EXACT SOLUTIONS FOR A SEMI-INFINITE SQUARE LATTICE GAS,

Abstract

The problem of a two-dimensional lattice gad with nearest neighbor infinite repulsion is considered by obtaining exact solutions for a sequence of semi-infinite spaces. The exact solutions are obtained for M x infinity spaces with 2 < or = M < or = 14 in even steps, and although there are no phase transitions in these spaces, a criterion for the point of 'closet approach' to a phase transition is established. The values of the thermodynamic variables evaluated at this point for each M are extrapolated to obtain the properties of the two-dimensionally infinite space. The data indicate a third-order phase transition occurring with probably infinite compressibility at an activity z = 3.799, a density = 0.7356, and a pressure = 0.7914. The density is obtained by a rigorous differentiation of the secular determinant that determines the value of the pressure for a given z, thus securing the accuracy of the calculations and enabling the extrapolated values of the thermodynamic variables to be estimated with good precision. (Author)

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1966
Accession Number
AD0630167

Entities

People

  • C. A. Morrison
  • D. E. Wortman
  • N. Karayianis

Organizations

  • Harry Diamond Laboratories

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Compressive Properties
  • Mathematics
  • Phase Transformations
  • Physical Properties
  • Precision
  • Sequences
  • Transitions
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Materials Science and Engineering.

Technology Areas

  • Space