Abstract Deformation, in large parts of the middle crust, results in strained rocks consisting of grains with variable dislocation densities and microstructures which are characterized by gradual distortion and subgrain structures. Post-deformation residence of these rocks at elevated temperatures results in microstructural adjustments through static recovery and recrystallization. Here, we employ a numerical technique to simulate intragrain recovery at temperatures at or below the deformation temperature. The simulation is based on minimization of the stored energy, related to misorientation through local rotation of physical material points relative to their immediate environment. Three temperature- and/or deformation-geometry-dependent parameters were systematically varied: (1) deformation-induced dislocation types, (2) dislocation mobility and (3) size of dislocation interaction volume. Comparison with previously published in situ experiments shows consistency of numerical and experimental results. They show temperature- and dislocation-type-dependent small-scale fluctuations in subgrain-boundary misorientations and orientation variation within subgrains. These can be explained by the combined effect of increase in dislocation interaction volume and activation of climb. Our work shows microstructure can be significantly modified even if the post-deformational temperature is at or below the deformation temperature: a scenario relevant for most deformed rocks.

Abstract This chapter introduces basic concepts of numerical modelling of materials on the atomic scale. An atomic interaction potential is at the core of each simulation. Static energy calculations and molecular dynamics simulations are common approaches to study crystal defects, such as point defects, dislocations and grain boundaries, phase transitions and diffusion processes in solids and liquids. The application of these powerful methods to geological materials is demonstrated with a number of examples. An important challenge for the future appears to be the crossover between accurate and predictive atomic-scale models and the continuum scale at which material properties are conventionally described. Some recent developments in this field are discussed.

Abstract All condensed phases (solids and liquids) have interfaces where they are in contact with other phases. Materials such as ceramics, metals and rocks comprise a multitude of grains of a single phase or of several different phases that are connected through a three-dimensional network of interfaces. Although the interfaces usually occupy only a negligible fraction of the overall volume, they control many of the material’s physical properties such as mechanical strength, toughness, electrical conductivity, magnetic susceptibility, effective diffusivities, corrosion resistance and many more. We refer to an aggregate of crystals of a single phase as a ‘polycrystal’. A composite material that is composed ofgrains ofdifferent phases is referred to as a ‘polyphase aggregate’. An interface, where two crystals of the same phase that only differ in their lattice orientations are in contact, is referred to as a ‘grain boundary’. An interface, where two different phases meet, constitutes a ‘phase boundary’. Solid-liquid, solid-vapour and liquid-vapour interfaces as well as interfaces between two different solids are phase boundaries. The topology and geometry of the grain- and phase-boundary network is controlled by a compromise between micro-structural equilibrium and space filling. Furthermore, the network of interfaces may evolve, e.g. under elevated temperatures. In the absence of mineral reactions and deformation, this evolution is driven by the reduction ofthe free energy associated with interfaces. Both grain and phase boundaries are essentially two-dimensional objects. For example, the generally employed formulation of the diffusion equation that approximates diffusion along an interface involves two spatial coordinates. The third dimension, which is perpendicular to the interface, is represented by a small characteristic width, which may be only a few inter-atomic distances. The effective diffusion coefficient that enters into the surface diffusion equation depends on the width of the surface. The microstructures and textures observed in rocks exhibit an overwhelming diversity ( Vernon, 2004 ). They bear important information on rock formation and have significant control over bulk-rock properties and behaviour. Interfaces are the locations where both reactions and chemical mass transfer take place, and they are thus central in mediating mineral reactions, rock alteration and deformation. Furthermore, epitaxial and topotaxial orientation relations are established at interfaces (see Habler and Griffths, 2017, this volume). In this chapter we introduce the phenomenological treatment of interfaces. The concepts of interfacial energy and surface tension are discussed and conditions for micro-structural equilibrium are derived. Thereafter, capillary force driven interface motions including coarsening and grain-growth are addressed. We investigate thermodynamic equilibrium at curved interfaces and its implication for the evolution of heterogeneous systems. Finally, we treat some specific properties and the motion of interfaces in crystalline materials. Although most of the considerations made in this chapter are ofa general nature, the applications we have in mind are related to minerals and rocks.

Abstract Crystallographic orientation relationships (CORs) of next-neighbour crystals represent a special case of crystallographic preferred orientation (CPO), where relative crystallographic orientations of neighbour-crystals follow defined rules of misorientation systematics (COR rules). The presence/absence and nature of crystallographic orientation relationships between next-neighbour crystals can be used to infer petrogenetic information from polycrystalline materials provided that the processes of COR formation are understood and parameters that control the kinetics of COR formation can be identified. After giving an overview on COR terminology, this chapter highlights non-genetic criteria for COR characterization, including a discussion of analytical methods that are used to constrain these criteria. The development of electron backscatter diffraction (EBSd) in scanning electron microscopy (SEM) has provided new information on CORs, which is complementary to data obtained from transmission electron microscopy (TEM) analysis. Based on these non-genetic criteria, different types of CORs are characterized. Subsequently, physical parameters that can potentially influence COR formation are discussed. Furthermore, different scenarios and mechanisms leading to COR formation are outlined together with examples from experiments and from natural mineral and rock systems. The different boundary conditions of COR formation in various petrogenetic scenarios and the potential mechanisms that have to be taken into account when studying COR genesis are addressed. This chapter highlights the necessity of a multi-stage investigative approach in COR studies. First, the presence/absence and nature of CORs needs to be analysed based on non-genetic criteria. In a second step the formation mechanism of the CORs under consideration must be constrained, before in a third step, petrogenetic information can potentially be inferred. Moving from the second to the third step requires understanding of the parameters controlling COR development, which is by no means complete and leaves open tasks for future COR research.

Abstract Mapping on the microstructural scale can contribute significantly to conventional field and larger scale mapping and understanding of spatial, temporal and process-oriented relationships. Here, electron backscattered diffraction (EBSD)-based microstructural maps are presented of subgrain and Dauphiné twin boundaries in undeformed sedimentary quartzite. ‘Plane matching’ analysis permits determination of the complete orientation of boundaries. A workflow is presented to facilitate the necessary crystallographic calculations. The resulting maps indicate: (1) boundary plane rotation angle/axis pairs, including tilt–twist components; (2) boundary migration vectors; and (3) conventional EBSD misorientation angle/axis pairs. Subgrain boundaries are general with small misorientations and boundary plane normal directions sub-parallel to grain boundary stress concentrations; rotation axes are oriented sub-parallel to the bedding dip (017°/10°E). Most exhibit bi-direction boundary migration vectors parallel to bedding normal. The EBSD misorientation analysis results are different as they only recognize the parallelism of adjacent crystal lattices. The differences are especially apparent for Dauphiné twin boundaries. Maps are presented of twin boundaries using matched plane analysis, including explanation for lateral twin migration. Driving forces to move twin boundaries are also estimated by mapping variations in Young's modulus between parents and twins; differences are significant, indicating that the Young's modulus and driving forces do not need to be large, explaining the propensity for twinning in many quartzites.