Misorientation analysis and the formation and orientation of subgrain … · 2009-03-11 · crystal structure but different crystal orientation and represents a two-dimensional lattice

ELSEVIER Tectonophysics 279 (1997) 55-78

TECTONOPHYSICS

Misorientation analysis and the formation and orientation of subgrain and grain boundaries

Geoffrey E. Lloyd ~'*, Andrew B. Farmer a, David Mainprice b

a Department of Earth Sciences, The UniversiO; Leeds, LS2 9JT, UK ~ Laboratoire de Tectonophysique, Universiti de Montpellier I1, 34095 Montpellier, Cedex 05, France

Accepted 2 May 1997

Abstract

In contrast to the behaviour of individual grains, both inter- and intra-granular boundaries within rocks have received much less attention. However, many geological processes, particularly during deformation (e.g., yielding, dislocation creep, recrystallisation, superplasticity and various fracture mechanisms), and petrophysical properties depend to some extent on the nature of boundaries present in a rock. In this contribution, we consider the role of intergranular and intragranular crystal boundaries. A precise characterisation of such boundaries depends on defining the crystallographic and dimensional orientations of the boundary and the misorientation between the adjacent regions (i.e. grains, subgrains, etc.) separated by the boundary. Although several theoretical descriptions of boundary configuration are available, practical precision is lacking and approximations are necessary. We describe two specific approximations for boundary formation and orientation obtained using the SEM electron channelling technique. The first is a geometrical interpretation of electron channelling patterns (ECP) in terms of the likely formation and orientation of the intervening boundary. The second considers the misorientation between adjacent regions across a boundary. This involves a model which assumes a simple geometrical relationship between crystal slip systems responsible for the rotation and misorientation between adjacent regions, and the formation and orientation of the resulting boundary. These approximations are capable of: (a) identifying trends in the dispersion of crystallographic directions during deformation; (b) identifying active slip systems; (c) calculating the relative Schmid Factors for each crystal slip system (and therefore the most likely system to be activated); (d) modelling synthetic misorientations and predicting the crystal slip systems and boundary configurations to be expected; and (e) comparing real data with synthetic models. Our analyses are illustrated via natural examples of dynamic recrystallisation in quartzite and a theoretical simulation of the behaviour of an individual quartz grain during deformation.

Keywords: crystallographic orientation; SEM; grain boundaries; subgrains

1. Introduction

Geologists have expended considerable effort over the years striving to understand the behaviour

*Corresponding author. Tel.: +44 (113) 233 5222; fax: +44 (113) 233 5259; e-mail: [email protected]

of mineral gra ins during deformation (e.g., Ardell et al., 1973; Bell and Etheridge, 1973; Tullis et al., 1973; Wilson, 1973; Vernon, 1975; Nicolas and Poirier, 1976; White, 1976, 1977, 1979; Bouchez, 1977, 1978; White et al., 1978; Guillop6 and Poirier, 1979; Schmid et al., 1980; Schmid and Casey, 1982, 1986; Tullis and Yund, 1982; Fitz Gerald et al.,

0040-1951/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PH S0040-1951(97)001 15-7

56 G.E. Lloyd et al./Tectonophysics 279 (1997) 55-78

1983; Barber, 1985; Urai et al., 1986; Knipe and Law, 1987; Groshong, 1988; Knipe, 1989; Law et al., 1990; Knipe and Rutter, 1990; Hirth and Tullis, 1992; Boland and Fitz Gerald, 1993). In contrast, the behaviour of the boundaries within and between grains has received comparatively little attention (e.g., Trepied et al., 1980; White and White, 1981; Toriumi, 1982; Joesten, 1983; Cobbold et al., 1984; Poirier, 1985; Jessell, 1986; McLaren, 1986; Means and Jessell, 1986; Means and Ree, 1988; Hay and Evans, 1988; Boland and Fitz Ger- ald, 1993). However, a realistic appreciation of the complete behaviour of a material requires knowledge of both grains and boundaries (e.g., Amelinckx and Dekeyser, 1959; Hu, 1972; Grimmer et al., 1974; Chadwick and Smith, 1976; Gifldns, 1976; Beere, 1978; Haessner and Hoffman, 1978; Bishop et al., 1979; Smith et al., 1979; Balluffi et al., 1981, 1982; Bleris et al., 1981; Gleiter, 1982; Haruna et al., 1992; Randle, 1992, 1993). Thus, the properties of polycrystalline rocks are likely to be controlled by both their constituent grains and their boundaries.

Boundary processes in rocks have been less widely emphasised because of an absence of reli- able experimental methods. Many of the systems of interest to materials scientists, and in particular the cubic metals on which most metallurgical the- ories of grain boundary behaviour are based and/or derived, are perhaps geologically unrealistic. Geol- ogists nevertheless can still learn much from the materials description of boundaries. This is important because many geological deformation processes (e.g., yielding, high-temperature creep, recrystallisation, the development of crystallographic preferred orientation, superplasticity and various fracture mod- es) are dependent on the processes which occur at boundaries (McLaren, 1986; Hay and Evans, 1988). Furthermore, many petrophysical properties also depend on boundary characteristics, not least because such processes may be the most active dynamic element in polycrystalline rocks. The specific behaviour of a rock may therefore depend on the frequency of a specific type of boundary present in the microstructure.

To understand the role of boundaries in the behaviour of rocks, particularly during deformation, demands a theory which relates microstructure, crystal texture and boundary properties, and an exper-

imental technique to derive the necessary information. In this contribution we discuss the various representations of microstructure, crystal texture and boundary properties which are available to the ge- ologist, and in particular the significance of misorientation analysis. The data required for misorientation analysis can now be obtained routinely by two related scanning electron microscope (SEM) techniques: electron channelling (EC) and electron backscattered diffraction (EBSD). However, there is still no general theory available for the correlation of microstructure, crystal texture, boundary characteristics and petrophysical properties. We must therefore make use of the coincident site lattice (CSL) model of grain boundaries and misorientations. Although limited, this model remains useful because it has been shown for materials that special properties are possessed by boundaries which have a high density of CSL in their structure.

Finally, we emphasise that our approach is essentially metallurgical in that we assume very pure systems with clean boundaries. Such an approach can only produce a partial description of the situation which exists in impure geological systems with unclean boundaries. However, to understand the behaviour of geological systems in which deformation mechanisms other than dislocation glide/climb (e.g., grain boundary sliding, bulk grain rotation, diffusive mass transfer, etc.) can also influence the formation and orientation of boundaries and the misorientation between adjacent subgrains/grains, first requires an understanding of the (relatively) simpler metallurgical configurations.

1.1. Boundao' types

For the purpose of this description, we assume that a boundary separates regions of different properties (e.g., chemical, physical, etc.). We shall confine our discussion to the following types of boundary. An intergranular high angle or grain boundary separates regions of the same composition and crystal structure but different crystal orientation and represents a two-dimensional lattice defect which introduces a misorientation into a crystal lattice con- tinuum without the occurrence of long-range stress fields (e.g., Poirier, 1985, p. 63). An intragranular crystal boundary separates regions of slightly dif-

G.E. Lloyd et al./Tectonophysics 279 (1997) 55-78 57

ferent and/or related crystal properties but the same composition and crystal structure and several types can be recognised, as follows.

A low angle or subgrain boundary separates regions in which the misorientation is typically less than 5-15 ° (Poirier, 1985, p. 65), depending on the material and type of bonding (N.B. for most minerals, the lower end of the range generally applies). The distinction between subgrains and grains on the basis of misorientation is usually expressed in terms of a particular crystal direction (e.g., for quartz, it is the c-axis misorientation), but this neglects significant relationships which may exist between other crystal directions (Lloyd and Freeman, 1994). A definition based on the total misorientation is therefore to be preferred (Mainprice et al., 1993). A twin boundary separates regions which have specific crystallographic relationships with each other (e.g., a Dauphin6 twin in quartz represents a 180 ° rotation about the c-axis, but because of the trigonal symmetry, this is equivalent to a 60 ° rotation about c, resulting in an interchange of r and z poles whilst maintaining a and m poles; see Mainprice et al., 1993). A deformation band boundary is a long but sharp transition between regions of slightly different crystallographic orientation and probably represents the concentration of the typically gradual change in orientation associated with undulose extinction (Groshong, 1988). Deformation lamellae (Groshong, 1988) are crystallographically oriented, narrow planar features with apparent widths of ~0 .5 -10 #m, that often occur in deformed grains. Initially, they were thought to represent dislocation slip bands, but observations on both experimentally and naturally deformed quartz (see Drury, 1993) show that they can also be associated with many defect substruc- tures (e.g., Brazil twins, glass, elongate subgrains, subgrain walls, and zones of different dislocation and water bubble content). A kink band boundary is a narrow, sharp feature across which a large crystallographic misorientation occurs within what was originally a region of constant orientation (e.g., Mawer and Fitz Gerald, 1993).

1.2. Boundary width

The effective width (reef) of a boundary can vary significantly, depending on the parameters and prop-

erties considered (e.g., Hay and Evans, 1988). For example, in terms of diffusion, a boundary width (~gb) can be defined as the region where grain boundary diffusion rates are higher than solid-state diffusion rates. In contrast, the structural width of a boundary (3str) includes the regions on either side of the boundary in which atoms are significantly displaced from their respective equilibrium positions. The relationship between ~gb and 6str is unknown; they may be similar or very different. Furthermore, boundaries in minerals may not be as close-packed as those in metals and hence are likely to be wider.

