X-ray diffraction study of molybdenum diselenide to 35.9 GPa

In situ high-pressure angle dispersive synchrotron X-ray diffraction studies of molybdenum diselenide (MoSe₂) were carried out in a diamond-anvil cell to 35.9 GPa. No evidence of a phase transformation was observed in the pressure range. By fitting the pressure-volume data to the third-order Birch-Murnaghan equation of state, the bulk modulus, K_0T, was determined to be 45.7±0.3 GPa with its pressure derivative, K′_0T, being 11.6±0.1. It was found that the c-axis decreased linearly with pressure at a slope of −0.1593 when pressures were lower than 10 GPa. It showed different linear decrease with the slope of a −0.0236 at pressures higher than 10 GPa.     

High pressure X-ray diffraction study of Fe2B

We report the results of a synchrotron based X-ray diffraction study of bct-Fe₂B under quasi-hydrostatic conditions from 0 to 50 GPa. Over this pressure range, no phase change or disproportionation has been observed. A weighted fit of the data to the Birch-Murnaghan equation of state yields a value of the bulk modulus, K, of 164±14 GPa and the first pressure derivative of the bulk modulus, K′, of 4.4±0.5. The compression is found to be anisotropic, with the a-axis being more incompressible than the c-axis.     

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.     

Equation of state of aluminum carbide Al4C3

Quasi-hydrostatic compression of aluminum carbide, Al₄C₃ has been studied to 6 GPa at room temperature using energy-dispersive X-ray powder diffraction with synchrotron radiation. A fit of the experimental p-V data to the Birch equation of state yields the values of the bulk modulus, B₀, of 130(5) GPa and the first pressure derivative of the bulk modulus, B′₀, of 4.6(9). The compression is found to be anisotropic, with the a-axis being more compressible than the c-axis.     

Synchrotron X-ray diffraction study of haüyne at high pressure

The compression behavior of a natural haüyne has been investigated to about 8.1 GPa at 300 K using in situ angle-dispersive X-ray diffraction and a diamond anvil cell at High Pressure Experiment Station, Beijing Synchrotron Radiation Facility (BSRF). Over this pressure range, no phase change or disproportionation has been observed. The isothermal equation of state was determined for the first time. The values of V₀, K₀, and K′₀ refined with a third-order Birch-Murnaghan equation of state are V₀=751.6±0.4 Å³, K₀=49±1 GPa, and K′₀=3.3±0.3, respectively.     

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.     

Structure and high pressure behaviour of organic crystals based on aromatically substituted 1,3,4-oxadiazoles

The crystalline structure of a new compound containing the 1,3,4-oxadiazole moiety, 4-(5-methyl-1,3,4-oxadiazole-2yl-)-N,N′-dimethyl-phenylamine (MODPA) was determined. It shows a monoclinic structure with space group P2₁/c and lattice parameters: a=1.02997(6), b=0.64840(4), c=1.58117(10) nm and β=99.4820(10)°. To study the intermolecular interactions in oxadiazole containing organic crystals, X-ray studies on MODPA and 2,5-diphenyl-1,3,4-oxadiazole (DPO) were performed up to 5 GPa at room temperature. The Murnaghan equation of state is used to describe the compression behaviour of both substances. From these results, the bulk modulus and its pressure derivative were determined. The values obtained are: K₀=6.3 GPa and K′₀=6.8 for MODPA and K₀=7.3 GPa and K′₀=6.7 for DPO. Additionally, measurements under increasing temperature at ambient pressure were carried out to evaluate the thermal expansion coefficient: α=1.8×10⁻⁴ K⁻¹ for MODPA and α=1.9×10⁻⁴ K⁻¹ for DPO.     

High pressure X-ray diffraction study of ReS2

The high-pressure behavior of rhenium disulfide (ReS₂) has been investigated to 51.0 GPa by in situ synchrotron X-ray diffraction in a diamond anvil cell at room temperature. The results demonstrate that the ReS₂ triclinic phase is stable up to 11.3 GPa, at which pressure the ReS₂ transforms to a new high-pressure phase, which is tentatively identified with a hexagonal lattice in space group P6?m2. The high-pressure phase is stable up to the highest pressure in this study (51.0 GPa) and not quenchable upon decompression to ambient pressure. The compressibility of the triclinic phase exhibits anisotropy, meaning that it is more compressive along interlayer directions than intralayer directions, which demonstrates the properties of the weak interlayer van der Waals interactions and the strong intralayer covalent bonds. The largest change in the unit cell angles with increasing pressures is the increase of β, which indicates a rotation of the sulfur atoms around the rhenium atoms during the compression. Fitting the experimental data of the triclinic phase to the third-order Birch-Murnaghan EOS yields a bulk modulus of K_OT=23±4 GPa with its pressure derivative K_OT′= 29±8, and the second-order yields K_OT=49±3 GPa.     

