Highly Efficient Free Energy Calculations of the Fe Equation of State Using Temperature-Dependent Effective Potential Method

Free energy calculations at finite temperature based on ab initio molecular dynamics (AIMD) simulations have become possible, but they are still highly computationally demanding. Besides, achieving simultaneously high accuracy of the calculated results and efficiency of the computational algorithm is still a challenge. In this work we describe an efficient algorithm to determine accurate free energies of solids in simulations using the recently proposed temperature-dependent effective potential method (TDEP). We provide a detailed analysis of numerical approximations employed in the TDEP algorithm. We show that for a model system considered in this work, hcp Fe, the obtained thermal equation of state at 2000 K is in excellent agreement with the results of standard calculations within the quasiharmonic approximation.

High pressure effects on U L3 x-ray absorption in partial fluorescence yield mode and single crystal x-ray diffraction in the heavy fermion compound UCd11

We report a study of high pressure x-ray absorption (XAS) performed in the partial fluorescence yield mode (PFY) at the U L3 edge (0–28.2 GPa) and single crystal x-ray diffraction (SXD) (0–20 GPa) on the UCd11 heavy fermion compound at room temperature. Under compression, the PFY-XAS results show that the white line is shifted by +4.1(3) eV at the highest applied pressure of 28.2 GPa indicating delocalization of the 5f electrons. The increase in full width at half maxima and decrease in relative amplitude of the white line with respect to the edge jump point towards 6d band broadening under high pressure. A bulk modulus of K0 = 62(1) GPa and its pressure derivative, K0 = 4.9(2) was determined from high pressure SXD results. Both the PFY-XAS and diffraction results do not show any sign of a structural phase transition in the applied pressure range.

Thermal equation of state of solid naphthalene to 13 GPa and 773 K: in situ X-ray diffraction study and first principles calculations

In a wide range of P-T conditions, such fundamental characteristics as compressibility and thermoelastic properties remain unknown for most classes of organic compounds. Here we attempt to clarify this issue by the example of naphthalene as a model representative of polycyclic aromatic hydrocarbons (PAHs). The elastic behavior of solid naphthalene was studied by in situ synchrotron powder X-ray diffraction up to 13 GPa and 773 K and first principles computations to 20 GPa and 773 K. Fitting of the P-V experimental data to Vinet equation of state yielded T 0 = 8.4(3) GPa and T' = 7.2 (3) at V0 = 361 Å(3), whereas the thermal expansion coefficient was found to be extremely low at P > 3 GPa (about 10(-5) K(-1)), in agreement with theoretical estimation. Such a diminishing of thermal effects with the pressure increase clearly demonstrates a specific feature of the high-pressure behavior of molecular crystals like PAHs, associated with a low energy of intermolecular interactions.

Deviatoric stress-induced phase transitions in diamantane

The high-pressure behavior of diamantane was investigated using angle-dispersive synchrotron x-ray diffraction (XRD) and Raman spectroscopy in diamond anvil cells. Our experiments revealed that the structural transitions in diamantane were extremely sensitive to deviatoric stress. Under non-hydrostatic conditions, diamantane underwent a cubic (space group Pa3) to a monoclinic phase transition at below 0.15 GPa, the lowest pressure we were able to measure. Upon further compression to 3.5 GPa, this monoclinic phase transformed into another high-pressure monoclinic phase which persisted to 32 GPa, the highest pressure studied in our experiments. However, under more hydrostatic conditions using silicone oil as a pressure medium, the transition pressure to the first high-pressure monoclinic phase was elevated to 7-10 GPa, which coincided with the hydrostatic limit of silicone oil. In another experiment using helium as a pressure medium, no phase transitions were observed to the highest pressure we reached (13 GPa). In addition, large hysteresis and sluggish transition kinetics were observed upon decompression. Over the pressure range where phase transitions were confirmed by XRD, only continuous changes in the Raman spectra were observed. This suggests that these phase transitions are associated with unit cell distortions and modifications in molecular packing rather than the formation of new carbon-carbon bonds under pressure.

