Obtained Bulk Modulus Research Articles

Effect of pressure on the structural properties of tantalum carbide

In this study, tantalum carbide (TaC) samples were placed in a diamond anvil cell to study the equation of state at room temperature and high pressure using synchrotron radiation X-ray diffraction. By fitting the data at ambient pressure and up to the highest pressure of 38.5[Formula: see text]GPa, we obtained the bulk modulus and first derivative of TaC as [Formula: see text] (6.8) GPa and [Formula: see text] (0.49), respectively. In addition, we calculated the bulk modulus and band structure of TaC under high pressure using density functional theory. The obtained bulk modulus is 267 (3)[Formula: see text]GPa. TaC is metallic in nature throughout the entire pressure range. We studied the high-pressure deviatoric stress of TaC using linewidth analysis method. We found that TaC can support a maximum differential stress of up to 18.6[Formula: see text]GPa at the highest pressure of 38.5[Formula: see text]GPa.

Phonon anharmonicity and equation of state parameters of orthovanadate Mg3(VO4)2: Raman Spectroscopy and X-ray diffraction investigation

Isothermal compression effect is investigated on structure and vibrational properties of orthovanadate Mg3(VO4)2 using Raman spectroscopy and X-ray powder diffraction up to pressures 20.2 and 25.7 GPa respectively. Isobaric temperature effect on the vibrational properties of Mg3(VO4)2 have also been investigated using Raman spectroscopy up to 1273 K. The present investigation indicates stable orthorhombic (Cmca) structure up to the highest pressure achieved and up to near its melting temperature. The high pressure structural behavior is similar to the isostructural compounds Zn3(VO4)2 and Ni3(VO4)2 unlike another isostructural compound Mn3(VO4)2 which is reported to show irreversible structural phase transformation. Experimental equation of state parameters are compared with those reported on the similar compounds and the obtained bulk modulus (141 GPa) of Mg3(VO4)2 matches very well with the empirically calculated value reported earlier. The anharmonicities estimated after combining both studies suggest dominant contribution of three phonon decay process.

First-principles investigation of the structural, elastic, anisotropic and electronic properties of Pmma-carbon

An investigation of the structural, elastic, anisotropic and electronic properties of the recently reported Pmma-carbon was performed by means of first-principles calculations in this paper. The Pmma-carbon phase possesses an orthorhombic symmetry with space group Pmma (No. 51). It contains 10 carbon atoms per unit cell and adopts an all-sp 3 4+6+8-membered rings bonding network. The structural stability of Pmma-carbon is verified by analysis of the total energy, phonon spectra and elastic constants. The obtained bulk modulus and shear modulus indicate that Pmma-carbon is a brittle material and possesses elastically anisotropic. It is identified that Pmma-carbon is a potential superhard material with a Vickers hardness surpassing 70 GPa, which is lower than that of diamond but comparable with c-BN. The analysis of electronic band structure and density of states reveals that Pmma-carbon is an insulator with a quasi-direct band gap of 4.45 eV. The X-ray diffraction patterns of Pmma-carbon are also provided for future identifying the carbon phase in experiments. The present findings enrich the existing superhard carbon materials family and broaden our understanding of superhard carbon phases.

A high-pressure study of Cr3C2 by XRD and DFT**Project supported by the Project of Ph. D. Special Research of Sichuan University of Arts and Science, China (Grant No. 2019BS006Z) and the Fund from the Chinese Academy of Sciences (Grant Nos. KJCX2-SW-N03 and KJCX2-SW-N20).

The equation of state (EOS) of Cr3C2 at high pressure is studied by the synchrotron radiation x-ray diffraction (XRD) in a diamond anvil cell (DAC) at ambient temperature, and density functional theory (DFT). The XRD analysis shows that the orthorhombic structure is maintained to a maximum pressure of 44.5 GPa. The XRD data show that the bulk modulus is K0 = 292 (18) GPa with . In addition, the high-pressure compression behavior of Cr3C2 is studied by first principles calculations. The obtained bulk modulus of Cr3C2 is 323 (1) GPa.

