  Impurity diffusion in Zr is potentially important for many applications of Zr
alloys, and in particular for their use of nuclear reactor cladding. However,
significant uncertainty presently exists about which elements are vacancy vs.
interstitial diffusers, which can inhibit understanding and prediction of their
behavior under different temperature, irradiation, and alloying conditions.
Therefore, first-principles calculations based on density functional theory
(DFT) have been employed to predict the temperature-dependent dilute impurity
diffusion coefficients for 14 substitutional alloying elements in hexagonal
closed packed (HCP) Zr. Vacancy-mediated diffusion was modeled with the
eight-frequency model. Interstitial contributions to diffusion are estimated
from interstitial formation and select migration energies. Formation energies
for each impurity in nine high-symmetry interstitial sites were determined,
including significant effects of thermal expansion. The dominant diffusion
mechanism of each solute in HCP Zr was identified in terms of the calculated
vacancy-mediated activation energy, lower and upper bounds of interstitial
activation energy, and the formation entropy, suggesting a rough relation with
the metallic radii of solutes. It is predicted that Cr, Cu, V, Zn, Mo, W, Au,
Ag, Al, Nb, Ta and Ti all diffuse predominantly by an interstitial mechanism,
while Hf, Zr, and Sn are likely to be predominantly vacancy-mediated diffusers
at low temperature and interstitial diffusers at high temperature, although the
identification of mechanisms for these elements at high-temperature is quite
uncertain.
