Realistic Pair Research Articles

On the Possibility of a Biaxial Smectic A Phase

Abstract The existence of a uniaxial-biaxial phase transition in a smectic A phase is shown theoretically, based on the more realistic anisotropic pair potential and within the mean field approximation. The resulting phase diagram exhibits successive phase transitions of isotropic-uniaxial nematic-uniaxial smectic A-biaxial smectic A and a uniaxial nematic-uniaxial smectic A-biaxial smectic A triple point. The possible assignment of the predicted biaxial smectic A to some phase classified recently as a smectic C is discussed.

A Structure Model and the Description of Structural Changes in Amorphous Metals

AbstractThe structure of an amorphous metal is assumed to consist of an arrangement of structural units which are generated from a basic unit by a coordination transformation. The parameters of the transformation matrix are distributed statistically. The basic unit is produced by energy relaxation of an assembly of dense random packed hard spheres and a dense arrangement of several icosahedral clusters of compressible spheres, respectively. The model provides realistic pair distribution functions. An interpretation of structural changes which occur during low‐temperature annealing and isothermal creep in amorphous substances is suggested.

Applications of liquid state physics to the Earth's core

By use of the modern theory of liquids and some guidance from the hard-sphere model of liquid structure, the following new results have been derived for application to the Earth's outer core. (1) d K/ dP ⋍ 5 − 5. 6P / K, where K is the incompressibility and P the pressure. This is valid for a high-pressure liquid near its melting point, provided that the pressure is derived primarily from a strongly repulsive pair potential φ. This result is consistent with seismic data, except possibly in the lowermost region of the outer core, and demonstrates the approximate universality of d K/d P proposed by Birch (1939) and Bullen (1949). (2) dln T M/dln ρ = ( γC V − 1)/( C V − 3 2 ), where T M is the melting point, ρ the density, γ the atomic thermodynamic Grüneisen parameter and C V the atomic contribution to the specific heat in units of Boltzmann's constant per atom. This reduces to Lindemann's law for C V = 3 and provides further support for the approximate validity of this law. (3) It follows that the “core paradox” of Higgins and Kennedy can only occur if γ < 2 3 . However, it is shown that γ < 2 3 ⇔ ∫ ∞ 0 (∂g/∂T) ρ r( d/ dr)(r 2 φ) dr > 0 , which cannot be achieved for any strongly repulsive pair potential φ and the corresponding pair distribution function g. It is concluded that γ > 2 3 and that the core paradox is almost certainly impossible for any conceivable core composition. Approximate calculations suggest that γ ∼ 1.3–1.5 in the core. Further work on the thermodynamics of the liquid core must await development of a physically realistic pair potential, since existing pair potentials may be unsatisfactory.

Quasiharmonic theory of two-dimensional crystals: I. Lennard-Jones potentials, quantum corrected cell theory, and the quantum mechanical principle of corresponding states

The quasiharmonic approximation of lattice dynamics is used to calculate the frequency spectrum, the dynamical contribution to the free energy, and the thermal expansion of a two-dimensional hexagonal lattice. Results for a Lennard-Jones (12, 6) pair potential are presented in a tabular form which enables corresponding-states scalings to be used to form estimates of the thermal expansion for a variety of adsorbed inert gas monolayers. The magnitude of anharmonic corrections to this approximation is tested by comparing the equilibrium lattice constant obtained from quasiharmonic theory with the results of a quantum-corrected cell-model theory. The conclusion is that the quasiharmonic theory may be used to calculate the lattice constant with a precision of 0.01 Å in a proposed analysis of the lateral interactions in an adsorbed xenon monolayer in the temperature range 1 to 50 K. These methods are readily extended to more realistic pair potentials and permit the inclusion of substrate-mediated interactions for physisorbed monolayers.

Structure and dynamics of a two-component metallic glass

The structure of a two-component metallic glass (Mg70Zn30) is described by a relaxed model structure of 800 atoms. The authors use realistic pair potentials calculated from general nonlocal pseudopotential theory, and periodic boundary conditions. The cluster has been given the shape of a regular rhombic dodecahedron, the most sphere-like space filling body. The homogeneity of the cluster is tested by the calculation of the spectrum of Einstein frequencies. The total and the two partial pair distribution functions, the corresponding structure factors S(k) and the dynamical structure factor S(k, omega ) for longitudinal and transverse waves for a whole series of k vectors are calculated. S(k, omega ) allows the determination of the range of reasonably well defined dispersion relations.

