Ion Distribution Models for Defect Fluorite Zro 2 - AO 1.5 (A = Ln , Y) Solid Solutions: I. Relationship between Lattice Parameter and Composition

The composition dependence of the lattice constant, a, in AxB1-xO2-0.5xV0.5x, fluorite-type solid solutions (B = Zr, A = {Nd-Yb, Y}, V = oxygen vacancy) is characterized by changes in slope at x ~ 1/3, which cannot be described by existing models. Moreover, over the range of 0.15 ≤ x ≤ 1/3 the a vs. x data on all systems can be fitted with a linear equation, a = q + rx, with the same intercept, q, however, over the range of 1/3 ≤ x ≤ 1/2 the data bifurcate requiring different intercepts for A={Nd-Gd] and for A={Dy-Yb,Y} systems, implying steeper slopes for the first group. An adequate description is achieved via close-packing models involving two anion species, O2- and V, and three combinations of cation species, namely 8A, 7B, 8B (0 ≤ x ≤ 1/3), 7A, 8A, 7B (1/3 ≤ x ≤ 1/2) and 8A, 6B, 7B (1/3 ≤ x ≤ 1/2), that take into an account the constraint on the average coordination number, K(x), of K(x) = 8 - 2x and two additional short-range order (SRO) constrains referring to vacancy-vacancy avoidance and vacancy-to-Zr association. The consistent fit to a vs. x data with these models requires the effective size of the oxygen vacancy to be larger than the radius of the oxygen anion by ~11%. The latter observation seems to play an important role in the understanding of structure-property relationships in AxB1-xO2-0.5xV0.5x systems.