crystallography basics - review...crystallography basics (continued) 3-d lattice showing position...
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Crystallography Basics - Review
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Crystallography Basics
(continued)
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Identical (same) environment: Same environment and basis positions after 2 different lattice translations in ‘blue’ :
- They can fill an infinite plane and can be arranged in different ways on lattice
Crystallography Basics
(continued)
lattice parameters
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Translation (lattice) vector
For example, if we want to go from one corner to another across a body diagonal…….
R
Crystallography Basics
(continued)
3-D lattice showing position vector (R or r) = primitive (or
lattice) vectors a, b and c with integer coefficients u, v and w
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If a,b,c cell lengths are
different, e.g. orthorhombic
If a,b,c cell lengths are
equal, e.g. cubic
[011]
[111]
[110]
[uvw]:
[001]
[101]
[100]
[325]=?
The Four 2-D Crystal Systems (Shapes)
2-D lattice showing position vector (R) = primitive (or
lattice) vectors a and b with integer coefficients u and v:
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The four 2-D crystal systems: (a) square, (b) rectangular, (c)
hexagonal and (d) oblique:
These are
the only 4
possible
2-D crystal
systems
Crystallography Basics
(continued)
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Mirror
planes
(reflection)
Mirror planes
180° in-plane
(2-fold)
rotation
Crystallography Basics
(continued)
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**Recently quasicrystals were discovered and do not belong to 1 of 230
8These are the only 7 possible 3-D crystal systems
(know them and their 6 lattice parameters)
Unit cell: smallest repetitive volume
which contains the complete lattice
pattern of a crystal.
The Seven 3-D Crystal Systems (Shapes)
from your Callister Book
Trigonal - has 3-fold
rotation (120°) normal to the
body diagonal, e.g. {11ī}
has 3-fold symmetry
denoted with triangle shape.
Monoclinic- has 2-fold
rotation (180°) normal to the
centers of 2 unit cell edges going
through the opposite sides of the
cell, e.g. {01ī} has 2-fold symmetry
denoted with diad shape.
The Seven 3-D Crystal Systems
(continued)
Cubic- has 2,3 and 4-fold
(90°) rotations, e.g. {001}
has 4-fold symmetry denoted
with square shape.
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Cubic Crystal System Symmetry
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From John D. Verhoeven, Fundamentals of Physical Metallurgy,
Wiley, New York, 1975, p. 16
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Summary of the
Seven 3-D Crystal Systems