Meddelanden
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Stockholms Universitets Institution
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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:
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 predom-inantly 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
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
1
Project aim
1.1
Why study substructure
dynam-ics?
Microstructures hold the key to understanding tec-tonic behaviour on the most fundamental of scales. Deformation of rocks in the crust and mantle mostly occurs by crystal-plastic mechanisms such as dislocation creep. Individual crystals within a rock respond to strain by forming defects in the crystal lattice. These form a microscale sub-structure of dislocation arrays, free dislocations and a network of subgrain boundaries (Humphreys and Hatherly, 2004 and references therein). On a macroscale these substructures effect the rheol-ogy of a rock (Ashby, 1969; Means and Xia, 1981; Ranalli, 1995; Passchier and Trouw, 2005). Thus, in order to investigate behaviour on a macroscale it is essential to understand substructure dynamics. As a rock is exhumed to the crust it is affected by a complex series of processes which change the sub-structure. In order to reconstruct this temperature-time path it is necessary to predict the results of these various changes. Post-deformational anneal-ing is of particular interest, as this is often the last process to affect a rock, occurring when pressure is removed but the system still retains a high tem-perature. It can still have a significant effect on the arrangement of the substructure. If we under-stand this process than we can potentially create a “window” through to the previous deformation conditions (Fig. 1).
The precursor studies to this project were con-ducted by Bestmann et al. (2005) and Piazolo et al. (2006). They conducted in-situ annealing experiments on a polycrystalline synthetic halite. Though substructural dynamics were not the focus of these papers, subgrain boundary behaviour was observed to vary from that predicted by classical theory. Polygonisation into a subgrain boundary network was not followed by an increase in misori-entation, but some boundaries exhibited a decrease with some dissipating altogether.
The project was begun with a number of specific aims which are as follows:
1. How does the substructure of a crystalline material evolve with annealing?
2. Definition of a subgrain boundary – what is the critical minimum misorientation angle in order for boundary behaviour to begin? 3. Which type of dislocations form different
types of subgrain boundaries? How is their
behaviour dependent on these types of dislo-cations?
4. Can we predict subgrain boundary be-haviour?
5. Can we use substructure and subgrain bound-ary behaviour to derive deformation and/or annealing conditions?
1.2
Overall approach
The project involves a three-technique approach. The starting point for this work began with 2D in-situ annealing experiments conducted inside the scanning electron microscope (SEM) and coupled with electron backscatter diffraction (EBSD). A comparison experiment was conducted using 3D X-ray diffraction (3DXRD) at the synchrotron facil-ity in Grenoble in order to rule out the potential of surface effects in 2D experiments. Numerical simu-lation directly accessing results from the 2D exper-iments allowed development of theories and itera-tive improvement of a new deterministic recovery model. This thesis discusses aspects of the above questions that we have answered throughout the project period as well as highlighting areas which need further research.
1.3
Mineral Substructure Dynamics
– a European wide-network
This PhD project is part of a European Science Foundation EUROCORES funded collaborative, EuroMinScI (European Mineral Science Initiative), which involves nine projects with researchers from twelve different countries. The purpose of the Eu-roMinScI project is to draw together experimental and computational techniques into integrated re-search programs with a focus on furthering atom-istic understanding of structures, properties and processes of minerals and metals.
The Collaborative Research Project (CRP) this study falls within involves ten linked projects from seven different countries. The main purpose of the CRP Mineral Substructure Dynamics (MinSubStr-Dyn) is to investigate substructural behaviour us-ing experimental techniques coupled with numeri-cal simulations. This project is directly linked with a number of the other individual projects in the CRP including that of A. Griera at the Universit´e Paul Sabatier in Toulouse and a group at the Ma-terials Research Division, Risø DTU in Denmark. Fig. 2 shows the setup of this PhD project, high-lighting how the associated projects are linked.
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
2.1
The deformed state
During deformation a crystal takes up strain by the introduction of defects, or “mistakes” into the lat-tice. Most of the energy necessary to deform a ma-terial is given out as heat, with only a small propor-tion (∼1%) remaining as stored energy which is de-rived from these defects (Humphreys and Hatherly, 2004). They occur as either point defects, which are vacancies or additional interstitial molecules in-serted into the lattice or as line defects (Hull and Bacon, 2001; Passchier and Trouw, 2005). Since point defects are extremely mobile except at low temperatures they do not contribute much to the overall stored energy of the system. Most of the stored energy is a result of accumulation of line de-fects, also known as dislocations. There are two types of dislocations, edge, which are due to an “extra” half lattice plane in the crystal and screw, which exist where part of the lattice is displaced over one lattice distance, and is thus twisted (Pass-chier and Trouw, 2005). Dislocations can be char-acterised by their Burgers vector which is a measure of the magnitude and direction of lattice displace-ment caused by the dislocation (Fig. 3)(Hull and
Bacon, 2001, Passchier and Trouw, 2005). As de-formation continues, dislocation density increases as a result of new dislocations becoming trapped in tangles with existing dislocations (Humphreys and Hatherly, 2004).
2.2
Post-deformational annealing
The addition of defects during deformation makes the crystal structure thermodynamically unstable due to the high stored energy (Fig. 3). Thermody-namics suggests that when the deforming process is removed, the defects should disappear (Humphreys and Hatherly, 2004). However, in reality these processes are extremely slow at low homologous temperatures. At higher temperatures however, these processes can be activated so that disloca-tions are removed or rearranged into lower energy configurations which can significantly alter the mi-crostructure (Heilbronner and Tullis, 2002). After deformation, a natural material in the crust re-mains at higher temperatures even when the pres-sure is removed. In other words as a rock is ex-humed through the crust it may undergo some post-deformational annealing and this is generally the last process to affect the rock (Fig. 1).
