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Graphite Unit Cell Structure
the broad range of subject matter. More than describing a form of the element Carbon, the term ‘graphite’
describes a specific structure. Therefore, only the most basic ‘ideal’, and ‘near ideal’ forms of Carbon graphite will
be discussed in order to keep focus.
Graphite structure may be elementally described by examining its unit cell. Graphite is a long-range order
arrangement of fused hexagons in a common plane. Several of these planes stack with some specific order of their
atom locations relative to neighboring planes and in this way, the graphite lattice
structure is defined.
The unit cell for Carbon graphite assumes different identities depending upon the arrangement of its layers. In
the first basic form of the structure, the unit cell is simple hexagonal, containing two atoms per unit cell and basal
plane axes [2-1-10], [-12-10] and [-1-120] (negative signs represent digits with ‘bars’ over them)(Reynolds, 5). The
simple hexagonal graphite lattice has a plane stacking order "A-A-A" (all planes have the same projection onto the
x-y plane) (Charlier, 46). In the "Bernal" graphite structure, the layer stacking sequence is "A-B-A-B", which
increases the unit cell to almost twice the 3-space volume of the simple hexagonal. It then follows and is a fact that
this stacking arrangement contains four atoms per unit cell (Charlier, 46). The atom locations in the Bernal
structure are shown here in terms of fractions of the unit cell dimensions ‘a’, ‘b’ and ‘c’ (Reynolds, 2). Interlayer
distances in the hexagonal Bernal, ‘ideal’ unit cell are have been measured with a c-axis distance of 3.3539+ 0.0001
Angstrom (Reynolds, 3).
Thirdly, the graphite structure arranges in a stacking structure that can be best described by a rhombohedral
unit cell. In the rhombohedral unit cell, the layer stacking order is "A-B-C-A-B-C". Unit cell atom locations can be
seen in following picture and are also in terms of fractions of unit cell dimensions: a, b and c. Turbostatic graphite is
another structure that can exist. In this structure there is no apparent order to c-axis stacking. This in turn creates
an approximate 2.6% increase in c-axis spacing between layers as compared to the common Bernal and
rhombohedral forms (Reynolds, 2). In the included chart we see the effect of disorder on interlayer spacing
(Ubbelohde, 44).
The Structure of Basal Graphite Planes
Basal planes of graphite are constructed as mentioned before, as a long -range network of fused hexagons.
Each Carbon atom in the lattice has bond structure that can be described by a Trigonal Planar VSEPR model, which
is easy to see in the resulting 120-degree bond angles. Bonds between Carbon atoms in the plane are hybridized
sp2 orbitals that produce an effective bond length of 1.415 Angstrom. These bonds are very short and extremely
strong (bonds in diamond for example are longer at 1.54 Angstrom) (Reynolds, 1). Carbon of course has four
valences, not three, and so this extra electron not yet accounted for serves the function of co-planar bonding,
interplanar bonding (although the bond would be very weak) and as a donor site for electrical conduction (Reynolds,
1).
Each Carbon atom in the ideal and pure lattice has the exact same relation to its neighbors as other atoms
do to theirs and all bonds throughout the lattice are equivalent. These homogenous layers of fused hexagons
remain almost free from each other with a c-axis average interlayer distance of 3.3539+ 0.0001 and an upper limit
distance of around 3.5 Angstrom (Reynolds, 3). Forces that keep the planes together consist of van der Waals
forces (weak attractions) as well as some loose overlap of "2pz orbitals (in the p state) perpendicular to the
graphitic planes" (Charlier, 46). This mechanism is partially what allows graphitic planes to be easily moved past
one another; thereby causing some of the outward characteristics, such as the property of graphite being a durable,
low friction material in most common environmental conditions.
Slip Systems
Graphite is a somewhat unique unit cell, in that it has a very limited slip system. In the unit cell, the only
allowed slip directions are any directions parallel to the basal planes.
