  We develop a first-principles model of thermally-activated cross-slip in
magnesium in the presence of a random solute distribution. Electronic structure
methods provide data for the interaction of solutes with prismatic dislocation
cores and basal dislocation cores. Direct calculations of interaction energies
are possible for solutes---K, Na, and Sc---that lower the Mg prismatic stacking
fault energy to improve formability. To connect to thermally activated
cross-slip, we build a statistical model for the distribution of activation
energies for double kink nucleation, barriers for kink migration, and roughness
of the energy landscape to be overcome by an athermal stress. These
distributions are calculated numerically for a range of concentrations, as well
as alternate approximate analytic expressions for the dilute limit. The
analytic distributions provide a simplified model for the maximum cross-slip
softening for a solute as a function of temperature. The direct interaction
calculations predict lowered forming temperatures for Mg-0.7at.%Sc,
Mg-0.4at.%K, and Mg-0.6at.%Na of approximately 250C.
