Fundamentals of Substructure Dynamics In-Situ Experiments and Numerical Simulation

Meddelanden fr˚an Stockholms Universitets Institution f¨or Geologiska Vetenskaper No. 342

Fundamentals of substructure dynamics In-situ experiments and numerical simulation

Verity Borthwick

Stockholm 2010

Department of Geological Sciences Stockholm University S-106 91 Stockholm Sweden A Dissertation for the degree of Doctor of Philosophy in Natural Science

Department of Geological Sciences Stockholm University S-106 91 Stockholm Sweden

Abstract Substructure dynamics incorporate all features occurring on a subgrain-scale. The substructure governs the rheology of a rock, which in turn determines how it will respond to different processes during tectonic changes. This project details an in-depth study of substructural dynamics during post-deformational annealing, using single-crystal halite as an analogue for silicate materials. The study combines three different techniques; in-situ annealing experiments conducted inside the scanning electron microscope and coupled with electron backscatter diffraction, 3D X-ray diffraction coupled with in-situ heating conducted at the European Radiation Synchrotron Facility and numerical simulation using the microstructural modelling platform Elle. The main outcome of the project is a significantly refined model for recovery at annealing temperatures below that of deformation preceding annealing. Behaviour is highly dependent on the temperature of annealing, particularly related to the activation temperature of climb and is also strongly reliant on short versus long range dislocation effects. Subgrain boundaries were categorised with regard to their behaviour during annealing, orientation and morphology and it was found that different types of boundaries have different behaviour and must be treated as such. Numerical simulation of the recovery process supported these findings, with much of the subgrain boundary behaviour reproduced with small variation to the mobilities on different rotation axes and increase of the size of the calculation area to imitate long-range dislocation effects. Dislocations were found to remain independent to much higher misorientation angles than previously thought, with simulation results indicating that change in boundary response occurs at ∼7o for halite. Comparison of 2D experiments with 3D indicated that general boundary behaviour was similar within the volume and was not significantly influenced by effects from the free surface. Boundary migration, however, occurred more extensively in the 3D experiment. This difference is interpreted to be related to boundary drag on thermal grooves on the 2D experimental surface. While relative boundary mobilities will be similar, absolute values must therefore be treated with some care when using a 2D analysis.

c Verity Borthwick ISBN 978-91-7447-187-8, p 1–23 Cover: Printed by US-AB SU, Stockholm 2010 Fundamentals of substructure dynamics In-situ experiments and numerical simulation

Verity Borthwick

This doctoral thesis consists of a summary and four manuscripts. The presented manuscripts are referred to as Manuscript I – IV in the text.

Manuscript I — Borthwick, V.E. and Piazolo, S. (2010) Post-deformational annealing at the subgrain scale: temperature dependent behaviour revealed by in-situ heating experiments on deformed single crystal halite. Journal of Structural Geology, 32, 982-996. Reprinted with permission from Elsevier

Manuscript II — Borthwick, V.E., Schmidt, S., Piazolo, S., Gundlach, C., Griera, A., Bons, P.D. and Jessell, M.W. (2010) The application of in-situ 3D X-ray Diﬀraction in annealing experiments: First interpretation of substructure development in deformed NaCl. Recrystallization and Grain Growth, Proceedings of the International Conference of Recrystallization and Grain Growth. In press.

Manuscript III — Borthwick, V.E., Schmidt, S., Piazolo, S. and Gundlach, C. In-situ 3DXRD annealing of a geological material: Evaluating the validity of 2D. To be submitted to Nature Geoscience.

Manuscript IV — Borthwick, V.E., Piazolo, S., Evans, L., Griera, A. and Bons, P.D. Numerical simulation coupled with in-situ annealing experiments: A new model for recovery. To be submitted to Acta Materialia.

The work of this thesis has principally been carried out by the author. All four manuscripts were predominantly written by the author with support, suggestions and extensive discussion from Sandra Piazolo. Experiments for Manuscript I were designed by Piazolo, and carried out with initial supervision by her and continued advice and assistance throughout the experimental process. Post-experimental processing and analysis was conducted by the author. For Manuscripts II and III the data reconstruction of full crystal diﬀraction patterns was conducted by Søren Schmidt. The six day experiment was run with the support of the other co-authors on II. Data analysis for both papers was conducted by the author. The numerical simulation in Manuscript IV was written by the author in close collaboration with the co-authors. Testing of the simulation and interpretation were conducted by the author with assistance from Sandra Piazolo.

Stockholm, October 2010 Verity Borthwick

To Mumedean and Grandpa Ronald, I know you would have been proud

Contents

1 Project aim 1 1.1 Why study substructure dynamics?...... 1 1.2 Overall approach...... 1 1.3 Mineral Substructure Dynamics – a European wide-network...... 1

2 Background 2 2.1 The deformed state...... 2 2.2 Post-deformational annealing...... 2 2.3 Halite as an analogue...... 4 2.4 2D In-situ annealing experiments...... 5 2.5 3D X-ray diﬀraction...... 5 2.6 Numerical simulation...... 6

3 Methods 6 3.1 2D in-situ annealing and EBSD...... 6 3.1.1 Data processing...... 6 3.2 3D X-ray diﬀraction...... 7 3.2.1 Data analysis...... 9 3.3 Numerical modelling...... 9 3.3.1 Data analysis...... 11

4 Results and discussion 11 4.1 Manuscript I...... 11 4.2 Manuscript II...... 12 4.3 Manuscript III...... 12 4.4 Manuscript IV...... 13