The driving force for post-deformational
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 and it occurs by two main processes; recovery and recrystallisation (Urai et al., 1986; Drury and Urai, 1990; Baker, 2000). We focus here on recovery, which is driven by the interaction of dislocations via their long-range stress fields and occurs through two main processes operating simultaneously: an-nihilation of dislocations of opposite signs and poly-gonisation, where dislocations align to form low energy arrays (Gottstein, 2004; Humphreys and Hatherly, 2004). Dislocation movement is con-trolled by two main mechanisms, glide along lattice planes and climb between them in order to over-come obstacles. In the case of screw dislocations moving in certain crystallographic planes, cross slip between lattice planes can also become important (Hull and Bacon, 2001). Any of these can be rate controlling, dependent on the type of dislocations in the system and the temperature of annealing (Nes, 1995). The velocity (v) of a dislocation is a function of the force (F ) on the dislocation and its mobility (M ):
v = M F (1) Mobility of the dislocation is thermally activated and of the type exp(−Q/kT ), thus the velocity can be rewritten as:
v = α × exp(−Q/kT (1 − σ/σb) (2)
where α is an independent material constant, σ the stress, σb the stress to overcome a barrier for
glide without help from thermal agitation and Q is the activation energy or total free energy needed to overcome that barrier without the help of stress.
Dislocation climb occurs by diffusional trans-port of vacancies to the dislocation with the fol-lowing velocity relationship:
v ≈ (β × exp(−Q/kT )b2)/kT σ (3) where β is a material dependent constant and b the Burgers vector.
Annihilation of dislocations of opposite Burg-ers vector can occur when two dislocations meet by glide along the same lattice plane. It can also occur between dislocations on different planes by a combination of glide and climb or in the case of screw dislocations glide and cross-slip (Humphreys and Hatherly, 2004).
In addition, if there are unequal numbers of dis-locations of two signs after deformation, polygoni-sation occurs. This is the process by which these dislocations rearrange to form low angle bound-aries, overlapping the area of distortion surround-ing each dislocation and thus reducsurround-ing the stored energy of the whole system (Hull and Bacon, 2001). This can be shown by calculating the energy of the boundary with respect to the misorientation angle: θ ≈ b/d (4) where θ is the misorientation angle and d is the dis-location spacing in the boundary (Humphreys and Hatherly, 2004).
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:
E = E0θ(A − ln θ) (5)
where E0 = Gb/4π(1 − v), A = 1 + ln(b/2πr0), G
is the shear modulus and r0 is the radius of the
dislocation core.
Based on this equation the energy of a bound-ary increases with increasing misorientation, but by combining Eq. (4) and (5), it can be seen that the energy per dislocation decreases. This occurs as the stress fields of the dislocations overlap with decreasing d (Hull and Bacon, 2001). As a result of this energy decrease the system favours bound-ary building. However for misorientation increase, dislocations within the boundary itself need to re-arrange to decrease the spacing. This is generally achieved by climb (Hull and Bacon, 2001). Both processes, dislocation movement into boundary and climb within a boundary, can be limiting with re-gard to misorientation increase of the boundaries.
Once a polygonised substructure is attained, the stored energy can be further lowered by a coars-ening of the substructure to reduce total bound-ary area (grain growth) (Humphreys and Hatherly, 2004). The driving pressure (P ) for subgrain coars-ening can be shown by the following relationship:
P = αE/r (6) where α is a shape factor of ∼1.5, E is the energy of the boundary (Eq. 5) and r is the subgrain radius. In particular, symmetrical tilt boundaries can move by glide of the edge dislocations that comprise the boundary (Humphreys and Hatherly, 2004). Mobility in this case is high, and migration can occur even at low temperatures (Parker and Wash-burn, 1952).
2.3
Halite as an analogue
For the study we have selected high purity, syn-thetic halite as the experimental material. Halite plays a significant role in fold-and-thrust belts, delta tectonics, basin evolution and hydrocarbon accumulation, as well as being a possible medium for storage of nuclear waste (e.g. Franssen, 1993 and references therein; Rempe, 2007; Schl´eder and Urai, 2007). Halite is a particularly good ana-logue for many metals, as it has similar bonding i.e. ionic and a cubic structure. The development of subgrain-scale microstructures in halite occurs at experimentally attainable conditions (∼20MPa and >200 oC) (Senseny et al., 1992) and shows many
similarities with that occurring at higher temper-atures and pressures in silicates, making it a good analogue for geological materials also (Guillope and
Poirier, 1979; Drury and Urai, 1990). There are, however, some differences between other crystalline geological materials and halite. The bonding in ge-ological materials such as silicates is not the same and the crystal structure generally has a lower sym-metry. This means that less easily activated slip systems are present, which has an affect on the activation of different deformation processes. For instance, high symmetry materials can deform by dislocation creep within a large range of pressure, temperature and strain rate, while low symmetry tend to switch more readily to grain boundary mi-gration or diffusion creep when dislocations become tangled.
Due to its ionic-bonded, cubic crystal structure, NaCl provides a simple starting point for studying these complex processes. In order to study sub-structural behaviour in more detail a single crystal of halite was used for the experiments. Using a sin-gle crystal resolved potential problems from rapid high angle grain boundary migration removing the substructure, as was experienced by Piazolo et al. (2006). The high purity of the sample meant that boundary pinning by impurities would be less likely to influence the results (Smith, 1948). Fluid con-tent at the boundaries can have a large effect on boundary mobility, so the samples were kept dry in a dessicator to reduce the possibility of atmospheric absorption of water (Trimby et al., 2000b).
Previous studies on the microstruc-tural/substructural behaviour of halite have been conducted. These include EBSD studies on the deformation microstructure of rock salt (Trimby et al., 2000a; Trimby et al., 2000b; Pennock et al., 2002; Pennock and Drury, 2005; Pennock et al., 2005; Pennock et al., 2006) and EBSD coupled with in-situ annealing of polycrystalline halite (Best-mann et al., 2005; Piazolo et al., 2006).
