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4.4  ·  Lattice-Preferred Orientation (LPO)  103
                                                               and may even ‘overtake’ that of other slip systems. At low
                                                               differential stress, only one slip system may be active,
                                                               but at higher differential stress, several slip systems can
                                                               operate simultaneously. In fact, for maintenance of co-
                                                               hesion between grains, five independent slip systems
                                                               should be operating (Lister 1977). In silicates, however,
                                                               which usually have low crystal symmetry, fewer slip sys-
                                                               tems are active and space problems are accommodated
                                                               at low temperature by lattice bending, kinking, fractur-
                                                               ing and, at high temperature, by dynamic recrystallisa-
                                                               tion or grain boundary sliding.
                                                                 The type of LPO pattern that is formed in a rock de-
                                                               pends on many factors, the most important of which are
                                                               (Schmid 1994):

                                                               1. The slip systems that are operating and the amount of
                                                                 activity on each slip system.
                                                               2. The ratio of stretching rates along the ISA of the flow,
                                                                 i.e. plane strain, flattening or constrictional flow. These
                                                                 rates determine in which direction crystals rotate and
                                                                 thereby the shape of the fabric (Fig. 4.41).
                                                               3. The finite strain. Usually, if the flow pattern does not
                                                                 change during deformation, the LPO pattern increases
                                                                 in strength and sharpness with increasing strain but
                                                                 undergoes only slight changes in geometry (Sect. 4.4.4.2).
                                                               4. The kinematic vorticity number. In initially isotropic
                                                                 materials, non-coaxial progressive deformation leads
                                                                 to LPO patterns with monoclinic symmetry, and co-
                                                                 axial progressive deformation to patterns with higher
                                                                 symmetry.
                                                               5. The activity of bulging and grain boundary migra-
                                                                 tion dynamic recrystallisation. Recrystallisation may
                                                                 influence an LPO pattern in several ways but the ef-
                                                                 fect is difficult to predict; it may weaken an existing
                                                                 pattern by generation of new, randomly oriented
                                                                 grains; or it may strengthen a pattern or part of a pat-
                                                                 tern by removing (consuming) certain grains with a
                                                                 relatively high dislocation density. Grains that are
                                                                 unfavourably oriented for slip may be removed by this
                                                                 process if they developed a high dislocation density
                                                                 because of constriction by neighbours (Jessell 1987;
                                                                 Ree 1990). However, the reverse is also possible; such
                                                                 grains may have low dislocation density, since all
                                                                 deformation is taken up in softer neighbours, and
                                                                 therefore consume grains favourably oriented for slip
                                                                 (Gleason et al. 1993). Evidence for both processes has
                                                                 been found in experiments. Static recrystallisation
                                                                 may also affect LPO patterns, but the effect is uncer-
                 Fig. 4.39. a Reorientation of a pile of books by slip: an axis normal to  tain (Humphreys and Hatherley 1995; Heilbronner
                 the books (bold line) rotates towards the direction of gravity. Develop-  and Tullis 2002; Park et al. 2001).
                 ment of LPO in crystals due to dislocation glide on slip systems oper-  6. Growth of grains from solution. The growth rate in
                 ates in a similar way. b Flattening of an aggregate of crystals with a  many minerals is dependent on crystallographic di-
                 single slip system normal to a crystallographic axis (bold line). c All crys-
                 tal axes rotate towards the compression direction except those parallel  rection, and growth of minerals from solution can
                 or normal to this direction. Those parallel to the compression direc-  therefore produce a preferred orientation (Shelley 1979,
                 tion may deform by kinking or twinning with rotation of the segments  1989, 1994).
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