Effect Of Three-body Interactions Research Articles

Effects of three-body interactions on the structure of clusters

The structure of 54 and 147 atom clusters was studied using molecular dynamics at constant temperature and incorporating three-body interactions to the usual pairwise additive potentials among atoms. The effects of three-body interactions of the triple-dipole and exchange overlap type on the aggregation of clusters are: (1) to diminish the coordination number resulting in a global expansion of the clusters; (2) to increase internal disorder in such a way as to lower the crystallization temperature; (3) to favor certain features characteristic of random close packing of spheres at the expenses of destroying locally paired tetrahedra and octahedra, in the temperature range 0.25 ⩽ T ⩽ 0.4.

Effects of three-body interactions on the structure of clusters

Effects of three-body interactions on the structure of clusters

Effect of three-body interactions on the formation entropy of monovacancies in copper, silver and gold

The vacancy formation entropy in Cu, Ag and Au is estimated from model calculations with explicit treatment of three-body interactions. The three-body interactions cause a rather strong relaxation around the vacancies and therefore lead to lower values for the formation entropy than usual pair-potential calculations.

Effect of three-body interactions on the electronic polarizabilities and photoelastic behaviour of ammonium halides

The effect of three-body interactions (TBI) on the electronic polarizabilities and photoelastic behaviour of ammonium halides has been studied in the framework of a three-body force shell model. This model takes proper account of Cauchy violation and gives and excellent description of various crystal properties of ionic solids. The strain derivatives of electronic polarizabilities have been evaluated through the influence of crystal potential on the polarizabilities of ions. The photoelastic behaviour has been studied by determining the strain derivatives of electronic dielectric constant. The strain derivatives of electronic polarizabilities and dielectric constants for ammonium halides are reported for the first time.

Depolarized light scattering studies of the collision induced polarizability anisotropy of atoms and spherical top molecules

New measurements are reported of the density dependent depolarization ratio for argon, krypton, xenon, methane and sulphur hexafluoride, and the results are analysed to provide values for the second and third depolarization virial coefficients. The relationships between the second depolarization virial coefficient, the zeroth moment of the two-body Rayleigh spectrum and the second Kerr virial coefficient are considered, and it is shown that they now provide consistent results for the collision-induced pair polarizability anisotropy. Former inconsistencies are attributed to insufficient allowance for the effects of three-body interactions. Calculations of the second and third depolarization virial coefficients based on the DID model and using the Maitland-Smith potential are in excellent agreement with the experimental results for argon, krypton and xenon.

Effect of three-body interactions on electronic polarizabilities and photoelastic behaviour of partially covalent crystals

We have investigated the effect of three-body interactions on the photoelastic behaviour and the electronic polarization of silver, thallium and copper halides, which are partially covalent in character and possess three different crystall structures. The cation, anion and molecular polarizabilities calculated in their crystalline state seem to be reliable as they follow a systematic trend. Our calculated values of the strain derivatives of the electronic dielectric constants are much closer to their experimental data than those obtained by earlier workers.

On Crystal Binding and Thermophysical Properties of Copper and Thallium Halides

An analysis of the cohesive and thermophysical properties of the halides of copper and thallium has been performed by modifying Hafemeister and Flygare (MHF) potential to include the three-body interaction effects. This modified HF potential is found to yield a better description of the above properties than those obtained by earlier workers. The universality of the present MHF potential with the importance of the significant role of the three-body and van der Waals interactions is also emphasised.

Effect of three-body interactions on the structure of small clusters

Minimum energy configurations of microclusters (up to six atoms) have been calculated using two- and three-body interactions. Structural changes were parametrically analyzed as a function of the intensity of three-body forces. The results are qualitative in nature; they indicate, however, that three-body interactions play an important role in the equilibrium structure of microclusters. The effect of the intensity of the three-body interactions on the structure of small clusters is not manifested in a continuous manner. Rather, changes in the energetically most stable structure occur abruptly. The results are in qualitative agreement with experimental observations as well as other calculations.

Effect of three-body interactions on the ordering of bcc binary alloys

The composition dependence of the order---disorder critical temperature is investigated for a model binary alloy equivalent to an Ising system with both the nearest-neighbor interactions ($J$) and the three-particle interactions ($P$) present. Using a real-space renormalization-group method for calculating the phase diagram, we find that for small three-body forces, the maximum critical temperature shifts from the 50-50 atomic percent composition proportionally to $\frac{P}{J}$. The proportionality constant is determined both from the renormalization-group method and from Griffith's smoothness postulate. The results of the two calculations agree with each other, and they are used to estimate the relative strength of the three-body potentials in iron cobalt. The estimate $\frac{P}{J}=0.11\ifmmode\pm\else\textpm\fi{}0.06$ indicates that three-body forces are small, so that the nearest-neighbor Ising model is a good first approximation for the description of ordering in FeCo.

