MCEN 5024. Fall 2003.
Covalent Crystal Structures.
In a covalent crystal, each atom is linked to a number of other atoms by covalent
bonds.
The number of such bonds will depend upon the number of valency electrons
available.
Especially important in the formation of covalently bonded crystals are the fourth
group of elements including carbon, silicon and geranium.
These can each form four covalent bonds and crystallize in the diamond structure.
This is the structure for the form of crystalline carbon stable at high temperature
and pressure.
The Bravais lattice is FCC and there are two atoms with coordinates (0, 0, 0) and
(1/4, 1/4, 1/4) associated with each lattice point.
The coordination number is four with the nearest neighbors at a distance of
N√3ao/4 arranged at the corners of a regular tetrahedron.
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MCEN 5024. Fall 2003.
The atoms centers lie at the corners of tri-equiangular nets in {111} planes.
If these are projected onto (111), the stacking sequence of successive (111)
planes can be described as CA AB BC CA AB BC.
Successive planes are not equally separated from each other.
The structure is loosely packed; the packing fraction is
√3π/16 = 0.34.
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MCEN 5024. Fall 2003.
Systematically moving from C to Si to Ge the lattice constant increases and the
respective binding energies and melting points drop sharply.
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MCEN 5024. Fall 2003.
Molecular Crystal Structures.
In molecular crystals there are two distinct kinds of binding present, that within the
molecules (intramolecular) and that between the molecules (intermolecular).
The structural arrangement of the molecules within the crystal will depend upon
the size and shape of the molecules as well as the strength of the intermolecular
forces (the latter depend on the mass of the molecules as well as on their polarity).
Because intermolecular forces are (by definition) weak, molecular crystals are
generally soft materials, which have a low melting point and a high coefficient of
thermal expansion.
Examples of Molecular Crystal Structures.
Methane
Methane freezes into an FCC crystal:
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MCEN 5024. Fall 2003.
Diatomic Molecules
Diatomic molecules such as 02, N2 and the halides cannot coordinate as spheres
because of their shape.
Hence they do not form cubic crystals but rather structures in which the unit cell
dimensions are not equal.
For example biatomic molecules of iodine are packed into an orthorhombic lattice
in a distinct layer structure.
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MCEN 5024. Fall 2003.
Linear Molecules
Linear molecules produce crystals, which vary markedly in the structure
for their three dimensions.
Tellurium forms a chain-like molecule because there are two covalent
bonds per atom.
These chains coordinate into a crystal by aligning themselves in one
direction, each chain assuming a helical conformation.
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MCEN 5024. Fall 2003.
The technologically most important class of linear molecular crystals is polymers.
For example, polyethylene crystallizes by aligning its chain-like molecules of CH2
units into a very regular 3-dimensional pattern consistent with an orthorhombic unit
cell.
Crystalline polymers also exhibit other higher-level structural characteristics of
interest including chain folds and spherulitic arrangements.
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MCEN 5024. Fall 2003.
Sheet structures.
Sheet structures result from a significant discrepancy between the bonding
strengths within layers versus that between layers.
For example, arsenic and certain forms of SiO2 based clays (Kaolinite) have this
characteristic.
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MCEN 5024. Fall 2003.
Polymorphism.
Overview
Many substances can exist in several crystal forms, stable only over limited ranges
of temperature, pressure or other external variables.
When this phenomenon occurs for an element (e.g. Fe), it is said to be allotropic;
when demonstrated by a compound (inorganic or organic), it is considered
polymorphous.
Different crystal forms of the same substance often significantly different physical
and mechanical properties.
Transformation Classification
Crystalline forms are mutually transformable into each other at a temperature
called the transition, transformation or inversion point.
This is the only temperature (for a given pressure) at which the two crystalline
forms can co-exist, i.e. the transition point lies on a thermodynamically stable
boundary in PVT space.
The transformation from the low temperature form to the high temperature form
usually involves some absorption of energy.
Reconstructive Transformations
Some transformations require considerable changes in the strength or even types
of bonding.
Such transformations are usually very slow and are called reconstructive.
Example: the transformation of diamond to graphite.
In the temperature range of 1700 to 1900oC, the diamond structure changes to the
graphitic structure:
Half of the atoms in any one hexagonal layer have atoms directly above and below
them at a distance of c/2.
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MCEN 5024. Fall 2003.
At room temperature c = 6.70 Å and a = 2.46 Å; thus the c/a = 2.72 is large; the
separation of the nearest neighbors in the basal planes is only 1.42 Å which is
much smaller than the separation between hexagonal sheets of 3.35 Å.
Graphite therefore possesses a layer structure because atoms are strongly
bonded within a sheet but the sheets are only weakly bonded to each other (van
der Waals forces).
So-called amorphous forms of carbon (carbon black, coke and coal) are
considered to be micro-crystallites of graphite randomly arranged in space,
They have low density and possess unsatisfied bonding opportunities, which allow
them to absorb other substances (gases and liquids) easily.
Under ordinary conditions, all forms of carbon are effectively stable.
The return transformation from graphite to diamond can take place at reasonable
rates only at high temperatures (1400-1500oC) and high pressure (tens of
kilobars).
Displacive transformations.
Other transformations involve only re-arrangements of atoms without breaking
bonds.
These usually occur much more quickly and are termed displacive
transformations.
Example: Iron
α (BCC)
γ (FCC)
δ (BCC)
melt.
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