Chemical Bonds in Solids pp 14-20 | Cite as

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

## Abstract

The absolute values of the squares of the structure amplitudes (F^{2}) 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 F^{2} were used also to find the shortest relative distance (u_{0} /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
Open image in new window Open image in new window for the Al ion and Open image in new window , Open image in new window 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 _{exp} ^{2} were extrapolated to absolute zero and compared with the theoretical values F _{theor} ^{2} It was found that F _{exp} ^{2} was less than the theoretical value due to the partial redistribution of the valence electrons away from the aluminum toward the nitrogen.

### Keywords

Anisotropy Attenuation Toluene Hexagonal Nitride## Preview

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### Literature Cited

- 1.G. A. Jeffrey, G. S. Parry, and R. L. Mozzi, J. Chem. Phys., 25: 1024 (1956).CrossRefGoogle Scholar
- 2.N. N. Sirota and N. M. Olekhnovich, Vestsi Akad. Navuk Belarus. SSR, Ser. Fiz.Tekh. Navuk, No. 1, p. 111 (1968).Google Scholar
- 3.R. W. James, The Optical Principles of the Diffraction of X-Rays, Bell, London (1950).Google Scholar
- 4.International Tables for X-Ray Crystallography, Vol. 3, Kynoch Press, Birmingham (1962).Google Scholar
- 5.N. N. Sirota, E. M. Gololobov, and N. M. Olekhnovich (Olechnovic), and A. U. Sheleg (Seleg), Krist. Tech., 1: 545 (1966).CrossRefGoogle Scholar