Mssbauer Effect in Lattice Dynamics: Experimental Techniques and Applications Book

Preface.

1 The Mössbauer Effect.

1.1 Resonant Scattering of g-Rays.

1.2 The Mössbauer Effect.

1.2.1 Compensation for Recoil Energy.

1.2.2 The Discovery of the Mössbauer Effect.

1.3 The Mössbauer Spectrum.

1.3.1 The Measurement of a Mössbauer Spectrum.

1.3.2 The Shape and Intensity of a Spectral Line.

1.4 The Classical Theory.

1.5 The Quantum Theory.

1.5.1 Coherent States of a Harmonic Oscillator.

1.5.2 Gamma Radiation from a Bound Nucleus.

1.5.3 Mössbauer Effect in a Solid.

1.5.4 Average Energy Transferred.

References.

2 Hyperfine Interactions.

2.1 Electric Monopole Interaction.

2.1.1 A General Description.

2.1.2 The Isomer Shift.

2.1.3 Calibration of Isomer Shift.

2.1.4 Isomer Shift and Electronic Structure.

2.2 Electric Quadrupole Interaction.

2.2.1 Electric Quadrupole Splitting.

2.2.2 The Electric Field Gradient (EFG).

2.2.2.1 Sources of EFG.

2.2.2.2 Temperature Effect on EFG.

2.2.3 Intensities of the Spectral Lines.

2.2.4 The Sign of EFG.

2.3 Magnetic Dipole Interaction.

2.3.1 Magnetic Splitting.

2.3.2 Relative Line Intensities.

2.3.3 Effective Magnetic Field 53

2.4 Combined Quadrupole and Magnetic Interactions.

2.5 Polarization of g-Radiation.

2.5.1 Polarized Mössbauer Sources.

2.5.2 Absorption of Polarized g-Rays.

2.6 Saturation Effect in the Presence of Hyperfine Splittings.

2.7 Mössbauer Spectroscopy.

References.

3 Experimental Techniques.

3.1 The Mössbauer Spectrometer.

3.2 Radiation Sources.

3.3 The Absorber.

3.3.1 Estimation of the Optimal Thickness.

3.3.2 Sample Preparation.

3.4 Detection and Recording Systems.

3.4.1 Gas Proportional Counters.

3.4.2 NaI(Tl) Scintillation Counters.

3.4.3 Semiconductor Detectors.

3.4.4 Reduction and Correction of Background Counts.

3.4.5 Geometric Conditions.

3.4.6 Recording Systems.

3.5 Velocity Drive System.

3.5.1 Velocity Transducer.

3.5.2 Waveform Generator.

3.5.3 Drive Circuit and Feedback Circuit.

3.5.4 Velocity Calibration.

3.5.4.1 Secondary Standard Calibration.

3.5.4.2 Absolute Velocity Calibration.

3.6 Data Analysis.

3.6.1 Fitting Individual Lorentzian Lines.

3.6.1.1 Spectra from Crystalline Samples.

3.6.1.2 Spectra from Amorphous Samples.

3.6.2 Full Hamiltonian Site Fitting.

3.6.3 Fitting Thick Absorber Spectra.

References.

4 The Basics of Lattice Dynamics.

4.1 Harmonic Vibrations.

4.1.1 Adiabatic Approximation.

4.1.2 Harmonic Approximation.

4.1.3 Force Constants and Their Properties.

4.1.4 Normal Coordinates.

4.2 Lattice Vibrations.

4.2.1 Dynamical Matrix.

4.2.2 Reciprocal Lattice and the Brillouin Zones.

4.2.2.1 Reciprocal Lattice.

4.2.2.2 Brillouin Zones.

4.2.3 The Born–von Karman Boundary Condition.

4.2.4 Acoustic and Optical Branches.

4.2.5 Longitudinal and Transverse Waves.

4.2.6 Models of Interatomic Forces in Solids.

4.3 Quantization of Vibrations: The Phonons.

4.4 Frequency Distribution and Thermodynamic Properties.

4.4.1 The Lattice Heat Capacity.

4.4.2 The Density of States.

4.4.2.1 The Einstein Model.

4.4.2.2 The Debye Model.

4.4.3 Moments of Frequency Distribution.

4.4.4 The Debye Temperature yD.

4.4.4.1 The Physical Meaning of yD.

4.4.4.2 Comparison of Results from Various Experimental Methods.

4.5 Localized Vibrations.

4.6 Experimental Methods for Studying Lattice Dynamics.

4.6.1 Neutron Scattering.

4.6.1.1 Theory.

4.6.1.2 Neutron Scattering by a Crystal.

4.6.2 X-ray Scattering.

4.7 First-Principles Lattice Dynamics.

4.7.1 Linear Response and Lattice Dynamics.

4.7.2 The Density-Functional Theory.

4.7.3 Exchange-Correlation Energy and Local-Density Approximation.

4.7.4 Plane Waves and Pseudopotentials.

4.7.5 Calculation of DOS in Solids.

References.

5 Recoilless Fraction and Second-Order Doppler Effect.

5.1 Mean-Square Displacement hu2i and Mean-Square Velocity hv2i.

5.2 Temperature Dependence of the Recoilless Fraction f.

5.3 The Anharmonic Effects.

5.3.1 The General Form of the Recoilless Fraction f.

5.3.2 Calculating the Recoilless Fraction f Using the Pseudoharmonic Approximation.

5.3.3 Low-Temperature Anharmonic Effect.

5.4 Pressure Dependence of the Recoilless Fraction f.

5.5 The Goldanskii–Karyagin Effect.

5.5.1 Single Crystals.

5.5.2 Polycrystals.

5.6 Second-Order Doppler Shift.

5.6.1 Transverse Doppler Effect.

5.6.2 The Relation between f and dSOD.

5.7 Methods for Measuring the Recoilless Fraction f.

5.7.1 Absolute Methods.

5.7.2 Relative Methods.

References.

