Defects in Ceramics

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Defects in Ceramics
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Free Energy ?G ?H -T?S
Defines whether a given transition between two
states is favourable ?G gt 0 Unfavourable ?G
0 Potential equilibrium ?G lt 0 Favourable At
a given temperature, a function of two
parameters- ?H Enthalpy- ?S Entropy
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Enthalpy H E PV

• A holistic measure of energetics encompassing
  all interbody forces (electrostatics,gravity,
  etc) and the useful work that can be extracted
  from the system (described by systemic
  parameters P V).

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Entropy SklnO

• A measure of a system's probabalistic likelihood
  where every possible configuration is equally
  likely.

Macrostate a system's description based on its
ensemble properties, the sum of its
indistinguishable parts.
Microstate a system's description based on the
properties of its distinguishable components
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Two particles in a box
There are 3 macrostates
There are 4 microstates
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Three particles in a box
There are 4 macrostates
There are 8 microstates
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In general,
This table was generated using the formula for
the of permutations for picking n items from N
total
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Applied Thermodynamics

• A system's order is thus inversely related to
  it's probability of configuration.
• In the case where N10, there is a 1/512 chance
  that all particles will occur on a single side.
  What about a mole?

• And so we see why, in a purely classical sense,
  impossible events can occur but are unlikely to
  the point of practical irrelevance.

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Entropy's Contribution ?SSf-Si

• As a state moves from a less probable state to a
  more probable state, ?Sgt0Thus, entropy's
  contribution to ?G in following probability is
  lt0!Using our simple construction, we can
  evaluate in what direction a system will shift a
  balance between configurational probability and
  energetics.

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Structural defects in Ceramics

• Schottky

Frenkel
A set of ions are missing such that electronic
neutrality is maintained
A set of ions leave the lattice into interstitial
positions
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Energetics of Defects

• Hi bonding E of perfect ceramic

?g average change in enthalpy per defect
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• A Frenkel defect is defined by the effective
  reaction
• 0 -gt I V
• Therefore NiNv

Apply Stirling's formula,
Minimizing G, where nltltN
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Intrinsic/Extrinsic Behaviour

• Intrinsic defects have a thermal activation
  energy
• Extrinsic defects are largely constant according
  to concentration
• Looking at MgO and NaCl, both of whose intrinsic
  populations are dominated by Schottky mechanisms
• MgO Ef 7.7eVNaCl Ef 2.4eV
• Can we thus expect MgO to have much higher
  purity levels than NaCL?

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Intrinsic/Extrinsic Behaviour

• We have to consider the two materials
  dramatically different intrinsic populations
• Due to MgO's much higher melting (and thus
  processing) temperature, impurities can only be
  reduced to 50 ppm, compared to 1 ppm for NaCl.
• Intrinsic behaviour is thus easily attainable
  for MgO but extremely difficult for NaCl up to
  Tm. 

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Krüger-Vink Notation
M, corresponds to the species V
vacancy C, charge is represented by ' Negative
charge Positive charge X no charge S, site
represents what site the defect has adopted, if
any i indicates an interstitial a
calcium ion with charge 2 in a magnesium
site e? an electron no site is specified
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Defect Formation Reaction Expressions
Schottky reaction in NaCl (dominant)
Frenkel reaction in AgCl (dominant)
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Solute Incorporation Reactions
NiO solute entering MgO lattice
According to the relative rates, Mg will
interact in an equilibrium
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Exciton Generation Reaction
Incoming EMR excites over band-gap
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Redox Reactions
Oxygen gas is released
Oxygen gas is absorbed
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Redox Reactions
The absorption of oxygen gas can be conveniently
expressed in two equivalent forms emphasizing
different defect types
One can thus hope to study the kinetics of
reactions by known, convenient quantities
governed by simple equilibrium reactions.
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Anodized Aluminum Oxide (AAO)
Why would a good ol fashioned ceramic form
well-ordered, straight nanoscale holes?