Experimental Equation Of State Research Articles

Determination of Ionic Radii from Metal Compressibilities

The critical degrees of metal compression were determined from the experimental equations of state. The degree of metal compression corresponds to the cation-cation contacts in the structure. The cation radii were determined from the metal compressibilities and are in satisfactory agreement with the empirical values.

Non-collinear magnetism in iron at high pressures

Using a first-principles based, magnetic tight-binding total energy model, the magnetization energy and moments are computed for various ordered spin configurations in the high pressure polymorphs of iron (fcc, or γ-Fe, and hcp, or ϵ-Fe), as well as ferromagnetic bcc iron (α-Fe). For hcp an antiferromagnetic spin configuration is more stable than non-magnetic ϵ iron up to about 50 GPa. Accounting for magnetism yields better agreement with the experimental equation of state, in contrast to the non-magnetic equation of state, which is in poor agreement with experiment below 50 GPa. We also studied non-collinear magnetism in γ- and ϵ-Fe. In ϵ-Fe the non-collinear effects are quite small energetically; in its stability field the collinear afmII structure is more stable than all non-collinear structures we explored.

Non-collinear magnetism in iron at high pressures

Using a first-principles based, magnetic tight-binding total energy model, the magnetization energy and moments are computed for various ordered spin configurations in the high pressure polymorphs of iron (fcc, or γ-Fe, and hcp, or ϵ-Fe), as well as ferromagnetic bcc iron (α-Fe). For hcp an antiferromagnetic spin configuration is more stable than non-magnetic ϵ iron up to about 50 GPa. Accounting for magnetism yields better agreement with the experimental equation of state, in contrast to the non-magnetic equation of state, which is in poor agreement with experiment below 50 GPa. We also studied non-collinear magnetism in γ- and ϵ-Fe. In ϵ-Fe the non-collinear effects are quite small energetically; in its stability field the collinear afmII structure is more stable than all non-collinear structures we explored.

4He Impurities in 3He: Energetics and Dynamics

We have developed the optimized Fermi Hypernetted Chain Theory of a single impurity atom in a Fermi liquid, and have applied the theory to a 4He atom in bulk 3He. Previous applications of the theory for one component have produced excellent agreement with the experimental equation of state of 4He; the resulting equation of state of bulk 3He is about 0.4 K above the experimental one. Within the same theory, we obtain the pressure dependence of the chemical potential of 4He in bulk 4He, 3He in 3He, as well as the chemical potential of a 4He impurity in 3He. The pressure dependence of the impurity chemical potential agrees well with the experimental data, but we have a constant energy offset of about 1.2 K that disallows conclusive statements. This offset is partly explained by the relative inaccuracy of the 3He equation of state. We then calculate the self-energy of a single 4He impurity in 3He. Our results for the effective mass m*4 fall within the experimental error of the best available data; they increase from about m*4/m4≈1.4 at zero pressure, to m*4/m4≈1.6 at p=20 atm. We show that this effective mass enhancement is, to about equal parts, due to hydrodynamic backflow and to the coupling to particle-hole excitations. When the latter are turned off in the “collective” approximation of the impurity-background correlations one obtains a significantly lower effective mass, m*4/m4≈1.2−1.35.

Talc under tension and compression: Spinodal instability, elasticity, and structure

Talc occurs as a product of alteration of ultramafic rocks and may be a significant constituent of oceanic lithosphere and the arc mantle wedge. We explore the physical properties and structure of talc over a wide pressure range with density functional theory using the variable cell shape plane wave pseudopotential method in the local density (LDA) and generalized gradient (GGA) approximations. For LDA, the theoretical equation of state agrees with room temperature experimental measurements of the volume to within 2% when estimated effects of lattice vibrations are accounted for. We predict a spinodal mechanical instability (vanishing bulk modulus) at a volume 4% larger than the experimental volume at ambient conditions. Results for compression and tension are well represented by a fourth‐order Birch‐Murnaghan finite strain expansion withK0= 37.8,K0′ = 13. 6,K0K0″ = −153, whereKis the bulk modulus, primes indicate pressure derivatives and subscript 0 refers to zero pressure. The estimated theoretical value ofK0at 300 K (29 GPa) is considerably less than that determined from the experimental equation of state, a difference we attribute to the constraints of strain compatibility in the polycrystalline laboratory sample. Thec* =csin β axis is found to be a factor of 7 more compressible than thebaxis, consistent with experimental data. Compression in thea–bplane is accommodated primarily by the Mg‐octahedra. The polyhedral bulk modulus of the Mg‐octahedra is considerably greater than one‐third the linear modulus of theaaxis. The difference is attributed to the increasing regularity of the Mg‐octahedra on compression as measured by the octahedral tilt angle. The t sheet maintains registry with the o sheet by rotation of the Si‐tetrahedra; the tetrahedral rotation angle rises from a value of 3° at the experimental volume to a theoretically predicted value of 22° at a volume of 170 Å3where the pressure is 26 GPa. Tetrahedral rotation leads to small Si‐O‐Si angles at the highest pressures investigated (<122° at 26 GPa), which leads us to speculate that talc may undergo pressure‐induced amorphization under low‐temperature compression.

