The Small Polaron Problem with an Application to Optical and DC Data of Reduced Barium Titanate

Abstract

Reflectivity data from 1 to 12 pm for four samples of reduced BaTiO, with dc conductivities between 20 and 240 (ncm)-l are analysed in terms of small a polaron theory. Quantitative agreement between theory and experiment is found except for the sample with the highest conductivity. By fitting the optical data it is found that the parameters of the theory the average frequency of the optical phonons, wo, and the number r] of phonons in the polarization cloud, have the values wo = 1.265 x 10'4 s-l and r] = 7. These parameters also determine the temperature dependence of the dc mobility. A weak temperature dependence of the mobility is found theoretically and is in agreement with the experimental data.

The synthesis, crystal growth, and characterization of nonstoichiometric magnetite

“…However, contrary to misconceptions frequently quoted in the literature, departures from the Arrheni,~s behaviour do not signal a breakdown of the small polaron model. Rather, if one accepts charge transport as occurring by thermally activated displacement of carriers then conventional theory (Holstein 1954;Reik and Heese 1967) predicts a mobility u(T) with a temperature dependence of the form uoc (~/T)exp { -r/tan h (~COo/4kT)}, (11) withT ~ = [sin h (tiO~o/2kT)]/2(liCoo/k)~, (12) in which there are two disposable parameters; the appropriate optical lattice frequency co o and the degree of coupling r/of the charge carriers to the lattice (roughly, the number of polarons clothing the electron or hole). These parametric degrees of freedom suffice to provide the needed curvature for a reasonable fit of the above equation to the data in figure 13.…”

Optical properties of charge carriers in magnetite and Mn ferrites

“…Fez+ ions) on the octahedral Fe3+ positions in explaining the electrical properties of the iron-excess manganese ferrites [ l l ] suggests the applicability of this theory also to the optical properties. The theory of the high-frequency electrical conductivity of small polarons was developed by several authors [5,12 to 141. The most convenient expressions, which we shall use in the following, were derived by Reik and Heese…”

“…The expressions (5) and (6) are rather complicated so that a computer has to be used to obtain the desired fit to the optical properties. This was done for the samples studied by means of the TESLA 200 computer with the parameters shown in Table 2.…”

“…I n Section 3 an explanation of the observed optical properties in terms of the small polaron theory of the non-diagonal hopping conductivity is attempted. Such an approach appeared fruitful earlier in explaining the optical properties of some perovskites [4,5], and the possibility of the application of this theory to optical properties of magnetite was also already proposed [6 to 81. However, in the case of magnetite, the lack of reliable experimental data prevented making any conclusive decisions.…”

Les titanates de baryum dopés ont-ils des propriétés semiconductrices ?

“…Des courbes de décroissance, en fin de régime, l'étude théorique montre qu'on peut déduire la plus FIG. 3 [6] ou Berglund et Baer [7].…”