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Ionic crystals have at least two atoms in their
base which are
ionized. Charge neutrality demands that the total charge in the base must be
zero; so we always need ions with opposing charge. |
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The binding between the ions is mostly
electrostatic and rather strong (binding energies around 1000 kJ/mol);
it has no directionality. |
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Ionic crystals thus can be described as an
ensemble of hard spheres which try to occupy a minimum volume while minimizing
electrostatic energy at the same time (i.e. having charge neutrality in small
volumes, too). |
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There are no free electrons, ionic crystals are
insulators. |
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Ionic crystals come in simple and
more complicated lattice types; the latter is true in particular for oxides
which are often counted among ionic crystals. Some prominent lattice types
follow |
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The NaCl
Structure
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The lattice is face
centered cubic (fcc), with
two atoms in the base: one at (0, 0, 0), the other one at
(½, 0, 0) |
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Many salts and oxides have this
structure, e.g. KCl, AgBr, KBr, PbS, ...
or
MgO, FeO, ... |
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The CsCl
Structure
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The lattice is cubic primitive with two atoms in the base at (0,0,0) and
(½, ½, ½). It is a common error to mistake it for a bcc
lattice. |
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Intermetallic compounds (not
necessarily ionic crystals), but also common salts assume this structure; e.g.
CsCl, TlJ, ...,
or AlNi, CuZn, |
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The
ZnS (or Diamond, or
Sphalerite) Structure
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The "zinc blende" lattice is face centered cubic (fcc) with two atoms in
the base at (0,0,0) and (¼, ¼, ¼). |
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It is not only an important lattice
for other ionic crystals like ZnS, which gave it its name, but also the
typical lattice of covalently bonded group IV
semiconductors (C (diamond form), Si, Ge) or
III-V compounds semiconductors (GaAs, GaP, InSb, InP, ..) |
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The ZnS lattice is easily confused with
the ZrO2 lattice below. |
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The
CaF2 or ZrO2 Structure
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The lattice is face
centered cubic (fcc) with three atoms in the base, one kind (the cations) at
(0,0,0), and the other two (anions of the same kind) at (¼,
¼, ¼), and (¼, ¾, ¼). |
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It is often just called the "fluorite structure". |
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Perovskite Structure
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The lattice is essentially cubic primitive, but may be distorted to some extent
and then becomes orthorhombic or worse. It
is also known as the BaTiO3 or CaTiO3
lattice and has three different atoms in
the base. In the example it would be Ba at (0,0,0), O at
(½, ½, ,0) and Ti at (½, ½,
½). |
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A particular interesting perovskite
(at high pressures) is MgSiO3. It is assumed to form the bulk
of the mantle of the earth, so it is the most abundant stuff on this planet,
neglecting its Fe/Ni core. The mechanical properties (including the movement of
dislocations) of this (and related) minerals are essential for geotectonics -
forming the continents, making and quenching volcanoes, earthquakes - quite
interesting stuff! |
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Spinel
Structure
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The spinel structure (sometimes
called garnet structure) is named after
the mineral spinel
(MgAl2O4); the general composition is
AB2O4. It is essentially cubic, with the O - ions forming a fcc
lattice. The cations (usually metals) occupy 1/8 of the
tetrahedral sites
and 1/2 of the octahedral sites and there are
32 O-ions in the unit cell. |
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This sounds complicated, but it is
not as bad as it could be; look at the drawing. We "simply" have two
types of cubic building units inside a big fcc O-ion lattice,
filling all 8 octants. |
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The spinel structure is very flexible with
respect to the cations it can incorporate; there are over 100 known
compounds. In particular, the A and B cations can mix! In other
words, the composition with respect to one unit cell can be
- (A8) (B16)O32, or
- A8 (B8A8)O32 =
A(AB)O4 in regular chemical spelling, or
- (A8/3B16/3)
(A16/3B32/3)O32
and so on, with the atoms in the brackets occupying the respective site at
random. |
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A few examples (in regular chemical symbols)
- Magnetite; Fe3+( Fe2+
Fe3+)O4
- Spinel; Mg2+( Al23+)O4
- Chromite; Fe3+(Cr23+)O4
- Jacobsite; Fe3+( Mn2+
Fe3+)O4
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The spinel structure is also
interesting because it may contain vacancies as regular part
of the crystal. For example, if magnetite is slowly oxidized by lying
around a couple of billion years, or when rocks cool, Fe2+
will turn into Fe3+ (oxidation, in chemical terms, means you
take electrons away). If all Fe2+ is converted into
Fe3+, charge balance requires a net formula of
Fe21,67O32 per unit cell and this means that 2,33
sites must be vacant - we have what is called a defect spinel. In a way, the composition is now
Fe21,67Vac2,33O3; having lots of
vacancies as an integral part of the
structure. |
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To index
Lattice and Crystal
Octahedral sites
Tetrahedral Sites
2.4.1 Point Defects in Ionic Crystals
Exercise 3.1-1: Calculate the Geometry Factor
Solution to Exercise 3.1-1
2.1.4 Mixed Point defects
7.1.2 The Coincidence Site Lattice
8.2.1 Case Studies
Interpreting HRTEM Images
© H. Föll (Defects - Script)
