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Solids crystalline well defined structures quartz amorphous no orderly structure glass SiO2 crystal lattice system of points describes arrangement of particles unit cell repeating structural unit unit cells simple cubic formed from packing spheres lattice crystalline solids unit cells hexagonal closest packing cubic packing in dimensions simple cubic “aaa” layers body centered cubic hexagonal closest pack “abab” layers “abab” layers cubic closest pack “abca” layers Three-Dimensional Cubic Lattices Simple cubic aaa 1/8 x =1 particle coordination number = Body-centered cubic abab (1/8 x ) + = particles coordination number = Face-centered cubic cubic closest pack abcabc (1/8 x ) + (1/2 x ) = particles coordination number = 12 Calculation of atomic radii r+ r+ r Cu faced-centered cubic density = 8.92 g/cm3 mass = 63.546 g/mol 63.546 g cm3 atoms mol unit cell 6.022 x 1023 atoms mol 8.92 g ( 4.732 x 10 -23 1/3 cm / unit cell ) = 3.617 x 10-8 cm lattice parameter, a (3.617 x 10-8)2 + (3.617 x 10-8)2 = (4r)2 r = 1.279 x 10-8 cm x 10-2 m pm = 127 pm x 10-12 m cm X-Ray Diffraction by Crystals diffraction interference between waves caused by object in their path constructive or destructive Bragg Equation nλ = 2d sinθ θ d Types of Crystalline Solids Covalent atoms in lattice Ionic ions in lattice Molecular molecules in lattice m.p depends on bonding forces ionic covalent H-bonding Cdiamond 3550 C NaCl 800 C o O H2O 0oC Covalent solids atoms in lattice carbon sp3 diamond sp2 sp2 graphite buckminsterfullerene hardest material known conduct electricity - π edoesn’t conduct electricity Covalent solids atoms in lattice metals every lattice point - atom of metal body-centered cubic face-centered cubic melting point hexagonal close packed Na 97oC share valence e- e- “sea” Cr 1890oC good conductors brass steel substitutional alloy interstitial alloy Ionic Solids composed of charged species – unit cell neutral each unit cell - stoichiometry of compound anions and cations different in size anions at lattice points cations in “holes” NaCl face-centered cubic CsCl simple cubic too small trigonal hole r = 0.225 R tetrahedral hole r = 0.414 R octahedral hole Molecular Solids molecules in lattice hemoglobin 1962 reaction center 1988 Perutz and Kendrew Deisenhofer, Huber and Michel