The crystalline order, even in 'clean' boundaries, breaks down in a narrow (on the scale of a few atoms?) defective core region, which may accommodate significant concentrations of impurities (Balluffi et al., 1981, 1982). Impurity concentrations can in- crease the effective boundary width (e.g., White and White, 1981). If a boundary contains a film of a second phase material, the two regions are actually joined by two phase boundaries. In contrast, a boundary fluid phase represents an amorphous layer and results in an incoherent boundary, although it has been suggested (Vernon, 1976; Rubie, 1986) that water can be incorporated structurally onto boundaries.

1.3. Coherency and coincidence

The regions on either side of any crystallographic boundary are related by three degrees of freedom, which define the relative rotation needed to bring the two lattices into coincidence. Two degrees of freedom define the axis of rotation whilst the third defines the rotation angle (i.e. a rotation axis~angle pair). However, this approach does not recognise the dimensional orientation of a boundary (plane), which requires two further degrees of freedom (see below). Twist boundaries are normal to their axis of rotation, tilt boundaries include their axis of rotation, whilst general boundaries include twist and tilt components. Thus, twist and tilt are equivalent to the edge and screw components of general dislocations (e.g., Poirier, 1985).

Alternatively, crystallographic boundaries can be considered in terms of coherency (e.g., Hay and Evans, 1988). The degree of coherency depends on the proportion of lattice planes/sites of two adja-


cent crystal regions which are continuous across the boundary, which in turn depends on their relative misorientation, the boundary plane orientation, various symmetry relationships and crystal chem- istry. The following types are recognised: coherent boundaries (e.g., twin boundaries), semi-coherent boundaries (e.g., subgrain boundaries, and incoherent boundaries (e.g., grain boundaries). As the coherency, or structural periodicity, of a boundary increases, the boundary energy decreases and the boundary becomes more stable.

The coherency of boundaries has been ratio- nalised in the coincident site lattice (CSL) theory (e.g., Brandon et al., 1964; Brandon, 1966; Ra- nagathan, 1966; McLaren, 1986; Grimmer, 1980, 1989a,b; Randle, 1992). The degree of coincidence, or the volume ratio of the primitive cells, (also known as the twin index or the multiplicity of the CSL, E) is the inverse of the proportion of lattice sites which are in coincidence (i.e. Z = 1, perfect coincidence; E = 2, one half of lattice sites are in coincidence; ~2 = 3, one third of lattice sites are in coincidence; etc.). For cubic crystals, only boundaries with E < 49 are considered to have a CSL relationship (Randle, 1993). The smallest possible misorientation angles between grains, subgrains, etc., can result in rotation axes (sub)parallel to specific crystallographic axes. These relationships can be tested to CSL theory.

1.4. Deformation and recrystallisation

Misorientation relationships between subgrains/grains with CSL are associated with low- energy boundary structures (Gleiter, 1982) and can have a profound effect on both the mechanical and chemical properties of the boundary, including grain boundary migration, grain boundary diffusion, phase transformation and grain growth (Peterson, 1979; Smith et al., 1979; Bishop et al., 1979; Gleiter, 1982; Forwood and Clareborough, 1991; Randle, 1993). Grain boundary sliding can also be affected by the presence or absence of CSL boundaries (Haruna et al., 1992), such that it may be difficult to deform materials via grain boundary sliding, even when the grain size is very small, if there are many CSL boundaries. Dislocation creep processes in rocks are indicated by the presence of dislocations, sub-

grains and the development of crystallographic preferred orientation or CPO (e.g., in quartzites, c- and a-axes). However, analysis of misorientations between grains can indicate whether additional rotations due to grain boundary sliding are present or absent (e.g., Beere, 1978). For example, Fliervoet and White (1995) interpreted rotations which were not perpendicular to any known Burgers vector, as being due to grain boundary sliding.

Boundary processes are also potentially important during recrystallisation, when the grain structure or configuration is often completely modified (e.g., Poirier, 1985, pp. 179-190). Static recrystallisation occurs during high-temperature annealing, usually following deformation, and is a thermally activated process involving the migration of grain boundaries driven by differences in free energy and/or crystallographic misorientation between adjacent grains. Dynamic recrystallisation occurs during deformation and represents the reworking of an existing grain texture (Poirier and Guillop6, 1979). Rotational dynamic recrystallisation involves progressive crystallographic misorientation without significant grain boundary migration, such that orientation relationships with the parental grain can still be recognised (Hobbs, 1968; Poirier and Nicolas, 1975; Urai, 1983). Migration dynamic recrystallisation is driven by strain energy differences between adjacent regions. Rotation and migration dynamic recrystallisation are therefore related and often cyclical processes distinguished by the relative misorientation between adjacent regions accommodated in the intervening boundaries (Drury and Urai, 1990), although the impurity content segregated into boundaries will also influence grain boundary mobility and migration (Guillop6 and Poirier, 1979).

2. Crystallographic basis

In general, the mobility of grain boundaries can be considered in terms of movement in directions either at a high angle to their plane (i.e. migration) or within their plane (i.e. sliding). The former can be caused by energy variations between adjacent grains, or by an applied shear stress, and therefore incorporates migrational dynamic recrystallisation processes. The latter occurs when an applied shear stress overcomes the shear strength of the

G.E. Lloyd et al. / Tectonophysics 279 (1997) 55-78 59

boundary and is capable of producing very large strains (e.g., superplastic behaviour) without significant intragranular deformation. However, it can also be postulated that a motion confined to the grain boundary plane which produces little intragranular deformation is compatible with a rotational dynamic recrystallisation process. The difference between the two depends on the misorientation between adjacent grains: in low angle (i.e. subgrain) boundaries, dislocations are free to move in their glide planes; in high angle (i.e. grain) boundaries, dislocation climb is required (Pond et al., 1978). The behaviour of grain boundary dislocations is therefore important in both rotational and migrational dynamic recrystallisation (Balluffi and Cahn, 1981), which in turn means that boundary orientation, the misorientation accommodated and the degree of lattice coincidence are also important.

As discussed by Fliervoet and White (1995), if a crystal is subdivided into subgrains, the geometry of the boundary (dislocation lines, boundary orientation, axis/angle pair of misorientation) can yield the active slip systems via Frank's formula, which states (Amelinckx and Dekeyser, 1959; Trepied et al., 1980; Forwood and Clareborough, 1991): the axis of misorientation between two subgrains should be perpendicular to the net Burgers vector of the dislocations required to accommodate the misorientation at a subgrain boundary. Thus, any low angle subgrain boundary can be formed with 1, 2 or 3 dislocation families (Friedel, 1964). Only where the boundary is composed of three families of dislocations with non-coplanar Burgers vector, will the axis of misorientation not be perpendicular to all three Burgers vectors. Trepied et al. (1980) showed that three non-coplanar Burgers vectors cannot make a subgrain boundary in quartz. With increasing dislocation content, subgrain walls eventually become high angle grain boundaries. If there are no additional rotations arising from grain boundary sliding processes, misorientation axes will still be normal to the Burgers vector in the former (sub)grain boundary (see Fliervoet and White, 1995).

It is reasonable to assume, particularly during a rotational recrystallisation event, that boundaries once formed maintain a constant orientation and the subgraioJgrain regions between the boundaries rotate. In contrast, in a migrational framework, the

orientation of subgrains/grain remains constant and the boundaries are mobile and migrate through the microstructure with changing orientation. In both cases, it is important to know the orientation of both the grains/subgrain and the boundaries, and the misorientation between adjacent grains/subgrains.

2.1. Grain/subgrain orientation and misorientation

In texture analysis (e.g., Bunge, 1982), the most frequently used representation of a crystallographic orientation, g, is the Euler angle triplet:

g ---- {qgl , ~, ~02} (la)

However, for misorientation analysis it is often more useful to use the rotation axis/angle pair (e.g., Randle, 1992):

g ---- [ u v w ] / + 0 ( l b )

The rotation axis/angle pair can be found simply from the rotation matrix by the following (e.g., Mainprice et al., 1993):

0 = c o s - ' {1/2 [g,1 +g22 +g33 - 1]} (2a)

g23 -- g32 u - - - - ( 2 b )

2sin0

g31 -- g13 v -- - - (2c)

2sin0

g~2 - g21 W - - - - ( 2 d )

2sin0 in which go are the components of the 3 x 3 orientation matrix.

For each crystal in a specimen, an experimental indexation will yield an orientation for which there are n symmetrically equivalent and physically in- distinguishable orientations. For example, in quartz (trigonal symmetry class - 3 m ) there are six proper (or pure) rotational symmetry operations, including the null operation, which will generate six equivalent orientations (note: proper rotations have a determinant of + 1 and are rotations rather than reflections, which are improper rotations with a determinant of - 1 ) .

The misorientation between two crystals labelled A and B of orientation gA and gB can also be represented in crystal co-ordinates by a matrix Ag.


We can then define the misorientation in terms of an Euler triplet:

Ag = {~Pl, q~, ~P2} (3a)

A g - I = {32" - - q32, ~b, 7g - @1} (3b)

Conversely, the misorientation can also be defined in terms of a rotation axis/angle pair:

Ag = [ u v w ] / + 0 = [fi~wl / - 0 (4a)

Ag -I = [fig',~'] / + 0 = [uvw] / - 0 (4b)

In this description, we have arbitrarily assigned a label A and B to each grain. Thus, we can inverse the labelling without the loss of any generality. Alterna- tively, the misorientation axis [uvw] can be plotted in the crystal reference A(Ag), or in the crystal reference B(Ag-J) . If we use exclusively crystal A as the reference, then the misorientation axis [uvw] can be plotted in the asymmetric unit (e.g., Euler angle triplet space, inverse pole figure) of the size usually used for the crystal symmetry in question. However, if we admit that A and B are interchangeable, then misorientations (Ag) and (Ag - l ) must be taken in to account (i.e. the true bi-crystallography). The bi- crystallography will reduce the asymmetric unit to a space smaller than the conventional unit.

