Thermal equation of state of goethite (α-FeOOH)

ABSTRACT

The pressure–volume–temperature (P–V–T) equation of state (EoS) of natural goethite (α-FeOOH) has been determined by an X-ray diffraction study using synchrotron radiation. Fitting the volume data to the third-order Birch–Murnaghan EoS yielded an isothermal bulk modulus, B₀ of 85.9(15)?GPa, and a pressure derivative of the bulk modulus, B′, of 12.6(8). The temperature derivative of the bulk modulus, (?B/?T)_P, was –0.022(9)?GPa?K^?1. The thermal expansion coefficient α₀ was determined to be 4.0(5)?×?10^?5?K^?1.     

In-situ X-ray diffraction study on β-CrOOH at high pressure and high-temperature

ABSTRACT

High pressure hydrous phases with distorted rutile-type structure have attracted much interest as potential water reservoirs in the Earth’s mantle. An in-situ X-ray diffraction study of β-CrOOH was performed at high pressures of up to 6.2?GPa and high-temperatures of up to 700?K in order to clarify the temperature effect on compression behaviors of β-CrOOH. The P-V-T data fitted to a Birch–Murnaghan equation of state yielded the following results: isothermal bulk modulus K_T0?=?191(4)?GPa, temperature derivative (?K_T/?T)_P?=??0.04(2)?GPa?K^?1, and volumetric thermal expansion coefficient α?=?3.3(2)?×?10^?5?K^?1. In this study, at 300?K, the a-axis became less compressible at pressures above 1–2?GPa. We found that the pressure where the slopes of a/b and a/c ratios turned positive increased with temperature. This is the first experimental study indicating the temperature dependence of the change in the axial compressibility in distorted rutile-type M³⁺OOH.     

Melting of B12P2 boron subphosphide under pressure

Melting of boron subphosphide (B₁₂P₂) to 26?GPa has been studied by in situ synchrotron X-ray powder diffraction in a laser-heated diamond anvil cell, and by quenching and electrical resistance measurements in a toroid-type high pressure apparatus. B₁₂P₂ melts congruently, and the melting curve has a positive slope of 23(6)?K/GPa. No solid-state phase transition was observed up to the melting in the whole pressure range under study.     

Advances in data reduction of high-pressure x-ray powder diffraction data from two-dimensional detectors: a case study of schafarzikite (FeSb(2)O(4))

Methods have been developed to facilitate the data analysis of multiple two-dimensional powder diffraction images. These include, among others, automatic detection and calibration of Debye-Scherrer ellipses using pattern recognition techniques, and signal filtering employing established statistical procedures like fractile statistics.All algorithms are implemented in the freely available program package Powder3D developed for the evaluation and graphical presentation of large powder diffraction data sets.As a case study, we report the pressure dependence of the crystal structure of iron antimony oxide FeSb(2)O(4) (p≤21?GPa, T = 298?K) using high-resolution angle dispersive x-ray powder diffraction. FeSb(2)O(4) shows two phase transitions in the measured pressure range. The crystal structures of all modifications consist of frameworks of Fe(2+)O(6) octahedra and irregular Sb(3+)O(4) polyhedra. At ambient conditions, FeSb(2)O(4) crystallizes in space group P4(2)/mbc (phase I). Between p = 3.2?GPa and 4.1?GPa it exhibits a displacive second order phase transition to a structure of space group P 2(1)/c (phase II, a = 5.7792(4)??, b = 8.3134(9)??, c = 8.4545(11)??, β = 91.879(10)°, at p = 4.2?GPa). A second phase transition occurs between p = 6.4?GPa and 7.4?GPa to a structure of space group P4(2)/m (phase III, a = 7.8498(4)??, c = 5.7452(5)??, at p = 10.5?GPa). A nonlinear compression behaviour over the entire pressure range is observed, which can be described by three Vinet equations in the ranges from p = 0.52?GPa to p = 3.12?GPa, p = 4.2?GPa to p = 6.3?GPa and from p = 7.5?GPa to p = 19.8?GPa. The extrapolated bulk moduli of the high-pressure phases were determined to K(0) = 49(2)?GPa for phase I, K(0) = 27(3)?GPa for phase II and K(0) = 45(2)?GPa for phase III. The crystal structures of all phases are refined against x-ray powder data measured at several pressures between p = 0.52?GPa, and 10.5?GPa.     

