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Unformatted text preview: Crystalline Solids CaF Unit Cell Crystal Lattice A 3 D a rra y o f p o ints wh e re e a c h p o int h a s a n id e ntic a l e nviro nm e nt. Unit Cell T h e re p e a ting unit (a unit c e ll is to a c rys ta l, like a "b ric k" is in a h o us e ) . In a g ive n c rys ta l a ll unit c e lls a re id e ntic a l. 2 Ionic radii and coordination number
Cation Anion Large cation & Large anion r(Cation)/r(Anion) ~0.72 Small cation & Large anion 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, anionanion contacts prevent this. The solution is to lower the coordination number Radius Ratio Rules
r(cation)/r(anion) 0.73 0.41 0.22 0.15 Coordination Number 8 6 4 3 Coordination Geometry Cube Octahedron Tetrahedron 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) ReO3 structure diag diag a a 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 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 Xrays have a wavelength comparable to spacings of atoms Single Crystal X-ray Diffraction A B Bragg's Law d The extra path length traveled by wave B (shown in red) is equal to 2d sin , where d is the spacing between planes. Constructive interference will only occur if this distance is an integer multiple of the wavelength (n). Xray Powder Diffraction
Divergence Slit Horizontal Diffraction Circle Sample (Vertical Flat Plate) Divergent Xray Source Antiscatter Slit 2 Horizontal Soller Slits Detector Receiving Slit Xray Powder Diffraction Pattern ...
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- Summer '07