Download or read book Introduction to Lattice Dynamics written by Martin T. Dove and published by Cambridge University Press. This book was released on 1993-10-21 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: The vibrations of atoms inside crystals - lattice dynamics - is basic to many fields of study in the solid-state and mineral sciences. This book provides a self-contained text that introduces the subject from a basic level and then takes the reader through applications of the theory.

Download or read book An Introduction to Lattice Dynamics written by Ajoy K. Ghatak and published by . This book was released on 1972 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Introduction to Lattice Dynamics Lattice Dynamics written by Ajoy K. Ghatak and published by . This book was released on 1972 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Principles of the Theory of Lattice Dynamics written by Harald Böttger and published by . This book was released on 1983 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Dynamics of Lattice Materials written by A. Srikantha Phani and published by John Wiley & Sons. This book was released on 2017-09-25 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a comprehensive introduction to the dynamic response of lattice materials, covering the fundamental theory and applications in engineering practice Offers comprehensive treatment of dynamics of lattice materials and periodic materials in general, including phononic crystals and elastic metamaterials Provides an in depth introduction to elastostatics and elastodynamics of lattice materials Covers advanced topics such as damping, nonlinearity, instability, impact and nanoscale systems Introduces contemporary concepts including pentamodes, local resonance and inertial amplification Includes chapters on fast computation and design optimization tools Topics are introduced using simple systems and generalized to more complex structures with a focus on dispersion characteristics

Download or read book Lattice dynamics written by Johan Tidholm and published by Linköping University Electronic Press. This book was released on 2020-11-02 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: The reason to perform calculations in material science usually falls into one of two categories: to predict or explain the origin of material properties. This thesis covers first-principle calculations for solids at extreme conditions, from both of the two mentioned categories. I primarily have studied the effects of high-pressure and high-temperature on lattice dynamics, mechanical and electronic properties. To treat the effects of temperature, ab initio molecular dynamics (AIMD) simulations and self-consistent phonon calculations, based on density functional theory, have been utilised. These approaches account for the temperature effects by considering thermally excited supercells as samples of a statistical ensemble. To extract properties from this representation, I have used methods which maps the supercell data to a unit cell representation or fits it to a simple model Hamiltonian. The small displacement method was used to analyse the dynamical stability for nitrides and polymorphs of silica, synthesised at high-pressure in a diamond anvil cell. The nitride compounds consist of a high amount of nitrogen either as chains, forming a porous framework together with transition metal atoms or as dinitrogen molecules, occupying the channels of the framework. The nitrogen chains consist of single- or double-bonded nitrogen atoms, making these compounds highly energetic. Polymorphs of silica can be used to model deep Earth liquids. These new polymorphs, named coesite-IV and coesite-V, consist of four-, five-, and six-oriented silicon. Some of the octahedra of the six-oriented silicon atoms, of these new phases, are sharing faces, which according to Pauling's third rule would make them highly unstable. My phonon calculations indicate these phases to be dynamically stable. Furthermore, my calculations predict higher compressibility for these new phases compared to the competing ones. By modelling silicate melts with coesite-IV and coesite-V, a more complex and compressible structure is expected, affecting the predicted seismic behaviour. I studied Kohn anomalies for body-centered cubic niobium by simulating this material with self-consistent phonon calculations. The electronic structure was studied by using a band unfolding technique, for which I obtained an effective unit cell representation of the electronic structure at elevated temperatures. Temperature primarily smeared the electronic states but did not induce significant shifts of the bands. In parallel, the anharmonicity of this system was studied using the temperature dependent effective potential method. Even close to the melting temperature, this element is remarkably harmonic. The experimentally observed disappearance of the Kohn anomalies with increased temperature is predominantly dependent, according to my calculations, on the temperature-induced smearing of the electronic states. Using stress-strain relations, accurate high-temperature elastic properties were predicted for Ti0.5Al0.5N. The simulations were performed with AIMD. The stresses were fitted using the least-squares method to a linear expression from which the elastic constants were derived. The results were compared with previously performed calculations that employed additional approximations. The results of the symmetry imposed force constant temperature dependent effective potential (SIFC-TDEP) method agrees well with our results. I also compared my results with TiN calculations that employed a similar methodology. My and the SIFC-TDEP results are reporting lower values for the polycrystalline moduli than the calculations for TiN. The data I generated were also used for a machine learned interatomic potential method, where moment tensor potentials were trained and evaluated, using this data. Den här avhandlingen handlar om beräkningar för material. När materialberäkningar utförs är det antingen för att förutsäga eller förklara egenskaper. De beräkningar som jag har gjort i denna avhandling är baserade på fundamentala fysiska lagar. Detta betyder att de är rent baserade på teori, och inte har anpassats efter resultat av experiment. Jag har i mitt arbete använt mig mycket utav en teori som kallas gitter dynamik. Den är definierad för periodiska material, det vill säga att atomerna i dessa material upprepas i periodiska mönster. Vi kan då anta att det finns en jämviktspunkt för alla atomerna, som de vibrerar omkring. Dessa vibrationer kan beskrivas som om atomerna påverkar varandra med fiktiva fjädrar. Genom att beräkna styrkan för dessa fjädrar kan vi beskriva vibrationerna av atomerna. Dessa vibrationer i sin tur är avgörande för materialets egenskaper. För att beskriva ett material vid en specifik temperatur har jag använt mig utav olika metoder för att simulera det. En simulering kan ses som ett “dator experiment”. Problemet är dock hur vi ska mäta egenskaperna i simuleringen. Ju större och mera komplex en simulering är, desto svårare blir det att beräkna egenskaperna av det simulerade materialet. Vi hamnar i en situation likt den vi skulle befinna oss om vi hade gjort ett experiment i verkligheten, och tvingas använda förenklade modeler för att kunna tolka resultatet. Jag har därför använt mig utav metoder för att utvinna vibrationer av atomer, elektrontillstånd eller elastiska egenskaper, specifikt utvecklade för att användas på denna typ utav simuleringar. Mitt arbete har kretsat kring hur dessa egenskaper påverkas av extrema temperaturer och tryck. De beräkningar jag har utfört vid höga tryck har varit för nyupptäckta nitrider och faser av kiseldioxid. Nitriderna är porösa material som innehåller en stor mängd kväve. Det höga kväveinehållet gör så att det lagras en stor mängd kemisk energi i enkel- och dubbelbindningar mellan kväveatomerna. De nya faserna av kiseldioxid har en betydelse för vår förståelse av jordens inre. Deras existens öppnar upp för att det kan finnas mera komplexa och ihoptryckbara flytande material, under jordens nedre mantel, än vad tidigare har varit antaget. Mina beräkningar har bekräftat strukturerna för dessa nyupptäckta material. Vid höga temperaturer har jag studerat för metallen niob hur vibrationerna av atomerna är relaterade till olika elektrontillstånd. För specifika vibrationer ökar frekvensen med ökad temperatur. Detta är något ovanligt eftersom vibrationernas frekvenser vanligtvis brukar minska med ökad temperatur. Mina simulering för denna metal överensstämmer med resultat från experiment. Orsaken till varför visa vibrationers frekvenser ökar kan jag förklara med att elektrontillståndens enskilda energier varierar över tid på grund av den ökade temperaturen. Jag har även använt mig av simuleringar för att beräkna elastiska egenskaper av legeringen Ti0.5Al0.5N. Ti1?xAlxN legeringar används som beläggningar på skärverktyg som används för metall. För att öka effektiviteten av beläggningen, behövs det detaljerad kunskap av dess mekaniska egenskaper för den temperatur som de används vid. Jag beräknade därför så noggrant som möjligt de elastiska egenskaperna för Ti0.5Al0.5N. Dessa beräkningar är avsedda för att användas som en referens för andra beräkningsmässigt billigare metoder. Datan som genererades från mina simuleringar användes även för en sådan metod, baserad på maskininlärning.

