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.     

Pressure dependence of crystal structure and molecular packing in anthracene

Anthracene molecular crystal has been investigated up to a pressure of 10.5 GPa at room temperature using variable shape variable size Monte Carlo simulations in an isothermal–isobaric ensemble. We have reported various structural quantities, such as cell parameters and unit cell volume, as a function of pressure and compared them with the experimental results [J. Chem. Phys. 119, 1078 (2003)]. The pressure dependence of angles θ, δ and χ which describe the relative packing of molecules in the crystal has been calculated. We report that anthracene molecular crystal does not exhibit any first order phase transition up to a pressure of 10.5 GPa which is consistent with the experimental observations by Oehzelt et al. [Phys. Rev. B 66, 174104 (2002)]. The calculated equation of state (EOS) has been fitted to a Murnaghan-type EOS with good agreement. The calculated bulk modulus and the pressure derivative of bulk modulus are 8.2 GPa and 8.9 respectively which are in agreement with the experimentally calculated values.     

高压下碱卤晶体的三参量等温状态方程

 由等温体积弹性模量的定义及其与压强关系的假设出发,导出了一个新的适用于高压下碱卤晶体的三参量等温状态方程。计算了室温下NaCl晶体在0～30 GPa压强范围内、CsCl晶体在0～40 GPa压强范围内的相对体积以及NaCl晶体在0～30 GPa压强范围内的等温体积弹性模量,计算结果与实验值一致。对等温体积弹性模量及其对压强的一阶、二阶导数与压强的关系进行了讨论,指出压强趋于无穷大时的等温体积弹性模量是常数。     

Equation of state for technetium from X‐ray diffraction and first-principle calculations

The ambient temperature equation of state (EoS) of technetium metal has been measured by X-ray diffraction. The metal was compressed using a diamond anvil cell and using a 4:1 methanol-ethanol pressure transmitting medium. The maximum pressure achieved, as determined from the gold pressureEquation of state for technetium from X-ray diffraction and first-principle calculations scale, was 67 GPa. The compression data shows that the HCP phase of technetium is stable up to 67 GPa. The compression curve of technetium was also calculated using first-principles total-energy calculations. Utilizing a number of fitting strategies to compare the experimental and theoretical data it is determined that the Vinet equation of state with an ambient isothermal bulk modulus of B_0T=288 GPa and a first pressure derivative of B′=5.9(2) best represent the compression behavior of technetium metal.     

Temperature derivatives of the bulk modulus of ZrB2 calculated by using the pressure derivative of the bulk modulus

The temperature dependence of the bulk modulus of ZrB₂ above room temperature was calculated by using the equations by Garai and Laugier (J. Appl. Phys. 101 (2007) p.023514) and Lawson and Ledbetter (Philos Mag. 91 (2011) p.1425). The present calculations involve the accurate data for pressure derivative of the bulk modulus for the Anderson–Grüneisen parameter in addition to the other experimental parameters involved. It is interesting to note that the cited equations derived by different thermodynamic approaches give almost equivalent values for the temperature dependencies of the bulk modulus of ZrB₂. The present results for the temperature derivatives of the bulk modulus of ZrB₂ vary from ?0.016?GPa/K at 300–400?K to ?0.022?GPa/K at 1500–1600?K, being in good agreements with the corresponding experimental values.     

Thermal equation-of-state of osmium: a synchrotron X-ray diffraction study

The pressure-volume-temperature behavior of osmium was studied at pressures and temperatures up to 15 GPa and 1273 K. In situ measurements were conducted using energy-dispersive synchrotron X-ray diffraction in a T-cup 6-8 high pressure apparatus. A fit of room-temperature data by the third-order Birch-Murnaghan equation-of-state yielded isothermal bulk modulus K₀=435(19) GPa and its pressure derivative K′₀=3.5(0.8) GPa. High-temperature data were analyzed using Birch-Murnaghan equation of state and thermal pressure approach. The temperature derivative of bulk modulus was found to be −0.061(9) GPa K⁻¹. Significant anisotropy of osmium compressibility was observed.     