For example, it is often convenient to consider quartz to have hexagonal crystal symmetry (e.g., see discussions in Fliervoet and White, 1995). Con- sequently, there are 12 crystallographically equivalent ways of indexing each grain, and therefore 144 ways of expressing misorientation (Grimmer, 1980). These misorientations occur in groups of twelve, each group having the same angle of misorientatiou and the rotation axes within each group are symmetrically equivalent. Thus, a misorientation between two hexagonal grains can be described in twelve different but equivalent ways, which gives twelve solutions of the axis/angle pair (Grimmer, 1980; For- wood and Clareborough, 1991; Randle, 1993). Any of these can be chosen as they are physically indistin- guishable, but usually the axis/angle pair giving the smallest possible rotation is chosen as the misorien- ration (Randle and Ralph, 1986; Randle, 1992, 1993; Mainprice et al., 1993). However, if the real trigonal symmetry of quartz is considered, there are only six possibilities for a crystal A and six for a crystal B

(i.e. 2 x 6 x 6 = 72 total possibilities for the bi-crystallographic descriptions). The smallest asymmetric unit for quartz misorientation is therefore a spherical triangle bounded by c [0001 ], In[ 10]-0] and In[ 1 TOO]. That is, the 60 ° sector of the crystallographic hemi- sphere traditionally used for inverse pole figures in quartz X-ray texture goniometry, rather than the 120 ° sector used in individual orientation work. Thus, it appears that the reduced inverse pole figure of 60 ° is the most appropriate asymmetric unit for the representation of a quartz bi-crystal (i.e. misorientations), unless we choose to ignore the ambiguity of labelling two grains A or B, in which case the 120 ° (sector is appropriate (e.g., Mainprice et al., 1993), although the increased area means that (mis)orientations will have diluted concentrations.

2.2. Boundao' orientation and formation

For a complete description of a grain or subgrain boundary orientation at least five parameters are needed (e.g., McLaren, 1986). For adjacent grains/subgrains with orientations gl and g2, the orthogonal reference frame in g2 must be rotated with respect to gl by the rotation matrix R whose components are functions of the three Euler angles ~Pl, 4), ~02 (e.g., Mainprice et al., 1993). The other two parameters describe the unit normal to the grain boundary plane in terms of azimuth and plunge.

If boundary orientation is controlled by crystal slip (i.e. rotational dynamic recrystallisation) then the orientation for a tilt boundary should lie between the normals to the glide planes in the direction of the Burgers vector (Fig. la). However, if grain boundary migration has occurred, the trace of the grain boundary need not be contained in the angular zone between the glide planes. Thus, the orientation of subgrain/grain boundary walls could help distin- guish between rotational and migrational processes. The orientation of subgrain/grain boundary walls can also help in the identification of specific crystal slip systems during rotational recrystallisation (as stated in Frank's formula - - see above) because slip operates on all surfaces parallel to the slip plane and there is a constant axis of rotation within the slip plane. Rotational recrystallisation must therefore produce tilt boundaries perpendicular to the slip plane and the slip vector. This means that any boundaries formed

G.E. Lloyd et al. / Tectonophysics 279 (1997) 55-78 61

L)

range o f rotat ional subgrain

boundar ies

/J;

b2

z initial boundary

orientation

later boundary orientation

X X

Z

slip ~-v direction system rotation

axis

Fig. 1. Determination of orientation and orientation relationships of boundaries formed during dynamic recrystallization. (a) Stereographic projection showing the relationship between slip plane and boundary trace for rotational dynamic recrystallisation. (b) Relationship between slip plane, slip plane normal, slip system rotation axis and boundary orientation. (c) Formation and orientation of boundaries due to crystal slip. Crystal slip leads to migration of most orientations away from their parental position, so boundaries build in a range of orientations defined by the kinematics of the slip system. Only the slip system rotation axis remains static.

during slip are constrained to lie in the plane con- taining the slip plane normal and the rotation axis (Fig. lb).

This interpretation assumes that tilt boundaries are built in a constant orientation defined by the orientation of the parental grain and the specific slip system. However, intracrystalline deformation by crystal slip leads to migration of most orientations away from their parental position (e.g., Lloyd and Freeman, 1994). Thus, boundaries can actually build in a range of orientations defined by the kinematics of the slip system involved (Fig. lc). As slip proceeds, several possibilities exist for the formation and orientation of boundaries: (1) they are built continuously in all orientations; (2) they are built discontinuously in specific orientations; and (3) they form at the parental orientation but continue to develop and therefore progressively rotate. These possibilities have intriguing implications for boundary characteristics, as follows.

Consider an initially undeformed grain.

(1) If boundaries build continuously, this results in pervasive deformation leading to a continuous bending of the grain about a single axis. In such cases, it will be difficult to recognise individual boundaries and actual subgrains/grains will not be observed (e.g., undulose extinction).

(2) If boundaries build discontinuously, this results in the concentration of deformation within the planar boundaries, which separate relatively deformation-free subgrain/grain regions (e.g., deformation bands). Because crystal slip produces boundaries perpendicular to the slip plane and the slip vector, such boundary traces will tend to be straight and make orthogonal (i.e. 'T') triple point contacts. These are inherently unstable and prone to modifica- tion via boundary migration processes.

(3) If boundaries form at the parental orientation but continue to develop thereafter, two alternatives are envisaged, both capable of producing curvipla- nar boundaries: (a) deformation is pervasive and increases away from some origin, leading perhaps to

62 G.E. Lloyd et al. / Tectonophysics 279 (1997) 55-78

intragranular deformation bands, etc.; (b) the initial boundary is a coherent element which forms and then progressively moves and rotates through the grain, accommodating more and more deformation whilst separating relatively undeformed regions.

The latter behaviour is characteristic of migrational recrystallisation. These possibilities probably represent end-members of a continuous sequence of processes. Such concepts are not unrelated to the ideas presented by Drury et al. (1985), Urai et al. (1986) and Drnry and Urai (1990) and suggest that a continuous relationship exists between rotational and migrational dynamic recrystallisation processes.

2.3. Analytical techniques: advantages and disadvantages

Knowledge of the formation and orientation of subgrain/grain boundaries and the misorientation between adjacent grains/subgrains is clearly important for a full appreciation and understanding of the behaviour of polycrystalline rocks. Unfortunately, the determination of both boundary orientation and grain/subgrain misorientation is difficult with most, if not all, microstrnctural analytical techniques which are currently available.

Transmitted light microscopy can be used to determine the exact crystallographic orientation, and hence misorientation, of minerals which possess known physical relationships, such as common twin laws (e.g., calcite, feldspars) or optic length fast/slow characteristics (e.g., olivine, pyroxene). For other minerals, only the orientation of a crystal direction which is optically unique (e.g., an axis of complete extinction, such as the c-axis of quartz) can be determined, which provides an inadequate representation of the complete orientation and therefore only an estimate of the complete misorientation. Light microscopy can also measure the dimensional orientation of boundaries because it is possible to focus on any part of a boundary contained within a thin-section. However, this provides only two of the five degrees of freedom required to define the exact relationship between two adjacent regions across their common boundary; the other three rely on the determination of the exact crystallographic orientation of a boundary between adjacent subgrains/grains (or the misorientation between them). Thus, for quartz, because only the orientation

of the crystal c-axis can be measured optically, there is insufficient optical information to determine the complete orientation of boundaries.

Transmission electron microscopy (TEM) can determine the complete orientation of both subgrains/ grains and boundaries (e.g., Gapais and White, 1982; Mawer and Fitz Gerald, 1993; Fliervoet and White, 1995), but usually only on a scale much smaller than that of a thin-section, or even individual grains. Thus, TEM analyses may only be representative of very small volumes (e.g., Gapais and White, 1982; Mawer and Fitz Gerald, 1993). But, because TEM analysis provides information on all crystallographic directions, it also allows the relationships between adjacent grains/subgrains to be determined in the form of the axis/angle pairs (e.g., Turner and Weiss, 1963, p. 328; Randle and Ralph, 1986; Randle, 1992, 1993).

Scanning electron microscopy (SEM) is capable of determining the complete crystallographic orientation of individual subgrains/grains and therefore the complete misorientation between them. The information is obtained from much larger specimens than in TEM analysis. Two approaches are possible (e.g., Joy et al., 1982; Lloyd, 1985, 1987, 1994; Schwarzer and Weiland, 1988; Schwarzer, 1990, Randle, 1992): (1) electron channelling (EC), involving electron channelling patterns (ECP); and (2) electron backscattered diffraction (EBSD), involving electron backscattered patterns (EBSP). Although much of the methodology is equally applicable to both techniques, in this study we have used the EC approach. However, the problem remains whether SEM techniques can be used to determine the complete orientation of boundaries. We investigate this possibility in the next section.

3. SEM analysis of boundary configurations

The SEM/EC observations described in this section may provide a useful guide in developing our understanding of subgrain/grain boundary formation and orientation. However, we must emphasise that this approach implicitly assumes that boundaries do indeed have a crystallographic orientation which is controlled by the misorientation between adjacent subgrains/grains. Unfortunately, this is the very relationship which we are trying to establish. Thus,


our SEM study does not, and indeed cannot, provide unequivocal evidence to support our contention that boundary orientation may be crystallographically controlled. All that we can report are some interesting observations which may be more than coincidental. In this study, we have made use of the computer program CHANNEL © (Schmidt and Olesen, 1989; Olesen and Schmidt, 1990) to index individual ECP, to identify specific EC bands (which are equivalent to crystal lattice planes) and to simulate specific ECP. The data were obtained from three dynamically recrystallised quartz porphyroclasts (Grains A, B, C) previously described by Lloyd and Freeman (1991, 1994).