Download or read book Lattice Dynamics written by Richard Fisher Wallis and published by . This book was released on 1965 with total page 758 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Phonons Theory and Experiments I written by Peter Brüesch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume treatment grew out of lectures the author gave at the "Ecole Poly technique Federale de Lausanne" during the years 1975-1980 for graduate students in experimental physics in their last year of study. It is written by an experimentalist with some interest in theory and is ad dressed mainly to experimentalists, but also to theoreticians interested in experiments. This treatment tries to bridge the gap between theory and experiments; it should assist experimentalists in the interpretation of their data in the vast field of lattice dynamics. An attempt has been made to provide not only the basic concepts but also a working knowledge in this field of solid-state physics. In this first volume, the basic concepts of the physics of phonons are developed and illustrated by many examples; it provides the background necessary for the interpretation of most experimental results. The second volume, which is in preparation, is devoted to experimental techniques, the interpretation of experiments, and discussion of phenomena which are directly related with phonons. The book is designed for introductory courses at the graduate level. It is believed that the book will also prove useful to those graduate students starting research in this or related fields, as well as to many workers already active in this branch of solid-state physics.

Download or read book Lattice Dynamics written by and published by . This book was released on 1969 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Lattice Dynamical Foundations Of Continuum Theories Elasticity Piezoelectricity Viscoelasticity Plasticity written by Attila Askar and published by World Scientific. This book was released on 1986-07-01 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a discussion of lattice dynamics for perfect and imperfect lattices and their relation to continuum theories of elasticity, piezoelectricity, viscoelasticity and plasticity. Some of the material is rather classical and close in spirit to solid state physics. A major aim here is to present a coherent theory for the four basic behavior types in the style of continuum mechanics. In each case, emphasis is on an explicit display of the physical mechanisms involved rather than general formalisms. The material is presented in terms of an atomistic picture for the discrete system. The basic ideas are believed to be relevant also at an intermediate scale in the continuum description of media with structure such as granular materials and composites.

Download or read book Lattice Dynamics written by Alexei A. Maradudin and published by . This book was released on 1969 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Lattice Dynamics written by R. F. Wallis and published by Elsevier. This book was released on 2013-09-03 with total page 747 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lattice Dynamics covers the proceedings of the 1963 International Conference on Lattice Dynamics, held at the H.C. Ørsted Institute of the University of Copenhagen on August 5-9. This book is composed of seven parts that focus on a better fundamental understanding of the interactions between atoms in solids and their role in lattice dynamics. The major topics covered include phonon dispersion curves, anharmonic effects, optical and dielectric effects, influence of defects on lattice vibrations, elasticity, and developments. Papers on the study of vibrational spectra by infrared absorption, X-ray and neutron scattering and the electron tunneling effects as well as papers on the influence of defects and on a variety of other problems in lattice dynamics are included. This book will prove useful to applied physicists and researchers in the field and related fields of lattice dynamics.

Download or read book Lattice dynamics written by A. A. Maradudin and published by . This book was released on with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Statistical Mechanics of Lattice Systems written by Sacha Friedli and published by Cambridge University Press. This book was released on 2017-11-23 with total page 643 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.

Download or read book Theory of Lattice Dynamics in the Harmonic Approximation written by Alexei A. Maradudin and published by . This book was released on 1971 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Lattice Dynamics and Statics of Alkali Halide Crystals written by J. R Hardy and published by . This book was released on 1979-11-01 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Dynamical Theory of Crystal Lattices written by Max Born and published by . This book was released on 1956 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: