Showing papers on "Interatomic potential published in 1980"

Thermal expansion in insulating materials

Abstract: A model of thermal expansion in terms of the Morse potential which was developed earlier for low temperatures is extended to high temperatures and applied to a semiempirical calculation of thermal expansion in insulating materials. In this model, the localized quantum mechanical solutions of the Morse potential are combined with the Debye model to give a localized-continuum description of thermal expansion. A set of empirical rules is developed for characterizing the interatomic potential in terms of the Morse potential. These are then applied to the quantitative calculation of thermal expansion in the alkali halide crystals and a group of binary high temperature materials with the aid of the known crystal structures, compressibilities, and Debye temperatures of these materials. Good agreement between calculated and experimental values is obtained for temperatures ranging between 0 K to values near the melting points. A discussion of the underlying basis of the empirical rules is given as well as their likely applicability to a wide range of insulating materials.

A reliable single parameter interatomic potential for argon

Abstract: A simple semiempirical approximation previously proposed for the isotropic intermolecular forces between two closed shell systems is tested in detail for the argon-argon interaction. The potential is based on the knowledge of the first-order coulomb interaction energy, a suitably damped three term long range asymptotic expansion of the second order coulomb energy, and a semiempirical representation of the exchange interaction energy which contains one adjustable parameter. The single adjustable parameter can be reliably determined by fitting the second virial coefficient for argon in the 130–773 K temperature range with the long range interaction coefficients being constrained within the theoretical bounds specified by Tang, Norbeck and Certain. The reliability of the potential is compared with that of several literature potentials by comparing the theoretical predictions obtained from the potentials with experimental results for the second virial coefficient, viscosity, thermal conductivity and thermal d...

The structure of small vacancy clusters in face-centred-cubic metals

Abstract: In face-centred-cubic metals it is possible to form four distinct types of close-packed trivacancy and 20 types of tetravacancy. The structures and energies of these clusters have been investigated using computer-simulation methods and an interatomic potential representing copper. One of the trivacancies and six of the tetravacancies are found to relax to collapsed forms and it is these clusters that have the lowest epergies.

Charge exchange and fine-structure excitation in O-H + collisions

Abstract: The charge exchange reaction O+H+ to O++H is reinvestigated after a detailed examination of the interatomic potential curves and the couplings responsible for the process. The long-range behaviour and the problem of the connection between the long-range and the short-range potentials are considered. The charge exchange collision is then treated in a close-coupling formalism and we take account of the fine-structure excitation process which can occur simultaneously. The results are in accordance with the experimental measurements of Fehsenfeld and Ferguson (1972) and are much smaller than the previous theoretical estimates.

Empirical determination of thermal expansion in insulators with no experimental input

Abstract: The localized-continuum model of thermal expansion which was applied to insulators in the previous paper is further refined by empirical means to allow the calculation of thermal expansion in insulating materials with no input other than the chemical formula. Estimation of the Madelung constants is made by using the empirical methods of Kapustinsky and Templeton while the atomic nearest-neighbour distances are estimated by using atomic radii tables. Approximate values of repulsive exponents are obtained by using an empirical scaling rule and a table of monovalent repulsive exponents. The Debye temperature is approximated by a simple formula involving the estimated parameters of the interatomic potential. Using this approach, thermal expansion is estimated in a group of binary and complex ternary materials and a group of complex salts. The agreement with experiment is generally good, although the elimination of experimental input appears to increase the probable error in the calculations by 15% to 20%. The results indicate that this approach is capable of predicting with reasonable accuracy the thermal expansion in a wide range of insulating materials with no experimental input and no adjustable parameters. The limitations of this method for certain cases is also discussed.

Shift and broadening of hyperfine components of the first doublet of cesium perturbed by foreign gases

Abstract: The collision broadening and shift of the hyperfine structure components of the ground-state splitting for the D_1 (8943 A) and D_2 (8521 A) cesium lines by noble gases (He, Ne, Ar, Kr, and Xe) and by light molecular gases (H_2 and N_2) under pressures not greater than 150 Torr and at a temperature of 295 K are investigated. The Lennard-Jones (12-6) interatomic potential constants are calculated for these systems, using the semiclassical theory of Lindholm-Foley (for Cs with Ne, Ar, Kr, Xe, and N_2 systems) and the quantum theory of Baranger (for Cs with He and H_2 systems), by comparing with our experimental results in fine structure. These potential constants are employed for the determination of the shift and broadening in hyperfine structure, using the hyperfine theory of collision broadening.

