This book presents an account of the course "Disordered Solids: Structures and Processes" held in Erice, Italy, from June 15 to 29, 1987. This meeting was organized by the International School of Atomic and Molecular Spectroscopy of the "Ettore Majorana" Centre for Scientific Culture. The objective of this course was to present the advances in physical modelling, mathematical formalism and experimental techniques relevant to the interpretation of the structures of disordered solids and of the physical processes occurring therein. Traditional solid-state physics treats solids as perfect crystals and takes great advantage of their symmetry, by means of such mathematical formalisms as the reciprocal lattice, the Brillouin zone, and the powerful tools of group theory. Even if in reality no solid is a perfect crystal, this theoretical approach has been of great usefulness in describing solids: deviations from perfect order have been treated as perturbations of the ideal model. A new situation arises with truly disordered solids where any vestige of long range order has disappeared. The basic problem is that of describing these systems and gaining a scientific understanding of their physical properties without the mathematical formalism of traditional solid state physics. While some of the old approaches may occasionally remain valid (e. g. chemical bonding approach for amorphous solids), the old ways will not do. Disorder is not a perturbation: with disorder, something basically new may be expected to appear.

This self-contained textbook aims to introduce the physics of structurally disordered condensed systems at the level of advanced undergraduate and graduate students. The topics discussed include the geometry and symmetries of the building blocks commonly used to obtain atomic structures, the various kinds of disorder, the phenomenology and the main theories of the glass transition, investigation of the structure of amorphous systems, the dependence of system structure on its dimensions (clusters), and the case of positional order in the absence of translational order (quasicrystals).

Structurally disordered solids are characterized by their lack of spatial order that is evidenced by the great variety of ordered solids. The former class of materials is commonly termed amorphous or glassy, the latter crystalline. However, both classes share, many of the other physical properties of solids, e. g. , me chanical stability, resistance to shear stress, etc. The traditional macroscopic distinction between the crystalline and the glassy states is that while the former has a fixed melting point, the latter does not. However, with the availability and production of a large number of materials in both crystalline and amorphous states, and their easy inter-convertability, simple de finitions are not possible or at best imprecise. For the present purpose, it is sufficient to say that in contrast to the crystalline state, in which the posi tions of atoms are fixed into adefinite structure, ex cept for small thermal vibrations, the amorphous state of the same material displays varying degrees of de parture from this fixed structure. The amorphous state almost always shows no long range order. Short range order, up to several neighbors, may often be retained, although averaged considerably around their crystalline values. It is generally believed that the amorphous state is a metastable one with respect to the crystal line ordered state, and the conversion to the crystal line state may or may not be easy depending on the na ture of the material, e. g.

This book presents a consistent mathematical theory of the non-electronic physical properties of disordered and amorphous solids, starting from the atomic-level dynamics and leading to experimentally verifiable descriptions of macroscopic properties such as elastic and viscoelastic moduli, plasticity, phonons and vibrational spectra, and thermal properties. This theory begins with the assumption of the undeniable existence of an “amorphous lattice”, which allows one to relegate the theoretical uncertainties about the ultimate nature of the glass transition to a subsidiary role and thus take a more pragmatic approach towards the modelling of physical properties. The book introduces the reader not only to the subtle physical concepts underlying the dynamics, mechanics, and statistical physics of glasses and amorphous solids, but also to the essential mathematical and numerical methods that cannot be readily gleaned from specialized literature since they are spread out among many often technically demanding papers. These methods are presented in this book in such a way as to be sufficiently general, allowing for the mathematical or numerical description of novel physical phenomena observed in many different types of amorphous solids (including soft and granular systems), regardless of the atomistic details and particular chemistry of the material. This monograph is aimed at researchers and graduate-level students in physics, materials science, physical chemistry and engineering working in the areas of amorphous materials, soft matter and granular systems, statistical physics, continuum mechanics, plasticity, and solid mechanics. It is also particularly well suited to those working on molecular dynamics simulations, molecular coarse-grained simulations, as well as ab initio atomistic and DFT methods for solid-state and materials science.

