I= INTERACTIONS WITHIN EXCHANGE COUPLED TRIADS OF TRANSITION METAL IONS
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Title of Thesis
INTERACTIONS WITHIN EXCHANGE COUPLED TRIADS OF TRANSITION METAL IONS

Author(s)
G. S. Akram Ali Shah
Institute/University/Department Details
University of Karachi/ Department of Physics
Session
2001
Subject
Number of Pages
84
Keywords (Extracted from title, table of contents and abstract of thesis)
exchange coupled triads, metal ions, energy structure, asymmetric triads, spin-orbit, trigonal field

Abstract
The purpose of this work is to describe the energy structure of asymmetric triads (d3-d3-d2 and d2-d2-d3) which can be used in interpreting the spectra of mixed valence transition metal ions. A many body technique has been developed to understand the structure of these two triads. The wave functions for crystal, and the difference between it and full Hamiltonian is then treated by perturbation theory, taken to second order. Ab-initio calculations have been performed using the second quantization formulation to calculate the exchange interactions within 3T1, 3T1, 4A2) and 4A2, 4A2, 3T1) ground manifolds. This leads to exchange matrices that describe the energy structure of triads. The energy levels associated with exchange coupled asymmetric triads have been studied and allowed electric dipole transitions have been predicted. The splitting of manifolds under the combined effects of exchange, trigonal field and spin-orbit interactions have been described

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842.85 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 Contents 0
45.15 KB
2 1 Interctions Within Triads 1
197.12 KB
  1.1 Introduction 1
  1.2 Strong Field Approach 5
  1.3 Strong Field Wave Functions For D2 And D3 Systems 8
  1.4 A Model For Triads Of Lons 9
3 2 Second Quantization Techniques 19
59.11 KB
  2.1 Indistinguishability Of Electrons In A System 19
  2.2 Slater Determinant 20
  2.3 Second Quantization For Electron 21
4 3 Perturbative Procedure 24
78.39 KB
  3.1 Some Introductory Concepets 24
  3.2 First Order Perturbation Theory 26
  3.3 Second Order Contribution 27
5 4 Exchange Matrices And Transformations 30
435.1 KB
  4.1 Exchange Interactions 30
  4.2 Exchange Matrices For (D3-D3-D2) Triad 39
  4.3 Exchange Matrices For (D2-D2-D3) Triad 68
  4.4 Group Theoretic Analysis 59
6 5 Conclusion 71
67.95 KB
  5.1 Energy Structure Of (D3-D3-D2) System 71
  5.2 Energy Structure Of (D2-D2-D3) System 74
  5.3 Vibronic Interactions 76
7 6 Appendices 78
73.18 KB
  6.1 Appeindix-I Number Of Allowed Terms For Strong Field Configurations 78
  6.2 Appeindix-Ii Table For Group D3h 79
  6.3 Acknowledgements 80
  6.3 References 81