2.4
2D
In-situ
annealing
experi-ments
The field of microstructural investigation has un-dergone many developments in recent years allow-ing us to more fully characterise behaviour of ge-ological materials during annealing. In the past, studies were restricted to examination of the “post-mortem” post-deformational annealing microstruc-ture (Covey-crump, 1997; Masuda et al., 1997; Heilbronner and Tullis, 2002; Barnhoorn et al., 2005). Real-time analyses were limited to optical microscopy on transparent rock analogues (e.g. oc-tachloropropane and norcamphor) (Ree and Park, 1997; Nam et al., 1999; Park et al., 2001), where only the c-axis could be determined. The full crys-tallographic orientation is needed, however, to
com-pletely characterise annealing behaviour. The de-velopment of the EBSD technique allows for this, with the Euler angle orientation for each point fully calculated (Prior et al., 1999 and references therein) and there have been a number of studies of the microstructure at different times during an-nealing in both geological materials (e.g. calcite) (Barnhoorn et al., 2005) and metals (Ferry and Humphreys, 1996; Huang and Humphreys, 2000; Huang and Humphreys, 2001; Huang et al., 2000; Ferry and Humphreys, 2006). Developments allow-ing the combination of in-situ annealallow-ing inside the scanning electron microscope with EBSD provide a powerful tool for the “real-time” analysis of post-deformational annealing (LeGall et al., 1999; Se-ward et al., 2002; Humphreys, 2004; Piazolo et al., 2005). A handful of studies have been carried out on various materials using this combined tech-nique including: titanium (Seward et al., 2004), aluminium (Huang and Humphreys, 1999; Piazolo et al., 2005; Kirch et al., 2008) rock salt (Bestmann et al., 2005; Piazolo et al., 2006), copper (Mirpuri et al., 2006; Field et al., 2007) and Al-Mn alloys (Lens et al., 2005).
2.5
3D X-ray diffraction
The major limitation of the 2D in-situ experiments is that we are analysing a three-dimensional struc-ture on a two-dimensional surface. Valuable infor-mation about substructural behaviour can be taken from these experiments, but it is difficult to pre-dict the influence of surface effects such as thermal grooving or surface tension (Frost et al., 1990 and references therein). Thermal grooving can be par-ticularly significant, resulting in subgrain boundary pinning at the groove tip and retardation of migra-tion rate as a result (Mullins, 1958; Brokman et al., 1995; Gottstein and Shvindlerman, 2010). New techniques such as serial sectioning with focused ion beam (FIB) tomography coupled with EBSD allow investigation of the interior of the crystal but of course such a method is destructive and would ef-fectively remove the “real-time” component of the experiments as we cannot compare the same sur-face before and after annealing (Xu et al., 2007). 3DXRD is a way to overcome this limitation as it allows us to examine the inside of the crystal non-destructively (Nielsen et al., 2001; Fu et al., 2003; Poulsen, 2004; Baruchel et al., 2008). 3DXRD is a technique which is becoming more readily avail-able to scientists in a number of different fields, in-cluding a growing number of structural geologists. 3DXRD can be coupled with in-situ heating exper-iments but until now this has been limited to the application to metals including aluminium
sen et al., 2001; Gundlach et al., 2004), Mg-Al alloy (Poulsen et al., 2004) and copper (Lauridsen et al., 2006).
2.6
Numerical simulation
Numerical simulation of microstructural behaviour and in particular recovery processes is an evolving field with many contributors. The strength of nu-merical simulation is that we can easily manipu-late the input data and parameters allowing us to study the underlying processes and theories (Bons et al., 2008). Different modelling techniques have been applied to microstructural problems including front-tracking models (Moldovan et al., 2002; Wey-gand et al., 2001), Monte Carlo algorithms (Holm et al., 2003; Holm et al., 2004; Gruber et al., 2009), phase field models (Sreekala and Haataja, 2007) and cellular automata models (Raabe and Becker, 2000; Miodownik, 2002). A previous study was car-ried out on polycrystalline halite by Piazolo et al. (2004) using a kinetic Monte Carlo Potts model in the 2D microstructural modelling platform Elle. As Potts models cannot fully be coupled to “real-time” behaviour we use this study as a basis on which to build a more deterministic model.
The microstructural modelling platform Elle has proven to be a powerful tool for analysis of the evolution of microstructures and the processes which control them. Elle has been used previously in many studies, investigating a variety of different processes (Piazolo et al., 2010a). These include: subgrain growth (Piazolo et al., 2004), isotropic and anisotropic grain growth (Bons et al., 2001; Jessell et al., 2003; Piazolo et al., 2004; Becker et al., 2008), strain localisation (Jessell et al., 2005), melt processes (Becker et al., 2004; Becker et al., 2008), strain rate portioning during porphyroblast growth (Groome and Johnson, 2008), cation ex-change (Park et al., 2004), two phase deforma-tion (Jessell et al., 2009), fracturing in granular aggregates (Koehn and Arnold, 2003), stylolites (Koehn et al., 2007), dynamic recrystallisation (Pi-azolo et al., 2002), strain localisation (Jessell et al., 2005) and recovery (Piazolo et al., 2010b).
While both experimental techniques and nu-merical simulation are very successful methods of studying microstructures, they do have inherent limitations. In-situ experiments have the possibil-ity of surface effects influencing behaviour and are restricted to materials which exhibit changes that are fast enough to observe on a human timescale and which respond under appropriate laboratory friendly conditions (Piazolo et al., 2004). The qual-ity of numerical simulation is limited by the rele-vance of the input data, the choice of
fundamen-tal laws and theoretical data and the availability and accuracy of physical constants (Piazolo et al., 2004).
The combination of these two techniques re-duces the limitations of both. By directly retrieving crystallographic orientation data from the experi-ments we provide a solid, physical basis on which to run the simulation. Since we have before and after heating maps we can directly compare the ef-fect of real annealing with simulated annealing and determine the validity of the model.
