The atomic structure of materials

1
The atomic structure of materials
2
How do Atoms Pack Together ?
3
Close Packing

• You can see how it works if you look at a pile of
  oranges in the supermarket. Notice how the
  oranges form a pattern. Each orange labelled A
  will be surrounded by six other oranges
  within one layer. Notice the holes labelled
  B and C. We can place a second layer of
  close-packed oranges on either the B-sites or the
  C-sites (but not both). In this way we can build
  up a 3D structure.

4
Cubic Close-Packed CCP

• Atoms lie on the corners of a cube, with
  additional atoms at the centers of each cube
  face for that reason it is often called face
  centered cubic or FCC. Many simple metals have
  this FCC structure, whose symmetry is described
  as Fm-3m where F means Face-centered,m signifies
  a mirror-plane (there are two) and -3 tells us
  that there is a 3-fold symmetry axis (along the
  body diagonal) as well as inversion symmetry

5
Hexagonal Close-Packing HCP

• This is the structure of sodium at low
  temperatures. No, we can't transform sodium to
  gold by stacking the atoms differently ! For such
  simple materials, the different properties are
  mainly due to the differences between the sodium
  and gold atoms themselves.

6
Body-Centered Cubic BCC

• The BCC structure is slightly less closely
  packed than FCC or HCP and is often the high
  temperature form of metals that are close-packed
  at lower temperatures. For example sodium changes
  from HCP to BCC above -237 degrees C ! The
  structure of iron (Fe) can be either CCP or BCC
  depending on its heat treatment, while metals
  such as chromium are always BCC.

7
Common SaltHow do Different Sized Atoms Pack ?
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Lithium Chloride

• Lithium is the smallest of all atoms with the
  exception of hydrogen, and the big chlorine atoms
  just pack together with the CCP structure,
  leaving the small lithium atoms to squeeze into
  the octahedral holes.

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Octahedron

• Why are the holes called octahedral ? Because
  each hole occupied by a lithium atom is
  surrounded by six chorine atoms at the vertices
  of an octahedron. Let's draw these atoms as small
  spheres to emphasize instead the "co-ordination
  polyhedrae". Such geometrical concepts are very
  popular with crystallographers since they help us
  understand the co-ordination of atoms (their
  nearest neighbors) in more complex structures, as
  we shall see.

10
Sodium Chloride

• The structure of sodium chloride should then be
  regarded as a cubic packing of almost equal
  spheres. But in practice these democratic
  considerations do not change the actual
  structure sodium ends up in the same position
  as poor lithium !

11
Zinc-Blende

• As well as octahedral holes in the CCP structure,
  there are also tetrahedral holes. In
  structures such as that of the zinc sulfide
  (ZnS) mineral zinc-blende the Zn atom prefers to
  occupy these tetrahedral holes, where it is
  surrounded by only four S-atoms. Note that only
  half of the tetrahedral holes are occupied in
  ZnS, where-as all of the octahedral holes are
  occupied in NaCl

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Co-ordination Polyhedrae

• Again it is possible to draw the co-ordination
  polyhedrae around zinc, but in this case it may
  be better to emphasise the actual bonds between
  the Zn and S atoms, using a so called
  ball-and-stick model. As well as CCP cubic close
  packing ABCABC.. of the large anions as in zinc
  blende, we might alternatively expect to find HCP
  hexagonal close packing ABAB.. in some similar
  materials.

13
ZnO Wurtzite

• HCP packing of oxygen anions (red) produces the
  ZnO wurtzite structure of zinc oxide. Notice that
  the co-ordination of Zn is still tetrahedral.
  Because there is little energy difference between
  the two types of structures, we can have more
  complex packing arrangements such as
  ABC.AB.ABC... which results in a whole series of
  polytype structures.

