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Unformatted text preview: Overview Solid = collection of atoms (~10 23 , a huge number) Crystalline: single crystals, polycrystalline materials Amorphous, glassy materials Others: liquid crystals, quasicrystals, partially ordered polymers, Theory of solids to explain and predict properties of solids This course is mostly about single crystals. Basic questions 1. Ground state properties: crystal structure, stability, nature of chemical bonds, electron density distribution, 2. Excited states and response functions to external forces or fields: stress, pressure, E field, B field, EM field, T, T gradient, electrons, neutrons, protons, ions, Probing excited states Concept of elementary excitations: quasiparticles, plasmons, phonons, magnons, polaritons, excitons, etc. Example, Raman scattering: phonon (quantum of lattice vibration), plasmon, etc. Example, optical absorption: Theory of solids ideally begins with quantum mechanics (& Maxwell's equations) H E ; H i t ; exact solutions difficult or impossible; not necessarily interested in details anyways. Models simplifications & approximations, keeping essential features of interest. Empirical theories parameters to fit known results; can be used to make predictions First-principles (ab-initio) theories no parameters. For example, input = atomic number Z; predictions may include crystal structure (fcc, bcc, hcp, ), lattice constant, melting point, speed of sound, phase transitions, superconducting T C , Development cycle: expt properties, phenomena theory (model) explanations & predictions for other properties and phenomena Ultimate goal explain and predict all properties and phenomena of interest: Optical properties: transparent or not, colors, reflection coefficient, Magnetic: ferro-, antiferro-, para-, & dia-magnetic Mechanical: density, sound speed, hardness, elasticity, toughness, stiffness, exciton (correlated electron hole pair) Chemical: reactivity Thermal: melting, specific heat, expansion, Surface & nanoscale phenomena Electrical: resistivity ( ) = inverse of conductivity ( ), Hall coeff., (ohm-cm), typical examples metals 10-6 10-5 Cu, Ag, Ni, Pu semimetals 10-3 Bi, graphite semiconductors 10-2 10 9 Si, Ge, GaAs insulators 10 14 10 23 Diamond, LiF *superconductors have = 0 below T C . varies by over 30 orders of magnitude (not including superconductors). Best insulators: fused silica > 5 x 10 22 ohm-cm; Teflon up to 10 26 ohm-cm. First-order business understand the differences among metals, semiconductors, insulators. Develop a theory of ....
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- Spring '08