Mean-Square Dynamic Displacements and Atomic Scattering Factors of Ions in Aluminum Nitride

Abstract

The absolute values of the squares of the structure amplitudes (F²) were determined for AIN in the temperature range 85–670°K using monochromatic Cu K_α, radiation. These values were used to calculate the mean-square dynamic displacements and the atomic scattering factors of the Al and the N ions. The values of F² were used also to find the shortest relative distance (u₀ /c) between the Al and the N ions along the c axis. This distance was 0.386 ± 0.001, which is different from 0.375 for a perfect structure (c/a= 1.633) and from 0.380 for the case of equal values of all the shortest atomic spacings (c/a = 1.600). The temperature dependences indicated that the mean-square dynamic displacements $(\overline{{{u}^{2}}})$ in AIN were anisotropic. Thus, at room temperature,these displacement were for the Al ion and , for the N ion. The linear expansion coefficient (α) was also anisotropic. In the temperature range 290–670^°K, the components of this coefficient were ${{\alpha }_{z}}=(3.0\pm 0.2)\cdot {{10}^{-6}}{{\deg }^{-1}}$ and ${{\alpha }_{xy}}=(3.8\pm 0.2)\cdot {{10}^{-6}}{{\deg }^{-1}}$. The experimental values F ²_exp were extrapolated to absolute zero and compared with the theoretical values F ²_theor It was found that F ²_exp was less than the theoretical value due to the partial redistribution of the valence electrons away from the aluminum toward the nitrogen.

“Crystals,” pp. 141–149 (see page 3).