Determination of elastic constants of Na0.5Bi0.5TiO3 from ab initio calculations

Elastic constants and bulk modulus for the tetragonal, rhombohedral, and cubic phase of Na_0.5Bi_0.5TiO₃ crystal were calculated from the first principles. From the calculated elastic constants, other structural properties such as bulk modulus, shear modulus, Young's modulus, and Poisson's ratio can be derived using respective relationships from Voight–Reuss–Hill approximation; bulk modulus was calculated as an example in this article. It was shown that elastic constants show different behavior for compression and elongation. The different values of elastic constants have been calculated for the direction parallel to the bismuth layer (crystallographic a(b)-axis) and the perpendicular direction (crystallographic c-axis). It seems to be caused by bismuth layer structure oxides of Na_0.5Bi_0.5TiO₃ crystal.     

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.     

Compression behavior of the delafossite-type metallic oxide PdCoO2 below 10 GPa

The compression behavior of delafossite-type metallic oxide PdCoO₂ below 10 GPa has been investigated by in situ high pressure X-ray diffraction measurement using synchrotron radiation. It is found that the delafossite-type structure of PdCoO₂ is stable below 10 GPa. It should be noted that compression behavior of PdCoO₂ is anisotropic. Pressure dependence of the lattice parameters indicates that the a-axis is more compressible than the c-axis. The lattice parameter ratio c/a in the hexagonal unit increases with increasing pressure. The calculated zero-pressure bulk modulus is 224 GPa. It is found that the above characteristic compression behaviors of PdCoO₂ are the same as those of the delafossite CuFeO₂. The compressibilities of the a-axis of both PdCoO₂ and CuFeO₂ are highly different although those of the c-axis are almost the same.     

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.     

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.     

First-principles study of structural and elastic properties of CrO2 at high pressure

The structural and elastic properties of CrO₂ in the rutile phase under high pressures have been investigated using pseudopotential plane-wave method based on density functional theory. The optimized lattice parameters and the bulk modulus at zero pressure agree well with available experimental and theoretical data. The elastic constants C ₁₁, C ₁₂, C ₄₄, C ₃₃, C ₁₃, and C ₆₆ at zero pressure are calculated to be 359.91, 264.69, 143.28, 309.45, 218.45, and 260.74 GPa, respectively. Elastic constants, bulk modulus, shear modulus, Young's modulus, and Poisson's ratio under pressures are obtained. Our results indicate that the rutile phase is mechanically stable below 11.99 GPa. The elastic anisotropy of rutile phase under pressures has also been predicted.     

Single-crystal elasticity of SrCO3 by Brillouin spectroscopy

ABSTRACT

The elastic stiffness tensor c_ij of synthetic strontianite (SrCO₃) was determined by Brillouin spectroscopy at ambient conditions. An inversion procedure based on Christoffel’s equation was used to determine the 9 independent elastic coefficients of orthorhombic strontianite from acoustic velocities measured along 69 different crystallographic directions in 3 randomly oriented crystal platelets. The best fit values of c₁₁, c₁₂, c₁₃, c₂₂, c₂₃, c₃₃, c₄₄, c₅₅ and c₆₆ are 153(1), 52(1), 38(11), 109.6(8), 43(15), 75(1), 28.0(5), 28.6(4) and 33.2(5) GPa, respectively. The linear compressibilities of a-, b- and c-axis at ambient conditions are 3(2), 4(6) and 10(8) 10^?3 GPa^?1. The adiabatic bulk modulus of strontianite is 64(4) GPa, intermediate between aragonite (CaCO₃) and witherite (BaCO₃), thus confirming a systematic linear relationship between cation radius and bulk modulus in aragonite-type carbonates. The shear modulus of strontianite has a value of 31(1) GPa, which is about 10% smaller in comparison to aragonite.     

