Two maxima in the conduction band density of states were located with respect to the bottom of the conduction band by comparing our data for the outermost core d and p electrons for these compounds with transition energies measured by uv absorption, uv ref lectivity, and electron-energyloss experiments. One maximum is located between 0. 8 and l. 4 eV above the bottom of the conduction band depending on the material and the other is located between 3 and 4 eV. This analysis showed that the higher peak was only observed in transitions from the outermost d levels of the cation while the lower peak was observed in transitions from all, of the core levels for which data were available. Both peaks correspond rather closely with the two lowest maxima which have been obtained in published density-of-states calculations for some of these compounds. ACKNOW LEDGMENTSWe wish to thank T. C. Collins for helpful discussions. We also wish to thank B. Terrants of the U. S. Air Force Materials Laboratory for furnishing the GaP and M. Davis of the U. S. Aj.r , Phys. Rev. Letters 25, 659 (19V0).The phonon dispersion relations in silicon and germanium are found to be nearly homo1ogous with small but significant deviations. These results, which have been obtained by thermalneutron spectrometry, are strongly supported by an analysis in which comparison is made with elastic constants, heat capacities, and Haman frequencies for these elements. Previously observed discrepancies between results obtained from shell-model calculations and from heat-capacity measurements are explained. Attempts are made to elucidate the origin of the observed differences between the dimensionless phonon frequencies of group-IVB elements with the diamond-type crystal structure.

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WEAK ABSORPTION TAILS IN AMORPHOUS SEMICONDUCTORStion cross section. In this interpretation the internal electric fields' ' make the glasses more transparent than a crystal with the same concentration of states in the gap. One can roughly visualize the nature of the effect with the following picture. As the percolation theory suggests, ' above the mobility edge, but close to it, the extended states do not exist in the whole volume V, of the sample but only in a part V, (Fig. 5). If we neglect transitions between states located at different sites, the absorption is reduced by a factor V, /V, . ACKNOWLEDGMENTS %'e are grateful to Miss Phys. C~4 93 (1971). These two authors ascribe the weak absorption tails (which they observed at absorption levels very different from each other) to indirect phononassisted transitions.However, the observed temperature dependence cannot be explained by the current theory of such transitions.More than 500 frequencies of phonons with reduced wave vectors evenly distributed over an irreducible section of the first Brillouin zone have been measured in germanium at 80 K with a neutron crystal spectrometer.The phonon density of states was calculated from the data with an improved sampling technique.Comparisons between thermodynamic quantities derived from calorimetric data and from the present spectrum reveal an excellent agreement. A critical-point scheme determined by use of a method originating from Phillips is also presented. The scheme properly satisfies the Morse relations and other topological conditions, and most of the van Hove singularities expected are clearly displayed in the spectrum.