1 Challenge the future Fractal structure of nuclear graphite from nm to mm : a neutron’s view Z....

1Challenge the future

Fractal structure of nuclear graphite from nm to mm :a neutron’s view

Z. Zhou*1, W.G. Bouwman1, H. Schut1, C. Pappas1

S. Desert2, J. Jestin2

S. Hartman3

1: Delft University of Technology, The Netherlands

2: Laboratoire Léon Brillouin, France

3: Paul Scherrer Institute, Switzerland

* [email protected]


Fractal

Nuclear graphite ?

Self-similar in different scales

West Lake, Hangzhou


Neutron techniques

Small angle scattered neutrons

Transmitted neutrons

Neutrons

Structure of pores

Neutron imaging

Visible structural information in

real space

Small Angle Neutron Scattering

SANSSpin-Echo Small Angle Neutron Scattering

SESANS


Study on graphite

1 Å 1 nm 1 μm 1 mm

SESANS Imaging

Size range (real space)

Q range (reciprocal space)

1 nm-1 10-3 nm-110 nm-1

2Q

l

SANS

PGA graphite sample


4sinQ

Small Angle Neutron Scattering (SANS)

Neutrons

Transmitted beam

Scattered beamSample

2D detector

Scattering vectorQ$$$$$$$$$$$$$$

PAXE and TPA in LLB, Saclay


SANS of PGA

Multiple scatteringPower law


* 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


SANS on PGA

Surface fractal dimension6 3.45 2.55sD

3I Q

4I Q


32 2

1( )

(1 ( ) )H

I q

qa

Random two phase media model

SANS simulation of the model

slope (3 2 )H

(6 ) (3 2 )

3 2

(3 ) / 2

Ds H

Ds H

H Ds

SANS of PGA2.55

0.225

Ds

H


1 Å 1 nm 1 μm 1 mm

SANS

Surface fractal

Ds = 2.55

SESANS

mon

ochr

omat

orm

agne

t 1

field

ste

pper

anal

yser

dete

ctor

pola

riser

guid

e fie

ld

Realisation SESANS @ TUD

sam

ple

pola

rise

r

pola

rise

r

M. Theo Rekveldt, Jeroen Plomp, Wim G. Bouwman, et al., Rev. Sci. Instrum. 2005

SESANS sensitive 30 nm – 20 um


gas

liquid

glass

crystal

SESANS probes density correlationE.g. colloidal phases as function of concentration


SESANS on PGA

1

2

1

22

( ) ( ) ( )1 2( )2

( ) exp( ( ( ) 1

0 5

)

.2

)

2

H

H

t

z zG z K

a aH

P z

H

z G

Surface fractal dimension

2. 53 52sD H


1 Å 1 nm 1 μm 1 mm

SANS

Surface fractal

Ds = 2.55

SESANS

Surface fractal

Ds = 2.55

Imaging


Neutrons

Imaging with Cold neutrons (ICON), PSI

Neutron imaging

Sample Detector

Neutron transmission image of PGA


Binary image obtained by thresholding the original image

Labelled pores which can be measured by DIPimage (a toolbox under Matlab)

Perimeter-area relation

2pDP AP is the contour perimeter length.

A is the enclosed area.

Dp is the fractal dimension of the bounding contour.

Relation between contour fractal dimension and surface fractal dimension of the object

1s pD D

Dp is the fractal dimension of the bounding contour.

Ds is the surface fractal dimension of the object.

Fractal analysis on image


Perimeter-area relationship

21.552

2.552 0.01.

08289

1

p

s

D

D Dp

Surface fractal dimension


1 Å 1 nm 1 μm 1 mm

SANS

Surface fractal

Ds = 2.55

SESANS

Surface fractal

Ds = 2.55

Imaging


Surface fractal Ds = 2.552


2D-Fourier Transform on image

2D Fourier transform3

2 2

1( )

(1 ( ) )

0.225

H

H

I q

qa

3I Q

Mass fractal dimension

(3 2

2. 5

)

5m

m

H D

D


1 Å 1 nm 1 μm 1 mm

SANS

Surface fractal

Ds = 2.55

SESANS

Surface fractal

Ds = 2.55

Imaging


Surface fractal Ds = 2.552

2D-Fourier transform

Mass fractal Dm = 2.55


Q (Å-1)

Sca

tte

ring

In

ten

sity

Data in Q-space over 7 orders of magnitude

Imaging

SANS

SESANS


Imaging

SANS

SESANS

Conclusion

Porosity of PGA graphite has a surface fractal structure with a

single fractal dimension Ds=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.

Sca

tterin

g In

tens

ity

Q (Å-1)


Zhengcao Li Tadashi Maruyama

Acknowledge

M. Haverty

P. Mummery

1 Challenge the future Fractal structure of nuclear graphite from nm to mm : a neutron’s view Z....

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Transcript of 1 Challenge the future Fractal structure of nuclear graphite from nm to mm : a neutron’s view Z....