Preferred Orientation Patterns Research Articles

Anisotropic convection with implications for the upper mantle

On the basis of polycrystalline theory describing the plasticity in olivine and enstatite, the flow in a convection cell has been simulated using a finite element formulation. The spatial variations in anisotropic properties are computed from the textures that evolve with the flow. A kinematically constrained equilibrium‐based assumption is used to partition the macroscopic deformation among crystals within an aggregate. We model the convection for one specific cell geometry and two sets of boundary conditions. A complete map of textures throughout the cell is obtained. The textured convection cell is structurally very heterogeneous and textures along streamlines do not correlate with the finite strain. The results of the simulations indicate that during up welling a strong texture develops rapidly. It convects during spreading and is attenuated during subduction. Results are compared with features of the upper mantle. In our predictions the pattern of preferred orientation during spreading is inclined to the flow coordinates due to deformation by simple shear. This is contrary to Hess' [1964] intuition that (001) slip planes of olivine orient themselves parallel to the flow planes, yet the pattern is consistent with natural fabric data. Significant differences are observed as a function of depth within the cell. The variations in the p wave velocities in this textured model mantle are analyzed and correspond well with observed seismic data.

Quartz c-axis fabrics in deformed conglomerates: some support for a skeletal approach to fabric analysis

Preferred orientation patterns of c-axes in deformed quartzite rocks are conveniently characterized by (1) their skeletal outline and (2) by the way this skeleton is populated by c-axes. It has been recognized that the fabric skeleton principally reflects the kinematics of the flow during at least the later part of the deformation history, whilst the distribution of c-axes over the fabric skeleton is less reliable in this respect, because the c-axes orientation distribution may be dominated by the effect of an uneven and non-random distribution of c-axes prior to deformation. Little evidence has been presented, however, to confirm this interpretation. Quartz c-axis fabrics in quartzite pebble conglomerates from southern Spain show variable and incomplete patterns in individual pebbles which, however, all have a similar fabric skeleton, and link to form more complete patterns when c-axes from several pebbles are plotted together. In view of the common deformation history of the pebbles within a given sample, the variable and incomplete fabrics in single pebbles can only be explained by the effect of initial non-randomness of c-axes prior to deformation. It follows that the c-axis orientation distribution in this case bears little relationship with the inferred kinematics of the flow whilst the fabric skeleton shows a consistent relationship with the kinematic framework.

Towards statistics of crystal orientations in quantitative texture anaylsis

By the application of Rodrigues parameters, crystal orientations are represented as points on the unit semi-hypersphere S4+ ⊃ \bb R4 or equivalently on the projective hyperplane H3 ⊃ \bb R4. For the statistical analysis of orientation data, probability models on S4+ ≡ H3 are required. Among different hyperspherical analogs of the normal distribution in Euclidean space, corresponding to various of its characterizations, the Bingham model distribution is characterized as the hyperspherical analog for statistical purposes. Maximum-likelihood estimates of its parameter matrices and single-sample significance tests of uniformity and rotational symmetry are presented. In terms of probability theory and stochastic processes, the hyperspherical Brownian-diffusion distribution is the analog of the normal distribution in Euclidean space. An orientation distribution derived by Savelova [Ind. Lab. (USSR), (1984), 50, 468–474] and erroneously related to a central-limit-type theorem for rotations by Matthies, Muller & Vinel [Textures Microstruct. (1988), 10, 77–96], with the Brownian-diffusion distribution on S4+ ≡ H3, recalls the fact that no simple analog of the central limit theorem in Euclidean space exists for arbitrary spaces and manifolds, e.g. for SP, SP+, SO(p), p ≥ 2. Therefore, interpretations of preferred orientations in terms of mechanisms of texture development related to an imaginary simple analog of the central limit theorem would generally be misleading. Individual crystal-orientation measurements may initially require different nonparametric methods of analysis. As a counterpart of pole-to-orientation density inversion of diffraction data, hyperspherical kernel orientation density estimation is suggested for individual orientation measurements. With the application of non-negative kernels, the estimated orientation density is always non-negative. The critical smoothing parameter of this method is determined on information-theoretical grounds. For patterns of preferred orientation too complex to be sufficiently approximated by the parametric Bingham model distribution, a clustering of individual orientation measurements into disjunct classes is suggested that relates similarity of orientations to multimodality of the estimated orientation density; each class of orientations may then be individually analyzed by parametric methods.

