Three-body Potential Model Research Articles

A non-ordinary state decomposition method for three-body potential peridynamics model

A non-ordinary state decomposition method is proposed for the bond shear form of three-body potential peridynamics (PD) model. To accomplish this formulation, the effective relative displacement between two points is first decomposed into the volumetric and deviatoric parts based on the definition of dilatation. Starting from this, we give decomposition forms of the elementary deformations and strain energy density of this PD model and finally express the PD force function in the form of the sum of dilatational and distortional parts, which enable the PD model to clearly reflect material response dependence on volume changes and shape distorsion. Combined with the computational scheme of strain and stress tensors presented in the paper, the proposed method is validated numerically. The study permits the possibility of introducing plastic incompressibility for the three-body potential PD model.

On deformation and fracture of PBX simulant employing modified three-body potential peridynamics model with deformation-based failure criteria

The modified three-body potential peridynamics (PD) model is used to study the macroscopic mechanical responses of polymer bonded explosive (PBX) mock materials. Combined with PD functions, under small deformation conditions, bond shear form of the PD model is derived from the micro-potential incorporating modified three-body interaction potential, giving some attention to the applicable condition for its two expression forms, i.e., general form and bond shear form. Subsequently, an improved mode Ⅱ failure criterion considering collective shear deformation of family members is proposed to enhance the deformation-based failure criteria adopted in the present study. A series of PBX simulants associated with elastic deformation and brittle fracture behaviors are carried out by the proposed numerical method. And the numerical results are verified by experimental and other numerical ones published previously, which show that the proposed numerical method is suitable for modeling PBX mock materials.

K¯D¯N molecular state as a “ uudsc¯ pentaquark” in a three-body calculation

We predict a new three-body hadronic molecule composed of antikaon $\overline{K}$, anticharm meson $\overline{D}$, and nucleon $N$ with spin-parity ${J}^{P}=1/{2}^{+}$ and isospin $I=1/2$. This state behaves like an explicit pentaquark state because its minimal quark configuration is $uuds\overline{c}$ or $udds\overline{c}$. Owing to the attraction between every pair of two hadrons, in particular the $\overline{K}\overline{D}$ attraction which dynamically generates ${D}_{s0}{(2317)}^{\ensuremath{-}}$ and $\overline{K}N$ attraction which dynamically generates $\mathrm{\ensuremath{\Lambda}}(1405)$, the $\overline{K}\overline{D}N$ system is bound, and the real (imaginary) part of its eigenenergy is calculated as $3253\phantom{\rule{4.pt}{0ex}}\text{MeV}$ (minus a few MeV) in a nonrelativistic three-body potential model. We discuss properties of this $\overline{K}\overline{D}N$ quasibound state which emerge uniquely in three-body dynamics.

Theoretical prediction of high pressure structural phase transition in PuBi with NaCl structure

ABSTRACTIn the present paper, we have investigated the high-pressure structural phase transition of plutonium bismuthide. We studied theoretically the structural properties of this compound (PuBi) by using the three-body potential model (TBI). This compound exhibits first order crystallographic phase transition from NaCl (B1) to body centred tetragonal (BCT) phase at 9.5GPa. The phase transition pressures, associated volume collapse and elastic behaviour of PuBi obtained from three body interaction (TBI) model show a good agreement with available experimental data.

Structural properties of BeO at high pressure

In the present paper, we have investigated the phase transition and elastic properties of BeO at high pressure using three-body potential model (TBPM). The present interaction potential consists of long-range coulomb and three-body interactions and short-range overlap repulsion effective up to second neighbour ions. We have studied the phase transition from wurtzite (B 4) to rock salt (B 1) for BeO. The phase transition pressure (P t) obtained from this approach shows a respectably good agreement with experimental and other theoretical data. We have also computed the collapse of relative volume changes (ΔV(P t)/V(0)). Three-body potential model has also been used to derive the correct expressions for third-order elastic constants and pressure derivatives of second-order elastic constants for BeO.

Structural Properties of CaS<sub>1-x</sub>Se<sub>x</sub> Mixed Crystal under High Pressure

The mixed ionic crystals are formed by the mixing of pure components and are truly crystalline and their lattice constants change linearly with concentration from one pure member to another. The present work is intended to investigate structural properties of CaS1-xSexunder high pressure. The structural properties of mixed compound CaS1-xSex(0≤x≤1) under high pressures have been evaluated using three body potential model (TBPM). This interaction potential has been calculated by using three model parameters. For this mixed compound, the experimental data has been generated by the application of Vegard’s law to experimental values available for pure end-point members.The Structure of CaS and CaSe has been Rock Salt (B1) at ambient pressure and with increasing pressure Rock Salt (B1) structure undergo a transition in Cesium Chloride (B2) at 40GPa and 38 GPa respectively and CaS1-xSexunder goes Rock Salt to Cesium Chloride (B1→B2) structure. The difference in phase transition pressure in end-point members is low. In the present work we have investigated structural properties at high pressure for five different concentration x (x=0, 0.25, 0.50, 0.75, 1) for CaS1-xSex. Phase transition pressure and relative volume collapse at different phase transition pressure for different values of x has been calculated. Predicted phase transition pressure and relative volume collapse are found in good agreement with experimental and other theoretical data. Linear variation of phase transition pressure and lattice constant of different composition show that Vegard’s law is valid for this alloy. We have evaluated the phase transition pressure from graphical analysis where the Gibb’s free energy difference ΔG [G(B1)-G(B2)] have been plotted against pressure (P) for CaS1-xSexfor different concentration x. The pressure at which ΔG approaches zero corresponds to phase –transition pressure (Pt). The relative volume changes, ΔV(Pt)/V(0), associated with the above mentioned compression have also been computed and plotted against pressure to get the phase diagram for CaS1-xSexin different concentration.

