My major research thesis examines that the Moon and probably all the terrestrial planets underwent an initial differentiation from largely a completely molten state. The resulting cumulate products were gravitationally unstable, resulting in an additional solid state differentiation that reintroduced heat producing elements deep within the planets but also created a heterogeneous mantle with characteristic depletions in the highly incompatible elements. The latter is recorded in the isotopic systematics of basalts derived throughout geological history.
The Moon, being the smallest planet, has preserved the stamp of the early differentiation because the vigor of thermal convection from a rapidly cooled planet was insufficient to rehomogenize the heterogeneous mantle. In contrast, the heterogeneities, particularly the isotopic anomalies, are more muted on the earth, presumably because plate tectonics as driven by the instabilities of the thermal boundary layers has effectively erased most, but not all evidence of the magma ocean.
Interestingly, the isotopic composition of ancient and young Martian magmas make it appear that Mars is more like the Moon than the earth. The extraordinary heterogeneity is persevered in both young and old mantle; this fact coupled with the very old crust indicates that magma ocean processes followed by mantle overturn produced a compositionally heterogeneous but gravitational stable mantle operated at the very earliest epochs. The live 182W and 142 Sm anomalies show that this event characterized the first 50 million years of Mars history (Hess and Parmentier, 2001). These ideas, if verified, will significantly reshape our ideas about the primordial evolution of the terrestrial planets.
Other topics of interest deal with the thermodynamic properties of thin liquid films at grain boundaries in large and nanoscale crystals. The results have application to the distribution and permeability of silicate melts in the earth's mantle and the stability of water/ice in permafrost in terrestrial or Martian environments (Hess and Longhi, 2001). Interestingly, the melt-crystal phase boundary can be depressed to significantly lower temperatures in thin films and crystal-liquid partition coefficients in thin and bulk films can be radically different.