Dynamic recrystallization of minerals
J. L. Urai, W.
D. Means
& G. S. Lister
Abstract
Dynamic
recrystallization
is an important process during deformation of many rock-forming
minerals,
occurring under a wide range of metamorphic conditions. It can strongly
influence mechanical properties and the development of microstructure.
In this
paper, we review existing work on dynamic recrystallization of minerals
and
mineral analogs. We examine the main driving forces and the processes
operating
on the grain scale as well as on the scale of grain boundaries,
especially
considering the case of a fluid filled grain boundary.
It is argued
that
impurity-hindered grain boundary migration can be significant in
dynamic
recrystallization of minerals, and a more general classification than
the
“rotation” and “migration” recrystallization regimes of Poirier and
Guillopé
& (1979) is proposed. We suggest that fabrics which develop during
dynamic
recrystallization are essentially deformation fabrics, although
recrystallization
processes can accelerate or modify the fabric.
We review the
effects of
dynamic recrystallization on flow stress, and conclude the paper with a
discussion of whether or not dynamic recrystallization can be called a
deformation mechanism.
Introduction
Dynamic
recrystallization
is one of the processes by which a crystalline aggregate can lower its
free
energy during deformation. Several definitions of the term have been
proposed
in the geological literature, differing in the inclusion of certain
processes
in the definition. Current use of the term can be best described as
requiring
the establishment of an array of grain boundaries in new material
positions
(Means, 1983); in other words it is the formation and/or migration of
grain
boundaries (Vernon, 1981). In many cases this leads to the development
of new
grains at the cost of old ones.
For the purpose
of the
present paper we will use the term in this broad sense. However, as it
will be
pointed out in the last section, there are certain problems associated
with
this usage.
When
recrystallization is
synchronous with deformation, it is called dynamic or syntectonic
recrystallization. In the absence of concurrent deformation it is
called static
recrystallization, or pre- or post-tectonic recrystallization as
appropriate.
The special kind of post-tectonic recrystallization that immediately
follows
dynamic recrystallization can be designated by the metallurgical term
metadynamic recrystallization (Djaic and Jonas, 1972). It should be
remembered,
however, that geological strain rates may decay rapidly relative to
relaxation
of thermal anomalies, so that dynamic recrystallization microstructures
may
suffer important modifications while strain rate decays and temperature
remains
high. On the other hand, there are probably geological circumstances
where
strain rate remains high while temperatures decrease, so that
microstructures
formed under steadily increasing deviatoric stress are superimposed.
These
complications make it exceptionally difficult to be exact about the
significance of natural microstructures and cautious use of terms
adopted from
the fields of metallurgy or ceramic science must be advocated.
When the
migrating
boundaries separate different phases, the process is called
neocrystallization
or a phase transition. This paper is concerned primarily with dynamic
recrystallization in circumstances where no new phases grow, although
significant compositional changes across migrating grain boundaries
between
grains of the same phase may occur (Etheridge and Hobbs, 1974; Vernon,
1975,
1977). We are thus dealing with the simplest kind of dynamic
recrystallization
possible in rocks - dynamic recrystallization of impure, single-phase
materials
like calcite marble, quartzites, glacier ice, or single-phase regions
of multi-phase
rocks.
Fig. 1.
Grain boundary
migration in deforming octachloropropane. Movement of selected marker
particles
in time lapse between a and b, relative to central particle, is
indicated by
arrows. Note movement of the boundary UVW with respect to the markers.
After
Means (1983). Scale bar is 0.2 mm.
As late as
1940,
geologists thought of recrystallization in rocks as a process involving
long-range (fluid-assisted) diffusive transfer and not requiring any
crystal-plastic deformation (Griggs, 1940; Harker, 1939) - the process
referred
to as “solution transfer” by Durney (1972). In metallurgy such
diffusion creep
processes are also known, but they have never been regarded as
recrystallization processes.
During the
fifties, the
development of concepts of recrystallization in the earth sciences was
profoundly influenced by existing metallurgical work on annealing
recrystallization, in which a metal is deformed at low temperature (T
< 0.4Tm)
and then statically heated. The following classical sequence is
observed:
primary recrystallization (growth to impingement of essentially
strain-free
grains in a deformed matrix), normal grain growth (during which the
average
grain size slowly increases), and secondary recrystallization (which
may occur
where normal grain growth is impeded and a few grains grow much larger
than the
others; Detert, 1978). This terminology was introduced to geologists in
such
textbooks as Fairbairn (1949) and Turner and Weiss (1963). One of the
first
attempts to apply these concepts to rocks was Voll (1960), but it was
soon
realized that too hasty application of the metallurgical concepts to
minerals
can lead to errors (Hobbs, 1966).
In the sixties
metallurgists were beginning to investigate dynamic recrystallization
in detail
(see early review by Honeycombe and Pethen 1972), and Griggs et al.
(1960)
reported limited amounts of dynamic recrystallization in experimentally
deformed marble.
Fig. 2.
Dependence of
grain boundary migration rate on angle of misorientation by tilt around
common
[111] direction in aluminium. After Liebmann and Lücke (1956).
Subsequent
experimental
investigation by geologists has been extended to quartz and quartzite
(Hobbs,
1968; Tullis et al., 1973), limestone (Schmid et al., 1980), rock salt
(Guillopé and Poirier, 1979), dunite (Ave Lallemant et al., 1970;
Chopra and
Paterson, 1981), pyroxenite (Etheridge and Kirby, in press), and
feldspars
(Marshall et al., 1976; DellAngelo et al., 1984; Tund and Tullis, 1984;
Tullis
and Tund, in press), and there has been extensive further work by
metallurgists
(reviewed by Sellars, 1978; Haessner and Hoffman, 1978; Mecking and
Gottstein,
1978). It has become clear from experiments that dynamic
recrystallization is
likely to exert major influences on the mechanical behaviour and
deformation
mechanisms in rocks, and on the microstructures and crystallographic
fabrics
that they display. Advances have also been made through microstructural
studies
of naturally deformed rocks, in particular by Poirier and Nicolas
(1975) who pointed
to the development of new grains by a subgrain rotation process. Some
further
stimulus for recrystallization studies has been provided recently by
experiments in transmitted light on materials with low melting points
(the
little known work of Wakahama on ice (1964), Urai et al. on camphor
(1980),
Means on para-dichlorobenzene (1981) and octachloropropane (1983),
Tungatt and
Humphreys on sodium nitrate (1981), and Urai on bischofite and
carnallite
(1983a,b)). Such experiments permit direct observation of grain-scale
processes
during dynamic and static recrystallization. In what follows we include
consideration of the driving forces for dynamic recrystallization and
the
intrinsic and extrinsic parameters that control these forces. Secondly,
we
consider details of the processes that occur on the scale of the grains
and on
the scale of the width of grain boundaries. It is important to realize
here
that while grain-scale processes can be studied without understanding
processes
on the atomic scale within grain boundaries, the analogies between
rocks and
other materials (metals, ceramics, analog materials”) are only valid so
long as
the often major differences on the atomic scale between minerals and
other
materials have little or no influence on the grain-scale processes. It
is also
important to understand the competition between various processes
operating.
This underscores the importance of factors determining the kinetics of
various
processes. Thirdly, we deal descriptively with the microstructures and
crystallographic
preferred orientations produced by dynamic recrystallization, with an
eye to
identifying features diagnostic of different recrystallization regimes
where
possible.
Driving Forces
Decrease in
four distinct
types of energy is available as a driving force for dynamic
recrystallization
processes: intragranular lattice defect energy, grain boundary energy,
chemical
free energy, and external load-supporting elastic strain energy. The
first and
last of these driving forces involve elastic distortional energy that
is
respectively locked into the material around defects or maintained in
the
material by an imposed stress. Grain boundary energy is primarily a
surface
energy.
During
annealing, lattice
defect energy is the driving force for primary recrystallization, while
grain
boundary energy becomes the dominant driving force for grain growth and
secondary recrystallization in regions of the material where lattice
defect
energy has been exhausted. The classification of annealing processes
into
primary recrystallization and grain growth/secondary recrystallization
is thus
a classification by driving force as well as a microstructural and
temporal
classification.
Fig. 3.
Creation of new
grains by grain boundary migration. (a) The bulge nucleation of Bailey
and
Hirsch (1962); note the appearance of “detached grains” due to
sectioning at
different levels in the sample. (b) The process is assisted by
formation of a
bridging subgrain boundary as proposed for dynamic recrystallization by
Means
(1981) and Etheridge and Kirby (in press).
During dynamic
recrystallization a classification of processes by dominant driving
force is
still possible in principle, but not so practical because lattice
defect energy
is continuously being supplied to the grains by the deformation. There
is
accordingly no particular time in a dynamic recrystallization history
when
lattice defect energy is exhausted over the polycrystal as a whole,
although
locally this may occur (Glover and Sellars, 1973; Guillopé and Poirier,
1979)
and processes driven by other driving forces may take over, at least
temporarily.
Intragranular
lattice
defect energy is the energy associated with vacancies, dislocations,
and
dislocation arrays within grains. In cold-worked metals it reaches
levels of 105
to 108 J m-3 (Haessner and Hoffman, 1978; Smith
et al.,
1980). In minerals few measurements have been made, but Paterson (1959)
and
Gross (1965) suggest 107 J m-3 from x-ray line
broadening
in a marble deformed experimentally at room temperature. Nicolas and
Poirier
(1976, p. 87) make a similar estimate for olivine with a dislocation
density of
1011 cm-2, such as might be established by
deformation at
low temperature.
At higher
temperatures and
lower dislocation densities much lower lattice defect energies are
expected.
Nicolas and Poirier (1976, p. 87) estimate 104 J m-3
for
olivine with a dislocation density of 108 cm-2, a
density
expected during steady state creep at stresses of the order of 100 MPa
(Kohlstedt and Weathers, 1980). At stresses of the order of 10 MPa, the
predicted driving force drops as low as 10-3 J m-3,
making allowance for the contribution from subgrain boundaries as well
as from
free dislocations.
Grain boundary
energies in
metals range from 102 to 104 J m-3 for
typical
grain sizes (Haessner and Hoffman, 1978), the grain boundary energy per
unit
area of boundary being of the
order of 5x10-5 J cm-2
(McLean, 1957, p. 233). Specific grain boundary energies in rocks are
not well
known but values of 4x10-5, 1x10-5, and 2.7x10-5
J cm-2 have been used by Spry (1969, p. 115), Paterson
(1959), and
Guillopé and Poirier (1979) respectively. The value of 4x10-5
J cm-2
translates into a driving energy of l04 J m-3 for
a
tenfold increase in grain size from 0.01 mm to 0.1 mm. Grain boundary
energies
of this order are thus
much lower than typical driving energies that can be
stored within grains by deformation at low temperature (McLean, 1957,
p. 234;
Detert, 1978). This can be further illustrated for the case of sodium
chloride,
considering a dynamically recrystallizing aggregate in which grain’
size is at
a steady state value, and a migrating grain boundary encounters
subgrains and
free dislocations (cf. Guillopé and Poirier, 1979, and Poirier and
Guillopé,
1979). The equation for the driving force is
F = 2025σ
+ 250 σ2
where F is the
total
driving force per unit area (in Pa) and σ
is the differential stress (in MPa). The two terms on the right hand
side
represent, respectively, the energy gained by elimination of subgrain
boundaries and free dislocations. For the second term on the right hand
side,
we used Kempter and Strunk’s (1977) relationship between stress and
dislocation
density
ρ =
1.6x1011 σ2
where ρ is dislocation
density
(in m-2). An energy per unit length of dislocation of 1.6x109
Jm-1 is calculated following the procedures of Nicolas and
Poirier
(1976, p. 87). For this aggregate, the driving force for grain growth
is given
by
F = 65 σ1.3
(Stüwe, 1978).