Oblique fabrics in porphyroclastic Alpine-type peridotites: a shear-sense indicator for upper mantle flow

A detailed structural study in Alpine-type peridotites of the ultramafic Voltri Massif in NW Italy reveals the existence of oblique fabrics in porphyroclastic tectonites. The dominant foliation of these tectonites is defined by stretched pyroxenes and aligned grains of spinel, which formed as a result of high-temperature flow in a km-scale shear zone bounded by a wall-rock of granular, virtually undeformed spinel-lherzolites. The oblique fabrics in these tectonites are characterized by elongate olivine grain shapes and a marked grain boundary alignment oriented at an angle of up to 40° to the tectonite foliation. In addition, kink-type subgrain boundaries are frequently parallel to (100), and show a preferred orientation at large angles to the tectonite foliation. Olivine lattice preferred orientation patterns in tectonites with this oblique grain shape fabric show bimodal distributions of [100] and [001]. The oblique fabrics and bimodal orientation distributions are inferred to result from the formation of high-angle kink-like grain boundaries followed by deformation-induced grain boundary migration at the expense of unfavourably oriented grains. The sense of shear derived from the oblique fabrics is consistent with the sense of shear derived from the lattice preferred orientation patterns, asymmetric pyroxene porphyroclast systems and the map-scale geometry of the shear zone in which these microstructures occur. It is therefore suggested that these oblique grain shape fabrics represent a reliable kinematic indicator for high-temperature flow in upper mantle shear zones.

Vorticity analysis in a metachert from the Sanbagawa Belt, SW Japan

Common tectonic features of deformed metachert include both sets of extended and shortened veins and quartz c-axis preferred orientation patterns. In such rocks information is also commonly available on the orientation and magnitude of the finite strain. These features can be used to derive two independent estimates of the degree of non-coaxiality during deformation. In an example from the Sanbagawa Belt, SW Japan, the two methods give consistent results and show that deformation was intermediate between simple and pure shear. Such types of progressive deformation distributed over a broad region could cause substantial subvertical thinning and be a significant factor in the exhumation of high P- T rocks in the region.

Local variations in quartz [ c]-axis orientations in non-coaxial regimes and their significance for the mechanics of S- C fabrics

The quartz [ c]-axis orientations of quartz-bearing S- C mylonites vary on the mm scale. Two specimens from different tectonic settings (the Variscan Schwarzwald, West Germany, and the Eastern Alps, Austria) are investigated. In the first specimen prism glide along ( a) predominates, and in the second specimen basal glide along ( a) predominates. In both specimens the pattern of [ c]-axis variations is similar—it is suggested to be characteristic of S- C mylonites. On the local scale, there are two patterns of preferred orientation: (1) a crossed-girdle, ‘type I’, which is inclined in a sense opposite to the inferred overall sense of shear. This occurs in moderately strained domains; (2) a single-girdle, which is slightly inclined in the same sense as the inferred overall sense of shear. This occurs in domains that suffered higher strain. Both types are considered to reflect stable orientations of the ‘easy glide direction; (crystallographic ( a) direction), at different stages of the deformational history. Two kinematic interpretations are discussed. Quartz [ c]-axis fabric variations reflect a spatial (and possibly also temporal) partitioning in flow path between domains that underwent either: (1) spinning coaxial flow and non-spinning non-coaxial flow; or (2) spinning non-coaxial flow and non-spinning non-coaxial flow, associated with variations in parameters of the deformation (such as magnitude of strain and strain rate) and perhaps also rate of recrystallization and recovery. In either interpretation, in moderately strained domains oblique [ c]-axis girdles are generated that cannot be used as shear-sense indicators.

Experimental study of grain-size sensitive flow of synthetic, hot-pressed calcite rocks

