The optical constants of amorphous Ge are determined for the photon energies from 0.08 to 1.6 eV. From 0.08 to 0.5 eV, the absorption is due to k-conserving transitions of holes between the valence bands as in p-type crystals; the spin-orbit splitting is found to be 0.20 and 0.21 eV in non-annealed, and annealed samples respectively. The effective masses of the holes in the three bands are 0.49 m (respectively 0.43 m); 0.04 m, and 0.08 m. An absorption band is observed below the main absorption edge (at 300 °K the maximum of this band is at 0.86 eV); the absorption in this band increases with increasing temperature. This band is considered to be due to excitons bound to neutral acceptors, and these are presumably the same ones that play a decisive role in the transport properties and which are considered to be associated with vacancies. The absorption edge has the form: ω2ϵ2∼(hω−Eg)2 (Eg = 0.88 eV at 300 °K). This suggests that the optical transitions conserve energy but not k vector, and that the densities of states near the band extrema have the same energy-dependence as in crystalline Ge. A simple theory describing this situation is proposed, and comparison of it with the experimental results leads to an estimate of the localization of the conduction-band wavefunctions.

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Optical Properties and Electronic Structure of Amorphous Germanium

A molecular‐kinetic theory, which explains the temperature dependence of relaxation behavior in glass‐forming liquids in terms of the temperature variation of the size of the cooperatively rearranging region, is presented. The size of this cooperatively rearranging region is shown to be determined by configuration restrictions in these glass‐forming liquids and is expressed in terms of their configurational entropy. The result of the theory is a relation practically coinciding with the empirical WLF equation. Application of the theory to viscosimetric experiments permits evaluation of the ratio of the kinetic glass temperature Tg (derived from usual ``quasistatic'' experiments) to the equilibrium second‐order transition temperature T2 (indicated by either statistical‐mechanical theory or extrapolations of experimental data) as well as the hindrance‐free energy per molecule. These parameters have been evaluated for fifteen substances, the experimental data for which were available. Hindrance‐free energies ...

On the Temperature Dependence of Cooperative Relaxation Properties in Glass‐Forming Liquids

An overview of relaxational phenomenology is given in a manner intended to highlight a number of the important problems which, notwithstanding much recent sophisticated investigation, continue to confront the field. The rapidly lengthening timescale for diffusional and/or reorientational motion, which provokes the glass transition, is examined within the framework of the ‘strong’ and ‘fragile’ classification of both liquids and plastic crystals. The behavior patterns observed are related to the topological features of the potential energy hypersurfaces which may characterize each extreme. In view of the implication that the observed glass transition is the kinetically obscured reflection of an underlying higher order thermodynamic transition which could be associated with a diverging length scale (at least for fragile systems), the problem of the basic diffusional length scale at the glass transition, using a probe molecule approach, is considered. Then, details of the kinetics of relaxation under isothermal conditions are reviewed to decide on the range of deviations from Debye behavior which may be encountered. A correlation with fragility is strongly indicated. The phenomena of serial decoupling of relaxational modes from the main structural relaxation as T g is approached is outlined and, finally, the additional phenomena that may be encountered in experiments that explore the state-dependence (or non-linearity) of relaxation are briefly examined.

Relaxation in liquids, polymers and plastic crystals — strong/fragile patterns and problems☆

The dielectric loss factor and dielectric permittivity of 8–16 mol% solutions of chlorobenzene, o‐dichlorobenzene, and 1‐chloronaphthalene in cis‐decalin; 50–60 mol% mixtures of pyridine with chlorobenzene, bromobenzene, 1‐chloronaphthalene, and toluene; 50–60 mol% mixtures of tetrahydrofuran with bromobenzene and 1‐chloronaphthalene; the pure liquids cis‐decalin, o‐terphenyl, iso‐propylbenzene, propylene carbonate; and two fused salt systems, 45 mol% Ca(NO3)2–KNO3 mixture and Ca(NO3)2·4H2O have been measured from 50 Hz to 1 × 105 Hz from − 196° in the vitreous state to about 30° above their respective glass transition temperatures. The Tg's of the organic glasses have been measured by DTA. With the exception of propylene carbonate, all glasses show the presence of one secondary relaxation between − 196° and their respective Tg's either as a peak or shoulder in a tanδ–temperature plot at a single frequency, or in the dielectric loss spectrum. Arrhenius plots of the frequency of maximum loss against temper...

Viscous Liquids and the Glass Transition. II. Secondary Relaxations in Glasses of Rigid Molecules

Recent attempts have been made to assess the relative merits of the free volume and entropy theories of viscous flow in glass‐forming liquids by accurate measurement of viscosity over wide temperature ranges, and subsequent comparison with the equations derived from these theories. In the author's view, this effort is misguided. The theories are crude and qualitative, and such tests are too stringent. It is better to make qualitative or semiquantitative comparison of a wide variety of physical phenomena; judged by this criterion, the entropy theory appears more successful. It is conjectured that further progress can be made by accepting the crude, naive character of any model we are likely to find tractable for the foreseeable future, and recognizing both the values and limitations of such models. A picture of the flow process in viscous liquids is proposed, in an attempt to answer certain questions about the molecular steps in flow either answered unsuccessfully or ignored by present theories, in the hop...

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J. D. Mackenzie

Papers

Modern Aspects of the Vitreous State