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Crystalline Solids CaF2 Unit Cell • Crystal Lattice – A 3D array of points where each point has an identical environment. • Unit Cell – The repeating unit (a unit cell is to a crystal, like a “brick” is in a house). In a given crystal all unit cells are identical. Ionic radii and coordination number Cation Anion Large cation & Large anion Small cation & Large anion r(Cation)/r(Anion) ~0.72 r(Cation)/r(Anion) ~0.3 Anions and cations want to stay in contact with each other, but when the cation becomes much smaller than the anion, anion-anion contacts prevent this. The solution is to lower the coordination number Radius Ratio Rules r(cation)/r(anion) Coordination Number Coordination Geometry 0.73 8 Cube 0.41 6 Octahedron 0.22 4 Tetrahedron 0.15 3 Trigonal Planar These are only meant to be used as rough guidelines, but the coordination number does goes down as the radius ratio [r(cation)/r(anion)] decreases. Ionic Crystal Structures (a) CsCl (b) NaCl (c) Zinc blende Decreasing coordination number Decreasing r(cation)/r(anion) Cell Edge vs. Radii Body centered cubic metal (i.e. Fe) Face centered cubic metal (i.e. Ag) diag ReO3 structure a diag a a 4rFe = √3 a Atoms touch along the body diagonal of the cubic unit cell 4rAg = √2 a Atoms touch along a face diagonal of the cubic unit cell a 2rRe + 2rO = a Atoms touch along an edge of the cubic unit cell Optical Diffraction Experiment Diffraction Spots Diffraction Slide X Laser L Diffraction Demo Take home message • The diffraction pattern is related but not equal to the grid pattern • Diffraction is most effective for monochromatic light whose wavelength is similar to the spacing of “slits” • For crystals X-rays have a wavelength comparable to spacings of atoms Single Crystal X-ray Diffraction Bragg’s Law A B d The extra path length traveled by wave B (shown in red) is equal to 2d sin q, where d is the spacing between planes. Constructive interference will only occur if this distance is an integer multiple of the wavelength (nl). X-ray Powder Diffraction Divergence Slit Horizontal Diffraction Circle Sample (Vertical Flat Plate) q Divergent X-ray Source 2q Antiscatter Slit Receiving Slit Horizontal Soller Slits Detector X-ray Powder Diffraction Pattern