The defect chemistry of the nitrogen incorporation into pure and cation (Y~(3+), Eu~(3+), Ce~(4+), Mg~(2+), Ca~(2+))-doped ziconia is quantitatively described using simple thermodynamic considerations, allowing the calculation of the anion vacancy concentration as a function of the nitrogen and oxygen pressure in the surrounding atmosphere. The effective equilibrium constants for the nitrogen incorporation into pure and cation-doped zirconia (K) can be expressed by KP_(O_2)~(1-/3)/P_(N_2) = 4[V_o~(00)]_N~3 and KP_(O_2)~(-3/2)P_(N_2) = (4[V_o~(00)]N([V_0~(00)]_N [V_0~(00)]_Y/(1-3[V_0~(00)-[V_o~(00)]_y)~3, respectively, and are in the order of 10~(-25) at 1900 deg C. Sievert's and Henry's law for gas solubility at high temperatures in melts and alloys were applied to model the results with only partial success.
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