Comparing
these two equations, it is apparent that at all reasonable stress
levels (e.g.
between 0.1 and 50 MPa), (dynamic) grain growth will be an unimportant
process
in dynamic recrystallization.
Grain boundary
energy
provides a particularly strong driving force for migration of
boundaries with a
small radius of curvature. As explained by McLean (1957, p. 233) and
Stüwe
(1978), this driving force is
F = 2γ/r
where γ is the grain
boundary
energy per unit area of boundary and r is the mean radius of curvature.
This
driving force, which makes curved boundaries tend to migrate toward
their
centers of curvature, is only around 102 J m-3
for
boundaries that are gently curved (r = 1 mm), but it rises dramatically
to J m-3
for tightly curved boundaries (r = 10-3 mm). 105
J m-3
is comparable with the minimum values of stored energy in cold worked
metals cited
previously, so 10-3 mm is often taken as the critical
(minimum) size
for growth of a new grain in primary recrystallization (McLean, 1957,
p. 234).
Returning to
the above
discussed aggregate of sodium chloride, which under a stress of 1 MPa
has a recrystallized
grainsize of about 10 mm, and using the above equation, it can be shown
that a
grain boundary with a radius of curvature of about 0.5 mm will provide
a local
driving force that is similar to that for strain induced grain boundary
migration. Therefore, although significant (dynamic) grain growth is
not
expected to occur while reduction of lattice defect energy is driving
dynamic
recrystallization, local grain boundary adjustments (such as
straightening out
of bulges and readjustments at triple points) can be important in
microstructural development. An example of this behaviour is shown in
Figure
16.
Chemical free
energy may
be involved as a driving force for dynamic recrystallization where
there is a
small difference in composition between crystals of the same phase on
either
side of a migrating boundary (Etheridge and Hobbs, 1974; Marshall et
al., 1976;
Vernon, 1975). There is unambiguous evidence for such a driving force
in the
phenomenon in metals known as diffusion-induced grain boundary
migration
(Hillert and Purdy, 1978; Pan and Balluffi, 1982), in which grain
boundaries
are made to migrate by diffusing substitutional impurity atoms along
them. At
least at the very start of this process, when the boundary begins to
migrate
and simultaneously becomes a compositional discontinuity, the driving
force
must be chemical in nature since no other driving force is evident.
Hillert and
Purdy (1979) estimate a chemical driving energy of 107 - 109
J m-3 for zinc diffusing in iron.
The difficulty
in confirming
chemically driven recrystallization in the mineralogical cases reported
so far
arises from uncertainty about whether the chemical change represents a
positive
part of the driving force, or a dragging force. The association of a
compositional change with a moving boundary may actually impede its
motion,
just as a grain size decrease (as compared to a grain size increase)
associated
with primary recrystallization must slightly impede rather than drive
primary
recrystallization (Nicolas and Poirier, 1976, p. 167).
Elastic strain
energy in
statically recrystallizing materials is expected to be localized mainly
in the
vicinity of lattice defects and in grain corners or other asperities,
where
“locked-in” stresses may persist. In dynamically recrystallizing
materials on
the other hand, a global elastic strain that supports the external load
is
superimposed on these local elastic strains. Reduction in the resulting
global
elastic strain energy may serve as a driving force for certain dynamic
recrystallization processes, just as it does for the intimately
associated
process of plastic deformation of grains by dislocation motion. The
possible
role of the load-supporting elastic strain energy as a driving force
for
dynamic recrystallization will be discussed in a later section. We can
note
here simply that if elastic strain energy at an initial stress of the
order of
10 MPa is fully dissipated, the driving energy available is of the
order of 103
J m-3. This may be about the upper limit for this driving
force in
naturally recrystallizing rocks. Masteller and Bauer (1978) give an
elastic
energy driving force of 102 Jm-3 for processes
(like the
dry grain boundary migration model of Kamb, 1959) where only part of
the
elastic strain energy is dissipated.
Grain-Scale Dynamic Recrystallization
Processes
Grain Boundary Migration
The motion of
grain
boundaries in deforming materials has two components: motion with the
material
and motion through the material. The latter is grain boundary
migration. It is
the essential process where recrystallization in the most literal sense
occurs:
material from the grain that is being consumed enters the grain
boundary region
and eventually recrystallizes on the lattice of a neighbouring grain
that is
growing. Figure 1 shows an example of grain boundary migration in
deforming
octachloropropane.
Grain boundary
migration
is usually thought of as a conservative process, where there is no net
gain or
loss of material in the vicinity of a migrating boundary. However, this
restriction is unnecessary and is, for example, violated in the case of
diffusion-induced grain boundary migration. Also, in materials
deforming
dominantly by diffusive mass transfer there is usually evidence for
significant
grain boundary migration occurring (McQueen and Baudelet, 1978; Gardner
and
Grimes, 1979). Although non-conservative grain boundary (and phase
boundary)
migration are likely to be important processes in rocks, we will not
discuss
them further in this paper.
In metals the
velocity of
grain boundary migration is known to be influenced by the
crystallographic
setting of the grains relative to each other and by the driving force
and
temperature. The crystallographic setting alone is a complicated
variable,
being specified in full by eight parameters (Haessner and Hoffman,
1978). Three
parameters are required to specify the rotation of one lattice with
respect to
the other (the misorientation); three more are required to specify the
translational position of one lattice with respect to the other, and
finally
two parameters are needed to specify the orientation of the boundary at
any
point. Figure 2 shows an example of the influence of misorientation on
grain
boundary migration rate in aluminum from Liebmann and Lücke (1956). A
five fold
increase in velocity of grain boundary migration is observed when the
misorientation is increased from 20 to 40 degrees for grains with a
common
[111] direction. Similar effects are also expected in statically
recrystallizing minerals. In dynamic recrystallization, an additional
effect is
expected. Orientation differences across a boundary may lead to
differences in
the rates of deformation across the boundary which in turn are related
to the
local driving forces for migration, and hence the velocity of migration
(Cobbold et al., 1984). In pure metals and in circumstances where the
driving
force can be measured, the velocity of grain boundary migration is
found to be
approximately proportional to the driving force. The proportionality
constant
is called the mobility (Smith et al., 1980). The physical significance
of the
mobility is not very clear, however, since it is not an intrinsic
property of
the material but depends itself on the driving force (Gleiter, 1969).
According to
Haessner and
Hoffman (1978), all studies of the temperature effect on grain boundary
migration velocity in metals show temperature dependence of Arrhenius
type with
activation energies of 25-125 kJ mol-1 or about half the
activation
energies for lattice self-diffusion. Lower values of the activation
energy are
observed for purer metals (Smith et al., 1980). Similar temperature
effects
have been demonstrated to occur in ice (Ohtomo and Wakahama, 1983) and
in rock
salt (Mueller, 1935).
Grain
boundaries migrate
toward their centers of curvature in static grain growth and secondary
recrystallization. In dynamic and primary recrystallization, on the
other hand,
grain boundaries commonly migrate away from their centers of curvature
(on the
scale of a thin section, but see Masteller and Bauer, 1978) and
initially
straight or gently curved boundaries may become wavy, lobate, or
sutured.
One of the ways
in which
grain boundary migration can begin is the bulge nucleation mechanism
(Fig. 3a)
of Bailey and Hirsch (1962). A similar mechanism has been invoked for
generation of new grains during dynamic recrystallization of metals
(Richardson
et al., 1966), where it occurs on grain boundaries at low strains (20%)
and on
grain boundaries and deformation band boundaries at higher strains
(Guillopé
and Poirier, 1979). A special feature of bulge nucleation in dynamic
recrystallization is that while several boundaries of a new grain may
be
established by grain boundary migration, full isolation of the grain
may
commonly be achieved by development of a bridging subgrain boundary and
its conversion
by progressive misorientation into a grain boundary (Fig. 3b).
Mineralogical
examples of
bulge nucleation have been reported on deformation band boundaries in
phlogopite (Etheridge and Hobbs, 1974) and plagio the mis-clase
(Vernon,
1975),and on grain boundaries in
See text
calcite (Vernon,
1981), diopside (Ave Lallemant,1978), and galena (McClay and Atkinson,
1977).
Grain migration
When a grain
exchanges
material with a neighbour, its center of mass shifts slightly. The
resulting
small change of position of the grain in the material is a normal
accompaniment
of grain boundary migration. If a grain simultaneously loses material
along
some of its boundaries and gains material along other parts it may move
through
the material by a distance of the order of a grain diameter or more.
This more
pronounced motion of grains through the material is referred to as
grain
migration. It should be pointed out that grain migration is markedly
different
from grain boundary sliding, where the migration of grains is
accompanied by
physical movement of material. An example of grain migration in
bischofite can
be seen in Figure 4.
Fig. 4.
Grain migration
in wet bischofite deformed in plane strain, at a strain rate of 5x105
s-1 and at 80 ºC. Compression direction is horizontal, and
cross
indicates position of a material marker. Scale bar is 0.2 mm. After
Urai
(1983b).
Grains that
migrate over a
distance of a diameter or more may enclose within their boundaries
material
that is entirely different from the material originally enclosed and
may thus
exist indefinitely in dynamically recrystallizing materials. In this
case,
grains can also be considered as migrating orientation domains,
temporarily
attached to particular particles of mass. This leads to an interesting
concept
when considering the interrelation of recrystallization processes and
the
development of crystallographic fabrics (see later section).
Where there is
a preferred
polarity of grain migration (for example normal to strain rate
gradients as in
a shear zone, or to gradients in chemical potential), there is the
possibility
of a transport mechanism for material present on grain boundaries,
resulting in
an apparent increase in diffusivity (Means, 1983).
The impurity
drag theory of catastrophic changes in
grain boundary migration rate
Based on the
theory of
Lücke and Stüwe (1971), Poirier and Guillopé (1979) re-examined
impurity-controlled grain boundary
migration. They considered the case of a
migrating
grain boundary in a material
which has a small (e.g.
10-100 ppm) content of
impurity
atoms. These atoms segregate on the migrating boundary as it sweeps
through the
crystal, and are capable of hindering its migration. There are two
possible
outcomes to this situation:
(a) “slow” or
“loaded” migration of
the boundary when it is
unable to break away from the impurity atmosphere and
must drag it along with it as it
migrates.
