Born Criteria Research Articles

First-principle analysis of the structural, mechanical, optical and electronic properties of wollastonite monoclinic polymorph

The structural, elastic, optical and electronic behavior of CaSiO3 monoclinic polymorph are estimated utilizing ultrasoft pseudo-potential technique operated in CASTEP code. The calculated lattice parameters, such as lattice constants, angle β, and unit cell volume, are in excellent agreement with the experimental data. The computed elastic constant shows that CaSiO3 monoclinic is mechanical stable according to Born criteria. In addition, the polycrystalline properties such as bulk modulus, shear modulus, Young's modulus, Poisson's ratio, elastic anisotropy, compressibility and Debye temperature are determined based on the computed values of the elastic constants. Cauchy pressure and Poisson's ratio indicating a dominant ionic nature of the brittle CaSiO3 monoclinic. An Indirect band gap Ε (C-Г) = 5.02 eV, Ε (C-B) = 5.26 eV, and a direct gap Ε (Г-Г) = 5.06 eV were obtained. Finally, optical properties, such as dielectric function, absorption coefficient, refractive index, conductivity, loss function, and reflectivity have been predicted for polarized incident radiation with electrical vector Ε parallel to the crystalline b-axis.

First-principles study of structural, elastic, electronic, thermodynamic and optical properties of Sc3SnX (X = B, C)

We have calculated the structural, elastic, electronic, thermodynamic and optical properties of Sc3SnX (X = B, C) using first-principles density functional theory (DFT). The optimized structural parameters are found to be in good agreement with the experimental results of Sc3SnX1-y (X = B, C). The mechanical stability of these compounds have been theoretically confirmed using Born criteria. Both materials are shown to be brittle in nature. The electronic band structures and electronic density of states (EDOS) are calculated. The electronic band structures show metallic characteristics with contribution predominantly from the Sc 3d orbital. The computed Peierls stress reveal that movement may occur much slowly compared to a selection of MAX phases. The calculated Vickers hardness for Sc3SnB and Sc3SnC are 4.45 and 4.04 GPa, respectively. The bulk modulus, specific heats, thermal expansion coefficient and Debye temperature are calculated as a function of temperature using the quasi-harmonic Debye model with phononic effects. Moreover optical functions are calculated and discussed for the first time. The reflectivity is found to be high in the IR-UV regions up to ∼12 eV for both Sc3SnB and Sc3SnC thus showing promise as good coating materials.

Ab Initio Prediction of the Structural, Electronic, Elastic, and Thermoelectric Properties of Half-Heusler Ternary Compounds TiIrX (X = As and Sb)

The structural, electronic, elastic, and thermoelectric properties of TiIrX (X = As and Sb) half-Heusler compounds with 18 valence electrons were studied using density functional theory. The generalized gradient approximation of Perdew–Burke and Ernzerhof used for calculation of the structural parameters and elastic properties of TiIrAs and TiIrSb denotes that the computed lattice constants were in excellent agreement with the available experimental data and previous theoretical works. Furthermore, the calculated elastic constants for both compounds satisfy the Born criteria indicating their mechanical stabilities. The modified Becke–Johnson potential (TB-mBJ) was used to provide a better description of the electronic structures, which indicate that both compounds are narrow-gap semiconductors. Additionally, the investigations of thermoelectric performance were carried out using the results of ab initio band-structure calculations and the semi-classical Boltzmann theory within the constant relaxation time approximations. The predicted values of the figure of merit ZT e are close to unity at room temperature. This reveals that TiIrAs and TiIrSb compounds are excellent candidates for practical applications in the thermoelectric devices.