Path-integral Monte Carlo simulations of solid neon at room temperature

The kinetic and potential energies and the pressure of solid neon at room temperature have been calculated by means of path-integral Monte Carlo simulations using the HFD-C2 pair potential. At these high densities, the quantum corrections to the kinetic energy are appreciable, but for the potential energy and pressure classical simulations (even with a nearest-neighbor model) are generally within $1%$ of the quantum-mechanical values. The present results for the pressure are significantly higher than the experimental equation of state in the 10--100-GPa range. It is shown that inclusion of many-body short-range interactions might bring the simulations in agreement with experiment.

Comparison of embedded-atom models and first-principles calculations for Al phase equilibrium

We have performed total energy calculations on Al in the face-centered cubic (fcc), body-centered cubic (bcc), ideal hexagonal close packed (hcp), and simple cubic (sc) crystal structures over a range of unit cell volumes. We employed density functional theory (DFT) in the local density approximation (LDA) and the generalized gradient approximation (GGA) as well as two different forms of the embedded-atom method (EAM) empirical atomistic potential with the aim of evaluating the predictive range of the EAM relative to first-principles methods. All four calculations correctly give the fcc structure as the preferred one at zero pressure, with the DFT results in good agreement with the experimental equation of state and the model potentials in exact agreement (by construction). The hcp structure is found to be fairly close in energy to the fcc structure in all cases, and the sc structure is always found to be energetically very unfavorable. However, for the energetics of the bcc phase there is a serious disagreement between first-principles and atomistic calculations: The bulk modulus of bcc Al is much lower as predicted by the model potentials, with the result that its energy approaches that of the fcc phase as the volume is reduced. For the potential of Mishin et al. an fcc → bcc phase transition is predicted at a pressure of 27.4 GPa, in disagreement with the experimental fact that fcc Al is stable to at least 220 GPa. Our DFT results are consistent with earlier DFT calculations and with experiment in predicting no transition over the density or pressure range considered.

Thermoelastic properties of periclase and magnesiowüstite under high pressure and high temperature

A simple thermodynamic model for calculating the high-pressure and high-temperature properties of MgO consistently is presented. The model explains experimental equation of state (EOS) to ∼220 GPa at room temperature and shock-wave EOS to ∼200 GPa very well. The calculated Hugoniot temperature amounts to 3400 K at 200 GPa. The input parameters are the volume of the unit cell, V 0, bulk modulus, K 0, its pressure derivative, K 0′, Debye temperature, Θ 0, and a parameter relating to the shear modulus, f 44, all in the static lattice at zero pressure which are estimated from experimental data at room temperature and zero pressure. The calculated thermal expansivity, α, and Anderson–Grüneisen parameters, δ T and δ S , at zero pressure are in agreement with experimental data to 1000–1250 K and those to 1800 K, respectively. Our model explains also experimental velocities v p and v s of compressional and shear waves to 1800 K at zero pressure very well. The pressure-dependence of α, v p and v s at room temperature agree reasonably with experimental data to 36 GPa at room temperature. Applying our model to magnesiowüstite, we have calculated the thermal EOS and shock-wave EOS in agreement with experimental data. The implication of our result together with our previous one of magnesium-silicate perovskite for the composition of the lower mantle is briefly discussed.