Phase Stability and Compressibility of 3R-MoN2 at High Pressure

We report phase stability and compressibility of rhombohedral 3R-MoN2, a newly discovered layer-structured dinitride, using in-situ synchrotron high-pressure x-ray diffraction measurements. The obtained bulk modulus for 3R-MoN2 is 77 (6) GPa, comparable with that of typical transition-metal disulfides (such as MoS2). The axial compressibility along a axis is more than five times stiffer than that along c axis. Such strong elastic anisotropy is mainly attributed to its layered structure with loosely bonded N-Mo-N sandwich interlayers held by weak Van der Waals force. Upon compression up to ~15 GPa, a new hexagonal phase of 2H-MoN2 occurs, which is irreversible at ambient conditions. The structural transition mechanism between 3R and 2H phases is tentatively proposed to be associated with the rotation and translation of sandwich interlayers, giving rise to different layer stacking sequences in both phases. At high temperature, the decomposition of 3R-MoN2 leads to the formation of hexagonal δ-MoN and the onset degassing temperature increases as the pressure increases. In addition, the low-temperature electrical resistivity measurement indicates that 3R-MoN2 behaves as a semiconductor with an estimated band gap of Eg ≈ 0.5 eV. 3R-MoN2 also shows weak antiferromagnetic properties, which probably originates from the occurrence of magnetic zigzag edges in the structure.

Vanadium Diboride (VB2) Synthesized at High Pressure: Elastic, Mechanical, Electronic, and Magnetic Properties and Thermal Stability.

Vanadium diboride (VB2) with an AlB2-type structure has been synthesized at 8 GPa and 1700 K in a D-DIA-type multianvil apparatus. The obtained bulk modulus is B0 = 262(2) GPa with fixed B' = 4.0 for VB2 via high-pressure X-ray diffraction measurements. Meanwhile, VB2 has also been demonstrated to possess a high Vickers hardness of 27.2 ± 1.5 GPa, a high thermal stability of 1410 K in air, among the highest for transition-metal borides, and an extremely low resistivity value (41 μΩ cm) at room temperature. Results from first-principles calculations regarding the mechanical and electronic properties of VB2 are largely consistent with the experimental observations and further suggest that VB2 possesses simultaneously the properties of a hard and refractory ceramic and those of an excellent electric conductor.

Experimental verification of spatially varying fracture-compliance estimates obtained from amplitude variation with offset inversion coupled with linear slip theory

The elastic compliance of a fracture can be spatially varying, reflecting the variation of microscale properties of the fracture, e.g., aperture, contact asperities, and fracture infill. Characterizing the spatial heterogeneity of a fracture is crucial in explaining the apparent frequency dependence of fracture compliance and in addressing the spatially varying mechanical and hydraulic properties of the fractured medium. Apparent frequency dependence of the estimated fracture compliance is caused when the used seismic wavelength is very large compared to the scale of heterogeneity. We perform ultrasonic laboratory experiments, and characterize the spatially varying compliance along a fluid-filled fracture. We simulate a horizontal fracture, and introduce heterogeneous fluid distribution along the fracture. We perform amplitude variation with offset (AVO) inversion of the P-P reflections, in which we obtain the theoretical angle-dependent reflection responses by considering the linear-slip model. The estimated compliance distribution clearly separates the dry region from the wet region of the fracture. The effective bulk modulus of the fluid is estimated using the derived values of the compliance. We find that the obtained bulk modulus is well-explained by the presence of minute quantity of air bubbles in the water. We also find new evidence of the existence of scattered waves generated at the boundary representing a sharp change in fracture compliance. The estimated boundary between the dry and the wet regions of the fracture, which is detected by AVO inversion, is slightly shifted compared with the actual location. This is possibly due to the interference of the scattered waves that are generated at the boundary. The linear-slip model can represent thin structures in rocks in a wide range of scale. Therefore, our methodology, results, and discussion will be useful in developing new applications for assessing laterally varying mechanical and hydraulic properties of thin nonwelded discontinuities, e.g., fractures, joints, and faults.

Ab-initio study of electronic and elastic properties of Mg(BH4)(NH2) complex hydride

Structural and electronic properties of complex hydride Mg(BH4)(NH2), applicable in hydrogen storage, were studied in framework of pseudopotential-density functional theory. This compound shows an indirect band gap of 4.95 eV which is categorized in insulator materials. The calculated total and partial density of states of this compound show that the hydrogen bonding in BH4 anion is mainly covalent and the hydrogen-hydrogen repulsion is more in anion BH4 than in anion NH2. The calculated bulk modulus from Birch-Murnaghan equation of state is in close agreement with that obtained from the elastic constants. The obtained bulk modulus (19.27 GPa) shows this compound is more ductile than binary and ternary hydrides and it does not have a brittle structure. Therefore, it is a good candidate for hydrogenation and dehydrogenation cycles. The stability of the structure in ambient pressure is also declared by calculating the elastic coefficients. However, the existence of elastic anisotropy in the compound demonstrates the less compressibility of it along the c axis than a and b axes. The small amount of Poisson ratio indicates that it is more stable against shear compared to common borohydrides. This point is important for hydride stability in hydrogenation and dehydrogenation cycles.