The field of charge conduction in disordered materials is a rapidly evolving area owing to current and potential applications of these materials in various electronic devices This text aims to cover conduction in disordered solids from fundamental physical principles and theories, through practical material development with an emphasis on applications in all areas of electronic materials. International group of contributors Presents basic physical concepts developed in this field in recent years in a uniform manner Brings up-to-date, in a one-stop source, a key evolving area in the field of electronic materials

This book gives a pedagogical introduction to the physics of amorphous solids and related disordered condensed matter systems. Important concepts from statistical mechanics such as percolation, random walks, fractals and spin glasses are explained. Using these concepts, the common aspects of these systems are emphasized, and the current understanding of the glass transition and the structure of glasses are concisely reviewed. This second edition includes new material on emerging topics in the field of disordered systems such as gels, driven systems, dynamical heterogeneities, growing length scales etc. as well as an update of the literature in this rapidly developing field.

This book, edited by M. A. Ramos and contributed by several reputed physicists in the field, presents a timely review on low-temperature thermal and vibrational properties of glasses, and of disordered solids in general. In 1971, the seminal work of Zeller and Pohl was published, which triggered this relevant research field in condensed matter physics. Hence, this book also commemorates about 50 years of that highlight with a comprehensive, updated review.In brief, glasses (firstly genuine amorphous solids but later on followed by different disordered crystals) were found to universally exhibit low-temperature properties (specific heat, thermal conductivity, acoustic and dielectric attenuation, etc.) unexpectedly very similar among them — and very different from those of their crystalline counterparts.These universal 'anomalies' of glasses and other disordered solids remain very controversial topics in condensed matter physics. They have been addressed exhaustively in this book, through many updated experimental data, a survey of most relevant models and theories, as well as by computational simulations.

The subject of low-energy excitations has evolved since two-level-tunneling systems were first proposed ~50 years ago. Initially they were used to explain the common anomalous properties of oxide glasses and polymers; now the subject includes a wide range of other materials containing disorder: amorphous semiconductors and metals, doped- mixed- and quasi-crystals, surface adsorbates, ... and topics such as dephasing of quantum states and interferometer noise. A fairly simple empirical description using a remarkably small range of parameters serves well to describe the effect of these excitations, but the structures causing these effects are known in only a few materials and the reasons for their similarity across disparate materials has only been qualitatively addressed.This book provides a unified, comprehensive description of tunneling systems in disordered solids suitable for graduate students/researchers wishing an introduction to the field. Its focus is on the tunneling systems intrinsic to glassy solids. It describes the experimental observations of 'glassy' properties, develops the basic empirical tunneling model, and discusses the dynamics changes on cooling to temperatures where direct excitation interactions become important and on heating to where tunneling gives way to thermal activation. Finally, it discusses how theories of glass formation can help us understand the ubiquity of these excitations.The Development of the basic tunneling model is the core of the book and is worked out in considerable detail. To keep the total within bounds of our expertise and the readers' patience, many related experimental and theoretical developments are only sketched out here; the text is heavily cited to allow readers to follow their specific interests in much more depth.

