Bulk Modulus B0 Research Articles

High pressure studies on uranium and thorium silicide compounds: Experiment and theory

The actinide silicides ThSi, USi and USi2 have been studied under high pressure using both theory and experiment. High pressure synchrotron X-ray diffraction experiments were performed on polycrystalline samples in diamond anvil cells at room temperature and for pressures up to 54, 52 and 26GPa, for ThSi, USi and USi2, respectively. At ambient conditions, the uranium silicides crystallize in tetragonal structures (space groups: I4/mmm for USi and I41/amd for USi2), while ThSi adopts an orthorhombic structure (space group: Pbnm) (including an anharmonic analysis of the silicon). These structures are found to be stable with no structural transitions observed up to the highest pressures achieved. The zero-pressure bulk modulus B0 and its pressure derivative B0′ at ambient pressure are obtained from the measured P–V relations. The experiments are accompanied by first principles calculations using the full-potential linear muffin-tin orbital method within the generalized gradient approximation for exchange–correlation effects. Experimental results are well reproduced by the calculated equation of state and ground state properties.

Materials Properties of Ultra-Incompressible Re2P

In situ high-pressure X-ray powder diffraction measurements on Re2P up to 37.0 GPa at ambient temperature in diamond-anvil cells were carried out at two different synchrotron facilities (ESRF and DESY). The compressibility of Re2P (Pnma, no. 62, a = 5.5464(17), b = 2.9421(8), c = 10.0483(35) Å,V = 163.97(9) Å3, Z = 4, Rp = 0.1008, wRp = 0.1341 at ambient conditions) was investigated and resulted in a bulk modulus of B0 = 320(10) GPa after fitting the experimental p–V data to a second- and third-order Birch–Murnaghan equation of state. In addition, the determined bulk modulus is compared to values obtained from an Eulerian strain versus normalized stress plot with values ranging form 315(7) to 321(15) GPa. These experimental findings are confirmed by density functional theory (DFT)-calculations ranking Re2P among ultra-incompressible materials. However, the Vickers hardness of a high-pressure sintered Re2P–RexCy composite material in the asymptotic hardness region was found to be of only 13(2) GPa. Electrical conductivity measurements indicate that metallic Re2P exhibits Pauli-paramagnetism. Analysis of temperature-dependent in situ X-ray diffractometry reveals an approximately isotropic expansion of the lattice parameters with a thermal expansion coefficient of (α(V) = 28.5–32.8(2)·10–6 K–1).

In situ high‐pressure synchrotron X‐ray diffraction study of the structural stability in the intermetallic compound Mn2Sb

AbstractCu2Sb‐type (Strukturbericht designation: C38) intermetallic compound Mn2Sb was studied up to 25.7 GPa at room temperature using the in situ synchrotron powder X‐ray diffraction (XRD) technique. Our results from the XRD analysis showed that the (C38)‐type Mn2Sb undergoes a pressure‐induced structural phase transition near 22.4 GPa. In the low‐pressure (LP) phase of Mn2Sb, an anisotropic compressibility was observed with greater compressibility along the a‐axis than the c‐axis. And the mechanism for the anisotropy of compressibility was discussed in terms of the stacking of crystallography. Fitted to a third‐order Birch–Murnaghan equation of state (BM‐EOS), the pressure–volume data of Mn2Sb yielded the stable lattice volume V0 = 109.45(3) Å3, bulk modulus B0 = 50.1(5) GPa, and its derivative $B'_{{\rm 0}} $ = 7.0(2) for the LP phase. We propose that the distortion of Mn(I)Sb4 tetrahedra may give rise to the structural instability of Mn2Sb under high pressure (HP).

Bond strengths of New Carbon-nitride-Related material C2N2(CH2)

A new carbon-nitride-related material C2N2(CH2) nanopletelet was synthesized by subjecting a precursor C3N4HxOy+Au in a laser-heating diamond anvil cell (LHDAC) to the pressure of 40 GPa and the temperature of 1200-2000 K. The synthesized C2N2(CH2) was accordingly found to be an orthorhombic unit cell of the space group Cmc21 with lattice constants a = 7.625Å, b = 4.490Å, and c = 4.047Å. The bulk modulus B0 was determined to be B0 = 258 ± 3.4 GPa, only the 60 % that of the diamond. C2N2(CH2) consists of the tetrahedrally coordinated C with three C-N single bond and the one C-C single bond, and the bridging carbon with the C-CH2-C bond. The C-N single bond length of the tetrahedron ranges from 1.444 to 1.503 Å. This bond length is close to the C-N single bond of 1.447 to 1.458 Å in the superhard β-C3N4. The compressibility of the C-N and C-C single bond of C2N2(CH2) ranges from 0.976 to 0.982 with the pressure of 30 GPa. These values are very close to the compressibility of the C-N and C-C single bond of 0.978 to 0.982 in β-C3N4, cubic-C3N4, and diamond.