(b) “fast” or “free”
migration of
the grain boundary, where the driving force for migration is sufficient
to
overcome impurity drag, and the boundary can break away from
the pinning atmosphere of impurity
atoms (Fig. 5).
Fig. 5.
Schematic
drawing illustrating
the transition from “slow”, impurity-controlled to
“fast”
impurity-free grain boundary migration. After Lücke and Stüwe (1971).
Free migration
can be
induced by an increase in temperature or by a change in misorientation
across
the boundary (both increasing grain boundary mobility), or by an
increase in
deviatoric stress, generating higher levels of defect density, and
consequently
a greater driving force. It can be seen from Figure 5 that a
catastrophic jump
(Zeeman, 1976) in migration velocity can occur above a critical driving
force.
Subgrain Rotation
Poirier and
Nicolas (1975)
called renewed attention to an important process of formation of high
angle
grain boundaries: progressive misorientation of subgrains during
recovery
(Garofalo et al., 1961) until high angle grain boundaries are formed.
In metals
this process has been reported to occur in alloys containing fine
second phase particles
(Hornbogen and Koester, 1978), in copper (Cairns et al., 1971) and in
magnesium
(Burrows et al., 1979).
In naturally
and
experimentally deformed minerals this “rotation recrystallization” has
been
shown to occur frequently, for example in quartz (White, 1976; Garcia
Celma,
1983), olivine (Poirier and Nicolas, 1975; Karato et al., 1982),
calcite
(Schmid et al., 1980; Vernon, 1981), albite (FitzGerald et al., 1983),
amphiboles (Biermann, 1979), pyroxenes (van Roermund, 1982), and halite
(Guillopé and Poirier, 1979; Carter and Hansen, 1983).
The main
evidence for
recrystallization by a subgrain rotation process comes from the
so-called
core-and-mantle structures (Gifkins, 1976; White, 1976) in partly
recrystallized rocks, where the cores of host grains pass out
transitionally
into mantles with increasing subgrain development and then into
aggregates of
recrystallized grains with similar size and orientations to the nearby
subgrains. Etheridge and Kirby (in press) have measured orientations in
experimentally
deformed clinopyroxene with this structure and found the expected
intermediate
orientations of the subgrains between the host and recrystallized
grains (Fig.
6).
Fig. 6. (a),
(b), and
(c): x, y, and z axes of host grain (full stars), subgrains (open
stars) and
mew grains (dots) in experimentally deformed and recrystallized
clinopyroxene.
After Etheridge and Kirby (in press).
Other
measurements have
been made in olivine (Poirier and Nicolas, 1975) in which this
intermediate
relationship is not clear, but the recrystallized grains are again
similar in
orientations to nearby subgrains and to the porphyroclast.
In more
completely
recrystallized rocks, groups of recrystallized grains with similar
orientations
are sometimes seen and these have been interpreted to represent former
single
grains that recrystallized by a subgrain rotation process. (Poirier and
Nicolas, 1975).
There is no
universal
value of misorientation across the boundary between two subgrains that
determines when the boundary between them becomes a grain boundary. As
a
practical matter Guillopé and Poirier (1979) took boundaries in halite
with
misorientations of 15 degrees or more to be grain boundaries, finding
that
these tended to be more mobile and to etch more readily than
lower-angle
boundaries. Poirier and Nicolas (1975) drew the distinction at the same
angle
in olivine. Fitzgerald et al. (1983), on the other hand, observed
marked
changes in boundary character in albite at misorientations as low as
1-5
degrees. The abrupt local structural changes that transform a
semi-coherent
subgrain boundary (capable of description as an orderly array of
discrete
dislocations) into an incoherent grain boundary must be somewhat
gradual for a
boundary as a whole and may depend on several of the misorientation
parameters
mentioned earlier.
Although
dynamic
recrystallization by a process involving subgrain rotation seems to be
well
established in rocks, and metallurgical examples have been cited as
well, many
details remain obscure. These include the exact mechanism by which
misorientation across grain boundaries is increased, and the role
played by
grain boundary migration when the grains are newly formed.
In principle
the
misorientation across a subgrain boundary may increase as deformation
proceeds
in two quite distinct ways. The subgrain boundary may stay fixed in the
material and receive dislocations of like sign from the de-forming
subgrains on
both sides (Fig. 7a). Alternatively, the subgrain boundary may migrate
through
the material and collect dislocations, and perhaps other subgrain
boundaries of
like sign, as it migrates, the subgrains themselves moving with respect
to each
other but not deforming internally (Fig. 7b). (This kind of migration
is easily
modelled by flexing a pad of paper into a fold form, holding the two
limbs
tightly between the fingers, and moving the hands vertically with
respect to
each other).
Fig. 7.
Alternative
ways of increasing the misorienation across subgrain boundaries. See
text for
discussion.
There is also a
range of
intermediate possibilities, involving internal deformation of one or
both
subgrains as well as migration of the boundary between them. The
geometry of
what is possible and impossible when a subgrain is simultaneously
increasing
its misorientation with respect to several neighbouring subgrains and
surrounded by boundaries (more or less capable of migration) needs to
be worked
out. Some relevant principles of deformation compatibility across
migrating
boundaries are discussed by Cobbold et al. (1984). It is clear that
subgrain
boundaries in real materials (especially tilt boundaries) can migrate
under
load (McLean, 1957, p. 211; Exell and Warrington, 1972; Guillopé and
Poirier,
1980). Subgrain boundaries of other types are found to be harder to
move, with
mobilities dependent on the rates of cross-slip and climb (Viswanathan
and
Bauer, 1973), but they are presumed to move in materials that maintain
an
equiaxed subgrain shape even at high strains (Sherby et al., 1977; Ion
et al.,
1982).
Questions about
the role
of grain boundary migration are raised, for example, by the
observations of
Fitzgerald et al. (1983) on albite. The new grains are about twice as
big as
the subgrains, and they have considerably reduced dislocation
densities. Both
observations suggest that some grain boundary migration takes place
during
rotation recrystallization, as does the observation in many rocks that
120º
triple junctions are much more frequent among recrystallized grains
derived
from subgrains than among the remaining subgrains themselves. When
rotation
recrystallization is understood better it may emerge that limited grain
boundary migration plays an essential role in this process.
Migration and Rotation
Recrystallization
In their
experiments on
NaCl single crystals, Guillopé and Poirier (1979) observed a three
orders of
magnitude increase in boundary migration velocity associated with the
catastrophic jump from “loaded” (impurity hindered) to “free”
migration. Based
on the above experiments they set up a classification of
recrystallization
regimes, namely:
(a) a regime where
the driving force
is not enough to cause the catastrophic jump to occur, and grain
boundary
migration occurs at negligible rates. In this regime, the alternative
mechanism
(progressive misorientation of subgrains until high angle grain
boundaries
form) is dominant. This is the rotation recrystallization (or in-situ
recrystallization)
(b)
the migration
recrystallization
(or discontinuous recrystallization) regime wherein grain boundaries
regularly
undergo the catastrophic jump in migration velocity. In this regime
rotation
recrystallization can still take place but is relatively unimportant.
While the first
classifications of recrystallization were based on differences in
driving
force, this classification is based on the nature of the processes
operating.
Rotation recrystallization is driven by load-bearing and locked-in
elastic
distortional energy, while migration recrystallization can be driven by
both
elastic distortional energy and by surface energy. On the other hand,
primary
recrystallization is driven by locked-in elastic distortional energy,
whereas
normal grain growth and secondary recrystallization are driven by
surface
energy.
Processes within Grain Boundaries
The growth of
understanding of grain boundary related processes and microstructures
in the
earth sciences shows close similarities with that in ceramics.
Information from
metallurgy has considerably stimulated the development of advances in
ceramic
science. However, not all aspects of behaviour of the two systems are
the same,
and Kingery (1974a,b) pointed out that there are marked differences
between
grain boundaries in metals and in ceramics. Ionic bonding in oxide
ceramic
systems causes an electrostatic potential on grain boundaries that
strongly
influences many aspects of their behaviour. Also, ceramic systems are
in
general much less pure than the (super) pure metals from which much of
the
information on grain boundaries has been obtained (Haessner, 1978).
The earth
sciences have
undergone similar development, but only recently has attention been
focussed on
questions concerning the nature of grain boundaries in earth materials.
White
and White (1981) noted that with respect to grain boundaries, rocks may
resemble ceramic systems more closely than metals. Using transmission
electron
microscopy, they pointed to the existence of grain boundary junction
tubes and
cavities with fluid at grain boundaries. Similar bubbles on grain
boundaries
were also reported by Christie and Ord (1980), Green and Radcliffe
(1975), and
Kirby and Green (1980). A 10-30 nm thick zone of preferential radiation
damage
along grain boundaries was also observed by White and White (1981).
(See,
however, Ricoult and Kohlstedt (1983), who proposed that this zone was
due to
later alteration, and that the structural width of high angle grain
boundaries
in olivine is only about 0.5 nm).
White and White
proposed
that the effective grain boundary width (this is the width which will
be found
by diffusivity measurements, for example) in minerals is much larger
than in
metals, and that the overall effect of these features was to shorten
effective
diffusion paths and thus enhance the rate of intercrystalline diffusion
processes. However, the above authors did not take into account that
the bubble
arrays on grain boundaries may in fact have been formed from a
continuous fluid
film which was present on the grain boundaries during deformation, and
was
transformed into bubbles afterwards (see Urai, 1983a,b; Urai et al.,
1982).
Formation of arrays of fluid inclusions from fluid-filled microcracks
is a well
known process in many minerals (Lemmleyn and Kliya, 1960; Roedder,
1981). Also,
the shape of the triple junction tubes (Smith, 1964) may be changed by
re-equilibration. It should be noted, however, that White and White’s
conclusions on the enhancement of intercrystalline transport processes
still
holds or gains support from such changes.
Although
analogies with
ceramic systems in many ways are more helpful than with metals, we
should realize
that grain boundaries in rocks are still more complicated. We are
dealing with
“dirty” systems and more direct observations on grain boundaries in
minerals
are needed to get insight into this problem. Limitations on results to
be
expected in the near future have been pointed out by Lücke (1976) who
showed
how many problems remain before understanding the behaviour of simple,
well-controlled grain boundaries. Even when the structure of these
boundaries
is understood (which is presently not the case), problems concerning
their
mobility will remain.
Although high
angle grain
boundaries in minerals can be of essentially solid state character,
there is
growing evidence that in some cases they contain fluid films which in
turn
strongly affect their mobility (Ohtomo and Wakahama, 1982, 1983; Urai,
1983a;
Toriumi, 1982). It appears that although the structure of these
boundaries is
fundamentally different from “dry” boundaries, recrystallization of
materials
containing fluid-filled grain boundaries produces similar macroscopic
features
to those observed in dry materials. For example, migration rates of
fluid
filled grain boundaries seem to depend on orientation, temperature and
driving
force. Also, catastrophic changes in boundary migration rate have been
observed
for both systems (Guillopé and Poirier, 1979; Urai, 1983b). Therefore,
models
describing the behaviour of such boundaries must be able to predict
these
effects.
