  Solid-solution strengthening results from solutes impeding the glide of
dislocations. Existing theories of strength rely on solute-dislocation
interactions, but do not consider dislocation core structures, which need an
accurate treatment of chemical bonding. Here, we focus on strengthening of Mg,
the lightest of all structural metals and a promising replacement for heavier
steel and aluminum alloys. Elasticity theory, which is commonly used to predict
the requisite solute-dislocation interaction energetics, is replaced with
quantum-mechanical first-principles calculations to construct a predictive
mesoscale model for solute strengthening of Mg. Results for 29 different
solutes are displayed in a "strengthening design map" as a function of solute
misfits that quantify volumetric strain and slip effects. Our strengthening
model is validated with available experimental data for several solutes,
including Al and Zn, the two most common solutes in Mg. These new results
highlight the ability of quantum-mechanical first-principles calculations to
predict complex material properties such as strength.