3
Methods
3.1
2D in-situ annealing and EBSD
Over the course of this project, in-situ annealing experiments were conducted inside a XL30 envi-ronmental field emission gun SEM using a GATAN heating stage (Fig. 4). The sample was heated in place on the stage while EBSD maps of the sur-face were taken (Dingley, 1984). Backscatter occurs due to the interaction of electrons from a stationary beam and atoms in the crystal lattice. The sample is tilted at 70o for optimum signal. The trajectory
of the backscattered electrons provides information about the arrangement of the crystal lattice and is collected with a fluorescent screen. The pattern is detected on the screen as Kikuchi bands, each of which corresponds to the position and orientation of a lattice plane (Fig. 5). Collected patterns were auto-indexed using HKL Channel 5 software (Ox-ford Instruments). An automatic Hough transform analysis is used to detect the edges of a number of bands (in this experiment 5-6 bands were selected). The pattern is then indexed by comparison of cal-culated solid angles to a known match unit for the mineral being analysed. For more specifics on data collection see Manuscript I.
While Prior et al. (1999) and Humphreys (2004) state that 0.5o is the reliable limit for
misorienta-tion between two points, Pennock et al. (2002) sug-gests an error limit of 0.3o. Since the same area was
mapped after each stage in our study we suggest a lower limit for our experiments and calculated an error limit of ± 0.1oafter remapping over the same
area and comparing results (for more details see Manuscript I).
3.1.1 Data processing
EBSD maps collected in the SEM are analysed using offline HKL Channel 5 software. Noise re-duction was applied to the data following a pro-cedure whereby non-indexed pixels with up to 6
Figure 4: SEM configuration for orientation mapping by EBSD during annealing (after Gottstein, 2004).
indexed neighbour pixels were automatically as-signed the most common orientation from neigh-bouring indexed pixels. A filter was also applied to remove single, isolated pixels or “wild spikes” from the data as there were likely to be indexing mistakes. To enhance subgrain boundary detec-tion, the Kuwahara edge detection filter was ap-plied in two passes (Kuwahara and Eiho, 1976; Humphreys, 2004). While processing, EBSD maps were compared to orientation contrast images to check that the substructure was accurately repre-sented and significant artefacts were not introduced (Prior et al., 1996).
Different ways of representing the data were utilised using the HKL software (Fig. 6). The col-lected crystallographic orientations were displayed in a number of ways including: textural deviation maps, inverse pole figure colouring, rotation axes and crystallographic orientation pole figures, and local misorientation maps. Specific features could be highlighted including subgrain boundaries and their misorientation axes.
In order to assess potential active slip systems and the type of subgrain boundary, boundary trace analysis can be used, as was done in Manuscript I (Lloyd et al., 1997; Prior et al., 2002). Boundary trace location is compared to rotation axis. If the rotation axis lies on the boundary trace, the bound-ary is likely to have a tilt geometry (i.e. made up of edge dislocations) (Fig. 7a). If the rotation axis lies perpendicular to the trace, a twist geometry is possible (i.e. made up dominantly of screw
dislo-cations) (Fig. 7b). These can then be related to known slip systems and based on the geometry the most likely can be found.
3.2
3D X-ray diffraction
3D X-ray diffraction allows for non-destructive in-vestigation of a crystal volume (Nielsen et al., 2001; Fu et al., 2003; Poulsen, 2004; Baruchel et al., 2008). This technique was used for Manuscript II and Manuscript III. A monochromatic beam is passed through the sample with a reciprocal pat-tern collected for those parts of the crystal that fulfill the Bragg condition. This means only those with the right wavelength for diffraction along crys-tal lattice planes will be indexed. In order to fully characterise the crystallographic orientation it is necessary to rotate the sample in space around the z axis by ω so that a full reciprocal pattern can be collected (Fig. 8).
3DXRD can be coupled with in-situ heating, similar to the SEM setup (section 3.1). A furnace is coupled to the system with the sample sitting in a heated copper bar with a thermocouple running in-side it. Temperature can be adjusted from outin-side the beam hutch. A fitted glass casing is continu-ously flooded with argon gas to keep the sample at a constant temperature (Fig. 8).
The diffraction pattern is collected by two de-tectors placed at different lengths from the sample. A high spatial resolution detector with a 5 µm pixel size is located a few mm from the centre of
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 misorienta-tion 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.
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 crystallographic orientation. A second low resolu-tion detector at a large distance provided the bulk diffraction pattern for the crystal (Fig. 8). Dur-ing heatDur-ing, small maps could be taken over a lim-ited rotation encompassing 1 or 2 subgrains (Fig. 9). These provide “real-time” maps of the changing substructure. It is necessary to pull the high spatial resolution detector further from the sample during heating, as it may be damaged by the increased temperature.
3.2.1 Data analysis
The syn-heating maps required minimal post-processing, as we examined the changes in the diffraction pattern and did not try to reconstruct the actual crystal structure. Images were treated for the effect of beam decay by correcting the greyscale for this. Composite stacked images from Manuscript II, were created by stacking the diffraction images for each minor rotation to make a 3D volume with the X and Y constituting the pix-els of the images and Z as the small rotation (Fig. 9).
The full crystal structure was reconstructed using the post-processing program, Grainsweeper (Schmidt et al., internal report). This is a stand alone program for reconstructing both un-deformed and un-deformed microstructures in mate-rials i.e. the crystallographic orientations as well as the grain morphologies are extracted simultane-ously (Schmidt, 2010, pers. comm.). The current resolution, which is limited by detector resolution, is 5 microns. The Grainsweeper program runs fully automatically once the geometric (global) param-eters from the experimental setup have been de-fined (beam energy, distance, tilt of the detector).
Each voxel in the map represents a crystallographic orientation, which can only give rise to intensities in small segments of the Debye-Scherrer rings due to constraints related to space group, lattice pa-rameters and beam energy. All signals on the de-tector which could originate from the chosen voxel are added to the Rodrigues space (each signal is a geodesic in this space) and a rough orientation dis-tribution function is created. The orientation space is then searched for signals higher than the back-ground (local maxima). A forward projection onto the detector estimates completeness of candidate orientations (the ratio of measured reflection over the number of expected reflections). The orienta-tion possessing maximal completeness is chosen to be the final orientation for the selected voxel.
The 2D voxel grid with crystallographic orien-tations for each layer from the reconstructed vol-ume was imported into the HKL Channel 5 soft-ware and post-processed in a similar manner to the 2D data (see section 3.1.2). 3D comparison im-ages were created using ImageJ, an image process-ing program. Other types of analysis investigated included subgrain boundary histograms, textural deviation maps, local misorientation maps and ro-tation axis pole figures.
