The phonon spectra of trigonal selenium at 77 and 298°K

Phonon dispersion curves in the principal symmetry directions of trigonal selenium single crystals have been measured by neutron inelastic scattering, using a three-axis spectrometer. The acoustic modes and the three lowest-lying optical modes (q = 0 energy transfers of 13·5 and 18·5 meV) have been measured at 77°K. The acoustic modes have also been measured at 298°K. There are small frequency shifts between the two temperatures, but the general agreement between the acoustic mode frequencies measured at the two temperatures is excellent. The data have been fit by a force constant model which assumes completely general harmonic forces between the first two neighbors in the same covalently bonded chain and axially symmetric forces derived from a potential of the form V = ? Ar^?m + Br^?n between all other atoms out to an interatomic distance of 6·5 . Fits were carried out with (m; n) = (3; 5) and (6; 12). For the former, the best values of A and B correspond to a Van der Waals equilibrium distance of 3·9and a minimum energy at this distance of 1·5 × 10^?13 ergs (about 2 kcal/mol). There are, however, significant discrepancies between the calculated and observed dispersion curves which indicate that a more sophisticated force model is needed.     

Ion-enhanced gas-surface chemistry: The influence of the mass of the incident ion

There are many examples of situations in which a gas-surface reaction rate is increased when the surface is simultaneously subjected to energetic particle bombardment. There are several possible mechanisms which could be involved in this radiation-enhanced gas-surface chemistry. In this study, the reaction rate of silicon, as determined from the etch yield, is measured during irradiation of the Si surface with 1 keV He⁺, Ne⁺, and Ar⁺ ions while the surface is simultaneously subjected to fluxes of XeF₂ or Cl₂ molecules. Etch yields as high as 25 Si atoms/ion are observed for XeF₂ and Ar⁺ on Si. A discussion is presented of the extent to which these results clarify the mechanisms responsible for ion-enhanced gas-surface chemistry.     

Exact class of inverse scattering solutions

After presenting a procedure for finding exact solutions to the Gelfand-Levitan equation for inverse scattering, we present explicit solutions for 3- to 6-pole reflection coefficients. The method is applicable to an arbitrarily large number of poles. Here we give the first explicit treatment of 4, 5, and 6 poles.     

Die Intrinsicviskosit?t von Polyacryls?ure bei verschiedenen Ionenst?rken: Verhalten des statistischen Kn?uels und des festen St?bchens

Ohne Zusammenfassung     

High-order methods for differential equations with large first-derivative terms

A method is developed to solve elliptic singular perturbation problems. Examples are presented in one and two dimensions for both linear and non-linear problems. In particular, examples are presented for fluid flow problems with boundary layers. In the one-dimensional case an approximating equation is developed using just three points. The method first presented is a fourth-order approximation but is extended to become a higher-order method. Results are included for the fourth-, sixth-, eighth- and tenth-order methods. The results are first compared with results found by Segal in an article about elliptic singular perturbation problems. The elliptic singular perturbation problems are compared with a method by Il'in and also with central and backward difference schemes from Segal's article. There was only one case where the results in Segal's paper were as accurate as the results presented in this paper. However, in this case the method used by Segal did not give accurate values for a second problem presented. The results are also compared with results given by Spalding and by Christie. The method of this paper was also tested on the solution of some non-linear diffusion equations with concentration-dependent diffusion coefficients. The results were superior to results presented by Lee and by Schultz. Finally, the method is extended to several two-dimensional problems. The method developed in this paper is accurate, easy to use and can be generalized to other problems.     

Analysis of beer iso-α-acids by micellar electrokinetic chromatography and multi-wavelength UV detection

The identification of beer bitter acids in a pre-isomerized hop extract by means of their UV-spectra is described. Preliminary data for the analysis of these compounds in beer samples are presented.