1 Challenge the future Fractal structure of nuclear graphite from nm to mm : a neutron’s view Z. Zhou *1, W.G. Bouwman 1, H. Schut 1, C. Pappas 1 S. Desert 2, J. Jestin 2 S. Hartman 3 1: Delft University of Technology, The Netherlands 2: Laboratoire Léon Brillouin, France 3: Paul Scherrer Institute, Switzerland *

2 Challenge the future  Fractal Nuclear graphite ? Self-similar in different scales West Lake, Hangzhou

3 Challenge the future  Neutron techniques Small angle scattered neutrons Transmitted neutrons Neutrons Structure of pores Neutron imaging Visible structural information in real space Small Angle Neutron Scattering SANS Spin-Echo Small Angle Neutron Scattering SESANS

4 Challenge the future  Study on graphite 1 Å1 nm1 μm1 mm SESANS Imaging  Size range (real space)  Q range (reciprocal space) 1 nm nm nm -1 SANS PGA graphite sample

5 Challenge the future  Small Angle Neutron Scattering (SANS) Neutrons Transmitted beam Scattered beam Sample 2D detector Scattering vector PAXE and TPA in LLB, Saclay

6 Challenge the future  SANS of PGA Multiple scattering Power law

7 Challenge the future * DFR Mildner, PL Hall, J. Phys. D: Appl. Phys. 19 (1986) 1535 Schematic diagram of scattering from fractal ojects * dimensionality of interfaces The interface is sensed as smooth on a distance smaller than dimensionality of clusters  Power laws measured by SANS

8 Challenge the future  SANS on PGA Surface fractal dimension

9 Challenge the future  Random two phase media model SANS simulation of the model SANS of PGA

10 Challenge the future 1 Å1 nm1 μm1 mm SANS Surface fractal D s = 2.55 SESANS

monochromator magnet 1 field stepper analyser detector polariser guide field Realisation TUD sample polariser M. Theo Rekveldt, Jeroen Plomp, Wim G. Bouwman, et al., Rev. Sci. Instrum SESANS sensitive 30 nm – 20 um

12 Challenge the future gas liquid glass crystal  SESANS probes density correlation E.g. colloidal phases as function of concentration

13 Challenge the future  SESANS on PGA Surface fractal dimension

14 Challenge the future 1 Å1 nm1 μm1 mm SANS Surface fractal D s = 2.55 SESANS Surface fractal D s = 2.55 Imaging

15 Challenge the future Neutrons Imaging with Cold neutrons (ICON), PSI  Neutron imaging Sample Detector Neutron transmission image of PGA

16 Challenge the future Binary image obtained by thresholding the original image Labelled pores which can be measured by DIPimage (a toolbox under Matlab)  Perimeter-area relation P is the contour perimeter length. A is the enclosed area. D p is the fractal dimension of the bounding contour.  Relation between contour fractal dimension and surface fractal dimension of the object D p is the fractal dimension of the bounding contour. D s is the surface fractal dimension of the object.  Fractal analysis on image

17 Challenge the future  Perimeter-area relationship Surface fractal dimension

18 Challenge the future 1 Å1 nm1 μm1 mm SANS Surface fractal D s = 2.55 SESANS Surface fractal D s = 2.55 Imaging  Perimeter-area relation Surface fractal D s = 2.552

19 Challenge the future  2D-Fourier Transform on image 2D Fourier transform Mass fractal dimension

20 Challenge the future 1 Å1 nm1 μm1 mm SANS Surface fractal D s = 2.55 SESANS Surface fractal D s = 2.55 Imaging  Perimeter-area relation Surface fractal D s =  2D-Fourier transform Mass fractal D m = 2.55

21 Challenge the future Q (Å -1 ) Scattering Intensity  Data in Q-space over 7 orders of magnitude Imaging SANS SESANS

22 Challenge the future Imaging SANS SESANS  Conclusion  Porosity of PGA graphite has a surface fractal structure with a single fractal dimension D s =2.55 over 7 orders of magnitude in length scale. This is remarkable, which can provide complementary information for modelling the structure of nuclear graphite. Scattering Intensity Q (Å -1 )

23 Challenge the future Zhengcao Li Tadashi Maruyama  Acknowledge M. Haverty P. Mummery