STRUCTURE, ELECTRON AND OSCILLATORY PROPERTIES OF ZINC NITRATE AND ITS CRYSTAL HYDRATES

Within the generalized gradient aproximation of the Density Functional Theory (DFT) with the PBE exchange-correlation functional in the basis of localized atomic orbital of CRYSTAL14 program code, the study is conducted to evaluate the structural, electronic and oscillatory properties of zinc nitrate and its crystal hydrates Zn(NO3)2 • nH2O (n = 2,4,6), with its tested method using the zinc oxide. The first-principle structural study is performed at the full optimization of the lattice distance and atomic positions for the zinc nitrate in the cubic lattice and that of crystal hydrates - in monoclinic lattice. Elastic properties of the nitrate are studied and the mechanical stability is approved using the Born criteria. Electronic properties of rated structures are assessed by energetic (energy-band picture, full and partial density of states) and spatial electron distribution (electronic and deformation density, population density of atomic membranes and density of their overlapping). Crystal hydrates show the electrostatic pattern of nitrogroup interaction and water molecules, availability of localized valence bands and areas of vacant state of anion and cation origin. Oscillatory properties are studied by calculation of frequencies and intensity of IR-active normal long-wave oscillation. In crystal hydrates, the appearance of additional oscillation frequency O-H in terms of nitrate 3000 cm-1 above the IR-spectrum in water molecules and within the area 1200÷1600 cm-1 - of hybrid with nitrogroups.

DFT - based study of electronic structures and mechanical properties of LiTaO3: ferroelectric and paraelectric phases

By applying ab initio calculation within density functional theory (DFT), we study the structure parameters, electronic band structure, elastic coefficients, polycrystalline elastic properties, anisotropy factors and Debye temperature of ferroelectric and paraelectric phases of LiTaO3 within the generalised gradient approximation at ambient pressure. The atomic structure in both phases is fully relaxed and the lattice constant, angle and atomic positions are well consistent with experimental values. The computed single-crystal elastic coefficients indicate that mechanical stability of LiTaO3 in both phases is confirmed using the generalised Born criteria. The shear, bulk and Young’s modulus, Poisson’s ratio, and Vickers hardness were computed according to theoretical elastic constants by Voight–Reuss–Hill method. Several anisotropy factors and indexes are computed to illustrate mechanical anisotropy. Both phases are shown to be weakly anisotropic. The Debye temperature is estimated using the longitude and transverse elastic wave velocity of the ideal polycrystalline LiTaO3 aggregates. We have found that LiTaO3 in both phases has an indirect energy band gap. The differences in the electronic structure and density of states for both phases are quite small. Our results indicate that the mechanical and bonding properties of both phases are very similar. The obtained results were compared with the available experimental and theoretical values.

Elastically confined martensitic transformation at the nano-scale in a multifunctional titanium alloy

A martensitic transformation (MT) is a typical first-order diffusionless crystal structural change with strong autocatalysis like avalanche at a speed of sound propagation. This unique characteristic, however, is undetectable in some multifunctional titanium alloys. Recently, a nano-scale elastically confined MT mechanism was proposed because a nano-scale Nb modulation in a Ti-Nb based alloy was observed. Here we analyze the elastic confinement in details and its induced novel properties in a wide temperature range. The statistical analyses of atom probe tomography (APT) data confirm the existence of the nano-scale Nb concentration modulation. The synchrotron X-ray diffraction (SXRD) profiles demonstrate that the nano-scale Nb modulation causes weak diffuse scattering, as evidenced by the extreme broad diffraction bands. The tensile tests find a critical temperature of ∼150 K, where the critical stress to induce the MT and Young's modulus reach the minimum and the superelastic strain reaches the maximum (∼4.5%) and keeps constant as the temperature decreases further to <4.2 K. To reveal these abnormal behaviors of the MT, the Born criterion governing the elastic stability of cubic crystal is modified by introducing an elastic confinement term and a new Clausius-Clapeyron relationship is established to evaluate the elastically confined MT. The results are consistent with the experimental findings, including the solely stress-induced (no thermally induced) reversibility.