Volume and structural study of Fe64Mn36 anti-ferromagnetic Invar alloy under high pressure

We have investigated the pressure variation of the volume and structure of an FCC Fe₆₄Mn₃₆ anti-ferromagnetic Invar alloy. The inclination of the pressure-volume (P-V) curve of the FCC structure becomes discontinuous at a pressure of 4 GPa. According to the bulk modulus at zero pressure estimated by the Birch-Murnaghan equation of state, the pressure between 4 and 10 GPa is 33 GPa larger than that at a pressure below 4 GPa. Considering previous experiments on magnetism at high pressure the Neel temperature at 4 GPa almost decreases to room temperature. These results suggest that the increase in the bulk modulus by 33 GPa can be attributed to the pressure-induced magnetic phase transition from anti-ferromagnetism to paramagnetism. Volume at zero pressure was estimated using the Birch-Murnaghan equation of state. The volume of FCC structure in the anti-ferromagnetic state was 1.17% larger than the volume in the paramagnetic state, namely, the spontaneous magnetostriction was 1.17%. Pressure-induced structural transition from FCC to HCP occurs with an increase in the pressure, especially at up to 5 GPa. The value of c/a is 1.62; this value almost corresponds to that of an ideal HCP structure. The bulk modulus of the HCP structure estimated by the Birch-Murnaghan equation of state is larger than that of the FCC structure, and the volume/atom ratio is smaller than that of the FCC structure.     

High-pressure powder diffraction study of TaO2F

TaO₂F, with a ReO₃-type structure, has been studied at up to 12.8 GPa using monochromatic synchrotron powder diffraction and diamond anvil cells. Two-phase transitions at ∼0.7 and 4 GPa were observed on compression. Below ∼0.7 GPa the cubic material was found to have a bulk modulus (K₀) of 36(3) GPa (K_p fixed at 4.0), similar to that reported for NbO₂F but much smaller than that of ReO₃. Immediately above 0.7 GPa on compression, the diffraction data were not fully consistent with a VF₃-type structure as previously proposed for NbO₂F. On decompression, the data between 8 and 4 GPa could be satisfactorily attributed to a single R-3c phase with a VF₃-type structure and an average bulk modulus of 60(2) GPa.     

In situ observations of temperature- and pressure-induced phase transitions in TiH2: Angle-dispersive and synchrotron energy-dispersive X-ray diffraction studies

We investigated the behavior of the structure of titanium hydride (TiH₂), an important compound in hydrogen storage research, at elevated temperatures (0-120 °C) and high pressures (1 bar-34 GPa). Temperature-induced changes of TiH₂ as indicated in the alteration of the ambient X-ray demonstrated a cubic to tetragonal phase transition occurring at about 17 °C. The main focus of this study was to identify any pressure-induced structural transformations, including possible phase transitions, in TiH₂. Synchrotron X-ray diffraction studies were carried out in situ (diamond anvil cell) in a compression sequence up to 34 GPa and in subsequent decompression to ambient pressure. The pressure evolution of the diffraction patterns revealed a cubic (Fm-3m) to tetragonal (I4/mmm) phase transition at 2.2 GPa. The high-pressure phase persisted up to 34 GPa. After decompression to ambient conditions the observed phase transition was completely reversible. A Birch-Murnaghan fit of the unit cell volume as a function of pressure yielded a zero-pressure bulk modulus K₀=146(14) GPa, and its pressure derivative K′₀=6(1) for the high-pressure tetragonal phase of TiH₂.     

X-ray diffraction and infrared spectroscopy of monazite-structured CaSO4 at high pressures: Implications for shocked anhydrite

X-ray diffraction and infrared spectroscopy of CaSO₄ are conducted to pressures of 28 and 25 GPa, respectively. A reversible phase transition to the monoclinic monazite-structure occurs gradually between 2 and ∼5 GPa with a highly pressure-dependent volume change of ∼6-8%. A second-order fit of the X-ray data to the Birch-Murnaghan equation of state yields a bulk modulus (K) of 151.2 (±21.4) GPa for the high-pressure monoclinic phase. In the high-pressure infrared spectrum, the infrared-active asymmetric stretching and bending vibrations of the sulfate tetrahedra split at the phase transition, in accord with the results of factor group analysis. Additionally, the tetrahedral symmetric stretching vibration, which is weak in the anhydrite phase, becomes strongly resolved at the transition to the monazite structure. The infrared results indicate that the sulfate tetrahedra are more distorted in the monazite-structured phase than in anhydrite. Kinetic calculations indicate that the anhydrite to monazite transformation may generate the phase transition observed near 30 GPa under shock loading in CaSO₄. Our results indicate that the anhydrite- and monazite-structured phases may be the only phases that occur under shock loading of CaSO₄ to pressures in excess of 100 GPa.     

