crystallography

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crystallography (???)
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Structure is important Type of structure we
discussed called crystal structure
(????) In crystals, atom groups (unit cells) are
repeated to form a solid material

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Structure is important "X-ray diffraction" is
important method for study of materials
X-ray diffraction works because of the
repeating nature of crystals
To understand X-ray diffraction, must
first understand repetition in crystals
The study of repetition in crystals is called
crystallography
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Repetition symmetry (???)Types of
repetition Rotation (??) Translation (??)
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RotationWhat is rotational symmetry?
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Imagine that this object will be rotated (maybe)
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Imagine that this object will be rotated (maybe)
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Imagine that this object will be rotated (maybe)
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Imagine that this object will be rotated (maybe)
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Was it?
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The object is obviously symmetricit has symmetry
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The object is obviously symmetricit has
symmetryCan be rotated 90 w/o detection
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so symmetry is really
doing nothing
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Symmetry is doing nothing - or at least doing
something so that it looks like nothing was done!
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What kind of symmetry does this object have?
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What kind of symmetry does this object have?
4 (???)
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What kind of symmetry does this object have?
4
m (?)
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What kind of symmetry does this object have?
4
m
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What kind of symmetry does this object have?
4
m
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What kind of symmetry does this object have?
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4mm (??)
m
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Another example
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Another example
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6mm
m
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And another
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And another
2
2
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What about translation?Same as rotation
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What about translation?Same as rotationEx
one dimensional array of points
Translations are restricted to only certain
values to get symmetry (periodicity)
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2D translationsLots of common examples
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Each block is represented by a point
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This array of points is a LATTICE (??)
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Lattice - infinite (???), perfectly periodic
(????) array of points in a space
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Not a lattice
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Not a lattice
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Not a lattice - .some kind of STRUCTURE because
not just points
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Another type of lattice - with a different
symmetry rectangular
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Another type of lattice - with a different
symmetrysquare
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Another type of lattice - with a different
symmetry hexagonal
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Back to rotation - This lattice exhibits 6-fold
symmetry hexagonal
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Periodicity and rotational symmetryWhat types
of rotational symmetry allowed?
object with 4-fold symmetry translates OK
object with 5-fold symmetry doesn't translate
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Periodicity and rotational symmetrySuppose
periodic row of points is rotated through ?
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Periodicity and rotational symmetryTo maintain
periodicity
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Basis vectors and unit cells
T t a t b
b
a
a and b are the basis vectors for the lattice
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In 3-D
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In 3-D
gt 221 direction
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Lattice parameters (????)
c
b
a
b
g
a
need 3 lengths - a, b, c 3 angles -
?, ?, ? to get cell shape
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The many thousands of lattices classified into
crystal systems (??)
System Interaxial Axes
Angles Triclinic a ? b ? g
? 90 a ? b ? c Monoclinic a
g 90 ? b a ? b ? c Orthorhombic a
b g 90 a ? b ? c Tetragonal
a b g 90 a b ? c Cubic
a b g 90 a b
c Hexagonal a b 90, g 120 a
b ? c Trigonal a b 90, g 120 a
b ? c
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When choosing unit cell, pick Simplest,
smallest Right angles, if possible Cell
shape consistent with symmetry
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Which one? Why?
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