The likelihood of a first-order liquid-liquid phase change in carbon f
rom a mostly graphitic configuration to one that is more tetrahedral i
n character is explored. Liquid-phase changes in other materials are n
oted. Pertinent data on liquid carbon are reviewed and the model is br
iefly described. The model is consistent with a positive diamond-melti
ng-line slope. Constraints on the strain energy between graphitic and
diamondlike liquid clusters allow a phase diagram with a liquid-liquid
transition and a graphite-liquid-liquid triple point. An upper limit
on the strain energy is the constraint that the graphite melting line
should have a reasonable curvature that agrees with melting-line data.
The transformation of liquid structure from graphitic to diamondlike
under compression significantly increases the compressibility.