Chapter 3 (conclusion)

1
Chapter 3 (conclusion)

• Silica-containing materials
• X-ray diffraction
• Applications of single crystals
• Polycrystalline materials

W.R. Wilcox, Clarkson University, last revised
September 17, 2013
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Silica

• The most common elements on earth are Si O
• SiO2 (silica) has 14 polymorphic crystal
  structures, of which ? quartz is the stable phase
  at room T P.
• http//en.wikipedia.org/wiki/Silicon_dioxide
• http//en.wikipedia.org/wiki/Quartz
• Also exists as an amorphous phase, "quartz glass"
  or "fused silica."
• The strong Si-O bonds lead to high melting
  temperatures (gt1600ºC)

crystobalite (stable above 1470oC)
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Silicates

• Bonding of adjacent SiO44- tetrahedra
  accomplished by the sharing of corners, edges, or
  faces

For example, quartz can be shown as

• Multivalent cations Ca2, Mg2, Al3 ionically
  bond SiO44- to one another.
• Examples
• Mg2SiO4 (Forsterite) with 1895oC melting point.
• Ca2MgSi2O7 (Åkermanite) with 1452oC melting
  point.

4
Layered Silicates

• Layered silicates (e.g., clays, mica, talc)
• SiO4 tetrahedra connected to form a
  two-dimensional plane
• A net negative charge is associated with each
  (Si2O5)2- unit
• This negative charge is balanced by anadjacent
  plane rich in positively charged cations

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Layered Silicates (continued)

• Kaolinite clay alternates (Si2O5)2- layers with
  Al2(OH)42 layers

Adjacent sheets of this type are loosely bound to
one another by van der Waals forces, and so are
easily separated.
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Silica Glass Structure

• Glasses are not crystalline they are amorphous.
• Silica glasses have short-range order, but not
  long-range order.
• Common silica glasses contain Na, Ca, Al, B
  oxides added to SiO2.
• The SiO4 remains the basic building block, but is
  portrayed in two dimensions as Si bonded to three
  O.
• Fused silica has nothing added

Additives prevent some O from bonding to two Si.
This lowers the melting point and the viscosity
of the melt. Soda-lime glass is the most common,
e.g. for windows.
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Characterization by X-Ray diffraction

• An important family of characterization methods.
• They utilize x-ray diffraction for various
  applications, e.g., identification of a material,
  obtaining crystal orientation, determination of a
  structure, viewing defects. See, for example
  http//en.wikipedia.org/wiki/X-ray_crystallography
  
• All techniques use a beam of x-rays of a single
  wavelength ? to strike a sample and a detector
  for the x-rays coming from the sample.
• First explanation was Bragg's Law in 1913
  (http//en.wikipedia.org/wiki/Bragg27s_law)
• Consider that crystallographic planes reflect the
  x-rays

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Bragg's Law for X-Ray Diffraction

• If diffracted beams from planes AA' and BB' are
  in phase, they reinforce one another. This
  occurs when the difference in the distances
  travelled by the two beams is a whole number n of
  wavelengths, n?. The difference here is
  2dhklsin? where h, k and l are the Miller indices
  of the planes.

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Bragg's Law

• n? 2dhklsin?
• As with many "laws" explaining phenomena, this is
  a simplification of scattering by real atoms.
• Nevertheless, it is an excellent first step in
  interpreting scattering of x-rays.
• It is a necessary condition for diffraction, but
  not always sufficient.
• For cubic structures only

• Note that for cubic structures the higher the
  indices for the planes, the smaller is dhkl, so
  the larger is ?.
• One technique utilizes powder or a
  polycrystalline solid as the sample, so that very
  many orientations are exposed to the beam.
• The motion of the beam and detector are
  synchronized

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X-Ray Powder Pattern
(110)
(211)
Intensity (relative)
(200)
Diffraction angle 2q
Diffraction pattern for polycrystalline a-iron
(BCC)
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Laue Methods for Single Crystals

• Utilize photographic film.
• Gives spots, each one of which is for a
  particular crystallographic plane.
• Symmetry of spots reveals the symmetry of the
  plane normal to the beam.

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Laue pattern for Mg (0001)
Six-fold symmetry As you go around, the same
pattern repeats 6 times.
? VMSE
13
http//minerva.union.edu/jonesc/scientific_photos
202010.htm
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Crystals as Building Blocks

• Many modern applications use synthetic single
  crystals, e.g. integrated circuits (computer
  chips), solar cells, infrared detectors, x-ray
  detectors, oscillators, solid-state lasers, light
  emitting diodes, magneto-optic memory devices,
  micro electromechanical systems, lenses, hard
  windows, etc.
• Jet engine turbine blades

• Many properties of crystals depend on
  crystallographicdirection, i.e. they are
  asymmetric.
• Most engineering materials are polycrystalline,
  i.e. they consist of many separate crystals
  called "grains."
• The grains may be randomly oriented or partially
  aligned, depending on how the material was
  produced.
• Grain sizes range from nm to cm. Some properties
  depend on grain size.
• For small randomly-oriented grains, the
  macroscopic properties are isotropic.

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Polycrystalline Example

• Electron-beam welded Nb-Hf-W plate.
• The small equiaxed grains on the two sides are
  the original unaffected material.
• The elongated grains in the middle result from
  being melted and refrozen by the electron beam
  (moved downward here).
• The equiaxed grains near the elongated grains
  have grown larger because of being heated without
  melting (heat-affected zone).