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Unformatted text preview: 1 Crystal Systems GLY 4200 Fall, 2010 William Hallowes Miller 1801 1880 British Mineralogist and Crystallographer Published Crystallography in 1838 In 1839, wrote a paper, treatise on Crystallography in which he introduced the concept now known as the Miller Indices 2 3 Notation Lattice points are not enclosed 100 Lines, such as axes directions, are shown in square brackets [100] is the a axis Direction from the origin through 102 is [102] 4 Miller Index The points of intersection of a plane with the lattice axes are located The reciprocals of these values are taken to obtain the Miller indices The planes are then written in the form (h k l) where h = 1/a, k = 1/b and l = 1/c Miller Indices are always enclosed in ( ) 5 Plane Intercepting One Axis 6 Reduction of Indices 7 Planes Parallel to One Axis 8 Isometric System All intercepts are at distance a Therefore (1/1, 1/1, 1/1,) = (1 1 1) 9 Isometric (111) This plane represents a layer of close packing spheres in the conventional unit cell 10 Faces of a Hexahedron Miller Indices of cube faces 11 Faces of an Octahedron Four of the eight faces of the octahedron 111 111 _ 111 __ 111 _ 111 111 _ 111 __ 111 _ 12 Faces of a Dodecahedron Six of the twelve dodecaheral faces 110 101 011 011 _ 110 _ 101 _ 110 101 011 011 _ 110 _ 101 _ 13 Octahedron to Cube to Dodecahedron Animation shows the conversion of one form to another 14 Negative Intercept Intercepts may be along a negative axis Symbol is a bar over the number, and is read bar 1 0 2 15 Miller Index from Intercepts Let a, b, and c be the intercepts of a plane in terms of the a , b , and c vector magnitudes Take the inverse of each intercept, then clear any fractions, and place in (hkl) format 16 Example a = 3, b = 2, c = 4 1/3, 1/2, 1/4 Clear fractions by multiplication by twelve 4, 6, 3 Convert to (hkl) (463) 17 Miller Index from Xray Data Given Halite, a = 0.5640 nm Given axis intercepts from Xray data x = 0.2819 nm, y = 1.128 nm, z = 0.8463 nm Calculate the intercepts in terms of the unit cell magnitude 18 Unit Cell Magnitudes a = 0.2819/0.5640, b = 1.128/0.5640, a = 0....
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 Spring '10
 WARBURTON

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