Partial Distribution Functions Research Articles

Structural study of superionic phase of AgI

A detailed analysis of the X-ray scattering intensity of alpha -AgI has been carried out by an anomalous scattering technique. The two partial interference functions Sijdif(Q) for Ag-Ag and Ag-I pairs were estimated using the newly developed theoretical equations of the intensity. The partial distribution functions for I-I, Ag-I and Ag-Ag pairs in this work are consistent with the results obtained from molecular dynamics by Vashishta and Rahman (1978). The intensities of Debye lines were also explained satisfactorily in terms of pair distribution function for Ag-I pairs.

Integrodifferential equations for partial distribution functions in classical statistical physics

Integrodifferential equations for partial distribution functions in classical statistical physics

Equations for generating functionals in classical and quantum statistical mechanics

This paper develops a formalism for the generating functionals for partial distribution functions in classical statistical mechanics and partial density matrices in quantum statistical mechanics. For the case of a large canonical ensemble, functional equations are written with respect to the functionals introduced. Each functional system creates a system of integral equations for distribution functions or density matrices.

Partielle Interferenz-und partielle Atomverteilungsfunktionen sowie elektrischer Widerstand von geschmolzenen Magnesium—Zinn-Legierungen

Abstract From measured intensity functions, published in a previous paper, partial interference functions, partial pair correlation functions, partial atomic distribution functions, and partial coordination numbers were calculated and discussed. According to the theory of Faber and Ziman, the electrical resistivity of molten Mg-Sn alloys was calculated from the partial interference functions and from pseudopotentials reported by Animalu and Heine. The calculated values, being normalized to the resistivity of the molten components, are in good agreement with values measured by a rotating field method. The partial interference functions are derived by the assumption of independency of concentration. This assumption is proved by discussion of the partial coordination numbers and the results of electrical resistivity determinations.

Recurrence relations for the expansion of partial distribution functions

An equation is examined for the generating functional of partial distribution functions. The solution of this equation can be written as an integropower series whose kernels determine all the distribution functions. A recurrence relation is obtained which can be used to construct successively all the kernels. This expansion is the same as an expansion in terms of irreducible coupled diagrams.

Partial Interference and Atomic Distribution Functions of Liquid Silver—Tin Alloys

The x-ray scatterings from liquid Ag–Sn alloys previously measured at temperatures 100°C above the respective liquidus temperatures have been reanalyzed. The total-interference functions (also called structure factors) I(K), where K=4π sinθ/λ, were first refined and then used to calculate the partial-interference functions Iij(K), assuming that they are approximately independent of the atomic concentrations. The least-squares analysis with five different atomic concentrations of Sn, i.e., 18.5, 25, 36.5, 50, and 68.5 at.%, yielded three Iij(K). The Fourier transform of Iij(K) leads to the partial radial distribution function (RDF)=4πr2ρij(r)/cj, and the reduced distribution function Gij(r)=4πr[ρij(r)/cj—ρ0], where ρij(r) is the partial radial density, cj is the atomic concentration of the j-atoms and ρ0 is the average atomic density. Thus calculated Iij(K) and Gij(r) were used to reproduce the measured I(K) and their corresponding G(r), and a remarkably good agreement was found between the measured and calculated values. Judging from the observed agreement, it can be concluded that for liquid Ag–Sn alloys the partial ISnSn(K), IAgAg(K), and ISnAg(K) are not influenced by the relative abundance of the elements. The resistivity of the alloys obtained with Iij(K) and the pseudopotential elements Ui(K) agrees well with those measured experimentally.

Surde nouvelles relations de recurrence entre les fonctions de distribution moleculaires

Synopsis It is shown that it is possible to generalize a method used by Price in his calculation *) of classical compressibility, in order to obtain some new recurrence relations between the partial distribution functions of consecutive orders, and their derivatives with respect to density or temperature. Both of these new sets of relations, include a term which is given by an integral having the same structure as the fluctuation-in-density integral.