Mechanical hardening of nanostructured Ba$_{0.9}R_{0.1}$F$_{2.1}$ ($R$ = rare-earth elements) crystals: size effect

The effect of strong deviations from stoichiometry in the structural type of fluorite (CaF$_2$) on the microhardness of Ba$_{0.9}R_{0.1}$F$_{2.1}$ crystals ($R$ is the rare earth elements La–Lu) has been studied. Mechanical hardening of heterovalent Ba$_{0.9}R_{0.1}$F$_{2.1}$ solid solutions in comparison with the BaF$_2$ matrix is due to the formation of nanosized clusters of point defects [Ba$_{8}R_{6}$F$_{69}$], replacing structural fragments [Ba$_{14}$F$_{64}$] (block type of isomorphism). It was found that, with a decrease in the cluster size from от [Ba$_{8}$La$_{6}$F$_{69}$] to [Ba$_{8}$Lu$_{6}$F$_{69}$], the microhardness of nanostructured Ba$_{0.9}R_{0.1}$F$_{2.1}$ crystals increases by 73%.