First-principles investigation on diffusion mechanism of alloying elements in dilute Zr alloys

Abstract

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

Non-classical interstitial sites and anomalous diffusion mechanisms in hcp-titanium

“…Other researchers have highlighted the importance of the Frank and Turnbull mechanism in other systems such as Fe, Cr, Be, Ni, Hf, Sn and self-diffusion in Zr at high temperature [40,27]. Such behaviour is experimentally confirmed by the work of Behar and co-workers [41] on the Pd diffusion in Ti.…”

“…Pasianot and Peréz [26] have used density functional theory to rationalise the peculiar diffusion behaviour of Fe, Co and Ni in Zr, and how this deviates from the Arrhenius behaviour. Lu et al [27] have investigated the interstitial diffusivity behaviour of a number of dilute large solute elements in Zr, and Jain and co-workers developed a Green's function approach to study the competition between the interstitial and vacancy-mediated behaviour of a number of solutes in Zr.…”

Solubility and vacancy-mediated inter-diffusion in the Zr-Nb-Cr system

“…The solubility and diffusivity of alloying elements in α-Zr, including Cr and Nb, has been extensively studied. Previous work [9][10][11] showed that Cr occupies both interstitial and substitutional sites in Zr. Both interstitial and vacancy mediated diffusivities of Cr in Zr have been calculated recently [12], showing that fast interstitial diffusion dominates under equilibrium conditions, in agreement with experimental measurements by Hood et al showing that Cr is an extremely fast diffuser in Zr [13,14].…”

“…Zr-2.5 wt% Nb alloys) [22]; but in all Zr alloys Nb retains some solubility in the α phase. Even though previously reported to be a vacancy mediated diffuser [23,24], it has recently been suggested that it is predominantly an interstitial diffuser with the octahedral site being the most stable interstitial site [11,25]. Interstitial diffusion mechanism of Nb in α-Zr, despite it preferentially occupying substitution sites, may be explained by the fact that the binding energy between solute and vacancy is not large enough to reduce the formation energy of the vacancy to levels competing with the low barrier for migration of interstitial Nb.…”

Unexpected variations in the kinetics of solid solution alloys due to local interactions

“…These processes include, but are not limited to, solid-state phase transformation [1][2][3][4][5], precipitation kinetics [6,7], solute segregation to defects [8][9][10][11], charging/discharging in a battery or a fuel cell [12][13][14], particular microstructure formation [5,15,16], or shape memory effects [17]. There have been numerous studies on solid-state diffusion based on first-principles calculations of either dilute alloys [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] or non-dilute alloys [35][36][37][38][39][40][41][42][43][44][45][46]. A brief, albeit incomplete, list of atomistic methods that are typically being used to estimate diffusion properties in solid-state...…”