A simple computer modelling of metallic amorphous structure

A metallic amorphous structure model has been constructed on a computer such that an assembly of atoms are spread at random in a cube, under the restriction that no two atoms are closer than a given core diameter, and are then subjected to relaxation through Johnson's interatomic potential (1964) to obtain a minimal energy configuration. The results, without depending on the core diameter, show both a high packing fraction ( eta =0.74) and a realistic pair distribution function.

Third Virial Coefficients for Helium

Third virial coefficient for helium is calculated using the realistic Beck pair potential. The first quantum correction and the triple-dipole dispersion interaction are included. The results are compared with experimental data and with theoretical values obtained using the MDD-2 pair potential.

Electron gas exchange for atoms

Current use of electron gas theory for exchange allows calculations of Hartree-Fock (HF) energies through the use of local potentials. A recent proposal of Gopinathan, Whitehead, and Bogdanovi\ifmmode \acute{c}\else \'{c}\fi{} to use a realistic pair correlation function ${f}_{\ensuremath{\uparrow}\ensuremath{\uparrow}}(1, 2)$ that incorporates the boundary conditions of Kutzelnigg, Del Re, and Berthier, which consider the finite number of electrons of a given spin, showed much better agreement with atomic HF calculations. This paper explores the use of an improved ${f}_{\ensuremath{\uparrow}\ensuremath{\uparrow}}(1, 2)$ either with the electron cloud form (exponential) or with a modified Wigner form. The total energies obtained from this method are in excellent agreement with HF total energies. The calculated total energies lie above the HF values; we interpret this as an open possibility for the inclusion of refinements such as the inhomogeneity corrections.

Correlations in the Motion of Particles inα-AgI: A Molecular-Dynamics Study

I have performed molecular-dynamics calculations for $\ensuremath{\alpha}$-AgI at 563 K using a realistic pair potential and a model system of 256 particles. I investigated the influence of ${\mathrm{I}}^{\ensuremath{-}}$ ions on single-particle motion in the ${\mathrm{Ag}}^{+}$ subsystem. In addition, I showed that correlations between different ions must be distinctly reflected in frequency-dependent conductivity.

Medium perturbations of atomic extravalence excitations

In this paper we present the results of an experimental study of the lowest 1S0→3P1 extravalence electronic excitation of atomic xenon in dense supercritical and subcritical fluid argon over the density range 0.1–1.4 g⋅cm−3, spanning the temperature region 80–300°K. Solvent perturbations were characterized in terms of the spectral shift, the linewidth and the first and the second moments of the absorption band. These energetic parameters exhibit a weak temperature sensitivity and a strong density dependence. The experimental data were analyzed in terms of the semiclassical theory of line broadening extended to account for guest–host and host–host correlations and incorporating realistic pair potentials in the ground and in the excited electronic states. The semiclassical theory results in manageable expressions for the first and for the second moments of the absorption band which are expressed in terms of a difference guest–host interaction potential together with the solute–solvent and the solvent–solvent radial distribution functions. The theory provides a semiquantitative account for the weak temperature dependence and for the marked density dependence of the energetic parameters specifying solvent perturbations and was utilized to extract quite reliable information concerning the excited state Xe(3P1)+Ar(1S0) potential.

Nonadditivity contribution to the surface tension of simple liquids

The Kirkwood-Buff formula has been extended to include three-body interactions by differentiation of the partition function with respect to the area. Assuming a step-function density profile (Fowler) and the superposition approximation (Kirkwood) for the triplet correlation function, the nonadditivity correction ${\ensuremath{\gamma}}_{3}$ to the surface tension is expressed as a septuple integral whose integrand contains the three-body interaction potential ${u}_{123}$ and the radial distribution function of the liquid $g(r)$. We use the triple-dipole interaction (Axilrod-Teller) for ${u}_{123}$ and the neutron diffraction data of Yarnell etal for liquid Ar at 85\ifmmode^\circ\else\textdegree\fi{}K to represent $g(r)$. It is necessary to make several changes of variable and inversions of the order of integration in order to transform the integral into a sextuple integral which can be programmed without incurring large errors due to cancellation. The result for Ar at 85\ifmmode^\circ\else\textdegree\fi{}K is ${\ensuremath{\gamma}}_{3}=\ensuremath{-}4.5$ erg/${\mathrm{cm}}^{2}$, which is not negligible when compared with the experimental surface tension (13.1 erg/${\mathrm{cm}}^{2}$). When ${\ensuremath{\gamma}}_{3}$ is combined with ${\ensuremath{\gamma}}_{2}$ [the surface tension computed in the Kirkwood-Buff-Fowler approximation from realistic pair potentials for Ar using the same $g(r)$ data], the total surface tension is significantly smaller than the experimental value.