3.3
Numerical modelling
The Elle modelling platform was developed to al-low incorporation of different microstructural pro-cesses into one program (Bons et al., 2008). Us-ing Elle, modellers can concurrently apply different processes to their starting microstructure and test how it evolves. We used this platform to build the new recovery model discussed in Manuscript IV which will be incorporated into the library of possi-ble processes, making it availapossi-ble for others in the
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 260oC and (c) is after heating 3h 20min at 260oC.
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 contains layered networks of nodes in which physi-cal and chemiphysi-cal information can be stored. Layer 1 consists of a network of boundary nodes (bnodes) and connecting boundaries which form a grain net-work of flynns (Fig. 10). Layer 2 consists of a regular grid of unconnected nodes (unodes), which can be arranged in a square or hexagonal pattern. These two layers can communicate with each other. Algorithms designed to represent specific processes can interact with this data structure in a number of ways including i) using the node values to deter-mine driving forces, ii) rearranging, creating or re-moving nodes, iii) reconnecting boundary segments and iv) changing the attributes stored in the nodes (Piazolo et al., 2004).
Elle allows for EBSD data to be directly im-ported into the program using EBSD2ELLE. This means we can use data from physical experiments to test the numerical model for validity based on the actual response of the microstructure during annealing.
3.3.1 Data analysis
Final data after running the simulation for the pre-scribed number of steps was converted to a text file using ELLE2EBSD. This can then be imported into the HKL Channel 5 program, where the data was analysed. Data comparison was made in a number of ways including: subgrain boundary histograms, rotation axis pole figures and local misorientation
maps.
4
Results and discussion
4.1
Manuscript I
Manuscript I, Post-deformational annealing at the subgrain scale: temperature dependent be-haviour revealed by in-situ heating experiments on deformed single crystal halite discusses temper-ature dependent annealing behaviour on single crystal halite, focusing on subgrain boundary be-haviour. The results from 2D in-situ annealing experiments conducted inside the scanning elec-tron microscope coupled with elecelec-tron backscatter diffraction had a number of important implications for the field. The experiment was conducted at a lower-temperature window, below the deformation temperature, which is not usually investigated in annealing studies. This window, however is partic-ularly relevant for geological settings, where rocks often stay at higher temperatures even after the deforming pressure is removed. We showed that annealing with a significant reduction in crystal-lographic orientation, and change in the subgrain structure by dislocation removal can occur, even at lower temperatures.
We found that before “classical” annealing be-haviour of polygonisation followed by increase in boundary misorientation begins, substructural be-haviour can fluctuate. Boundaries undergo both increases and decreases in misorientation at
tain temperatures. Subgrain boundaries cannot be grouped under one definition reflecting their be-haviour and must be treated accordingly. Bound-aries could be specifically associated with different slip systems, most generally they could be grouped into two categories based on their slip system asso-ciation: primary boundaries (those aligned with the predominant slip systems (011)[011] or (011)[011], which occurred more frequently throughout the whole sample) and secondary boundaries (with (101)[101] and (101)[101] which were only found in the more deformed central part of the crystal). We could further subdivide boundaries into four differ-ent categories based on their behaviour, morphol-ogy and orientation.
Behaviour showed three distinctly temperature-dependent regimes:
Regime I (<300 oC) Primary boundaries
in-crease in misorientation, while secondary bound-aries decrease. Dislocations annihilate and some rearrange to form new subgrain boundaries which subdivide subgrains into regions of like orientation. Regime II (∼300 oC) All boundaries decrease in misorientation. Dislocation annihilation and new boundary formation continue.
Regime III (>300 oC). All remaining
bound-aries increase in misorientation. No new boundary formation after this point. Secondary boundaries demonstrate a change in rotation axis.
During all three regimes some minimal bound-ary movement occurred.
From these results we suggested a model of substructural evolution. Annealing behaviour is strongly dependent on dislocation type, in partic-ular their mobility and spatial range of influence. This is, of course, strongly linked to temperature of annealing. At lower temperatures, we postulated that climb has not been activated yet, and that at 300 oC there is a decrease in boundary
misorien-tation since dislocation separation can no longer increase. At >300 oC climb is activated, so
dis-location mobility is increased and separation can also increase. As temperatures increase the range over which dislocations can influence one another increases.
4.2
Manuscript II
Manuscript II, The application of in-situ 3D X-ray Diffraction in annealing experiments: First interpretation of substructure development in de-formed NaCl details preliminary results from the six day 3D annealing experiment conducted at the synchrotron in Grenoble. This experiment is the first of its kind conducted on a geological material. Experiments were designed to test the possibility of
surface effects from a 2D surface during annealing. We examined both a single layer (before and after heating) from the 3D reconstruction of diffraction patterns and syn-heating analysis which was con-ducted to follow changes in “real-time”. A number of key processes were identified, which were:
1. increase and decrease in misorientation of the subgrain boundaries
2. subgrain subdivision where two parts of the subgrain rotate away from each other to form areas of like orientation with a new boundary forming between them
3. boundary movement
Comparison of syn-heating maps to recon-structed layers indicated similar processes occur-ring in both. Preliminary analysis suggested that 3D X-ray diffraction is a powerful technique for ex-amining post-deformational annealing. We demon-strated that reconstruction was possible even with highly complex microstructures.
4.3
Manuscript III
Manuscript III, In-situ 3DXRD annealing of a geological material: Evaluating the validity of 2D furthers the ideas and observations from Manuscript II, with complete analysis of the fully reconstructed 3D data. Results supported the servations made in Manuscript II. Processes ob-served involved the rearrangement of dislocations, including alignment into arrays with formation of new subgrain boundaries, increase and decrease in boundary misorientation with complete dissipation in some cases and extensive boundary movement. Comparison to the results from the Manuscript I indicated that boundary movement was much more common in the 3D experiment, than the 2D, on the order of 4 to 28 times more likely. This is a partic-ularly significant result as it indicates that the 2D experiment does experience some effect from having a free surface. Some thermal grooving of bound-aries occurred in the 2D experiment. It is thus suggested that the subgrain boundaries experience some drag at the tip of these grooves, which signif-icantly retards migration rate, similar to described and predicted behaviour for high angle boundaries (Mullins, 1958; Brokman et al., 1995; Gottstein and Shvindlerman, 2010). This means we have to deal with boundary movement in 2D with some care, and absolute migration rate may not be accurate. General boundary behaviour (increase and decrease in misorientation) exhibited similar behaviour in the 3D volume, however.
