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Use of a Pure Phonon Theory in the Interpretation of IR Spectrum of a NiO Powder

Volume 36, Number 3 (June 1982) Page 325-327

Iglesias, Juan E.; Rendon, Jose L.; Serna, Carlos J.

From the work of Ruppin and Englman it became clear that particle size and shape have a great influence in the IR spectrum of a polar crystal and that these effects can be accounted for quantitatively by theoretical calculations. A number of such calculations have been made on the basis of the polariton theory, applicable to finite specimens of arbitrary size, and pure phonon theories, applicable to samples much smaller than the incident radiation wavelength. In the latter theories, the photon component in the polariton can be neglected. Compared with the polariton theory, the limitation of the phonon theories is more apparent than real since the particle size is reduced in practice to less than 2 μm. Furthermore, only the sphere, cylinder, and slab geometries are solved within the Mie (polariton) theory, whereas phonon theories can be applied to the more general ellipsoid geometry by using appropriate depolarization factors (see, for example, Ref. 6). Recently, an analytical comparison between the exact Mie theory and the approximate method of the phonon theory has been carried out for spherical particles, and it was shown that there is an influence of the complex index of refraction in addition to the particle size, i.e., the phonon theory gives accurate results for the absorbed field under the sole restriction that |n| q ≪ 1 where, n = n - ik (complex refractive index) and q = 2πs/λ (s = radius of the sphere).