B. E. Hobbs

Recrystallization of single crystals of quartz

Abstract Three types of experiment have been carried out to investigate the influence of stress, strain and initial crystallographic orientation on the recrystallization of single crystals of quartz. These experiments are: (1) stress annealing experiments, in which the specimen is loaded to a high differential stress at a relatively low temperature and the temperature then rapidly increased to a higher value while the differential stress is present; (2) annealing experiments in which the specimen is deformed at a low temperature and then heated under hydrostatic stress at a higher temperature; (3) syntectonic recrystallization experiments in which the specimen is deformed to high strains at a constant strain rate and high temperature. All experiments were conducted at 10 or 15 kbar confining pressure and at temperatures in the range 300°–1,400°C. Recrystallization does not take place in any of these experiments unless trace amounts of (OH) are present in the quartz structure. In both stress annealing and annealing experiments, nucleation of new grains takes place along narrow kink bands and the new grains have approximately the same orientation of c as that within the kink zones. The host orientation appears to exert a considerable control over the orientations of grains that ultimately grow to form an aggregate of polygonal grains. Grains in which c lies at 20°–40° to the adjacent host c-axis grow fastest; grains in which c lies at 0°–10° to the adjacent host c-axis rarely appear in the final preferred orientation. In syntectonic recrystallization experiments, nucleation and growth of new grains from submicroscopic regions does not appear to take place. Rather, subgrains that form in deformation bands at low strains increase their relative misorientations as the strain increases until an array of diversely oriented grains with sharp grain boundaries develops. The resulting preferred orientations may be interpreted in terms of a host control similar to that observed in annealing experiments or as a tendency for new grains to form with c-axes at 50° to the axis of shortening. At 15 kbar confining pressure and temperatures above 800°C, coesite nucleates and grows in highly strained single crystals of quartz.

The simulation of fabric development in plastic deformation and its application to quartzite: The model

Abstract The Taylor-Bishop-Hill model for polycrystalline deformation has been applied as the basis of a computer program for simulating the development of preferred crystallographic orientations in deforming rocks in which the predominant mode of deformation is dislocation glide within the grains. The model assumes homogeneous deformation on the scale of the grains and rigid-plastic flow obeying Schmids critical resolved shear stress law for the glide systems. The input data for the simulation are the initial orientation distribution, the set of possible glide systems and their relative critical shear stresses, and the details of the deformation including its path, which can involve non-coaxial deformation histories in the general case. The analysis is applied to model quartzites in which four possible choices of glide systems and their critical resolved shear stresses are considered, for three different deformations. Some of the simulated fabrics bear close similarity to observed fabrics, suggesting that fabric development as a result of rotation of crystal axes during dislocation glide is potentially an important geological process, and that the Taylor-Bishop-Hill model is suitable for analyzing it. From the profound influence of deformation history on the simulated fabric and the sensitivity of the fabric to the choice of glide systems and their relative critical shear stresses, important possibilities are suggested for gaining information about geological environment and deformation history from the analysis of natural deformation fabrics.

The strength of the continental crust, detachment zones and the development of plastic instabilities

Abstract The maximum strength of the continental crust is constrained by the geothermal gradient, the lithological make-up of the crust, and whether or not the Byerlee relation holds to the base of the continental crust. If this linear (Byerlee) relation holds, then maximum shear stress levels sustained at low geothermal gradients (10–20°C km −1 ) could be as high as 300 MPa in the upper part of the mantle for strike-slip regimes, and up to 700 MPa in thrust regimes towards the base of the crust. However, if Byerlees relation breaks down at moderate temperatures and pressures, and if such breakdown is associated with the transition from unstable to stable sliding on pre-existing faults, then the maximum stress levels in the crust, being set by the shear stress at the breakdown depth, are much lower, ca. 300 MPa for low geothermal gradients and thrust regimes. The lithosphere is quite weak below the crust for geothermal gradients greater than 20 ° C km −1 so attempts to treat the lithosphere as an elastic slab for time scales for which plastic flow contributes significantly to the deformation should be questioned. For a geothermal gradient of 10°C km −1 , the entire continental crust and part of the upper mantle behave as an elastic-brittle slab. At higher geothermal gradients, the distribution of strength is variable vertically according to the magnitude of the geothermal gradient and the lithological make-up; large contrasts in strength occur across rheologically defined boundaries as well as across lithological boundaries. At these higher geothermal gradients, such contrasts in strength could act as nuclei for detachment zones within the continental crust and upper mantle. Detachment at or near the Moho is to be expected only for low geothermal gradients. Lateral variations in the geothermal gradient produce shallowly dipping zones of highly contrasting strength throughout the continental crust and uppermost mantle possibly resulting in flat lying thrusts and normal faults which may ramp upwards through the crust. Instabilities leading to seismic events which occur solely during plastic shearing should be common in thrust terranes where the stresses are relatively high (ca. 100–200 MPa), for geothermal gradients ranging from 10 to 50°C km −1 and for quartz-rich, felsic, mafic, and peridotitic rock types. Thrust terranes are therefore predicted to be characterized by coseismic plastic instabilities on all detachment zones throughout the crust and into the uppermost mantle but embryonic rift zones should be aseismic at depth ( > ca. 10 km).

