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Point defects in ionic crystals
including oxides (e.g. NaCl or SnO2), point defects are quite
important. The scientifc community working with those materials has its own way
for dealing with point defects, which differs in some respects from the
viewpoint of the metal and semiconductor community. There are historical and
"cultural" reasons for this, but there are also good reasons.
Essentially, in dealing with more complicated crystals - and ionic materials or
oxides are always more complicated than metals or simple semiconductors - a
more chemical point of view is traditional and useful. Let us look at some
important points that have to be considered in this context. |
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First, we look at the
stochiometryof these crystals
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Ionic crystals must consist of at least two different kinds of
ions. They may then contain point defects in concentrations far above thermal
equilibrium (as defined relative to a perfect crystal), if the real material is
non-stochiometric. If you imagine a single crystal of, let´s say, NaCl
with the composition Na1 - dCl and
d << 1, i.e close to, but not exactly at
stochiometry (which is what you always would expect in reality) your only way
of forming a crystal seems to be to use some point defects as integral part of
the crystal. You might consider, e.g., to introduce a concentration of
d vacancies on the Na lattice site, to put a
concentration of d Cl- ions in an
interstitial position, or to mix both defect types in a ratio where the sum of
the concentration equals somhow d. |
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But now let´s think again. If you consider a crystal of
Na1 - dCl, you are really talking about a
crystal with N atoms of negatively charged Cl-- ions and N (1 -
d) positively charged Na+ ions, which
means that the crystal would carry a net negative charge of edN and thus a dramatically high energy. No such crystal
can exist. |
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This leads us to the second point,
the necessity for charge equilibrium or
"zero net charge condition". |
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If we stay with the above example of NaCl, we are forced to
conclude that a NaCl crystal would be necessarily perfectly stochiometric - it
cannot grow in any other way. However, no crystal exists without some
impurities. If, for example, some Ca atoms are to be included into an otherwise
perfectly stochiometric NaCl crystal, they will always be doubly charged
Ca++ ions, and we now must remove twice the number of Na+
ions to preserve charge neutrality (or introduce twice the number of additional
Cl- ions). Obviously we now must introduce a Na vacancies for
every Ca++ ion included in the crystal (or Cl-
interstitials and so on). |
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The concentration of vacancies now could be much higher than
the thermal equilibrium concentration. But we still may have
equilibrium; namely chemical
equilibrium, or, if the defects are charged,
electrochemical equilibrium!
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We see with this simple example, that
there is a linkage between stochiometry, charge neutrality, impurities and
defects, with the added complication that it is not necessarily clear which
kinds of point defects must be present in what concentration. |
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We also see that point defects in
concentration that have nothing to do with the thermal equilibrium
concentration in perfect crystals may be be an integral part of a real
ionic crystal. |
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The simple example, however, makes
also clear that stochiometry, impurity, and charge neutrality considerations
still do not tell us exactly what kinds of point defects are needed in what
concentration, but at best will give some integral numbers. |
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Let us look at a third point. It
concerns the surface and its interaction with the surroundings - this is where
many applications come in. |
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Consider a ZrO3 crystal in thermal equilibrium with
a gas containing a certain O2 concentration, at a temperature, where
the oxygen in the crystal is mobile to some extent (maybe because there are
O-vacancies?). We must expect some "chemical" reaction to take place.
Some additional oxygen may be incorporated into the crystal, or some oxygen may
diffuse out of the crystal into the gas. Whatever happens in this case will be
determined by the conditions for chemical equilibrium, or, in other word, by
the chemical
potentials of the participating species. |
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Again, we must excpect that point defects are involved in
whatever happens across the interface. We might even expect for the particular
example given (which happens to describe the principle of an oxygen sensor)
that some electrical effects take place because introducing excess oxygen
(always negatively charged) into the crystal or taking some out, will
dinfluence the charge distributions and thus electrical potentials in the
crystal. |
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The commom denominator in all
considerations made so far was: We always had some kind of linkage between
"chemistry" as expressed in reactions between atoms or in
stochiometric considerations, and point defects. |
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We now get the idea of what needs to
be done for a general treatment of point defects and ionic crystals: |
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