High pressure X-ray diffraction study of copper hydride at room temperature

Abstract

High pressure X-ray studies on CuH up to 23 GPa have been performed at room temperature using a gasketed diamond anvil cell. The experimental data on the molar volume of CuH as a function of pressure have been fitted to Murnaghan's equation of state giving a bulk modulus: B₀ = 72.5±2 GPa and B₀ = 2.7 ± 0.3. By comparison with the equation of state for pure copper the effective additive volume of hydrogen has been evaluated as a function of pressure. It decreases from 3.2 cm³/mol H, at ambient pressure reaching a flattening value of 1.7cm³hol H at about 60 GPa. This suggests a continuous transition of CuH from ionic or covalent character at normal pressure to metallic hydride behavior at high pressure     

Thermoelastic behaviour of hexagonal graphite-like boron nitride

Abstract

A synchrotron X-ray diffraction study on hexagonal graphite-like boron nitride (h-BN) was performed under high pressures and temperatures. From the measured P-V-Trelation for h-BN (with a three-dimensional ordering parameter P₃ = 0.9) in the temperature range from 298 to 1273 K and up to 6.7 GPa, the thermoelastic parameters are derived by fitting a modified high temperature Birch-Murnaghan equation of state. The results are: bulk modulus B₀[GPa] = 27.6-0.0081(T[K]-298) and its pressure derivative B¹ = 10.5 + 0.0016(T [K] - 298). These values are for samples with P₃ = 0.9 and are quite different for samples with different values of the order parameter. This parameter is shown to have a leading role in the determination of the thermoelastic properties of h-BN, which explains and reconciles the differences between previous results.     

Elastic, thermal and structural properties of platinum

The thermal equation of state (EOS) for platinum has been calculated to 300 GPa and 3000 K using ab initio molecular dynamics employing the local density approximation (LDA) and the projector augmented-wave methods (PAW). Direct ab initio molecular dynamics avoids the simplifying assumptions inherent in empirical treatments of thermoelasticity. A third-order Birch-Murnaghan equation EOS fitted to the 300 K data yielded an isothermal bulk modulus of B_T0=290.8 GPa and a pressure derivative of B_T′=5.11, which are in better agreement with the measured values than those obtained by previous calculations. The high-temperature data were fitted to a thermal pressure EOS and a Mie-Grüneisen-Debye EOS. The resulting calculated thermal expansion coefficient, α₀, temperature derivative of the isothermal bulk modulus, (∂B_T/∂T)_V, and second temperature derivative of the pressure, (∂²P/∂T²)_V, were 1.94×10⁻⁵ K⁻¹, −0.0038 GPa K⁻¹, and 1.7×10⁻⁷ GPa² K⁻², respectively. A fit to the Mie-Grüneisen-Debye EOS yielded values for the Grüneisen parameter, γ₀, and its volume dependence parameter, q, of 2.18 and 1.75, respectively. An analysis of our data revealed a strong volume dependence of the thermal pressure of platinum. We also present a qualitative analysis of the effects of intrinsic anharmonicity from the calculated Grüneisen parameter at high temperatures.     

Equation of state and thermal stability of Al3BC

The lattice parameters of Al₃BC have been measured up to 5 GPa at ambient temperature using energy-dispersive X-ray powder diffraction with synchrotron radiation. A fit to the experimental p-V data using Birch-Murnaghan equation of state gives values of the Al₃BC bulk modulus 116(4) GPa and its first pressure derivative 9(2). In the 1.6-4.8 GPa range at temperatures above 1700 K Al₃BC undergoes incongruent melting that results in the formation of Al₃BC₃, AlB₂ and liquid aluminum.     

Equation of state of boron subarsenide B12As2 to 47 GPa

Compressibility of boron subarsenide B₁₂As₂ has been studied by synchrotron X-ray diffraction up to 47?GPa at room temperature in a diamond anvil cell using Ne pressure transmitting medium. A fit of experimental p–V data by Vinet equation of state yielded the bulk modulus of 150(4) GPa and its first pressure derivative of 6.4(3). No pressure-induced phase transitions have been observed.     

Applicability of equation of state in extreme compression region and study of diatomic solids under pressure

In the present study, the expression of first pressure derivative of bulk modulus B′?earlier derived by Goyal and Gupta EoS [7] is corrected and the validity of the EoS is then verified in extreme compression region. The expressions of second and third order pressure derivative $(B^{{}^{″}},B^{″\prime })$of bulk modulus are obtained. The values of B′, B²B? to BB″,?Grunesien parameters?λ_∞,?γ_∞,?q_∞ at infinite pressure (P?→?∞)?are calculated using the identities [11–13] to check the validity of the equation in extreme compression region. The Goyal and Gupta EoS is then used to study the volume compression in diatomic solids, LiH and MgO. The values of pressure, bulk modulus and its first order pressure derivative at different compressions are calculated and compared with the results obtained from Hama–Suito EoS. The results justify the validity of the present EoS in high pressure region and the results for diatomic solids are also found in good consistency with the compared results.     