3.1. Parallelism of lattice and boundary

Because the angular spread of ECPs is rarely greater than 4-10 °, the constituent EC bands must be oriented (sub)vertical with respect to the ECP plane, and hence the region from which the pattern was derived as well as the specimen surface (Fig. 2a). Thus, if a boundary also has a subvertical dimensional orientation, and if this orientation is crystallographically determined, then by drawing the trace of the boundary on to the ECP, it should be possible to recognise a parallel EC plane. The crystallographic orientation of the boundary can then be determined (e.g., Fig. 2b) by indexing the specific EC band.

(a) I electrOnbeam I

specimen ~ surface

. . . . . ~ p

formation subvertical lattice planes observed in ECP image

shallow' lattice planes not . . . . . . observed in ECP image

(b)

1 I EC band in both ECP s parallel to boundary trace

(c) j

EB1 band with minimum (zero) displacement EB2 band with intermediate displacement EB3 band with maximum displacement

Fig. 2. Practical analysis of boundary configurations using SEM. (a) Because the angular spread of ECPs is rarely greater than +10 °, the individual EC bands observed can be considered to be oriented subvertically with respect to the ECP and therefore both the region from which the ECP was derived and the specimen surface. (b) If it can be confirmed that a boundary is also oriented dimensionally subvertically, then by drawing the trace of the boundary on the ECP from the boundary region, it may be possible to recognise a parallel EC (crystal lattice) plane which might represent the crystallographic orientation of the boundary. (c) Because adjacent subgrains have only slight misorientation their partial ECP are similar, resulting in variable displacement of EC bands across the boundary plane, including one band with zero displacement. (d) Although adjacent grains can have a large misorientation, they may still share a sufficient number of EC bands in their partial ECP to allow the dimensional and crystallographic orientations of the grain boundary plane to be estimated in a similar manner to subgrain boundaries.


E C P n e o b l a s t 1

E C P n e o b l a s t 2

T Z A c c e l e r a t i n g v o l t a g e = 3 0 k V

X ~ 7 d e g r e e s

Fig. 3. Example use of SEM/EC and the computer program C H A N N E L <~ to determine grain boundary dimensional and crystallographic orientation relationships between adjacent_ _ neoblasts in Grain B of Lloyd and Freeman (1991, 1994). Top panel. Simulated ECP for neoblast 1. Note orientation of the {231 I}__EC band is parallel to the trace of the common grain boundary. Bottom panel. Simulated ECP for neoblast 2. Note orientation of the {2131 } EC band is parallel to the trace of the common grain boundary.

For example, although the ECP ~br Grain B

neoblasts l and 2 are different (Fig. 3), they do contain several common EC bands. Of these, {2311 } in neoblast 1 and {2131} in neoblast 2 (i.e. the same set of crystal planes) are not only subparallel to each other, but also to the trace of the common grain boundary. We emphasise again that this does not provide unequivocal evidence for the orientation of

the boundary, but it remains possible that the boundary plane is subparallel to the common EC band (i.e. crystal plane). If so, the fact that the EC bands are from the same lattice set and therefore share the same characterist ics (e.g., latt ice spacing, atomic positions, etc.) suggests that this may also represent a CSL boundary.

G.E. Lloyd et al./Tectonophysics 279 (1997) 55 78 65

3.2. Dimensional orientation of lattice and boundary

The dimensional orientations and individual lengths of boundary traces within a single grain can be measured with respect to both the structural co-ordinate system and the dimensional orientation of the EC bands observed in the ECE Thus, any relationship between crystal orientation and preferred boundary dimensional orientation can be established. For example, Lloyd and Freeman ( 1991) argued that the systematic change in azimuth and plunge of polygonal subgrain c-axes in Grain B indicates an overall curvature of {0001 } basal planes across the grain, with the c-axes occupying a segment of a great circle dipping at ~ 10 °. This suggests that poly- gonised subgrain boundaries are essentially vertical and hence normal to the XZ plane of section, with a preferred orientation of boundary lengths subparallel to Z, and a minor peak at 25-45 ° to X (Fig. 4a). It is also possible (with the usual assumptions in mind) to determine boundary orientations in terms of crystallographic planes by comparison with EC bands, because these are also oriented (sub)vertical to the specimen XZ plane. The dominant peak in subgrain boundary orientations coincides with the crystal planes [2313], [1212] and [2314], whereas the (bimodal) minor peak coincides with the crystal planes [1100], [4401], [4511], [5502]. Overlaying the ECP for two adjacent polygonal subgrains (e.g., 43 and 44) clearly shows the relative displacement of the (subvertical) EC bands involved (see Fig. 4b). The minimum displacement is shown by the [1214] EC band, whilst maximum displacement is shown by the [3501] EC band. The former is very close to parallelism with the crystal planes which cover the bulk of the polygonal boundary traces (see Fig. 4a) and is also subparallel to the specimen Z axis.

3.3. Partial ECP

It is often possible to obtain partial ECP from adjacent subgrains/grains by positioning the electron beam on their common boundary. For subgrains, because the two (or more) regions have only slight misorientation, the partial ECP mostly contain the same but somewhat displaced EC bands. How- ever, because the bands have different orientations in three-dimensions, their relative displacements across

the boundary are different (Fig. 2c). The dimensional and crystallographic orientations of the grain boundary plane can then be determined in a similar manner to subgrain boundaries (see above). For grains, although their large misorientation usually means that their ECP are different, a sufficient number of EC bands may be shared by the partial ECP (e.g., Fig. 2d) to make this approach applicable. For example, due to the only slight misorientations between the polygonal subgrains in Grain B (Lloyd and Freeman, 1991), their ECP are very similar with poles close to {1121} (e.g., Fig. 4b). The general parallelism of the electron channelling bands suggests (see above) that the polygonal subgrains are separated by essentially tilt boundaries.

3.4. Summary

Based on the above, and keeping in mind our original assumptions, the following geometrical arguments can be applied to SEM/EC analysis.

(1) Any EC band not displaced across a boundary must contain the boundary rotation axis, whilst the EC band with the maximum displacement yields the angular deviation across the boundary.

(2) If the non-displaced EC band is normal to the boundary trace and the maximum displaced EC band is both parallel to the boundary trace and repeated on both sides of the boundary, then the rotation axis must be contained within the boundary, which must therefore be a tilt boundary.

(3) The magnitude of tilt is twice the angular distance between either parallel EC band and the boundary, whilst the orientation of the boundary plane is parallel to the plane which bisects the angle between the two parallel EC bands.

(4) If the non-displaced EC band is both parallel to, and also contains, the boundary trace and the maximum displaced EC band is normal to the boundary trace, then the rotation axis must be perpendicular to the boundary, which must therefore be a twist boundary.

(5) The magnitude of twist is equal to the angular distance between maximum displaced EC band, whilst the orientation of the boundary plane is parallel to the zero displacement EC band which contains the trace of the boundary plane.

(6) If there are no EC bands which have zero

66 G.E. Lloyd et al./ Tectonophysics 279 (1997) 55-78

~D

(a)

400

"-'~ 300 t

200

100

00 X

Dimensional orientation of specific crystal planes

i

Dimensional 90 180 orientation Z X (in degrees)

0o-14] 0-11~ p-41o]

11-1141

1t-214] [I-moll

~313] I ECP No.43 7 degs.

minimum ------! displaced - h--

E C band Y X

(b)

[1-~1~1 II-Io01

t3-~t]

|~,41o1

~/.t-l,q O-toll [Io-14] I la l~ l l ' ~ to l

['Z413! 0.214]

rio-t4]

~t-141

~ J l s ]

13"~11

[I-tOll [1-~,14| I'Z'~t31 [WILY/

ECP No.44

maximum displaced EC band


displacement across a boundary trace, or if the zero and maximum displacement EC bands are neither parallel nor normal to the trace, then the boundary must be a general boundary or have both twist and tilt components.

(7) General boundaries are unlikely to have significant crystallographic orientations unless the tilt and twist components have acted in sympathy.

Based on these arguments, we suggest that the polygonal subgrain boundaries in Grain B of Lloyd and Freeman (1991, 1994) are tilt boundaries which have been constructed parallel to specific crystallographic planes. Their overall shape is parallelop- ipedal, elongate subparallel to Z, within the range of crystal planes comprising [2313], [1214], [2314] and [3301]. In contrast, neoblast boundaries show little if any tendency for preferred orientation. They are therefore much less likely to be oriented parallel to these crystal planes simply because the crystallographic orientation of the neoblasts is usually very different to that of the subgrains.

4. SEM misorientation analysis

In its strictest sense, CSL theory (Brandon et al., 1964; Brandon, 1966; Ranagathan, 1966) includes the crystallographic orientation of a boundary plane relative to the adjacent crystallites, the magnitude of the mismatch across the boundary and the type of boundary (i.e. symmetrical/asymmetrical tilt/twist, etc.), as well as the proportion of coincident lattice sites between the adjacent crystallites. Unfor- tunately, as we have already seen, the orientation of a boundary between adjacent crystallites is often difficult to determine. The definition and description of CSL are therefore often relaxed to a comparison of the misorientation (e.g., axis/angle pair) between

the crystallites and theoretical tables (e.g., Randle and Ralph, 1986). Thus, clear distinction is required between the study of true CSL type analysis and the description of mismatches between crystallites given by rotations of a definable magnitude, which is more appropriately termed misorientation (texture) analysis. Furthermore, the construction of CSL descriptions has been confined to high symmetry classes (e.g., cubic and hexagonal); no such data are available for low symmetries (e.g., trigonal, triclinic) of geological significance. Also, although McLaren (1986) used CSL theory to investigate the structure of twin boundaries in quartz, no mathematical model was presented; the CSL were discovered by rotating transparencies of atomic models over one another, in a manner similar to the use of Moire models (e.g., Bollman, 1970), until coincidences were achieved. This approach led McLaren (1986) to suggest that CSL sites in quartz were rare except for twin relationships.