Abstract Synthetic calcite rocks of controlled grain-size were prepared by crushing large, clear calcite crystals, centrifuged to separate restricted grain-size fractions, cold-pressed and then hot-pressed to produce low-porosity polycrystals of mean grain-size covering the range 2–40 µm. These were deformed dry over the range 400–700°C, mainly at 200 MPa confining pressure, to investigate the onset with decreasing grain-size of grain-size sensitive flow. The deformation of the fine-grained material can be described by a flow law of the form ė = A exp (− H/RT ) σ n d m in which at low stresses (<25 MPa differential stress) A = 10 4.9 , H = 190 kJ mol −1 , n = 1.7 and m = −1.9, when strain-rate, ė , is in s −1 , stress, σ, is in MPa and grain-size, d is in µm. At higher stresses (25–250 MPa) A = 100, H = 190 kJ mol −1 , n = 3.3 and m = −1.3. In the low stress regime, grains remain equidimensional during flow, a pre-existing preferred crystallographic orientation produced during cold-pressing tends to weaken and grain-boundary sliding is important. At higher stresses, a grain flattening fabric develops, the pre-existing preferred crystallographic orientation pattern is preserved, and recovery-accommodated intracrystalline plastic flow is inferred to be the dominant deformation mechanism. Grain-size sensitivity of the flow stress persists even into the intracrystalline plastic flow regime. Grain-size insensitive flow only develops at grain-sizes greater than 40 µm, as demonstrated by reference to mechanical data for the flow of Carrara and Taiwan marbles. The flow laws which describe most of the experimental data do not extrapolate well through the lowest strain-rate data at the coarser grain-sizes. This indicates that a complete description of the flow, which can be used reliably to extrapolate to geological conditions, requires one or more of the material parameters A, n and m to be a function of one or more of stress, strain-rate and grain-size. This implies variable contributions from different deformation mechanisms as the deformation conditions change.

Microfabric development in the Torridonian rocks of the Kishorn Nappe, Lochalsh, North-West Scotland

Microstructural trends and quartz c -axis preferred orientation patterns have been studied in the Torridonian rocks of the recumbent Lochalsh syncline, and related to possible deformation, recovery and recrystallization mechanisms. The major microstructural trends observed in the quartz, with increasing deformation, include increased host grain flattening and progressive development of optical strain features, together with increases in c-axis misorientation in individual grains and the degree of recrystallization. The dominant mechanisms responsible for the optical strain features were dislocation glide and climb, but the dominant mechanism responsible for the total strain of the deformed rocks was a diffusive mass transfer process accompanied by grain boundary sliding. The development of new grains was principally due either to subgrain rotation or to nucleation of new grains by grain boundary bulging. The quartz c-axis orientation patterns show no overall recognisable trend, and the patterns obtained from host and new grains are markedly different. Angular relationships observed between host and new grains indicate that host control may be important during incipient recrystallization, but in the specimens showing significant recrystallization this relationship is not evident, due either to new grain rotation or an overall stress control.

Development of texture and elastic anisotropy during deformation of hcp metals

The inner core of the earth most likely consists of ϵ (hcp) iron and shows anisotropy of seismic velocities which could be explained by crystallographic preferred orientation developing during convective flow. This paper summarizes deformation mechanisms in hcp metals and applies the Taylor theory of polycrystal deformation to analogs of ϵ‐iron for different strain histories. The pattern of preferred orientation is then used to calculate elastic properties of deformed polycrystals with special emphasis on anisotropy.

Efficient use of the velocity gradients tensor in flow modelling

For models of fabric development in rocks, with vorticity as a variable parameter, the choice of an unsuitable reference frame for instantaneous flow can hamper clear presentation of results. The orientation of most fabric elements which develop in deforming rocks is attached to some principal direction of instantaneous flow: syntaxial fibres, crystallographic preferred orientation patterns, steady state foliations and immobilised rigid objects seem to orient themselves in a fixed position relative to instantaneous stretching axes ( d i ), while shape fabric elements and mica preferred orientation approach parallelism with the extensional apophysis ( I 1) of the flow. Models for development of such fabric elements benefit from a choice of reference frame attached to either d i or l 1.

Preferred lattice orientations of plagioclase from amphibolite and greenschist facies rocks near the Insubric Line (Western Alps)

Preferred lattice orientations of plagioclase, measured by the universal stage, from deformed amphibolite and greenschist facies rocks near the Insubric Line (Western Alps), reflect the type and orientation of the strain system: either (001) or (010) are oriented parallel or subparallel to the schistosity and form more or less complete girdles around the stretching direction. By the preferred orientation patterns dominant (010) [001] slip is indicated and, additionally, slip on (001) parallel to the a direction, possibly at somewhat higher temperatures and/or at a higher An content of the plagioclase. It is suggested that obliquities of the symmetry-planes of the orientation patterns against the principle axes of strain are related to the sense of shearing.