5 Summary and conclusions 13

6 Main outcomes 14

7 Future work 16

8 Acknowledgements 16

1 Project aim behaviour dependent on these types of dislocations? 1.1 Why study substructure dynamics? 4. Can we predict subgrain boundary behaviour? Microstructures hold the key to understanding tectonic behaviour on the most fundamental of scales. 5. Can we use substructure and subgrain bound- Deformation of rocks in the crust and mantle ary behaviour to derive deformation and/or mostly occurs by crystal-plastic mechanisms such annealing conditions? as dislocation creep. Individual crystals within a rock respond to strain by forming defects in the crystal lattice. These form a microscale sub- 1.2 Overall approach structure of dislocation arrays, free dislocations The project involves a three-technique approach. and a network of subgrain boundaries (Humphreys The starting point for this work began with 2D and Hatherly, 2004 and references therein). On in-situ annealing experiments conducted inside the a macroscale these substructures effect the rheol- scanning electron microscope (SEM) and coupled ogy of a rock (Ashby, 1969; Means and Xia, 1981; with electron backscatter diffraction (EBSD). A Ranalli, 1995; Passchier and Trouw, 2005). Thus, comparison experiment was conducted using 3D X- in order to investigate behaviour on a macroscale it ray diffraction (3DXRD) at the synchrotron facil- is essential to understand substructure dynamics. ity in Grenoble in order to rule out the potential of As a rock is exhumed to the crust it is affected by a surface effects in 2D experiments. Numerical simu- complex series of processes which change the sub- lation directly accessing results from the 2D exper- structure. In order to reconstruct this temperature- iments allowed development of theories and itera- time path it is necessary to predict the results of tive improvement of a new deterministic recovery these various changes. Post-deformational anneal- model. This thesis discusses aspects of the above ing is of particular interest, as this is often the last questions that we have answered throughout the process to affect a rock, occurring when pressure project period as well as highlighting areas which is removed but the system still retains a high tem- need further research. perature. It can still have a significant effect on the arrangement of the substructure. If we understand this process than we can potentially create 1.3 Mineral Substructure Dynamics a “window” through to the previous deformation – a European wide-network conditions (Fig.1). The precursor studies to this project were con- This PhD project is part of a European Science ducted by Bestmann et al. (2005) and Piazolo Foundation EUROCORES funded collaborative, et al. (2006). They conducted in-situ annealing EuroMinScI (European Mineral Science Initiative), experiments on a polycrystalline synthetic halite. which involves nine projects with researchers from Though substructural dynamics were not the focus twelve different countries. The purpose of the Eu- of these papers, subgrain boundary behaviour was roMinScI project is to draw together experimental observed to vary from that predicted by classical and computational techniques into integrated re- theory. Polygonisation into a subgrain boundary search programs with a focus on furthering atom- network was not followed by an increase in misori- istic understanding of structures, properties and entation, but some boundaries exhibited a decrease processes of minerals and metals. with some dissipating altogether. The Collaborative Research Project (CRP) this The project was begun with a number of specific study falls within involves ten linked projects from aims which are as follows: seven different countries. The main purpose of the CRP Mineral Substructure Dynamics (MinSubStr- 1. How does the substructure of a crystalline Dyn) is to investigate substructural behaviour us- material evolve with annealing? ing experimental techniques coupled with numerical simulations. This project is directly linked with 2. Definition of a subgrain boundary – what is a number of the other individual projects in the the critical minimum misorientation angle in CRP including that of A. Griera at the Université order for boundary behaviour to begin? Paul Sabatier in Toulouse and a group at the Ma- terials Research Division, Risø DTU in Denmark. 3. Which type of dislocations form different Fig.2 shows the setup of this PhD project, high- types of subgrain boundaries? How is their lighting how the associated projects are linked.

1 Figure 1: A cartoon depicting a rock being exhumed through the crust to the surface. Pictures are in chronological order a) The rock is subjected to high pressure and temperature in the crust and mantle. b) Erosion occurs and the rock is slowly brought to the surface. c) As the rock is exhumed pressure and temperature decrease, but temperature decrease occurs much more slowly and the rock is subjected to post-deformational annealing conditions. d) The rock reaches the surface with a preserved frozen-in microstructure from which the geologist tries to reconstruct the temperature-time path.

2 Background Bacon, 2001, Passchier and Trouw, 2005). As deformation continues, dislocation density increases 2.1 The deformed state as a result of new dislocations becoming trapped in tangles with existing dislocations (Humphreys and During deformation a crystal takes up strain by the Hatherly, 2004). introduction of defects, or “mistakes” into the lattice. Most of the energy necessary to deform a ma- 2.2 Post-deformational annealing terial is given out as heat, with only a small propor- tion (∼1%) remaining as stored energy which is de- The addition of defects during deformation makes rived from these defects (Humphreys and Hatherly, the crystal structure thermodynamically unstable 2004). They occur as either point defects, which due to the high stored energy (Fig.3). Thermody- are vacancies or additional interstitial molecules in- namics suggests that when the deforming process is serted into the lattice or as line defects (Hull and removed, the defects should disappear (Humphreys Bacon, 2001; Passchier and Trouw, 2005). Since and Hatherly, 2004). However, in reality these point defects are extremely mobile except at low processes are extremely slow at low homologous temperatures they do not contribute much to the temperatures. At higher temperatures however, overall stored energy of the system. Most of the these processes can be activated so that disloca- stored energy is a result of accumulation of line de- tions are removed or rearranged into lower energy fects, also known as dislocations. There are two configurations which can significantly alter the mi- types of dislocations, edge, which are due to an crostructure (Heilbronner and Tullis, 2002). After “extra” half lattice plane in the crystal and screw, deformation, a natural material in the crust re- which exist where part of the lattice is displaced mains at higher temperatures even when the pres- over one lattice distance, and is thus twisted (Pass- sure is removed. In other words as a rock is ex- chier and Trouw, 2005). Dislocations can be char- humed through the crust it may undergo some post- acterised by their Burgers vector which is a measure deformational annealing and this is generally the of the magnitude and direction of lattice displace- last process to affect the rock (Fig.1). ment caused by the dislocation (Fig.3)(Hull and The driving force for post-deformational anneal-

2 Figure 2: The setup of the PhD project and linked EuroMinSci projects. VB = Verity Borthwick.

ing is the reduction of stored energy in the system glide without help from thermal agitation and Q is and it occurs by two main processes; recovery and the activation energy or total free energy needed to recrystallisation (Urai et al., 1986; Drury and Urai, overcome that barrier without the help of stress. 1990; Baker, 2000). We focus here on recovery, Dislocation climb occurs by diffusional trans- which is driven by the interaction of dislocations port of vacancies to the dislocation with the fol- via their long-range stress fields and occurs through lowing velocity relationship: two main processes operating simultaneously: annihilation of dislocations of opposite signs and poly- v ≈ (β × exp(−Q/kT ) b2)/kT σ (3) gonisation, where dislocations align to form low energy arrays (Gottstein, 2004; Humphreys and where β is a material dependent constant and b the Hatherly, 2004). Dislocation movement is con- Burgers vector. trolled by two main mechanisms, glide along lattice Annihilation of dislocations of opposite Burg- planes and climb between them in order to over- ers vector can occur when two dislocations meet come obstacles. In the case of screw dislocations by glide along the same lattice plane. It can also moving in certain crystallographic planes, cross slip occur between dislocations on different planes by between lattice planes can also become important a combination of glide and climb or in the case of (Hull and Bacon, 2001). Any of these can be rate screw dislocations glide and cross-slip (Humphreys controlling, dependent on the type of dislocations in and Hatherly, 2004). the system and the temperature of annealing (Nes, In addition, if there are unequal numbers of dis- 1995). The velocity (v) of a dislocation is a function locations of two signs after deformation, polygoni- of the force (F ) on the dislocation and its mobility sation occurs. This is the process by which these (M): dislocations rearrange to form low angle boundaries, overlapping the area of distortion surround- v = MF (1) ing each dislocation and thus reducing the stored energy of the whole system (Hull and Bacon, 2001). Mobility of the dislocation is thermally activated This can be shown by calculating the energy of the and of the type exp(−Q/kT ), thus the velocity can boundary with respect to the misorientation angle: be rewritten as: θ ≈ b/d (4) v = α × exp(−Q/kT (1 − σ/σ ) (2) b where θ is the misorientation angle and d is the dis- where α is an independent material constant, σ location spacing in the boundary (Humphreys and the stress, σb the stress to overcome a barrier for Hatherly, 2004).

3 Figure 3: A deformed crystal lattice showing a dislocation. On the left of the image is a deformed crystal and the right shows the same crystal without deformation. The Burgers vector is shown, which is the magnitude and direction of the lattice distortion caused by the dislocation. This distortion increases the stored energy of the system (Wikimedia commons).