We shall now
examine a
number of aspects of fluid-filled grain boundaries which could be used
when
constructing such models.
The structure
of a
fluid-filled grain boundary can be described in terms of the two
crystal-liquid
interfaces, and the fluid layer between these. In the general case of a
curved
boundary the interfaces must contain kinks or macrosteps. Two possible
configurations are illustrated in Figure 8. Migration of this boundary
will
occur by dissolution at one interface, diffusion through the fluid and
deposition on the other interface. The process resembles the migration
of fluid
inclusions in crystals (Anthony and Cline, 1974; Olander et al., 1982;
Roedder,
1981), and has been proposed to occur in ice (Ohtomo and Wakahama,
1983).
Fig. 8. Two
possible
structures of a grain boundary containing a fluid phase. Note the possible
association of some of the steps on the growing interface with screw
dislocations. Distance between grid lines is about 10 unit cells. The
configuration in B resembles the island structure proposed by Raj
(1982).
Depending on
conditions,
migration rate can be controlled by any of the three processes
(although
dissolution is unlikely to become rate controlling). If diffusion
across the
fluid is rate controlling, boundary migration rates will be a
continuous
function of driving force. A more detailed description of this case is
given in
Appendix. In the case of deposition being the rate-limiting step,
discontinuous
changes in migration rate may be expected and examples of this are well
documented in the crystal growth literature. For example, with
increasing supersaturation
there may be a change in the rate-determining growth mechanism (e.g.
from
spiral growth on screw dislocations to two-dimensional nucleation,
Nielsen and
Christoffersen, 1981; Fig. 9).
Fig. 9.
Growth rate
versus concentration for a crystal growing from solution. Sudden
changes in
growth rate are caused by a switch in ratedetermining mechanism. After
Nielsen
and Christoffersen (1982).
Strictly
speaking, this
only applies for growth of an F-face (Hartmann 1973), but similar
changes can
be envisaged for other interfaces. The surface may also undergo the
roughening
transition (Human et al., 1981). Alternatively, these changes may be
enhanced
by adsorbed impurities (Kern, 1969; Elwell and Scheel, 1975, p. 210).
Also, migration
rate of
the boundary will be orientation dependent. This can be shown by
considering
Gleiters (1969) model for metallurgical grain boundaries. This model is
similar
to the above one in that the grain boundary is envisaged as the two
grain
surfaces (containing kinks), separated by a grain boundary region. As
Gleiter
has shown, migration rate of the boundary is a function of the kink
density on
the interfaces and therefore orientation dependent. Recently, Ohtomo
and
Wakahama (1983) applied this model to explain the orientation
dependence of the
migration rate of grain boundaries in ice.
Let us now
assume that
migration rate is indeed enhanced by the presence of the fluid. In this
case,
migration rate will be dependent on film thickness as shown in Figure
10.
Fig. 10.
Schematic
drawing of grain boundary rate (in unspecified units) versus of the
fluid film.
See text for discussion.
With increasing
thickness,
migration rate will first increase due to the presence of the fluid.
This
increase will be somewhat gradual, because in very thin fluid films the
diffusion coefficient can be expected to be higher than in a bulk fluid
(Rutter, 1976; Drost-Hansen, 1969). This increase can be as much as
four orders
of magnitude for a film thickness of 2 nm (Rutter, 1983). Above a
certain thickness,
however, diffusion across the fluid can be expected to become rate
controlling,
and migration rate becomes inversely proportional to film thickness
(see
Appendix).
Assuming that
no
significant lateral transport of matter takes place during migration,
this type
of behaviour can be used to explain why in wet bischofite migrating
grain
boundaries leave fluid inclusions behind (Urai, 1983a,b; Urai et al.,
1982). If
the boundary thickness is locally increased (for example when the
boundary
incorporates a fluid inclusion or another fluid-filled grain boundary),
the
thicker section will slow down and will be left behind by the rest of
the
boundary.
There is
growing evidence
in metallurgical and ceramic literature that grain boundary structure
during
migration is fundamentally different from the equilibrium structure
(Kingery,
1974 a,b; Smidoda et al., 1978; Gleiter, 1982). This also seems to hold
for
grain boundaries containing a fluid phase: the fluid film present
during
migration may break up into an array of fluid inclusions after the
boundary
stops migrating (Urai, 1983; Spiers et al., 1984).
In conclusion,
in spite of
the major differences in processes on the scale of grain boundaries,
recrystallization of both “dry” and “wet” materials appears to produce
similar
textures and microstructures, and the classification which will be
presented in
the next section can be applied to both systems.
A New Classification of
Recrystallization Regimes
The
classification into
rotation versus migration recrystallization (Poirier and Guillopé,
1979)
implies negligible rates of grain boundary migration in the “slow” (or
“loaded”) migration regime. However, the theory of Lücke and Stüwe
makes no
predictions concerning the absolute values of boundary migration
velocity and we
see no reason why boundary velocities in the slow migration regime
should be a
priori negligible in comparison with rates of deformation and the rate
of
subgrain misorientation. In recent experiments with other
polycrystalline
materials (both mineral and organic), boundary velocities in the slow
migration
regime have been shown to contribute significantly to the
microstructural
development (Urai, 1983b).
This means that
the
classification into rotation versus migration recrystallization does
not
describe the full range of phenomena occurring during recrystallization.
In the next
section a new,
more general division of recrystallization regimes will be described,
based on
the competition between three microstructural processes and their
effects on
microstructural development. These are:
(a) “fast” or “free”
migration of
grain boundaries;
(b)
“slow” or
“loaded” migration of
grain boundaries;
(c
) progressive
misorientation of subgrains.
Depending on which of these processes is dominant, seven different recrystallization regimes can be defined (Table A).
Table A. A
list of the
seven different recrystallization regimes.
Note, however,
that since
the “fast” migration regime is not always separated from the “slow”
migration
regime by several orders of magnitude increase in migration rate (Fig.
11),
these regimes are not always microstructurally distinct, and may grade
continuously one into the other. Furthermore, since we qualitatively
judge the
importance of a process by means of its impact on the frozen-in
microstructure,
not all of these regimes can be expected to be distinguishable.
Fig. 11.
Schematic
drawing illustrating the effect of a third variable (in this case,
temperature)
on the transition shown in Fig. 5, in terms of a cusp-catastrophe.
After Zeeman
(1976).
We will now
examine the
parameters which may influence the material to recrystallize in a
certain
regime. The description given is at best qualitative, because of the
interdependence of these parameters and the differences in magnitude of
different
effects. For example, small changes in one parameter may put the
behaviour of a
material into a certain regime regardless of the countereffects of
other
parameters.
Intrinsic Parameters
Crystal
structure and
available slip systems will to a certain extent influence the ability
of a
material to undergo heterogeneous deformation and to form subgrains.
For
example, stacking fault energy is well known to influence cross-slip
and climb
in metals. On the other hand, defect concentration or chemistry can
also have a
strong effect on the ability to form subgrains (Hobbs, 1981, 1983;
Urai,
1983a).
The primary
intrinsic
factors influencing grain boundary mobility are misorientation angles
across
grain boundaries and the basic structure of clean, impurity-free grain
boundaries. However, grain boundary mobility can also be strongly
influenced by
impurities. Firstly, substitutional impurities have the tendency to
segregate
on grain boundaries, and force it to migrate in the “slow” migration
field
(Lücke and Stüwe, 1971). The higher the impurity content, the more
difficult it
seems to cause the catastrophic jump to occur; even relatively low
impurity
contents have been shown to completely inhibit “free” migration
(Guillopé and
Poirier, 1979).
Secondly,
impurity atoms
on a grain boundary may also segregate to form a new phase. (Obviously,
if this
second phase has a different origin, the reasoning below still holds).
Here,
there are two possibilities: if the second phase has a low solubility
in the
host, it will act as an inert phase and exert a dragging force on the
grain
boundary (Stüwe, 1978; Ashby and Centamore, 1968; Fig. 12).
Fig. 12. (a)
Interaction of a mica grain with a migrating grain boundary in quartz.
(b)
Recrystallized grains in marble, growing Crossed polarizers, scale bar
is 0.2
mm.
Graphite may be
an example
in geology. Another example is the different recrystallized grain sizes
in
rocks having layers with slightly different contents of a second phase
(Hobbs
et al., 1976, p. 112). On the other hand, if the phase is fluid and a
solvent
of the host material, it may greatly enhance grain boundary mobility.
Major
effects of this type were found to occur in polycrystalline silicon
doped with
boron (Schins, 1982), and for fluid-filled grain boundaries in salt
minerals
(Urai, 1983; Spiers et al., 1984). The enchancement of grain boundary
migration
in olivine by the presence of water (Chopra and Paterson, 1981) and the
presence of thin (100 nm) melt films on migrating grain boundaries in
olivine
(Toriumi, 1982) is also consistent with this mechanism. The effect of a
fluid
phase may be in general more important than the dragging effect of
impurities,
i.e. a fluid film may completely eliminate the dragging effect of
impurities.
Note, however, that other types of interaction of grain boundaries and
fluid
inclusions are also reported (Wilkins and Barkas, 1978).
Finally,
heterogeneities
in impurity distribution, grain structure, or defect concentration may
allow a
process to occur locally in a material, even if average values of the
relevant
parameters would not predict its occurrence. For example, rapidly
migrating
grain boundaries in bischofite (see Fig. 15 in Urai, 1983a and Fig. 26)
were
observed to stop before consuming a whole new grain, leaving over areas
where
rotation and slow migration was operating. Also there is some evidence
that
boundaries which have recently migrate can have a higher mobility than
“old”
boundaries, and consequently “fast” migration may occur in newly
recrystallized
areas while it is impeded in the old grains.
Extrinsic Parameters
Generally,
subgrain
rotation is favoured by relatively high deviatoric stress and low
temperature
deformation (Fig. 13 after Guillopé, 1981), while “fast” migration
occurs at
increasing deviatoric stress and temperature. However, the picture is
in fact
more complex: the magnitude of the catastrophic jump may be different
for every
point of the critical curve, and it may even disappear completely (Fig.
11). At
very high temperature arc deviatoric stress, “fast” migration may be
completely
inhibited by the very rapid multiplication of defects behind a
migrating
boundary (Sellars, 1978; Guillopé, 1981). Also, it should be kept in
mind that
the Lücke and Stüwe theory could not be applied to explain the
empirically
found transition from rotation to migration which occurs at lower
temperatures
(Guillopé, 1981). In addition, nothing is known about the effect of a
grain
boundary fluid film on the shape of the curve in Figure 13, although
there is
some evidence suggesting that in the case of NaCl migration rates are
significant at much lower temperatures (Spiers et al., 1984).
