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They are a method for predicting ionic vs. covalent that predates electronegativity (by three decades) and make use of ionic and atomic radius data that was becoming available through x-ray crystallography.
To use Fajans' Rules, assume your binary compound is ionic and identify the potential cation and anion.
By Fajans' Rules, compounds are more likely to be ionic if: there is a small positive charge on the cation, the cation is large, and the anion is small. For example, NaCl is correctly predicted to be ionic since NaX+ is a larger ion with a low charge and ClX- is a smaller anion.
Compounds are more likely to be covalent if: there would be a large positive charge on the cation, the cation would be small, and the anion would be large. For example, AlI3is correctly predicted to be covalent since it would have a small cation with a high charge and a large anion
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