Hi everyone,
According to Hume-Rothery rules, the ionic radii difference should be less than or equal to 15% for the dopant to be substitutional.
When I dope a higher ionic radius with a difference (eg. > 20%) in A-site of ABO3 perovskite structure. I want to know the criteria for the formation of interstitial or substitutional defect?
Assuming the solubility of solute in the solvent i.e., there is no formation of dopant related oxides as an impurity phase.
Thanks in advance..
The Hume-Rothery rules are for solutions in metals. Are you interested instead in the radius ratio rule? It defines the coordination of ionic structures, especially with regard to the types of cation sites.
Thank you Prof. Jeffrey for your clarification on Hume-Rothery rules.
What is the dopant-type model will work for perovskite type structures or in general oxides?
A search on the Web shows a number of scholarly articles on the topic.
Rules in materials chemistry serve as a guide only. They are more like a rule of thumb. Only experimental results assure it is substitutional or interstitial doping. Please refer to the nice book authored by D.M. Smyth, The Defect Chemistry of Metal Oxides.
of course you have to consider ionic radius in all cases which are much closer to the real size of the present atoms in oxides. Ionic radius are also kown as Shannon radii
(you can Google : Shannon + abulafia to find a table).
On the other side, Interstitials are not very common in pervoskite oxides. Essentially because there is no space for them.
For instance, the compounds with oxygen excess like ABO3+d generally correspond in fact to compounds with A and B-site vacancies, the oxygen sites occupancy being 1 and the number of interstitials zero.
hoping it helps
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