There are two ways (Fig. 5a) to represent the misorientation between two crystallites (Pospiech et al., 1986): (1) by rotation of the axes of one crystallite into alignment with the axes of the other crystallite (i.e. via rotations about each of the three Euler angles); and (2) by a single rotation about an axis which is common to both crystallites (i.e. an axis/angle pair). Due to the ease with which axis/angle pairs may be calculated from the data generated via SEM/EC analysis, this method has been adopted in the present study. But, as discussed previously, due to crystal symmetry considerations, there is no single solution to the number of axis/angle pairs which exist. Randle and Furley (1991) chose the axis/angle pair solution which gave the closest match to a theoretically derived low index CSL arrangement. They justified this choice, which need

Fig. 4. Dimensional and crystallographic orientations of polygonal subgrain, subgrain and neoblast boundaries in Grain B of Lloyd and Freeman (1991, 1994). (a) Distribution of sum of boundary lengths against dimensional orientation of boundary traces measured relative to X in the specimen XZ plane. Also represented are the orientations of those crystallographic planes which are approximately normal (i.e. subvertical) to the XZ plane. Subgrain boundaries have a preferred dimensional orientation subparallel to Z, with a minor orientation at 20-45 ° to X. These which may also be crystallographically orientated parallel to the crystal planes indicated. In contrast, neoblast boundaries have no preferred orientation, either dimensionally or crystallographically. (b) C H A N N E L @ simulated ECPs for adjacent polygonal subgrains 43 (left) and 44 (right) from Grain B of Lloyd and Freeman (1991, 1994). The pattern/subgrain normals are subparallel to the { 1121 } pole. Overlaying the patterns (centre) clearly shows the relative displacement of EC bands; the shaded regions indicate both the minimum, [1214], and maximum, [3301], displacements. This might constrain the dimensional and crystallographic orientation of the common boundary plane to be parallel to the minimum displacement band, (i.e. [ 1214]).

6 8 G.E. L loyd et a l . /Tec tonophys ics 279 (1997) 5 5 - 7 8

S

f2a

o

E

Z

:2

= E ' -

• .: ~ ._~ ~

,-~ ©

~ ~.~

~ N . . . .


not be the pair with the lowest angular magnitude, by stating that it would yield the lowest energy configuration. However, most (all but one?) of the possible solutions, including all those with high angular magnitudes, can usually be envisaged in terms of point group rotations about crystal symmetry axes. Thus, and because of the general lack of three dimensional boundary orientation data and the unavailability of CSL descriptions for quartz, we have chosen from the set of possible misorientations the axis/angle pair with the lowest angular magnitude as the definition of the misorientation between two crystallites. This choice is in agreement with both Pospiech et al. (1986) and Mainprice et al. (1993).

4.1. Misorientation plots and data

Axis/angle pair misorientations are plotted in misorientation space: a cylinder with cross-section equivalent to a stereographic projection (Pospiech et al., 1986). The axis component plots as azimuth and plunge on the base and the angle plots at a height equivalent to the magnitude above the base (Fig. 5b). If the misorientation space is contoured, slices through it may be viewed in a similar fashion to orientation distribution function diagrams. However, the three-dimensional appearance can be greatly sim- plified (Farmer, 1992) to a single, standard stereographic projection by representing the range of angle magnitudes via colour/shading (Fig. 5c). In addition, misorientation axes plots can be defined in terms of either the specimen reference frame (i.e. a pole figure) or the crystal reference frame (i.e. an inverse pole figure). The choice depends on what is intended to be shown. For example, a pole figure definition is ideal for depicting orientation differences between crystallites and the kinematic framework (as in this study), but an inverse pole figure definition would be more appropriate to compare the crystallographically controlled deformation processes within a specimen (e.g., Lind, 1996).

Axis/angle pair misorientation data sets can be collected in several ways.

(1) Nearest neighbour analysis (Randle, 1992) represents a two-dimensional approximation of the three-dimensional relationship between two crystallites across their common boundary, but obviously it is impractical to consider all of the boundaries in a

specimen, although it is possible to weight the data according to the length of boundary to achieve some statistical representation of the whole specimen.

(2) Grid node analysis (Pospiech et al., 1986) attempts to achieve a statistical representation of the specimen, rather than the exact situation which exists across an individual boundary between two crystallites.

(3) Factoral grain analysis (Farmer, 1992) com- pares every crystallite in the data set with every other crystallite, irrespective of whether they share a common boundary or not, which can have advantages, as follows: (a) it is analogous to the grid node method in polycrystalline aggregates; (b) it is as rigorous as nearest neighbour analysis when applied to single crystals; (c) it emphasises misorientation differences between crystallites, which is useful because the accuracy of misorientation determination via axis/angle pairs decreases with decreasing misorientation and; (d) it provides misorientation texture diagrams which can be more readily related to other aspects of the specimen (e.g., deformation history).

4.2. A model for misorientation analysis

As with the traditional type of fabric diagrams, misorientation plots can be used to determine both the macroscopic deformation process, or the activity of specific crystal slip systems. However, before an interpretation can be made a model is required to explain the physical processes responsible for the misorientation textures observed. The model we have chosen (Farmer, 1992) is based on the assump- tion that a simple geometrical relationship exists between the dislocation (crystal) slip system which gives rise to the rotation and misorientation between two crystallites and the resulting (sub)grain boundary. Such simple relationships have been applied to low angular misorientation boundaries (Kelly and Groves, 1970; Nicolas and Poirier, 1976; Doukhan and Trepied, 1985; Poirier, 1985) and the dispersion of subgrain orientations (Lloyd and Freeman, 1991, 1994; Buatier et al., 1991).

For an initially crystallographically uniform crystal, an intragranular microstructure forms by the addition of dislocations into subgrain walls, which progressively rotates the lattice. The walls consist of arrays of regularly stacked dislocations, such that the

70 G.E. Lloyd et al./ Tectonophysics 279 (1997) 55-78

plane of the wall is approximate ly mutually perpendicular to both the slip plane and slip direction for tilt walls and parallel to the slip plane for twist walls. Thus, for tilt walls up to 15 ° (Nicolas and Poirier, 1976; Doukhan and Trepied, 1985; Buatier et al., 1991), the misorientat ion axis will be confined to the plane of the subgrain wall and perpendicular to the slip direction, whilst for twist walls, the misorientat ion axis will be perpendicular to the slip plane. However, this geometr ical model is subject to several assumptions, as follows:

(1) it remains to be just if ied over a range of scales of observation;

(2) misorientat ions must remain small for the geometr ical constraints to remain valid;

(3) misorientat ions observed at one magnification need not relate to those observed at higher/ lower magnifications (White, 1977);

(4) although the interpretations placed on misorientation axes are l inked to the dispersion paths of subgrain orientations (e.g., L loyd and Freeman, 1991, 1994), the depict ion of dispersion paths is not as sensitive to the angular mismatch as is the misorientat ion axis.

4.3. Applications of misorientation plots

The fol lowing examples of the applicat ions of misorientat ion plot analysis are based on the approach of Farmer (1992).

4.3.1. Interpretation of trends Lloyd and Freeman (1991, 1994) interpreted ro-

tation axes derived from crystal lographic dispersion plots s imply as being due to the formation of tilt walls. Thus, the rotation axis between two mis- matched crystal l i tes must be contained within the slip plane and be perpendicular to the slip direction (Fig. 6a). Unfortunately, this is not a unique interpretation and a number of alternative solutions are feasible, including: a twist axis mismatch (Fig. 6b); a number of slip planes in a crystal lographic zone with their glide directions contained in a plane normal to the zone (Fig. 6c); and a combinat ion of twist and tilt mismatches (Fig. 6d). However, with addit ional information (e.g., subgrain boundary orientation), the number of alternative interpretations may be reduced (Bouchez, 1977). Furthermore, the occurrence of

(d)

(e) (f)

Fig. 6. Application of misorientation plots: interpretation of trends in crystal data (after Farmer, 1992). See text for discussion. (a)-(d) Various combinations of crystal slip arrangements for the production of a point cluster on a misorientation plots (or crystal axis dispersion plots of Lloyd and Freeman, 1991, 1994). (e)-(f) Two examples by which girdle distributions of misorientation axes may occur on a misorientation plot. (a) Pure tilt wall, rotation axis is contained within the slip plane and slip direction. (b) Twist axis mismatch, rotation axis is perpendicular to the slip plane. (c) A number of slip planes in a crystallographic zone with their common glide directions contained within a plane normal to the zone. (d) Combination of twist and tilt (i.e. general) mismatches. (e) Presence of a number of slip directions contained within the same plane. (f) Zonal arrangement of slip systems with a common slip direction.

girdle distributions of both misorientat ion and dispersion axes may be explained by the presence of a number of slip directions contained within the same plane (Fig. 6e) or by a zonal arrangement of slip systems with a common slip direction (Fig. 6f).

4.3.2. Identification of crystal slip systems There have been several recent reviews of the

techniques available for determining dislocation

G.E. Lloyd et al./ Tectonophysics 279 (1997) 55-78 71

(crystal) slip systems responsible for crystal plastic deformation (e.g., Law, 1990; Wenk and Christie, 1991; Schmid, 1994). The obvious drawback to most techniques is a compromise between spatial location, complete crystallographic determination and sam- ple size/resolution. However, the SEM techniques provides a full crystallographic description from a known position at spatial high resolution and therefore offer unique opportunities to study slip system activity. Here, we identify active crystal slip systems for quartz by correlating observed misorientation plots and crystal pole dispersion figures with those predicted for known quartz slip systems, together with the vector notation of the corresponding misorientation axis (see Table 1 for details), assuming that only tilt wall mismatches occur (e.g., Fig. 6a). Each plot (e.g., Fig. 7) includes the principal crystallographic poles and their predicted dispersion paths, the crystal slip plane and slip direction, the plane of the predicted mismatch boundary (which is perpendicular to the slip direction), and the misorientation axes for all equivalent slip systems.