Experimental and theoretical study ofLi3Nat high pressure

X rays from the Cornell High Energy Synchrotron Source were used to study the crystal structure of ${\mathrm{Li}}_{3}\mathrm{N}$ over a pressure range of 0 to 35 GPa at ambient temperature. Before loading, both the hexagonal ${D}_{6h}^{4}$ ${(P6}_{3}/mmc)$ and the hexagonal ${D}_{6h}^{1}$ $(P6/mmm)$ phases were present. At modest pressure, the ${D}_{6h}^{1}$ structure transforms completely into the ${D}_{6h}^{4}$ structure. A two-parameter Birch equation was fitted to the data to determine the equation of state (EOS) of the ${D}_{6h}^{4}$ structure, which is compared with a theoretical equation of state produced by our total-energy calculations in the framework of the local-density approximation. The experimental EOS was then used to determine the change in Gibb's free energy as a function of pressure for ${\mathrm{Li}}_{3}\mathrm{N}$ to 35 GPa at ambient temperature. The likelihood of a phase transition to a cubic structure at 35 GPa (as calculated by theory) based on observed optical changes is discussed.

Experimental equation of state of the shape memory alloy Ti50Ni48Fe2 AT 0-8 GPa and 298 K

The influence of hydrostatic pressures (up to 8 GPa) at 298 K on the pressure curves of the volume and volume elastic modulus of the B2 phase of Ti50Ni48Fe2 single crystals is investigated by an ultrasonic pulse-phase technique. It is proposed on analysis of the results that the alloy undergoes a B2→R martensitic, transition at 4.0–5.4 GPa. It is shown that the universal equation of state accurately describes the pressure dependence of volume over the entire pressure range.

Rotational ordering in solid deuterium and hydrogen: A path integral Monte Carlo study

The path-integral Monte Carlo method with a constant-pressure ensemble is used to study both translational and orientational transitions in the phase diagram of ${\mathrm{D}}_{2}$ and ${\mathrm{H}}_{2}$ up to megabar pressures. With an intermolecular interaction potential determined to agree with the experimental equation of state, a rotational order-disorder phase transition is observed. The phase line for this transition is in quantitative agreement with part of the phase diagram for both ${\mathrm{D}}_{2}$ and ${\mathrm{H}}_{2}$. No structural phase transition, and no transitions to the D-A and H-A phases (phase III) are observed. We attribute this in part to the limitations of simulation cell size.

X-Ray Structural Study of Li3N at High Pressure

ABSTRACTThe equation of state (EOS) of Li3N has been determined by energy-dispersive x-ray diffraction (EDXD) using synchrotron radiation up to 35 GPa at ambient temperature. Both the hexagonal D6h4(P63/mmc) and the hexagonal D6h1(P6/mmm) phases were present at ambient pressure. The D6h1 -structure completely transforms into the D6h4 -structure at modest pressure. The change in Gibb's free energy as a function of pressure for Li3N was calculated using the experimental EOS.

Thermal and pressure properties of amorphous polymers: relation to probe spectroscopy

We discuss the elements of a statistical thermodynamic theory of an equilibrium melt and its corresponding quasi-equilibrium glass. It involves a lattice model with a fraction h of vacancies as a measure of structural disorder. In the equilibrium melt the function h (V, T) is derived by a minimization of the configurational free energy. In the glass of specified formation history it is obtained from the experimental equation of state. The interpretation of this function as a free volume quantitiy in the frame of the lattice model results in important connections betwen thermodynamic and kinetic processes. In the present context the theory establishes correlations between the properties of the matrix and the characteristics of the o-positronium species

Zones of plastic deformation ? Main object of mechanics of real solids

The center of the model of modern mechanics of continuum contains the concept of determining relations: Hooke's law in the elasticity range, various equations of state of viscoelastoplastic bodies. These relations, supplementing Newton's mechanics equations, play the central role in all, or at least in the large majority of experimental investigations. They represent a central channel through which the theory is "saturated" with hypotheses; the hypotheses are not compulsory if instead of them we use direct experimental methods of closing the mechanics equations by direct experimental information. In this work, we discuss mainly the direct dynamic statistical observations of the application of experimental equations of state in situations in which the effects discovered in recent years operate, i.e., the superplasticity effect, the Spitsyn-Troitskii electroplastic effect, Kop'ev effect. Examination of the extreme effects of plasticity explains the principle of its normal effects. This type of examination makes it possible to formulate a new concept of the zonal plasticity mechanism, i.e., the zone of plastic deformation becomes the main object of the mechanics of condensed media. This concept represents the direct formulation of experimental observation; it contains no aprlori information and is equally suitable for any materials, composites or noncomposites.