The energy of the boundary E, is given (Read and Shockley, 1950) as: P = αE/r (6) where α is a shape factor of ∼1.5, E is the energy of E = E θ(A − ln θ) (5) the boundary (Eq.5) and r is the subgrain radius. 0 In particular, symmetrical tilt boundaries can move by glide of the edge dislocations that comprise where E = G /4π(1 − v), A = 1 + ln(b/2πr ), G 0 b 0 the boundary (Humphreys and Hatherly, 2004). is the shear modulus and r is the radius of the 0 Mobility in this case is high, and migration can dislocation core. occur even at low temperatures (Parker and Wash- Based on this equation the energy of a bound- burn, 1952). ary increases with increasing misorientation, but by combining Eq. (4) and (5), it can be seen that the energy per dislocation decreases. This occurs 2.3 Halite as an analogue as the stress fields of the dislocations overlap with For the study we have selected high purity, syn- decreasing d (Hull and Bacon, 2001). As a result thetic halite as the experimental material. Halite of this energy decrease the system favours bound- plays a significant role in fold-and-thrust belts, ary building. However for misorientation increase, delta tectonics, basin evolution and hydrocarbon dislocations within the boundary itself need to re- accumulation, as well as being a possible medium arrange to decrease the spacing. This is generally for storage of nuclear waste (e.g. Franssen, 1993 achieved by climb (Hull and Bacon, 2001). Both and references therein; Rempe, 2007; Schléderand processes, dislocation movement into boundary and Urai, 2007). Halite is a particularly good ana- climb within a boundary, can be limiting with re- logue for many metals, as it has similar bonding gard to misorientation increase of the boundaries. i.e. ionic and a cubic structure. The development Once a polygonised substructure is attained, the of subgrain-scale microstructures in halite occurs at stored energy can be further lowered by a coars- experimentally attainable conditions (∼20MPa and ening of the substructure to reduce total bound- >200 oC) (Senseny et al., 1992) and shows many ary area (grain growth) (Humphreys and Hatherly, similarities with that occurring at higher temper- 2004). The driving pressure (P ) for subgrain coars- atures and pressures in silicates, making it a good ening can be shown by the following relationship: analogue for geological materials also (Guillope and

4 Poirier, 1979; Drury and Urai, 1990). There are, pletely characterise annealing behaviour. The de- however, some differences between other crystalline velopment of the EBSD technique allows for this, geological materials and halite. The bonding in ge- with the Euler angle orientation for each point ological materials such as silicates is not the same fully calculated (Prior et al., 1999 and references and the crystal structure generally has a lower sym- therein) and there have been a number of studies metry. This means that less easily activated slip of the microstructure at different times during an- systems are present, which has an affect on the nealing in both geological materials (e.g. calcite) activation of different deformation processes. For (Barnhoorn et al., 2005) and metals (Ferry and instance, high symmetry materials can deform by Humphreys, 1996; Huang and Humphreys, 2000; dislocation creep within a large range of pressure, Huang and Humphreys, 2001; Huang et al., 2000; temperature and strain rate, while low symmetry Ferry and Humphreys, 2006). Developments allow- tend to switch more readily to grain boundary mi- ing the combination of in-situ annealing inside the gration or diffusion creep when dislocations become scanning electron microscope with EBSD provide a tangled. powerful tool for the “real-time” analysis of post- Due to its ionic-bonded, cubic crystal structure, deformational annealing (LeGall et al., 1999; Se- NaCl provides a simple starting point for studying ward et al., 2002; Humphreys, 2004; Piazolo et al., these complex processes. In order to study sub- 2005). A handful of studies have been carried structural behaviour in more detail a single crystal out on various materials using this combined tech- of halite was used for the experiments. Using a sin- nique including: titanium (Seward et al., 2004), gle crystal resolved potential problems from rapid aluminium (Huang and Humphreys, 1999; Piazolo high angle grain boundary migration removing the et al., 2005; Kirch et al., 2008) rock salt (Bestmann substructure, as was experienced by Piazolo et al. et al., 2005; Piazolo et al., 2006), copper (Mirpuri (2006). The high purity of the sample meant that et al., 2006; Field et al., 2007) and Al-Mn alloys boundary pinning by impurities would be less likely (Lens et al., 2005). to influence the results (Smith, 1948). Fluid con- tent at the boundaries can have a large effect on 2.5 3D X-ray diffraction boundary mobility, so the samples were kept dry in a dessicator to reduce the possibility of atmospheric The major limitation of the 2D in-situ experiments absorption of water (Trimby et al., 2000b). is that we are analysing a three-dimensional struc- Previous studies on the microstructure on a two-dimensional surface. Valuable infor- tural/substructural behaviour of halite have been mation about substructural behaviour can be taken conducted. These include EBSD studies on the from these experiments, but it is difficult to pre- deformation microstructure of rock salt (Trimby dict the influence of surface effects such as thermal et al., 2000a; Trimby et al., 2000b; Pennock et al., grooving or surface tension (Frost et al., 1990 and 2002; Pennock and Drury, 2005; Pennock et al., references therein). Thermal grooving can be par- 2005; Pennock et al., 2006) and EBSD coupled with ticularly significant, resulting in subgrain boundary in-situ annealing of polycrystalline halite (Best- pinning at the groove tip and retardation of migra- mann et al., 2005; Piazolo et al., 2006). tion rate as a result (Mullins, 1958; Brokman et al., 1995; Gottstein and Shvindlerman, 2010). New 2.4 2D In-situ annealing experi- techniques such as serial sectioning with focused ments ion beam (FIB) tomography coupled with EBSD allow investigation of the interior of the crystal but The field of microstructural investigation has un- of course such a method is destructive and would ef- dergone many developments in recent years allow- fectively remove the “real-time” component of the ing us to more fully characterise behaviour of ge- experiments as we cannot compare the same sur- ological materials during annealing. In the past, face before and after annealing (Xu et al., 2007). studies were restricted to examination of the “post- 3DXRD is a way to overcome this limitation as it mortem” post-deformational annealing microstruc- allows us to examine the inside of the crystal non- ture (Covey-crump, 1997; Masuda et al., 1997; destructively (Nielsen et al., 2001; Fu et al., 2003; Heilbronner and Tullis, 2002; Barnhoorn et al., Poulsen, 2004; Baruchel et al., 2008). 3DXRD is 2005). Real-time analyses were limited to optical a technique which is becoming more readily avail- microscopy on transparent rock analogues (e.g. oc- able to scientists in a number of different fields, in- tachloropropane and norcamphor) (Ree and Park, cluding a growing number of structural geologists. 1997; Nam et al., 1999; Park et al., 2001), where 3DXRD can be coupled with in-situ heating exper- only the c-axis could be determined. The full crys- iments but until now this has been limited to the tallographic orientation is needed, however, to com- application to metals including aluminium (Laurid-