Fig. 13.
Critical curve
in a plot of temperature vs. driving force, indicating the conditions
under
which transition from “slow” to “fast” migration can take place. Note
that this
curve can be seen as the projection of the hinge-line of the surface
shown in
Figure 11, into temperature-driving force space. For very high stress
and
driving force, formation of substructures behind the migrating boundary
is so
rapid that the driving force for migration disappears. In this regime,
no grain
boundary migration is possible. After Guillopé, 1981.
Kinetic Factors
For a process
to become
microstructurally dominant, its rate should be large compared with the
rates of
other processes that influence the
microstructure.
It is
impossible to specify absolute magnitudes, however. For example, even
if the
rate of subgrain rotation is significant, grain boundaries may sweep
the
microstructure so frequently that no significant misorientations are
reached.
Also, if migration of grain boundaries occurs in “waves” as compared
with a
more continuously distributed process (Luton and Sellars, 1969),
microstructures may undergo cyclic changes under otherwise constant
conditions,
and these would be difficult to recognize in a static, “frozen”
microstructure.
If “slow” and
“fast”
migration are to be both significant, then we can expect catastrophic
jumps in
migration rate to be moderate (less than a hundred fold), except in the
case
when areas of fast migration are strongly localized. A further
complication is
that impurity drag on a grain boundary disappears for very low
migration rates
(Lücke and Stüwe, 1971), where the impurity atmosphere can stay in the
vicinity
of the boundary. Therefore, even during “slow” (or “loaded”) migration,
microstructures resembling those formed by “fast” (or “free’) migration
may be
formed.
If the rate of
surface
energy driven grain boundary migration is significant during dynamic
recrystallization, then the interlimb angles at triple junctions will
have a
tendency to adjust towards 120 degrees. To illustrate this point, we
measured
apparent angles at grain boundary junctions in the in-situ deformation
experiment described in Means (1983). Figure 14a shows the distribution
of
angles in the undeformed material with a well developed foam texture
(Fig. 14a
in Means, 1983). Here, there is a more or less symmetrical distribution
of
angles around 120 degrees, as is expected for a typical grain growth
texture
(McLean, 1957). Figure 14b is a compilation of data obtained during
deformation
up to 31% strain (Fig.14b, c, d, and e in Means, 1983).
Fig. 14.
Distribution of apparent angles between
grain boundaries in the experiment described by Means (1983). (a)
Undeformed
sample, number of measurements = 83; (b) data collected at 11, 21, 26,
and 36%
strain, number of measurements = 217. See text for discussion.
In this case,
there is a
general broadening of the distribution, with a possible second maximum
developing
between 160 and 180 degrees, while angles below 30 or above 180 degrees
are
absent. This distribution junctions to a significant effect of surface
energy
driven grain boundary migration: readjustment at triple junctions which
have
recently been relatively unaffected by more rapid grain boundary
migration, and
the dynamic effect of surface tension in the case of triple junctions
migrating. (This is the case when two grains are simultaneously
consuming a
third one or when a grain simultaneously grows into two others. In both
cases
surface tension of the grain boundary which is either growing or being
consumed
will tend to cause a deviation from 180 degrees).
Development of Microstructures
While in-situ
studies of
deformation have enhanced our insight into the development of
recrystallization
microstructures, they have also served to show the difficulties in
inferring
processes that operated from observation of static microstructures. So,
in this
section we first describe the variety of microstructures which can
develop in
different materials, and second, we will try to establish diagnostic
microstructures that can be used in the study of materials with more
restricted
possibilities of observation. A few points should be noted before
commencing.
The combination
of
different processes operating will determine the recrystallization
regime (see
Table A) the material is in. However, in each particular regime there
will be a
variety of microstructures, due to differences in starting grainsize
and
differences in recrystallized fraction. It is generally easier to
interpret
static microstructures when relicts of old grains are present.
“Slow” and
“fast”
migration will be judged by distances traveled in comparison with the
grain
diameters. Absolute values of migration rate are very hard to estimate
from
static sections. For example, Mercier (1980) interpreted the
discontinuities in
recrystallized grain size versus depth profiles (based on observations
on
peridotite xenoliths) in terms of the transition from rotation to
migration
recrystallization as defined by Poirier and Guillopé (1979). However,
because
of the reasons given above, a distinction between “slow” and “fast”
migration
regimes is questionable, In fact, Merciers observation that migration
recrystallized grainsize in olivine is smaller than the rotation
recrystallized
one, suggests that grain boundary migration has taken place in the
“slow”
regime.
Subgrain Rotation Microstructures
These will in
general be
characterized by clusters of grains having similar orientations (see
also Fig.
6 and Figs. 15 and 16).
Fig. 15.
Development of highly misoriented
subgrains in experimentally deformed carnallite. Extinction directions
in each
subgrain are indicated. Crossed polarizers, scale bar is 0.5 mm.
Fig. 16.
Progressive misorientation of subgrains in
naturally deformed clinopyroxene. Extinction directions in each
subgrain are
indicated. Crossed polarizers, scale bar is 0.2 mm.
Variations in
orientation
should proceed more or less smoothly across the cluster, or in an ABAB
fashion
as in microfolding (Garcia Celma, 1982). Local deviations from this
smooth
pattern of misorientation due to heterogeneous strain in the grains
seems to be
rather common.
Recrystallized
grainsize
should be more or less equal to the optically visible subgrain size.
Complications
in this
relatively simple pattern will arise in zones between two old grains,
where it
is frequently not possible to ascribe new grains to one of the hosts.
Also, it
is not clear how microstructure develops after misorientations between
subgrains have become large enough for the subgrains to become grains.
Furthermore, clusters similar to those mentioned above may be formed
(Garcia
Celma, 1983) if in an aggregate the development of a strong preferred
orientation
is accompanied by limited grain boundary readjustment.
In many
naturally deformed
rocks where subgrain rotation has been dominant, grains with
orientations
unrelated to those in a cluster or new grains larger than the optically
visible
subgrain size usually point to the occurrence of some grain boundary
migration
(Figs. 17 and 18), and we suggest that true rotation recrystallization
may be
rather rare in nature.
Fig. 17.
Naturally deformed and recrystallized
quartzite, showing evidence for both progressive misorientation of
subgrains
and grain boundary migration. Crossed polarizers,
scale bar is 0.2 mm.
Fig. 18.
Development of a microstructure very
similar to that shown in Fig. 17, in an in-situ experiment with
octachloropropane deformed in simple shear (shear plane parallel to the
photograph). Room temperature, scale bar is 0.5 mm.
Grain Boundary Migration
Microstructures
Intragranular
lattice
defect energy driven grain boundary migration is
characterized
by a
deviation from equilibrium grain boundary shapes, i.e. serrated (Fig.
19) or
lobate grain boundaries. The direction of grain boundary migration can
sometimes be inferred when old grain - new grain relationships are
clear (Fig.
20), or when one of the grains is clearly much more deformed than the
other
(Fig. 21). The onset of grain boundary migration can sometimes occur at
twin
boundaries (Fig. 22) or at kink band boundaries (e.g. Etheridge, 1975;
Wilson
and Bell, 1979; Fig. 23).
Fig. 19.
Grain boundary migration in naturally
deformed feldspar from Central West Greenland. Crossed polarizers,
scale bar is
0.1 mm.
Fig. 20.
Development of equiaxed new grains in
experimentally deformed carnallite. Crossed polarizers, scale bar is
0.1 mm.
Fig. 21.
Grain A replacing grain B in a naturally
deformed feldspar. Note serration of grain boundary associated with
twins in B,
and the bulge in the boundary, growing into a micro-shear. Crossed
polarizers,
scale bar is 0.1 mm.
Fig. 22. (a)
Twin boundary migration in
experimentally deformed carnallite. Crossed polarizers, scale bar is 1
mm. (b)
Twin boundary migration in a naturally deformed marble. Crossed
polarizers,
scale bar is 0.1 mm.
Fig. 23.
Kink band boundary migration in an in-situ
experiment with paradichlorobenzene, deformed in simple shear. Crossed
polarizers, scale bar is 0.1 mm.
Discontinuous
changes in
grain boundary migration rate will tend to produce a bimodal
distribution in
recrystallized grainsize. The two populations of new grains may not
only differ
in size, but also in morphology (Fig. 24). The presence of both “slow”
and
“fast” migration rates and of subgrain rotation will result in the
development
of complex microstructures. An example is shown in Figure 25.
Fig. 24.
Development of bimodal grain size
distribution in experimentally deformed carnallite. Crossed polarizers,
scale
bar is 0.2 mm.
Fig. 25.
Progressive misrorientation of subgrains
and grain boundary migration producing bimodal distribution in
migration
recrystallized grain size. Experimentally deformed carnallite; crossed
polarizers, scale bar is 0.2 mm.
Grain migration
tends to
make the picture even more complicated. While the effect of grain
migration on
recrystallized microstructure has not been investigated, dissection
microstructures have been reported for a number of analogue materials.
In thin
section, “left over grains” or “left over clusters of subgrains (Fig.
26) are
seen.
Fig. 26.
Schematic
drawing of the formation of “left over” grains by dissection of
original grain
A.
Such
microstructures have
two possible interpretations in three dimensions. These are shown in
Figure 27.
The case of one large, amoeba-shaped grain has been described by Bader
(1951)
for glacier ice; while average grainsize in thin section was a few mm,
some
grains in the interlocking aggregate had a total diameter of up to 30
cm. If
during dynamic recrystallization dissection occurs repeatedly in a
small volume
of material, “orientation families” (see Fig. 14 of Urai, 1983a) will
be
formed.
Fig. 27. Two
possible
interpretations of a “dissection” microstructure. See text for
discussion.
If two slighty
misoriented
subgrains simultaneously start consuming neighbouring grains, the
process will
result in an edge-wise propagation the subgrain boundary. Although this
is a
fain straightforward process, it should be kept in mind when
interpreting
grains which have developed subgrains as “old” grains which are being
consumed
their neighbours (Means and Dong, 1982), or when interpreting new
grains
containing subgrains as being dynamically recrystallized.
Recrystallization and the Development
of a Grain Shape Preferred Orientation
There are
several ways in
which recrystallization can modify the development of a shape preffered
orientation in deforming materials. For example, Lister and Dornsiepen
(1982)
argued that during coaxial deformation, dynamic recrystallization may
take
place preferentially along and towards grain-boundary microshears,
resulting in
preferential alignment of grain boundaries along planes of high shear
stress (Fig.
28).
Fig. 28.
Grain boundary
alignment in experimentally deformed Carrara marble (see Schmid et al.,
1980).
Crossed polarizers, scale bar is 0.1 mm.
Oblique
foliations were
shown to develop in recrystallizing material undergoing progressive
simple shear
by Means (1981) and Lister and Snoi (1984). Lister and Snoke argued
that while
during deformation grains slowly elongate and rotate towards
parallelism with
the shear plane, under the appropriate conditions grain boundary
migration will
continuously restore equiaxed shape in some grains, and depending on
grain
boundary mobility, part of the grains will be elongated in a direction
at some
angle to the shear plane.
