In Kroger-Vink notation, V''_O represents what kind of defect?
AA vanadium atom on an oxygen site with two positive charges
BAn oxygen vacancy with an effective charge of 2+ relative to the perfect lattice
CAn oxygen interstitial with two negative charges
DA vacancy on a cation site with two negative charges
In Kroger-Vink notation, V represents a vacancy (not vanadium), the subscript O indicates the oxygen site, and the two dots (sometimes written as superscript primes or dots) indicate an effective charge of 2+ relative to the perfect lattice. Removing O^2- from an oxygen site leaves behind the 2+ charge that was being compensated, so the vacancy carries effective positive charge. This notation is essential for writing defect equilibria that properly conserve charge relative to the perfect crystal.
Question 2 True / False
Schottky defects cannot exist in a stoichiometric compound because creating a vacancy on one sublattice would destroy charge neutrality.
TTrue
FFalse
Answer: False
Schottky defects maintain charge neutrality by creating vacancies on BOTH sublattices in the stoichiometric ratio. In NaCl, a Schottky pair consists of one Na+ vacancy (V'_Na) and one Cl- vacancy (V-dot_Cl). The charges balance: one effective negative charge from the cation vacancy plus one effective positive charge from the anion vacancy equals zero net charge. This paired creation is precisely what preserves stoichiometry and charge neutrality, which is why Schottky defects are thermodynamically favorable — they increase configurational entropy without violating any conservation laws.
Question 3 Short Answer
Why does doping ZrO2 with Y2O3 (yttria) create oxygen vacancies, and why is this technologically important?
Think about your answer, then reveal below.
Model answer: When Y^3+ substitutes for Zr^4+ in the ZrO2 lattice, each substitution introduces one effective negative charge (Y'_Zr). To maintain charge neutrality, oxygen vacancies (V''_O, each with 2+ effective charge) must form: two Y'_Zr are compensated by one V''_O. These oxygen vacancies are mobile at high temperatures, making yttria-stabilized zirconia (YSZ) an excellent oxygen-ion conductor. This is the basis of solid oxide fuel cells and oxygen sensors.
This example illustrates extrinsic defect chemistry — intentionally introducing aliovalent dopants to create specific defect populations. The defect reaction is: Y2O3 -> 2Y'_Zr + 3O_O + V''_O. The site balance (same number of cation and anion sites occupied) and charge balance (net effective charge = 0) must both be satisfied. YSZ with 8 mol% Y2O3 has enough oxygen vacancies to achieve ionic conductivities of ~0.1 S/cm at 1000 C, making it the electrolyte material in most solid oxide fuel cells.
Question 4 True / False
Increasing temperature always increases the concentration of intrinsic point defects in a crystal.
TTrue
FFalse
Answer: True
Intrinsic defect formation is an endothermic process with a positive entropy change. The equilibrium defect concentration follows n ~ exp(-Delta_H_f / 2kT) for Schottky or Frenkel defects. As temperature rises, the exponential increases monotonically, so defect concentration always increases with temperature. This is a direct consequence of the thermodynamic driving force: at any finite temperature, the entropy gained by introducing defects outweighs the enthalpy cost, up to the equilibrium concentration. At the melting point, defect concentrations typically reach 0.01-0.1% of lattice sites.