The simplest statistical-mechanical model of crystalline formation (or alloy formation) that includes electronic degrees of freedom is solved exactly in the limit of large spatial dimensions and infinite interaction strength. The solutions contain both second-order phase transitions and first-order phase transitions (that involve phase separation or segregation) which are likely to illustrate the precursor physics behind the static charge-stripe ordering in cuprate systems. In addition, we find that the spinodal-decomposition temperature satisfies an approximate scaling law.