Elasticity of Prussian‐Blue‐Analogue Nanoparticles

We report on the elastic properties of Ni/[Fe(CN)6] Prussian‐blue‐analogue nanoparticles investigated by high‐pressure synchrotron X‐ray diffraction and nuclear inelastic scattering. For 3 nm and 115 nm particles, we have obtained bulk moduli of (30.3 ± 3.8) GPa and (24.5 ± 3.2) GPa, with Debye sound velocities of (2496 ± 46) m s–1 and (2407 ± 38) m s–1, respectively. Combining these results, Poisson's ratio, Young's modulus, the shear modulus, and the transversal/longitudinal sound velocities have been calculated for each particle size. All of these physical quantities suggest a stiffening of the lattice when the particle size decreases, which is mainly attributed to the reduction of iron ions on the particle surface.

Li0.5Ni0.5Mn2O4 spinel: Its synthesis, structure and high pressure properties

A new Li-Ni-Mn spinel of the composition Li0.5Ni0.5Mn2O4 was successfully prepared by thermal decomposition of citrate complexes followed by quenching from 1048 K. The distribution of cations in this oxide was deduced from X-ray powder diffraction and XPS measurements. High pressure powder X-ray diffraction measurements were performed up to pressures of approximately 6 GPa. The cubic spinel phase remained stable within the pressure range of this study. The bulk modulus calculated from the second order Birch–Murnaghan equation of state with the data following from our study was B0 = 136 (3) GPa, while the initial volume was V0 = 578.4 (3) Å3. The obtained bulk modulus fits into the general trend of compressibility increasing with growing lithium content at tetrahedral sites. The result of the experiment reported here has provided the first proof of the earlier postulated tendency.

Phase boundary between cubic B1 and rhombohedral structures in (Mg,Fe)O magnesiowüstite determined by in situ X-ray diffraction measurements

The phase relations and equation of state of (Mg0.08Fe0.92)O magnesiowustite (Mw92) have been studied using the Kawai-type high-pressure apparatus coupled with synchrotron radiation. To determine the phase boundary between the NaCl-type cubic (B1) and rhombohedral (rB1) structures in Mw92, in situ X-ray observations were carried out at pressures of 0–35 GPa and temperatures of 300–1473 K. Au and MgO were used as the internal pressure markers and metallic Fe as oxygen fugacity buffer. The phase boundary between B1 and rB1 structures was described by a linear equation P (GPa) = 1.6 + 0.033 × T (K). The Clapeyron slope (dP/dT) determined in this study is close to that obtained at pressures above 70 GPa but steeper than that obtained for FeO. An addition of MgO to FeO structure expands the stability field of the rB1 phase to lower pressures and higher temperatures. Thus, the rB1 phase may be stabilized with respect to the B1 phase at a lower pressures. The pressure–volume–temperature equation of state of B1-Mw92 was determined up to 30 GPa and 1473 K. Fitting the hydrostatic compression data up to 30 GPa with the Birch–Murnaghan equation of state (EoS) yielded: unit cell volume (V 0,T0), 79.23 ± 4 A3; bulk modulus (K 0,T0), 183 ± 4 GPa; its pressure derivative (K′ T ), 4.1 ± 0.4; (∂K 0,T /∂T) = −0.029 ± 0.005 GPa K‒1; a = 3.70 ± 0.27 × 10−5 K−1 and b = 0.47 ± 0.49 × 10−8 K−2, where α0,T = a + bT is the volumetric thermal expansion coefficient. The obtained bulk modulus of Mw92 is very close to the value expected for stoichiometric iron-rich (Mg,Fe)O. This result confirms the idea that the bulk modulus of (Mg,Fe)O is greatly affected by the actual defect structure, caused by either Mg2+ or vacancies.