Analysis of subgrain area change during anneal-ing with relation to the number of neighbouranneal-ing subgrains indicated that it is likely that the Von-Neumann-Mullins criteria is upheld for 2D layers in a 3D volume (Neumann, 1952; Mullins, 1956). Two subgrains that did not uphold the criteria were pos-sibly misrepresented by the cutoff or so close to the edge of the analysis area that not all neighbours were resolved.
This experiment demonstrates that 3DXRD is an applicable technique for crystalline geological materials. It was possible to fully reconstruct the crystal with the Grainsweeper processing, even though it exhibited large, continuous changes in ori-entation which present as a blurry diffraction pat-tern that is difficult to resolve.
4.4
Manuscript IV
Manuscript IV, Numerical simulation coupled with in-situ annealing experiments: A new model for recovery discusses the results from a numeri-cal simulation written to model the recovery pro-cess. This was done using the microstructural modelling platform Elle which allows the crys-tallographic information collected from electron backscatter diffraction to be used as the starting microstructure for the simulation. We incorporated extensively the results and derived interpretation of process details from Manuscript I to design the model. Results from the simulation indicated a number of interesting implications for the field. The paper supported the hypothesis of tempera-ture and dislocation type dependent annealing be-haviour discussed in Manuscript I. Dislocation type dominance was reflected in varying the ro-tation mobilities on different roro-tation axes which were specifically chosen to imitate the slip sys-tems active in the 2D experiment. This replicated most of the interesting fluctuating misorientation behaviour, which leads us to conclude that bound-aries do behave in ways that are specific to their dislocation makeup and should be treated us such. It also suggests that rather than being fixed and organised once they are aligned into an LAB, dis-locations can still be independent to much higher misorientation angles than previously thought.
The main weakness of the simulation was that it was impossible to preserve higher angle behaviour while still generating the fluctuating behaviour of lower angle boundaries. Different methods of cal-culating stored energy using the Read-Shockley re-lationship could represent either type of the be-haviour but not both. An attempt to combine two types of calculations, indicated that this behaviour switched from lower angle, to higher angle at a
crit-ical cutoff of ∼7o (in halite). The Read-Shockley relationship has been supported by experimental results, but most of these show a data poor region, between two distinct, almost straight line relation-ships. Our critical cutoff falls in this data-poor transition zone.
Results also indicate that the range of influence of the dislocation core radius has a significant effect. In the simulation, we increased neighbourhood size to try and replicate behaviour and found that this was important in order to accurately replicate the results as closely as possible.
We thus proposed support for the model of sub-structural evolution suggested in Manuscript I and presented a simulation for recovery which can be used for other materials where the deformation geometry is well constrained.
5
Summary and conclusions
Returning to the main project aims detailed in sec-tion 1.1 we summarise the results in terms of how far this PhD project has advanced understanding of substructure dynamics, specifically based on the initial aims of the project.
From Manuscript I we learned a great deal about how the substructure of a crystalline mate-rial evolves during annealing. Observations of vary-ing substructural behaviour from Bestmann et al. (2005) and Piazolo et al. (2006) were confirmed. Subgrain boundaries were found to both increase and decrease in misorientation, with some dissipat-ing completely. Boundary behaviour was specific to different types of boundaries and thus it is not enough to view all subgrain boundaries in the same light. Annealing behaviour was highly temperature dependent, with three regimes identified. This led to the proposal of a model for substructural evolu-tion reliant on dislocaevolu-tion type and its temperature-dependent mobility. Manuscript II and III fur-ther supported the behaviour observed in the 2D in-situ annealing experiments, as we could see similar response of the 3D volume. However, Manuscript III did reveal that there were some surface effects causing an influence in the 2D experiments, by sub-grain boundary pinning on thermal grooves. This suggested that subgrain boundary movement was actually a lot more extensive than shown in the 2D experiments. Evidence in Manuscript III sug-gested that the Von Neumann-Mullins criteria for grain growth were fulfilled for 2D layers in a 3D volume.
Manuscript I allowed us to begin to define a subgrain boundary in terms of the critical misori-entation angle at which boundary behaviour begins.
We observed that even once subgrain boundaries had been formed, dislocations did not seem to be completely fixed and could still annihilate resulting in decrease in boundary misorientation and some-times complete dissipation. Manuscript IV fur-ther developed this idea, as the numerical simu-lation supported the model of substructural evo-lution we proposed in Manuscript I. In particu-lar, it did appear that dislocations could still be independent in a boundary setting, to much higher angles of misorientation than previously thought. Manuscript IV provided some information about where the cutoff misorientation for boundary be-haviour might be. Different methods of calcula-tion of stored energy revealed that at a misori-entation ∼7o (in halite) the boundary behaviour switched from lower angle fluctuating behaviour to higher angle boundary development. It was found that misorientation angles that fell in the data-poor “transition zone” of the more well-defined parts of the Read-Shockley relationship could not be prop-erly represented.
In Manuscript I we discovered some evidence about the type of dislocations that form different types of subgrain boundaries and how this affects their behaviour. Subgrain boundaries were subdi-vided into different categories based on their be-haviour during annealing. We could associate the boundaries with two main groups of dislocations in-troduced during deformation and it was found that these groups behaved significantly differently dur-ing annealdur-ing. In Manuscript IV we tested this theory by varying rotation mobilities on three rota-tion axes that we considered controlled behaviour in the 2D experiment of Manuscript I. We found that we could replicate the fluctuating boundary misorientation behaviour only by varying the mo-bilities and dominance of these different axes. In Manuscript I, we suggested a specific group of dis-locations (represented in the simulation by rotation axes) would be dominant during each temperature dependent regime and this model was supported by the results from the numerical simulation.