5 sen et al., 2001; Gundlach et al., 2004), Mg-Al alloy tal laws and theoretical data and the availability (Poulsen et al., 2004) and copper (Lauridsen et al., and accuracy of physical constants (Piazolo et al., 2006). 2004). The combination of these two techniques re- 2.6 Numerical simulation duces the limitations of both. By directly retrieving crystallographic orientation data from the experi- Numerical simulation of microstructural behaviour ments we provide a solid, physical basis on which and in particular recovery processes is an evolving to run the simulation. Since we have before and field with many contributors. The strength of nu- after heating maps we can directly compare the ef- merical simulation is that we can easily manipu- fect of real annealing with simulated annealing and late the input data and parameters allowing us to determine the validity of the model. study the underlying processes and theories (Bons et al., 2008). Different modelling techniques have been applied to microstructural problems including 3 Methods front-tracking models (Moldovan et al., 2002; Wey- gand et al., 2001), Monte Carlo algorithms (Holm 3.1 2D in-situ annealing and EBSD et al., 2003; Holm et al., 2004; Gruber et al., 2009), phase field models (Sreekala and Haataja, 2007) Over the course of this project, in-situ annealing and cellular automata models (Raabe and Becker, experiments were conducted inside a XL30 envi- 2000; Miodownik, 2002). A previous study was car- ronmental field emission gun SEM using a GATAN ried out on polycrystalline halite by Piazolo et al. heating stage (Fig.4). The sample was heated (2004) using a kinetic Monte Carlo Potts model in in place on the stage while EBSD maps of the sur- the 2D microstructural modelling platform Elle. As face were taken (Dingley, 1984). Backscatter occurs Potts models cannot fully be coupled to “real-time” due to the interaction of electrons from a stationary behaviour we use this study as a basis on which to beam and atoms in the crystal lattice. The sample build a more deterministic model. is tilted at 70o for optimum signal. The trajectory The microstructural modelling platform Elle of the backscattered electrons provides information has proven to be a powerful tool for analysis of about the arrangement of the crystal lattice and is the evolution of microstructures and the processes collected with a fluorescent screen. The pattern is which control them. Elle has been used previously detected on the screen as Kikuchi bands, each of in many studies, investigating a variety of different which corresponds to the position and orientation processes (Piazolo et al., 2010a). These include: of a lattice plane (Fig.5). Collected patterns were subgrain growth (Piazolo et al., 2004), isotropic auto-indexed using HKL Channel 5 software (Ox- and anisotropic grain growth (Bons et al., 2001; ford Instruments). An automatic Hough transform Jessell et al., 2003; Piazolo et al., 2004; Becker analysis is used to detect the edges of a number of et al., 2008), strain localisation (Jessell et al., 2005), bands (in this experiment 5-6 bands were selected). melt processes (Becker et al., 2004; Becker et al., The pattern is then indexed by comparison of cal- 2008), strain rate portioning during porphyroblast culated solid angles to a known match unit for the growth (Groome and Johnson, 2008), cation ex- mineral being analysed. For more specifics on data change (Park et al., 2004), two phase deforma- collection see Manuscript I. tion (Jessell et al., 2009), fracturing in granular While Prior et al. (1999) and Humphreys (2004) aggregates (Koehn and Arnold, 2003), stylolites state that 0.5o is the reliable limit for misorienta- (Koehn et al., 2007), dynamic recrystallisation (Pi- tion between two points, Pennock et al. (2002) sug- azolo et al., 2002), strain localisation (Jessell et al., gests an error limit of 0.3o. Since the same area was 2005) and recovery (Piazolo et al., 2010b). mapped after each stage in our study we suggest a While both experimental techniques and nu- lower limit for our experiments and calculated an merical simulation are very successful methods of error limit of ± 0.1o after remapping over the same studying microstructures, they do have inherent area and comparing results (for more details see limitations. In-situ experiments have the possibil- Manuscript I). ity of surface effects influencing behaviour and are restricted to materials which exhibit changes that 3.1.1 Data processing are fast enough to observe on a human timescale and which respond under appropriate laboratory EBSD maps collected in the SEM are analysed friendly conditions (Piazolo et al., 2004). The qual- using offline HKL Channel 5 software. Noise re- ity of numerical simulation is limited by the rele- duction was applied to the data following a pro- vance of the input data, the choice of fundamen- cedure whereby non-indexed pixels with up to 6

6 Figure 4: SEM configuration for orientation mapping by EBSD during annealing (after Gottstein, 2004). indexed neighbour pixels were automatically as- cations) (Fig.7b). These can then be related to signed the most common orientation from neigh- known slip systems and based on the geometry the bouring indexed pixels. A filter was also applied most likely can be found. to remove single, isolated pixels or “wild spikes” from the data as there were likely to be indexing 3.2 3D X-ray diffraction mistakes. To enhance subgrain boundary detection, the Kuwahara edge detection filter was ap- 3D X-ray diffraction allows for non-destructive in- plied in two passes (Kuwahara and Eiho, 1976; vestigation of a crystal volume (Nielsen et al., 2001; Humphreys, 2004). While processing, EBSD maps Fu et al., 2003; Poulsen, 2004; Baruchel et al., were compared to orientation contrast images to 2008). This technique was used for Manuscript check that the substructure was accurately repre- II and Manuscript III. A monochromatic beam sented and significant artefacts were not introduced is passed through the sample with a reciprocal pat- (Prior et al., 1996). tern collected for those parts of the crystal that Different ways of representing the data were fulfill the Bragg condition. This means only those utilised using the HKL software (Fig.6). The col- with the right wavelength for diffraction along crys- lected crystallographic orientations were displayed tal lattice planes will be indexed. In order to fully in a number of ways including: textural deviation characterise the crystallographic orientation it is maps, inverse pole figure colouring, rotation axes necessary to rotate the sample in space around the and crystallographic orientation pole figures, and z axis by ω so that a full reciprocal pattern can be local misorientation maps. Specific features could collected (Fig.8). be highlighted including subgrain boundaries and 3DXRD can be coupled with in-situ heating, their misorientation axes. similar to the SEM setup (section 3.1). A furnace is In order to assess potential active slip systems coupled to the system with the sample sitting in a and the type of subgrain boundary, boundary trace heated copper bar with a thermocouple running in- analysis can be used, as was done in Manuscript side it. Temperature can be adjusted from outside I (Lloyd et al., 1997; Prior et al., 2002). Boundary the beam hutch. A fitted glass casing is continu- trace location is compared to rotation axis. If the ously flooded with argon gas to keep the sample at rotation axis lies on the boundary trace, the bound- a constant temperature (Fig.8). ary is likely to have a tilt geometry (i.e. made up The diffraction pattern is collected by two de- of edge dislocations) (Fig.7a). If the rotation axis tectors placed at different lengths from the sample. lies perpendicular to the trace, a twist geometry is A high spatial resolution detector with a 5 µm pixel possible (i.e. made up dominantly of screw dislo- size is located a few mm from the centre of rota-

7 Figure 5: Schematic depiction of the EBSD procedure. A diﬀracted pattern is collected from the sample surface which gives information about the arrangement of lattice planes in space and allows resolution of the crystal structure (Svahnberg, 2010 modiﬁed from ebsd.com).

