Crystal Defects

1
Crystal Defects

• Perfect crystals do not exist even the best
  crystals have 1ppb defects.
• defects are imperfections in the regular
  repeating pattern and may be classified in terms
  of their dimensionality (Point vs. Extended).
• Point Defects
• Vacancies
• given a perfect crystal (e.g. of Cu), an atom can
  be placed on the outside of the cell to produce a
  vacancy ( ?) remember atom migration.
• e.g. TiO has 11 stoichiometry and NaCl
  structure, but has 15 vacancies on the Ti sites
  and 15 vacancies on the O sites. Both sets of
  vacancies are disordered.

2
Crystal Defects

• driving force? movement of the atom requires
  breaking (endothermic) and making (exothermic) of
  bonds. Because the atom is moving from an
  internal site (w/say 6 bonds) to an external site
  (w/say 3 bonds), there are more bonds broken than
  being made, so this is an overall endothermic
  process.
• counteracting this is an obvious large increase
  in disorder (from perfect crystal to defect) in
  addition, atoms around the vacated site can
  vibrate more, further increasing the disorder.

?G(n) n?H nT?S n defects

• Implications
• n? 0 ?G 0, so no driving force.
• there is some min value of n which is most
  stable.
• there is some minimum n after which ?G becomes
  positive.
• as T? nmin and nmax will also increase.

?G(n)
max min
n ?
3
Crystal Defects

• Ionic Crystal Defects
• in pure metal compounds, dont need to worry
  about electroneutrality.
• in an ionic crystal, the interior and surface
  must remain neutral.
• Shottky Defect
• take anions and cations and place them on surface
  in equal numbers.
• stoichiometric effect equal numbers of anion and
  cation vacancies.
• may be randomly distributed, but tend to cluster
  because of oppositely charged vacancies.
• most important with alkali halides.
• at room temp, 1 in 1015 pairs vacant in NaCl, so
  1mg sample has 10,000 Shottky Defects.

4
Crystal Defects

• Frenkel Defect
• take cation out of position and cram it into an
  interstitial site (void between normal atomic
  position).
• Ag surrounded by 4Cl- stabilizes this defect.
• tendency for vacancy and interstitial to form
  nearby pair.
• also a stoichiometric deffect (vacancies
  interstitials).

5
Crystal Defects

• Color Centers (aka F-center Ger farbenzentre)
• electron trapped in an anion vacancy.
• possible mechanism high energy radiation (x-ray,
  ?-ray) interacts with alkali halide, causing
  halide to lose an electron. The electron moves
  through the crystal until it encounters a halide
  vacancy. It is trapped there by strong
  electrostatic forces (i.e. 6 cations!).
• a series of energy levels are available for the
  electron within the vacancy often in the visible
  region (deep purple in KCl smoky quartz
  amethyst).
• found for a series of alkali halides
• absorption energy, Emax a a-1.8
• a cubic lattice parameter (length of the edge
  of the cubic unit cell).

Note E is inversely proportional to a.
6
Crystal Defects
Large E little a.
Emax a a-1.8
Large a little E.
7
Crystal Defects

• Extended Defects.
• have seen that many vacancies are initially
  random, but can cluster
• when vacancy density gets high, the material will
  try to do something to get rid of them.
• Sheer Planes
• e.g. ReO3 bright red, Re Oh h.s. d7, conducting.
• normal crystal (cut through face) note
  metal-containing Ohs with shared corners.
• when heated, the compound starts losing O atoms
  these vacancies tend to line up in a plane
  through the center of a unit cell.
• the structure sheers itself (½ unit cell length)
  so that the octahedrons now have shared edges.
  There are more and more sheer planes as Os are
  lost.

8
Crystal Defects

• Dislocations.
• important class of defect responsible for the
  malleability of metals explains the process of
  work hardening of metals.
• dislocations are line-defects instead of the
  loss of atoms (as with point defects), they can
  be looked at as an extra partial line or plane of
  atoms.
• looks like a perfect crystal, but if you look at
  the figure from a low angle, you see an extra
  partial line.

