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cdweasel
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What is a Lattice Point
A point in the lattice. "Any point with identical surrounding as a given reference point".
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What is a lattice
Empty periodic pattern
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What is a Lattice Vector
base at origin to a lattice point
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What is a Basis Vector
the lattice vectors that form the unit cell
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List the axis systems
- - Cubic: a=b=c, all angles 90
- - hexagonal: a=b not c, two angles 90, one 120
- - tetragonal: a=b not c, all angles 90
- - orthorhombic: a not b not c, all angles 90
- - trigonal: a=b=c, all angles equal, less than 120 not equal to 90
- - monoclinic: no sides equal, all angles 90
- - triclinic: no sides equal, no angle equal
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List the Bravais Lattices
- Cubic: Primitive (P), body centered (I), face centered (F)
- Tetragonal: Primitive (P), body centered (I)
- Orthorhombic: Primitive (P), Single face centered (C), body centered (I), all face centered(F)
- Monoclinic: Primitive (P), single face centered (I)
- triclinic: Primitive (P)
- trigonal: Primitive (P)
- hexagonal: primitive (P)
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What is the Structure Matrix
used to transform lattice vector to cartesian vector
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What is a Metric Tensor
Tensor used to determine dot product of lattice vectors (the dot product must be evaluated in cartesian coordinates).
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What is symmetry
the spatial relationship between identical objects in patterns
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What is a Symmetry Operation
produces an image object from an original object where both the original and image objects are congruent (all distances and angles remain the same).
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List the Symmetry Operations
- inversion -
 - Translation
- rotation - n
- reflection - m (or 1/m for mirror planes perpendicular to rotation axis)
- roto-inversion -
 - glide - am/m
- screw - nk
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List the Symmetry Elements
- translation vector
- rotation axis
- mirror plane
- inversion center
- roto-inversion axis
- glide plane
- screw axis
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What is a Symmetry Element
an imaginary object that performs a symmetry operation
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What is the Multiplicity of a symmetry operation
the number of repetitions required to produce an image identical (not just congruent) to the original
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What is a Chiral Object
the image of an original object formed by reflection or inversion
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What are Generating Elements
the symmetry elements that can be combined to generate a point group (sometimes bycreating new symmetry elements)
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Hermann-Mauguin symbols
- 1-triclinic, C1,order 1
-triclinic, C1,order 2- 2 -monoclinic, C2, order 2
- m-monoclinic, Cs, order 2
- 2/m- monoclinic, C2h, order 4
- 222- orthorhombic, D2, order 4
- 2mm- orthorhombic, C2v, order 4
- mmm- orthorhombic, D2h, order 8
- 4 -tetragonal, C4, order 4
- tetragonal, S4, order 8- 4/m- tetragonal, C4h, order 8
- 422- tetragonal, D4, order 8
- 4mm- tetragonal, C4v, order 8
- tetragonal,D2d, order 8- 4/mmm - tetragonal, D4h, order 16
- 3 - trigonal,C3, order 3
- trigonal, C3i, order 6- 32 - trigonal, D3, order 6
- 3m - trigonal, C3v, order 6
- trigonal,D3d, order 12- 6 - hexagonal, C6, order 6
- hexagonal, C3h, order 6- 6/m - hexagonal, C6h, order 12
- 622 - hexagonal, D6, order 12
- 6 m m - hexagonal, C6v, order 12
- hexagonal,D3h, order 12- 6/m mm - hexagonal,D6h, order 24
- 23 - cubic,T, order 12
- cubic, Th, order 24- 432 - cubic, O, order 24
- cubic, Td, order 24 - cubic, Oh, order 48
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Identify Hermann-Maugiun - 1st digit 1
Triclinic
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Identify Hermann-Maugiun - 1st digit 2 or m
monoclinic
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Identify Hermann-Maugiun - 3 digits (2 or m)
orthorhombic
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Identify Hermann-Maugiun - 1st digit 4
tetragonal
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Identify Hermann-Maugiun - 1st digit 3
trigonal
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Identify Hermann-Maugiun - 1st digit 6
hexagonal
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Identify Hermann-Maugiun - 2nd digit 3
cubic
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