Triplet correlations in disordered systems: A study for liquid rubidium

The triplet correlation function for liquid rubidium is determined by molecular dynamics. Calculations were based on a realistic pair potential for a density rho =0.0107 AA-3 and a temperature T=319K. The results are compared with various models.

The volocity autocorrelation function and the effect of the long-range interaction in liquid rubidium

For liquid rubidium at 319°K moleculardynamics calculations using a realistic pair potential and a model system of 432 atoms have been performed. The cut-off radius for the potential was taken alternatively at 4.5 and 9.8 Å. The corresponding velocity autocorrelation functions and fourth moments of the scattering law were determined. The differences in the results for the two cut-off radii are attributed to long-range effects.

Interatomic potentials and phonon spectra of dilute rare-gas mixtures

We have applied existing theoretical results for the impurity induced ir absorption in dilute alloys to study the following rare-gas mixtures: Ar–Ne, Ar–Kr, Kr–Ar, and Kr–Xe. The theory takes into account both mass and force-constant changes, within the harmonic approximation. In evaluating the latter, attempts were made to use realistic pair potentials. We have, surprisingly, identified a resonance mode for an argon crystal doped with neon, and a localized mode in krypton doped with xenon system. The predicted resonance mode agrees well with the observed spectrum of Keeler and Batchelder. Our model for krypton doped with xenon gives rise to a localized mode which happens to fall very close to the band edge. Any attempt to shift this mode far from the band edge would require an unreasonably large change in the force constant around the xenon site. Within the framework of our model and the assumption of randomly distributed impurity atoms, we find it difficult to support the observation of this mode claimed by Obriot et al. However, once allowance is made for the experimental resolution, their in-band recorded spectra for both Kr–Ar and Kr–Xe agree fairly well with the theoretical predictions. On comparing our results for the in-band absorption of the Ar–Kr system, with the experiments of Keeler and Bachelder, we found it necessary to allow for the finite lifetime of pure-lattice phonons even at low temperatures. Such an effect appears to have a profound influence on the relative intensities in different regions of the absorption band. This effect does not appear to have been discussed previously in the literature.

Influence of the two-body potential on the radial distribution function of liquid 4He

The theoretical ground-state radial distribution function of liquid 4He appears to depend much more sensitively on the range of the assumed two-body potential than on its depth. Fairly good agreement with experiment is obtained by using realistic pair potentials.

Lattice Dynamics of fcc Argon with Three-Body Forces

Phonon spectra are calculated for fcc $^{36}\mathrm{Ar}$ at 4, 40, and 77 \ifmmode^\circ\else\textdegree\fi{}K using the pair potential for argon atoms derived by Bobetic and Barker. The calculation employs a quasiharmonic basis with three-body forces and a perturbation-theory treatment of the anharmonicity. Poor agreement is obtained with the experimental temperature shifts of transverse phonons propagating along the $[\ensuremath{\xi}00]$ direction. Self-consistent phonons are also calculated at 0 \ifmmode^\circ\else\textdegree\fi{}K for both the Bobetic-Barker and Dymond-Alder potentials. On the basis of existing phonon data, the latter appears to be ruled out as a realistic pair potential.

The Second Virial Coefficient for the Realistic Pair Potential.

An analytical formulation for the second virial coefficient is given for a spherically symmetric potential function of a simple form which has been called a realistic pair potential. This potential, given as an inverse relationship with rasa function of U, is capable of being much softer than a Lennard-Jones in the extreme of close approach. Differing forms of the result are given, including an expression by means of the generalized hypergeometric series. The result is also expressed in terms of the second virial coefficient for the (12, 6) potential.

On the theory of nuclear reactions

The collision of a non-relativistic nucleon with a nucleus is considered in the second quantization representation, the Hamiltonian of the system containing the nucleon-nucleon interaction potentials. The formulae for the optical potential, the scattering amplitudes and the reactions are obtained. It is shown that these amplitudes can be represented as a sum of two parts, one of which has a resonance character and corresponds to the compound nucleus mechanism. The optical potential parameters are calculated in the statistical model of the nucleus with realistic pair forces between the nucleons.