Dual mode ultrasonic interferometry in multi-anvil high pressure apparatus using single-crystal olivine as the pressure standard

Acoustic measurements of compressional (P) and shear (S) wave travel times were performed in a 1000-ton uniaxial split-cylinder apparatus (USCA-1000) of the Kawai-type up to 10?GPa at room temperature, using dual mode lithium niobate transducers and ultrasonic interferometry. The cell pressures were calibrated continuously by in-situ measurements of the travel times in a single crystal San-Carlos olivine buffer rod inside the cell assembly. Elastic compressional and shear wave velocities in a dense, fine-grained polycrystalline Al₂O₃ were measured simultaneously to 10?GPa; from these data, the elastic moduli and their pressure derivatives were obtained for the longitudinal modulus {L ₀?=?461(3)?GPa, L ₀′?=?7.0(1)}, the shear modulus {G ₀?=?162(2)?GPa, G ₀′?=?1.9(1)} and the bulk modulus {K ₀?=?245(3)?GPa, K ₀′?=?4.5(1)}.     

First-principles calculations of structural stability and mechanical properties of tungsten carbide under high pressure

The structural stability and mechanical properties of WC in WC-, MoC- and NaCl-type structures under high pressure are investigated systematically by first-principles calculations. The calculated equilibrium lattice constants at zero pressure agree well with available experimental and theoretical results. The formation enthalpy indicates that the most stable WC is in WC-type, then MoC-type finally NaCl-type. By the elastic stability criteria, it is predicted that the three structures are all mechanically stable. The elastic constants C_ij, bulk modulus B, shear modulus G, Young?s modulus E and Poisson?s ratio ν of the three structures are studied in the pressure range from 0 to 100 GPa. Furthermore, by analyzing the B/G ratio, the brittle/ductile behavior under high pressure is assessed. Moreover, the elastic anisotropy of the three structures up to 100 GPa is also discussed in detail.     

High volumetric hydrogen density phases of magnesium borohydride at high-pressure: A first-principles study

The previously proposed theoretical and experimental structures,bond characterization,and compressibility of Mg(BH 4) 2 in a pressure range from 0 to 10 GPa are studied by ab initio density-functional calculations.It is found that the ambient pressure phases of meta-stable I4 1 /amd and unstable P-3m1 proposed recently are extra stable and cannot decompose under high pressure.Enthalpy calculation indicates that the ground state of F 222 structure proposed by Zhou et al.[2009 Phys.Rev.B 79 212102] will transfer to I4 1 /amd at 0.7 GPa,and then to a P-3m1 structure at 6.3 GPa.The experimental P 6 1 22 structure(α-phase) transfers to I4 1 /amd at 1.2 GPa.Furthermore,both I4 1 /amd and P-3m1 can exist as high volumetric hydrogen density phases at low pressure.Their theoretical volumetric hydrogen densities reach 146.351 g H 2 /L and 134.028 g H 2 /L at ambient pressure,respectively.The calculated phonon dispersion curve shows that the I4 1 /amd phase is dynamically stable in a pressure range from 0 to 4 GPa and the P-3m1 phase is stable at pressures higher than 1 GPa.So the I4 1 /amd phase may be synthesized under high pressure and retained to ambient pressure.Energy band structures show that they are both always ionic crystalline and insulating with a band-gap of about 5 eV in this pressure range.In addition,they each have an anisotropic compressibility.The c axis of these structures is easy to compress.Especially,the c axis and volume of P-3m1 phase are extraordinarily compressible,showing that compression along the c axis can increase the volumetric hydrogen content for both I4 1 /amd and P-3m1 structures.     

High-pressure neutron diffraction study of BaFe<Subscript>2</Subscript>As<Subscript>2</Subscript>

The crystal structure of BaFe₂As₂ was studied by high-pressure neutron powder diffraction in the pressure range from ambient to 6.5 GPa as well as in the temperature range from 12 K to 293 K at 4.4 GPa and no pressure or temperature induced phase changes were observed. The compression mechanism of BaFe₂As₂ was found to be anisotropic as the a- and c-axes are reduced by 2.49 and 3.66%, respectively at 6.5 GPa. Within the FeAs layers the Fe-As and Fe-Fe bonds decrease by 2.49 and 3.66%, respectively. The Ba-As distance decreases by 3.70% while the As-As inter-atomic distance along the c-axis exhibits a complex pressure dependence. The bulk modulus B ₀ and its pressure derivative B ₀' were determined to be B ₀ = 59(2) GPa and B ₀' = 6.1(7) at ambient temperature.     

High pressure X-ray diffraction study on icosahedral boron arsenide (B12As2)

The high pressure properties of icosahedral boron arsenide (B₁₂As₂) were studied by in situ X-ray diffraction measurements at pressures up to 25.5 GPa at room temperature. B₁₂As₂ retains its rhombohedral structure; no phase transition was observed in the pressure range. The bulk modulus was determined to be 216 GPa with the pressure derivative 2.2. Anisotropy was observed in the compressibility of B₁₂As₂—c-axis was 16.2% more compressible than a-axis. The boron icosahedron plays a dominant role in the compressibility of boron-rich compounds.     