Instability, softening and localization of deformation

Abstract Material strain softening is commonly taken as a necessary and sufficient condition for localization in deforming rocks. However, there is a wide range of experimental and theoretical information which shows that localization can occur in sands, brittle rocks and ductile metals under strain-hardening conditions. This paper aims to bring these two contrasted views together. Three separate criteria are necessary in order to understand localization behaviour. The first involves the stability of the deforming system. The second determines whether a deforming system will undergo bifurcation so as to cease deforming in a homogeneous mode and instead deform in an inhomogeneous mode such as barrelling or localization. The stability and bifurcation criteria are independent of each other since barrelling is a stable mode whereas localization is unstable. The third criterion establishes if the unstable bifurcation mode is one of localization or of some other kind. Localization may arise from the presence of vertices on the yield surface (as in the case of pressure insensitive, rate dependent metals and in brittle rocks due to the development of preferred microfractures for slip) or from the constitutive relation being such that the plastic strain-rate vector is not normal to the yield surface (as in the cases of pressure sensitive, dilatant rocks, of materials deforming by crystal-plastic processes involving dislocation cross-slip and/or climb, and of visco-plastic materials in which voids are forming due to diffusive processes). It is important to distinguish between material and system softening (or hardening) behaviour. The theory for a kinematically unconstrained shortening experiment (that is, rigid, frictionless platens) indicates that localization can occur in strain-hardening materials but the system must strain-soften from then on; that is, localization occurs at peak stress for the system even though the material may continue to harden (or soften). However, the addition of kinematic constraints (such as friction at elastic platens, a constraint to deform in plane strain or at constant volume) means that localization may occur in a system that is monotonically strain hardening. Shear zones in naturally deformed rocks show ample evidence of dilatant behaviour in that evidence for the passage of large volumes of fluid during localization is common as is the development of dilatant vein systems. As such, since shear zones are strongly constrained by the elastic and (limited) plastic response of the relatively undeformed rocks surrounding the shear zones, strain-hardening behaviour of the system is to be expected as the norm, even if the rocks within the shear zones are undergoing material strain-softening.

Chemical and deformational controls on recrystallization of mica

Chemical and microstructural data from one experimentally and two naturally deformed and recrystallized micas are discussed in terms of established metallurgical mechanisms for strain-induced nucleation and growth during recrystallization. It is suggested that none of these nucleation mechanisms is applicable, and that nucleation is driven by energy from both chemical and permanent strain sources. Subsequent growth of the nuclei is influenced by the deformation or by coincidence lattice relationships.

