Context and sources: Hard sphere crystallization
John G. Kirkwood in 1938.
Smithsonian Institution Archives, Accession 90-105, Science Service Records, Image No. SIA2008-4847.
Elizabeth Monroe and John Kirkwood were the first to theorize that hard spheres crystallize via a first-order transition. Their result received little immediate attention, but its numerical demonstration—nearly two decades later—using the latest molecular simulation methods on some of the rare electrical computers in existence is an early landmark of the field. The occurrence of crystallization in a system without attraction between particles was surprising for many scientists. The Kirkwood-Alder transition, as it is now commonly known, has since been observed in various experimental systems.
One would conclude, therefore, that [for hard spheres] a limiting density exists above which a liquid type of distribution and a liquid structure cannot exist. Above this density, only structures with crystalline long range order would then be possible. This speculation should, however, be regarded as highly tentative, since the existence of a limiting value of [density] may be a mathematical consequence of certain of our approximations and without physical significance.
John G. Kirkwood, “Molecular Distribution in Liquids,” Journal of Chemical Physics 7 (1939), 919–925, https://doi.org/10.1063/1.1750344.
It is the purpose of the present note to present a brief outline of a theory of fusion based upon the concept of an order-disorder transformation. The theory is similar in principle to that of Lennard-Jones and Devonshire, but goes beyond it by allowing to the molecules of the liquid phase a continuum of sites, rather than restricting them to a lattice with merely a somewhat greater multiplicity of sites than are accessible in the solid. … The theory predicts a first-order transition from a completely disordered density distribution to one of crystalline order at [finite density].
John G. Kirkwood and Elizabeth Monroe, “On the Theory of Fusion,” Journal of Chemical Physics 8 (1940), 845–846, https://doi.org/10.1063/1.1750591.
The manner in which complete canonical averaging would connect the two separate, overlapping branches of the equation of state is at present undetermined. A first-order phase transition is, however, strongly suggested.
W. W. Wood and J. D. Jacobson, “Preliminary Results from a Recalculation of the Monte Carlo Equation of State of Hard Spheres,” Journal of Chemical Physics 27 (1957), 1207–1208, https://doi.org/10.1063/1.1743956.
A calculation of molecular dynamic motion … consists of solving exactly (to the number of significant figures carried) the simultaneous classical equations of motion of several hundred particles by means of fast electronic computers. … In the transition region the effect of the number of particles might appear in the average time the system spends in each branch, such that for an infinite system a horizontal line might appear, characteristic of the first-order transition which is strongly indicated by the present results.
B. J. Alder and T. E. Wainwright, “Phase Transition for a Hard Sphere System,” Journal of Chemical Physics 27 (1957), 1208–1209, https://doi.org/10.1063/1.1743957.
Last fall, there was something similar—a round table on statistical mechanics at Seattle [at the International Congress on Theoretical Physics, held at the University of Washington, September 17-21, 1956]—and there I finished the discussion on hard spheres with a vote. The vote was simply on the matter of your belief in what you have heard, whether a gas of hard spheres has a transition point or not; at Seattle, the vote was even. Now, of course, with Mr. Kirkwood here, we have weighted [sic] the evidence a little bit. May I ask first of the panel to put up their hands if they believe there is a transition in the classical case. … Now those who believe there is not a transition. … Even, again!
George E. Uhlenbeck, “Round Table on Statistical Mechanics,” in The Many-Body Problem, edited by Jerome K. Percus (Interscience Publishers, 1963): 493-509. This volume is the proceedings of the Symposium on the Many-Body Problem held at the Stevens Institute of Technology in Hoboken, NJ, January 28-29, 1957.
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Cite this resource
Patrick Charbonneau, “Elizabeth Monroe Boggs,” Women in the History of Quantum Physics collection, American Institute of Physics, 2026, https://www.aip.org/history/elizabeth-monroe-boggs.