Single-crystal elasticity of the rhodochrosite at high pressure by Brillouin scattering spectroscopy

ABSTRACT

The sound velocity properties of single-crystal rhodochrosite (MnCO₃) were determined up to 9.7?GPa at ambient temperature by Brillouin scattering spectroscopy. Six elastic constants were calculated by a genetic algorithm method using the Christoffel's equations at each pressure. The elastic constants increased linearly as a function of pressure and its pressure derivatives ?Cij/?P for C₁₁, C₃₃, C₄₄, C₁₂, C₁₃, C₁₄ were 5.86 (±0.36), 3.82 (±0.44), 2.06 (±0.39), 5.07 (±0.27), 5.34 (±0.44), 1.52 (±0.24), respectively. Based on the derived elastic constants of rhodochrosite, the aggregate adiabatic bulk and shear moduli (K_s and G) were calculated using the Voigt-Reuss-Hill averages and the linear fitting coefficients (?K_s/?P)_T and (?G/?P)_T were 5.05(±0.26) and 0.73(±0.05), respectively. The aggregate V_p of rhodochrosite increased clearly as a function of pressure and its pressure derivative ?V_p/?P was 7.99(±0.53)?×?10^?2?km/(s?GPa), while the aggregate V_s increased slowly and ?V_s/?P was only 1.19(±0.12)?×?10^?2?km/(s?GPa). The anisotropy factor for As of rhodochrosite increased from ～40% at 0.8?GPa to ～48% at 9.7?GPa, while A_p decreased from ～19% to ～16% at the corresponding pressure.     

High pressure studies on α-cristobalite form of Al0.5Ga0.5PO4: hydrostatic versus non-hydrostatic conditions

High pressure angle-dispersive X-ray diffraction investigations have been carried out on α-cristobalite form of Al_0.5Ga_0.5PO₄. Our investigations show that the structural stability of this phase under high pressure depends on the nature of pressure conditions in the diamond anvil cell. Under hydrostatic pressure conditions using neon as a pressure transmitting medium, ambient orthorhombic C222₁ phase transforms to orthorhombic Cmcm phase at 4.9?GPa. The high pressure Cmcm phase remains stable up to the highest pressure in the experiment, i.e. 19?GPa. The values of bulk modulus for C222₁ and Cmcm phases are 19(2) and 126(4)?GPa, respectively. In contrast to this, under non-hydrostatic pressure conditions, transformation of ambient C222₁ phase to Cmcm phase has not observed up to 17.4?GPa. Instead, a new monoclinic phase P2₁ is observed which contains layers of six coordinated Al/Ga ions separated by less dense five coordinated Al/Ga ions.     

Strength and equation of state of molybdenum triboride under 80 GPa pressure,using radial X-ray diffraction

The strength and equation of state of molybdenum triboride have been determined under nonhydrostatic compression up to 80?GPa, using an angle-dispersive radial X-ray diffraction technique in a diamond anvil cell (DAC). The RXD data yield a bulk modulus and its pressure derivative as K_0?=?342(6)?GPa with K₀′?=?2.11(17) at ψ?=?54.7°. Analysis of diffraction data using the strain theory indicates that the ratio of differential stress to shear modulus (t/G) ranges from 0.002 to 0.050 at pressures of 4–80?GPa. Together with theoretical results on the high pressure shear modulus, our results here show that molybdenum triboride sample under uniaxial compression can support a differential stress of ～10?GPa when it started to yield with plastic deformation at ～30?GPa. In addition, we draw a conclusion that MoB₃ is not a superhard material but a hard material.     

Static compression of rare earth metal holmium to 282 GPa

ABSTRACT

The phase transitions and equation of state measurements were carried out on rare earth metal Holmium (Ho) to 282?GPa using toroidal diamond anvils thereby doubling the pressure range to which it has been studied previously. The first set of experiment employed standard beveled diamond anvils utilizing copper as an x-ray pressure standard to 217?GPa. The second set of experiment employed toroidal diamond anvils utilizing platinum as an x-ray pressure standard to 282?GPa. The recently proposed 16-atom orthorhombic structure (oF16) appeared to be stable between 103 and 282?GPa. The scaled axial ratio (c/a) shows a narrow range of variation of 1.58?±?0.05 for the five known crystalline phases of Ho to 282?GPa. The experimental equation of state of Ho is presented up to a threefold volume compression V/V_o?=?0.322.     