Optical studies of methane under high pressure.

Physical properties of solid methane have been studied at room temperature under high pressure in a diamond-anvil cell. Internal modes have been followed up to 20 GPa by Raman scattering. The refractive index has been measured by a newly developed method up to 12 GPa and the elastic properties determined by Brillouin scattering up to 32 GPa. In the plastic phase I, the experimental equation of state and the elastic properties were analyzed with reference to rare-gas solids, i.e., with use of self-consistent harmonic calculations with various pair potentials. The best agreement is obtained with Aziz's Hartree-Fock+dispersion-C krypton-krypton potential. From analogies with rare-gas and ${\mathrm{NH}}_{3}$ solids, a hcp structure is proposed for phase IV. The IV-VII phase transition is shown to be orientational in nature.

Three-body exchange interaction in dense helium

Self-consistent phonon and Monte Carlo calculations show that the three-body exchange interaction is important in dense helium. Together with a realistic pair potential and the Axilrod-Teller three-body dispersion interaction, it brings calculations into agreement with the experimental equation of state. This interaction stabilizes the hcp structure for pressures greater than about 60 GPa. A speculative phase diagram of high-pressure helium is proposed.

Equation of state for fluid hydrogen-isotopes H2, D2, and T2 up to their freezing points at 300 K

The calculations of the P-V isotherms of fluid hydrogen isotopes H2, D2, and T2 up to their freezing pressures around 55 kbar at 300 K have been performed by using the modified hard-sphere variational perturbation theory with a quantum correction for four kinds of intermolecular potentials. The results by the use of the potentials of Silvera-Goldman and Nellis et al. agreed well with the experimental equation of state. The quantum pressures (ΔP) were estimated as a function of volume for H2, D2, and T2 at 300 and 200 K, and the dependences of ΔP on volume, molecular mass, and temperature were discussed.

Equation of State for Fluid and Solid Hydrogen-Isotopes H2, D2, and T2

ABSTRACTThe calculations of the P-V isotherms of fluid hydrogen isotopes H2 , D2 , and T2 up to their freezing pressures at 200, 300 and 500 K have been performed for 4 kinds of intermolecular potentials by using the modified hard-sphere variational perturbation theory with a quantum correction. By comparing the results with the 300 K experimental equation of state, it has turned out that the agreement is good for the potentials of Silvera-Goldman and Nellis et al. except near the freezing point of H2 . The quantum pressures were estimated, and their dependences on volume, molecular mass, and temperature are discussed quantitatively. We discuss the discrepancy of the P-V isotherms between experiments by Brillouin scattering and theoretical results for H2 near the freezing point, including the recent solid isotherms to higher pressures.

Core polarization and the equation of state of potassium

We calculate the zero-temperature equation of state of potassium with a model Hamiltonian that includes core-polarization effects. Density fluctuations in the ion cores lead to van der Waals interactions that are dynamically screened by the valence electrons. They also lead to screening of other static interactions, effects that are incorporated through the use of a background dielectric function ${\ensuremath{\epsilon}}_{c}(q)$. Inclusion of core-polarization effects yields significant improvement between the theoretical and experimental equations of state, particularly at high pressures.

Modern potentials and the properties of condensedHe4

The Green's-function Monte Carlo method has been used to calculate the properties of the ground-state $^{4}\mathrm{He}$ with several modern potentials. One potential, dubbed HFDHE2, by Aziz et al., gave very good agreement with the experimental equation of state in both the liquid and crystal phases. Other properties such as the structure factor and the momentum distribution also compare well with the experiment. In both phases, perturbative estimates of the three-body Axilrod-Teller potential were computed. When they are added to the two-body energies, the total energy is no longer in agreement with experiment. Further investigation on the nature of three-body interactions in the $^{4}\mathrm{He}$ may be necessary to elucidate this problem.