Structure and nuclear density distribution in the cheralite—CaTh(PO4)2: studies of its behaviour under high pressure (36 GPa)

The crystal structure of the cheralite—CaTh(PO4)2—has been revisited by neutron diffraction and its behaviour under high pressure investigated by X-ray diffraction up to 36 GPa. The neutron diffraction data at ambient pressure gave a more accurate determination of the Ca/Th cation position than previous XRD data, taking advantage that the neutron scattering lengths of calcium and thorium are of same order of magnitude. The nuclear density distribution was also determined using the maximum entropy method (MEM) confirming that the two cations are not located at the same position in the unit cell but are slightly displaced from one another along a specific direction in order to minimize the electrostatic repulsion with the surrounding phosphorus atoms. At high pressure, the compound did not show any phase transition or amorphization. From the evolution of the unit-cell volume as a function of the pressure, the zero-pressure bulk modulus B0 and its pressure derivative B0 ′ have been determined by fitting the experimental compressibility curve to the Birch–Murnaghan equation of state. The results are B0 = 140(2) GPa and B 0 ′ = 4.4(4) GPa.

High pressure monoclinic phases of Sb2Te3

Abstract The effect of pressure on nanostructured rhombohedral α-Sb2Te3 (phase I) was investigated using X-ray diffraction (XRD) and Raman spectroscopy (RS) up to 19.2 and 25.5 GPa, respectively. XRD patterns showed two new high pressure phases (named phases II and III). From a Rietveld refinement of XRD patterns of α-Sb2Te3, the unit cell volume as a function of pressure was obtained and the values were fitted to a Birch–Murnaghan equation of state (BM-EOS). The best fit was obtained for bulk modulus B0=36.1±0.9 GPa and its derivative B 0 ′ = 6.2 ± 0.4 (not fixed). Using the refined structural data for α-Sb2Te3, for pressures up to 9.8 GPa, changes in the angle of succession [Te–Sb–Te–Sb–Te], in the interaromic distances of Sb and Te atoms belonging to this angle of succession and in the interatomic distances of atoms located on the c axis were examined. This analysis revealed an electronic topological transition (ETT) along the a and c axes at close to 3.7 GPa. From the RS spectra, the full widths at half maximum (FWHM) of the Raman active modes of α-Sb2Te3 were plotted as functions of pressure and showed an ETT along the a and c axes at close to 3.2 GPa. The XRD patterns of phases II and III were well reproduced assuming β-Bi2Te3 and γ-Bi2Te3 structures similar to those reported in the literature for α-Bi2Te3.

Hartree analysis of χ for a pressure-responsive diblock copolymer: Temperature-pressure superposition

The response of small-angle neutron scattering (SANS) to pressure for a molten block copolymer in the disordered state has been studied through a Hartree (fluctuation correction) analysis. A slightly polydisperse diblock copolymer from deuterated polystyrene and poly(n-propyl methacrylate), denoted as dPS-b-PPrMA, was chosen for our purpose, because its ordering transition is highly sensitive to pressure. It was shown that the isotherms of effec- tive Flory-Huggins parameters χ's from the Hartree analysis are superposed into a characteristic curve when χ is scaled by χ(P0) at a reference pressure P0, and plotted against pressure difference ∆P (≡P-P0) divided by temperature dependent bulk modulus B0 at P0. Such a procedure required a scale factor τ, which was completely determined by B0. The established superposition yielded the interconvertibility of temperature and pressure effects on the Hartree χ. This behavior of χ was revealed to manifest that components of χ rely on the ratio of volume V to V0 at the refer- ence P0, which is an exclusive function of ∆P/B0 to satisfy the temperature-pressure superposition concept in volu- metric properties of polymeric liquids.

Pressure-induced structural change in orthorhombic perovskite GdMnO3

Structural stability of the perovskite-type GdMnO3 has been investigated by the synchrotron angle-dispersive x-ray diffraction technique up to 63 GPa in a diamond anvil cell. GdMnO3 stays in an orthorhombic structure but undergoes an isostructural phase transition with ∼5% volume reduction at 50 GPa. In the parent orthorhombic phase, the compressions along a, b and c axes exhibit a large anisotropic behavior. With increasing pressure, our results show that the distortion and tilts of the MnO6 octahedra are reduced continuously and the orthorhombic structure evolves towards higher symmetry. By fitting the observed pressure–volume data using the third-order Birch–Murnaghan equation of state, we obtain the bulk modulus B0 = 156(3) GPa with B0′ = 6.5(3) for the starting orthorhombic phase. Upon decompression, the starting orthorhombic phase is recovered.