First-principles investigations on structural,elastic, electronic properties and Debye temperature of orthorhombic Ni3Ta under pressure

The structural, elastic, electronic properties and Debye temperature of Ni₃Ta under different pressures are investigated using the first-principles method based on density functional theory. Our calculated equilibrium lattice parameters at 0 GPa well agree with the experimental and previous theoretical results. The calculated negative formation enthalpies and elastic constants both indicate that Ni₃Ta is stable under different pressures. The bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratio ν are calculated by the Voigt–Reuss–Hill method. The bigger ratio of B/G indicates Ni₃Ta is ductile and the pressure can improve the ductility of Ni₃Ta. In addition, the results of density of states and the charge density difference show that the stability of Ni₃Ta is improved by the increasing pressure. The Debye temperature Θ _D calculated from elastic modulus increases along with the pressure.     

The high-pressure structural transition in MnS: an ab initio study

The structural phase transition between B1 (α-MnS) and B3 (β-MnS) is investigated using a density functional theory method. The structural phase transition pressure Pt from α-MnS to β-MnS, which is determined on the basis of the third-order Birch–Murnaghan equation of states, is 30.75?GPa. Also, the lattice parameters a, the bulk modulus B and pressure derivative of bulk modulus B′, which are generally in good agreement with experiments and other theoretical values, are obtained under zero pressure. For further investigation of the structural phase transition pressure of MnS, the relative volumes V/V ₀, the bulk modulus B, first and second pressure derivatives (B′ and B″) of bulk modulus for the two structures of MnS have been calculated under various pressures.     

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.     

Structural study of pressure-induced magnetic phase transitions in manganites Pr0.7Ca0.3Mn1-y Fe y O3 (y?=?0, 0.1)

A crystal and magnetic structure of manganites Pr_0.7Ca_0.3Mn_1?y Fe _y O₃ (y = 0, 0.1) has been studied by means of powder neutron diffraction at pressures up to 4 GPa in the temperature range 15-300 K. Under high pressure, an appearance of A-type antiferromagnetic state in both systems was observed. Both compounds exhibit anisotropic compression of the lattice which leads to the apical compression of MnO₆ octahedra along the crystallographic b-axis. The calculated from obtained structural data pressure dependence of the charge-carrier bandwidth is in a qualitative agreement with observed pressure behavior of insulator-metal transition temperature within the framework of the double-exchange model.     

Isothermal equation of state for the skutterudites CoSb3 and LaFe3CoSb12

The thermoelectric materials CoSb₃ and LaFe₃CoSb₁₂ with skutterudite structure were subjected to high pressures using a diamond anvil high-pressure cell up to 20 GPa. Energy-dispersive X-ray diffraction was used to determine the dependence of the lattice parameter on pressure. No major change in the X-ray diffraction spectra was observed for both compounds, constituting evidence that both compounds are stable within this pressure range, despite their relatively open structures. Three distinct isothermal equations of state for solids under high pressure were fitted to the experimental data to determine the bulk modulus for both compounds. The filled skutterudite showed a greater compressibility than the unfilled one, this difference can be understood in terms of the larger lattice parameter of the former.     

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.     

X-ray diffraction and Raman spectra of merrillite at high pressures

ABSTRACT

The compressibility and effect of pressure on the vibrations of merrillite, Ca₉NaMg(PO₄)₇, were studied by using diamond anvil cell at room temperature combined with in-situ synchrotron X-ray diffraction and Raman spectroscopy up to about 18 and 15?GPa, respectively. The pressure-volume data was fitted by a third-order Birch–Murnaghan equation of state to determine the isothermal bulk modulus as K₀ ?=?87.2(32) GPa with pressure derivative K₀′?=?3.2(4). If K₀′?=?4, the isothermal bulk modulus was obtained as 81.6(10) GPa. The axial compressibility was estimated and an axial elastic anisotropy exists since a-axis is less compressible than the c-axis. The Raman frequencies of all observed modes for merrillite continuously increase with pressure, and the pressure dependences of stretching modes (v ₃ and v ₁) are larger than those of the bending modes (v ₄ and v ₂) and external modes. The isothermal mode Grüneisen parameters and intrinsic anharmonicity of merrillite were also calculated.     