Equation of state of turbostratic boron nitride

Abstract

The lattice parameters of turbostratic boron nitride (tBN) have been measured to 6.1 GPa at room temperature using energy-dispersive powder diffraction with synchrotron radiation. A fit to the experimental p-V data using Birch-Murnaghan equation of state gives values of the tBN bulk modulus 17.5(8) GPa and its pressure derivative ll.4(5). These values point to significantly higher compressibility of turbostratic BN as compared to three-dimensionally ordered graphite-like hexagonal and rhombohedral boron nitride.     

MgCNi3超导体在静水压下的弹性性质

 在0.1 MPa到0.5 GPa压力范围内，采用脉冲回波重合法（Pulse-Echo Overlap Method）测量了MgCNi₃超导体的横波及纵波声速，计算了体弹模量B、剪切模量G等弹性参数以及德拜温度、比热等热力学参数随压力的变化。常压下的θ_D与c_V的值分别为454.82 K和111.30 J/(mol·K)。对B-p曲线作线性拟合，得到体弹模量B₀在零压附近的导数B′₀，由此建立了MgCNi₃的状态方程。     

Compression behavior of nanocrystalline anatase TiO2

We present a synchrotron X-ray diffraction study of pressure-induced changes in nanocrystalline anatase (with a crystallite size of 30-40 nm) to 35 GPa. The nanoanatase was observed to a pressure above 20 GPa. Direct transformation to the baddeleyite-TiO₂ polymorph was seen at 18 GPa. A fit of the pressure versus volume data to a Birch-Murnaghan equation yielded the following parameters: zero-pressure volume, V₀=136.15 Å³, bulk modulus, K_T=243(3) GPa, and the pressure derivative of bulk modulus, K′=4 (fixed). The bulk modulus value obtained for the nanocrystalline anatase is about 35% larger than that of the macrocrystalline counterpart.     

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.     

Volume compression of thallium to 45 GPa

Abstract

High-pressure structural transition and volume compression for thallium were investigated to 45 GPa in a diamond anvil cell using the angular dispersive X-ray diffraction technique. Except for the known polymorphic transition at 3.7 GPa, no other structural change was observed in this pressure range. The equation of state of the high pressure phase has been obtained: its initial bulk modulus, B₀ = 33.1 GPa, is lower by 10% than that of the hexagonal phase at normal pressure.     

High pressure studies up to 50GPa of CuO

Abstract

Copper oxide has been studied at high pressure up to 50 GPa. A monoclinic structure was compatible with the measurements at all pressures, and no phase change was observed. A bulk modulus, B₀, = 98 GPa, and its pressure derivative B′₀ = 5.6 was obtained.     

Compression of volume and lattice parameters of 2H-CsCdBr3 under high pressure

Abstract

Powder x-ray diffraction experiments have been performed on 2H-CsCdBr₃. at room temperature up to 25 GPa. At normal pressure this compound shows unidimensional electronic properties. Such unidimensional behaviour is not evident in terms of elastic bulk properties under pressure. No phase transformation occurs in this pressure range. The a and c lattice parameters steadily decrease with pressure; their ratio lowers by only 2% up to 25 GPa. The bulk modulus is low, 21.2 GPa, and is in very good agreement with the bulk modulus-volume systematics for ionic compounds. The value of the first pressure derivative is also typical of ionic compounds.     

Equation of state and structural phase transition in FeBO3 at high pressure

The evolution of X-ray diffraction patterns in FeBO₃ under high pressures up to 63 GPa has been investigated at room temperature in a diamond anvil cell. A structural phase transition at a pressure of 53±2 GPa was found for the first time. The transition is of the first-order type with a hysteresisless drop of the reduced unit cell volume of about 8.6%. Apparently, the transition is isostructural. At pressures below the transition, the equation of state for FeBO₃ was fitted. In the third-order approximation of the Birch-Murnagan equation of state, the bulk modulus K and its first pressure derivative K′ were found to be 255±25 GPa and 5.0±1.2, respectively.