Born Stability Criteria Research Articles

Pressure-induced phase transition and elastic properties of barium chalcogenides

Two-body, Born–Mayer type potential considered up to the third nearest-neighbor interaction have been used to investigate the B1–B2 phase transition and elastic properties of barium chalcogenides at high pressure. The computed values of B1–B2 phase transition pressure, equation of state (compression curve), bulk modulus, and its first-order pressure derivative are given along with the available experimental and other theoretical values. This study supports the Born's stability criterion and shows that the third nearest-neighbor interaction has an important role to predict the B1–B2 phase transition pressure in barium chalcogenides.

Ab initiothermodynamic and elastic properties ofAGaH4hydrides (A=Li, Na, K, Rb, and Cs)

Systematic properties of the $A{\text{GaH}}_{4}$ alkali gallium hydrides ($A=\text{Li}$, Na, K, Rb, and Cs) are investigated within density functional theory. Seven ground-state crystal structures are identified, with two energetically indistinguishable structures found for both ${\text{LiGaH}}_{4}$, whose structure is as yet undetermined experimentally, and ${\text{CsGaH}}_{4}$. Born effective charge tensors, static and high-frequency dielectric tensors, and phonon dispersion relations incorporating longitudinal-optical/transverse-optical mode splittings are computed. Our results indicate that ${\text{LiGaH}}_{4}$ and ${\text{NaGaH}}_{4}$ have technologically interesting standard enthalpies of formation near $\ensuremath{-}30\text{ }\text{kJ}/\text{mole}$ ${\text{H}}_{2}$. We find, however, that ${\text{LiGaH}}_{4}$ is thermodynamically unstable with respect to both LiGa and LiH, providing a possible explanation for its challenging synthesis. The Born stability criteria are evaluated with the computed elasticity tensor components, ${C}_{ij}$. All seven structures are found to be both elastically and vibrationally stable.

STRUCTURAL PHASE TRANSITION IN BORON COMPOUNDS AT HIGH PRESSURE

The high-pressure induced structural phase transitions and pressure induced elastic and anharmonic behavior of boron compounds viz. BN, BP, and BAs have been investigated using an inter-ionic potential approach based on charge transfer effect. These compounds go to NaCl phase (B1) under pressure from zinc blende phase (B3). The variations of second-order elastic constants and their combinations follow a systematic trend with pressure, identical to that observed in other compounds of zinc blende structure family. Shear stiffness constants decrease with increasing pressure up to phase transition pressure. The bulk moduli of these compounds are in reasonably good agreement with other theoretical and experimental data. The values of phase transition pressure of these compounds obtained by using the present approach are also in good agreement with those predicted by using the pseudo potential approach. The present approach has also succeeded in predicting the Born and relative stability criterion for stable zinc blende phase of these compounds. We also present a set of third-order elastic constants and pressure derivatives of second-order elastic constants for boron compounds.

Structural stability and theoretical strength of Cu crystal under equal biaxial loading

Cu has been used extensively to replace Al as interconnects in ULSI and MEMS devices. However, because of the difference in the thermal expansion coefficients between the Cu film and the Si substrate, large biaxial stresses will be generated in the Cu film. Thus, the Cu film becomes unstable and even changes its morphologies which affects the device manufacturing yield and ultimate reliability. The structural stability and theoretical strength of Cu crystal under equal biaxial loading have been investigated by combining the MAEAM with Milstein-modified Born stability criteria. The results indicate that, under sufficient tension, there exists a stress-free BCC phase which is unstable and slips spontaneously to a stress-free metastable BCT phase by consuming internal energy. The stable region ranges from −15.131 GPa to 2.803 GPa in the theoretical strength or from −5.801% to 4.972% in the strain respectively.

