Geology Reference
In-Depth Information
atomistic approach the interatomic forces between atom pairs form the starting
point for a computer simulation of the grain boundary core structure. The energy
of a representative group of atoms constituting the core structure is calculated
assuming a pairwise interaction potential and the atomic configuration found that
minimizes this energy with respect to variations in atomic positions and to slight
relative translations of the two crystals (see, for example, Balluffi et al.
1981
;
Farkas
2000
; Gleiter
1979
; Guyot and Simon
1976
; Hahn and Gleiter
1981
;
Harrison et al.
1976
; Karki and Kumar
2007
; Mishin and Farkas
1998
; Priester
1980
). Although such calculations have many limitations, when applied to metals
they have generally indicated that the grain boundary core is very narrow, of the
order of two atomic distances, that there exist energy minima for certain relative
orientations of the grains, and that there are often tendencies for delocalization of
vacancies and dislocation cores with accompanying reduction in the free volume
associated with these defects. Also it has been found that the deduced structure of
the grain boundary core can generally be described in terms of the linking of
polyhedral groups of atoms (Ashby et al.
1978
; Pond et al.
1979
). Less progress
has been made with similar calculations for the more complicated situations
involving non-metallic compounds of relevance to mineral systems but it may be
expected that the above general findings for metals will probably again apply and,
in particular, that polyhedral grouping will be an important concept in describing
the structure of the grain boundary core. However, as with metals (Gleiter
1979
), it
may be that for more refined treatment the electronic energy structure of the grain
boundary will also have to be taken into account.
Some idea of the likely properties of grain boundaries specific to mineral systems
can be gained from reviews on grain boundaries in ceramics by Kingery (
1974
) and
Balluffi et al. (
1981
). On the whole, similar geometrical properties can be expected to
those for metals, with perhaps a greater tendency to faceting. Also the width of the
grain boundary core can again be expected to be very narrow; an estimate by Ricoult
and Kohlstedt (
1983
), based on extrapolation from electron diffraction studies on
low-angle boundaries, indicate that for high-angle grain boundaries in olivine the
width will be less than about 1 nm, that is, similar to the unit cell dimensions. Specific
studies on minerals include Wirth (
1986
), Johnson et al. (
2004
), Hiraga et al. (
2004
),
Kuntcheva et al. (
2006
), and Drury and Pennock (
2007
). However, mineral grain
boundaries are likely to have electrical charges associated with them and a greater
variety in core structure can be expected than in metals because of the greater range in
types of bonding and interatomic potentials. Finally, impurity segregation and pre-
cipitation at grain boundaries will be of particular importance in mineral systems,
both because of their relative impurity and because of strong electrical interactions
between grain boundaries and impurities.
Similar notions can probably be extended to the interphase boundaries between
different minerals, which exist in all but the simplest rocks. One may speculate that
the polyhedral grouping of atoms in a narrow core region will again be important,
perhaps with affinities to intermediate structures, but the geometrical properties of
the interface region will be complicated by the lack of commensurateness between
the
two
crystal
lattices
(Warrington
1980
).
For
references
on
interphase