The following
two
experimental examples illustrate the variety of effects
recrystallization can
have on grain shapes. Figure 29 shows an in-situ experiment with
paradichlorobenzene deformed in simple shear. It illustrates the
formation of a
ribbon grain by coalescence of formerly distinct grains having similar
orientations.
Fig. 29.
Development of
ribbon grains in paradichlorobenzene deformed in simple shear at 0.9 Tm.
At a shear strain rate of 10-6 s-1, see Means and
Dong
(1982). Strars are passive marker particles, solid lines are grain
boundaries,
and broken lines are sibgrain boundaries. Orientation of grains was
estimated
by their extinction direction and interference colour. Edges of
rectangular
grid in each grain are parallel to their extinction direction. Grains
with a
grid in (a) and (b) are the recognizable predecessors of parts of the
ribbon in
(c). Scale bar is 0.1 mm.
The opposite
effect is
illustrated in Figure 30. Here, an elongated grain is dissected,
resulting in
three more or less equiaxed “left over” grains. Obviously more work is
needed
before the formation of shape preferred orientations by dynamic
recrystallization is fully understood.
Fig. 30.
Dissection of
a grain, resulting in the breakdown of a shape preferred orienatation.
Paradichlorobenzene deformed in simple shear. Bulk cumulative shear
strain
between (a) and (g) is about 1.
Diagnostic Microstructures
One of the
important
conclusions emerging from in-situ observations of recrystallization is
that a
dynamically recrystallizing material can be optically entirely subgrain
free,
e.g. as opposed to Whites (1977) suggestion that optically
subgrain-free grains
were indicative of static recrystallization. Furthermore, a moderately
well-developed 120º maximum of angles between grain boundaries does not
seem to
be inconsistent with dynamic recrystallization (see Fig. 14b).
Diagnostic
microstructures
for dynamic grain boundary migration will be found if the newly grown
grains
can be shown to be deformed themselves (it is assumed that a second
phase of
deformation can be ruled out). Note, however, that (as has been pointed
out
above) the presence of subgrains in a new grain does not necessarily
indicate
deformation.
“Orientation
families”,
especially if they can be shown to consist of the amoeba-shaped grains
shown in
Figure 27, are also thought to be strong indications of dynamic
recrystallization. Oblique foliations (Means, 1981; Lister and Smoke,
1984)
have been shown to be characteristic of but not diagnostic for dynamic
recrystallization.
The distinction
between
dynamic and static rotation recrystallization will in general be a
difficult
one in the absence of grain boundary migration. However, if newly grown
grains
which have developed subgrains can be shown to be dissected by another
new
grain, (see Fig. 13 of Urai, 1983a), rotation recrystallization can be
shown to
have occurred during deformation.
Recrystallization and
Crystallographic
Fabric Development
The development
of
crystallographic preferred orientation during deformation has received
considerable attention in theory, experiment, and study of natural
examples. In
spite of the fact that many of the natural examples studied have also
undergone
recrystallization and experimental evidence that recrystallization can
considerably modify fabrics) little is known about the effect of
dynamic
recrystallization on fabric development. In what follows we will
discuss these
effects separately for the cases of progressive misorientation of
subgrains,
and for grain boundary migration by considering their effects on
reorientation
trajectories.
Progressive Misorientation of Subgrains
Rotation
recrystallization
in general can lead to a more pronounced heterogeneous deformation
within,
grains. It is therefore interesting to discuss the factors influencing
heterogeneity of deformation. In deformed quartzites which have larger
clasts
in a matrix of finer grains, the c-axis has been observed to vary in
orientation over more than 120 degrees within a single grain, for
example, if
microfolding takes place on the readily activated basal plane slip
system (e.g.
Bouchez, 1977; Mancktelow, 1981; Fig. 31). The spread of grain
orientations
that results from rotation recrystallization is obviously related to
the spread
of orientations caused by heterogeneous deformation.
Fig. 31. (a)
Heterogeneous deformation in a clast from the Angers quartzite
(Bouchez, 1977),
illustrated by the change in orientation of traces of the basal plane.
(b) The
spread in c-axis orientations in this clast.
Reorientation
trajectories
of individual grains depend primarily on three factors: a) the
kinematics of deformation,
b) the active deformation mechanisms) and c) the orientation of the
grain
relative to the cinematic axes. Taylor-Bishop-Hill theory allows the
prediction
of specific reorientation trajectories for individual grains.
Heterogeneity of
deformation in naturally deformed rocks (e.g. Fig. 31) makes such
predictions
difficult, and adequate models have not yet been formulated.
However,
average
reorientation trajectories for the development of type II
crossed-girdle
fabrics can be predicted as the result of the careful work of Bouchez
(1976).
These are shown in Figure 32. Basal slip leads to rapid clearing of
“kinking”
orientations (i.e. orientations which dispose the basal plane at high
angles to
the axis of extension disappear from the pole because of rapid
reorientation
due to microfolding and/or kinking). Prism <a> slip then appears
to
activate, leading to reorientation of the crystal lattice towards
orientations
which dispose these dislocation glide systems in the orientations most
favorable for their continued operation, namely with the c-axis
parallel to the
intermediate axis of strain.
Fig. 32. (a)
Type II
crossed-girdle c-axis fabric, showing two planar concentrations
intersecting in
a maximum centered on the Y-axis of the finite strain ellipsoid.
Diagram (b)
shows inferred reorientation trajectories which give rise to this
fabric.
Figure 33
considers the
case of a deforming old grain surrounded by a colony of new grains.
Only a part
of the stereogram in Figure 32 is shown, with reorientation
trajectories
leading from the rapidly clearing, eventually pole-free areas to a
girdle
converging towards an end-orientation. Heterogeneous deformation leads
to a
considerable spread in the orientation of new grains. Although these
are
initially controlled by the orientation of the host, they subsequently
move as
separate entities along reorientation trajectories.
Fig. 33.
Detail of the
stereogram of fig 32-b, showing c-axis orientations of a
heterogeneously
deforming old grain (fine dots) and recrystallized grains derived from
it
(heavy dots) at four subsequent times t0…t3. See
text for
discussion.
Various
circumstances
result depending on the rate at which the orientation of the old grain
is
scattered by the production of new grains, as well as on how the
scattering
takes place. The convergence or divergence of the reorientation
trajectories
affects the development of maxima, but maxima are affected
(transiently) as
well by acceleration or deceleration along the reorientation
trajectories. In
the first case (Fig. 33a, since all trajectories lead to the same end
orientation, recrystallization has little effect except to reduce the
intensity
of the maximum, or to hold it at a steady state value. In the second
case (Fig.
33b), scattering of the orientation of the old grain is more
systematic, and
leads to an acceleration in the rate of fabric development. For
example, Garcia
Celma (1983) examined quartz mylonites from the Cap de Creus (Spain)
and showed
that new grains appeared to have “jumped” 30-40 degrees towards the
fabric
skeleton relative to the orientation of the old grain. The new grains
defined
the skeleton of the same fabrics that are eventually defined by the old
grains
at higher strains, i.e. recrystallization accelerated the definition of
what is
essentially still a deformation fabric.
Grain Boundary Migration
Single slip
end-orientations
Schmidt (1925)
suggested
that all maxima in quartz c-axis fabrics in naturally deformed rocks
were
single slip end-orientations. At that time there was little
understanding of
the kinematics of natural rock deformation) so the slip systems he
predicted
are not relevant here. However, recent work (Schmid et al., 1981;
Bouchez et
al., 1983; Lister and Dornsiepen, 1982) has suggested that many maxima
in
naturally produced quartz fabrics are indeed single slip end
orientations, so
that Schmidt’s (single slip) hypothesis can be reexamined using our
improved
understanding of the kinematics of rock deformation. The significance
of
end-orientations has also been discussed by Lister and Paterson (1982).
In the
case of progressive simple shear, such end-orientations are usually
single slip
orientations because grains in such orientations (slip plane parallel
to the
bulk shear plane, slip direction parallel to the bulk shear direction)
are able
to deform using one dislocation glide system only. The single slip
hypothesis
suffers from the limitation that not all natural rock deformation takes
place
as the result of simple shear, and the complex effects of multislip
(Lister et
al., 1978) are not taken into account. Multislip theory based on
Taylor-Bishop
Hill analysis accurately predicts observed fabric skeletons (Lister and
Hobbs,
1980), but it does not predict Y-axis maxima, for example.
Single slip
end-orientations can be reached by multislip, without
recrystallization. Note,
however, that theoretical models (e.g. Etchecopar, 1977; Lister et al.,
1978;
Lister and Paterson, 1979; Lister and Hobbs, 1980) have not been able
to
explain single slip end-orientations by deformation-induced
reorientation
alone. Etchecopar`s (1977) analysis pragmatically resorts to cutting up
ill-fitting grains, and states that in practice similar effects might
be
expected as the result of heterogeneous deformation, or because of
recrystallization (Bouchez et al., 1983).
Hence it
remains an open
question as to whether single slip orientations can indeed arise solely
because
of deformation induced reorientation, or if there are additional
effects
because of recrystallization during deformation that are essential for
the
development of so called single slip end orientations.
The different
effects of
grain boundary migration
Ice
deformed in progressive simple shear (Hudleston, 1980;
Bouchez and Duval, 1982) develops two c-axis maxima (Fig. 34a) linked
by a
girdle across the intermediate axis of strain (Y). With increasing
shear
strain, one maximum disappears, and what remains is a single maxima of
c-axes
oriented so the (easy) basal slip plane is parallel to the bulk shear
plane
(Fig. 34b). Recrystallization probably plays an important role in the
development of this deformation fabric.
Fig. 34. (a)
and (b):
Development of c-axis preferred orientation in ice deformed in
progressive
simple shear. After Bouchez and Duval (1982). (c), (d) and (e):
Recrystallization
in a through-grain microshear. See text for discussion.
This effect may
arise
because one of the two end orientations is in fact metastable, and
recrystallization enables a switch from one end orientation to the
other
(Bouchez and Duval, 1983). A mechanism for this process is as follows.
Consider
a grain oriented so that the c-axis lies parallel to the metastable end
orientation. Grain boundary shear zones can develop, or through-grain
microshears (Fig. 34c-e), and in the volume of the grain affected by
the
microshear the easy slip plane is rotated towards parallelism with the
flow
plane of the microshear (Fig. 35; see also Fig. 2 of Vernon, 1977).
Fig. 35. (a)
Through-grain microshear in naturally deformed mica grain. Crossed
polarizers,
scale bar is 0.2 mm. (b) Recrystallized grains around the edge of a
mica fish.
Crossed polarizers, scale bar is 0.1 mm.
Since the
microshear was
approximately parallel to the bulk shear plane, the lattice of the
distorted
crystal in the microshear is now approximately parallel to the bulk
flow plane,
i.e. with the c-axis approximately normal to the bulk flow plane.