Figure 6: Data analysis techniques on the same mapped area. a) shows an angular deviation of 8o in greyscale (scale bar below). Subgrain boundaries are shown in interpolated colour scale from light blue (1o) to red (7o). b) Band contrast map showing the accuracy of indexing overlaid with subgrain boundaries coloured for misorientation axis (pole figure colouring in the corner). c) Colour coded local misorientation map outlining the intensity of crystal deformation by comparing the average misorientation of a pixel with the 8 neighbours surrounding it. Scale bar shown below. d-f) Lower hemisphere equal area pole figures. d) Crystallographic orientation of {110} poles to planes. e) Rotation axis scatter plot. f) Contoured rotation axis scatter plot. g) Subgrain boundary histogram showing the relative frequency of different misorientation angles.

8 Figure 7: Different boundary geometries. a) tilt geometry showing the rotation axis lies on the slip plane (made up of edge dislocations). b) twist geometry where the rotation axis is perpendicular to the slip plane (made up of screw dislocations). (Svahnberg, 2010: Modified after Prior et al., 2002 and Kruse et al., 2001). tion. This provides detailed information about the Each voxel in the map represents a crystallographic crystallographic orientation. A second low resolu- orientation, which can only give rise to intensities tion detector at a large distance provided the bulk in small segments of the Debye-Scherrer rings due diffraction pattern for the crystal (Fig.8). Dur- to constraints related to space group, lattice pa- ing heating, small maps could be taken over a lim- rameters and beam energy. All signals on the de- ited rotation encompassing 1 or 2 subgrains (Fig. tector which could originate from the chosen voxel 9). These provide “real-time” maps of the changing are added to the Rodrigues space (each signal is a substructure. It is necessary to pull the high spatial geodesic in this space) and a rough orientation dis- resolution detector further from the sample during tribution function is created. The orientation space heating, as it may be damaged by the increased is then searched for signals higher than the back- temperature. ground (local maxima). A forward projection onto the detector estimates completeness of candidate 3.2.1 Data analysis orientations (the ratio of measured reflection over the number of expected reflections). The orienta- The syn-heating maps required minimal post- tion possessing maximal completeness is chosen to processing, as we examined the changes in the be the final orientation for the selected voxel. diffraction pattern and did not try to reconstruct The 2D voxel grid with crystallographic orien- the actual crystal structure. Images were treated tations for each layer from the reconstructed vol- for the effect of beam decay by correcting the ume was imported into the HKL Channel 5 soft- greyscale for this. Composite stacked images from ware and post-processed in a similar manner to the Manuscript II, were created by stacking the 2D data (see section 3.1.2). 3D comparison im- diffraction images for each minor rotation to make ages were created using ImageJ, an image process- a 3D volume with the X and Y constituting the pix- ing program. Other types of analysis investigated els of the images and Z as the small rotation (Fig. included subgrain boundary histograms, textural 9). deviation maps, local misorientation maps and ro- The full crystal structure was reconstructed tation axis pole figures. using the post-processing program, Grainsweeper (Schmidt et al., internal report). This is a 3.3 Numerical modelling stand alone program for reconstructing both un- deformed and deformed microstructures in mate- The Elle modelling platform was developed to al- rials i.e. the crystallographic orientations as well low incorporation of different microstructural pro- as the grain morphologies are extracted simultane- cesses into one program (Bons et al., 2008). Us- ously (Schmidt, 2010, pers. comm.). The current ing Elle, modellers can concurrently apply different resolution, which is limited by detector resolution, processes to their starting microstructure and test is 5 microns. The Grainsweeper program runs fully how it evolves. We used this platform to build the automatically once the geometric (global) param- new recovery model discussed in Manuscript IV eters from the experimental setup have been de- which will be incorporated into the library of possi- fined (beam energy, distance, tilt of the detector). ble processes, making it available for others in the

9 Figure 8: Diagram of the setup for 3DXRD adapted from Poulsen (2004) for the case in which the monochromatic beam has a linear focus. The diﬀracted beam emitted from the sample as it is rotated around the ω axis has a Bragg angle 2θ and azimuthal angle η. The created pattern is collected at two diﬀerent distances from the sample. The co-ordinates of the laboratory system are also shown. The inset shows an EBSD map corresponding to one layer taken through the sample.

Figure 9: Small rotation maps taken over one subgrain. (a) shows the composition of the 3D subgrain maps. The maps are made up of successive stacked layers with the z-dimension as the omega rotation of the sample. The position of the blue and red outlined layers is shown in the small inset 3D map. (b) is after heating 22min at 260 oC and (c) is after heating 3h 20min at 260 oC.

10 Figure 10: (a) Data structure for the Elle microstructural modelling platform (after Bons et al., 2008). (b) shows a rough schematic of the unode grid overlaying part of the substructure to demonstrate where information points lie. In reality the unode grid is very fine, with one unode per EBSD map pixel. future to use the process. The Elle data structure maps. contains layered networks of nodes in which physical and chemical information can be stored. Layer 1 consists of a network of boundary nodes (bnodes) 4 Results and discussion and connecting boundaries which form a grain network of flynns (Fig. 10). Layer 2 consists of a 4.1 Manuscript I regular grid of unconnected nodes (unodes), which Manuscript I, Post-deformational annealing at can be arranged in a square or hexagonal pattern. the subgrain scale: temperature dependent be- These two layers can communicate with each other. haviour revealed by in-situ heating experiments on Algorithms designed to represent specific processes deformed single crystal halite discusses temper- can interact with this data structure in a number ature dependent annealing behaviour on single of ways including i) using the node values to deter- crystal halite, focusing on subgrain boundary be- mine driving forces, ii) rearranging, creating or re- haviour. The results from 2D in-situ annealing moving nodes, iii) reconnecting boundary segments experiments conducted inside the scanning elec- and iv) changing the attributes stored in the nodes tron microscope coupled with electron backscatter (Piazolo et al., 2004). diffraction had a number of important implications Elle allows for EBSD data to be directly im- for the field. The experiment was conducted at a ported into the program using EBSD2ELLE. This lower-temperature window, below the deformation means we can use data from physical experiments temperature, which is not usually investigated in to test the numerical model for validity based on annealing studies. This window, however is partic- the actual response of the microstructure during ularly relevant for geological settings, where rocks annealing. often stay at higher temperatures even after the deforming pressure is removed. We showed that 3.3.1 Data analysis annealing with a significant reduction in crystallographic orientation, and change in the subgrain Final data after running the simulation for the pre- structure by dislocation removal can occur, even at scribed number of steps was converted to a text file lower temperatures. using ELLE2EBSD. This can then be imported into We found that before “classical” annealing be- the HKL Channel 5 program, where the data was haviour of polygonisation followed by increase in analysed. Data comparison was made in a number boundary misorientation begins, substructural be- of ways including: subgrain boundary histograms, haviour can fluctuate. Boundaries undergo both rotation axis pole figures and local misorientation increases and decreases in misorientation at cer-