6 Mössbauer Scattering Methods.

6.1 The Characteristics and Types of Mössbauer g-ray Scattering.

6.1.1 The Main Characteristics.

6.1.2 Types of Scattering Processes.

6.2 Interference and Diffraction.

6.2.1 Interference between Nuclear Resonance Scattering and Rayleigh Scattering.

6.2.2 Observation of Mössbauer Diffraction.

6.3 Coherent Elastic Scattering by Bound Nuclei.

6.3.1 Nuclear Resonance Scattering Amplitude.

6.3.2 Coherent Elastic Nuclear Scattering.

6.3.2.1 Scattering Amplitude.

6.3.2.2 Nuclear Bragg Scattering (NBS).

6.3.2.3 Nuclear Forward Scattering (NFS).

6.3.2.4 Scattering Cross-Sections.

6.3.3 Lamb–Mössbauer Factor and Debye–Waller Factor.

6.4 Rayleigh Scattering of Mössbauer Radiation (RSMR).

6.4.1 Basic Properties of RSMR.

6.4.2 Separation of Elastic and Inelastic Scatterings.

6.4.3 Measuring Dynamic Parameters Using RSMR.

6.4.3.1 The Fixed Temperature Approach.

6.4.3.2 The Variable Temperature Approach.

6.4.4 RSMR and Anharmonic Effect.

6.4.4.1 Using Strong Mössbauer Isotope Sources.

6.4.4.2 Using Higher Temperature Measurements.

References.

7 Synchrotron Mössbauer Spectroscopy.

7.1 Synchrotron Radiation and Its Properties.

7.1.1 The Angular Distribution of Radiation.

7.1.2 The Total Power of Radiation.

7.1.3 The Frequency Distribution of Radiation.

7.1.4 Polarization.

7.2 Synchrotron Mössbauer Sources.

7.2.1 The meV Bandwidth Sources.

7.2.2 The meV Bandwidth Sources.

7.3 Time Domain Mössbauer Spectroscopy.

7.3.1 Nuclear Exciton.

7.3.2 Enhancement of Coherent Channel.

7.3.3 Speed-Up of Initial Decay.

7.3.4 Nuclear Forward Scattering of SR.

7.3.5 Dynamical Beat (DB).

7.3.6 Quantum Beat (QB).

7.3.7 Distinctions between Time Domain and Energy Domain Methods.

7.3.8 Measurement of the Lamb–Mössbauer Factor.

7.4 Phonon Density of States.

7.4.1 Inelastic Nuclear Resonant Scattering.

7.4.2 Measurement of DOS in Solids.

7.4.3 Extraction of Lamb–Mössbauer Factor, SOD Shift, and Force

7.5 Synchrotron Methods versus Conventional Methods.

References.

8 Mössbauer Impurity Atoms (I).

8.1 Theory of Substitutional Impurity Atom Vibrations.

8.1.1 The General Method.

8.1.2 Mass Defect Approximation.

8.1.2.1 Resonance Modes.

8.1.2.2 Localized Modes.

8.2 The Mannheim Model.

8.3 Impurity Site Moments.

8.3.1 The Einstein Model.

8.3.2 The Einstein–Debye Model.

8.3.3 The Maradudin–Flinn Model.

8.3.4 The Visscher Model.

8.3.5 The Mannheim Model..

8.4 Examples of Mössbauer Studies of 57Fe, 119Sn, and 197Au Impurities.

8.4.1 57Fe Impurity Atoms.

8.4.2 119Sn Impurity Atoms.

8.4.3 197Au Impurity Atoms.

8.5 Interstitial Impurity Atoms.

8.5.1 57Fe Impurities in Au.

8.5.2 57Fe Impurities in Diamond.

References.

9 Mössbauer Impurity Atoms (II).

9.1 Metals and Alloys.

9.1.1 Metals.

9.1.2 Alloys.

9.1.2.1 The b-Ti(Fe) Alloy.

9.1.2.2 CuaZn Alloy (Brass).

9.2 Amorphous Solids.

9.2.1 The Alloy YFe2.

9.2.2 The Alloy Fe80B20.

9.3 Molecular Crystals.

9.3.1 The Concept of Effective Vibrating Mass Meff.

9.3.2 Vibrational DOS in Molecular Crystals.

9.3.2.1 The Mode Composition Factor e2(l, j).

9.3.2.2 An Example.

9.4 Low-Dimensional Systems.

9.4.1 Thin Films.

9.4.2 Nanocrystals.

References.

Appendices.

Appendix A Fractional Intensity e(v) and Area A(ta).

Appendix B Eigenstate Calculations in Combined Interactions.

B.1 Electric Quatrupole Perturbation.

B.2 The Coefficients ai,mg and bj,me.

Appendix C Force Constant Matrices (F) in fcc and bcc Lattices.

Appendix D Nearest Neighbors Around a Substitutional Impurity.

Appendix E Force Constants for Central Forces.

Appendix F Lattice Green’s Function.

F.1 Definition of Green’s Function.

F.2 The Real and Imaginary Parts of G.

F.3 Symmetry Properties of the G-Matrices.

F.4 The Mean Square Displacement hu2(0)i and the Recoilless Fraction f.

F.5 Relations Between Different Green’s Functions Gab(l l0,w).

Appendix G Symmetry Coordinates.

Appendix H Mass Absorption Coefficients.

Copyright Acknowledgments.

Subject Index.