J. L. Urai, W. D. Means & G. S. Lister
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.
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  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.
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.
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  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).
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.
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.
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.
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.
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.
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.
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.
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).
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.
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.
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.
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.
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.
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.
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.
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.
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.
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).
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.
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.
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.
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.
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.
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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