11 tain temperatures. Subgrain boundaries cannot be surface effects from a 2D surface during annealing. grouped under one definition reflecting their be- We examined both a single layer (before and after haviour and must be treated accordingly. Bound- heating) from the 3D reconstruction of diffraction aries could be specifically associated with different patterns and syn-heating analysis which was con- slip systems, most generally they could be grouped ducted to follow changes in “real-time”. A number into two categories based on their slip system asso- of key processes were identified, which were: ciation: primary boundaries (those aligned with the predominant slip systems (011)[011] or (011)[011], 1. increase and decrease in misorientation of the which occurred more frequently throughout the subgrain boundaries whole sample) and secondary boundaries (with 2. subgrain subdivision where two parts of the (101)[101] and (101)[101] which were only found in subgrain rotate away from each other to form the more deformed central part of the crystal). We areas of like orientation with a new boundary could further subdivide boundaries into four differ- forming between them ent categories based on their behaviour, morphology and orientation. 3. boundary movement Behaviour showed three distinctly temperature- dependent regimes: Comparison of syn-heating maps to recon- Regime I (<300 oC) Primary boundaries in- structed layers indicated similar processes occur- crease in misorientation, while secondary bound- ring in both. Preliminary analysis suggested that aries decrease. Dislocations annihilate and some 3D X-ray diffraction is a powerful technique for ex- rearrange to form new subgrain boundaries which amining post-deformational annealing. We demon- subdivide subgrains into regions of like orientation. strated that reconstruction was possible even with Regime II (∼300 oC) All boundaries decrease highly complex microstructures. in misorientation. Dislocation annihilation and new boundary formation continue. 4.3 Manuscript III Regime III (>300 oC). All remaining boundaries increase in misorientation. No new boundary Manuscript III, In-situ 3DXRD annealing of formation after this point. Secondary boundaries a geological material: Evaluating the validity of demonstrate a change in rotation axis. 2D furthers the ideas and observations from During all three regimes some minimal bound- Manuscript II, with complete analysis of the fully ary movement occurred. reconstructed 3D data. Results supported the ob- From these results we suggested a model of servations made in Manuscript II. Processes ob- substructural evolution. Annealing behaviour is served involved the rearrangement of dislocations, strongly dependent on dislocation type, in partic- including alignment into arrays with formation of ular their mobility and spatial range of influence. new subgrain boundaries, increase and decrease in This is, of course, strongly linked to temperature boundary misorientation with complete dissipation of annealing. At lower temperatures, we postulated in some cases and extensive boundary movement. that climb has not been activated yet, and that at Comparison to the results from the Manuscript I 300 oC there is a decrease in boundary misorien- indicated that boundary movement was much more tation since dislocation separation can no longer common in the 3D experiment, than the 2D, on the increase. At >300 oC climb is activated, so dis- order of 4 to 28 times more likely. This is a partic- location mobility is increased and separation can ularly significant result as it indicates that the 2D also increase. As temperatures increase the range experiment does experience some effect from having over which dislocations can influence one another a free surface. Some thermal grooving of bound- increases. aries occurred in the 2D experiment. It is thus suggested that the subgrain boundaries experience 4.2 Manuscript II some drag at the tip of these grooves, which significantly retards migration rate, similar to described Manuscript II, The application of in-situ 3D X- and predicted behaviour for high angle boundaries ray Diffraction in annealing experiments: First (Mullins, 1958; Brokman et al., 1995; Gottstein and interpretation of substructure development in de- Shvindlerman, 2010). This means we have to deal formed NaCl details preliminary results from the with boundary movement in 2D with some care, six day 3D annealing experiment conducted at the and absolute migration rate may not be accurate. synchrotron in Grenoble. This experiment is the General boundary behaviour (increase and decrease first of its kind conducted on a geological material. in misorientation) exhibited similar behaviour in Experiments were designed to test the possibility of the 3D volume, however.

12 Analysis of subgrain area change during anneal- ical cutoff of ∼7o (in halite). The Read-Shockley ing with relation to the number of neighbouring relationship has been supported by experimental subgrains indicated that it is likely that the Von- results, but most of these show a data poor region, Neumann-Mullins criteria is upheld for 2D layers in between two distinct, almost straight line relation- a 3D volume (Neumann, 1952; Mullins, 1956). Two ships. Our critical cutoff falls in this data-poor subgrains that did not uphold the criteria were pos- transition zone. sibly misrepresented by the cutoff or so close to the Results also indicate that the range of influence edge of the analysis area that not all neighbours of the dislocation core radius has a significant effect. were resolved. In the simulation, we increased neighbourhood size This experiment demonstrates that 3DXRD is to try and replicate behaviour and found that this an applicable technique for crystalline geological was important in order to accurately replicate the materials. It was possible to fully reconstruct results as closely as possible. the crystal with the Grainsweeper processing, even We thus proposed support for the model of sub- though it exhibited large, continuous changes in ori- structural evolution suggested in Manuscript I entation which present as a blurry diffraction pat- and presented a simulation for recovery which can tern that is difficult to resolve. be used for other materials where the deformation geometry is well constrained. 4.4 Manuscript IV Manuscript IV, Numerical simulation coupled 5 Summary and conclusions with in-situ annealing experiments: A new model for recovery discusses the results from a numeri- Returning to the main project aims detailed in sec- cal simulation written to model the recovery pro- tion 1.1 we summarise the results in terms of how cess. This was done using the microstructural far this PhD project has advanced understanding modelling platform Elle which allows the crys- of substructure dynamics, specifically based on the tallographic information collected from electron initial aims of the project. backscatter diffraction to be used as the starting From Manuscript I we learned a great deal microstructure for the simulation. We incorporated about how the substructure of a crystalline mate- extensively the results and derived interpretation rial evolves during annealing. Observations of vary- of process details from Manuscript I to design ing substructural behaviour from Bestmann et al. the model. Results from the simulation indicated (2005) and Piazolo et al. (2006) were confirmed. a number of interesting implications for the field. Subgrain boundaries were found to both increase The paper supported the hypothesis of tempera- and decrease in misorientation, with some dissipat- ture and dislocation type dependent annealing being completely. Boundary behaviour was specific haviour discussed in Manuscript I. Dislocation to different types of boundaries and thus it is not type dominance was reflected in varying the ro- enough to view all subgrain boundaries in the same tation mobilities on different rotation axes which light. Annealing behaviour was highly temperature were specifically chosen to imitate the slip sys- dependent, with three regimes identified. This led tems active in the 2D experiment. This replicated to the proposal of a model for substructural evolu- most of the interesting fluctuating misorientation tion reliant on dislocation type and its temperature- behaviour, which leads us to conclude that bound- dependent mobility. Manuscript II and III fur- aries do behave in ways that are specific to their ther supported the behaviour observed in the 2D in- dislocation makeup and should be treated us such. situ annealing experiments, as we could see similar It also suggests that rather than being fixed and response of the 3D volume. However, Manuscript organised once they are aligned into an LAB, dis- III did reveal that there were some surface effects locations can still be independent to much higher causing an influence in the 2D experiments, by sub- misorientation angles than previously thought. grain boundary pinning on thermal grooves. This The main weakness of the simulation was that it suggested that subgrain boundary movement was was impossible to preserve higher angle behaviour actually a lot more extensive than shown in the 2D while still generating the fluctuating behaviour of experiments. Evidence in Manuscript III sug- lower angle boundaries. Different methods of cal- gested that the Von Neumann-Mullins criteria for culating stored energy using the Read-Shockley re- grain growth were fulfilled for 2D layers in a 3D lationship could represent either type of the be- volume. haviour but not both. An attempt to combine two Manuscript I allowed us to begin to define a types of calculations, indicated that this behaviour subgrain boundary in terms of the critical misori- switched from lower angle, to higher angle at a crit- entation angle at which boundary behaviour begins.

