Jing Fu-Qian

Analytic equation of state for the exponential-six fluids based on the Ross variational perturbation theory

An analytic expression of radial distribution function of hard spheres is developed in terms of a polynomial expansion of nonlinear base functions and the Carnahan–Starling equation of state (EOS). The comparison with the Monte-Carlo data and the Percus-Yevick expression shows that the expression developed gives out better results. The expression is very simple that can make most perturbation theories become analytic ones, and a simple analytic EOS for the fluids with continuous exponential-six potential is established based on the Ross variational perturbation theory. The main thermodynamic quantities have been analytically derived, the resulting expressions are surprisingly simple, the variational procedure is greatly simplified and the calculations are absolutely convergent. The numerical results are compared with the Monte-Carlo data and the original non-analytic theory. It is shown that the precision of the analytic EOS is as good as the original non-analytic one.

Extension of the Wu–Jing equation of state for highly porous materials: Thermoelectron based theoretical model

A thermodynamic equation of state (EOS) for thermoelectrons is derived which is appropriate for investigating the thermodynamic variations along isobaric paths. By using this EOS and the Wu–Jing (WJ) model, [Q. Wu and F. Jing J. Appl. Phys. 80, 4343 (1996)] an extended Hugoniot EOS model is developed which can predict the compression behavior of highly porous materials. Theoretical relationships for the shock temperature, bulk sound velocity, and the isentrope are developed. This method has the advantage of being able to model the behavior of porous metals over the full range of applicability of pressure and porosity, whereas methods proposed in the past have been limited in their applicability.A thermodynamic equation of state (EOS) for thermoelectrons is derived which is appropriate for investigating the thermodynamic variations along isobaric paths. By using this EOS and the Wu-Jing (W-J) model, an extended Hugoniot EOS model is developed which can predict the compression behavior of highly porous materials. Theoretical relationships for the shock temperature, bulk sound velocity, and the isentrope are developed. This method has the advantage of being able to model the behavior of porous metals over the full range of applicability of pressure and porosity, whereas methods proposed in the past have been limited in their applicability.

A Direct Comparison between Static and Dynamic Melting Temperature Determinations below 100 GPa

A preliminary experiment of sound velocity measurements for porous iron with initial average density of 6.275 g/cm3 has been performed at pressures below 100 GPa, in order to clarify a long-standing problem that the static melting temperature Tm, mostly below 100 GPa due to its technical limitations, is notably lower than the extrapolated melting data inferred from the shock wave experiments made above 200 GPa, for the sake of making a direct comparison between the experimental static and dynamic melting temperatures in the same pressure region. With the lately proposed Hugoniot sound velocity data analysis technique [Chin. Phys. Lett. 22 (2005) 863], the results deduced from this Hugoniot sound velocity measurement is Tm = 3200 K at 87 GPa and Tm = 3080 K at 80 GPa, which are in good agreement with the two latest static data of Tm = 3510 K at 105 GPa and Tm = 2750 K at 58 GPa, which utilized modern improved double-side laser heating and in situ accurate x-ray diffraction techniques in experiments. It can be concluded that consensus Tm data would be obtained from static and shock wave experiments in the case that the recently improved techniques are adopted in investigations.

Three Semi-empirical Analytic Expressions for the Radial Distribution Function of Hard Spheres*

Three simple analytic expressions satisfying the limitation condition at low densities for the radial distribution function of hard spheres are developed in terms of a polynomial expansion of nonlinear base functions and the Carnahan–Starling equation of state. The simplicity and precision for these expressions are superior to the well-known Percus–Yevick expression. The coefficients contained in these expressions have been determined by fitting the Monte Carlo data for the first coordination shell, and by fitting both the Monte Carlo data and the numerical results of Percus-Yevick expression for the second coordination shell. One of the expressions has been applied to develop an analytic equation of state for the square-well fluid, and the numerical results are in good agreement with the computer simulation data.

Extension of the Wu-Jing equation of state for highly porous materials: Calculations to validate and compare the thermoelectron model

In order to verify and validate the newly developed thermoelectron equation of state (EOS) model that is based on the Wu-Jing (W-J) EOS, calculations of shock compression behavior have been made on five different porous metals-iron, copper, lead, tungsten, and aluminum-which are commonly used as standards. The model was used to calculate the Hugoniot, shock temperature, sound velocity, and unloading isentrope for these materials and comparisons were made to previous calculations and available data. Based on these comparisons, it is felt that the model provides information in good agreement with the corresponding experimental and theoretical data published previously. This suggests that the new model can satisfactorily describe the properties of shocked porous materials over a wide range of pressure and porosity.In order to verify and validate the newly developed thermoelectron equation of state (EOS) model that is based on the Wu–Jing EOS [J. Appl. Phys. 80, 4343 (1996); Appl. Phys. Lett. 67, 49 (1995)], calculations of shock compression behavior have been made on five different porous metals: iron, copper, lead, tungsten, and aluminum which are commonly used as standards. The model was used to calculate the Hugoniot, shock temperature, sound velocity, and unloading isentrope for these materials and comparisons were made to previous calculations and available data. Based on these comparisons, it is felt that the model provides information in good agreement with the corresponding experimental and theoretical data published previously. This suggests that the new model can satisfactorily describe the properties of shocked porous materials over a wide range of pressure and porosity.