Bulk modulus of two-dimensional liquid dusty plasmas and its application

From the recently obtained equation of state [Feng et al., J. Phys. D: Appl. Phys. 49, 235203 (2016) and Feng et al., Phys. Plasmas 23, 093705 (2016); Erratum 23, 119904 (2016)], the bulk modulus of elasticity K of 2D liquid dusty plasmas is analytically derived as the expression of the temperature and the screening parameter. Exact values of the obtained bulk modulus of elasticity K are reported and also plotted in the 2D plane of the temperature and the screening parameter. As the temperature and the screening parameter change, the variation trend of K is reported and the corresponding interpretation is suggested. It has been demonstrated that the obtained bulk modulus of elasticity K can be used to predict the longitudinal sound speed, which agrees well with previous studies.

Experimental and theoretical high pressure study of calcium hydroxyaluminate phases

Five calcium hydroxyaluminate phases have been investigated by synchrotron powder diffraction at high-pressure: two hydrogarnets, kuzelite, stratlingite and ettringite. The obtained bulk modulus, K0, for kuzelite, stratlingite and ettringite were 23(1), 27(1) and 30(3)GPa, respectively. Kuzelite and stratlingite underwent transformations above 1GPa likely releasing interlayer water. Kuzelite becoming markedly amorphous and stratlingite remained crystalline, K0=58(6)GPa in the 1.5–5.5GPa pressure range. The structural behavior for hydrogarnet samples is prone to the use of pressure transmitting media. K0 for Ca3Al2(OH)12 was 81(2) and 76(2)GPa for silicone oil and alcohol mixture, respectively. A similar study for Ca3Al1.7Fe0.3(OH)12 yielded 73(1) and 58(1)GPa for silicone oil and alcohol mixture, respectively. Atomistic calculations using periodic Density Functional Theory showed that the softening in iron-doped katoite, when compared to stoichiometric katoite, can be assigned primarily to greater compressibility of CaO dodecahedra, which overcompensates strengthening of hydrogen bonding between Al/Fe hydroxide groups.

Theoretical Calculations of Mechanical, Electronic, and Chemical Bonding in CaN2, SrN2, and BaN2

Abstract We present a first-principles density functional theory-based study about the impact of pressure on the structural and elastic properties of bulk CaN2, SrN2, and BaN2. Non-spin and spin polarized calculations indicate that the non-spin polarized ground state was more favourable with magnetic moments of 1.049 μB, 1.059 μB, and 1.014 μB for CaN2, SrN2, and BaN2, respectively, and these were in good agreement with previous experimental and theoretical data. The high bulk modulus of CaN2, SrN2, and BaN2 confirm that those compounds have low compressibility and high hardness. The obtained bulk modulus, N-N bond length, and optimized structure parameters are similar to those from previous studies.With an increase in applied pressure the independent elastic constants of CaN2, SrN2, and BaN2 indicated the presence of mechanical instability at 20, 15, and 10 GPa, which is possibly related to phase transitions in addition to a decrease in N-N bond length.

High-pressure x-ray diffraction study of YBO3/Eu3+, GdBO3, and EuBO3: Pressure-induced amorphization in GdBO3

Angle-dispersive synchrotron X-ray diffraction measurements were performed on vaterite-type YBO3/Eu3+, GdBO3, and EuBO3, respectively, up to 41 GPa at room temperature using a diamond-anvil cell. Pressure-induced amorphization was observed in hexagonal GdBO3 with a significant compression along the c-axis. Compared to the ions of the distorted GdBO3 phase, its anions may lose their long-range order prior to the cations at high pressures. Based on the experimental pressure-volume data, the obtained bulk moduli of YBO3/Eu3+ and GdBO3 are 329 and 321 GPa, respectively, which are more than 90% larger than that of EuBO3 (167 GPa) and are presumably attributed to Gd3+ and Y3+ with a high density of d valence electrons.

PHASE TRANSITION, ELASTIC AND THERMODYNAMIC PROPERTIES OF BERYLLIUM VIA FIRST PRINCIPLES

The phase transition, elastic and thermodynamic properties of beryllium (Be) have been studied at high pressures by plane-wave ultrasoft pseudopotential density functional theory (DFT) within the generalized gradient approximation (GGA). It is found that the hcp → bcc phase transition of Be occurs at 506 GPa (T = 0 K ) and occurs at 1200 K (P = 0 GPa ). The coefficients of linear thermal expansion of the hexagmal close-packed (hcp), bcc and orthorhombic Be have been calculated. The hcp → orthorhombic → bcc phase transitions do not occur in all range of pressures, that is to say, the orthorhombic Be is not an intermediate phase between the hcp and bcc Be. The obtained bulk modulus (B0) are 113.2 GPa (for hcp Be), 113.1 GPa (for bcc Be) and 70.5 GPa (for orthorhombic Be), respectively.