Lattice dynamics and Born instability in yttrium aluminum garnet,Y3A15O12

We report lattice dynamics calculations of various microscopic and macroscopicvibrational and thermodynamic properties of yttrium aluminum garnet (YAG),Y3Al5O12, as a function of pressure up to 100 GPa and temperature up to 1500 K. YAG is animportant solid-state laser material with several technological applications. Garnet has acomplex structure with several interconnected dodecahedra, octahedra and tetrahedra.Unlike other aluminosilicate garnets, there are no distinct features to distinguish betweenintramolecular and intermolecular vibrations of the crystal. At ambient pressure, lowenergy phonons involving mainly the vibrations of yttrium atoms play a primary role in themanifestations of elastic and thermodynamic behavior. The aluminum atoms in tetrahedraland octahedral coordination are found to be dynamically distinct. Garnet’s stability can bediscerned from the response of its phonon frequencies to increasing pressure. The dynamicsof both octahedral and tetrahedral aluminum atoms undergo radical changes undercompression which have an important bearing on their high pressure and temperatureproperties. At 100 GPa, YAG develops a large phonon bandgap (90–110 meV) andits microscopic and macroscopic physical properties are found to be profoundlydifferent from that at the ambient pressure phase. There are significant changesin the high pressure thermal expansion and specific heat. The mode Grüneisenparameters show significant changes in the low energy range with pressure. Ourstudies show that the YAG structure becomes mechanically unstable aroundP = 108 GPa due to the violation of the Born stability criteria. Although this does not rule outthermodynamic crossover to a lower free energy phase at lower pressure, this places an upper boundof P = 110 GPa for the mechanical stability of YAG.

THE STABILITY OF FCC CRYSTAL Cu UNDER UNIAXIAL LOADING IN [001] DIRECTION

Uniaxial loading tests of copper with inter-atomic potential finite-element model are carried out to determine the corresponding ideal tension and compression strength using the modified Born stability criteria. The influence of biaxial stresses applied perpendicularly to the [100] loading axis, on the ideal strength is investigated, and tension-compression asymmetry in ideal strength under [100] loading is also studied. The results suggest that asymmetry for yielding strength of [100] nanowires may result from anisotropic character of crystal instability. Moreover, the results also reveal that the critical resolved shear stress in the direction of slip is not an accurate criterion for the ideal strength since it cannot capture the dependence on the loading conditions and hydrostatic stress components for the ideal strength.

High-pressure induced structural phase transition in alkaline earth CaX (X = S, Se and Te) semiconductors: NaCl-type ( B1) to CsCl-type ( B2)

The present paper addresses the pressure-induced structural aspects of NaCl-type ( B1) to CsCl-type ( B2) structure in alkaline earth chalcogenides (AECs) calcium chalcogenides (CaX; X = S, Se and Te) by formulating an effective interionic interaction potential (EIoIP) with long-range Coulomb interactions and the Hafemeister and Flygare type short-range overlap repulsion extended upto the second neighbor ions and the van der Waals (vdW) interaction. The vdW coefficients are evaluated following the Slater-Kirkwood variational method, as both the ions are polarizable. The present calculations have revealed reasonably good agreement with the available experimental data on structural transition ( B1 to B2 structure), the phase transition pressures ( P t ) of 40 (CaS), 38 (CaSe) and 34 (CaTe) GPa as well the elastic properties. The calculated values of the volume collapses [Δ V( P)/ V(0)] are also closer to their observed data. Further, the variations of the second and third order elastic constants with pressure have followed a systematic trend, which are almost identical to those exhibited by the observed data measured for other semiconducting compounds with rocksalt ( B1) type crystal structure. The Born and relative stability criteria is valid in Ca monochalcogenides.

Theoretical Strength of Face-Centred-Cubic Single Crystal Copper Based on a Continuum Model

The constitutive relation of single crystal copper based on atomistic potential is implemented to capture the nonlinear inter-atomic interactions. Uniaxial loading tests of single crystal copper with inter-atomic potential finite-element model are carried out to determine the corresponding ideal strength using the modified Born stability criteria. Dependence of the ideal strength on the crystallographic orientation is studied, and tension-compression asymmetry in ideal strength is also investigated. The results suggest that asymmetry for yielding strength of nano-materials may result from anisotropic character of crystal instability. Moreover, the results also reveal that the critical resolved shear stress in the direction of slip is not an accurate criterion for the ideal strength since it could not capture the dependence on the loading conditions and hydrostatic stress components for the ideal strength.