4.3.3. Schmid Factor analysis The model is capable of constructing Schmid Fac-

tor plots for a specified principal stress orientation from the measured orientation data. The magnitude of the Schmid Factor for a specific slip direction is represented by a circle of equivalent diameter. For example, consider a single quartz grain oriented with its basal plane approximately NE-SW (i.e. the c-axis is positioned approximately NW-SE), subjected to N-S compression (Fig. 8a). We can use our model to compare the relative activity of different slip systems by representing their respective Schmid Factors by the size of a circle centred on their slip direction. In Fig. 8a, we have compared basal-a slip with prism-a slip. The largest circle (largest Schmid Factor), and therefore the most likely system to be activated, is for basal-a slip in the direction marked by X; both systems are equally likely to be activated at Y; whilst at the intermediary a-axis the respective Schmid Fac- tors for both systems are small and their activation is unlikely.

Table 1 Crystal slip systems identified in quartz (Linker et al., 1984)

Slip system

Symbol Numeric

{ hkil } [UVTW] { hkil } [UVTW]

Rotation axes

[U T V W]

(c) [+a] (0001) [11-20] [ 1.000 - 1.000 0.000 {m} [+a] { 10-10} [1-210] <0.000 0.000 0.000

(c) (0001) [ - 1.000 2.000 - 1.000 [ c - a] [ 1-213] [-0.418 0.836 -0 .418 [c+a] [- 12-13] [-0.418 0.836 -0 .418

{r} [+a] { 10-11 } [1-210] [ - 1.000 0.000 1.000 [c+a] [- 1-1231 [ -0 .687 1.000 -0 .313 [c-a] [-2113] [-0.313 1.000 -0 .687

{ z } [ + a ] { 01 - 11 } [2-1-10] [0 .000 1.000 - 1 .000 [c--a] [ 1-213] [ - 1.000 0.313 0.687 [c+a] [- 1-123] [ - 1.000 0.687 0.313

{ 7r' } [ + a ] { 1-102 } [ 11-20] [ - 1.000 1.000 0.000 {zr } [+a] { 10-12} [1-21 O] [1.000 0.000 -1 .000 {a} {c) { 11-20} (0001) [-- 1.000 1.000 0.000 {~'} [c-a] {2-1-12} [-21131 [0.000 --1.000 1.000 { ~ } [c+a] { 11-22 } [- 1-123] [ - 1.000 1.000 0.000 {s} [c+a3] {2-1-11 } [-1-123] [ -0 .285 1.000 -0 .715

[c+a2] [-12-13] [0.285 0.715 - 1.000 {s} [c--a2] { 11-21 } [-1-123] [ - 1.000 0.715 0.285

[c -a l ] [-2113] [--0.715 1.000 -0 .285

o.ooo1 1 . 0 0 0 > 0.000 1.000

- 1.000 2.000 0.374

-0 .374 -2 .000

0.374 -0 .374

1.000 -1 .000

0.000 0.000 0.000 0.855

-0 .855 0.855

-0 .855

A

G.E. Lloyd et al. / Tectonophysics 279 (1997) 55-78

A a ~

v .~ .~

:. ... ,¢ .::.. .:/ /"::: ~ s ; . : ' 4 , "- " . ' - " " ' " " ':: '" " : ' " ~ . 2

A + ,-J v ~ .~ I~ ~ ~

V ~ ~ ,,.., "~

- I - - - ~ I ~

. ~ £

I 0 - I ~.=- ~,

44

" o E

o ~

© ..~

72

A ct:l

V V -~ u"

,W~ r" ..~ "-a

Q c~

s~ -~

< ~

i..T,, ~ 'v.


4.3.4. Synthetic misorientation model The model can be used to investigate expected

misorientation distributions in specific situations (e.g., pure tilt walls). The misorientation axes for individual slip systems are plotted in stereographic projection form and indicate the slip potential of each system in terms of the Schmid Factor. The grain boundary orientation associated with the largest Schmid Factor is also indicated. In other words, the relative magnitudes of individual slip systems determined via Schmid Factor analysis are duplicated in the corresponding position in the misorientation axis diagram. For example, for the individual quartz grain considered in the previous example (Fig. 8a), the slip system with the highest Schmid Factor was basal-a oriented in the position indicated by X. If

we now duplicate all the Schmid Factor circles in the positions mutually perpendicular to their respective slip directions and slip plane normals (Fig. 8b), the largest circle defines the position of the misorientation axis for the most active slip system. The orientation (of any boundaries formed during slip on this system is therefore predicted by our model to be normal to the slip direction (i.e. the plane ZZ').

4.3.5. Comparison of synthetic and real data Due to the form in which the synthetic model

operates, the comparison between real and predicted misorientations is subject to a number of non-trivial problems (Farmer, 1992), as follows. Real deform- ing aggregates maintain both stress equilibrium and strain compatibility (e.g., Wenk and Christie, 1991):

0.1 O'l

(oool

....................... ° ........................ / \ - I,.' o<1120> ~ {1100} ~~ . {10]'1 }

O"1 • {01]'1 } Fig. 8. Application of misorientation plots-III (after Farmer, 1992). See also Table 1, (a) Schmid Factor analysis comparing basal-a slip with prism-a slip for a quartz single crystal compressed parallel to N-S. The diameter of the circles centred on the three a-axes indicates the magnitude of the Schmid Factor. The large circle occurs at X for basal-a slip. (b) Synthetic misorientation model for a quartz single crystal compressed parallel to N-S, based on Schmid Factor analysis for basal-a and prism-a slip systems. The most probable misorientation axis occurs at the largest circle for basal-a slip at X, and should therefore form boundaries parallel to ZZ'.

74 G.E. Lloyd et al./Tectonophysics 279 (1997) 55 78

if a crystallite deforms differently to its neighbours, the difference must be accommodated within the immediate vicinity by heterogeneous intragranular or grain boundary deformations. Real misorientation data provide an opportunity to investigate this situation and its relationship to existing models for CPO development. Ideally, this would involve models and data being analysed, compared and improved in an iterative manner. Unfortunately, such a procedure is beyond the scope of existing CPO and microstructural development models. For the moment, we must make do with qualitative understanding based up on: (1) complete crystallographic orientation data for subgrains within an aggregate of grains; (2) misorientation data between subgrains within individual grains; (3) assessment of these two data sets in terms of spatial location; and (4) microstructural information relating to all aspects of the aggregate. If we accept these limitations, together with the basic assumptions discussed above, misorientation axes may be considered as representing the slip systems which have been active. In addition, Schmid Factors for all systems can be derived if the imposed stress system is known and by comparison between real and synthetic data it is possible to evaluate the accommodation of deformation between grains in an aggregate. However, several problems exist in the comparison of real and synthetic data.

(1) In the current model, the Schmid Factor is sensitive only to stress direction, not magnitude nor finite strain.

(2) Only misorientation axes are predicted rather than angles because the model does not involve imposed strain.

(3) The models should be based on a physical re- ality (e.g., stress equilibrium or strain compatibility), but this is not a trivial problem, although with certain assumptions the synthetic model is compatible with the stress equilibrium approach.

(4) Synthetic misorientation plots are only valid for aggregates if slip systems with comparable crit- ical resolved shear stress (crss) only are plotted on the same figure.

5. Conclusions

(1) Knowledge of the nature of boundaries which exist in rocks is an important but neglected aspect

to our understanding of rock behaviour, particular during deformation.

(2) Various types of boundary exist; this contribution has concentrated on inter- and intra-granular crystal boundaries.

(3) A complete characterisation of such boundaries depends on the crystallographic and dimensional orientations of the boundary and the crystallographic misorientation between the adjacent regions.

(4) Although several theoretical descriptions of boundary configuration are available, practical determination of the formation and orientation of boundaries is lacking and/or inappropriate on the scales (i.e. specimen dimensions and boundary lengths and numbers) required for statistical accuracy.

(5) However, several approximations are available which make use of the data now readily available via SEM techniques (i.e. electron channelling and electron backscattered diffraction), although these approaches implicitly assume that boundaries have a crystallographic orientation controlled by the misorientation between adjacent subgrains/grains (i.e. the ve©' relationship trying to be established).

(6) Thus, SEM studies cannot provide unequivocal evidence to support the contention that boundary orientation may be crystallographically controlled. All that can be deduced are some interesting observations which may be more than coincidental.

(7) One SEM approximation depends on recog- nising potential geometrical relationships between the dimensional orientation of a boundary and the crystallographic orientations of the adjacent regions, as revealed via the configurations of the ECP, to predict the likely crystallographic orientation of the boundary.

(8) Another SEM approximation assumes that a specific relationship exists between crystal slip systems and the formation and orientation of boundaries, such that analysis of the misorientation between adjacent regions is sufficient to characterise completely the boundary.

(9) This approach is capable of: (a) identifying trends in the dispersion of crystallographic directions during deformation; (b) identifying the active slip systems; (c) calculating the relative Schmid Fac- tors for each crystal slip system (and therefore the most likely system to be activated); (d) modelling synthetic misorientations and predicting the crystal


slip systems and boundary configurations to be expected; and (e) comparing real data with synthetic models.

(10) Nevertheless, these approximations represent only a part of the knowledge needed to develop a complete understanding of the formation and orientation of boundaries, as well as the significance of boundaries to rock behaviour.

(11) Development of such an understanding will rely on the formulation of better models (i.e. closer approximations), the acquisition of more data, and a comparison with more natural situations.