Structural phase transition of refractory metal carbides at high pressure

There has been significant concern in analyzing the structural stability, structural properties, and pressure-induced structural phase transition of refractory metal carbides, RC (R = Ti, Zr, Hf, V, Nb, and Ta), by using the three-body force potential model calculation modified approach. The more accurate description of the interionic spacing (r0) suggests that the interactions considered in the present computation are capable of correctly predicting the structural properties of these materials. In the preset paper, we have investigated the relative stability of the two competitive phases of metal carbides and discussed the possible phase transitions from its parental NaCl (B1) type phase to its most stable CsCl (B2) type phase in the pressure range 344–572 GPa. The computed interionic spacing (r0) and phase transition pressures (PT) are in reasonable agreement with the other reported data.

High Pressure Phase Transition and Allied Behavior οf Samarium Compounds

(Received March 6, 2012; revised version February 16, 2013; in nal form February 26, 2013) A theoretical study of the phase transition of samarium monochalcogenides using three-body interaction potential model is carried out at high pressure. The three-body interaction potential includes long range Coulombic, three-body interaction forces and short range overlap repulsive forces operative up to next nearest neighbor ions. We have investigated phase transition pressures, volume collapses, elastic behavior, stability criteria and various thermo physical properties at various high pressure. The results found are well suited with available experimental data. In this paper third order elastic constants are also reported for the rst time which helps in understanding the nature of interionic forces in ionic solids which paved the experimentalist to work in speci c direction.

Pressure-induced phase transition and thermophysical properties of cubic refractory metal nitrides: theory

The present paper reports the structural stability, pressure-induced phase transition, and thermophysical properties for refractory metal nitrides (viz: TiN, ZrN, HfN, VN, NbN, and TaN) computed using a three-body force potential model. The structural phase transitions from a parental NaCl (B1) type phase to the most stable CsCl (B2) type phase has been observed in the pressure range 162–370 GPa. Study includes the computation of thermophysical properties (U, f, θD, υ0,γ, β, αV/CV), where some of the properties are being reported for the first time on these materials.

Phase transition, structural, mechanical and thermal properties of erbium pnictides under pressure

In this article, we have investigated the high-pressure structural phase transition of erbium pnictides (ErX; X = N, P and As). An extended interaction potential model has been developed (including the zero-point energy effect in three-body interaction potential model). Phase transition pressures are associated with a sudden collapse in volume. The phase transition pressures and associated volume collapses have been predicted successfully. The elastic constants, their combinations and pressure derivatives are also reported. The pressure behaviour of elastic constants, bulk modulus and shear modulus have been presented and discussed. Moreover, the thermophysical properties such as molecular force constant (f), infrared absorption frequency (υ 0), Debye temperature (θ D) and Grunneisen parameter (γ) have also been predicted.

Pressure-induced Structural Phase Transitions in Ti1-xZrxC Solid Solution

In present paper we have analyzed the relative Structural stability and pressure dependent B1→B2 structural phase transformations in Ti1-xZrxC solid solution. For the present work, we have used three-body force potential model which includes the long range as well as short range interactions, where Coulomb and three body interactions are the contents of long range part and the van der Waals multipole interactions and the Hafemeister and Flygare overlap repulsive interactions (effective up to the next nearest neighbors) makes the short range part. The calculated transition pressures are 490, 461, 431, 402 and 372 GPa for TiC, Ti0.75Zr0.25C, Ti0.50Zr0.50C, Ti0.25Zr0.75C, and ZrC compounds respectively.

Structural and Thermophysical Properties of Cadmium Oxide

We have studied the structural and thermophysical properties of cadmium oxide (CdO), using the Three-Body Potential (TBP) model. Phase transition pressures are associated with a sudden collapse in volume. The phase transition pressures and related volume collapses obtained from this model show a generally good agreement with available experimental others data. The thermophysical properties like molecular force constant, Debye temperature, and so forth, of CdO are also reported.