Mechanical stability and strength of a single Au crystal

The structural stability and theoretical strength of a Au face-centered cubic (FCC) crystal under uniaxial loading is investigated by combining the modified analytical embedded atom method (MAEAM) with Born stability criteria. The results show that under sufficient compression, there exists a stress-free body-centered cubic (BCC) phase, which is unstable and slips spontaneously to a stress-free metastable body-centered tetragonal phase by consuming internal energy. The structural energy difference between the BCC and FCC phases is in good agreement with the experimental value. The stable region ranged from –2.21 GPa to 6.31 GPa in the theoretical strength or from –9.83% to 7.87% in the strain correspondingly.PACS Nos.: 62.20.–x, 61.50.Ks, 81.05.Bx

Elastic and thermodynamic properties of OsSi, OsSi2 and Os2Si3

All components of the elasticity tensors for OsSi (P213), OsSi2 (Cmca) and Os2Si3 (Pbcn and P-4c2) were computed by means of the stress–strain method in the framework of the density functional theory. The total energies and stress were calculated using density functional theory within the local density and conjugate gradient approximations. From the knowledge of the elastic constants, the Born stability criteria were discussed and the Debye approximation was used to evaluate the enthalpies of formation (ΔHf) of the different compounds. The ΔHf calculated at 298K for OsSi is in correct agreement with the experimental data but for Os2Si3(Pbcn) ΔHf is 30kJ/mol of atoms more exothermic than the measured one. Moreover, we have found that from 1200K the P-4c2 phase of Os2Si3 is most stable from the energy point of view than the Pbcn structure.

Study of high-pressure phase transition of CeTe and EuTe through three-body interaction potential approach

The high pressure phase transition of lanthanum monotellurides having NaCl-type (B 1) structure have been studied using three-body interaction potential (TBIP) approach. The potential model consists of long-range Coulombic, three-body interaction forces, short-range overlap repulsive forces operative up to next nearest neighbor ions, van der Walls interactions and zero point energy effects. To understand the effect of pressure on elastic constant and their combinations, they have also been studied. The Born stability criterion was also found to be fulfiled in the present study. Our calculated results of phase transitions, volume collapses and elastic behavior of these monotellurides are found to be close to the experimental results. This shows that the inclusion of three-body interaction effects makes the present model suitable for high-pressure studies.

Complete determination of the elastic moduli ofα-quartz under hydrostatic pressure up to 1 GPa: an ultrasonic study

Using the ultrasonic pulse-echo technique and a newly developed method to treat the data, all the elasticcompliances of α-quartz have been obtained as a function of hydrostatic pressure up to 1 GPa with great accuracy.Fifteen independent measurements were performed in five directions of high symmetry(X,Y,Z,Y′ and Z′). The pressure dependence of the six second-order elastic and twopiezoelectric constants were deduced. The pressure derivatives ofc14 andc44 are positive,whereas that of c66 is negative, in contradiction to previously published results. Under ambient conditions, the linear and bulkmoduli Ba0 = 103.4(0.5) GPa, Bc0 = 137.0(0.5) GPa and B0 = 37.5(0.2) GPa calculated from our determination of the elastic tensor are in goodagreement with the published values. However, we find a clear discrepancywith published values for the pressure derivative of the bulk modulusB′ = 4.7(0.5). From these results, the Born stability criteria have been calculated as a function of pressure andcompared with previous results. Their behavior can help to explain the structural instability ofα-quartz at around 18 GPa.

