We know that the tolerance factor t is generally represented:
t = (rA+rO) / [sqrt(2)*(rB+rO)]
where r is the ionic radius for the perovskite ABO3.
But for the double perovskites A2B'B''O6, how to choose the rB?
Can the mean value (rB'+rB'')/2 be used to stand in the rB in the formula? If so, a large rB' with a small rB'' could be a favourable rB. But could the so different ionic radii give rise to the stable perovskites phase of A2B'B''O6?
Many thanks!
The tolerance factor is not a deep theory, just a convenient rule for the preliminary estimation. Sometimes the compositions with t close to 1 do not form perovskite phases and sometimes it is possible to force the system to form the perovskite phase even though t is very far from 1. In case of the two ions with very different radii in the same position one should expect almost complete ordering of these ions and calculation of the average t will not give any information about the stability of the structure.
If there is a too much difference in ionic radii of B and B' cations then you may not be able to synthesize such double perovskites under ambient conditions. Basically, tolerance factor gives you a rough idea of how much disorder can be tolerated. However, a brute force like high pressure can force many perovskites to adapt cubic structure.
Try to use this software Perovskite Structure Prediction: http://www.unf.edu/~michael.lufaso/spuds/index.html
More about tolerance factor
http://abulafia.mt.ic.ac.uk/publications/theses/levy/Chapter3.pdf
http://abulafia.mt.ic.ac.uk/publications/theses/levy/Chapter3.pdf
http://www.unf.edu/~michael.lufaso/spuds/index.html
Tolerance factor sometimes does not mean the perovskite wont form especially when you are doping both the A and B site at the same. What is important is that is that you are able to get the various HKL values and they are in correspondence with literature
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