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

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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 barb2right 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 barb2right 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 πε 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 barb2right insulators usually absorb in both visible and UV METALLIC. s-p shell covalent bonds. But d shell electrons “leftover” (smaller value of n barb2right 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 barb2right conductors barb2right 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 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 barb2right large kinetic energy barb2right 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 barb2right 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 if far apart barb2right N degenerate(equal) states overlap
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