Acknowledgements

It is a pleasure to contribute to this thematic volume honouring Adolph Nicolas. His original work in microstructure, petrofabrics and mineral physics has significantly guided our own researches over the years. We are also grateful to Niels-Henrik Schmidt (for access to his ECP/EBSP-indexing program CHANNEL@), Brett Freeman (for stimulating our interest in dynamic recrystallisation of Dalradian quartzites), and to Andy Lind and Berndt Neumann (for discussions regarding misorientation analysis). The comments of Jean-Luc Bouchez and the jour- nal's referees, Holger Sttinitz and an anonymous reviewer, contributed significantly to the final ver- sion of this paper. ABF acknowledges receipt of a U.K. NERC studentship.

References

Amelinckx, S., Dekeyser, W., 1959. The structure and properties of grain boundaries. Solid State Phys. 8, 325-499.

Ardell, A.J., Christie, J.M., McCormick, J.W., 1973. Dislocation images in quartz and the determination of Burgers vectors. Philos. Mag. 29, 1399-1411.

Balluffi, R.W., Cahn, R.W., 1981. Mechanism for diffusion induced grain boundary migration. Acta Metall. 29, 493-500.

Balluffi, R.W., Bristowe, P.D., Sun, C.P., 1981. Structure of high-angle grain boundaries in metals and ceramic oxides. J. Am. Ceram. Soc. 64, 23-30.

Balluffi, R.W., Brookman, A., King, A.H., 1982. CSL/DSC lattice model for general crystal-crystal boundaries and their line defects. Acta Metall. 30, 1453-1470.

Barber, D.J., 1985. Dislocations and microstructures. In: Wenk, H.R. (Ed.), Preferred Orientation in Deformed Metals and Rocks - - An Introduction to Modern Texture Analysis. Aca- demic Press, London, pp. 149-182.

Beere, W., 1978. Stresses and deformation at grain boundaries.

Philos. Trans. R. Soc. London A288, 177-196. Bell, T.H., Etheridge, M.A., 1973. The deformation and recrys-

tallization of quartz in a mylonite zone. Tectonophysics 32, 235-267.

Bishop, G.H., Harrison, R.J., Kwok, T., Yip, S., 1979. Com- ments on sliding and migration based on computer molecular dynamics simulations of grain boundaries. In: Balluffi, R.W. (Ed.), Grain Boundary Structure and Kinetics. ASM, Metals Park, pp. 373-377.

Bleris, G.L., Antonopoulos, J.G., Karakostas, T., 1981. Grain boundary analysis in TEM V. A criterion for the identification of a CSL and a characterisation of an approximate CSL. Phys. Status Solidi A67, 249-257.

Boland, J.N., Fitz Gerald, J.D., 1993. Defects and Processes in the Solid State: Geoscience Applications. The McLaren Volume, Developments in Petrology 14. Elsevier, Amsterdam, 470 pp.

Bollman, W.A., 1970. Crystal Defects and Crystalline Interfaces. Springer-Verlag, Berlin.

Bouchez, J.-L., 1977. Plastic deformation of quartzites at low temperatures in an area of natural strain gradient (Angers, France). Tectonophysics 39, 25-80.

Bouchez, J.-L., 1978. Preferred orientations of quartz a axes in some tectonites: kinematic inferences. Tectonophysics 49, T25-T30.

Brandon, D.G., 1966. The structure of high angle grain boundaries. Acta Metall. 14, 1479.

Brandon, D.G., Ralph, B., Raganathan, S., Wald, M.S., 1964. A field ion microscope study of the atomic configuration of grain boundaries. Acta Metall. 12, 813.

Buatier, M., Van Roermund, H.L.M., Drury, M.R., Lardeaux, J.M., 1991. Deformation and recrystallisation mechanisms in naturally deformed omphacites from the Sesia Lanzo Zone. Tectonophysics 195, 11.

Bunge, H.-J., 1982. Fabric analysis by orientation distribution functions. Tectonophysics 78, 1.

Chadwick, G.A., Smith, D.A., 1976. Grain Boundary Structure and Properties. Academic Press, London, 388 pp.

Cobbold, P.R., Means, W.D., Bayly, M.B., 1984. Jumps in deformation gradients, and particle velocities across propagating coherent boundaries. Tectonophysics 108, 283-298.

Doukhan, J.-C., Trepied, L., 1985. Plastic deformation of quartz single crystals. Bull. Mineral. 108, 97-123.

Drury, M.R., 1993. Deformation lamellae in metals and minerals. In: Boland, J.N., Fitz Gerald, J.D. (Eds.), Defects and Processes in the Solid State: Geoscience Applications. The McLaren Volume, Developments in Petrology 14. Elsevier, Amsterdam, pp. 195-212.

Drury, M.R., Urai, J.L., 1990. Deformation-related recrystallization processes. Tectonophysics 172, 235-253.

Drury, M.R., Humphreys, F.J., White, S.H., 1985. Large strain deformation studies using polycrystalline magnesium as a rock analogue, part II. dynamic recrystallization mechanisms at high temperatures. Phys. Earth Planet. Inter. 40, 208-222.

Farmer, A.B., 1992. A Microstructural Investigation of Natu- ral Deformation in Quartz Aggregegates. Unpublished Ph.D. thesis, University of Leeds, 307 pp.

76 G.E. Lloyd et al./Tectonophysics 279 (1997) 55 78

Fitz Gerald, J.D., Etheridge, M.A., Vernon, R.H., 1983. Dy- namic recrystallization in a naturally deformed albite. Textures Microstruct. 5,219-237.

Fliervoet, T.E, White, S.H., 1995. Quartz deformation in a very fine grained quartzo-feldspathic mylonite: a lack of evidence for dominant grain boundary sliding deformation. J. Struct. Geol. 17, 1095-1109.

Forwood, C.T., Clareborough, L.M., 1991. Electron Microscopy of Interfaces in Metals and Alloys. IOP Publications, Bristol.

Friedel, J., 1964. Dislocations. Pergamon Press, Oxford. Gapais, D., White, S.H., 1982. Ductile shear bands in a naturally

deformed quartzite. Textures Microstruct. 5, 1-17. Gifkins, R.C., 1976. Grain boundary sliding and its accommo-

dation during creep and superplasticity. Metall. Trans. 7A, 1225.

Gleiter, H., 1982. On the structure of grain boundaries in metals. Mater. Sci. Eng. 52, 91-131.

Grimmer, H., 1980. A unique description of the relative orientation of neighbouring grains. Acta Crystallogr. A36, 382- 389.

Grimmer, H., 1989a. Systematic determination of coincidence orientations for all hexagonal lattices with axial ratio c/a in a given interval. Acta Crystallogr. A45,320-325.

Grimmer, H., 1989b. Coincidence Orientations of Grains in Rhombohedral and Hexagonal Materials. Paul Scherrer ln- stitut, Wurlingen.

Grimmer, H., Bollmann, W., Warrington, D.H., 1974. Coinci- dent-site lattices and complete pattern-shift lattices in cubic crystals. Acta Crystallogr 30A, 197.

Groshong, R., 1988. Low-temperature deformation mechanisms and their interpretation. Geol. Soc. Am. Bull. 100, 1329-1360.

Guillop6, M., Poirier, J.R, 1979. Dynamic recrystallization during creep of single crystalline halite: an experimental study. J. Geophys. Res. 84, 5557-5567.

Haessner, E, Hoffman, S., 1978. Migration of high angle grain boundaries. In: Haesnner, F. (Ed.), Recrystallization of Metal- lic Materials. Reider, Stuttgart, pp. 63-95.

Haruna, T., Shibayanagi, T., Hori, S., Furushiro, N., 1992. Effect of grain boundary characters on grain boundary sliding during superplastic deformation. Trans. Mater. JIM 33, 374-379.

Hay, R.S., Evans, B., 1988. Intergranular distribution of pore fluid and the nature of high-angle grain boundaries in lime- stone and marble. J. Geophys. Res. 93, 8959-8974.

Hirth, G., Tullis, J., 1992. Dislocation creep regimes in quartz aggregates. J. Struct. Geol. 14, 145-159.

Hobbs, B.E., 1968. Recrystallisation of single crystals of quartz. Tectonophysics 6, 353-401.

Hu, H., 1972. The Nature and Behaviour of Grain Boundaries. Plenum Press, New York.

Jessell, M.W., 1986. Grain boundary migration and fabric development in experimentally deformed octachtoropropane. J. Struct. Geol. 8, 527-542.

Joesten, R., 1983. Grain growth and grain boundary diffusion in quartz from the Christmas Mountain (Texas) contact aureole. Am. J. Sci. 283A, 233-254.

Joy, D.C., Newbury, D.E., Davidson. D.L., 1982. Electron chan-

nelting patterns in the scanning electron microscope. J. Appl. Phys. 53, RSI-R122.

Kelly, A., Groves, G.W., 1970. Crystallography and Crystal De- fects. Longman, London, 428 pp.

Knipe, R.J., 1989. Deformation mechanisms - recognition from natural tectonites. J. Struct. Geol. 11, 127-146.

Knipe, R.J., Law, R.D., 1987. The influence of crystallographic orientation and grain boundary migration on microstructural and textural evolution in an SC mylonite. Tectonophysics 135, 153-169.

Knipe, R.J., Rutter, E.H., 1990. Deformation Mechanisms, Rhe- ology and Tectonics. Geol. Soc. London, Spec. Publ. 54.

Law, R.D., 1990. Crystallographic fabrics: a selective review of their applications to research in structural geology. In: Knipe, R.J., Rutter, E.H. (Eds.) Deformation Mechanisms, Rheology and Tectonics. Geol. Soc. London, Spec. Publ. 54, 335-352.