A synchrotron study of high-pressure transformations in TiH0·74

Abstract

The crystal structure of the TiH_0·74 alloy was studied by the energy dispersive X-ray diffraction technique in the pressure range to 30·5 GPa at temperatures to 630 K. A phase transformation to the (η + ω) two-phase state was found to occur above 7 GPa at room temperature, then (η+ω)-TiH_0·74 remained stable up to P=30·5 GPa. Another phase transformation resulting in a single-phase state, ζ-TiH_0·74, was found to occur upon heating (η+ω)-TiH_0·74 above T ? 560 K. Both high-pressure phases, η and ζ, were indexed on the basis of the tetragonal sublattices of the Ti atoms with nearly the same specific volumes. It is assumed from the relation of the specific volumes that the hydrogen atoms occupy the tetrahedral interstices in the ζ-phase and the octahedral interstices in the η-phase.     

Phase relations in the Fe-P system at high pressures and temperatures from ab initio computations

ABSTRACT

Based on the first-principles calculations within the density functional theory and crystal structure prediction algorithms iron phosphide phases stable under pressure of the Earth’s core and temperatures up to 4000?K were determined. A new low-temperature modification FeP-P2₁/c stable above ～75?GPa was predicted. Fe₂P with the allabogdanite structure has been established to be stable in the low-temperature region at ambient conditions. At 750?K it transforms into the barringerite structure. The transition from Fe₃P with schreibersite structure to Fe₃P-Cmcm was observed at 27?GPa, and the phase transition boundary is nearly isobaric. Fe₂P and FeP are thermodynamically stable at the Earth’s inner core pressures and 0?K according to the obtained results, whereas Fe₃P stabilizes with respect to decomposition to Fe?+?Fe₂P at high temperatures above ～3200?K.     

Investigations of phase transition, elastic and thermodynamic properties of GaP by using the density functional theory

The phase transition of gallium phosphide (GaP) from zinc-blende (ZB) to a rocksalt (RS) structure is investigated by the plane-wave pseudopotential density functional theory (DFT). Lattice constant a₀, elastic constants c_ij, bulk modulus B₀ and the pressure derivative of bulk modulus B₀' are calculated. The results are in good agreement with numerous experimental and theoretical data. From the usual condition of equal enthalpies, the phase transition from the ZB to the RS structure occurs at 21.9 GPa, which is close to the experimental value of 22.0 GPa. The elastic properties of GaP with the ZB structure in a pressure range from 0 GPa to 21.9 GPa and those of the RS structure in a pressure range of pressures from 21.9 GPa to 40 GPa are obtained. According to the quasi-harmonic Debye model, in which the phononic effects are considered, the normalized volume V/V₀, the Debye temperature θ, the heat capacity C_v and the thermal expansion coefficient α are also discussed in a pressure range from 0 GPa to 40 GPa and a temperature range from 0 K to 1500 K.     

SrB4O7:Sm2+: an optical sensor reflecting non-hydrostatic pressure at high-temperature and/or high pressure in a diamond anvil cell

A systematic investigation on the fluorescent spectra of SrB₄O₇:Sm²⁺ was performed in detail at high-temperature up to 623?K and/or high pressure up to 23.2?GPa with different pressure-transmitting media (PTMs), respectively. Combined with experiment data of previous research, the change of the ⁷D₀–⁵F₀ line (0–0 line) full width at half maximum (FWHM) of SrB₄O₇:Sm²⁺ under different pressure environments was specifically discussed. The results indicate that the FWHM of 0–0 line is sensitive to the non-hydrostatic pressure environment in 2-propanol, and methanol and ethanol mixture (ME) PTMs at ambient temperature. The first-order and the second-order derivation of the temperature dependence of 0–0 line FWHM at ambient pressure are 1.48(±0.21)?×?10^?4?nm/K and 9.63(±0.63)?×?10^?7?nm²/K² below 623?K. The 0–0 line FWHM is also sensitive to the non-hydrostatic pressure environment in ME at high-temperature and high pressure simultaneous, the non-hydrostatic transition pressures are 9.6?GPa at 323?K, 11.0?GPa at 373?K, 14.4?GPa at 423?K, respectively. SrB₄O₇:Sm²⁺ is recommended as an optical sensor to reflect the change of pressure environment in liquid media at high-temperature and/or high pressure.     

Studies on Im-3-type KSbO3 using high pressure X-ray diffraction and Raman spectroscopy

In situ X-ray diffraction and Raman scattering experiments using a diamond anvil cell revealed that Im-3-type KSbO₃ remains stable up to 40.5?GPa with a bulk modulus K₀?=?101.6 (7)?GPa. Rietveld structure refinements and mode Grüneisen parameters suggested that the stability mechanism of this three-dimensional cubic tunnel structure was attributed to the isotropic compression for all types of Sb–O bonding in the unit of SbO₆ octahedron. Isotropic structure adjustment with external pressure reflected the nature that Im-3-type KSbO₃ model structure has a high ionic tolerance with a change in the chemical pressure in the isomorphous substitutions.