Studies in the theory of solids

Smith, Darryl Lyle

Permalink

https://hdl.handle.net/2142/30695 Copy

Description

Title

Studies in the theory of solids

Author(s)

Smith, Darryl Lyle

Issue Date

1974

Director of Research (if dissertation) or Advisor (if thesis)

Dow, J.D.

Department of Study

Physics

Discipline

Physics

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• kinematic
• single crystal
• x-ray edge anomalies
• Aluminum
• lithium
• Hamiltonian
• crystal impurities

Language

en

Abstract

"I: The accuracy of a recently proposed method of extracting kinematic low-energy-electron-diffraction intensities from averages of experimental data taken at constant momentum transfer is examined by using calculated intensities in lieu of the data. These ""dynamical"" intensities are evaluated using the isotropic-scatterer inelastic-collision model. As the model parameters are known ~ priori, both the kinematical and dynamical intensities are specified exactly without appeal to any empirical procedures. Comparison of the kinematical and averaged-dynamical intensities reveals systematic discrepancies between the two on the order of 10-100% for parameters characteristic of electrons with energies 50 ~ E ~ 100 eV incident on clean surfaces of monatomic metals. These discrepancies arise because the averaging does not remove completely the effects of multiple scattering from strongly scattering ion cores. A general (geometrical) formulation of the relation between the kinematical and dynamical intensities is proposed. Within the framework of this formulation appropriate measures of the averaged intensities, kinematic intensities, and their differences are constructed. For physically reasonable model parameter~ the averaging method is shown to be capable of determining the values of expansions (contractions) of the uppermost-layer spacings at clean single-crystal surfaces to within a few percent. II: The many-electron theory of x-ray edge anomalies is examined in the light of existing data and new experimental tests of the theory are suggested. The K~ emission, L2,3 emission, L2,3 satellite emission, and L ,3 2 absorption spectra of aluminum are shown to exhibit threshold shapes which cannot all be consistently explained using the present form of the threshold theory. We show that the threshold theory predicts a dramatic change in the absorption threshold of lithium if impurities are introduced into the material. Experimentally, this effect is not observed demonstrating that the present form of the threshold theory cannot explain the absorption edge shape of lithium. The threshold theory also predicts the edge shape of electron energy loss spectra and tests of the dependence on core-electron angular momentum are suggested: (i) for transitions from d or f core level to conduction bands, the inelastic electron scattering spectral shape S(q.m) should be dramatically enhanced as the momentum transfer hq is increased from zero. (ii) For the L2,3 edges, S(~,m) should flatten perceptibly with increasing q. These experiments are in progress and should greatly clarify the range of validity of the threshold theory. III: A model Hamiltonian is used to consider resonant energy transfer between impurities in a crystal. A nonperturbative calculation of excitation probabilities is presented which is valid for all values of the electron-phonon coupling. When the electron-phonon coupling is strong, our result reduce to that of the well-known F~rster-Dexter theory. When the electron-phonon coupling is negligible, our results reduce to that of the two level model first considered by Perrin. We determine the condition for dissipative or periodic energy transfer in terms of the model parameters and relate these parameters to the impurity optical spectra."

Type of Resource

text

Permalink

http://hdl.handle.net/2142/30695

Copyright and License Information

© 1974 Darryl Lyle Smith

Owning Collections