Phase transition of iron-based single crystals under ramp compressions with extreme strain rates

Recent widespread interests on strain rate effects of phase transition under dynamic loadings bring out present studies. α→ε phase transition of iron, as a prototype of martensite phase transition under dynamic loadings, exhibits huge diverges in its transition pressure (TP) among experiments with different pressure medium and loading rates, even in the same initial samples. Great achievements are made in understanding strain or stress dependence of the TP under dynamic loadings. However, present understandings on the strain rate dependence of the TP are far from clear, even a virgin for extreme high strain rates. In this work, large scale nonequilibrium molecular dynamics simulations are conducted to study the effects of strain rates on the phase transition of iron-based single crystals. Our results show that the phase transition is preceded by lattice instabilities under ramp compressions, but present theory, represented by modified Born criteria, cannot correctly predict observed onsets of the instability. Through considering both strain and strain gradient disturbances, new instability criteria are proposed, which could be generally applied for studying instabilities under either static or dynamic loadings. For the ramp with a strain rate smaller than about 1010 s−1, the observed onset of instabilities is indeed equal to the one predicted by the new instability criteria under small gradient disturbances. The observed onsets deviates from the predicted one at lager strain rates because of finite strain gradient effect —— nonzero higher order stresses and work conjugates of the strain gradient. Interestingly, the strain rate (ε˙) dependence of the TP also exhibits an obvious change at the same strain rate, i.e., 1010 s−1. When ε˙ ≤ 1010 s−1, a certain power law is obeyed, but it is not applicable at larger strain rates. This strain rate effect on the TP is well interpreted with nucleation time and the finite strain gradient effect. According to these basic understandings, the roles of strain rates on nucleation and growth of the phase transition are studied. Besides, initial shock formation time at extreme strain rates is analyzed, which also exhibits a deviation from a scaling law.

Abnormal Elasticity of Single-Crystal Magnesiosiderite across the Spin Transition in Earth's Lower Mantle.

Brillouin light scattering and impulsive stimulated light scattering have been used to determine the full elastic constants of magnesiosiderite [(Mg_{0.35}Fe_{0.65})CO_{3}] up to 70GPa at room temperature in a diamond-anvil cell. Drastic softening in C_{11}, C_{33}, C_{12}, and C_{13} elastic moduli associated with the compressive stress component and stiffening in C_{44} and C_{14} moduli associated with the shear stress component are observed to occur within the spin transition between ∼42.4 and ∼46.5 GPa. Negative values of C_{12} and C_{13} are also observed within the spin transition region. The Born criteria constants for the crystal remain positive within the spin transition, indicating that the mixed-spin state remains mechanically stable. Significant auxeticity can be related to the electronic spin transition-induced elastic anomalies based on the analysis of Poisson's ratio. These elastic anomalies are explained using a thermoelastic model for the rhombohedral system. Finally, we conclude that mixed-spin state ferromagnesite, which is potentially a major deep-carbon carrier, is expected to exhibit abnormal elasticity, including a negative Poisson's ratio of -0.6 and drastically reduced V_{P} by 10%, in Earth's midlower mantle.

First-principles study on the electronic, elastic and thermodynamic properties of three novel germanium nitrides**Project supported by the National Natural Science Foundation of China (Nos. 61475132, 11475143, 61501392, 11304141) and the National Training Programs of Innovation and Entrepreneurship for Undergraduates (No. 201510477001).

The ultrasoft pseudo-potential plane wave method combined with the quasi-harmonic approach have been used to study the electronic, elastic and thermodynamic properties of the tetragonal, monoclinic and orthorhombic Ge3N4. The negative formation enthalpies, the satisfactory of Born's criteria and the linear variations of elastic constants with pressure indicate that the three polymorphs can retain their stabilities in the pressure range of 0–25 GPa. The three Ge3N4 are brittle solids at 0 GPa, while they behave in ductile manners in the pressure range of 5–25 GPa. t- and o-Ge3N4 are hard materials but anisotropic. m-Ge3N4 has the largest ductility among the three phases. The results reveal that m-Ge3N4 belongs to an indirect band gap semiconductor, while t- and o-Ge3N4 have direct band gaps. For the thermal properties, several interesting features can be observed above 300 K. o-Ge3N4 exhibits the largest heat capacity, while m-Ge3N4 shows the highest Debye temperature. The results predicted in this work can provide reference data for future experiments.

Structural, elastic, electronic and optical properties of Cu3MTe4 (M = Nb, Ta) sulvanites — An ab initio study

The elastic, electronic, and optical properties of [Formula: see text] [Formula: see text], [Formula: see text] are investigated for the first time using the density-functional formalism. The optimized crystal structure is obtained and the lattice parameters are compared with available experimental data. Different elastic moduli are calculated. The Born criteria for mechanical stability are found to be fulfilled from the estimated values of the elastic moduli, [Formula: see text]. The band structure and the electronic energy density of states (EDOS) are also determined. The band structure calculations show semiconducting behavior for both the compounds. The theoretically calculated values of the band gaps are found to be strongly dependent on the nature of the functional representing the exchange correlations. Technologically significant optical parameters (e.g., dielectric function, refractive index, absorption coefficient, optical conductivity, reflectivity, and loss function) have been determined. Important conclusions are drawn based on the theoretical findings.

Structure and Properties of Egyptian Blue Monolayer Family: XCuSi4O10 (X = Ca, Sr, and Ba).

Motivated by the recent experimental advances in exfoliating Egyptian blue monolayers, we have carried out extensive calculations using density functional theory to understand their geometry, stability, mechanical properties, electronic structures, and magnetism. Upon exfoliation from the bulk, XCuSi4O10 (X = Ca, Sr, and Ba) monolayers are found to change symmetry from tetragonal to orthorhombic. They all satisfy Born criteria and are mechanically stable. Each Cu site carries a magnetic moment of 1.0 μB but with degenerate ferromagnetic and antiferromagnetic coupling states. From Ca to Sr and Ba, as the atomic number increases, the thickness, elastic constants, Young's moduli, and Poisson's ratios of the monolayers increase, while the band gaps decrease. Applying strain can tune the magnitude of energy band gaps, but the direct gap feature remains. Complementing the widely studied graphene, MXenes, black phosphorus, and dichalcogenide sheets, the Egyptian blue monolayers add additional features to the family of two-dimensional materials.

On estimations of the melting temperature of graphene-like compounds

Abstract—Three approaches to the problem of determining the melting temperature considered as the temperature of thermal instability of a two-dimensional hexagonal structure are discussed. These approaches are (i) Naya–Iziri–Ishii’s approximation, (ii) the Lindemann criterion, and (iii) the Born criterion. The Harrison method of bonding orbitals is used for numerical estimations. Graphene, silicene, germanene, and 12 IV–IV and III–V compounds are considered. It is shown that the Lindemann and Born criteria give close and more real results in comparison to Naya–Iziri–Ishii’s approximation. To obtain rough estimates of the “bulk” and “surface” melting temperatures, the expressions T b ~ 104 K/a 2 and T s ~ 2T b /3, where the spacing between the nearest neighbors a is given in angstroms, are proposed.

Structural and mechanic properties of RFeO3 with R = Y, Eu and La perovskites: a first-principles calculation

The structural and elastic properties of the RFeO3 phases with R = Y, Eu, and La were investigated using first-principles plane-wave pseudopotential density functional theory with the generalized gradient approximation (GGA). The ground state properties (equilibrium cell constants) agree well with the reported experimental results. Our results showed an increase in the unit-cell volume (V) with the increase of ionic radii. We calculate a set of elastic parameters (bulk modulus B VRH , shear modulus G VRH , Young’s modulus E VRH and Poisson’s ratio ν) in the framework of the Voigt-Reuss-Hill (VRH) approximation. The sound velocities (v l , v t ) and Debye temperature (θ D ) were calculated using these elastic moduli. The calculated elastic constants were positives and satisfy the well-known Born criteria, indicating that the orthorhombic structure is stable. Finally, the ratio G VRH /B VRH suggests that the RFeO3 phases are ductile in nature.

Universal elastic-hardening-driven mechanical instability in α-quartz and quartz homeotypes under pressure.

