Nota de FísicaPublicado
Bragg Law and Darwin Model of Scattering Upon Inclusion of Ewald Self-Consistency Principle
W.A. Keller
1993
Dados da publicação
- Autores
- W.A. Keller
- Tipo
- Nota de Física
- Status
- Publicado
- Data de publicação
- 1993
- Descrição
- A scattering unit concept is used to solve Maxwell's equations for a Darwin-type model of a crystal. The latter is taken to be a stack of identical and equally spaced dipole planes. The self-consistent solution obtained for one of the planes is extended to series of planes representing the whole crystal. The solution obtained in closed-form, depends upon: a) continuity of all vectors which define the EM field between the adjoining units and b) geometric similarity of EM fields which activate the dipoles at different planes. Once both conditions are satisfied they bring about: the modified Bragg law and a hyperbola relating phase-shifts of both waves equivalent to the main equation of the dynamic theory. While the model is a development upon that of Darwin, the two divergent points from his model are: a) vectorial waves are used to define the EM field instead of scalar waves, b) interaction of all dipoles within the same plane is taken into account, wherein the principle of energv conservation is obeyed. Our model accepts: i) an imperfect upper crystal surface, ii) the second incident wave at the lower crystal surface may be of arbitrary amplitude and phase, iii) periodicity deviations due to the thermal motion or defects, iv) any actual crystal size (small or big).
- Ano
- 1993
- Número
- CBPF-NF-028/93
- Vínculo com tese
- Não
- Vínculo com bolsa
- Não