Lattice Dynamics
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Introduction To Lattice Dynamics
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Author : Martin T. Dove
language : en
Publisher: Cambridge University Press
Release Date : 1993-10-21
Introduction To Lattice Dynamics written by Martin T. Dove and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-21 with Science categories.
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.
Principles Of The Theory Of Lattice Dynamics
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Author : Harald Böttger
language : en
Publisher:
Release Date : 1983
Principles Of The Theory Of Lattice Dynamics written by Harald Böttger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Crystal lattices categories.
Lattice Dynamics
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Author : Alexei A. Maradudin
language : en
Publisher:
Release Date : 1969
Lattice Dynamics written by Alexei A. Maradudin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Crystal lattices categories.
Lattice Dynamics
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Author : R. F. Wallis
language : en
Publisher: Elsevier
Release Date : 2013-09-03
Lattice Dynamics written by R. F. Wallis and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-03 with Science categories.
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.
Lattice Dynamics
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Author : Johan Tidholm
language : en
Publisher: Linköping University Electronic Press
Release Date : 2020-11-02
Lattice Dynamics written by Johan Tidholm and has been published by Linköping University Electronic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-02 with Electronic books categories.
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.
An Introduction To Lattice Dynamics
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Author : Ajoy K. Ghatak
language : en
Publisher:
Release Date : 1972
An Introduction To Lattice Dynamics written by Ajoy K. Ghatak and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Science categories.
Lattice Dynamics Of Molecular Crystals
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Author : S. Califano
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lattice Dynamics Of Molecular Crystals written by S. Califano and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The lattice dynamics of molecular crystals has undergone an enor mous progress in these last twenty years or so. The experimental and theoretical advances have been realized by two different approaches. From one side molecular spectroscopists have been primarily interested in the vibrational properties of the molecules themselves subjected to the perturbing influence of the crystal environment. From the other side the lattice dynamical theory familiar in solid state physics for atomic lattices has been extended to molecular arrays. Although the overlap between the two approaches has been considerable the reference material is rather scattered in specialized papers. The purpose of this book is to partly fill this gap and to discuss the lattice dynamical theory of molecular crystals in a compact and specialized form. As such, the book is not intended exclusively for researchers and specialists in the field but also for graduate students entering an activity in solid state mo lecular spectroscopy.
Lattice Dynamics
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Author : Richard Fisher Wallis
language : de
Publisher:
Release Date : 1965
Lattice Dynamics written by Richard Fisher Wallis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Crystal lattices categories.
Theory Of Crystal Space Groups And Lattice Dynamics
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Author : J. L. Birman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Theory Of Crystal Space Groups And Lattice Dynamics written by J. L. Birman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Reissue of Encyclopedia of Physics/Handbuch der Physik, Vol. XXV/2b I am very pleased that my book is now to be reprinted and rebound in a new format which should make it accessible at a modest price to students and active researchers in condensed matter physics. In writing this book I had in mind an audience of physicists and chemists with no previous deep exposure to symmetry analysis of crystalline matter, non to the use of symmetry in simplifying and refining predictions of the results of optical experiments. Hence the book was written to explain and illustrate in all necessary detail how to: 1) describe the space group symmetry in terms of space group symmetry operations; 2) obtain irreducible representations and selection rules for optical infra-red and Raman and other transition processes. On the physical side I redeveloped the traditional theory of classical and quantum lattice dynamics, illustrating how space-time symmetry designations in the equations of motion can: 1) simplify and rationalize calculations of the classical eigenvectors of the dynamical equation; 2) permit classification of the eigenstates of the quantum lattice-dynamic pro blem; 3) give specific selection rules for optical infra-red and Raman lattice processes, and thus make "go, no-go" predictions including polarization of absorbed or scattered radiation; and 4) simplify the modern many-body theories of optical processes.
Lattice Dynamical Foundations Of Continuum Theories Elasticity Piezoelectricity Viscoelasticity Plasticity
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Author : Attila Askar
language : en
Publisher: World Scientific
Release Date : 1986-07-01
Lattice Dynamical Foundations Of Continuum Theories Elasticity Piezoelectricity Viscoelasticity Plasticity written by Attila Askar and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-07-01 with categories.
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.