As a fundamental property of pressure-induced amorphization (PIA) in ice and ice-like materials (notably α-quartz), the occurrence of mechanical instability can be related to violation of Born criteria for elasticity. The most outstanding elastic feature of α-quartz before PIA has been experimentally reported to be the linear softening of shear modulus C44, which was proposed to trigger the transition through Born criteria B3. However, by using density-functional theory, we surprisingly found that both C44 and C66 in α-quartz exhibit strong nonlinearity under compression and the Born criteria B3 vanishes dominated by stiffening of C14, instead of by decreasing of C44. Further studies of archetypal quartz homeotypes (GeO2 and AlPO4) repeatedly reproduced the same elastic-hardening-driven mechanical instability, suggesting a universal feature of this family of crystals and challenging the long-standing idea that negative pressure derivatives of individual elastic moduli can be interpreted as the precursor effect to an intrinsic structural instability preceding PIA. The implications of this elastic anomaly in relation to the dispersive softening of the lowest acoustic branch and the possible transformation mechanism were also discussed.

First-principles investigation of thermodynamic, elastic and electronic properties of Al3V and Al3Nb intermetallics under pressures

The thermodynamic, elastic, and electronic properties of D022-type Al3V and Al3Nb intermetallics were studied using the first-principle method. The results showed the pressure has profound effects on the structural, mechanical and electronic properties in both Al3V and Al3Nb. Thermodynamically, the formation enthalpies for Al3V and Al3Nb were derived, which agreed well with available experimental and theoretical values. Comparably, Al3Nb was a more stable phase with the more negative Hf than Al3V. Mechanically, the calculated elastic constants showed linearly increasing tendencies, and satisfied the Born's criteria from 0–20 GPa, indicating the mechanically stability of Al3V and Al3Nb under this pressure range. Further, the mechanical parameters (i.e., bulk modulus (B), shear modulus (G), and Young's modulus (E)) were derived using the Voigt-Reuss-Hill (VRH) method, and in good agreement with available experimental results at the ground state. All these parameters presented the linearly increasing dependences on the external pressure. The B/G ratios and Poisson's ratio indicated that the Al3V and Al3Nb crystals should exhibit brittle behavior at 0–20 GPa. Additionally, the bulk modulus can be obtained through fitting the Birch-Murnaghan equation (B0), computing by VRH method (BH), and deriving from the elastic theory (Brelax) in both intermetallics. The uniformity of these calculated bulk moduli in each compound exhibited the excellent reliability and self-consistency. In addition, Debye temperature was estimated from the average sound velocity. The Debye temperature showed an increasing dependence on the pressures. Finally, through density of states analysis, Al3V and Al3Nb were suggested to possess naturally metallic behavior. Under pressures, it was noted that the shapes of peaks and pseudogaps exhibited relative few changes, suggesting Al3V and Al3Nb has kept structurally stable up to 20 GPa. At zero pressure, Al3Nb was considered as a more structurally stable phase with the more number of bonding electrons per atom than Al3V. This conclusion was in consistent with the one drawn from the thermodynamic analysis.

MECHANICAL AND THERMAL PROPERTIES OF PRASEODYMIUM MONOPNICTIDES: AN ULTRASONIC STUDY

We have computed ultrasonic attenuation, acoustic coupling constants and ultrasonic velocities of praseodymium monopnictides PrX ( X : N , P , As , Sb and Bi ) along the 〈100〉, 〈110〉, 〈111〉 in the temperature range 100–500 K using higher order elastic constants. The higher order elastic constants are evaluated using Coulomb and Born–Mayer potential with two basic parameters viz. nearest-neighbor distance and hardness parameter in the temperature range of 0–500 K. Several other mechanical and thermal parameters like bulk modulus, shear modulus, Young's modulus, Poisson ratio, anisotropic ratio, tetragonal moduli, Breazeale's nonlinearity parameter and Debye temperature are also calculated. In the present study, the fracture/toughness (B/G) ratio is less than 1.75 which implies that PrX compounds are brittle in nature at room temperature. The chosen material fulfilled Born criterion of mechanical stability. We also found the deviation of Cauchy's relation at higher temperatures. PrN is most stable material as it has highest valued higher order elastic constants as well as the ultrasonic velocity. Further, the lattice thermal conductivity using modified approach of Slack and Berman is determined at room temperature. The ultrasonic attenuation due to phonon–phonon interaction and thermoelastic relaxation mechanisms have been computed using modified Mason's approach. The results with other well-known physical properties are useful for industrial applications.