Stiffening of nanoscale anatase Ti0.9Zr0.1O2 upon multiple compression cycles

The compression behavior of nanoscale Zr-doped anatase was studied by means of a diamond anvil cell experiment with alternating cycles of compression and decompression in the stability field of anatase (up to 13 GPa). We found that multiple cycles of compression lead to stiffening of the material: Precompressed samples of nanoanatase Ti_0.9Zr_0.1O₂ have a higher bulk modulus (K₀=249(9) and 266(6) GPa) compared with the sample when compressed for the first time (K₀=211(7) GPa). Upon compression, the crystallite size remains the same and the crystalline areas are free of defects. After the experiment, the crystallites are surrounded by amorphous rims, confirming the theoretical prediction by Pischedda et al. [Ultrastability and enhanced stiffness of similar to 6 nm TiO₂ nanoanatase and eventual pressure-induced disorder on the nanometer scale, Phys. Rev. Let. 96 (2006) 035509] for nanoscale anatase, but yielding much lower pressures (12 GPa) for the onset of partial amorphization.     

Structural, high pressure and elastic properties of transition metal monocarbides: A FP-LAPW study

The structural, elastic and thermal properties of four transition metal monocarbides ScC, YC (group III), VC and NbC (group V) have been investigated using full potential linearized augmented plane wave (FP-LAPW) method within generalized gradient approximation (GGA) both at ambient and high pressure. We predict a B₁ to B₂ structural phase transition at 127.8 and 80.4 GPa for ScC and YC along with the volume collapse percentage of 7.6 and 8.4%, respectively. No phase transition is observed in case of VC and NbC up to pressure 400 and 360 GPa, respectively. The ground state properties such as equilibrium lattice constant (a₀), bulk modulus (B) and its pressure derivative (B′) are determined and compared with available data. We have computed the elastic moduli and Debye temperature and report their variation as a function of pressure.     

In vitro ultrasonic and mechanic characterization of the modulus of elasticity of children cortical bone

The assessment of elastic properties in children’s cortical bone is a major challenge for biomechanical engineering community, more widely for health care professionals. Even with classical clinical modalities such as X-ray tomography, MRI, and/or echography, inappropriate diagnosis can result from the lack of reference values for children bone. This study provides values for elastic properties of cortical bone in children using ultrasonic and mechanical measurements, and compares them with adult values. 18 fibula samples from 8 children (5–16 years old, mean age 10.6 years old ±4.4) were compared to 16 fibula samples from 3 elderly adults (more than 65 years old). First, the dynamic modulus of elasticity (E_dyn) and Poisson’s ratio (ν) are evaluated via an ultrasonic method. Second, the static modulus of elasticity (E_sta) is estimated from a 3-point microbending test. The mean values of longitudinal and transverse wave velocities measured at 10 MHz for the children’s samples are respectively 3.2 mm/μs (±0.5) and 1.8 mm/μs (±0.1); for the elderly adults’ samples, velocities are respectively 3.5 mm/μs (±0.2) and 1.9 mm/μs (±0.09). The mean E_dyn and the mean E_sta for the children’s samples are respectively 15.5 GPa (±3.4) and 9.1 GPa (±3.5); for the elderly adults’ samples, they are respectively 16.7 GPa (±1.9) and 5.8 GPa (±2.1). E_dyn, ν and E_sta are in the same range for children’s and elderly adults’ bone without any parametric statistical difference; a ranking correlation between E_dyn and E_sta is shown for the first time.     

Full potential calculation of structural, elastic properties and high-pressure phase of binary noble metal carbide: ruthenium carbide

We present in this paper the results of an ab initio theoretical study within the local density approximation (LDA) to determine in rock-salt (B1), cesium chloride (B2), zinc-blende (B3), and tungsten carbide (WC) type structures, the structural, elastic constants, hardness properties and high-pressure phase of the noble metal carbide of ruthenium carbide (RuC).The ground state properties such as the equilibrium lattice constant, elastic constant, the bulk modulus, its pressure derivative, and the hardness in the four phases are determined and compared with available theoretical data. Only for the three phases B1, B3, and WC, is the RuC mechanically stable, while in the B2 phase it is unstable, but in B3 RuC is the most energetically favourable phase with the bulk modulus 263 GPa, and at sufficiently high pressure (P_t=19.2 GPa) the tungsten carbide (WC) structure would be favoured, where ReC-WC is meta-stable.The highest bulk modulus values in the B3, B2, and WC structures and the hardnesses of H(B3)=36.94 GPa, H(B1)=25.21 GPa, and H(WC)=25.30 GPa indicate that the RuC compound is a superhard material in B3, and is not superhard in B1 and WC structures compared with the H(diamond)=96 GPa.     

