Total-energy band calculations that show the coexistence of a high-spin and low-spin state in fcc transition metals and alloys are presented. The energy difference between the two states is shown to be a function of the electron concentration and to vanish at 8.6. At larger electron concentrations the low-temperature state is the high-spin state, and the thermal expansion is shown to pause at a system-dependent characteristic temperature. At lower electron concentrations the low-temperature state is the low-spin state, and enhanced thermal expansion is expected. An analysis that leads to a qualitative understanding of the thermal properties of Invar and that implies a connection with martensitic transformations and spin glasses in related alloys is presented. For Invar a magnetic collapse from the high-spin to the low-spin state at a pressure of 55 kbar is predicted. © 1990 The American Physical Society.