Electron Paramagnetic Resonance Spectroscopy: Fundamentals

              Preface

              Fundamental constants. Units conversion.

            1 The electron paramagnetic resonance phenomenon

                 1.1  What is a spectroscopic experiment?

                 1.2  Magnetic spectroscopies

                 1.3  Diversity of paramagnetic centers

                 1.4  Principle of an EPR experiment

                 1.5  Basic instrumentation for an EPR spectrometer

                 1.6  Important points for applications

                 1.7 Appendices : magnetic moment of a particle uniformly moving along a circular

                       trajectory. Why are O₂ and B₂ molecules paramagnetic ? Effect of the

                       modulation on the detected signal

                 1.8  Exercises

            2  Hyperfine structure of the spectrum in the isotropic regime

                 2.1  Various origins of the structures of an EPR spectrum

                 2.2  Hyperfine interactions

                 2.3  The isotropic regime

                 2.4  Spectrum given by a paramagnetic center interacting with several nuclei

                        in the isotropic regime

                 2.5  Important points for applications

                 2.6  Appendices : The spin label technique. Pascal's triangles.

                 2.7  Exercises

            3 Introduction to the spin states space formalism

                 3.1  Introduction

                 3.2  Spin states space associated with an angular momentum

                 3.3  Possible spin states and energy levels of a paramagnetic center

                         in a magnetic field

                 3.4  Transition probability and allowed transitions

                 3.5  Possible spin states and allowed transitions in the presence

                         of hyperfine interactions

                 3.6  Important points for applications

                 3.7  Appendices : Diagonalization of H_Zeeman in any basis. Perturbation methods

                 3.8  Exercices

            4 Consequences of the anisotropy of  G and A matrices on the shape of spectra

               given by radicals and transition ions complexes

                 4.1  Introduction

                 4.2  The G matrix

                 4.3  Shape of the spectrum given by paramagnetic centers without hyperfine

                        interaction

                 4.4  Effects of an isotropic hyperfine interaction on the EPR spectrum shape

                 4.5  Effect of  molecules motion on the EPR spectrum: isotropic and

                        very low motion regimes

                 4.6  Important points for applications

                 4.7  Appendices : splitting of the electrons energy levels in an octahedral complex.

                        Possible values of g' for a rhombic G matrix. Expression of the resonance lines

                        density for a center with axial symmetry. Energy levels for any direction of the

                        field for anisotropic G and A matrices. An example of study carried out on a

                        monocrystal: identifying the Ti³⁺fluorescence site in LaMgAl₁₁O₁₉.

                 4.8  Exercices

            5  Intensity of the spectrum, saturation, spin-lattice relaxation

                 5.1  Introduction

                 5.2  Intensity of the spectrum at thermal equilibrium

                 5.3  Saturating the signal

                 5.4  Spin-lattice relaxation

                 5.5  Important points for applications

                 5.6  Appendices: Fermi golden rule. Expression of the intensity factor for a

                        center with axial symmetry with S = ½. Homogeneously and inhomogeneously

                        broadened lines.

                 5.7  Exercices

            6   Zero field splitting. EPR spectra given by paramagnetic centers with spin 

                  greater than ½

                 6.1  Introduction

                 6.2  The D matrix

                 6.3  Definition and characteristics of the "high field" and "low field" cases

                 6.4  General properties of the spectrum in the high field case

                 6.5  Shape of the spectrum in the high field case

                 6.6  EPR spectra given by complexes with half integer spins

                 6.7  EPR spectra given by complexes with integer spins in the low field case

                 6.8  Important points for applications

                 6.9  Appendices : resonance line intensity at high temperature in the high field

                         limit. Shape of the low field spectrum given by a center with S = 1

                 6.10 Exercises

            7   Effect of dipolar and exchange interactions on the EPR spectrum.

                 Biradicals and polynuclear complexes.

                 7.1  Introduction

                 7.2  Origin and description of intercenter spin-spin interactions

                 7.3  Effect of weak interactions on the spectrum

                 7.4  Effect of strong exchange interactions on the spectrum

                 7.5  Effect of intercenter interactions on the intensity of the spectrum

                         and on relaxation properties.

                 7.6  Important points for applications

                 7.7  Appendix. Equivalent Hamiltonian for a trinuclear complex

            8  EPR spectra given by rare earth and actinide complexes

                 8.1  Rare earth ions

                 8.2  Rare earth complexes : effect of the interactions of electrons with ligands

                 8.3  EPR spectra given by rare earth complexes with half integer J values

                 8.4  EPR spectra given by rare earth complexes with integer J values

                 8.5  Actinide complexes

                 8.6  Important points for applications

            9  Effect of instrumental parameters on the shape and intensity of the  

                spectrum. Introduction to numerical simulation techniques.

                 9.1  Introduction

                 9.2  Scanning  and modulating

                 9.3  Effect of microwave power and frequency. Importance of temperature.

                 9.4  Numerical simulation of the spectrum saturation

                 9.5  Introduction to numerical simulation of spectra

                 9.6  Important points for applications

                 9.7  Appendices : Basic properties of the convolution product. Quantitative analysis

                         of the saturation curve for an inhomogeneous line. Quantitative study of the

                         relaxation broadening of the spectrum. Use of standards. Numerical

                         simulation software.

                 9.8  Exercises

            10  Appendices

                 10.1 Magnetic moment of a free atom or ion.

                 10.2  G and A matrix of a transition ion complex in the ligand field approximation.

                 10.3  Dipolar interactions between a nucleus and electron spin magnetic moments

                 10.4  Properties of angular momentum operators. Projection coefficients and

                          equivalent operators. Application to the Landé formula and to the dipolar  

                          component of hyperfine interactions.

                 10.5   Spin density

                 10.6   Calculation of the spin-lattice relaxation time T₁ for the direct process

                 10.7   Matrix elements of operators defined from the components of an angular

                           momentum.

            11 Correction of exercises

            12 Glossary

            13 References

            16 Index