In the casting of single-crystal turbine blades, the composition (c) and temperature (T) dependencies of the liquid-phase molar volume (V (c, T)) play a critical role in driving convective instabilities and the associated formation of solidification defects. In support of a current effort aimed at the development of validated mathematical criteria for predicting the formation of solidification defects in Ni-based superalloys, ab-initio molecular dynamics (AIMD) simulations have been performed to calculate atomic volumes of Ni-Al-W melts. For elemental Ni and binary Ni-Al and Ni-W compositions, AIMD-calculated volumes agree to within 0.5-1.5% of recently measured values. For ternary Ni-Al-W melts, where direct experimental measurements are unavailable, AIMD results are in excellent agreement with the predictions of a recently proposed parametrization for V (c, T) in multicomponent superalloys. The results thus help to establish the accuracy of this recently proposed model in its application to the Ni-Al-W system.