09solids1 - Solids - types MOLECULAR. Set of single atoms...

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P461 - Solids 1 Solids - types • MOLECULAR. Set of single atoms or molecules bound to adjacent due to weak electric force between neutral objects (van der Waals). Strength depends on electric dipole moment • No free electrons b poor conductors • easily deformed, low freezing temperature freezing boiling bonding energy He 1 K 4 K H 14 K 20 K Ar 84 K 87 K .08 eV/molecule H 2 O 273 K 373 K 0.5 eV/mol CH 4 90 K 111 K 0.1 eV/mol • correlates with bonding energy
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P461 - Solids 2 Ionic Solids • Positive and negative ions. Strong bond and high melting point. no free electrons b poor conductor • similar potential as molecule. ~5 eV molecules and ~6 eV solid (NaCl) • each Cl- has 6 adjacent Na+, 12 “next” Cl-, etc • energy levels similar to molecules except no rotations….electronic in UV and vibrational in IR. Often transparent in visible R Potential vs sep distance R = + = = + R e all R e Cl V R e Na V 0 2 0 2 0 2 4 7 . 1 2 4 12 ) 12 ( 4 6 ) 6 ( πε
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P461 - Solids 3 • COVALENT. Share valence electrons (C, H, etc) • strong bonds (5-10 eV), rigid solids, high melting point • no free electrons b insulators • usually absorb in both visible and UV • METALLIC. s-p shell covalent bonds. But d shell electrons “leftover” (smaller value of n b lower energy but larger <r>) • can also be metallic even if no d shell if there is an unfilled band • 1-3 eV bonds, so weaker, more ductile, medium melting temp • “free” electrons not associated with a specific nuclei. Wavelength large enough so wavefunctions overlap and obey Fermi-Dirac statistics b conductors b EM field of photon interacts with free electrons and so absorb photons at all λ
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P461 - Solids 4 Bands in Diatomic Molecules-Reminder assume all valence electrons are shared • if both atoms are the same then | ψ| 2 same if switch atom(1) and atom(2) --- electron densities around each atom are the same (even sort of holds if different atoms like CO) H(1s) <-- very far apart ---> H(1s) close together H(“1s”)H(“1s”) electron wavefunctions overlap -“shared” • two energy levels (S=0,1) (spatial symmetric and antisymmetric)which have 2 2 | ) 1 , 2 ( | | ) 2 , 1 ( | ψ = E R=infinity (atoms) 1s*1s Vib and rot bands
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P461 - Solids 5 Bands in Solids lowest energy levels very similar to free atoms b large kinetic energy b large p, small λ • little overlap with electrons in other atoms and so narrow energy band • higher energy levels: larger λ wavefunctions of electrons from different atoms overlap • need to use Fermi-Dirac statistics • many different closely spaced levels: Band p h eV n Z K = = λ 6 . 13 2 2 3s,3p 2s,2p 1s 4s,4p,3d E
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P461 - Solids 6 Multielectron energy levels • 3/2 symmetric spin. Each 1/2 has different mixed symmetry b 3 different spacial wavefunctions and (usually) 3 different energy levels • the need for totally antisymmetric wave functions causes the energies to split when the separation distance R < wavelength
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09solids1 - Solids - types MOLECULAR. Set of single atoms...

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