Suppose that
in these rotated areas subgrains are formed, and their misorientation
with the
host reaches a critical value so that high-angle grain boundaries are
formed,
and these new grains begin consuming the host grain. By this process,
the
entire volume of the grain can be switched from the metastable end
orientation
to the stable “single slip” end orientation.
This process
has been
demonstrated in recrystallization of mica (Lister and Snoke, 1984), and
serves
as an example of how deformation-induced reorientation and
recrystallization
can interact to produce what is essentially a recrystallization fabric
whose
elements are in fact related to the dislocation glide systems active in
the
plastically deforming mineral grains.
Reorientation
trajectories
predicted using the Taylor-Bishop-Hill analysis seem to support this
concept of
a metastable end orientation. In Figure 36 one hundred randomly
oriented grains
of model quartzite C (Lister and Hobbs, 1980) were subjected to a
progressive
simple shear. A strong fabric rapidly develops and two maxima appear
quite
early in the deformation history. Note that if the orientation of a
grain in
the metastable end orientation is perturbed, it will either return to
this end
orientation, or reorient rapidly toward the girdle perpendicular to the
shear
direction. Once this flip has taken place, the rate of further
reorientation is
very slow, since orientations in this girdle are favorable for single
slip.
Fig. 36.
Development of
preferred orientation in a model quartzite undergoing progressive
simple shear,
as predicted by the Taylor-Bishop-Hill model. See text for discussion.
In general, an
orientation
favorable for single slip, once created, will continue to deform, but
it will
tend to deform relatively homogeneously. Because there is no tendency
to
undergo multislip, it is conceivable that the dislocation substructure
associated with it has relatively low internal elastic distortional
energy. For
example, in quartz mylonites described by Garcia Celma (1982), grains
oriented
for single slip survive as megacrysts in a dynamically recrystallizing
matrix.
Microstructural evidence which could indicate growth of these
orientations is
usually ambiguous. In comparison, grains in multislip orientations
support more
of the imposed stress (Kamb, 1972) and also have more tendency to
deform
heterogeneously, hence to recrystallize faster.
Therefore we
suggest that
during dynamic recrystallization, grains in single slip orientations
may grow
at the expense of their neighbours. This was argued to happen in shear
zones of
camphor by Urai and Humphreys (1981). On the other hand, grains in
multislip
orientations or in orientations leading to heterogeneous deformation
(e.g.
kinking) on one slip system will be preferentially consumed by their
neighbours
(Shelley, 1972; Tullis, 1976), although grains in strong orientations
may
survive during coaxial deformation as “augen” (Tullis et al., 1973;
Buiskool
Toxopeus, 1977).
In the
situation discussed
above, the basic processes affecting fabric development are:
(a) some grains may
reorient for
some time and then are consumed and disappear and
(b) other grains
grow (and
multiply).
Now we move on
to discuss
the more complex cases of dynamic recrystallization, involving
substantial
amounts of grain migration. Considering the history of a particular
volume of
material, there will be a constant interplay between
deformation-induced
reorientation along the trajectories described above, and “trajectory
switching” when grain boundary migration causes a sudden switch in the
orientation of a particular volume of material. On the other hand, one
can also
consider the history of grains which are not bound to a particular
volume of
material. These grains migrate through the material, and at the same
time they
continuously reorient. Again some grains may disappear and some may
grow larger
(Fig. 37). The fabrics developing in this case can be argued to be
essentially
deformation fabrics. Note that grains reorient under constantly
changing local
stress and strain conditions because of constant changes in grain shape
and
neighbours present. This may cause more complex effects if these
changing local
stress heterogeneities, possibly acting as local accommodation
mechanisms,
change the local reorientation trajectories enough to alter the
resulting
fabric skeletons.
Fig. 37.
Reorientation
trajectories of a number of grains in an octacloroprophane deformed in
simple
shear. Area of grain in thin section at each increment is indicated by
circles.
Size of circles (in the plane of paper) is proportional to grain area
(see
Jessell, 1984). Trajectories end in a starburst for grains that are
completely
consumed.
Bell and
Etheridge (1976)
showed that recrystallized quartz grains in the mylonites they studied
defined
the same fabrics as did the older, more deformed grains.
Recrystallization did
not prevent the development of a deformation fabric. Lister and Price
(1978) argued
that recrystallization was not dramatically important in affecting or
modifying
fabric during deformation, and that the same fabrics would develop even
if
recrystallization did not occur. On the other hand, Friedman and Higgs
(1982)
and Skrotzki and Welch (1983) showed that recrystallization can produce
large
changes in the fabrics developed. We argue, however, that the essential
element
of the Lister-Price hypothesis still stands, namely that
crystallographic
fabrics that develop during dynamic recrystallization can be
essentially
deformation fabrics, with properties similar to fabrics formed without
recrystallization taking place. The fabric skeleton may be differently
populated as a result of dynamic recrystallization, and maxima may
develop
differently, but the fabrics are deformation fabrics, since their
characteristics are controlled by the mechanisms allowing
crystal-plastic
behaviour of the various grains.
Dynamic Recrystallization and Flow
Stress
The onset of
dynamic
recrystallization can have a strong effect on mechanical properties. In
most
cases this is a softening and ductility enhancing effect, which in turn
can
lead to localization of strain and the development of shear zones.
The fundamental
processes
responsible for this effect are: (i) changes in grain size, (ii)
changes in
dislocation density and substructure, (iii) changes in preferred
orientation,
and (iv) changes in impurity concentration, defect chemistry, and grain
boundary structure. The effect on mechanical behaviour is a combination
of
these.
Changes in Grain Size
While
progressive
misorientation of subgrains can only result in a reduction of
grainsize, grain
boundary migration can either increase or decrease grainsize. If
dislocation
creep remains the dominant deformation mechanism, then a decrease in
grainsize
should result in an increase in flow stress at a constant strain-rate
(e.g.
Nicolas and Poirier, 1976, p. 129). This effect, however, is only
important in
rock deformation at low homologous temperatures (Schmid, 1982).
More generally,
if grain
boundary migration can occur unaffected by impurities, the material
will tend
to adjust its grainsize (either way) to arrive at the value determined
by the
deformation conditions (Fig. 38). Full adjustment in grain size
generally occurs
less rapidly than the onset of steady state creep (Schmid et al.,
1980). On the
other hand, recrystallized grainsize does not seem to be strain
dependent (Ross
et ml., 1980).
Fig. 38.
Torque-twist
curves for polycrystalline nickel deformed in torsion at 880 ºC,
showing the
effect of variation of initial grain size. After Sah et al., (1974).
The most
important
parameter controlling recrystallized grainsize is the flow stress. The
relationship has been empirically determined for many metals and
minerals (see
reviews by Mercier et al., 1977; Etheridge and Wilkie, 1981), and there
have
been attempts to develop a theoretical basis for the relationship (see
Twiss,
1977; White, 1979; Edward et al., 1982).
However, many
problems
remain before recrystallized grainsize can be reliably used to estimate
paleostress (White, 1979; Christie and Ord, 1980). One of these was
pointed out
by Poirier and Guillopé (1979) and Guillopé and Poirier (1979). From
their
experiments on NaCl it became clear that rotation and migration
recrystallization will produce different recrystallized grainsizes at
the same
stress. Based on these results, several workers established both
rotation and
migration recrystallized grainsize versus stress relationships (Schmid
et al.,
1980; Mercier, 1980; Zeuch, 1983).
However, in
some cases the
picture is in fact even more complicated. Depending on the deformation
regime,
different types of bimodal grain size distributions may develop, and
the
microstructure may consist of a mixture of rotated, “slow” migrated,
“fast”
migrated and “left over” grains. Clearly it will be necessary to
separate the
different types of grains before trying to apply the empirically found
relationships to grain size data.
A strong
decrease in
grainsize by recrystallization can also result in a change in the
dominant
deformation mechanism to diffusive mass transfer (Stocker and Ashby,
1973;
White, 1976; Baudelet, 1974). This in turn should result in a strong
weakening
of the material. On the other hand, Etheridge and Wilkie (1979) argued
that
unless second phase particles enhance grainsize reduction, dynamic
recrystallization alone is not capable of causing a weakening necessary
to form
mylonite zones. Onset of grain boundary sliding at high temperature and
low
differential stress conditions was demonstrated in experimentally
deformed
Carrara marble (Schmid et al., 1980).
The possibility
of the
combined operation of diffusion creep and dynamic recrystallization has
been
discussed by McQueen and Baudelet (1978) and Zeuch (1983). Although it
has
never been shown to have occurred in rocks, the opposite effect, grain
growth
during diffusion creep, is also possible, (Fig. 39), and results in an
increase
in flow stress.
Fig. 39.
Stress-strain
curve for fine grained 60/40 brass deformed at constant rates and at
600 ºC.
Note strain hardening due to a decrease in grain size. After Suery and
Baudelet
(1977).
Changes in Dislocation Density
Strain induced
migration
of grain boundaries will result in a strong decrease in dislocation
density
across the interface. This effect is most clearly demonstrated by
deformation
experiments with single crystals, where growth of a new grain causes a
sudden
weakening (Mecking and Gottstein, 1978). An example of polycrystalline
materials is shown in Figure 40. In this case after a critical strain,
recrystallized grains appear simultaneously in most of the sample,
resulting in
a drop of the flow stress. The new grains become deformed in turn and
recrystallize, until the process is sufficiently out of phase in
different
parts of the sample to eliminate the stress drops.
Fig. 40.
Stress-strain
curves for polycrystalline nickel, deformed in torsion at 0.7 Tm
and
a surface strain rate of 3.5x10-3 s-1. Broken
line is for
impure material where only recovery occurs. Solid line shows the
behaviour of
99.9% purity material in which, after a critical strain, dynamic
recrystallization is initiated. After Sellars (1978).
In this case,
the effect
of recrystallization was estimated by comparing samples with different
impurity
contents (Sellars, 1978). Another possible way of doing this is shown
in Figure
41. In this case, deformation of identical samples of wet bischofite at
different values of confining pressure is compared. While during steady
state
flow at high confining pressures extensive dynamic recrystallization is
occurring, lowering of the confining pressure causes development of
cracks at
grain boundaries and an inhibition of grain boundary migration.
Fig. 41.
Stress-strain
curves for polycrystalline bischofite deformed at 60 ºC and a strain
rate of 10-5
s-1. At a confining pressure of 28 MPa, addition of small
amounts of
water causes strong weakening, associated with intracrystalline effects
and the
onset of recrystallization. In wet samples deformed at atmospheric
pressure,
there is a temporary hardening, caused by the development of grain
boundary
cracking which in turn inhibits their migration. After Urai (1983a).
This in turn
results in an
initial increase of the flow stress, until cataclastic flow becomes
dominant.
In both of the cases discussed above, recrystallization resulted in a
decrease
of the flow stress by about a factor of two.