Re‐analysis of single‐crystal neutron‐diffraction data on UO2 using third cumulants

Abstract: The single-crystal neutron diffraction data on UO2, recorded by Willis [Proc. R. Soc. London Ser. A, (1963), 274, 134-144] over the temperature range 293 to 1373 K have been re-analysed. The analysis was carried out with a structure-factor equation which included the third-cumulant coefficient, c123, of the O atom. (The symmetry of the fluorite structure reduces the remaining third-cumulant coefficients of O and all the third cumulants of U to zero.) Apart from the overall scale factor, there were three parameters to be refined at each temperature: the isotropic B factors of U and O and c123 of O. The temperature variation of the B factors is in reasonably close agreement with that predicted from lattice dynamics [Dolling, Cowley & Woods (1965), Can. J. Phys. 43, 1397-1413]. If c123 is to be ascribed to the influence of anharmonic forces on the motion of the atoms, an Einstein model of the interatomic potential predicts that c123 should be approximately proportional to T2, where T is the absolute temperature. The experimental data are consistent with this prediction, but data of higher accuracy are required for a rigorous test.

Collision-induced Raman spectra of neon and the diatom polarizability

Abstract: Two collision-induced Raman spectra of gaseous neon are obtained, one with the linear polarization of the incident beam parallel to the direction of observation, and the other perpendicular. Absolute intensities are determined relative to nitrogen lines of known intensities. The comparison reveals the presence of a polarized contribution previously seen only in one other gas, helium. In addition, a depolarized component is obtained which agrees with and supplements an earlier measurement. For a direct comparison with experiment, collision-induced Raman spectra are also computed from wave mechanics, using models of the invariants (trace and anisotropy) of the neon diatom polarizability as input. For the depolarized spectrum an empirical model of the anisotropy is obtained which differs from the classical point-dipole expression by only 10% at the internuclear separation of 2.69 \AA{}, the root of the interatomic potential. Similar attempts are made to develop an empirical trace model that is consistent with both the polarized spectrum and an earlier measurement of the second virial dielectric coefficient.

Density of electronic states in amorphous metals: Effect of structural variation due to interatomic-potential softness

Abstract: A study has been made of the effect of structural changes in hard-sphere models due to relaxation under soft interatomic potentials on the density of $d$ states in amorphous transition metals. We have used models based on Morse, Morse truncated, and Lennard-Jones forms of interatomic potentials. It is found that the bandwidth increases as the hard-sphere model is relaxed and the average density of states in various relaxed models has double-peaked structure except for Morse potential where an extra little peak appears near the bottom of the band. A study has also been made of the local density of states in two models and it is found that the local density of states is governed by the local radial distribution of near neighbors.

Interaction energy between two ground-state helium atoms using many-body perturbation theory

Abstract: Diagrammatic many-body perturbation theory is applied to the calculation of potential-energy curves for ${\mathrm{He}}_{2}$. Both model and shifted perturbative procedures are described. The shifted scheme produces a spurious $R$ dependence for the long-range interatomic potential in both second and third order. Variational-perturbative upper-bound methods produce energies that approach an incorrect asymptotic limit at large internuclear distances. In contrast, the model-perturbative scheme in both second and third order achieves a proper distance dependence for the ${\mathrm{He}}_{2}$ potential curve. Four basis sets are employed to illustrate basis-set effects.

The shape of the inner-wing satellites of self-broadened first resonance lines of caesium and rubidium

Abstract: Theoretical satellite profiles have been calculated by means of the modified quasi-static approximation. Comparison with the experimental results shows that the shape of the theoretical satellite band depends on precise knowledge of the interatomic potential curves. A simple quadratic approximation of the 0g-(2P32/+2P32/+2S12/) potential curve near the extremum was also tested in the case of the caesium 8565 AA satellite band.