13 We observed that even once subgrain boundaries systems, which can, however, be derived from de- had been formed, dislocations did not seem to be tailed microstructural studies for example, using a completely fixed and could still annihilate resulting Burgers vector analysis program (Wheeler et al., in decrease in boundary misorientation and some- 2009) or boundary trace analysis (Lloyd et al., 1997; times complete dissipation. Manuscript IV fur- Prior et al., 2002). ther developed this idea, as the numerical simu- The final aim of the project was to determine lation supported the model of substructural evo- if we could use substructure and subgrain boundary lution we proposed in Manuscript I. In particu- behaviour to derive deformation and/or annealing lar, it did appear that dislocations could still be conditions. If we focus first on deformation con- independent in a boundary setting, to much higher ditions we see that this is more difficult. While angles of misorientation than previously thought. the substructure changed significantly in the exper- Manuscript IV provided some information about iments (Manuscript I), many of the changes were where the cutoff misorientation for boundary be- increase and decrease of boundary misorientation. haviour might be. Different methods of calcula- This unfortunately does not tell us much about the tion of stored energy revealed that at a misori- specifics of the deformation conditions as we can- entation ∼7o (in halite) the boundary behaviour not follow back through a number of recognisable switched from lower angle fluctuating behaviour to changes to determine the original conditions. How- higher angle boundary development. It was found ever, in Manuscript II and III, it is evident that that misorientation angles that fell in the data-poor a lot more subgrain boundary movement occurs in “transition zone” of the more well-defined parts of a 3D volume than 2D because of the surface ef- the Read-Shockley relationship could not be prop- fect of thermal grooving. An in-depth study of this erly represented. subgrain growth behaviour has not yet been made, In Manuscript I we discovered some evidence but could possibly assist in the aim of deriving de- about the type of dislocations that form different formation conditions. The experiments are a little types of subgrain boundaries and how this affects more helpful when it comes to annealing conditions. their behaviour. Subgrain boundaries were subdi- From Manuscript I we see three distinctly tem- vided into different categories based on their be- perature dependent regimes which were supported haviour during annealing. We could associate the by the numerical simulation (Manuscript IV). A boundaries with two main groups of dislocations in- number of changes could indicate that the climb troduced during deformation and it was found that temperature (Regime III) has been reached and this these groups behaved significantly differently dur- suggests that in a sample where the deformation ing annealing. In Manuscript IV we tested this geometry is well-constrained, we could indeed de- theory by varying rotation mobilities on three rota- termine the temperature of annealing. tion axes that we considered controlled behaviour The work of this PhD project has begun to in the 2D experiment of Manuscript I. We found answer some of the many questions surrounding that we could replicate the fluctuating boundary substructure dynamics and how useful they are in misorientation behaviour only by varying the mo- determining past conditions and predicting future bilities and dominance of these different axes. In ones. There are many questions still to be answered Manuscript I, we suggested a specific group of dis- and four years work on one crystal of salt is just locations (represented in the simulation by rotation the beginning. With this in mind we present some axes) would be dominant during each temperature potential work to be conducted in future studies dependent regime and this model was supported by (section 7). the results from the numerical simulation. In part we have answered the question, can we predict subgrain boundary behaviour? Manuscript 6 Main outcomes IV details a numerical simulation for recovery which can be used to predict some boundary be- The main outcomes of this thesis are twofold: haviour. The results from the experiments de- 1. Development of a significantly refined model scribed in Manuscript I could be supported by for recovery in crystalline material. the simulation (Manuscript IV) though it was difficult to reproduce both lower angle fluctuating 2. Advancement of analytical techniques com- boundary behaviour and higher angle behaviour. bined with awareness of their strengths and While we suggest that it is possible to predict much shortcomings. of subgrain boundary behaviour with the simulation, it is dependent on a significant knowledge of The developed recovery model is particularly the deformation geometry and thus activated slip relevant for geological materials as it focuses on

14 recovery active at temperatures below the defor- Figure 11: Schematic of the recovery model. De- mation temperature. The model was suggested in tails from the numerical simulation are shown, the Manuscript I and has been supported and im- dominant rotation axis used in replicating each proved by the results from Manuscript IV. This regime as well as the size of the neighbourhood model is significant for materials with a primarily from which the energy calculation was made (bot- activated slip system and a secondary slip system tom right hand corner). which is only activated later in the deformation Regime I (Fig. 11a): Dislocation movement process. We thus envisage a starting dislocation occurs predominantly by glide. ρps glide into sub- budget where primary dislocations (ρps) have been grain boundaries increasing them in misorientation, mostly arranged into higher misorientation bound- while the large number of free ρss result in a de- aries, while secondary dislocations (ρss), emplaced crease in secondary subgrain boundaries. In order later mostly remain free in the subgrain interior to model this with simulation, the secondary rota- with only a few resolved into subgrain boundaries. tion axis was made dominant by varying rotation Three temperature-dependent regimes were deter- mobilities (Manuscript IV), which gave similar mined in Manuscript I and processes occurring results. Dislocations also annihilate in the subgrain during them are detailed here: interior and when there are none available of opposite signs, begin to line up into low energy arrays. Long range dislocation effects are not as significant during this Regime and this could be reproduced in the numerical model by using an energy calculation assuming neighbourhood influence at a short range (Manuscript IV). Regime II (Fig. 11b): Dislocation movement still occurs predominantly by glide. Sec- ondary boundaries continue to decrease in misorientation, but at a reduced rate as the number of ρss available dwindles. To model this in the simulation the primary rotation axis was made dominant (Manuscript IV). Primary subgrain boundaries decrease in misorientation also by annihilation in the boundary vicinity, since dislocation separation can only increase by climb between lattice planes. Dislocation annihilation and low energy ar- ray building continues, and new boundaries begin to form. The long-range influence of dislocations increases which was modelled by increasing the neighbourhood influence to a larger range for the energy calculation (Manuscript IV). Regime III (Fig. 11c): The activation temperature for climb is now reached. Subgrain boundaries increase in misorientation as dislocation separation within boundaries can increase. Long-range influence of dislocations extends significantly as modelled by increasing the neighbourhood influence to an even larger range for the energy calculation (Manuscript IV). It is clear from the results of the manuscripts that dislocations remain independent in boundaries to much higher angles of misorientation than previously thought. The simulation results suggest that, for halite, they start to become locked in the boundary at a misorientation of ∼7o, with fluctuating behaviour of increases and decreases in misorientation below that angle. The work of this project has advanced some of the analytical techniques used to study microstruc-

