# Schottky Defect in AB2 type crystals

Are there any examples of Schottky defect in ${\ce{AB_2}}$ type crystals.
Does Schottky defect require that the cation and anion be of equal size?
According to me it is not necessary that the two ions are of equal size as even ${\ce{NaCl}}$ shows Schottky defect but ${\ce{Na+}}$ has radius is 95 pm and ${\ce{Cl-}}$ has radius of 181 pm which is a bit less than double of that of ${\ce{Na+}}$

• I suppose schottkey or other defects are based on thermodynamics that is if energy required to pair a cation and anion is higher that the energy required for the defect then that defect is more probable to be seen. I think it is just an observation that cation and anion of similar sizes show schottkey defect – Suraj S May 12 '17 at 15:29

Schottky defect occurs when equal number of positive and negative ions are missing from the lattice thereby maintaining net electrical neautrality and leading to a decreased density in the lattice (since there are now less number of ions) . It is observed to be occurring in cations and anions of similar sizes.

NOW CONSIDER THAT AN ION IS AT THE LATTICE POSITION AND A DEFECT IS TO BE OCCURRED.

There are 2 ways stoichiometric conditions can be satisfied. - either by loosing this ion as well as another of opposite charge in equal ratio(SCHOTTKY) , OR not losing this ion at all , but just shifting it's position from lattice position to interstitial one.(FRENKEL)---- If we think logically ,

Since it's a stoichiometric defect it should maintain neautrality as well as loose cations and anions in a certain ratio.

If the sizes were very different , there are chances the smaller ion would occupy an interstitial space causing it to create a hole and still maintain neutrality and ratio without losing any ions. (Which is what happens in Frenkel defect) . Since however ions are of similar sizes , one can't occupy an interstitial space .. and therefore losing equal no. Of anions and cations is the only way to go. You can think of these as 2 cases of defect... Yes it's not necessary the ions are of similar sizes for a defect to occur BUT IF THEY ARE...They are most likely to cause the Schottky defect and if not , then Frenkel Defect. As for your NaCl doubt , I would suggest try finding the critical radius ratio for one ion to occupy the interstitial space . This way you can verify whether it can perform Frenkel defect or not ..Or why it's performing Schottky. Hope this helps.

EDIT:- I can't find any examples of ${\ce{AB2}}$ type as such , but you can again try finding critical ratio of ions in ${\ce{AB2}}$ lattices to decide what type of defect they are likely to occur.