DOI: 10.1063/1.1841195. Hard-Sphere Lattice Gases. II. Plane-Triangular and Three-Dimensional Lattices

Hard-Sphere Lattice Gases. II. Plane-Triangular and Three-Dimensional Lattices

10.1063/1.1841195

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

Exact low-density and high-density series are derived for the plane-triangular (pt) lattice gas, and in three dimensions, for the simple cubic (sc) and body-centered cubic (bcc) lattice gases, with first-neighbor exclusions. The series are studied by the ratio and Padé approximant extrapolation techniques. In all cases we find a continuous transition to an ordered state at the activities zt=11.05±15 (pt), 1.09±7 (sc) and 0.77±5 (bcc), and the densities ρt/ρ0=0.832±8 (pt), 0.427±20 (sc) and 0.355±20 (bcc). The grand potentials at these points are (pv0/kBT) = Γt=0.839±5 (pt), 0.380±10 (sc) and 0.290±15 (bcc). In all cases the uncertainties refer to the last decimal places. The ordered state is characterized by a long-range order parameter which vanishes continuously and rapidly at the transition point. The transition is signed from above and below by the rapid divergence (faster than a simple pole) of the ``staggered compressibility.'' Apparently, the isothermal compressiibility also diverges to infinity from either side but with considerably less rapidity.

Bibliography

Gaunt, D. S. (1967). Hard-Sphere Lattice Gases. II. Plane-Triangular and Three-Dimensional Lattices. The Journal of Chemical Physics, 46(8), 3237â3259.

Authors 1

David S. Gaunt (first)

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Dates

Type	When
Created	20 years, 7 months ago (Jan. 5, 2005, 11:35 p.m.)
Deposited	1 year, 6 months ago (Feb. 8, 2024, 9:10 p.m.)
Indexed	4 weeks ago (Aug. 6, 2025, 8:21 a.m.)
Issued	58 years, 4 months ago (April 15, 1967)
Published	58 years, 4 months ago (April 15, 1967)
Published Print	58 years, 4 months ago (April 15, 1967)

Funders 0

None

BibTeX

@article{Gaunt_1967, title={Hard-Sphere Lattice Gases. II. Plane-Triangular and Three-Dimensional Lattices}, volume={46}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1841195}, DOI={10.1063/1.1841195}, number={8}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Gaunt, David S.}, year={1967}, month=apr, pages={3237–3259} }

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