Pure shear and simple shear calcite textures. Comparison of experimental, theoretical and natural data

The pattern of lattice preferred orientation (texture) in deformed rocks is an expression of the strain path and the acting deformation mechanisms. A first indication about the strain path is given by the symmetry of pole figures: coaxial deformation produces orthorhombic pole figures, while non-coaxial deformation yields monoclinic or triclinic pole figures. More quantitative information about the strain history can be obtained by comparing natural textures with experimental ones and with theoretical models. For this comparison, a representation in the sensitive three-dimensional orientation distribution space is extremely important and efforts are made to explain this concept. We have been investigating differences between pure shear and simple shear deformation incarbonate rocks and have found considerable agreement between textures produced in plane strain experiments and predictions based on the Taylor model. We were able to simulate the observed changes with strain history (coaxial vs non-coaxial) and the profound texture transition which occurs with increasing temperature. Two natural calcite textures were then selected which we interpreted by comparing them with the experimental and theoretical results. A marble from the Santa Rosa mylonite zone in southern California displays orthorhombic pole figures with patterns consistent with low temperature deformation in pure shear. A limestone from the Tanque Verde detachment fault in Arizona has a monoclinic fabric from which we can interpret that 60% of the deformation occurred by simple shear.

Kinematic and tectonic significance of microstructures and crystallographic fabrics within quartz mylonites from the Assynt and Eriboll regions of the Moine thrust zone, NW Scotland

ABSTRACTUsing a combination of optical microscopy and X-ray texture goniometry, an integrated microstructural and crystallographic fabric study has been made of quartz mylonites from thrust sheets located beneath, but immediately adjacent to, the Moine thrust in the Assynt and Eriboll regions of NW Scotland. A correlation is established between shape fabric symmetry and pattern of crystallographic preferred orientation, a particularly clear relationship being observed between shape fabric variation and quartza-axis fabrics.Coaxial strain paths dominate the internal parts of the thrust sheets and are indicated by quartzc- anda-axis fabrics which are symmetrical with respect to foliation and lineation. Non-coaxial strain paths are indicated within the more intensely deformed quartzites located near the boundaries of the sheets by asymmetricalc- anda-axis fabrics. These kinematic interpretations are supported by microstructural studies. At the Stack of Glencoul in the northern part of the Assynt region, the transition zone between these kinematic (strain path) domains is located at approximately 20 cm beneath the Moine thrust and is marked by a progression from symmetrical cross-girdlec-axis fabrics (30cm beneath the thrust), through asymmetrical cross-girdlec-axis fabrics to asymmetrical single girdlec-axis fabrics (0·5 cm beneath the thrust).Tectonic models (incorporating processes such as extensional flow, gravity spreading and tectonic loading) which may account for the presence of strain path domains within the thrust sheets are considered, and their compatibility with local thrust sheet geometries assessed.

Calcite fabrics in a natural shear environment, the Helvetic nappes of western Switzerland

The aim of this contribution is to describe and interpret the crystallographic orientations and microstructures of calcite in the Upper Jurassic limestones of the Helvetic nappes between the Mont Blanc and Aar massifs, over a distance along strike of about 180 km. The c-axis preferred orientation pattern, which could be inferred, is regionally very constant. The c-axis point maxima are everywhere subperpendicular to the regional strike of the chain. There is an obliquity between the orientation of the macroscopically dominant cleavage and the microscopically visible long axes of individual grains: the c-axis maxima in most specimens are parallel to the axis of shortening of the microscopic grain-shape fabric. This fabric geometry indicates either continuous shear deformation, or, alternatively, a two stage deformation history. The obliquity of the grain-shape fabric may be due to the fact that the flattening plane of the individual grains reflects only the last increment of a continuous shear process, or it may represent a later finite deformation, which has led to the formation of a regionally developed second cleavage. There is a systematic relationship between the direction of these late shear movements and the main overthrust direction as given by the finite strain pattern. This suggests that the microfabric of the rocks was acquired during a progressive rotation with time of the main overthrust direction. The observed pattern of preferred orientation has been correlated by several authors with intracrystalline deformation mechanisms, a combination of slip on r and twinning on e. However, the e-twinning observed in the specimens investigated is younger than the development of the crystallographic fabric. A new method for stress determination from e-twinning is proposed.

Secondary lineation in a high-T quartzite (Galicia, Spain): an explanation for an abnormal fabric

Using refractory inclusions in quartz grains as a marker for the X finite direction ( Xf) of the strain undergone by the quartzites it is shown, in our case, that the shape preferred orientation of the quartz grains ( Xq). is perpendicular to Xf within the foliation plane and is a secondary lineation. According to that reinterpreted frame, the lattice preferred orientation patterns become ‘normal’, resulting from the dominant activity of the {m} ( a) slip systems in a non-coaxial shear regime, and not from [c] slip. Development of Xq is attributed to grain-growth during a post-tectonic thermal event, with a faster rate of boundary migration parallel to [c] and without substantial change in the lattice fabric. TEM data give support to the latter interpretation but do not demonstrate the absence of [c] slip. This example suggests that a close examination of the significance of the grain-shape lineations is necessary in case of high-temperature deformations. Operation of [c] as a dominant slip direction, identified in experimental deformation of high water-content synthetic quartz crystals, is still to be established in natural quartz tectonites.

