Kroger-Vink notation
/ KRUH-ger VINK /
Defect chemistry needs an alphabet, and Kroger-Vink notation is it — a compact way to name any point defect and then to write balanced 'chemical equations' for defects, just as ordinary chemistry writes reactions for molecules. Every symbol carries three pieces of information at once: WHAT species is there, WHERE it sits, and WHAT effective charge it carries.
The rule is: main symbol = the species (a chemical symbol for an atom, V for a vacancy, e for an electron, h for a hole); subscript = the site it occupies (the chemical symbol of the site's normal owner, or i for an interstitial); superscript = the EFFECTIVE charge, meaning the charge RELATIVE to the perfect lattice, not the absolute ionic charge. A superscript dot (•) marks one unit of positive effective charge, a prime (') marks one unit of negative, and a cross (written ^x here) marks neutral. So O_O^x is a normal oxide ion on its own site (neutral); V_O•• is an oxygen vacancy (missing a 2- ion leaves a net +2); V_Mg'' is a magnesium vacancy (net 2-); Ca_Zr'' is calcium substituting for zirconium (a 2+ ion where a 4+ belonged, net 2-); e' is a free electron; h• is a hole.
Its power is that defect reactions must obey three conservation laws, and the notation makes each easy to check: (1) MASS balance (same atoms each side, with vacancies contributing no mass), (2) CHARGE balance (the effective charges — dots minus primes — must sum equally on both sides), and (3) SITE-RATIO balance (the ratio of cation to anion sites must stay fixed, e.g. 1:1 in MgO, so you cannot create a cation site without a matching anion site). Master these three and you can write any Schottky, Frenkel, doping, or redox reaction correctly.
The dissolution of yttria in zirconia, in Kroger-Vink notation, is Y2O3 --(2 ZrO2)--> 2 Y_Zr' + 3 O_O^x + V_O••, where the 2 ZrO2 over the arrow supplies the host sites. Check it: 2 Y and 3 O of mass appear on each side; the effective charges on the right sum to zero, since two Y_Zr' give 2- and the V_O•• gives 2+; and 2 cation sites plus 4 anion sites keep the 1:2 ratio of the fluorite lattice.
Every legal defect reaction balances mass, charge, and site ratio at once — the notation is built so you can verify all three by eye.
The superscript is EFFECTIVE charge, not real ionic charge. A normal O2- ion on its site is written O_O^x (neutral), because relative to the perfect lattice it is exactly what belongs there — a beginner trap worth memorising.