If I have a ABX3 cubic perovskite single crystal, and AX partial Schottky defects (A+ and X- ions leave the bulk and form a AX secondary phase at ABX3's surface, leaving A and X vacancies behind) are formed as temperature is raised, how exactly is the AX secondary phase disposed at the single crystal's surface? The single crystal was cleaved along the [001] faces and AX is also cubic, but their lattice parameters differ significantly (> 10%). Will AX be oriented in the [001] direction? If this is the case, will AX try to match ABX3's lattice parameter and be under such high tensile strain (> 10%)?
Thanks in advance for your help!
PS: A reference (preferably containing microscopy images) showing how a secondary phase due to partial Schottky defects is disposed at the surface in perovskites or even in other materials would also be very appreciated!
(001) planes of the ABX3 and AX phases match each other, but not directly. The diagonal of the ABX3 is the edge of the AX. So, the ratio of the lattice constants should be 1:√2.
Please, refer to the attached figure for comparison.
Dear Missyul’,
Thank you so much for your answer!
The possibility of the two coordinate systems (the one that represents perovskite's primitive cubic unit cell and the one that represents rock salt's conventional fcc unit cell) being rotated by 45º relative to each other indeed makes much more sense than the non-rotated configuration I pictured before. But even in this case the strain seems too high to me. For NaVF3 (a = 3.94 A), for example, NaF (a = 4.63 A; a/√2 = 3.28 A ) would be under a strain over 20%! Does it really happen?
Best regards
Dear Rodolpho,
This is not real rotation of planes, just different choice of the unit cell (primitive for the perovskite structure and centered for the rock-salt structure).
As for the large parameter misfit, I can imagine two explanations. First, amount of the Schottky defects cannot be very large and corresponding amount of the AX phase will be only enough to form a few atomic layers, where large deviation from the bulk lattice parameter is not impossible. Second, instead of the surface AX phase the Ruddlesden-Popper phase-like dislocations can be formed inside the crystal. Usually such dislocations are discussed for the perovskite films (for example, http://dx.doi.org/10.1016/S0022-0248(01)01962-5 or http://dx.doi.org/10.1016/j.tsf.2013.09.057), but why not assume them for the bulk?
Dear Missyul’,
Thank you for answering!
Yes, you're right, it is only a matter of choice of unit cell. I expressed myself poorly before. I edited my previous answer to make it more scientifically accurate.
Thank you for the references on the second explanation!
As for the first explanation, I agree with you about the theoretical possibility of large deviations from bulk lattice parameters if the secondary phase has only a few atomic layers, but I wonder if there is any experimental evidence for this. I'm performing some atomistic simulations in this direction and I'd really like to have some experimental evidence as support...
Thank you, both of you for writing here as I got some understanding relative to my problem. Thank you so much.
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