Determination of the energy relaxation time in GaSb from microwave harmonic mixing and transport phenomena

The energy relaxation time τ_? of GaSb has been determined independently from microwave harmonic mixing experiments in the range of 160–200 K and from the current-voltage characteristics at 300 and 77 K. From measurements of the i.r. Faraday effect at 300 K valley populations as a function of the electric field strength are obtained which are in agreement with values calculated with help of the energy relaxation time obtained by methods mentioned before. For the evaluation of the data a two-band model has been used. The results obtained from the microwave experiments are extrapolated to 300 and 77 K assuming polar optical mode scattering. Good agreement of these values and the results obtained from the current-voltage characteristics and the Faraday measurements was found. The values for 300 and 77 K are 4 × 10⁻¹² sec and approximately 1·6 × 10⁻¹¹ sec, respectively.     

Edge partitions of the complete symmetric directed graph and related designs

We show that the edges of the complete symmetric directed graph onn vertices can be partitioned into directed cycles (or anti-directed cycles) of lengthn−1 so that any two distinct cycles have exactly one oppositely directed edge in common whenn=p ^e>3, wherep is a prime ande is a positive integer. When the cycles are anti-directedp must be odd. We then consider the designs which arise from these partitions and investigate their construction. We would like to thank the Mathematics Department of the University of Arizona for their hospitality during January 1979 when this work was begun. Partial support was provided for this research by the Natural Sciences and Engineering Research Council of Canada under Grant A-4792.     

Quadriken und ihre Teilquadriken

Ohne Zusammenfassung     

Nucleophilic aromatic substitution. Part XV. Phase-transfer catalysis of sulfodechlorination and identification of a primary product of sulfite ion with 1-chloro-2, 4-dinitrobenzene

With conventional phase-transfer catalysis using quaternary ammonium salts, yields of 2, 4-dinitrobenzenesulfonic acid ( 2 ) in the sulfodechlorination of 1-chloro 2.4-dinitrobenzene ( 1 ) with sulfite ions are no better than those obtained with the classical method in aqueous ethanol (80–82%). Yields up to 97% and a very pure product are obtained, however, by using protonated tertiary amines as catalysts. The optimum chain-length of the amine is found with tributylamine. On mixing solutions of the reagents and catalysts a strong bluish-red colour develops immediately, but disappears within ca. 1 h. Comparison of the NMR. spectrum of this primary product with model adducts of sulfite ions and di- and trinitrobenzene derivatives demonstrates that the primary addition of the nucleophile to 1-chloro-2, 4-dinitrobenzene does not take place at C (1), but at C(5). It is shown that the increments calculated for a C-SO group and for the 1, 3-dinitro- and 1, 3, 5-trinitropentadienyl ring moieties can be employed for the approximate calculation of ¹H-chemical shifts using Clerc & Pretsch's modification of the Shoolery rules [3].     

The Crystal Structure of Dimethylamino Titanium Trichloride

Green crystals of Me₂NTiCl₃ associate to a chain polymer via four Ti‐Cl‐Ti bonds and generation of hexacoordinated Ti atoms. Like Et₂NTiCl₃ its amino group is not involved into forming Ti‐N‐Ti bridges. This is due to a short Ti‐N bond to the planar coordinated N atom of the Me₂N group.