1. A Study of Crack Formation and its Effective Internal Surface Area using X-ray Micro-Tomography (XMT) University of Johannesburg Energy Postgraduate Conference 2013

2. Introduction  X-ray Microtomography (also referred to as micro CT) is a radiographic imaging technique that can produce 3D images of a material's internal structure at a spatial resolution < 1μm (Landis et al. 2010).  Fractal techniques have been used extensively to characterize crack formation via details of the crack surface roughness. They represent defects in solid materials To find convenient scale invariant ways for their characterisation Phase reactions occur at the fluid-material interface The larger the effective area of interaction the faster the reaction rate Why cracks are important to study

3. Intuitive definition of dimension Consider a geometric object F, with measure  (F) F  (F)   (F) Line segmentLength2 1 = 2 RectangleArea2 2 = 4 ParallelepipedVolume2 3 = 8 s dim F =   (F) r= 1/s  resolution If F is scaled by a factor of 2 say, how does the measure scale?

4. Von Koch Curve (Self-similar Construct) 1 D line segment Divide into 3 units (s=1/3 unit ) New patterns generated, N= 4 Repeat the recipe for each new straight line segment Repeat on new smaller scale –. r We have a theoretical algorithm that creates a self-similar structure – the Von Koch curve. It has fractal geometry - a mixture of 1 D and 2D characters.

5. Dimension of the Von Koch Curve Scale (compass setting) Length 1/3 (1/3) 2 (1/3) 3 4/3 (4/3) 2 (4/3) 3 Compass dimension (D com ) D frac = 1 + D com =1.2619

6. Determining the D f of Fracture Cracks Crack surface Section  to surface Fractal character At large and small distance scales relationship may break down S = scale L = Length S L

7. Acquisition and Reconstruction Tomographic reconstruction

8. Penumbra No penumbra, sharp focus with magnification, M, increasing as d f increases: Microfocus X-ray Geometry Micro-focus X-ray technology uses micrometer sized source to produce sharp image projections at micrometer scale resolution dsds dfdf SourceSample Detector

9. Preliminary results Compass dimension(D com ) D com =0.45 D frac = 1 + D com = 1.45 Log/Log plot for the crack of the coal sample

10. Conclusions  Inherent crack surface geometry will be revealed over many orders of magnitude and analysed for fractal nature   CT measures with fundamental fractal nature will be identified  Best presentation and interpretation of data forthcoming from fractal measures will be sought