Arthur Paskin

Structure of liquid metals

Abstract A brief review is given of the structure of liquid metals. The structure is examined from the viewpoints of how the pair potential in metals gives rise to various structural properties and how the structure of liquid metals effects other properties. Use is made of the Paskin and Rahman molecular dynamic calculations on liquid sodium to illustrate the insensitive nature of the structure to details in the pair potential. Diffraction data are used to demonstrate that a law of corresponding states exists, at the melting point, for simple liquids, metals and insulators. The molecular dynamic calculations of sodium are also used to demonstrate that some time dependent correlation functions may be more sensitive to the form of the pair potential than the structure factor is to the potential. Some analysis is also made of the role of structure in the electrical resistivity. It is noted that more accurate structure data are needed to answer some of the questions raised in recent attempts to use the struct...

A relation between structure and pair potential for liquid metals

Abstract We emphasize the importance of considering the relationship between the structure of a liquid and the interatomic potential directly from the point of view of wave vector space (k space). Although the Ornstein-Zernike equation was not originally derived from this point of view, this equation when transformed into the k-space representation has direct physical content, when coupled with a normal mode representation according to the approaches of Pines and Bohm (1952), and Percus and Yevick (1958). These normal modes are defined isothermally, and the relation to the dynamical modes of the liquid is discussed. The use of a simple k-space relationship between the transform of the Ornstein-Zernike direct correlation function and the transform, Vk , of the interatomic potential is explored. This leads to a correspondingly simple relationship between the structure factor and the interatomic potential. It is equivalent to a generalized Debye-Huckel equation and is expected to be valid only under special ...

The effects of granularity on the diffracted intensity in powders

Abstract : The particle size, shape and the geometry of packing may affect the diffracted intensity in a powder. Previous considerations of the satistical aspects of the problem have yielded some what conflicting results. The present treatment contributes toward resolving these results by providing a simplified but still exact formu lation of the expression for the intensity. It is shown that in addition to the usual expression for the intensity associated with an infinite homogeneous solid there is a corrective term. This term depends in detail on tr1 correlations between a rays absorbing path in and out of the powder. The correction term vanishes when there are no correlations between these paths. As an example of the effect of correlations, we have obtained the correction term for a simple model of a powder which should be a good approximation in the limit of small porosity. The correction is found to go to zero in the limit of normal incidence in accord with the rigorous results.

Application of a structure factor-potential relationship to the electrical resistivity of the liquid alkali metals

Abstract In the Ziman formulation for the electrical properties of liquid metals, the resistivity depends on an average of the product of the structure factor and the pseudopotential. Ascarelli, Harrison and Paskin have derived a relationship for small wave vector between the structure factor and the pseudopotential for liquid metals such as the alkali metals. This formulation has been used over the entire range of wave vector (k = 0 to 2k F). The resistivities of Na, K, Rb and Cs calculated with no adjustable parameters are within 25% of the observed values, while Li is underestimated by about a factor of five. The temperature dependencies of all but Li (which is anomalously non-linear) are in similar agreement with experiments made at constant volume.

Fraction of total energy and entropy of magnetic order attained at the curie temperature by antiferromagnetic salts

Abstract Recent magnetic calculations of B rown and L uttinger based on the B ethe -P eierls -W eiss method of computing magnetic order in ferro- and antiferro-magnetic spin configurations are extended to obtain the fraction of the total energy of magnetic order and the fraction of the total entropy of magnetic order realized at the Curie temperature. Calculations are carried out both quantum mechanically and classically. To a good approximation both methods give the same results for spin equal to or greater than unity. Calculations are also compared with data obtained from further analysis of magnetic specific heat curves obtained by H ofmann , P askin , T auer and W eiss from analysis of the experimental specific heat data of antiferromagnetic salts. The calculated fractional energy is in good agreement with experiment while the calculated fractional entropy is greater than that observed.

Factors controlling the production of fission-fragment tracks in thin metal films

Abstract It has been suggested recently that the production of fission-fragment tracks in thin metal films is controlled by crystallite size and degree of contact between crystallites as evidenced by film resistivity. The effects of crystallite size have already been investigated. In this paper we report on the results of a quantitative investigation of the role of resistivity and film thickness in track production. Using thin evaporated palladium films we demonstrate that films whose resistivity approaches bulk values do not show evaporation tracks, and that those whose resistivities are in excess of ten times bulk value do show such tracks. We further demonstrate that tracks are not produced in films whose thickness is much in excess of the crystallite dimensions, even when the resistivity is high.

Ordering and segregation in terms of the polar model of an alloy

Abstract In earlier work, Mott (1937) showed that the electrostatic energy of CuZn could account for most of the ordering energy. Harrison and Paskin (1962) have subsequently found that the introduction of more recent concepts of electron screening in metals when applied to AB alloys leads to a polar model resembling that suggested by Mott (1937). We show here that the polar contribution calculated by following the procedure of Mott (1937), always leads to ordering whereas the Harrison and Paskin (1962) formulation can account for ordering or segregation. In both polar calculations (Mott 1937 and Harrison and Paskin 1962), the origin of the ordering energy is the incomplete (or excessive) screening of the A and B ionic charges. We denote the relevant charges in an atomic polyhedron surrounding an x-type of atom as Qx = Qx i—Qx e, where Qx i equals the ionic charge of x minus the average number of conduction electrons per atom and – Qx e is the electronic charge screening Qx i. Mott (1937) makes an electro...