Simple theory of microwave absorption in alkali halides

Abstract

The intrinsic microwave absorption coefficient P of alkali halides is well explained by lifetime-broadened two-phonon difference processes, in contrast to energy-conserving twoand three-phonon processes as previously thought. A simple closed-form expression for p with no adjustable parameters gives excellent agreement with the magnitude, frequency dependence, and temperature dependence of P in LiF, NaC1, KBr, and KI. As tu increases from to & to, /3 to co=to, +yz93 the frequency and temperature dependence of p at 293 K Here co, =20 cm ' for NaCl is the frequency difference between the transverse-acoustical and transverse-optical phonon modes at the Brillouin-zone edge along the [111]direction, and y is the combined-phonon inverse lifetime at 293 K. The temperature dependence of the phonon frequencies and other parameters must be included in order to explain the temperature dependence of the experimental results. The present lifetime-broadened results reduce to previous energy-conservation results {apart from smoothing, which explains the lack of sharp structure in p, but otherwise has little effect in general) and agree with experimental results in the region co & co, +y. Previous energy-conserving results disagree with the T and co dependence and magnitude of the experimental results in the region co & co, .

Microwave dielectric loss in oxides: Theory and experiment

“…Sparks et al 12 build on earlier work by Stolen and Dransfeld. 13 14 produced general rules for significant transitions in addition to those allowed by group theory.…”

“…In the NaCl structure, Eldridge 14 shows that transitions are not allowed at the X point, but are at the L point. This might be the reason why, in the Sparks et al 12 model, only the transitions between the transverse-acoustic ͑TA͒ and transverse-optic ͑TO͒ branches at the L point are considered. Contributions coming from other interband processes ͑such as those between acoustic branches or higher-frequency branches͒ are not considered although they are not forbidden by the model.…”

“…However, because of the finite lifetime of the phonons, the gap between phonon branches is not well defined and cannot be determined with a higher precision than h times the inverse of the thermal phonon lifetime. In the model by Sparks et al 12 such relaxation of the energy conservation constraint due to the poor definition of the energy gap is introduced explicitly in terms of a Lorentzian broadening of the branches. Losses are then calculated in terms of two-phonon difference processes between acoustic and optic branches and are expressed as a function of the linewidth ͑␥͒ of the Lorentzian line shape.…”

“…In this article, we report loss measurements as a function of temperature in single crystal and polycrystalline MgO and Al 2 O 3 . These experimental data are then interpreted in terms of the Sparks et al 12 formulas, where the linewidth ␥ of the phonons at the zone boundary, which is temperature dependent, is used either as a fitting parameter ͑MgO͒ or is approximated in terms of the linewidth at the zone center directly measured by Raman spectroscopy (Al 2 O 3 ).…”

Characteristics of Millimeter-wave Heating and Smart Materials Synthesis

“…In an ionic crystal with low concentration of vacancies, however, the multi-phonon process is also the important mechanism for the absorption of microwave energy in the range from 2 to 20 GHz. According to Sparks et al, 13) eЉ ph (w) is given by the following equation where w f and G are the resonant frequency of fundamental reststrahrent transverse phonon mode and relaxation velocity coefficient, respectively.…”