exemplary for transpupillary thermotherapy (TTT). Porcine globes ex vivo and rabbit eyes in vivo are irradiated with a diode laser (lambda=810 nm, P< or =3 W, phi=2 mm) for 60 s. Simultaneously, pulses from a N2-laser pumped dye laser (lambda=500 nm, tau=3.5 ns, E approximately 5 microJ) are applied on the retina. Following its absorption, an ultrasonic pressure wave is emitted, which is detected by a transducer embedded in a contact lens. Using the previously measured temperature-dependent Gruneisen coefficient of chorioretinal tissue, a temperature raise in porcine eyes of 5.8 degrees C(Wcm2) after 60 s is observed and confirmed by simultaneous measurements with an inserted thermocouple. In a rabbit, we find 1.4 degrees C(Wcm2) with, and 2.2 degrees C(Wcm2) without perfusion at the same location. Coagulation of the rabbit's retina occurs at DeltaT=21 degrees C after 40 s. In conclusion, this optoacoustic method seems feasible for an in vivo real-time determination of temperature, opening the possibility for feedback control retinal laser treatments.