Fred J' Grieman

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Fred J. Grieman
Solids (Lecture 1) Probing structure via
X-rays Crystal Lattices Unit Cells
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Solid Structures
Rigidity Atoms, molecules or ions vibrate about
fixed position No translation - limited
rotation
Two types Crystalline can be anisotropic
properties depend on direction through
solid Amophrous glasses, plastics
Considered super cooled liquids
quartz
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Crystalline Solids Possess long-range order in
their structure Probing Structure several
methods X-ray most important
Diffraction Pattern results from long range
order symmetry X-ray beam scattered by
electrons in atoms Monochromatic source
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• Three pieces of information from diffraction
  pattern
• Angles of diffraction from beam (positions of
  spots)
• distances between atoms
• 2) Symmetry in diffraction pattern
• symmetry in solid crystal
• 3) Intensity of scattered rays (brightness of
  spots)
• identification of atoms
• Scattering causes interference

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Quantitative relationship Bragg Law
?
Picture shows scattered beam at angle where
reinforcement is occuring This occurs when
n? (2)dsin?
Difference in path length
dsin? twice
angle of beam
Can determine d (distance between planes
knowing ?, n, and ?
Must be integer of wavelengths to
constructively interfere. called order
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Systematic order gives symmetry in crystal which
gives symmetry in diffraction pattern For
example
6- fold rotational symmetry
Mirror Symmetry Three dimensional object, so
must collect data from several angles.
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Surprisingly, only a few different kinds of
symmetry found Crystals classified into only 7
crystal systems
These symmetries imposes conditions on the unit
cell of a crystal The Unit Cell is the repeating
unit from which the whole crystal can be built
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Unit cell from structure and symmetry of the
solid Two dimensional example in text
Pick a point in the crystal (lattice point)
(Note atoms dont have to be at lattice points,
but they can be) Put in all points that have the
same surroundings Pull out gridwork of points
(crystal lattice 3 dimensional
array of points
that have the same
environment)
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Unit cell defined by eight points of the crystal
lattice which are corners of the cell giving 3
pairs of parallel faces Every unit cell has the
same and type of atoms in the same
positions Crystal made by stacking unit
cells Lattice points that are shared by adjacent
unit cells only contribute a fraction to that
unit cell
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Picking unit cell for crystal 2 guiding
factors 1) select cell that has symmetry of
crystal 2) select smallest cell that has
symmetry of crystal Primitive cell is
smallest cell contains 1 lattice point
actually 8 lattice points at corners 8 (1/8
lattice point) 1 lattice point
Smallest, but doesnt have symmetry of
crystal. Missing mirror planes
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Usually require larger unit cell most common
face centered
body
centered

side-centered
8(1/8) 1 2 lattice points/unit cell 8(1/8)
2(1/2) 2 lattice points/unit cell 8(1/8)
6(1/2) 4 lattice points/unit cell
(correction from Oxtoby text)
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From unit cell dimensions and formula units in
cell can determine volumes, densities, and
estimate Avogados Number (See text and
homework.) Intensties depend upon type of atom
because different atoms have different
scattering probabilities (Chem 162)
Chem1bsec3 webpage Crystal Instruction