First, is there a general relationship between vacancies and CTE. For a material with a positive CTE, will increasing Shottky defects increase CTE?
Second, I have 4 different samples of Prussian Blue NaFe[Fe(CN)6], and I suspect they have varying [Fe(CN)6] anion vacancies from 0 - 25%, probably balanced by Na+ cation vacancies or change in the other Fe valance. I had an idea that I could quickly show qualitatively that my samples had increasing vacancy concentration by finding CTE via dilatometry. Do you think that would be compelling evidence if it was possible?
Vacancies in the ionic solid would create strain which is accompanied by strain energy. The number of vacant sites will have its reflection on the quantum of energy generated as the vacancies formation would lead to perturbation of the adjoining ions which further leads to bond stretching and weakening between the ions in the neighborhood of vacant sites. The coefficient of expansion May be altered to the extent commensurate with concentration of vacancies. The relation between temperature and vacancy concentration is also important in this regard.
https://www.sciencedirect.com/search?qs=coefficient%20of%20thermal%20expansion%20affects%20vacancy%20concentration%20in%20an%20ionic%20solid&show=25&sortBy=relevance
I am not sure about your second suggestion that measuring enhanced CTE in your ionic crystal is the strict evidence for existence there enhanced vacancies concentration. This conclusion is correct only if vacancies are the ONLY reason for CTE increase. What about other factors, like concentration variations, micro cracks or imperfect density of the real crystal?
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