Elastic properties of Se and As2Se3 glasses under pressure and temperature

The sound velocities and their pressure and temperature variations of Se and As₂Se₃ glasses have been determined by means of a pulse superpositions method, and other elastic constants and their pressure and temperature derivatives were calculated from these data. The bulk modulus was found to be 94·6 kbar for Se glass and 143·7 kbar As₂Se₃ glass, both of which are higher than the values calculated from the previous compression data. No anomaly was observed in any of the pressure and temperature dependence of elastic behavior of these glassses. Furthermore, the comparison of the pressure and temperature derivatives of the bulk modulus indicates that the thermodynamic self-consistency is satisfied on these materials. The bulk moduli of these glasses and crystalline As and Se were used to obtain an empirical bulk modulus-volume relationship for compounds in the As?Se system. The acoustic Grüneisen parameter was calculated and compared with the thermal Grüneisen parameter.     

Structural and thermodynamic properties of WB at high pressure and high temperature

The structure parameters and electronic structures of tungsten boride (WB) have been investigated by using the density functional theory (DFT). Our calculating results display the bulk modulus of WB are 352±2 GPa (K′₀=4.29) and 322±3 GPa (K′₀=4.21) by LDA and GGA methods, respectively. We have analyzed the probable reason of the discrepancy from the bulk modulus between theoretical and experimental results. The compression behavior of the unit cell axes is anisotropic, with the c-axis being more compressible than the a-axis. By analyzing the bond lengths information, it also demonstrated that WB has a lower compressibility at high pressure. From the partial densities of states (PDOS) of WB, we found that the Fermi lever is mostly contributed by the d states of W atom and p states of B atom and that the contributions from the s, p states of W atom and s states of B atom are small. Moreover, using the Gibbs 2 program, the thermodynamic properties of WB are obtained in a wide temperature range at high pressure for the first time in this work.     

Equation of state of CaMnO3: a combined experimental and computational study

Elastic properties of CaMnO₃ are of primary importance in the science and technology of CaMnO₃-based perovskites. From X-ray diffraction experiments performed at pressures up to 100 kbar using a diamond-anvil cell to hydrostatically compress our sample, a bulk modulus, K ₀, of 1734(96) kbar was obtained after fitting parameters to the third-order Birch–Murnaghan equation of state. Mean field, semiclassical simulations predict, for the first time, the third-order equation-of-state parameters and show how the bulk modulus increases with pressure (the zero pressure value being 2062.1 kbar) and decreases with the extent of nonstoichiometry caused by the formation of oxygen vacancies. These trends are amplified for the shear modulus. A more accurate model that allows for the explicit reduction of Mn ions, or localization of excess electrons, yields qualitatively similar results. The experimental and calculated axial ratios show the same trends in their variation with rising pressure.     

Possible transformation of YBa2Cu3O7 under pressure

Crystal structure measurements on the high-T _c material YBa₂Cu₃O₇ were carried out under pressure. Several X-ray reflections do not reveal a uniform shift with increasing pressure. Two models are presented, which show the experimental data to be consistent with an extensivec-axis orb-axis decrease, respectively.     

On ionic conduction in the α-phase of PbSnF4

The structure re-refinement of tetragonal PbSnF₄ was executed using data reported earlier. The rms amplitude in M2(Sn) site is larger in (001) plane than along the c-axis and the thermal vibrations of F3 fluorine ions are very large, i.e. B_eq = 12.415(20) A². M2F₈ polyhedra form a distorted cube. The fluorine ions on the F3 site are present between the M2 ion layers. The fluorine ions on the F3 site are located between the M2 ion layers and their weak bonds to Sn ions play an important role in the conduction. The ionic conductivity in the (001) plane is higher than that in the 001 direction.     

Equation of state of silicon nitride carbodiimide Si2CN4

The lattice parameters of silicon nitride carbodiimide Si₂CN₄ have been measured up to 8 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-Murnaghan equation of state yields the values of the bulk modulus of 8.8(2) GPa and its first pressure derivative of 3.4(1). The compression is found to be anisotropic, with the b-axis being significantly more compressible than the a-and c-axes.