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Anti-Fluorite Li2S

• The anti-fluorite Li2S structure (not shown),
  like zinc-blende ZnS, consists of cubic close
  packed anions S, but now all of the tetrahedral
  holes are occupied - by small Li cations. When
  the cations are larger, such as those of calcium,
  the more common CaF2 fluorite structure (shown
  opposite) is favoured, with the sites of the
  cations (blue) and anions (yellow) interchanged.
  The fluorite structure is favoured when the
  cations are so big that they need eight anions to
  cover them.

15
TiO2 Rutile

• The TiO2 rutile or cassiterite (SnO2) structure
  is adopted by quadri-valent metals or di-valent
  metal fluorides, such as MnF2. Here the blue Ti
  cations are in octahedral holes between the red
  oxygen anions, which is readily seen when we draw
  their co-ordination octahedrae.

16
SnO2 Cassiterite

• Actually, the cation-anion distances are not all
  quite equal, two being a little longer than the
  other four. The SnO2 cassiterite co-ordination
  octahedrae are then slightly stretched along one
  axis. Such elongated octahedrae are relatively
  common for di-valent and quadri-valent cations.

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Diamond Structure

• Returning to zinc-blende, we note that this
  tetrahedrally coordinated FCC structure takes a
  particularly simple form when there is only one
  kind of atom - it is the structure adopted by two
  of the most common elements, silicon and carbon,
  and is known as the diamond structure (more
  later).

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Cristobalite SiO2.

• Many mineral structures are based on variations
  of the diamond or silicon structure. For example,
  if we replace the silicon atoms (Si) by silicon
  oxide units (SiO4) they pack together in a
  similar way to form the mineral cristobalite
  SiO2. We see that the SiO4 units are tetrahedrae,
  and that these tetrahedrae are connected by all
  corners in cristobalite to form a relatively
  dense silica structure

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Perovskites

• Perovskites such as BaTiO3 with formula ABX3 are
  a common type of mineral structure, and include
  many interesting materials such as
  ferro-electrics and superconductors. The large
  blue A-cations and red X-anions, often oxygen,
  are cubic close packed, with the smaller
  B-cations occupying the octahedral holes between
  the X-anions.

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Static Displacement

• At high temperature, the small green B-cations
  can "rattle around in the larger holes between
  oxygen, maintaining cubic symmetry. The static
  displacement only occurs when the structure is
  cooled below a certain transition temperature. We
  have illustrated a dispacement along the z-axis,
  resulting in tetragonal symmetry (z remains a
  4-fold symmetry axis), but at still lower
  temperatures the symmetry can be lowered further
  by additional displacements along the x- and
  y-axes

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Dynamic 3D-Drawing

• An alternative type of structural transition,
  called anti-ferroelectric, is also common in
  perovskites. If the A-cation is too large for
  close packing, the X-cations can be displaced
  instead. But since the BX6 octahedrae are
  relatively rigid units connected at their apexes,
  they twist together as in NaNbO3. Again, we have
  a dynamic 3D-drawing of this anti-ferroelectric
  transition. There is no net dipole moment in such
  anti-ferroelectric structures. Again, as the
  temperature is lowered, a succession of
  transitions can occur, with the octahedrae
  twisting around different axes.

22
Diamond

• The covalent bonding in diamond consists of
  electrons that are intimately shared between the
  carbon atoms. We already saw that these strong
  covalent bonds are usually represented by drawing
  them as sticks between the atoms. Diamond is
  important because it is the hardest substance
  known, and can be used for making sharp cutting
  tools, such as used in drilling for oil. Other
  important materials, such as silicon and
  germanium used for computer chips also have the
  diamond structure.

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Graphite.

• There is a common alternative to diamond for the
  structure of carbon - graphite. The carbon atoms
  in graphite are also strongly joined by covalent
  bonds, but only within a plane, unlike the 3D
  network of bonds in diamond. These planes of
  carbon atoms simply stack together one on top of
  the other, with only very weak forces between
  them. The planes of carbon atoms can then easily
  slip over each other, and graphite is therefore
  an important lubricant ! Talcum powder feels
  smooth for similar reasons.