An empirical method is described for separating the energy band gap versus temperature curves of semiconductors, in particular germanium and silicon, into their constituent dilation and vibrational parts. The EG versus T curves of semiconductors consist of a near-linear sloping part above 150 K. The mechanisms responsible for this behaviour have been attributed to lattice dilation and acoustic and optical lattice vibrations /l/. The present model involving these quantities determines the manner in which a single average frequency within the acoustic and the optical branches affects the band gap. Hence the analysis considers the importance of average quantities in determining the physical behavior of the materials.The following relation is used to describe the E versus T curves:where Ei, A, x, B, el, and Q2 are parameters. The first term in (1) represents the effect of lattice dilation. It is a function of T raised to the power x and has the flexibility to account for any general dilation expected for the crystal. lattice. The same results can be qualitatively obtained using the expression A(l i BT + C g + . . .), but the form used in (1)

Electron-nuclear-double-resonance (ENDOR) studies are reported for the isotope "Cr'+ enriched to 96% in guanidinium aluminum sulfate hexahydrate (GAlSH). The measurements were done at 4. 2'K and X-band microwave frequencies . The study allowed accurate values of the spin-Hamiltonian hyperfine parameters to be determined and ENDOR patterns to be classified. The sign of the zero-field splitting parameter D was found to be negative, where previously only a positive relative value had been quoted. A linear relationship was found when plotting values of Q' vs A-B, utilizing data obtained in GA1SH and previous results of RbGa and CsGa alums. The best value of the quadrupole moment of "Cr was determined to be Q = -0.028+ 0.005 b.

The spin Hamiltonian zero-field splitting parameter D is measured as a function of temperature for trigonally distorted Cr3+⋅6H2O magnetic complexes in families of hydrated crystals. The purpose of the study is to classify the isomorphs of the crystals via their magnetic behavior so that use can be made of similarities and differences between the members when analyzing data obtained from electron–nuclear double resonance (ENDOR) measurements. The D vs T curves are found to form well ordered patterns within a family of isomorphs, and the patterns are significantly different for each type of crystal. When the straight line part of the curves between 195 and 297 °K are extrapolated to high temperature, the existence of common crossing points is found. The orderly nature of the patterns is expected to provide an additional aid in describing the physical behavior of the crystals. The crystals studied are alums, guanidinium aluminum sulfate hexahydrate (GAlSH) and its isomorphs, and aluminum chloride hexahydrate (AlCl3⋅6H20). The Cr3+ ion is doped as a small impurity in most of the crystals but some concentrated crystals are also studied. Electron spin resonance measurements are made at X-band microwave frequencies (∼9.4 GHz) at the four temperatures 4.2, 77, 195, and 297 °K whenever possible.

An empirical method is used to separate the indirect energy band gap vs. temperature curve of diamond semiconductor into its constituent lattice dilation and vibrational parts. The vibrational mechanism is described in terms of average frequencies over the acoustical and vibrational phonon bands. The results are found to be in agreement with the corresponding averages over the phonon density of states, which are also calculated. The pattern of behaviour exhibited by the group IV A semiconductors from this point of view is discussed.

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