Ab initiostudies of solid bromine under high pressure

Crystal structures of bromine under high pressure have been studied by employing plane-wave pseudopotential method with the generalized gradient approximation. It is found that the band overlap in the molecular $Cmca$ phase, which causes the pressure-induced insulator-to-metal transition, occurs at about $55\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. Geometry optimization shows that the bromine changes to a face-centered orthorhombic (fco) phase with equal interatomic distances ${d}_{1}={d}_{2}={d}_{3}$ at about $75\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, but this fco structure is mechanically unstable with shear elastic stiffness coefficient ${C}_{66}<0$. For understanding the structure of this phase, we have modeled an incommensurate structure by a rational approximation with modulation vector $k=(0.25,0,0)$ according to the previous research results in solid iodine. Our results show that the enthalpy of this modulated phase is lower than that of the fco solid, and the elastic stiffness coefficients $({C}_{ij})$ satisfy the Born stability criteria, indicating that the modulated structure is more thermodynamically stable and mechanically stable. In addition, through comparing the x-ray diffraction patterns of our structure with the experimental one, we conclude that the structure of bromine phase V is close to our modulated structure. It is clearly illustrated that the phase transition from $Cmca$ phase to the incommensurate phase is associated with the instability of the shear elastic stiffness coefficient ${C}_{44}$ which is related to the softening of the long-wavelength part of the transverse branch near the center of the first Brillouin zone. With the increasing of pressure, the modulated phase transforms into the monatomic phase II with body-centered orthorhombic structure at about $100\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, which is in agreement with the experimental result.

Stability of BCC transition metals under hydrostatic loading

The structural stability and theoretical strength of BCC transition metals Cr, Mo and W under hydrostatic loading have been investigated by combining the modified analytical embedded atom method (MAEAM) with modified Born stability criteria. For all three BCC transition metals Cr, Mo and W, the stable regions are controlled by shear modulus μ only. Determined stable regions are 0.917–1.079, 0.907–1.090, 0.904–1.095 in the relative deformation a/ a 0 and corresponding compressive and tensile theoretical strengths are 161.0 and 28.15, 162.3 and 34.56, 198.8 and 41.60 GPa for Cr, Mo, W, respectively. The calculated stresses are consistent well with the results of ab initio calculation.

Phase transformation and elastic behavior of MgX (X=S, Se, Te) alkaline earth chalcogenides

Pressure induced structural aspects of NaCl-type ( B1) to CsCl-type ( B2) structure in alkaline earth chalcogenides (AECs) magnesium chalcogenides (MgX; X=S, Se, and Te) are presented. An effective interionic interaction potential (EIoIP) with long-range Coulomb interactions and the Hafemeister and Flygare type short-range overlap repulsion extending up to the second neighbor ions and the van der Waals (vdW) interaction is developed. The vdW coefficients are evaluated following the Slater–Kirkwood variational method, as both the ions are polarizable. The present calculations have revealed reasonably good agreement with the available experimental data on structural transition ( B1– B2 structure), the phase transition pressures P t of 167 (MgS), 170 (MgSe), and 176 (MgTe) GPa as well the elastic properties. The calculated values of the volume collapses [Δ V( P)/ V(0)] are also closer to their observed data. Further, the variations of the second and third order elastic constants with pressure have followed a systematic trend, which are almost identical to those exhibited by the observed data measured for other semiconducting compounds with rocksalt ( B1) type crystal structure. The Born and relative stability criteria is valid in Mg monochalcogenides.

High pressure structural (B1–B2) phase transition and elastic properties of II–VI semiconducting Sr chalcogens

Abstract We evolve an effective interionic interaction potential (EIoIP) with long-range Coulomb interactions and the Hafemeister and Flygare type short-range overlap repulsion extended up to the second neighbor ions and the van der Waals (vdW) interaction to discuss the pressure induced structural aspects of NaCl-type (B1) to CsCl-type (B2) structure in alkaline earth chalcogenides (SrX; X = S, Se and Te). Particular attention is devoted to evaluate the vdW coefficients following the Slater–Kirkwood variational method, as both the ions are polarizable. The present calculations have revealed reasonably good agreement with the available experimental data on the phase transition pressures (Pt = 17.5, 14.5, 12.5 GPa) and the elastic properties. The calculated values of the volume collapses [ΔV(P)/V(0)] are also closer to their observed data. Further, the variations of the second- and third-order elastic constants with pressure have followed a systematic trend, which are almost identical to those exhibited by the observed data measured for other semiconducting compounds with rocksalt (B1) type crystal structure. Also the Born and relative stability criteria is valid in strontium monochalcogenides.