This thesis is a first-principles theoretical investigation of solid materials with high degrees of anharmonicity. These are systems where the dynamics of the constituent atoms is too complex to be well-described by a set of uncoupled harmonic oscillators. While theoretical studies of such systems pose a significant challenge, they are under increasing demand due to the prevalence of these sytems in next-generation technological applications. Indeed, very anharmonic systems are ubiquitous in envisioned materials for future solid-state batteries and fuel-cells, thermoelectrics and optoelectronics. In some of these cases, the anharmonicity is a “side-effect” that simply has to be dealt with in order to accurately model certain properties, while in other cases the anharmonicity is the origin of the high-performance of the material. There are two main parts to the thesis: The first is on materials with perovskite-related structures. This is a very large class of materials, members of which are typically highly anharmonic, not least in relation to a series of complex phase transformations between different structural modifications. In the thesis, I have studied a specific class of such phase-transformations that relate to tilting of the framework of octahedra that make up the structure. The oxide CaMnO3 and a set of inorganic halide perovskites were taken as model systems. The results shed some light on the experimentally observed differences between the local and average atomic structure in these systems. I have further studied Cs2AgBiBr6, a member of the so-called lead-free halide double perovskites. I rationalized its temperature induced phase transformation and found high degrees of anharmonicity and ultra-low thermal conductivity. Finally, I studied the influence of nuclear quantum effects, which are often ignored in computational modelling, on the structure and bonding in the hybrid organic-inorganic lead-halide perovskite, CH3NH3PbI3. The second part of the thesis deals with theoretical studies of the phase stability of dynamically disordered solids. These are solids which have some sort of time-averaged long-range order, characteristic of a crystalline solid, but where the anharmonicity is so strong that the basic concept of an equilibrium atomic position cannot be statically assigned to all atoms. Examples include certain solids with very fast ionic conduction, so called superionics, and solids with rotating molecular units. This absence of equilibrium atomic positions makes many standard computational techniques to evaluate phase-stability inapplicable. I outline a method to deal with this issue, which is based on a stress-strain thermodynamic integration on a deformation path from an ordered variant to the dynamically disordered phase itself. I apply the method to study the phase stability of the high-temperature ?-phase of Bi2O3, which is the fastest know solid oxide ion conductor, and to Li2C2, whose high temperature cubic phase contains rotating C2 dimers. The thesis exemplifies the need to go beyond many of the standard approximations used in first-principles computational materials science if accurate theoretical predictions are to be made. This is true, in particular, for many emerging material classes in the field of energy materials. I den konventionella teoretiska modellen för ett (kristallint) fast material antags varje atom kunna tillordnas en jämviktsposition. Rörelsen av atomerna runt dessa jämviktspositioner antags sedan ofta vara harmoniskt, d.v.s. hyfsat kunna beskrivs i termer av en samling (kvantmekaniska) fjädrar. Denna avhandling behandlar teori- och beräkningsstudier av material där ett eller båda av dessa antaganden inte är giltiga, så kallade anharmoniska material. En nogrann teoretisk behandling av sådana material är ofta ordentligt utmanande. I takt med en snabb teknologiska utveckling ställs allt mer specifika och stränga krav på de material som behövs för diverse applikationer. Inom flertalet områden dyker då denna typ av komplexa och anharmoniska material upp som potentiella kandidater. Till exempel som fastelektrolyter för batterier och bränsleceller eller som solcellsmaterial. Inom vissa applikationer är denna anharmonicitet en bieffekt som man helt enkelt måste ta hänsyn till för att kunna göra noggranna teoretiska förutsägelser om diverse materialegenskaper, i andra fall är anharmoniciteten själva ursprunget för materialets goda egenskaper. I den första delen av avhandlingen behandlar jag material som har, eller är nära relaterade till, den så kallade perovskitstrukturen. Detta är en väldigt stor klass av material, och strukturen dyker därför upp inom en mängd olika tillämpningar, inte minst i lovande solcellsmaterial. Dessa material är ofta mycket anharmoniska, vilket tar sig uttryck bland annat i en rad komplexa fastransformationer mellan olika typer av perovskitmodifikationer. I perovskitoxiden CaMnO3, samt i en samling halogenperovskiter, har jag har studerat en specifik typ av fastransformationer som tillkommer på grund av rotationer av de oktaedrar som utgör en del av strukturen. Jag har fortsatt studerat den väldigt kraftiga anharmoniciteten i den så kallade blyfria halogendubbelperovskiten Cs2AgBiBr6, och slutligen har jag studerat hur en kvantmekanisk behandling av atomkärnorna, något som oftast inte görs, påverkar materialegenskaper i CH3NH3PbI3, en så kallad hybrid organisk-inorganisk bly-halogenperovskit, som är ett extremt lovande solcellsmaterial. I den andra delen av avhandlingen studerar jag dynamiskt oordnade fasta material. I dessa material är atomernas rörelse för komplex för att varje atom ska kunna tilldellas en statisk jämviktsposition. Material i denna klass är, till exempel, lovande som fastelektrolyter i bränsleceller och batterier. Mer specifikt studerar jag en typ av fasövergång, från en ordnad fas till en fas med dynamisk oordning, som ofta sker när dessa material värms upp. Jag introducerar en beräkningsmetod för att utvärdera deras fasstabilitet. Metoden är baserad på en så kallad termodynamisk integration, utförd mellan en ordnad variant och den dynamiskt oordnade fasen själv. Metoden gör det möjligt att beräkna fastransformationstemperaturer i denna typ av material. Jag applicerar metoden på Bi2O3, som i sin ?-fas är det fasta material med högst känd syrejonledningsförmåga, samt på Li2C2 vars kubiska fas innehåller roterande C2 molekyler. Resultaten stämmer bra överens med kända experimentella mätningar.