In part we have answered the question, can we predict subgrain boundary behaviour? Manuscript IV details a numerical simulation for recovery which can be used to predict some boundary be-haviour. The results from the experiments de-scribed in Manuscript I could be supported by the simulation (Manuscript IV) though it was difficult to reproduce both lower angle fluctuating boundary behaviour and higher angle behaviour. While we suggest that it is possible to predict much of subgrain boundary behaviour with the simula-tion, it is dependent on a significant knowledge of the deformation geometry and thus activated slip
systems, which can, however, be derived from de-tailed microstructural studies for example, using a Burgers vector analysis program (Wheeler et al., 2009) or boundary trace analysis (Lloyd et al., 1997; Prior et al., 2002).
The final aim of the project was to determine if we could use substructure and subgrain boundary behaviour to derive deformation and/or annealing conditions. If we focus first on deformation con-ditions we see that this is more difficult. While the substructure changed significantly in the exper-iments (Manuscript I), many of the changes were increase and decrease of boundary misorientation. This unfortunately does not tell us much about the specifics of the deformation conditions as we can-not follow back through a number of recognisable changes to determine the original conditions. How-ever, in Manuscript II and III, it is evident that a lot more subgrain boundary movement occurs in a 3D volume than 2D because of the surface ef-fect of thermal grooving. An in-depth study of this subgrain growth behaviour has not yet been made, but could possibly assist in the aim of deriving de-formation conditions. The experiments are a little more helpful when it comes to annealing conditions. From Manuscript I we see three distinctly tem-perature dependent regimes which were supported by the numerical simulation (Manuscript IV). A number of changes could indicate that the climb temperature (Regime III) has been reached and this suggests that in a sample where the deformation geometry is well-constrained, we could indeed de-termine the temperature of annealing.
The work of this PhD project has begun to answer some of the many questions surrounding substructure dynamics and how useful they are in determining past conditions and predicting future ones. There are many questions still to be answered and four years work on one crystal of salt is just the beginning. With this in mind we present some potential work to be conducted in future studies (section 7).
6
Main outcomes
The main outcomes of this thesis are twofold: 1. Development of a significantly refined model
for recovery in crystalline material.
2. Advancement of analytical techniques com-bined with awareness of their strengths and shortcomings.
The developed recovery model is particularly relevant for geological materials as it focuses on
recovery active at temperatures below the defor-mation temperature. The model was suggested in Manuscript I and has been supported and im-proved by the results from Manuscript IV. This model is significant for materials with a primarily activated slip system and a secondary slip system which is only activated later in the deformation process. We thus envisage a starting dislocation budget where primary dislocations (ρps) have been
mostly arranged into higher misorientation bound-aries, while secondary dislocations (ρss), emplaced
later mostly remain free in the subgrain interior with only a few resolved into subgrain boundaries. Three temperature-dependent regimes were deter-mined in Manuscript I and processes occurring during them are detailed here:
Figure 11: Schematic of the recovery model. De-tails from the numerical simulation are shown, the dominant rotation axis used in replicating each regime as well as the size of the neighbourhood from which the energy calculation was made (bot-tom right hand corner).
Regime I (Fig. 11a): Dislocation movement occurs predominantly by glide. ρps glide into
sub-grain boundaries increasing them in misorientation, while the large number of free ρss result in a
de-crease in secondary subgrain boundaries. In order to model this with simulation, the secondary rota-tion axis was made dominant by varying rotarota-tion mobilities (Manuscript IV), which gave similar results. Dislocations also annihilate in the subgrain interior and when there are none available of oppo-site 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 move-ment still occurs predominantly by glide. Sec-ondary boundaries continue to decrease in misori-entation, but at a reduced rate as the number of ρss available dwindles. To model this in the
sim-ulation the primary rotation axis was made domi-nant (Manuscript IV). Primary subgrain bound-aries decrease in misorientation also by annihila-tion in the boundary vicinity, since dislocaannihila-tion sep-aration 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 in-creases which was modelled by increasing the neigh-bourhood influence to a larger range for the energy calculation (Manuscript IV).
Regime III (Fig. 11c): The activation temper-ature for climb is now reached. Subgrain bound-aries increase in misorientation as dislocation sepa-ration within boundaries can increase. Long-range influence of dislocations extends significantly as modelled by increasing the neighbourhood influ-ence to an even larger range for the energy calcula-tion (Manuscript IV).
It is clear from the results of the manuscripts that dislocations remain independent in boundaries to much higher angles of misorientation than previ-ously thought. The simulation results suggest that, for halite, they start to become locked in the bound-ary at a misorientation of ∼7o, with fluctuating be-haviour of increases and decreases in misorientation below that angle.
The work of this project has advanced some of the analytical techniques used to study
tures. We demonstrated that analysis and resolu-tion of a crystalline geological material with a large amount of internal deformation was possible us-ing 3D X-ray diffraction. This was the first in-situ 3DXRD annealing experiment conducted on a geo-logical material. The results led to some important implications for 2D analysis techniques, such as the 2D in-situ annealing experiments performed inside the SEM. Boundary migration was found to occur to a much larger extent within a 3D volume than was observed on the 2D analysis surface. This has been interpreted as boundary pinning by thermal grooves on the analysis surface retarding migration rate. This means that while relative migration rates will be similar, absolute rates in a 2D analysis need to be treated with some care.
A new model for recovery was developed using the microstructural modelling platform Elle. This was tested on experimental results from the 2D in-situ annealing experiments. The model is suitable for samples where the deformation geometry is well-constrained.
