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By means of a solid state electrochemical method, the activity of sodium oxide dissolved in various samples of ceramic Na-(β + β″)-alumina was measured as a function of the composition of the ceramics, with the independent variable being adjusted by the sodium activity in the ambience. Taking into account all the relevant findings, thelg   aNa   2   O$\lg {\rm{ }}a_{{\rm{Na}}_2 {\rm{O}}} $    vs.lg  ⁡       aNa$\lg {\rm{ }}a_{{\rm{Na}}} $    relationship can quantitatively be described by a polynomial of third degree with respect tolg  ⁡       aNa.$\lg {\rm{ }}a_{{\rm{Na}}} .$    The gradual change of the sodium oxide activity indicates that the thermodynamic behaviour of the material is mainly determined by the occurrence of nonstoichiometric phases with easy transitions from one stoichiometry to the other one.

Relationship between the sodium oxide activity of ceramic (Na-β + β ″ )-alumina and the sodium activity in the ambience of the material