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16 Cards in this Set
- Front
- Back
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What is the term used for 2 symmetry operations that have identical results? |
isomorphic |
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In crystallography are rotations assumed to go in the clockwise or counterclockwise direction? |
counter-clockwise |
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What are the 4 fundamental symmetry operations? |
rotation, translation, reflection, inversion |
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What is meant by a symmetry operation "of the first kind"? Of the second kind? |
First kind: chirality (handedness) of object is unchanged. AKA proper operations. e.g. translations, rotations. Second kind: chirality of object is changed. AKA improper operations. e.g. inversion, reflection |
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A symmetry operation preserves __________, is coincident with _______, and all _________ are identical. |
the lattice (i.e. distances & positions), the original structure, physical properties |
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Define isometric. |
An isometric operation that leaves the metric properties of space unaltered (i.e. no stretching, twisting, etc.). Can be reduce to either a translation, rotation, reflection, or any combo of these. |
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Define enantiomorph. |
Two objects related by a reflection operation |
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How can you tell from a symmetry operation matrix if the symmetry operator will change the handedness of an object? |
If the determinant of the matrix is 0 (it will change the handedness of the object) |
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Explain the difference between a point group and what I call a “compound” symmetry operation. |
A point group describes all symmetry elements that pass through a given point. A compound symmetry element is a fundamental symmetry operator where 2 operations occur simultaneously. |
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What six unique symmetry operations are compatible with a 2D point group that is a member of a 2D net? |
1, 2, 3, 4, 6, m |
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What ten unique symmetry operators are compatible with a 3D point group that is part of 3D lattice? |
1, 2, 3, 4, 6, m, inversion, 3-bar, 4-bar, 6-bar |
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What is the difference between a symmetry operation and a symmetry element? |
operation: the mathematical thing that moves the object, producing a pattern when repeated. element: the location (point, line, plane) about which the operation takes place |
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What does the point group order tell you about the number of times an object is repeated throughout the point group? |
point group order = number of times an object is repeated throughout the point group |
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Is the point group order an absolute, a maximum, or a minimum? When (if possible) can the number of objects generated by the symmetry operations be different from the point group order |
maximum. can be different (fewer) at "special locations" (i.e. if the object is on top of a symmetry element). |
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For the 2D point groups “nm” adding a mirror generates two types of notation. The even groups all have two “m”s while the odd groups only have 1 “m”. Why the discrepancy |
In the even groups, adding a mirror plane produces another implied mirror. This is not the case for odd groups. |
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Where do vacancies come from? |
surfaces, grain boundaries, dislocations |