Ramp compression of diamond to five terapascals

The recent discovery of more than a thousand planets outside our Solar System, together with the significant push to achieve inertially confined fusion in the laboratory, has prompted a renewed interest in how dense matter behaves at millions to billions of atmospheres of pressure. The theoretical description of such electron-degenerate matter has matured since the early quantum statistical model of Thomas and Fermi, and now suggests that new complexities can emerge at pressures where core electrons (not only valence electrons) influence the structure and bonding of matter. Recent developments in shock-free dynamic (ramp) compression now allow laboratory access to this dense matter regime. Here we describe ramp-compression measurements for diamond, achieving 3.7-fold compression at a peak pressure of 5 terapascals (equivalent to 50 million atmospheres). These equation-of-state data can now be compared to first-principles density functional calculations and theories long used to describe matter present in the interiors of giant planets, in stars, and in inertial-confinement fusion experiments. Our data also provide new constraints on mass-radius relationships for carbon-rich planets.

Cationic radii from structures of extremely compressed solids

The cationic radii of metals are derived from the compressibility of solids assuming that extreme compression of metals leads to direct contacts between cations (= atomic cores). In an extremely compressed binary compound the heteronuclear separations are equal to the sum of the cationic radius of the metal and the covalent radius of the nonmetal.

Effect of laser annealing of pressure gradients in a diamond-anvil cell using common solid pressure media

Pressure media are one of the most effective deterrents of pressure gradients in diamond-anvil cell (DAC) experiments. The media, however, become less effective with increasing pressure, particularly for solid pressure media. One of the most popular ways of alleviating the increase in pressure gradients in DAC samples is through laser annealing of the sample. We explore the effectiveness of this technique for six common solid pressure media that include: alkali metal halides LiF, NaCl, KCl, CsCl, KBr, as well as amorphous SiO2. Pressure gradients are determined through the analysis of the first-order diamond Raman band across the sample before and after annealing the sample with a near-infrared laser to temperatures between ~2000 and 3000 K. As expected, we find that in the absence of sample chamber geometrical changes and diamond anvil damage, laser annealing reduces pressure gradients, albeit to varying amounts. We find that under ideal conditions, NaCl provides the best deterrent to pressure gradients before and after laser annealing, at least up to pressures of 60 GPa and temperatures between ~2000 and 3000 K. Amorphous SiO2, on the other hand, transforms in to harder crystalline stishovite upon laser annealing at high pressures resulting in increased pressure gradients upon further compression without laser annealing.

New boron nitride structures B4N4: a first-principles random searching application

The present investigation searched for new boron nitride (BN) polymorphs by means of first-principles simulations. The ab initio random structure searching strategy was implemented. The electronic and mechanical properties and equation of states of three new metastable BN crystal forms with equilibrium energies close to the most stable B4N4 form, c-BN, are presented. Results show either dynamically stable semiconductors or insulators, one of which is even slightly harder than c-BN. The equation of states is also presented and a phase transition is predicted.

Evidence of superdense aluminium synthesized by ultrafast microexplosion

At extreme pressures and temperatures, such as those inside planets and stars, common materials form new dense phases with compacted atomic arrangements and unusual physical properties. The synthesis and study of new phases of matter at pressures above 100 GPa and temperatures above 10(4) K--warm dense matter--may reveal the functional details of planet and star interiors, and may lead to materials with extraordinary properties. Many phases have been predicted theoretically that may be realized once appropriate formation conditions are found. Here we report the synthesis of a superdense stable phase of body-centred-cubic aluminium, predicted by first-principles theories to exist at pressures above 380 GPa. The superdense Al phase was synthesized in the non-equilibrium conditions of an ultrafast laser-induced microexplosion confined inside sapphire (α-Al(2)O(3)). Confined microexplosions offer a strategy to create and recover high-density polymorphs, and a simple method for tabletop study of warm dense matter.