Elastic constants and bulk modulus of semiconductors: Performance of plane-wave pseudopotential and local-density-approximation density functional theory

The first-principles pseudopotential plane-wave method with the local density approximation (LDA) is performed to calculate the elastic constants of AB-type semiconductors. The calculated data are compared with other literature data and agree well with the experimental results. The bulk modulus B0 and its pressure derivation B0′ are obtained by fitting the energy–volume points to Birch–Murnaghan equation of state. Moreover, in terms of the Voigt–Reuss–Hill approximation, the bulk modulus BH is also successfully obtained.

Structural and Elastic Properties of AlAs under Pressure from First-Principles Calculations

A first-principles plane wave method with the ultrasoft pseudopotential scheme in the frame of the density functional theory (DFT) is performed to calculate the structural and lattice parameters, the bulk modulus B0 and its pressure derivative B0' of the zinc-blende AlAs, rocksalt AlAs and NiAs-AlAs. The elastic parameters of the zinc-blende AlAs, rocksalt AlAs and NiAs- AlAs were calculated. We also calculate the phase transition pressures between different phases. Our results are satisfactory. Our results are consistent with other results.

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 cij, bulk modulus B0 and the pressure derivative of bulk modulus B′0 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 Cv 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.

Thermal Expansion of Alkaline-Earth-Metal Disilicides AeSi2 (Ae= Ca, Sr, and Ba)

The thermal expansion of alkaline-earth-metal disilicides AeSi2 (Ae= Ca, Sr, and Ba) has been investigated at temperatures ranging from room temperature to 873 K using powder X-ray diffractometry. The coefficients of linear thermal expansion, αi's, of AeSi2 range from 9 ×10-6 to 18 ×10-6 K-1, which are larger than those of Si (2.6 ×10-6 K-1 at 298 K) and group 4–7 transition-metal disilicides [(6–11) ×10-6 K-1 at 298 K]. The coefficients of volume thermal expansion, αV, range from 3.2 ×10-5 to 4.8 ×10-5 K-1 in AeSi2. The αV becomes larger in the order of CaSi2, SrSi2, and BaSi2. This order of magnitude of αV is related to the order of magnitude of bulk modulus B0 using Grüneisen's rule. The residual stresses in AeSi2 film are discussed using the obtained αi.

Structural and Thermodynamic Properties of Perovskite-Type Superconductor ZnNNi<SUB>3</SUB> by First-Principles Calculations

The structural and thermodynamic properties of the non-oxide superconductor ZnNNi3 are investigated by using ab initio plane-wave pseudo potential density functional theory method within the generalized gradient approximation (GGA). The calculated lattice constants, the bulk modulus and its pressure derivative, and elastic constants of ZnNNi3 at zero temperature and pressure are in good agreement with the available theoretical and experimental data. The thermodynamic properties of ZnNNi3 are predicted by using the quasi-harmonic Debye model. The pressure-volume-temperature (P-V-T) relationship, the bulk modulus B0 and bulk modulus B, the variations of the thermal expansion

Structural stability and Raman scattering of InN nanowires under high pressure

High-pressure in situ angular dispersive x-ray diffraction study on the wurtzite-type InN nanowires has been carried out by means of the image-plate technique and diamond-anvil cell (DAC) up to about 31.8 GPa. The pressure-induced structural transition from the wurtzite to a rocksalt-type phase occurs at about 14.6 GPa, which is slightly higher than the transition pressure of InN bulk materials (∼12.1 GPa). The relative volume reduction at the transition point is close to 17.88%, and the bulk modulus B0 is determined through fitting the relative volume-pressure experimental data related to the wurtzite and rocksalt phases to the Birch–Murnaghan equation of states. Moreover, high-pressure Raman scattering for InN nanowires were also investigated in DAC at room temperature. The corresponding structural transition was confirmed by assignment of phonon modes. We calculated the mode Grüneisen parameters for the wurtzite and rocksalt phases of InN nanowires.

