The Nature of Minerals and Rocks as Materials - Materials Science for Structural Geology - page 5

( 1981 ), Tilley ( 1986 , 1998 , 2008 ), and Kelly et al. ( 2000 ). Crystal defects can be
conveniently classified dimensionally as point, line, interfacial, and bulk defects.
Point defects are generally regarded as being of particular importance for
transport properties such as diffusion and electrical conductivity. Basically, they
arise either at a normal atom site through the absence of the atom (vacancy) or the
substitution of another type of atom (substitutional; usually a foreign atom), or at a
site not normally occupied through the insertion of an extra atom (interstitial; may
be foreign or not). The defects involving foreign atoms are called extrinsic defects,
as opposed to intrinsic or native defects. In compounds, combinations of these
single defects occur, especially if stoichiometry or charge balance is to be pre-
served; thus, in binary compounds a Schottky pair is a pair of vacancies, one of
each type, and a Frenkel pair is a combination of a native interstitial and its
corresponding vacancy (sometimes restricted to the cation).
The principal line defect is the dislocation, of central importance in crystal
plasticity and discussed later ( Chap. 6 ) . Stacking faults, twin boundaries, antiphase
boundaries, and crystallographic shear surfaces are the simplest of the interfacial
or extended defects. Crystallographic shear surfaces (Wadsley defects) can,
however, occur in such concentrations as to be regarded as an aspect of the
structure itself rather than a perturbation, especially if periodically spaced as in
Wadsley shear phases, common in certain non-stoichiometric oxides, such as those
of W, Ti, and Nb (Fine 1975 ; O'Keeffe and Hyde 1985 , 1996 ). High concentra-
tions of point defects can also be clustered and ordered, as in the case of the
vacancies in wüstite, Fe 1-x O. These assemblages can be regarded as volume
defects. Other volume defects are cavities, precipitates, and precipitation segre-
gations, for example, Guinier-Preston zones (Guinier 1938 ; Preston 1938 ).
The presence of defects can change the electronic structure and properties of a
crystal significantly. A small perturbation of the crystal potential may be insuffi-
cient to split off any electron energy levels to positions outside the bands of the
perfect crystal but, when the perturbation exceeds a certain amount, localized
energy states can appear in the band gaps of insulators, corresponding to attenu-
ated rather than propagating wave functions (Adler 1975 ; Flynn 1972 , p. 190;
Madelung 1978 , p. 378). Such localized states can be treated as approximating a
hydrogen-like situation if the perturbing potential is not too great, in which case
the localized levels lie near to the band from which they are split off and are said to
be ''shallow'' levels within the band gap. As the defect states fall deeper in the gap,
electrons occupying them become more strongly localized and treatment by a
hydrogen-like approximation is no longer valid. Defects such as substitutional
impurities of higher nuclear charge tend to give rise to occupied localized levels
falling below the conduction band of the pure crystal and are known as donors;
the converse acceptor defects, deficient in nuclear charge, tend to give rise to
unoccupied localized levels above the valence band. When a donor level is
unoccupied or acceptor level occupied, the defect is said to be ionized or charged.
In strongly ionic materials, impurity states tend to be highly localized because of
the relatively low dielectric constant and the impurity defects are often ionized in