Effects of twenty impurity and alloy elements on the strength of a Zr(0001)/Zr(0001) Σ7 twist grain boundary were studied using a first-principles density functional approach. A ranking in the order of most weakening to most strengthening was: Cs, I, He, Te, Sb, Li, O, Sn, Cd, H, Si, C, N, B, U, Ni, Hf, Nb, Cr, and Fe. Segregation energies for these elements to the grain boundary and the Zr(0 001) surface were also calculated. Calculations showed that the weakening grain boundary elements He, I, and Cs have a strong driving force for segregation to the grain boundary from bulk Zr. Zircaloy cladding failures (pellet-clad interactions) in commercial fuel systems and separate effects test results provide context for these computational results.