Law, R.D., Schmid, S.M., Wheeler, J., 1990. Simple shear deformation and quartz crystallographic fabrics: a possible natural example from the Torridon area of NW Scotland. J. Struct. Geol. 12, 29-46.

Lind, A., 1996. Microstructural Stability and the Kinetics of Textural Evolution. Unpublished Ph.D. thesis, University of Leeds, 316 pp.

Linker, M.E, Kirby, S.H., Ord, A., Christie, J.M., 1984. Effects of compression direction on the plasticity and rheology of hydrolytically weakened synthetic quartz. J. Geophys. Res. 89, 4241.

Lloyd, G.E., 1985. Review of instrumentation, techniques and applications of SEM in mineralogy, in: White, J.C. (Ed.), Applications of Electron Microscopy in the Earth Sciences. Mineral. Assoc. Can. Short Course 11, 151-188.

Lloyd, G.E., 1987. Atomic number and crystallographic contrast images with the SEM: a review of backscattered electron techniques. Mineral. Mag. 51, 3-19.

Lloyd, G.E., 1994. An appreciation of the SEM electron channelling technique for microstructural analysis of geological materials. In: Bunge, H.-J., Siegesmunde, S., Skrotzki, W., Weber. K. (Eds.), Textures of Geological Materials. DGM Informationsgesellschaft Verlag, Oberursel, pp. 109-126.

Lloyd, G.E., Freeman, B., 1991. SEM electron channelling analysis of dynamic recrystallization in a quartz grain. J. Struct. Geol. 13, 945-953.

Lloyd, G.E., Freeman, B., 1994. Dynamic recrystallization of quartz and quartzites. J. Struct. Geol. 16, 867-881.

Mainprice, D., Lloyd, G.E., Casey, M., 1993. Individual orientation measurements in quartz polycrystals - - advantages and limitations for texture and petrophysical property determina- tions. J. Struct. Geol. 15, 1169 1187.

Mawer, C.K., Fitz Gerald, J.D., 1993. Microstructure of kink band boundaries in naturally deformed Chewings Range quartzite. In: Boland, J.N., Fitz Gerald, J.D. (Eds.), Defects and Processes in the Solid State: Geoscience Applications. The McLaren Volume, Developments in Petrology 14. Else- vier, Amsterdam, pp. 49 67.

McLaren, A.C., 1986. Some speculations on the nature of high-angle grain boundaries in quartz rocks. In: Hobbs, B.E., Heard, H.C. (Eds.), Mineral and Rock Deformation: Labo-


ratory Studies. The Paterson Volume. Am. Geophys. Union, Geophys. Monogr. 36, 233-247.

Means, W.D., Jessell, M.W., 1986. Accommodation migration of grain boundaries. Tectonophysics 127, 67-86.

Means, W.D., Ree, J.H., 1988. Seven types of subgrain boundaries in octachloropropane. J. Struct. Geol. 10, 765-770.

Nicolas, A., Poirier, J.P., 1976. Crystalline Plasticity and Solid State Flow in Metamorphic Rocks. John Wiley, London, 444 pp.

Olesen, N.O., Schmidt, N.H., 1990. The SEM/ECP technique applied on twinned quartz crystals. In: Knipe, R.J., Rutter, E.H. (Eds.), Deformation Mechanisms, Rheology and Tectonics. Geol. Soc. London, Spec. Publ. 54, 369-374.

Peterson, N.L., 1979. Grain boundary diffusion-structural effects, models and mechanisms. In: Balluffi, R.W. (Ed.), Grain Boundary Structure and Kinetics. ASM Metals Park, pp. 209- 238.

Poirier, J.P., 1985. Creep of Crystals - - High Temperature De- formation Processes in Metals, Ceramics and Minerals. Cam- bridge University press, 260 pp.

Poirier, J.P., Guillopr, M., 1979. Deformation induced recrystallization of minerals. Bull. Mineral. 102, 67-74.

Poirier, J.P., Nicolas, A., 1975. Deformation-induced recrystallization due to progressive misorientation of subgrains, with special reference to mantle peridotites. J. Geol. 83, 707-720.

Pond, R.C., Smith, D.A., Southerden, P.W.J., 1978. On the role of grain boundary dislocations in high temperature creep. Philos. Mag. A. 37, 27~-0.

Pospiech, J., Sztwiertnia, K., Haessner, E, 1986. The misorientation distribution function. Textures Microstruct. 6, 201.

Ranagathan, S., 1966. On the geometry of coincident site lattices. Acta Crystallogr. 21, 197.

Randle, V., 1992. Microtexture Determination and its Applica- tions. Institute of Materials, London, 174 pp.

Randle, V., 1993. The Measurement of Grain Boundary Geome- try. Institute of Physics Publication, Bristol.

Randle, V., Furley, J., 1991. Experimental aspects of the use of electron back scattering for characterisation of microtexture and mesotexture. Textures Microstruct. 14-18, 877-883.

Randle, V., Ralph, B., 1986. A practical approach to the determination of the crystallography grain boundaries. J. Mater. Sci. 21, 3823-3828.

Rubie, D., 1986. The catalysis of mineral reactions by water and restrictions on the presence of aqueous fluid during metamor- phism. Min. Mag. 50, 399-415.

Schmid, S.M., 1994. Textures of geological materials: computer model predictions versus empirical interpretations based on rock deformation experiments and field studies. In: Bunge, H.-J., Siegesmunde, S., Skrotzki, W., Weber, K. (Eds.), Tex- tures of Geological materials. DGM Informationsgesellschaft Verlag, Oberursel, pp. 279-302.

Schmid, S.M., Casey, M., 1982. Microfabrics of deformed rocks: a review. Mitt. Geol. Inst. ETH Zurich, N.E 239a.

Schmid, S.M., Casey, M., 1986. Complete fabric analysis of some commonly observed quartz c-axis patterns. In: Hobbs, B.E., Heard, H.C. (Eds.), Mineral and Rock Deformation: Lab-

oratory Studies. The Paterson Volume. Am. Geophys. Union, Geophys. Monogr. 36, 263-296.

Schmid, S.M., Paterson, M.S., Bolland, J.N., 1980. High temperature flow and dynamic recrystallization in Carrera Marble. Tectonophysics 65, 245-280.

Schmidt, N.-H., Olesen, N.O., 1989. Computer-aided determination of crystal lattice orientation from electron channelling patterns in the SEM. Can. Mineral. 27, 15-22.

Schwarzer, R.A., 1990. Measurement of local textures with transmission electron and scanning electron microscopes. Textures Microstruct. 13, 15-30.

Schwarzer, R.A., Weiland, H., 1988. Texture analysis by the measurement of individual grain orientations - - electron mi- croscopical methods and application on dual phase steel. Tex- tures Microstruct. 8-9, 551-577.

Smith, D.A., Rae, C.M.F., Grovenor, C.R.M., 1979. Grain boundary migration. In: Balluffi, R.W. (Ed.), Grain Boundary Struc- ture and Kinetics. ASM Metals Park, pp. 337-371.

Toriumi, M., 1982. Grain boundary migration in olivine at atmo- spheric pressure. Phys. Earth Planet. Inter. 30, 26-35.

Trepied, L., Doukhan, J.C., Paquet, J., 1980. Subgrain boundaries in quartz. Theoretical analysis and microscopic observations. Phys. Chem. Mineral. 105, 176-180.

Tullis, J., Yund, R.A., 1982. Grain growth kinetics of quartz and calcite aggregates. J. Geol. 90, 301-318.

Tullis, J., Christie, J.M., Griggs, D.T., 1973. Microstructures and preferred orientations of experimentally deformed quartzites. Geol. Soc. Am. Bull. 84, 297-314.

Turner, EJ., Weiss, V., 1963. Structural Analysis of Metamorphic Tectonites. McGraw-Hill, New York.

Urai, J.L., 1983. Water assisted dynamic recrystallization and weakening in polycrystalline bischofite. Tectonophysics 96, 125-127.

Urai, J.L., Means, W.D., Lister, G.S., 1986. Dynamic recrystallization of minerals. In: Hobbs, B.E., Heard, H.C. (Eds.), Mineral and Rock Deformation: Laboratory Studies. The Pa- terson Volume. Am. Geophys. Union, Geophys. Monogr. 36, 161-199.

Vernon, R.H., 1975. Deformation and recrystallization of a pla- gioclase grain. Am. Mineral. 60, 884-888.

Vernon, R.H., 1976. Metamorphic Processes. Allen and Unwin, London.

Wenk, H.-R., Christie, J.M., 1991. Review paper - - comments on the interpretation of deformation textures in rocks. J. Struct. Geol. 13, 1091-1110.

White, J.C., White, S.H., 1981. On the structures of grain boundaries in tectonites. Tectonophysics 78, 613-628.

White, S.H., 1976. The effects of strain on the microstructures, fabrics and deformation mechanisms in quartz. Philos. Trans. R. Soc. London, Ser. A 283, 69-86.

White, S.H., 1977. Geological significance of recovery and recrystallisation processes in quartz. Tectonophysics 39, 143- 170.

White, S.H., 1979. Grain and subgrain size variations across a mylonite zone. Contrib. Mineral. Petrol. 70, 193-202.

White, S.H., Burrows, S.E., Carreras, J., 1978. Textural and microstructural development in a naturally deformed quartzite:


a metallurgical approach. In: Gottstein, G., Luecke, K. (Eds.), 5th Int. Conf. Textures of Materials, Aachen 2, pp. 21 t -220.

Wilson, C.J.L., 1973. The prograde microfabric in a deformed

quartzite sequence Mount lsa, Australia. Tectonophysics 19, 39-81.

Documents

Misorientation analysis and the formation and orientation of subgrain … · 2009-03-11 · crystal structure but different crystal orientation and represents a two-dimensional lattice