X-ray diffuse scattering from alkali, silver, and europium β -alumina

Crystals of varying compensation mechanism (extra oxygen bridges or Co²⁺ substitution) and phase (β or β^'') have been grown by adding cobalt oxide to a melt containing NaCO₃, Al₂{O}₃$, and ${Bi}₂O₃ in the proportion 2.9:4.4:100. In (1+x)Na₂O·11Al₂O₃ the value of x is {~}0.16(3) for crystals grown from the melt and {~}0.38(3) for crystals grown from the flux. Diffuse x-ray scattering measurements confirm the formation of Al Frenkel defects which lock the extra oxygen ions in the diffusing plane. Rods of diffuse scattering are observed in β-alumina grown from the flux with Ag, K, Rb, and Eu substituted for Na in the diffusing plane. The rods are at (h+1/3,k+1/3) and (h+2/3,k+2/3) but not at integral (hk). A two-dimensional short-range-order model consisting of three types of cells: (i) containing one diffusing ion, (ii) two ions, and (iii) 2 ions plus an extra bridge [cells (ii) and (iii) have no diffusing ions in the Eu case] agrees semiquantitatively with the observed data. The conditional probability for doubly occupied cells or defect cells being nearest neighbors is P₂₂(1)=P₃₃(1)~0.05 (random value is 1/6) and the correlations are assumed to fall off as e^-RξR1/2 with the signs of the coefficients given by a superlattice which isolates cell (ii) and (iii). The correlation lengths in the plane and the activation energy for ionic conductivity both vary linearly with the concentration of extra bridges for K β-alumina. The correlation lengths in units of a₀ are 0.9(1), 1.2(1), 2.5(1), and 6.1(5) for Na, Ag, K, and Rb from the flux and 1.0(1), 1.2(1), 1.3(1) for Ag, K, and Rb from melt-grown crystals.