To a first
approximation,
these effects could be argued not to affect the strain rate sensitivity
of flow
stress. An additional effect may be envisaged, however. Suppose that
continuous
recrystallization keeps a large part of the grains present in the
material
permanently at very low strain levels. Strain rate sensitivity of flow
stress
at very low strains is not necessarily the same as at higher strains
because,
for example, of changes from single slip to multislip. This may result
in a
change in the strain rate sensitivity of the flow stress.
Based on
competition
between recovery and recrystallization processes and experimental
evidence,
Sellars (1978) proposed the existence of a minimum stress level below
which
recrystallization cannot operate. Based on this relationship, he
constructed
the field for the occurrence of dynamic recrystallization in an
Ashby-deformation
map. Twiss and Sellars (1978) attempted to derive a similar
relationship for
olivine. However, it should be noted that these results neglect the
occurrence
of recrystallization by progressive misorientation of subgrains and by
surface
energy driven grain boundary migration and will only apply for a
limited set of
materials and conditions.
Changes in Preferred Orientation
Kamb (1972) and
Bouchez
and Duval (1982) mention increases of up to an order of magnitude in
strain
rate in torsion tests on ice, associated with the transition from a
double
maximum to a single maximum fabric, associated with more and more
grains
arriving in single slip orientations. Similar effects were found in
simple
shear deformation of Solenhofen limestone and Carrara marble by Schmid
(1983).
Fabric softening is expected to be most important in noncoaxial
deformation,
such as progressive simple shear.
Changes in Impurity Concentration and
Defect Chemistry
Depending on
the
composition of the intragranular phase and the possible presence of
fluid
inclusions in the grains (Kekulewala et al., 1981), grain boundary
migration
may be an effective way to change impurity concentration or defect
chemistry.
This in turn may have large effects on creep behaviour (Hobbs, 1981;
1983). At
present, no data are available to support this hypothesis.
Another effect
may occur
in a fine grained material, where most grain boundaries start
migrating. There
is some evidence that the coefficient of diffusion in a migrating grain
boundary can be much higher than in a stationary one (Smidoda et al.,
1978).
Because of this effect, the contribution of diffusion assisted grain
boundary
sliding to the total strain may strongly increase and the material may
be
weakened.
Dynamic Recrystallization as a
Deformation Mechanism
A deformation
mechanism is
a process on one scale that accommodates an imposed deformation on some
larger
scale. Griggs (1940) listed syntectonic recrystallization as a
deformation
mechanism, but he was referring to deformation by localized
dissolution, grain
boundary transport, and reprecipitation the process currently termed
solution
transfer (Durney, 1972). This process involves non conservative motion
of grain
boundaries and clearly is a deformation mechanism. Handin (1966)
likewise
listed recrystallization as a possible deformation mechanism, but
seemed to
broaden the definition to include the metallurgical model of
recrystallization
taking place conservatively, in dry materials, and driven by stored
strain
energy. It is not clear whether he thought metallurgical
recrystallization
could be a deformation mechanism or not. Other geological writers,
adopting the
metallurgical conception of recrystallization, (Flinn, 1965; Vernon,
1975;
White, 1977; Etheridge and Wilkie 1979) seen to draw a clear
distinction
between deformation mechanisms and recovery or recrystallization
processes. The
present authors subscribe to this view. Recrystallization, even when it
accompanies deformation, is thought of as essentially a structural
transformation and not as a transformation of the positions of
particles of the
material (a deformation). However, we want to note a point which may
leave the
matter somewhat open.
Consider the
case of a
mechanical twin boundary or a Paterson and Weiss (1966) kink boundary.
Such a
boundary can migrate under load, without any deformation in the host or
the
kink (twin). With the passing of the boundary there is an
instantaneous,
boundary-parallel shear. Migration of such a boundary can therefore be
called a
deformation mechanism.
Kinking and
twinning
(although they usually involve migration of a boundary) are not usually
regarded as recrystallization. However, in recent work Cobbold et al.
(1984)
investigate the general case of the migration of a boundary under the
condition
that continuity of material lines and planes across the migrating
interface is
preserved. These boundaries behave in a similar way to Paterson and
Weiss kink
boundaries or twin boundaries except that the theory places fewer
restrictions
on the deformations proceeding on either side of the boundary, so long
as
material continuity is preserved across the boundary. Migration of any
high
angle grain boundary can (under the appropriate conditions) be of this
type,
and carry with it an instantaneous boundary-parallel shear of the
material
traversed. It is yet to be shown that the model of Cobbold et al. is a
valid
description of grain boundary migration in nature. If it is, however,
then
migration of these boundaries may be called a deformation mechanism.
Definitions of Recrystallization
From the
previous sections
it is evident that there are basically two ways to define
recrystallization,
depending on what scale of observation we choose.
On the scale of
grain
boundaries, recrystallization is the process involving migration of
grain
boundaries. This is the definition commonly used in metallurgy (Cahn,
1965).
Here atoms enter the grain boundary where they exist in a more
disordered
state, and after some time they re-crystallize on the other side of the
boundary. On this scale of observation, progressive misorientation of
subgrains
is not a recrystallization process.
On the other
hand, on the
grain scale, (where the classical cases of recrystallization involve
the
replacement of “old” grains by “new” grains), progressive
misorientation of
subgrains, possibly accompanied by minor boundary migration, can
produce
microstructures which have strong similarities to the ones produced by
grain
boundary migration.
On this scale
of
observation, grain boundary migration and formation of new grains by
progressive misorientation of subgrains can both be called
recrystallization.
This has led workers to propose definitions including both processes:
for
example “recrystallization is the development and/or migration of a
high-angle
boundary” (Vernon, 1981) and “recrystallization is the appearance of
grain
boundaries in new material positions” (Means, 1983). It should be
pointed out,
however, that these definitions are formulated a little too broadly,
because
strictly speaking they include such processes as cracking and possibly
kinking.
On the grain scale of observation, a more cautious definition, such as
“recrystallization is the progressive misorientation of subgrains to
form new
grains and/or the migration of high angle grain boundaries (Haessner
and
Hoffman, 1978) would be more appropriate.
Acknowledgements:
We wish to
thank J.P.
Poirier, M. Guillopé, J.C.C. Mercier, P. Hartman and W. Heijnen for
many
inspiring discussions on recrystallization and crystal growth.
We also want to
thank M.
Etheridge and M. Jessell for permission to use their yet unpublished
data, and
J. Grocott and S.M. Schmid for providing the samples for Figures 19 and
28.
This work was
financed by
the Netherlands Organization for the Advancement of Pure Research
(ZWO), by NSF
grant EAR 8306166 (J.L.U.), and by NSF grant EAR 8205820 (W.D.M.).
Magda Martens,
Diana
Paton, Lauren Bradley, Katrina Idleman, and Bruce Idleman have been a
great
help during various stages of preparation of the manuscript. Drawings
were
produced at the Institute for Earth Sciences, Utrecht, and at the
Bureau of
Mineral Resources, Canberra.
Appendix: A
Simple Model
for the Migration of a Grain Boundary in the Presence of a Fluid Phase
Consider two
crystals of
identical composition and crystal structure, completely free of
impurities.
They are in an unspecified orientation with respect to each other,
separated by
a fluid film (between 10 and 1000 mm thick) of a saturated solution of
the
crystals. One of the crystals has a much higher dislocation density
than the
other. The grains are externally unstressed and the fluid is at
atmospheric
pressure.
Because the
crystal with
the higher dislocation density is not in equilibrium with the solution,
a local
supersaturation will develop near the interface, resulting in a
concentration
gradient across the fluid film, and the boundary may start to migrate.
To get some
insight into
migration kinetics, let us assume that:
(i)
diffusion
across the fluid layer is the rate limiting
step in the process (i.e. inter-face kinetics are relatively
unimportant).
(ii)
diffusion
coefficient in the fluid film is equal to
that in a bulk fluid.
Let the
concentration in
the fluid in equilibrium with the unstrained crystal be Co
and the
concentration in the fluid in equilibrium with the strained crystal Cs
(in
mol/m3 solution). Thickness of the fluid film is d (in m),
density
of the solid ρsol
(in kg m-3), diffusion coefficient of the migrating species
in the
fluid D (in m2 s-1) and molecular weight of the
solid M
(in kg/mol). Then:
Vgb
= D (Cs-Co)
M/d ρsol (1)
where Vgb
is
the grain boundary migration rate along orthogonal trajectories.
Let us consider
two cases.
The first case is bischofite where at 60 ºC and a film thickness of
about 50
nm, migration rates of 10x10-6 m/s have been measured (Urai,
1983).
Taking:
ρsol
= 1590 kg m-3 (Agron and Busing, 1969), M = 0.20333 kg/mol, Co
= 114.9 mol MgCI2/1000 mol H20 (= 63100 mol MgCI2.6H20/m3
soln; Dietzel and Serowy, 1959); D =0.8x10-9 m2
sec-1
(Harris et al., 1978; Caldwell and Eide, 1981); we get an increase in
concentration by a factor of 7.8x10-5 on one side of the
fluid film,
necessary to drive the process.
The second case
is the
(hypothetical) case of halite, where the following relationship holds:
W = 2.092x10-10
ρ ln(1/(6x10-8
√ρ))
where W is the
stored
energy of dislocations and is the dislocation density (Nicolas and
Poirier,
1976; a more detailed calculation by Huntington et al., 1955 gives
somewhat
higher values).
To get a rough
idea of the
stress needed to generate this dislocation density, we can use:
ρ =
1.6 x 1011 τ2
where τ is the shear
stress (in
MPa) and ρ
the dislocation density (Kemter and Stunk, 1977). Assuming a
dislocation
density of 2.5x1013 m-2, (corresponding to a
shear stress
of 12.5 MPa), we get a stored energy of about 3 J/mol. For this
crystal, the
difference in chemical potential with respect to the unstrained crystal
is
∆µ = ∆F + p ∆V
where ∆F is the
difference
in molar Helmholtz energy between the strained and unstrained state, ∆V
is the
change in molar volume due to the presence of dislocations, and p is
the
pressure of the fluid phase. For ∆F, we take the above mentioned value
of 3
J/mol, and neglecting the p ∆V term, we get ∆µ = 3 J/mol. Now at 25 ºC:
RT ln(as/ao)
= 3.0 J/mol
where as
and ao
are activities of solutions in equilibrium with the strained,
respectively
unstrained state, and:
as/ao
exp(3.O/RT) = 1.00126 (see Bosworth, 1981)
From solubility
data of
NaCl in water (Langer and Offerman, 1983) and activity coefficients
listed by
Robinson and Stokes (1955) and Pytkowitz (1979), we calculate co
=
54531 mol/m3 soln and cs = 54558 mol/m3
soln;
(this is an increase by a factor of 1.00049). Using eq. 1 with M =
0.05844
kg/mol, ρsol
= 2170 kg/m3, and D = l.5x 10-9 m2/s,
we get Vgb
= 2x10-5 m/s. So, by assuming reasonable values of
dislocation
density, we get comparable values for bischofite and halite.
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