The effect of pressure on the crystal structure of bianthrone

Bianthrone [10(10-oxoanthracen-9-ylidene)anthracen-9-one] consists of two tricyclic anthraceneone units connected by a carbon–carbon double bond. Crystals of the form obtained under ambient conditions are yellow and contain folded centrosymmetric conformers in which the central ring of the anthraceneone unit is non-planar. When hydrostatic pressure is applied the crystals assume a red colouration which gradually deepens as pressures increases. The colour change is limited in extent to the surface of the crystals, the bulk remaining yellow. Comparison of high-pressure, single-crystal UV–vis spectra and powder diffraction data demonstrate that the colour change is associated with the formation of a polymorph containing a conformer in which the tricyclic fragments are planar and the molecule is twisted about the central C—C bond. Single-crystal diffraction data collected as a function of pressure up to 6.5 GPa reveal the effect of compression on the yellow form, which consists of layers of molecules which stack along the [010] direction. The structure remains in a compressed form of the ambient-pressure phase when subjected to hydrostatic pressure up to 6.5 GPa, and the most prominent effect of pressure is to push the layers closer together. PIXEL calculations show that considerable strain builds up in the crystal as pressure is increased with a number of intermolecular contacts being pushed into destabilizing regions of their potentials.

Relationship Between Interfacial Strain and the Elastic Response of Multilayer Metal Film

We have used x-ray diffraction and picosecond transient piezoreflectance to investigate the structural and elastic properties of three distinct multilayer systems: Mo/Ni, Pt/Ni and Ti/Ni. We demonstrate that the commonly observed lattice expansion perpendicular to the film plane is not a bulk effect, but is localized at the interface between the contacting metals. Incorporating the measured interfacial expansion into a universal binding relation, we show that the measured elastic softening versus compositional repeat distance can result from the interfacial strain.

A High-Pressure Test of Birch's Law

The compressional wave velocities of polycrystalline NaCl and KCl have been measured to over 17 gigapascals, with the use of Brillouin scattering and the diamond anvil cell. This pressure corresponds to 40% compression for NaCl and 60% compression for KCl (including the volume change across the B1-B2 transition). The data obey Birch's Law, which predicts that the velocity of each material is linear with density, except across the B1-B2 phase transition in KCl. This deviation from Birch's Law can be rationalized in terms of an interatomic potential model wherein the vibrational frequencies of the nearest neighbor bonds decrease when going to the eight-coordinated B2 structure from the six-coordinated B1 structure.

Synchrotron X-ray Diffraction Measurements of Single-Crystal Hydrogen to 26.5 Gigapascals

The crystal structure and equation of state of solid hydrogen have been determined directly to 26.5 gigapascals at room temperature by new synchrotron x-ray diffraction techniques. Solid hydrogen remains in the hexagonal close-packed structure under these pressure-temperature conditions and exhibits increasing structural anisotropy with pressure. The pressure-volume curve determined from the x-ray data represents the most accurate experimental measurement of the equation of state to date in this pressure range. The results remove the discrepancy between earlier indirect determinations and provide a new experimental constraint on the molecular-to-atomic transition predicted at higher pressures.

Compressional behavior of solid NeHe2 up to 90 GPa

NeHe(2) was compressed to about 90 GPa using a diamond anvil cell technique. The crystal structure was confirmed to be stable with hexagonal symmetry in the investigated pressure range and its p-V equation of state was determined by angular dispersive x-ray diffraction with synchrotron radiation. With the help of ab initio calculations, the compressibility and inter-atomic distances of NeHe(2) were compared with those of a helium and neon mixture of the same composition. This study shows that the bulk modulus of NeHe(2) is between those of neon and helium and that linear compressibilities of the inter-atomic distances are different from those of the elementary solids. This material can be a pressure-transmitting medium, providing both a large sample space and good quasi-hydrostatic conditions.