Sense of nappe emplacement from quartz c-axis fabrics; an example from the Betic Cordilleras (Spain)

Preferred crystallographic orientation patterns (fabrics) in zones of ductile deformation beneath nappes are a potentially useful indicator of the sense of nappe translation. Quartz c-axis fabrics from a shear zone beneath the pile of Higher Betic nappes in the Betic Cordilleras (Spain) have distinctly asymmetric topologies, revealed by constructing a fabric skeleton. These skeletons closely resemble those produced by computer simulations of quartz fabric development basedon Taylor-Bishop-Hill theory. The fabric asymmetry indicates a northerly sense of transport for the nappes, consistent with field evidence from the same area. Analyses of both c- and a-axis fabrics based on asymmetric intensity distributions within the fabric give equivocal results, and may reflect the presence of earlier preferred orientation patterns, predating nappe emplacement.

Effects of tableting procedures on the preferred orientation of crystalline particles.

The effects of tableting procedures on the preferred orientation of phenacetin and aspirin crystals in a tablet were investigated. Among aspects of tableting procedures which might affect the preferred crystal orientation, the granulation process, the shape of the punch and the addition of magnesium stearate were investigated. A wet granulation method decreased the mobility of crystals during compression, and thus reduced the degree of preferred orientation. This phenomenon was considered to be one of reasons for the improved lamination properties seen with the granulation method. The shape of the punch affected the preferred orientation ; a concave punch caused a more complex preferred orientation pattern than a flat punch. The preferred orientation was considered to correspond to the stress distribution in a tablet. Magnesium stearate reduced the interparticle friction and facilitated the attainmnet of preferred orientation. The characteristic preferred orientation of crystals in the neighborhood of the upper surface and side surface of a tablet was investigated. The broadest faces of crystals were aligned in parallel to the upper punch face and the die wall.

The microfabric of calcite tectonites from the Helvetic Nappes (Swiss Alps)

Summary The crystallographic orientations of calcite in tectonites from the Morcles Nappe and the Glarus Overthrust have been measured by X-ray texture goniometry. The orientation data are represented by pole figures, inverse pole figures and as orientation distribution functions. The patterns of preferred orientation observed in the specimens from the Morcles Nappe are correlated with intracrystalline slip mechanisms. The patterns exhibit quasiaxial symmetry and in some cases the axis of symmetry is oblique to the symmetry of the macroscopic fabric. This obliquity is interpreted as the result of a rotational strain path and may be used to infer direction and sense of shear. Some specimens of the Lochseiten mylonite from the Glarus Thrust show no strong preferred crystallographic orientation. This suggests that grain boundary sliding was the major deformation mechanism.

Oblique girdle orientation patterns of quartz C-axes from a shear zone in the basement core of the Maggia Nappe Ticino, Switzerland

In the granitic basement of the Maggia Nappe, a pre-existing quartz C-axis fabric has been modified by later shearing. The progressive changes in the preferred orientation patterns of quartz across one boundary of a shear zone are described. A single girdle fabric is developed and a reference framework to specify the ‘obliquity’ of such fabrics with respect to the major axes of the finite strain ellipsoid, is introduced.

Petrofabric analysis of Saxony Granulites by optical and X-ray diffraction methods

The regional development of distinct patterns of preferred orientation of quartz c-axes in the Saxony Granulites has been well documented in the literature. A suite of specimens representative of these fabrics has been examined both by optical universal stage, to determine quartz c-axis orientation, and by X-ray diffraction, to obtain orientation data from r, z, m and a. The data are combined to yield inverse pole figures of schistosity and lineation. The finite strain of the Saxony Granulites is thought to be essentially a flattening and there is no evidence that the deformation path is other than one of continuous flattening. Elongation in the plane of the schistosity is local and not extreme. Because of this apparently simple deformation picture, and because preliminary transmission electron microscopy reveals the presence of dislocation structures similar to those found in deformed metals, an attempt is made to interpret the quartz orientation in terms of dislocation slip mechanisms. There is some evidence that the activation of different mechanisms is perhaps primarily controlled by temperature. At least some of the patterns of preferred orientation of quartz were probably produced by deformation in the field of stability of α-quartz.