An X-ray diffraction study of lattice compression of theL10-type intermetallic phase PdZn

Abstract: The pressure dependence of the lattice parameters of PdZn having an L10-type structure has been measured up to 24 GPa (240 kbar) with a diamond-anvil-type cell and sodium chloride as an internal-pressure marker. The axial ratio c/a, which was originally 0.814 (1) [between the two extreme values 1.00 and 0.707 (= 1/ \sqrt{2}) for this type of structure], does not decrease but increases with increasing pressure and after reaching 0.822 at 10 GPa it remains almost constant on further compression. The equation of state has been derived for the L10-type structure assuming pairwise interactions between like atoms and between unlike atoms and comparison is made between the calculated and observed compression curves of the a and c axes. The anisotropy in the lattice compressibility leads to a considerably larger interatomic potential for the unlike atom pair than for the like atom pair.

Calculation of the lattice distortion due to carbon in α -iron

Abstract: A method for calculating the static displacements of lattice atoms near a defect atom is presented and applied to carbon occupying the octahedral site in α-iron. The interaction between lattice atoms and the defect is assumed to extend to second neighbors, but a defect-lattice atom interatomic potential is neither assumed nor constructed. Instead the displacements of the first and second neighbors of the defect atom are treated as adjustable parameters, which can be determined experimentally, and the displacement field is calculated as a function of these parameters. A central, two-body Morse potential is used to describe the interaction of lattice atoms, and the lattice atom displacements are calculated for both harmonic and anharmonic (quartic) approximations of the potential. The latter calculation requires an iterative procedure that obtains self-consistent anharmonic displacements without sacrificing the convenience of the matrix inversion technique that is used to solve the harmonic problem.

A closed form for the second virial coefficient of the Lennard-Jones gas

Abstract: The Lennard-Jones interatomic potential for spherically symmetric particles is given by U(r)=M/rm-N/rn, where r is the separation of the centres of the particles, and M and N are positive constants. The classical second virial coefficient for such a gas is evaluated in closed form for the case m=2n, in terms of the parabolic cylinder functions. To leading order, dipole-dipole interactions give n=6, so these results are applicable to the case m=12, which is fortuitously close to the best empirical value.

A new composite interatomic potential

Abstract: A new interatomic potential is proposed and its validity over a large atomic separation is assured by comparing calculated nuclear stoppings and range parameters with experimental results.

Time correlation functions in classical dense fluids

Abstract: The velocity autocorrelation functions and memory functions of dense classical fluids may be directly obtained from the static radial distribution function g(r) in an approximate way. Following the Mori projection operator formalism, the memory functions may be related to the fluctuating force correlation. At low densities, these functions may be evaluated by following the trajectories of particle pairs in the interatomic potential. At higher densities, the force correlation functions can be evaluated approximately from particle pair trajectories via the potential of the mean force. The results for argon fluids at various densities and temperatures agree satisfactorily with the molecular dynamics and the Enskog values. The decrease of the diffusion coefficient with density is partly due to the nature of g(r) which reflects the stronger clustering of atoms at higher densities.

Computer simulation of atomic structure of Fe75P25 amorphous alloy.

Abstract: A computer model of the amorphous structure of Fe75P25 alloy has been constructed by random positioning of the two species of atoms followed by relaxation. Taking acount of the similarity in partial radial distribution functions (PRDF's) between amorphous Fe75P25 reported in the literature and crystalline Fe3P, a special non-spherical interatomic potential has been used for the Fe-P pair to stabilize the trigonal prism unit that constitutes the Fe3P crystal. The PRDF curves obtained show general agreement with experimental ones. In particular, the characteristic wide splitting of the second peak in Fe-P PRDF is reproduced. This indicates that the structure of amorphous Fe75P25 reflects chemical interaction between Fe and P atoms.

Re-examination of the Structures of Plane Faults in B.C.C. Metals

Abstract: The structures of the twin boundary and the stacking fault in body-centered cubic metals have been studied by computer simulation. Particular consideration has been given to the method of the lattice relaxation in order to distinguish more than one stable configuration, if any, of a fault. With the use of the Johnson potential as the interatomic potential, it is confirmed that two types of {112} twin boundaries, the symmetrical boundary and the displaced boundary, are stable. Two kinds of {112} stacking faults, I1 and I2, are found. The I1 fault is stable only under shear stress. The change in the crystal energy is traced in correspondence with the configurational change of a fault. The structures of multilayer faults are also studied.