Effect of covalency on high pressure phase transition and elastic behaviour of compound semiconductors: Gallium Pnictides and their alloys

We present the results of our calculations on phase transition and elastic properties of Gallium Pnictides by taking three-body interaction potential model, which is modified by taking covalency effect. Phase transition pressures are associated with a sudden collapse in volume showing the occurrence of first order phase transition. The elastic constants are also reported. Our model is able to explain Cauchy violation. The present study is extended to Gallium Pnictide alloys GaPxAs1−x, GaAsxSb1−x and GaPxSb1−x by using Vegard’s law. Our results are in general in good agreement with experimental and theoretical data where available.

TBI Calculations of the Elastic Properties and Structural Phase Transformation in Novel Materials: Yttrium Nitride

We have carried out high pressure theoretical structural studies of yttrium nitride to examine the phase transition phenomena from the NaCl structure to CsCl structure by using a three-body potential model. The phase transition pressure (140 GPa) predicted by this approach is close to the phase transition pressure, predicted by others (138 GPa). Yttrium nitride is a novel and less explored material. Under high pressure yttrium nitride goes through a sudden collapse in volume showing the first order phase transition. To understand the effect of pressure we studied bulk properties, elastic constants and their combination. The pressure volume equation of state provides meaningful signatures of physical and chemical phenomena under high pressure. Moreover we have successfully checked the stability criterion for this compound.

A simple model for calculating the bulk modulus of the mixed ionic crystal: NH4Cl1−x Br x

The ammonium halides are an interesting systems because of their polymorphism and the possible internal rotation of the ammonium ion. The static properties of the mixed ionic crystal NH4Cl1 − xBrx have been recently investigated, using the three-body potential model (TDPM) by applying Vegard’s law. Here, by using a simple theoretical model, we estimate the bulk modulus of the alloys NH4Cl1 − xBrx, in terms of the bulk modulus of the end members alone. The calculated values are comparable to those deduced from the three-body potential model (TDPM) by applying Vegard’s law.

Theoretical study of theKKK¯system and dynamical generation of theK(1460)resonance

The $K K\bar K$ system is investigated with a coupled channel approach based on solving the Faddeev equations considering the $KK\bar K$, $K\pi\pi$ and $K\pi\eta$ channels and using as input two-body $t$-matrices that generate dynamically the $f_0(980)$ and $a_0(980)$ resonances. In the present calculation, a quasibound state around 1420 MeV with total isospin $I=1/2$ and spin-parity $J^\pi=0^-$ is found below the three kaon threshold. This state can be identified with the K(1460) resonance listed by the Particle Data Group. We also study the $KK\bar K$ system in a single channel three-body potential model with two-body effective $KK$ and $K\bar K$ interactions, in which the $K\bar K$ interaction is adjusted to reproduce the properties of the $f_0(980)$ and $a_0(980)$ resonances as $K\bar K$ bound states, obtaining a very similar result to the one found in the Faddeev approach.

Elastic properties of alkaline earth oxides under high pressure

In this article, we have investigated the high-pressure structural phase transition of alkaline earth oxides using the three-body potential (TBP) model. Phase transition pressures are associated with elastic constants. An effective inter-ionic interaction potential (TBP) with long-range Coulomb interactions and the Hafemeister–Flygare type short-range overlap repulsion and the vdWl interaction is developed. The present calculations have revealed reasonably good agreement with the available experimental data on structural transition (B1–B2 structure). The phase transition pressures Pt of MgO, CaO, SrO, and BaO occur at 220, 45, 40, and 100 GPa, respectively. Further, the variations of the second-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. It is found that TBP promises that we would be able to predict phase transition pressure and elastic constants for other chalcogenides as well. The results may be useful for geophysical study.

Structural phase transition in NdAs

A consistent calculation has been performed to describe the structural phase transition of NdAs using a well known three-body interaction potential model (TBIPA). Phase transition pressure is associated with a sudden collapse in the volume. The computed results on the phase transition pressure, volume collapse and pressure derivative of bulk modulus have shown a reasonably good agreement with their accurately measured data. In view of its overall success TBIPM has been regarded an adequate and appropriate model suitable for high-pressure studies.

Theoretical analysis of static properties of mixed ionic crystal: NH4Cl1−x Br x

In the present paper, we have investigated the static properties of the mixed ionic crystal NH4Cl1ixBrx using three-body potential model (TBPM) by the application of Vegard's law. The results for the mixed crystal counterparts are also in fair agreement with the pseudo-experimental data generated from the application of Vegard's law. The results for the end point members (x = 0 and 1) are in good agreement with the experi- mental data. The results on compressibility, molecular force constant, infrared absorption frequencies and Debye temperature are presented probably for the flrst time for these mixed crystal counterparts.

Final-state interaction between nucleons in elastic deuteron breakup within the three-body potential model

The diffraction deuteron breakup has been investigated within the three-body potential model, where the final-state interaction between nucleons is described nonperturbatively with respect to the pn potential. The triple differential cross section of the (d, pn) reaction on 40Ca at deuteron energies of 140, 200, and 270 MeV and small emission angles of nucleons have been calculated for two schemes of the kinematically complete experiment. Noneikonal and nonadiabatic corrections to the cross section are small and do not change the shape of the peak in the proton energy spectra.