Geometric Basis of Phase Change

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Abstract
A consideration of the higher j‐mers by association theory shows that starting with the 7‐mer and going up to 19‐mer, spherically symmetric atoms can pack in an unsymmetrical arrangement in which more bonds exist among the atoms in the array than if the atoms were packed symmetrically. The asymmetric pattern is then the model for the liquid while the symmetric array yields the crystal. The transition from the liquid to the crystal is difficult by homogeneous nucleation because it requires a cooperative effort of, in the neighborhood of 12–15 atoms. Heterogeneous nucleation is, however, simple since by this mechanism the region where the liquid j‐mers are more stable than the crystal j‐mers is bypassed. Methods of calculating the equilibrium constants and the concentrations of the various species are derived from association theory. The critical value where the formation of higher close‐packed j‐mers becomes important is when the value of the equilibrium constant exceeds 1.

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