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 a grain boundary and a Zr (0001) surface were also investigated. 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. Iodine adsorption, dissociation, and diffusion on a Zr (0001) surface were also studied. Molecular iodine (I2) spontaneously dissociated on this surface and adsorption isotherms show significant adsorption site occupancy even at extremely low I₂ partial pressures. Diffusion of iodine atoms on a Zr (0001) surface was calculated to be quite fast with an activation energy Q = 6.8 kJ/mol and D0 = 2.0×10-4 cm²/sec. Zircaloy cladding failures (pellet-clad interactions) in commercial fuel systems and separate effects test results provide context for these computational results.