Three-body interaction effects on cohesive properties of alkali halides

I t is now well known that three-body interactions (1.3) arise due to the overlap of adjacent ions and play a significantly impor tant role in the description of lattice dynamical, dielectric and elastic properties (4.~) of ionic crystals. However, the problem of investigation of their role to predict the cohesive properties has received very scant at tent ion. I t happened only recently when SIIA~.~A et al. (v) have studied the effect of three-body interactions (TBI) on cohesive energy of alkali halides via Singh and Vcrma model (4). The results obtained by them have led to the conclusion that the effect of TBI incorporated in the manner of SINGH and V~RMA (4) introduce large deviations while their inclusion through Basu and Sengupta model (s) is free from such limitations. With such remark in mind we have recalculated the cohesive energy of rocksalt and cesium-chloride type alkali halides on the basis of Singh and Verma model with Coulomb, Born-Mayer type overlap repulsive and three-body interactions. The results obtained by us show excellent agreement with measured cohesive energies for all the alkali halides except for LiF and RbI. Itowever, the deviation in these extreme solids also is not more than 14%. The aims of this paper are twofold. The aim of this work is to introduce TBI in the manner indicated by Singh, because the numerical calculations performed by Sharma have been found in error. We will also show that the inclusion of Van tier Waals interactions and zero-point energy improves the agreement remarkably. The agreements thus obtained are almost exact and comparable to those already obtained by Sarkar and Sengupta (8) using three-body potential of Basu and Sengupta (s) together with vdW dipole-dipole and dipole-quadrupole interactions and second-neighbour short-range interactions.

The inclusion of three-body forces and the condition of equilibrium into the models of Krebs and Cheveau

It is proposed that the effects of three-body interactions on the phonon dispersion curves of metals be investigated by adding the third-order perturbation term in the electron-ion potential obtained by Lloyd and Sholl (1968) for a local electron-ion potential to the model of Krebs (1965) with two-body forces, or the model of Cheveau (1968) extended to second-nearest neighbours. The constraining equation required by equilibrium is determined for the phenomenological models of Krebs and Cheveau. The constraint equation can be used as an additional equation for determining unknown parameters in these models.

Crystal Dynamics of Magnesium Oxide

The crystal dynamics of magnesium oxide have been studied by incorporating the effect of three-body interactions in the framework of the shell model on the lines of the work of Singh and Verma [Phys. Rev. B 2, 4288 (1970)]. The theoretical dispersion curves in the three symmetry directions and specific-heat variation with temperature have been calculated and compared with the corresponding experimental results. The experimentally observed second-order infrared absorption and the Raman spectra have also been interpreted by using the critical-point analysis and the combined-density-of-states approach. An excellent agreement has been obtained with the recently measured neutron-scattering, specific-heat, and second-order infrared-absorption and Raman-scattering data.

Three-Body Interaction Effects in High-Energy Scattering from Deuterons

Corrections to the Glauber multiple-scattering expansion due to three-body interactions are studied. The particular interaction considered corresponds to the scattering of an incident particle from a pion being exchanged by the two nucleons composing a deuteron. It is shown that the resulting correction to the scattering amplitude must be modified to take into account the possibility of absorption on the nucleons. A crude numerical estimate indicates corrections of about -0.4% to the total cross section at very high energy. The effect on the differential cross section at large momentum transfer is difficult to estimate reliably, but the formulas obtained suggest that the corrections could become quite important unless there is a strong off-shell damping mechanism.

Validity of the Assumption of Two-Body Interactions in Molecular Physics

The treatment of three-body van der Waals forces between hydrogen or helium atoms, given in an earlier paper, is extended to the heavy rare gas atoms. Two of the three atoms are supposed to be close together (e.g., nearest neighbors in a crystal), whereas the third atom is considerably farther away. Expressions are given for the induced dipole-dipole and dipole-quadrupole components of the field. The electronic charges in the atoms are represented by Gaussian distribution functions. The results are applied to a determination of the most stable crystal structure of the heavy rare gases at absolute zero temperature (excluding zero-point energy); it is found that the face-centered cubic crystal is favored over the hexagonal close-packed by about one-tenth of one percent of the van der Waals cohesive energy, if the first and second shells of neighbors are excluded from the region of summation for the third atom. If this restriction is dropped, then the difference between the two structures vanishes, while the effect itself rises abruptly and very steeply. The effect of three-body interactions in general is to weaken the attractive forces in the crystalline state. Under the above restriction, the relative magnitude of these interactions is twenty percent of the van der Waals cohesive energy for xenon. The three-body forces vanish identically if the Gaussian goes over into a Dirac $\ensuremath{\delta}$ function.