Ab initio study of the structural, mechanical, and dynamical properties of the rare-earth dihydrides XH2 (X=Sc, Y, and La)

The structural, electronic, mechanical, dynamical and thermodynamic properties of rare-earth dihydrides XH2 (X=Sc, Y, and La) with the cubic fluorite structure have been systematically investigated by using the projector augmented wave (PAW) method within the generalized-gradient approximation. The calculated lattice parameters, electronic structures and elastic constants of XH2 agree well with available experimental data and other theoretical results. Both the lattice constants and the equilibrium unit cell volumes increase in accordance with heavier rare-earth atom. From the obtained bulk modulus, shear modulus and Young's modulus, the resistance to volume change, shear deformations, and even tensile and compressive deformations weakens from ScH2 to LaH2 successively. The brittle/ductile properties of the three compounds are determined by the ratio of B/G and the Cauchy pressure C12−C44. Poisson's ratio, elastic anisotropy factor, Debye temperature, and sound velocities of XH2 are also predicted. Especially, the phonon dispersion curves and corresponding phonon density of states of XH2 are determined using a linear-response approach to density functional perturbation theory (DFPT) successfully, the phonon frequencies (in THz) obtained at the zone-center (Γ-point) for infrared-active modes T1u and Raman-active modes T2g are ScH2: T1u=29.294, T2g=35.279; YH2: T1u=27.295, T2g=32.624; and LaH2: T1u=24.286, T2g=28.004. Our results show that the three compounds can be stabilized dynamically and mechanically in the ground state phase of the cubic fluorite structure. The thermodynamic functions such as phonon contributions to the internal energy E, the Helmholtz free energy F, the entropy S, the changes of H–H298.15 and G–G298.15 and the constant volume specific heat CV under high temperatures are also obtained based on phonon density of states.

Ab initio study of structural and electronic properties of LiBe compound

The ab initio calculations are performed to study structural and electronic properties of binary intermetallic compound LiBe. Calculations are performed applying the generalized gradient and the local density approximations within the density functional theory implementing the CRYSTAL code. We have obtained bulk modulus, lattice parameters and pressure derivative of the bulk modulus by calculating ground state energy of the monoclinic structure of LiBe compound. We also present the structure factors for a few planes of the monoclinic structure. Among electronic properties, the electronic band structure and the density of states are calculated for the compound.

Experimental invalidation of phase-transition-induced elastic softening in CrN

We report experimental results of phase stability and incompressibility of CrN. The obtained bulk moduli for cubic and orthorhombic CrN are 257 and 262 GPa, respectively. These results invalidate the conclusion of phase-transition-induced elastic softening recently reported based on nonmagnetic simulations for cubic CrN [Nature Mater. 8, 947 (2009)]. On the other hand, they provide the only experimental evidence to support the computational models involving the local magnetic moment of Cr atoms [Nature Mater. 9, 283 (2010)], indicating that atomic spin has a profound influence on the material's elastic properties. We also demonstrate that nonstoichiometry in CrN${}_{x}$ has strong effects on its structural stability.

First-principles investigations on the electronic, elastic and thermodynamic properties of Cr2MC(M=Al, Ga)

We investigate the electronic, elastic and thermodynamic properties of nanolaminate Cr2MC(M=Al, Ga) by using the ab initio pseudopotential total energy method. Our results show that they have shown almost identical volume compressibilities. The axial compressibility investigations show that the c axis is always stiffer than a axis. The internal coordinate calculations revealed that the values of Cr atoms in Cr2AlC are always larger than those in Cr2GaC. The elastic constants calculations demonstrated the structural stability within 050 GPa. The obtained bulk moduli by quasi-harmonic Debye model observed that the bulk moduli of Cr2MC(M=Al, Ga)decrease with temperature at 0 GPa, but increase at 300 GPa. We also found that the Debye temperatures of Cr2GaC are always smaller than those of Cr2AlC at any conditions. However, the opposite cases can be found in thermal expansion coefficients, Grneisen parameter, entropy and heat capacity when comparing their respective counterparts between Cr2GaC and Cr2AlC. The electronic density of states and energy band distribution demonstrated that the Cr2MC(M=Al, Ga) have shown similar profiles with the only exception of the more localized s and p electrons in Cr2GaC than their respective counterparts in Cr2AlC.