Single-crystal elastic constants of magnesium difluoride (MgF2) to 7.4 GPa

The six independent elastic constants (C₁₁, C₁₂, C₁₃, C₃₃, C₄₄, and C₆₆) of single-crystal MgF₂ in the rutile structure have been measured by Brillouin spectroscopy at room temperature from ambient conditions to 7.4 GPa. Measurements were performed on two monocrystals with perpendicular faces, (001) and (100). A quasi-linear fit from finite strain theory was applied to the experimental data revealing the pressure dependence of the six elastic constants of MgF₂. The shear modulus C_S=1/2(C₁₁−C₁₂), and the aggregate shear (Voigt–Reuss–Hill) modulus G show a softening with increasing pressure, indicating the approach of the rutile-to-CaCl₂-type structural phase transition at P~9 GPa. The adiabatic bulk modulus (Reuss average) and its pressure derivative have been determined: K_0S=105.1±0.3 GPa, (∂K_0S/∂P)_T=4.14±0.05. The pressure–volume equation of state of MgF₂ was computed self-consistently from the Brillouin data. Our results are in good agreement with X-ray diffraction data. As the phase transition is approached, MgF₂ becomes strongly anisotropic and develops partially auxetic behavior (a negative Poisson's ratio in certain directions).     

Elasticity of single-crystal phase D (a dense hydrous magnesium silicate) by Brillouin spectroscopy

Phase D (MgSi₂O₆H₂) is the only hydrous magnesium silicate, where all Si atoms are octahedrally coordinated. The single-crystal elastic constants of phase D have been measured by Brillouin spectroscopy at ambient conditions. The elastic constants C₁₁, C₃₃, C₄₄, C₁₂, C₁₃ and C₁₄, based on a trigonal unit cell, are 284.4±3.0, 339.4±9.1, 120.7±1.9, 89.4±4.2, 126.6±3.1 and −4.7±1.4 GPa, respectively. The aggregate adiabatic bulk modulus, using the Voigt-Reuss-Hill (VRH) scheme, is 175.3±14.8 GPa and the shear modulus is 104.4±13.6 GPa. These data yield the compressional-wave velocity, V_p=9.70±0.51 km/s, and the shear-wave velocity, V_s=5.59±0.36 km/s, at ambient conditions. Thus, phase D is not only the most closely packed but the least compressible hydrous magnesium silicate known to date.     

A high-pressure and high-temperature synthesis of platinum carbide

High-pressure synthesis is a powerful method for the preparation of novel materials with high elastic moduli and hardness. Additionally, such materials may exhibit interesting thermal, optoelectronic, semiconducting, magnetic, or superconducting properties. We report on the new high-pressure, high-temperature synthesis of platinum carbide. The experiments were performed in a laser-heated diamond anvil cell and data were collected using the synchrotron X-ray diffraction method at pressures >75 GPa at high-temperatures. The new platinum carbide has a rock-salt type structure, with space group Fm3m and cubic symmetry. It was confirmed to remain stable to at least 120 GPa. This structure is the same as that of other metal carbides reported in previous studies. After decompression, the new high-pressure phase was recoverable at ambient pressure. The Birch-Murnaghan equation of state for this new phase was determined from the experimental unit cell parameters, with K₀=301 (±15) GPa, and K′₀=5.2 (±0.4).     

Elastic and thermodynamic properties of CaB6 under pressure from first principles

The elastic and thermodynamic properties of CsCl-type structure CaB₆ under high pressure are investigated by first-principles calculations based on plane-wave pseudopotential density functional theory method within the generalized gradient approximation (GGA). The calculated lattice parameters of CaB₆ under zero pressure and zero temperature are in good agreement with the existing experimental data and other theoretical data. The pressure dependences of the elastic constants, bulk modulus B (GPa), and its pressure derivative B′, shear modulus G, Young's modulus E, elastic Debye temperature Θ_B, Zener's anisotropy parameter A, Poisson ratios σ, and Kleinmann parameter ζ are also presented. An analysis for the calculated elastic constants has been made to reveal the mechanical stability of CaB₆ up to 100 GPa. The thermodynamic properties of the CsCl-type structure CaB₆ are predicted using the quasi-harmonic Debye model. The pressure-volume-temperature (P-V-T) relationship, the variations of the heat capacity C_V, Debye temperature Θ_D, and the thermal expansion α with pressure P and temperature T, as well as the Grüneisen parameters γ are obtained systematically in the ranges of 0-100 GPa and 0-2000 K.