Geometric attributes of a many-body-system potential energy function suggest a natural description of that system in terms of inherent structures (local potential minima), and intra-basin vibrational displacements away from those discrete structures. This description is applied herein to the isobaric thermal expansion property (alpha). Starting with the virial form of the pressure equation of state, two distinct contributions to alpha can be unambiguously identified. The first (alpha(vib)) arises from intra-basin anharmonic thermal vibrations; the second (alpha(str)) seems from thermally induced structural shifts in basin occupancy. Only alpha(vib) appears for nondefective crystals, and for glasses below their T-g＇s. An approximate analysis for liquid water suggests that alpha(str) alone manifests a Liquid-phase density maximum, thought shifted to slightly higher temperature than the observed density maximum at 4 degrees C.