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Lecture 12 Crystallography.ppt

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Lecture 12 Crystallography.ppt

* * 3-D Space Groups As in the 17 2-D Plane Groups, the 3-D point group symmetries can be combined with translations to create the 230 3-D Space Groups Also as in 2-D there are some new symmetry elements that combine translation with other operations Glides: Reflection + translation Screw Axes: Rotation + translation A point group is a group of geometric symmetries that keep at least one point fixed. A space group is some combination of the translational symmetry of a unit cell including lattice centering, the point group symmetry operations of reflection, rotation and rotoinversion, and the screw axis and glide plane symmetry operations. The combination of all these symmetry operations results in a total of 230 unique space groups describing all possible crystal symmetries. 230 Space Groups Notation indicates lattice type (P,I,F,C) and Hermann-Mauguin notation for basic symmetry operations (rotation and mirrors) Screw Axis notation as previously noted Glide Plane notation indicates the direction of glide – a, b, c, n (diagonal) or d (diamond) Triclinic Monoclinic Orthorhombic Tetragonal Hexagonal Isometric * * * * * * * * * * * * * * * * * * * * * * There are also several non-primitive lattice choices P = Primitive C = C-face Centered F = all-Face centered I = body-centered One might expect that each choice is possible for every lattice type, but not so. Why not ? * There are also several non-primitive lattice choices P = Primitive C = C-face Centered F = all-Face centered I = body-centered One might expect that each choice is possible for every lattice type, but not so. Why not ? * * * * * * Lecture 12 Crystallography Internal Order and 2-D Symmetry Plane Lattices Planar Point Groups Plane Groups Internal Order and Symmetry Repeated and symmetrical arrangement (ordering) of atoms and ionic complexes in minerals creates a 3-dimensional lattice array Arrays are generated by translatio

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