The structure of Y(O, F) 2+ materials can be described in terms of a YX slab based

The structure of Y(O, F)_2+δ materials can be described in terms of a YX slab based on a square grid of anions alternating with a hexagonal anion grid as shown in Figure 2.16.

 Figure 2.16

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(a) Confirm that the composition of a material with ideal anion arrays (all nearest anion- anion distances equal) would be MX2.155. (b) State whether you'd expect this MX2.155 material to be commensurate or incommensurate. (c) Assume that the triangles are compressed slightly in the b direction such that horizontal rows of anions align after five squares and six triangles as in Figure 2.16. Calculate the composition of this material. Repeat your calculation for a system in which anions align after six squares and after seven triangles. (d) State the relationship you'd expect between the square and triangular anion grid in Y706F9.