Dynamic Failure of Shock-Loaded Glass

Failure wave generations on both impacted surface and internal surface inside the sample have been observed for K9 glass under planar shock wave loading, which demonstrates that formation of failure wave is a process related to the surface microcracks nuclei developing. Based on these observations, a hypothesis is suggested that the large local strains resulting from the rearrangement of SiO4 tetrahedral within the permanent densification region behind the shock wave front and then strains releasing due to the surface microcracks developing could be responsible for the failure wave generation.

Analytic Potential Energy Function for Doubly Charged Ions HBe2+, HB2+, and HF2+

It is well known that the potential curve of ground state for almost all neutral diatomic molecules has only one minimum. However, the doubly charged diatomic ions may have both potential minimum and maximum or singly repulsive branch. In order to describe the potential of this kind of diatomic ions, two of the authors Zhu and Wang have proposed a new analytical potential function with four parameters ai(i?=?1,???,4), and ??=?R - Rmin for those with both minimum and maximum, and ??=?R for those with singly repulsive branch. The present work has derived this new potential function for H Be2+ with Rmin?=?0.182 nm, Rmax?=?0.335 nm and ?E?=?Emax - Emin?=?0.84 eV, and for HB2+ with Rmin?=?0.147 nm, Rmax?=?0.185 nm and ?E?=?Emax - Emin?=?0.062 eV. It is found that the potential for HF2+ is one with singly repulsive branch. The dissociation limits, parameters ai(i?=?1,???,4), force constants and spectroscopic data of these ions all are given out.

Equation of state and conductivity of shocked heavy water

Hugoniot equation-of-state, ranging from 10 to 43 GPa, and electrical conductivities, over the range from 18 to 39 GPa, of heavy water (D2O) were measured by using a two-stage light-gas gun. It is found that there exists an abrupt volume contraction at around 20 GPa, similar to behavior of light water (H2O) that occurs at a higher pressure around 25 GPa. Considering the phase transition phenomena mentioned above, together with the electrical conductivity data, the shock-induced changed in liquid D2O and H2O are discussed in detail.Hugoniot equation-of-state, ranging from 10 to 43 GPa, and electrical conductivities, over the range from 18 to 39 GPa, of heavy water (D2O) were measured by using a two-stage light-gas gun. It is found that there exists an abrupt volume contraction at around 20 GPa, similar to behavior of light water (H2O) that occurs at a higher pressure around 25 GPa. Considering the phase transition phenomena mentioned above, together with the electrical conductivity data, the shock-induced changed in liquid D2O and H2O are discussed in detail.

Modification to the Newton-Laplace formula of sound velocity at high pressure

The Newton-Laplace (NL) formula of sound velocity is shown being invalid at high pressure, and a modified formula is derived based on the Rankine-Hugoniot relations. The derivation shows that the transmission of sound should be a process satisfying the energy conservation condition instead of the adiabatic condition in the NL formula. The agreement of equations of state for metallic liquids deduced from sound velocity data through the modified formula with the direct experimental P-V data is evidently improved as compared with that deduced through the NL formula.

Analytic Debye-Grüneisen equation of state for a generalized Lennard-Jones solids

The approximate method to treat the practical quantum anharmonic solids proposed by Hardy, Lacks and Shukla is reformulated with explicit physical meanings. It is shown that the quantum effect is important at low temperature, it can be treated in the harmonic framework; and the anharmonic effect is important at high temperature and tends to zero at low temperature, it can be treated by using a classical approximation. The alternative formulation is easier for various applications and is applied to a Debye-Gruneisen solid with the generalized Lennard-Jones intermolecular interaction. The expressions for the Debye temperature and Gruneisen parameter as a function of volume are analytically derived. The analytic equation of state is applied to predict the thermodynamic properties of solid xenon at normal-pressure with the nearest-neighbour Lennard-Jones interaction and is further applied to research the properties of solid xenon and krypton at high pressure by using an all-neighbour Lennard-Jones interaction. The theoretical results are in agreement with the experiments.