15 tures. We demonstrated that analysis and resolu- information. Now that it has been shown that tion of a crystalline geological material with a large the crystal structure of materials with high inter- amount of internal deformation was possible us- nal subgrain misorientation can be resolved, it fol- ing 3D X-ray diffraction. This was the first in-situ lows that further 3DXRD experiments on highly 3DXRD annealing experiment conducted on a geo- deformed materials, with annealing conditions ap- logical material. The results led to some important propriate for the furnace setup, should be exam- implications for 2D analysis techniques, such as the ined. 2D in-situ annealing experiments performed inside While the numerical simulation, as presently the SEM. Boundary migration was found to occur constructed can replicate a lot of the specific to a much larger extent within a 3D volume than boundary behaviour, including misorientation in- was observed on the 2D analysis surface. This has crease and decrease, it cannot move boundaries. been interpreted as boundary pinning by thermal The simulation next needs to be coupled with a grooves on the analysis surface retarding migration boundary movement process. There are a number rate. This means that while relative migration rates of grain boundary migration processes built into will be similar, absolute rates in a 2D analysis need Elle and these should be investigated to determine to be treated with some care. if they might be appropriate. It is important to A new model for recovery was developed using choose a deterministic method, however, since one the microstructural modelling platform Elle. This of the most important features of the simulation was tested on experimental results from the 2D in- is the possibility of linking it to real-time. The situ annealing experiments. The model is suitable simulation should also be applied to other materi- for samples where the deformation geometry is well- als. Rotation axes can be chosen specifically for the constrained. material of choice, if the deformation geometry is fairly well constrained. 7 Future work 8 Acknowledgements This study has raised some interesting questions about substructure dynamics in geological materi- First and foremost I would like to thank my super- als. Since all parts of this study have focused on visor, Sandra. I could not have asked for a better analysing the behaviour of one halite crystal, TL1, guide through this PhD process. Thank you for it would obviously be of great benefit to extend this always having your door open to me, for count- to crystals deformed in different manners and even less phone calls on the weekend when the SEM was other materials. Testing if similar behaviour oc- playing up again, for many nights spent discussing curs in different minerals with lower symmetry is papers after the kids had gone to bed and for al- difficult to conduct in-situ, but the high pressure- ways being enthusiastic no matter what happened. temperatures setups of the synchrotron could be I feel extraordinarily privileged to have had the op- used. Applying these ideas to natural examples portunity to work with you these last four years from “natural laboratories”, with similar conditions and lucky to count you among my friends. would also be beneficial. We do also have a num- I would also like to thank Pat, Sandra’s other ber of halite samples from the same series as the half, for letting me steal so much of his wife’s time. TL1 crystals, deformed with similar strain rates but And his own time! It is a little difficult to ignore at different temperatures. Annealing experiments an EBSD user if they are your wife’s student but I have been conducted on a number of these but the really do appreciate all the time spent on the week- data has not yet been analysed. We also have a ends talking me through another problem. You series with varying final strains (0.05-0.20) which went above and beyond the call of duty. we have not yet conducted experiments on. Anal- I acknowledge the financial support of European ysis of these two series should further reveal the Science Foundation under the EUROCORES Pro- significance of strain and temperature dependence gramme, EuroMinSci, MinSubStrDyn and am ex- on annealing behaviour. tremely grateful to have been part of this collabo- While syn-heating maps from the 3DXRD ex- rative project. Also the Knut och Alice Wallenberg periment have been partially analysed, a further stiftelse, which funded the experimental setup. full analysis is necessary. In order to do this, a To my Co-authors, it has been a pleasure work- new technique will need to be developed to sepa- ing with you on these papers. Thanks for all the rate orientation from subgrain shape, as both these great feedback, countless drafts and fun times while parameters are contained in the diffraction pattern doing experiments and writing numerical models. information. This will provide us with much more I would also like to thank the rest of the Min-

16 SubStrDyn (how do we pronounce that again?) me company when I was at my most stressed, so group. Being part of such an awesome scientific thank you for being the dearest, sweetest, little cat community has been a wonderful experience that I in the whole world. have really appreciated. In particular thanks very Katty, I would never even have come to Sweden much to my co-supervisor Paul and to Dan, Mark, in the first place if it hadn’t been for you. I am Dave, Lynn, Albert, Jens and Joyce. You made this so glad I did! And I’m really grateful that I got really fun! to share this experience with you, both of us going To my fellow long-suffering office mates, He- through the ups and downs of a PhD and moving lena, Henrik and Brigitte. It’s been a lot of fun to a new country. You were always around as a wedging into our tiny office together and I couldn’t sounding board for my problems, and really have have asked for three nicer people to share it with. been this last twenty years in fact. Who knew that Thanks for listening to my stupid ideas, putting up those tiny third-graders with terrible, green uni- with my general and often dreadful mess and wa- forms would end up on the other side of the world tering my plants while I was away (I think they get becoming Doctors? better attention when I am not in town). I couldn’t have done this without my friends I want to thank my family, Mummy, Daddy and in the department. For all those people who were Maddy. You have always believed in me no mat- around for coffees and beers and put up with my inter what. You have always told me that I could do appropriate lunchtime conversation, I am so grate- whatever I wanted, that nothing was out of reach. ful to you. My time here would not have been the Daddy, you once told me as I carefully placed my same without you. As in it would have been bad. feet in your footprints saying “Daddy look, I’m fol- So thanks goes to Cecile, Xavier, George, Linda, lowing in your footsteps” that, that was fine but Paulina, Johanna, Daniela, Malin, Teodora, Iain, that I need to make a few of my own. I did follow Patrick, Tonny, Emma, Jose and Duc. If I have your footsteps to geology, somewhere deep down forgotten anyone please forgive me... it’s not that the years of looking at rocks with you as a child I don’t have lots of love for you, it’s just that my inspiring me. So here I give to you this... my own brain is so full of PhD right now that everything footprint. I couldn’t ask for a better family. I feel else is gone. You guys are awesome! grateful for you guys every day. Every step of this And all the other wonderful people in the De- PhD you have all been there listening to me and partment! I can’t name you all here since it would encouraging me when I was down. If you must call take up a whole extra page but it has been such me Dr Bubbywump then fine. You have earned the a pleasure to work with you these last years. I right to. do want to particularly thank Anders and Mari- And last but not least, Jesper. You have born anne, without whose help my experiments would the brunt of living with someone who was doing a have been a complete mess. Also Eve for always PhD and I think most people will agree that this is having her door open for panicking PhD students. not an easy thing. And yet, you have always been Vicky, thanks for being such an inspiring presence, patient with the crazy rollercoaster of my life. And I really enjoyed teaching structural geology with to think, three and a half of those four years we you. shared a space of 18m2! You have dried my tears I want to thank Pyewacket, my cat at home in when I was sad, you have shared my joy when I Australia. Having you sitting with me for the last was happy, you have even let me yell at you when I writing up phase really helped, even if you did think needed someone to be angry at. I couldn’t ask for it was fun to play with the mouse/pen/computer a better partner in this life and I could not have screen and knock over my coffee on more than one made it through this without you standing by my occasion (thankfully not into my laptop). You kept side.

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