Crystal_Systems_F10

Crystal_Systems_F10 - 1 Crystal Systems GLY 4200 Fall 2010...

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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 X-ray Data • Given Halite, a = 0.5640 nm • Given axis intercepts from X-ray 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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Crystal_Systems_F10 - 1 Crystal Systems GLY 4200 Fall 2010...

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