First-principles molecular dynamics calculations of the equation of state for tantalum

The equation of state of tantalum (Ta) has been investigated to 100 GPa and 3,000 K using the first-principles molecular dynamics method. A large volume dependence of the thermal pressure of Ta was revealed from the analysis of our data. A significant temperature dependence of the calculated effective Grüneisen parameters was confirmed at high pressures. This indicates that the conventional approach to analyze thermal properties using the Mie-Grüneisen approximation is likely to have a significant uncertainty in determining the equation of state for Ta, and that an intrinsic anharmonicity should be considered to analyze the equation of state.

Diamond at 800 GPa

A new compression technique, which enables the study of solids into the TPa regime, is described and used to ramp (or quasi-isentropically) compress diamond to a peak pressure of 1400 GPa. Diamond stress versus density data are reported to 800 GPa and suggest that the diamond phase is stable and has significant material strength up to at least this stress level. Data presented here are the highest ramp compression pressures by more than a factor of 5 and the highest-pressure solid equation-of-state data ever reported.

Toward an internally consistent pressure scale

Our ability to interpret seismic observations including the seismic discontinuities and the density and velocity profiles in the earth's interior is critically dependent on the accuracy of pressure measurements up to 364 GPa at high temperature. Pressure scales based on the reduced shock-wave equations of state alone may predict pressure variations up to 7% in the megabar pressure range at room temperature and even higher percentage at high temperature, leading to large uncertainties in understanding the nature of the seismic discontinuities and chemical composition of the earth's interior. Here, we report compression data of gold (Au), platinum (Pt), the NaCl-B2 phase, and solid neon (Ne) at 300 K and high temperatures up to megabar pressures. Combined with existing experimental data, the compression data were used to establish internally consistent thermal equations of state of Au, Pt, NaCl-B2, and solid Ne. The internally consistent pressure scales provide a tractable, accurate baseline for comparing high pressure-temperature experimental data with theoretical calculations and the seismic observations, thereby advancing our understanding fundamental high-pressure phenomena and the chemistry and physics of the earth's interior.

High-Pressure Studies of Cyclohexane to 40 GPa

We present data from two room temperature synchrotron X-ray powder diffraction studies of cyclohexane up to approximately 40 and approximately 20 GPa. In the first experiment, pressure cycling was employed wherein pressure was varied up to approximately 16 GPa, reduced to 3.5 GPa, and then raised again to 40 GPa. Initially, the sample was found to be in the monoclinic phase (P12(1)/n1) at approximately 8.4 GPa. Beyond this pressure, the sample adopted triclinic unit cell symmetry (P1) which remained so even when the pressure was reduced to 3.5 GPa, indicating significant hysteresis and metastability. In the second experiment, pressure was more slowly varied, and the monoclinic unit cell structure (P12(1)/n1) was observed at lower pressures up to approximately 7 GPa, above which a phase transformation into the P1 triclinic unit cell symmetry occurred. Thus, the pressure onset of the triclinic phase may be dependent upon the pressurizing conditions. High-pressure Raman data that further emphasize a phase transition (probably into phase VI) around 10 GPa are also presented. We also have further evidence for a phase VII, which is probably triclinic.

Applicability of isothermal unrealistic two-parameter equations of state for solids