Geodynamic modelling of the Century deposit, Mt Isa Province, Queensland

This paper is concerned with an example of quantitative modelling of orebody formation as a guide to reducing the risk for future mineral exploration. Specifically, the paper presents a detailed 3–D numerical model for the formation of the Century zinc deposit in northern Queensland. The model couples fluid flow with deformation, thermal transport and chemical reactions. The emphasis of the study is a systems approach where the holistic mineralising system is considered rather than concentrating solely on the mineral deposit. In so doing the complete plumbing system for mineralisation is considered with a view to specifying the critical conditions responsible for the ore deposit occurring where it does and having the size and metal grades that are observed. The numerical model is based on detailed geological, tectonic, isotopic and mineralogical data collected over the past 20 years. The conclusions are that the Century zinc deposit is located where it is because of the following factors: (i) a thermal anomaly is associated with the Termite Range Fault due to advection of heat from depth by fluid flow up the Termite Range Fault; (ii) bedding‐plane fissility in the shale rocks hosting the Century zinc deposit has controlled the wavelength and nature of D1 folding in the vicinity of the deposit and has also controlled increases in permeability due to hydrofracture of the shales; such hydrofracture is also associated with the production of hydrocarbons as these shales passed through the ‘oil‐window’; (iii) Pb–Zn leached from crustal rocks in the stratigraphic column migrated up along faults normal to the Termite Range Fault driven by topographic relief associated with inversion at the end of the Isan Orogeny; these fluids mixed with H2S derived at depth moving up the Termite Range Fault to mix with the crustal fluids to precipitate Pb–Zn in a plume downstream from the point of mixing. Critical factors to be used as exploration guides are high temperatures, carbonaceous fissile shales now folded into relatively tight D1 folds, fault‐controlled plumbing systems that enable fluid mixing, depletion of metals upstream of the deposit and,in particular,a very wide Fe‐depletion halo upstream of the deposit.

Finite element modelling of temperature gradient driven rock alteration and mineralization in porous rock masses

We present finite element simulations of temperature gradient driven rock alteration and mineralization in fluid saturated porous rock masses. In particular, we explore the significance of production/annihilation terms in the mass balance equations and the dependence of the spatial patterns of rock alteration upon the ratio of the roll over time of large scale convection cells to the relaxation time of the chemical reactions. Special concepts such as the gradient reaction criterion or rock alteration index (RAI) are discussed in light of the present, more general theory. In order to validate the finite element simulation, we derive an analytical solution for the rock alteration index of a benchmark problem on a two-dimensional rectangular domain. Since the geometry and boundary conditions of the benchmark problem can be easily and exactly modelled, the analytical solution is also useful for validating other numerical methods, such as the finite difference method and the boundary element method, when they are used to deal with this kind of problem. Finally, the potential of the theory is illustrated by means of finite element studies related to coupled flow problems in materially homogeneous and inhomogeneous porous rock masses.

Finite element analysis of steady-state natural convection problems in fluid-saturated porous media heated from below

In this paper, a progressive asymptotic approach procedure is presented for solving the steady-state Horton-Rogers-Lapwood problem in a fluid-saturated porous medium. The Horton-Rogers-Lapwood problem possesses a bifurcation and, therefore, makes the direct use of conventional finite element methods difficult. Even if the Rayleigh number is high enough to drive the occurrence of natural convection in a fluid-saturated porous medium, the conventional methods will often produce a trivial non-convective solution. This difficulty can be overcome using the progressive asymptotic approach procedure associated with the finite element method. The method considers a series of modified Horton-Rogers-Lapwood problems in which gravity is assumed to tilt a small angle away from vertical. The main idea behind the progressive asymptotic approach procedure is that through solving a sequence of such modified problems with decreasing tilt, an accurate non-zero velocity solution to the Horton-Rogers-Lapwood problem can be obtained. This solution provides a very good initial prediction for the solution to the original Horton-Rogers-Lapwood problem so that the non-zero velocity solution can be successfully obtained when the tilted angle is set to zero. Comparison of numerical solutions with analytical ones to a benchmark problem of any rectangular geometry has demonstrated the usefulness of the present progressive asymptotic approach procedure. Finally, the procedure has been used to investigate the effect of basin shapes on natural convection of pore-fluid in a porous medium

Dislocations associated with optical features in naturally-deformed olivine

Transmission electron microscopy has been used for the direct observation of dislocations in naturally-deformed olivine. The dislocations are arranged in arrays forming low-angle sub-boundaries which have been identified with features observed in the optical microscope. Comparison of this dislocation substructure with that observed in olivine, and in metals, experimentally deformed under various conditions, suggests that the deformation in nature has occurred by creep. Possible mechanisms of creep, involving the cooperative glide and climb of dislocations, are discussed.

Dislocation Structure of the Deformation Lamellae in Synthetic Quartz; a Study by Electron and Optical Microscopy

Single crystals of experimentally deformed synthetic quartz showing optical deformation lamellae were examined by transmission electron microscopy. Dislocations are distributed fairly uniformly throughout the crystal. However, parallel to the trace of the deformation lamellae, which may be irrational, there are walls of tangled dislocations whose characteristics suggest that they are directly associated with the lamellae. The nature and formation of the optical image is discussed in detail.