High-pressure neutron diffraction study of BaFe2As2

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 stability of bismuth sillenite: A Raman spectroscopic and x-ray diffraction study

High pressure behavior of the compound Bi12SiO20 is investigated using in situ Raman spectroscopic and synchrotron-based angle dispersive x-ray diffraction techniques. Results indicate that the compound remains stable in the ambient pressure cubic structure up to 26 GPa. From the structural studies, bulk modulus B0, and its pressure derivative B′ of Bi12SiO20 are evaluated to be 36 GPa and 16.7 GPa, respectively. Mode Grüneissen parameters of various Raman active modes of Bi12SiO20 are also reported. The stability of Bi12SiO20 at high pressure is discussed in the light of the pressure-induced amorphization reported in bismuth-orthosilicate (Bi4Si3O12) and -orthogermanate. Comparison of the observed phonon behavior with that reported for Bi4Si3O12 reveals that two of the Raman modes in Bi4Si3O12 have negative pressure dependencies clearly indicating dynamic instability while Bi12SiO20 does not show any signatures of zone-center instabilities.

Synchrotron X-ray Diffraction and Infrared Spectroscopy Studies of C60H18 under High Pressure

In situ high-pressure angle-dispersive synchrotron X-ray diffraction and high-pressure mid-infrared (IR) spectrum measurements of C60H18 were carried out up to 32 and 10.2 GPa, respectively. Our diffraction data indicated that the fcc structure of C60H18 was stable up to 32 GPa. The bulk modulus B0 was determined to be 21 ± 1.16 GPa, about 40% higher than that of C60. The C−H vibrations still existed up to 10.2 GPa, and the vibrational frequencies decreased with increasing pressure. IR-active vibrational frequencies and their corresponding eigenvectors of C60H18 were simulated by DMOL3. The effects of the hydrogen atoms attached to the fullerene molecular cage on the stability of the structure under high pressure are discussed.

First-Principles Calculations of Thermodynamic Properties of Superhard Orthorhombic $\beta-BC_2N$

We investigate the thermodynamic properties of the potential superhard or- thorhombic structure boron-carbonitride b-BC2N by using ab initio plane-wave pseu- dopotential density functional theory method within both local density approxima- tion (LDA) and generalized gradient approximation (GGA). The lattice parameters (a, b and c), equilibrium volume V, bulk modulus B0 and its pressure derivative B0' have been calculated, and compared with those of diamond and cubic boron nitride (c-BN). The obtained results are in excellent agreement with the available experimental data and other theoretical results. Through the quasi-harmonic Debye model, we also in- vestigate the thermodynamic properties of b-BC2N. The variation of the thermal ex- pansion a, the heat capacity CV and the Gr ¨ uneisen parameter g with pressure P and temperature T, as well as the pressure-normalized volume (P-Vn) and the pressure- bulk modulus (P-B) relationship of b-BC2N are obtained systematically.

First-principles study of typical precipitates in creep resistant magnesium alloys

First-principles calculations were performed to study the mechanical properties of typical precipitates of creep resistant magnesium alloys (Mg2Si, Mg2Ge, Mg2Sn and Mg3Zn3Y2). Formation enthalpies and cohesive energies, elastic constants C11, C12, C44, bulk modulus B0, Young's modulus E, shear modulus G, the ratios of shear modulus to bulk modulus G/B0, negative Cauchy pressure parameter (C12-C44) and Poisson's ratio ν of four precipitates were discussed. The results show that Mg2Si and Mg2Ge are stiffer than Mg3Zn3Y2. The charge density was further investigated to clarify the electronic causes.

Characterization of the pressure-induced second-order phase transition in the mixed-valence vanadate BaV6O11

The pressure dependence of the structure of the mixed-valence vanadate BaV6O11 was studied with single-crystal X-ray diffraction in a diamond-anvil cell. The compressibility data could be fitted with a Murnaghan equation of state with the zero-pressure bulk modulus B0 = 161 (7) GPa and the unit-cell volume at ambient pressure = 387.1 (3) A3 (B' = 4.00). A phase transition involving a symmetry reduction from P6(3)/mmc to P6(3)mc can be reliably detected in the high-pressure data. The estimated transition pressure lies in the range 1.18 < P(c) < 3.09 GPa. The transition leads to a breaking of the regular Kagomé net formed by part of the V ions. While in the ambient pressure structure all V-V distances in the Kagomé net are equal, they split into inter-trimer and intra-trimer distances in the high-pressure phase. In general, these changes are comparable to those observed in the corresponding low-temperature transition. However, the pressure-induced transition takes place at a lower unit-cell volume compared with the temperature-induced transition. Furthermore, overall trends for inter-trimer and intra-trimer V-V distances as a function of the unit-cell volume are clearly different for datapoints obtained by variation of pressure and temperature. The behavior of BaV6O11 is compared with that of NaV6O11. While in the latter compound the transition can be explained as a pure volume effect, in BaV6O11 an additional degree of freedom related to the valence distribution among the symmetrically independent vanadium sites has to be taken into account.