The aim of the present study, an extension of a recent one (Bose Roy and Bose Roy 2005 J. Phys.: Condens. Matter 17 6193), is to assess and compare the curve-fitting utility of the isothermal unrealistic two-parameter equations of state for solids (EOS), proposed at different stages in the development of the EOS field, for the purposes of smoothing and interpolation of pressure-volume data, and extraction of accurate values of the isothermal bulk modulus and its pressure derivative. To this end, 21 such EOSs are considered, formulated by/labelled as Born-Mie (1920), Born-Mayer (1932), Bardeen (1938), Slater-Morse (1939), Birch-Murnaghan (1947), Pack-Evans-James (1948), Lagrangian (1951), Davydov (1956), Davis and Gordon (1967), Onat and Vaisnys (1967), Grover-Getting-Kennedy (1973), Brennan-Stacey (1979), Walzer-Ullmann-Pan'kov (1979), Rydberg (1981), Dodson (1987), Holzapfel (1991), Parsafar-Mason (1994), Shanker-Kushwah-Kumar (1997), Poirier-Tarantola (1998), Deng-Yan (2002) and Kun-Loa-Syassen (2003). Furthermore, all these EOSs are compared with our three-parameter EOS, as well as its two-parameter counterpart proposed in this work. We have applied all the EOS models, with no constraint on the parameters, to the accurate and model-independent isotherms of nine solids. The applicability has been assessed in terms of an unbiased composite test, comprising fitting accuracy, agreement of the fit parameters with experiment, stability of the fit parameters with variation in the compression/pressure ranges and on the basis of the number of wiggles of the data deviation curves about the fit parameters. Furthermore, a rigorous method is devised to scale the relative adequacy of the EOSs with respect to the test parameters. A number of remarkable findings emerge from the present study. Surprisingly, both the old EOSs, the Born-Mie and the Pack-Evans-James, are significantly better in their curve-fitting capability than the Birch-Murnaghan EOS which has been widely used and continues to be used for curve-fitting purposes as a standard EOS in the literature. The Born-Mayer as well as the Walzer-Ullmann-Pan'kov models also fit isotherms better than the Birch. The performance of the EOS based on the Rydberg potential-that has been rediscovered by Rose et al (1984 Phys. Rev. B 29 2963), and strongly promoted by Vinet et al (1989 J. Phys.: Condens. Matter 1 1941) as the so-called universal equation of state, and is currently used as a standard EOS along with that of the Birch-is very poor, on a comparative scale. Furthermore, the curve-fitting capability of our original three-parameter EOS, and more importantly its two-parameter counterpart, is superior to all the isothermal unrealistic two-parameter EOSs so far proposed in the literature.

Structure, metastability, and electron density of Al lattices in light of the model of anions in metallic matrices

This paper reports a theoretical investigation of the structure, stability, and electron charge density of cubic, rhombohedral, hexagonal, and monoclinic Al lattices. The equations of state and the elastic constants are computed from total energy calculations at different volumes and unit cell strains using the density functional theory approximation. The topology of the electron density is analyzed within the crystalline implementation of the atoms in molecules formalism. The results are discussed in light of the so-called anions in metallic matrices model, which permits the interpretation of the chemical bonding and the explanation of the existence of particular symmetries of inorganic crystals. First, the Al sublattices are identified as the reference building blocks of AlX(3) (X = F, Cl, OH) compounds. The calculations reveal that the equilibrium zero-pressure Al-Al shortest distance is around 2.75 A in all of the Al matrixes, similar to the value observed in the stable face centered cubic structure of Al at room conditions. Second, at their zero-pressure equilibrium geometries, the Al sublattices are found to fulfill the mechanical stability criteria or, alternatively, to show mechanical instabilities that are compatible with the distortions observed for the structures in AlX(3) crystals. However, at the equilibrium volumes of the AlX(3) crystals, all of the Al matrices violate the spinodal condition, and the cohesion and stabilization are provided by the nonmetallic X atoms. Third, the structural anisotropy of the Al sublattices seems to be the main factor to discriminate metallic matrices able to host nonmetallic elements. The inhomogeneities of the electron charge density, which favor the arrival of nonmetallic elements and the crystal formation, are notably enhanced in passing from the fcc structure of pure Al to the less isotropic Al matrices observed in AlX(3) compounds.

Accurate equation of state of AlPdMn up to 35 GPa and pressure effect on the frozen-in phason strain

Angle-dispersive monochromatic x-ray diffraction spectra from a perfect single-grain AlPdMn quasicrystal have been obtained under hydrostatic pressure in a diamond anvil cell up to 35 GPa. More than 50 Bragg peaks with sharpness comparable to that at ambient conditions were observed up to the maximum pressure, indexed and used to measure the hypercubic 6D lattice parameter, providing the most accurate determination of the equation of state in this pressure range to date. Within the instrumental resolution, the absence of broadening of the diffraction peaks indicates the absence of structural transition and/or unusual configurational entropy change expected from previous studies through pressure-induced amorphization or phason defects.