9
Crystal Defects

• edge dislocations are easily moved by slipping
  like a carpet too heavy to drag, but can move
  small wrinkle.
• the presence of a distortion relaxes the
  requirement that entire planes of interatomic
  bonds must distort and break simultaneously for
  plastic deformation to occur. Instead, plastic
  deformation can accompany the motion of a
  dislocation through a crystal.

plastic irreversible elongation (e.g. pulling
wire) by movement of planes.
10
Crystal Defects

• can get rid of dislocations this gets rid of
  maleability and material becomes brittle (e.g.
  bend Cu wire).
• movement of dislocations is key to plastic
  deformation, therefore, increasing resistance to
  deformation (strengthening the metal) requires
  either eliminating the distortions or preventing
  them from moving (pinning them).
• dislocations are often pinned by other defects in
  the crystal new dislocations are created during
  deformation and become pinned by the initial
  dislocation.
• the build-up of pinned dislocations leads to the
  hardening of the metal in a process known as work
  hardening.

11
Crystal Defects

• e.g. moving an entire rug requires lots of
  energy. A single wrinkle serves as a dislocation
  in facilitating the movement of the rug at any
  time only a small part of the rug moves, so
  little energy required.
• work hardening is like having multiple tangled
  wrinkles in the rug---one wrinkle pins the other.
• a work-hardened metal can be softened again by
  annealing (heating) at high temperatures
  increased thermal motion allows atoms to
  rearrange and go to lower energy states.
• so, work hardening adds edge dislocations so that
  planes no longer slip.

12
Crystal Defects

• can strengthen materials with sheer planes by
  adding impurities.

if impurity prefers shorted bond lengths, then
this is a stable situation. Cu Zn ? bronze Cu
Sn ? brass
edge dislocation strains bond lengths, etc.
13
Stress Strain

• Experiment measure width and length of wire
  pull and re-measure repeat.
• initial
• pull
• breaks at
• s stress force/unit area
• e strain ?l/lo
• yield strength increases as dislocations
  increase.
• distortions get tangled up like spaghetti too
  many cause material to become brittle.
• e.g. Fe sword add impurities and pound becomes
  hard dislocations climb to surface anealing
  makes material soft by getting rid of distortions.

some materials, e.g. glass break after a certain
point brittle fracture. linear portion
reversible.
s
0.1
e
cross-sectional area (larger diameter would
require more force to break).
again, linear portion reversible, so below yield
point no permanent elongation occurs elastic
deformation
change in length/ initial length
s
so
20
e
above yield point plastic elongation occurs.
14
Burgers Vectors (Bergers Circuit)

• Way to describe dislocation.

4 3
3 4
4 3
3 4
Above Burgers circuit for dislocation-free
material.
note compressed bonds and elongated bonds.
To Right Do same with dislocation and end up
past starting point. Vector b distance to
get back to curcuit.
15
Burgers Vectors

• Screw dislocation with Bergers vector. Note
  direction is direction of screw axis.
• Crystals often will grow along screw dislocation.

16
Impurities and Doping

• Impurities are elements present in the material
  that are different from those in the compound
  formula.
• Dopants are intentionally added impurities (to
  make alloys or affect changes in properties).
  Alloy formation most likely when dopant anions
  and cations are close in size to original
  material.
• Isovalent dopants substitution species have the
  same charge.
• NaClAgCl ? Na1-xAgxCl (alloy on cation site)
• AgBrAgCl ? AgBr1-xClx (alloy on anion site)
• Aleovalent dopant substitution species has
  different charge.
• NaClCaCl2 could be either Na1-2xCax?xCl
• or Na1-xCaxClClxi
• either could happen experimentally, first is
  found.

vacancy
interstitial