VACANCY MECHANISM OF MELTING AND SURFACE ROUGHENING OF METAL NANOPARTICLES

Within the limits of the uniform approach with the assistance of the vacancy mechanism the description of melting and surface roughening of both free nanoparticles and nanoparticles deposited on the surface of solid body under conditions of thermodynamic equilibrium is offered. Surface roughening of a spherical particle is represented as a phase transition in vacancy subsystem, in which supersaturation is formed by reducing the particle size. It is shown that interaction between vacancies result in to the unification of vacancies on a surface in vacancy clusters, that can be regarded as the appearance of a surface roughness of nanoparticles. It is shown that increasing concentration of vacancies caused by the modification of effective vacancy formation energy with decreasing sizes of nanoparticles result into a modification of shear modulus of material. By vanishing the shear modulus (Born criteria of melting) the dependence of temperature of fusion of nanoparticles of different metals on radius was determined.

Ab initio investigation into the elasticity of ultrahigh-pressure phases of SiO2

In this study, we report the elastic properties of three ultrahigh-pressure phases of SiO2: pyrite, cotunnite and Fe2P types between 300 and 1,500 GPa calculated by means of the density functional ab initio method. It is generally thought that materials tend to be more compact and isotropic with increasing pressure. These three ultrahigh-pressure phases of silica are mechanically stable in the investigated pressure range according to the Born criteria, while the cotunnite and Fe2P types are unstable at lower pressure. The elastic azimuthal anisotropy of these ultrahigh-pressure phases of silica shows that all the structures counterintuitively have considerable anisotropies even at multimegabar pressures. Among the three investigated structures, the cotunnite type of SiO2 is the most elastically anisotropic phase due to a soft compression along the b axis combined with a large distortion of the polyhedrons that make the structure. This might also be related to its thermodynamic unfavorability compared to the Fe2P type under extreme pressure condition. The bond property analyses clearly show that the Si–O bond remains an ionic-covalent mixed bond even at multimegabar pressures with an invariable ionicity with pressure. This argument can explain the monotonously pressure dependence of the elastic anisotropy in the case of pyrite, while the changes in the velocity distribution patterns out of the thermodynamic instability range largely contribute to those of the cotunnite and Fe2P types.

First Principle Calculations on Structures and Properties of Diamond-Like B&lt;sub&gt;2&lt;/sub&gt;(CN)&lt;sub&gt;3&lt;/sub&gt; Compounds

Diamond-like B-C-N compounds have the excellent potential properties like diamond or cubic boron nitride. In this paper, diamond-like B2(CN)3compound has been studied by first principle calculations. After geometry optimization, hexagonal and monoclinic B2(CN)3models were obtained. According to the band structure and density of state calculated, they are conducting. The relative stability was proved using elastic constants calculated by Born criterion. The monoclinic B2(CN)3is one of hard material with theoretical Vickers hardness 38 GPa.

High pressure behavior and structural properties of transition metal carbides

A pressure induced structural phase transition from NaCl-type (B1) to CsCl-type (B2) structure has been predicted in transition metal carbides, namely TiC, ZrC, NbC, HfC, and TaC by using an interionic potential theory with modified ionic charge (Zm ), which includes Coulomb screening effect due to d-electron. The phase transition pressure (PT ) relies on large volume discontinuity in pressure–volume relationship, and identifies the structural phase transition from B1 phase to B2 phase. The variation of second-order elastic constants with pressure follows a systematic trend identical to that observed in other compounds of NaCl-type structure. The Born criterion for stability is found to be valid in transition metal carbides.