Geology Reference
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statistical tendency to order in the neighborhood of a given site, it is known as
short-range ordering but of it persists over large domains it is known as long-
range ordering. Mistakes or faults in the long-range ordering give rise to antiphase
boundaries separating antiphase domains. Long-range ordering introduces a longer
periodicity into the structure, to which the term superlattice is attached. For an
example of long-range ordering in a mineral, see Redfern et al. ( 2000 )
When long-range ordering is not complete, the degree of ordering can be
described by the Bragg-Williams long-range order parameter S, defined by
S ¼ p r
1 r
ð 1 : 1 Þ
where p is the probability that a given site is occupied by a given species of atom
and r is the fraction of this species that could potentially occupy this site. The
parameter S can thus vary from zero for complete disorder to unity for complete
order. The degree of short-range ordering, in contrast, is defined by the Bethe
short-range order parameter s ; defined by
s ¼ q q r
q m q r
ð 1 : 2 Þ
where q is the actual fraction of unlike atoms on neighboring sites and q r ; q m are
the
corresponding
fractions
at
maximum
randomness
and
maximum
order,
respectively.
1.3 The Constitution of Rocks
1.3.1 Rocks as Aggregates of Grains
Rocks, as aggregations of mineral grains, have mechanical properties mainly
determined by the following factors:
1. The properties of the mineral grains themselves, as surveyed in the previous
section, assuming that the deformation is penetrative to the grain scale.
2. The mutual interactions of the mineral grains, especially as it affects the
intragranular deformation.
3. The manner in which the grains are stuck together, including the nature of the
grain boundaries and of any binding cements.
4. The ease of access of fluids, involving both porosity and permeability.
5. The existence of a hierarchy of structures on different scales, as, for example, in
conglomerates, oolites, layered complexes, or chemically segregated rocks.
Strain compatibility between grains undergoing plastic deformation is a com-
plicated issue in rocks because of the tendency to low symmetry in the mineral
grains, the existence of contrasting properties between different types of grains in
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