Variations in composition and temperature of the liquid-phase molar volume (V(c,T)) play a critical role in driving convective instabilities during the casting of single-crystal turbine blades. These instabilities have long been associated with the formation of large highly mis-oriented grains (i.e., freckle defects) that produce significant degradation in materials properties of these critical aerospace components. Ab initio molecular dynamics (AIMD) simulations have been performed for elemental, binary and ternary alloys of Ni with Al, W, Re, and Ta, as well as a RENE-N4 multi-component superalloy, to compute equations of state at 1830 and 1750K. Where comparisons with measurements are available, AIMD-calculated volumes agree to within 0.6-1.8% of experiment. Results are compared with recently published parameterizations of V(c,T) developed using binary experimental data from a narrow range of compositions. Also, structural analysis of the AIMD results based on radial distribution functions augmented with common-neighbor analysis and bond angle distributions reveal a strong tendency for icosahedral short range order for Ni-W and Ni-Re alloys. Finally, a new constant pressure methodology was added to the AIMD package that has allowed the efficient simulation of highly complex alloys, such as an eight component model of a RENE-N4 Ni-based superalloy.