Amorphous Solids: Low-Temperature Properties (Topics in Current Physics)

It is now ten years since it was first convincingly shown that below 1 K the ther­ mal conductivity and the heat capacity of amorphous solids behave in a way which is strikingly different to that of crystalline solids. Since that time there has been a wide variety of experimental and theoretical studies which have not only defined and clarified the low temperature problem more closely, but have also linked these differences between amorphous and crystalline solids to those suggested by older acoustic and thermal experiments (extending up to 100 K). The interest in this somewhat restricted branch of physics lies to a considerable extent in the fact that the differences were so unexpected. It might be thought that as the tempera­ ture, probing frequency, or more generally the energy decreases, a continuum de­ scription in which structural differences between glass and crystal are concealed should become more accurate. In a sense this is true, but it appears that there exists in an amorphous solid a large density of additional excitations which have no counterpart in normal crystals. This book presents a survey of the wide range of experimental investigations of these low energy excitations, together with a re­ view of the various theoretical models put forward to explain their existence and nature.

1. Introduction.- 1.1 Historical Background.- 1.2 Tunneling States.- 1.2.1 Energy Levels.- 1.2.2 Transition Probabilities and Relaxation Times.- 1.3 Organization of the Book.- References.- 2. The Vibrational Density of States of Amorphous Semiconductors.- 2.1 The Vibrational Density of States.- 2.2 Experimental Techniques.- 2.3 The Theoretical Problem.- 2.4 Brute Force Theory.- 2.4.1 Turning the Handle.- 2.4.2 Some Results of Brute Force.- 2.5 More Refined Approaches.- 2.5.1 Analytical Ideas.- 2.5.2 The Bethe Lattice.- 2.5.3 Indirect Numerical Methods.- 2.6 The Incorporation of Matrix Elements.- 2.7 Can One Derive Structural Information from g(?)?.- 2.8 A Less Myopic View of the Field.- References.- 3. Low Temperature Specific Heat of Glasses.- 3.1 Review of the Experimental Situation.- 3.2 Comparison with Theoretical Models.- 3.2.1 The Tunneling Model.- 3.2.2 The Cellular Model.- 3.3 Summary and Outlook.- References.- 4. The Thermal Expansion of Glasses.- 4.1 Theoretical Background.- 4.2 The High Temperature Expansion of Vitreous Silica.- 4.3 The Low Temperature Expansion of Glasses.- 4.3.1 Experimental Results.- 4.3.2 Discussion.- References.- 5. Thermal Conductivity.- 5.1 Thermal Transport in Crystalline Materials.- 5.2 Thermal Transport in Amorphous Materials.- 5.2.1 The Phonon Mean Free Path.- 5.2.2 Phonon Scattering Mechanisms.- 5.2.3 Summary.- 5.3 Probing the Localized Excitations.- 5.4 Synopsis.- References.- 6. Acoustic and Dielectric Properties of Glasses at Low Temperatures.- 6.1 General Comments.- 6.2 Acoustic and Dielectric Properties Above 10 K.- 6.2.1 Absorption.- 6.2.2 Sound Velocity and Dielectric Constant.- 6.3 Acoustic and Dielectric Properties Below 10 K.- 6.3.1 Acoustic and Dielectric Absorption.- a) Relaxation Effects.- b) Resonant Interaction.- 6.3.2 Sound Velocity and Dielectric Constant.- 6.3.3 Acoustic Dielectric “Cross”-Experiments.- 6.4 Theoretical Description of the Acoustic and Dielectric Properties by Two-Level Systems.- 6.4.1 Dynamical Properties of Two-Level Systems.- 6.4.2 Absorption Due to a Distribution of Two-Level Systems.- 6.4.3 Variation of Sound Velocity and Dielectric Constant.- 6.5 Comparispn Between Theory and Experiment.- 6.6 Microscopic Description: Tunneling Model.- 6.7 Summary.- References.- 7. Relaxation Times of Tunneling Systems in Glasses.- 7.1 Background.- 7.2 Resonance Dynamics of Two-Level Systems.- 7.2.1 Tunneling Model.- 7.2.2 Longitudinal Relaxation Time T1.- a) One-Phonon Relaxation.- b) Conduction Electron Relaxation.- 7.2.3 Transverse Relaxation Time T’2.- 7.2.4 Spontaneous Echo Decay.- 7.2.5 Stimulated Echo Decay.- 7.3 Experiments Measuring Relaxation Times.- 7.3.1 Acoustic Saturation.- 7.3.2 Saturation Recovery.- 7.3.3 Linewidth.- 7.3.4 Two-Pulse Phonon Echo.- 7.3.5 Two-Pulse Electric Echo.- 7.3.6 Three-Pulse Phonon Echo.- 7.3.7 Three-Pulse Electric Echo.- 7.4 Critical Assessment of Data.- 7.4.1 T1 Results.- a) Three-Pulse Echoes.- b) Saturation Recovery.- c) Distribution of Decay Times.- 7.4.2 T’2 Results.- a) Two-Pulse Echoes.- b) Linewidth.- 7.5 Conclusions.- References.- 8. Low Frequency Raman Scattering in Glasses.- 8.1 Introductory Comments.- 8.2 Vibrational Raman Spectrum of First Order.- 8.2.1 Experimental Results.- 8.2.2 Theory of Low-Frequency Spectrum.- a) Continuum Theory.- b) Bond Polarizabil ity Model.- 8.3 Quasielastic Spectrum.- 8.3.1 Experimental Results.- 8.3.2 Theory.- a) Physical Origin of the Quasielastic Scattering.- b) Relation Between Raman Scattering and Ultrasonic Absorption.- c) Defect Model.- 8.4 Conclusion.- References.- Additional References with Titles.- Subject and Material Index.