Ion distribution models for defect fluorite ZrO2 - AO1.5 (A = Ln, Y) solid solutions: I. Relationship between lattice parameter and composition.

The composition dependence of the lattice constant, a , in A x B 1- x O 2-0.5 x V 0.5 x , 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 – 2 x 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 A x B 1- x O 2-0.5 x V 0.5 x systems. Average coordination numbers of A and B cations in A x B 1- x O 2-0.5 x solid solutions (B = Zr; A = Ln , Y) deviate from the total average coordination number, K = 8 − 2 x , due to cation-vacancy association effects. Two contrasting solutions to the total average seem to exist within the range of 1/3 < x < 2/3. Image, graphical abstract [ABSTRACT FROM AUTHOR]