7
Future work
This study has raised some interesting questions about substructure dynamics in geological materi-als. Since all parts of this study have focused on analysing the behaviour of one halite crystal, TL1, it would obviously be of great benefit to extend this to crystals deformed in different manners and even other materials. Testing if similar behaviour oc-curs in different minerals with lower symmetry is difficult to conduct in-situ, but the high pressure-temperatures setups of the synchrotron could be used. Applying these ideas to natural examples from “natural laboratories”, with similar conditions would also be beneficial. We do also have a num-ber of halite samples from the same series as the TL1 crystals, deformed with similar strain rates but at different temperatures. Annealing experiments have been conducted on a number of these but the data has not yet been analysed. We also have a series with varying final strains (0.05-0.20) which we have not yet conducted experiments on. Anal-ysis of these two series should further reveal the significance of strain and temperature dependence on annealing behaviour.
While syn-heating maps from the 3DXRD ex-periment have been partially analysed, a further full analysis is necessary. In order to do this, a new technique will need to be developed to sepa-rate orientation from subgrain shape, as both these parameters are contained in the diffraction pattern information. This will provide us with much more
information. Now that it has been shown that the crystal structure of materials with high inter-nal subgrain misorientation can be resolved, it fol-lows that further 3DXRD experiments on highly deformed materials, with annealing conditions ap-propriate for the furnace setup, should be exam-ined.
While the numerical simulation, as presently constructed can replicate a lot of the specific boundary behaviour, including misorientation in-crease and dein-crease, it cannot move boundaries. The simulation next needs to be coupled with a boundary movement process. There are a number of grain boundary migration processes built into Elle and these should be investigated to determine if they might be appropriate. It is important to choose a deterministic method, however, since one of the most important features of the simulation is the possibility of linking it to real-time. The simulation should also be applied to other materi-als. Rotation axes can be chosen specifically for the material of choice, if the deformation geometry is fairly well constrained.
8
Acknowledgements
First and foremost I would like to thank my super-visor, Sandra. I could not have asked for a better guide through this PhD process. Thank you for always having your door open to me, for count-less phone calls on the weekend when the SEM was playing up again, for many nights spent discussing papers after the kids had gone to bed and for al-ways being enthusiastic no matter what happened. I feel extraordinarily privileged to have had the op-portunity to work with you these last four years and lucky to count you among my friends.
I would also like to thank Pat, Sandra’s other half, for letting me steal so much of his wife’s time. And his own time! It is a little difficult to ignore an EBSD user if they are your wife’s student but I really do appreciate all the time spent on the week-ends talking me through another problem. You went above and beyond the call of duty.
I acknowledge the financial support of European Science Foundation under the EUROCORES Pro-gramme, EuroMinSci, MinSubStrDyn and am ex-tremely grateful to have been part of this collabo-rative project. Also the Knut och Alice Wallenberg stiftelse, which funded the experimental setup.
To my Co-authors, it has been a pleasure work-ing with you on these papers. Thanks for all the great feedback, countless drafts and fun times while doing experiments and writing numerical models.
I would also like to thank the rest of the
SubStrDyn (how do we pronounce that again?) group. Being part of such an awesome scientific community has been a wonderful experience that I have really appreciated. In particular thanks very much to my co-supervisor Paul and to Dan, Mark, Dave, Lynn, Albert, Jens and Joyce. You made this really fun!
To my fellow long-suffering office mates, He-lena, Henrik and Brigitte. It’s been a lot of fun wedging into our tiny office together and I couldn’t have asked for three nicer people to share it with. Thanks for listening to my stupid ideas, putting up with my general and often dreadful mess and wa-tering my plants while I was away (I think they get better attention when I am not in town).
I couldn’t have done this without my friends in the department. For all those people who were around for coffees and beers and put up with my in-appropriate lunchtime conversation, I am so grate-ful to you. My time here would not have been the same without you. As in it would have been bad. So thanks goes to Cecile, Xavier, George, Linda, Paulina, Johanna, Daniela, Malin, Teodora, Iain, Patrick, Tonny, Emma, Jose and Duc. If I have forgotten anyone please forgive me... it’s not that I don’t have lots of love for you, it’s just that my brain is so full of PhD right now that everything else is gone. You guys are awesome!
And all the other wonderful people in the De-partment! I can’t name you all here since it would take up a whole extra page but it has been such a pleasure to work with you these last years. I do want to particularly thank Anders and Mari-anne, without whose help my experiments would have been a complete mess. Also Eve for always having her door open for panicking PhD students. Vicky, thanks for being such an inspiring presence, I really enjoyed teaching structural geology with you.
I want to thank Pyewacket, my cat at home in Australia. Having you sitting with me for the last writing up phase really helped, even if you did think it was fun to play with the mouse/pen/computer screen and knock over my coffee on more than one occasion (thankfully not into my laptop). You kept
me company when I was at my most stressed, so thank you for being the dearest, sweetest, little cat in the whole world.
Katty, I would never even have come to Sweden in the first place if it hadn’t been for you. I am so glad I did! And I’m really grateful that I got to share this experience with you, both of us going through the ups and downs of a PhD and moving to a new country. You were always around as a sounding board for my problems, and really have been this last twenty years in fact. Who knew that those tiny third-graders with terrible, green uni-forms would end up on the other side of the world becoming Doctors?
I want to thank my family, Mummy, Daddy and Maddy. You have always believed in me no mat-ter what. You have always told me that I could do whatever I wanted, that nothing was out of reach. Daddy, you once told me as I carefully placed my feet in your footprints saying “Daddy look, I’m fol-lowing in your footsteps” that, that was fine but that I need to make a few of my own. I did follow your footsteps to geology, somewhere deep down the years of looking at rocks with you as a child inspiring me. So here I give to you this... my own footprint. I couldn’t ask for a better family. I feel grateful for you guys every day. Every step of this PhD you have all been there listening to me and encouraging me when I was down. If you must call me Dr Bubbywump then fine. You have earned the right to.
And last but not least, Jesper. You have born the brunt of living with someone who was doing a PhD and I think most people will agree that this is not an easy thing. And yet, you have always been patient with the crazy rollercoaster of my life. And to think, three and a half of those four years we shared a space of 18m2! You have dried my tears
when I was sad, you have shared my joy when I was happy, you have even let me yell at you when I needed someone to be angry at. I couldn’t ask for a better partner in this life and I could not have made it through this without you standing by my side.
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