Planar stacking effect on elastic stability of hexagonal boron nitride

The elastic stability of five hexagonal boron nitride (h-BN) stacking sequences is investigated with density functional theory. All components of the elasticity tensor are computed and used to evaluate the Born stability criteria. Phonon spectra are computed for one elastically stable and one elastically unstable h-BN structure and the normal modes associated with instability are identified. Charge density difference contour plots provide a qualitative connection between elastic stability and charge transfer.

Pressure induced structural phase transition and elastic behavior of Y and Sc antimonides

Pressure induced structural aspects of NaCl-type (B1) to CsCl-type (B2) structure in yttrium and scandium antimonides are presented. An effective interionic interaction potential (EIOP) with long-range Coulomb, van der Waals (vdW) interaction and the short-range repulsive interaction upto second-neighbor ions within the Hafemeister and Flygare approach with modified ionic charge is developed. Particular attention is devoted to evaluate the vdW coefficients following the Slater–Kirkwood variational method, as both the ions are polarizable. Our results on vast volume discontinuity in pressure volume phase diagram identifies the structural phase transition from B1 to B2 structure. The estimated value of the phase transition pressure ( P t) and the magnitude of the discontinuity in volume at the transition pressure are consistent as compared to the reported data. The variations of elastic constants and their combinations with pressure follow a systematic trend identical to that observed in others compounds of NaCl-type structure family and the Born and relative stability criteria is valid in yttrium and scandium antimonides.

The stability of FCC crystal Ni under uniaxial loading

Taking Ni as an example, the structural stability and theoretical strength of FCC crystals under uniaxial loading were investigated by combining the modified analytical embedded atom method (MAEAM) with modified Born stability criteria. The results revealed that, under sufficient compression, there existed a stress-free instable BCC phase and then a stress-free metastable BCT phase corresponding to local maximum and minimum internal energy, respectively. The stable region ranged for the theoretical strength from −5.143 eV/nm 3 with a corresponding strain of −9.94% under compression to 10.396 eV/nm 3 with a corresponding strain of 9.66% under tension.

Ab initiostudies of phonon softening and high-pressure phase transitions ofα-quartzSiO2

Density functional perturbation theory calculations of $\ensuremath{\alpha}\ensuremath{-}$quartz using extended norm conserving pseudopotentials have been used to study the elastic properties and phonon dispersion relations along various high symmetry directions as a function of bulk, uniaxial, and nonhydrostatic pressure. The computed equation of state, elastic constants, and phonon frequencies are found to be in good agreement with the available experimental data. A zone boundary ($1∕3$, $1∕3$, 0) K-point phonon mode becomes soft for pressures above $P=32\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. Around the same pressure, studies of the Born stability criteria reveal that the structure is mechanically unstable. The phonon and elastic softening are related to the high pressure phase transitions and amorphization of quartz, and these studies suggest that the mean transition pressure is lowered under nonhydrostatic conditions. The application of uniaxial pressure results in a post-quartz crystalline monoclinic $C2$ structural transition in the vicinity of the K-point instability. This structure, intermediate between quartz and stishovite has two-thirds of the silicon atoms in octahedral coordination while the remaining silicon atoms remain tetrahedrally coordinated. This monoclinic $C2$ polymorph of silica, which is found to be metastable under ambient conditions, is possibly one of the several competing dense forms of silica containing octahedrally coordinated silicon. The possible role of high pressure ferroelastic phases in causing pressure induced amorphization in silica are discussed.