Evidence of a fcc-hcp transition in aluminum at multimegabar pressure

The structure phase transition and the equation of state (EOS) of the third-period simple metal Al were investigated at pressure up to 333 GPa by powder x-ray diffraction experiments. The theoretically predicted fcc-hcp transition was observed at the reduced volume V/V0 of 0.509(1), corresponding to the pressure of 217+/-10 GPa. From the obtained pressure-volume data, the pressure derivative of the bulk modulus K0' for the EOS of fcc-Al was determined to be 4.83(3) by fitting to the Vinet formulation with a fixed value 72.7 GPa of K0 obtained from previous ultrasonic experiments.

Spin transition of iron in magnesiowüstite in the Earth's lower mantle

Iron is the most abundant transition-metal element in the mantle and therefore plays an important role in the geochemistry and geodynamics of the Earth's interior. Pressure-induced electronic spin transitions of iron occur in magnesiowüstite, silicate perovskite and post-perovskite. Here we have studied the spin states of iron in magnesiowüstite and the isolated effects of the electronic transitions on the elasticity of magnesiowüstite with in situ X-ray emission spectroscopy and X-ray diffraction to pressures of the lowermost mantle. An observed high-spin to low-spin transition of iron in magnesiowüstite results in an abnormal compressional behaviour between the high-spin and the low-spin states. The high-pressure, low-spin state exhibits a much higher bulk modulus and bulk sound velocity than the low-pressure, high-spin state; the bulk modulus jumps by approximately 35 percent and bulk sound velocity increases by approximately 15 percent across the transition in (Mg0.83,Fe0.17)O. Although no significant density change is observed across the electronic transition, the jump in the sound velocities and the bulk modulus across the transition provides an additional explanation for the seismic wave heterogeneity in the lowermost mantle. The transition also affects current interpretations of the geophysical and geochemical models using extrapolated or calculated thermal equation-of-state data without considering the effects of the electronic transition.

A High-Pressure Structure in Curium Linked to Magnetism

Curium lies at the center of the actinide series and has a half-filled shell with seven 5f electrons spatially residing inside its radon core. As a function of pressure, curium exhibits five different crystallographic phases up to 100 gigapascals, of which all but one are also found in the preceding element, americium. We describe here a structure in curium, Cm III, with monoclinic symmetry, space group C2/c, found at intermediate pressures (between 37 and 56 gigapascals). Ab initio electronic structure calculations agree with the observed sequence of structures and establish that it is the spin polarization of curium's 5f electrons that stabilizes Cm III. The results reveal that curium is one of a few elements that has a lattice structure stabilized by magnetism.

Hard superconducting nitrides

Detailed study of the equation of state, elasticity, and hardness of selected superconducting transition-metal nitrides reveals interesting correlations among their physical properties. Both the bulk modulus and Vickers hardness are found to decrease with increasing zero-pressure volume in NbN, HfN, and ZrN. The computed elastic constants from first principles satisfy c11 > c12 > c44 for NbN, but c11 > c44 > c12 for HfN and ZrN, which are in good agreement with the neutron scattering data. The cubic delta-NbN superconducting phase possesses a bulk modulus of 348 GPa, comparable to that of cubic boron nitride, and a Vickers hardness of 20 GPa, which is close to sapphire. Theoretical calculations for NbN show that all elastic moduli increase monotonically with increasing pressure. These results suggest technological applications of such materials in extreme environments.

High pressure study of a Zr-based bulk metallic glass and its composite

Energy dispersive X-ray diffraction was used to study the structural evolution of a bulk metallic glass (BMG) alloy and its composite with W particles under hydrostatic pressure. The diffraction data, especially the pair distribution function (PDF) of the BMG allowed the direct measurement of its elastic strain. The results suggest that PDF patterns of BMGs can be used to deducetheir strain evolution in composites as well as in monolithic form. Although the PDF method of strain measurement in amorphous alloys offers lower resolution compared to the analysis of Bragg reflections from crystalline materials, the PDF techique yields valuable information about the deformation of BMGs.