E-Journal of Advanced Maintenance Vol.9-2 (2017) 138-144
Japan Society of Maintenology

Why graphite ? A Structural Study from the Atomic to the Macrocsopic
scales.
Zhou ZHOU1*, Wim BOUWMAN1, Henk SCHUT1, Catherine PAPPAS1
1

Department of Radiation Science and Technology, Delft University of Technology, Mekelweg 15,2629 JB Delft, The Netherlands
ABSTRACT
Graphite is an important moderator material in nuclear reactors, which has a complex structure, wherecomplexity refers to two main respects: defects and disorder within the crystallites, and porosity including
cracks and pores with lengths varying over six orders of magnitude, from nanometers to millimeters. A
comprehensive characterization of the structure, needed e.g. to predict structural changes for long-term safe
operation of nuclear reactors, requires the complementary input from several techniques to cover the relevant
length scale range. In this work X-ray/neutron diffraction, small angle neutron scattering (SANS), spin echo
SANS (SESANS) and neutron imaging have been applied to investigate the structure of nuclear graphite fromatomic to macroscopic length scales: from nm to mm. The results provide a key to model and quantify disorderat the atomic level. At the meso- and macro-scopic levels a fractal structure is found that spans over an
extraordinary large scale of lengths of 6 orders of magnitude and has fractal dimensions close to 2.5, a casewhere surface and mass fractal dimensions coincide.
KEYWORDS

ARTICLE INFORMATION

graphite, diffraction, neutron irradiation, structure characterization,neutron scattering, neutron radiography, stacking fault, fractal

Article history:
Received 7 November 2016
Accepted 27 April 2017

1.

Introduction

Since Chicago Pile 1 in 1942, graphite has been used as a neutron moderator and structuralcomponent in several types of nuclear reactors. More recently, it has been considered as the materialof choice for the next generation Very High Temperature Reactor (VHTR). During operation of
nuclear reactors, graphite undergoes significant dimensional, physical and mechanical properties
changes due to the irradiation damage. It is thus important to investigate these changes and link themto the structure. The ultimate goal is to be able to predict the lifetime of graphite under irradiation as
this is closely related to the safe operations of nuclear reactors [1].
Structural investigations often involve X-ray diffraction (XRD) and scanning/transmission
electron microscopy (SEM/TEM). XRD is indeed the most common method for studying atomic
structures. However, the correct interpretation of XRD patterns from graphite samples is not trivial
because of (a) the inherent disorder, which can significantly affect the shape of the diffracted peaks,and (b) the high penetration depth of X-rays. Electron microscopy enables the investigation on thedefects and porous structure. However, it probes only surface layers and does not provide aquantitative description of the bulk material. Therefore, the results may not be directly relevant to thebulk properties e.g. of a graphite block inside a nuclear reactor [2].
In this work, the crystal structure of nuclear graphite has been investigated by both X-ray andneutron diffraction [3]. The diffraction patterns have been analyzed using a structural model, which
has been developed specifically for graphite and quantifies the inherent disorder of the atomic
structure. In addition, the structure of the pores has been studied explored by combining small angle
neutron scattering (SANS), spin-echo SANS (SESANS) and neutron imaging [4]. The combination ofthese techniques provides structural information over six orders of magnitude in length, from*

Corresponding author, E-mail: Z.Zhou-1@tudelft.nl

ISSN-1883-9894/10 © 2010 – JSM and the authors. All rights reserved.

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Z. Zhou, et al./ Title of the Papernanometers to millimeters, which is needed in order to understand the graphite structure at the mesoand macro-scopic levels. The ultimate goal would be to establish a direct link between the changes instructure and the macroscopic behavior of nuclear graphite.

2.

Experimental

2.1 Graphite samples
Five different types of non-irradiated graphites have been investigated including four nuclear
grade graphites: PGA (used in the early gas-cooled Magnox reactors in UK), PCEA (a candidate forthe very high temperature reactor in USA), IG110 (currently used in HTGR reactors in Japan) andRID (used at the research reactor of the Reactor Institute Delft), as well as a non-nuclear graphite
1940 PT, which is a high-density graphite manufactured for refractory applications.
Irradiated graphite samples were provided by the graphite irradiation program INNOGRAPH-1c
conducted by the Nuclear Research and Consultancy Group (NRG) in the High Flux Reactor (HFR) in
Petten, The Netherlands. The samples were irradiated at a high temperature of 750 ºC with low doses(~1.5 and ~2.2 dpa) and for confidentiality reasons they are kept anonymous in this work [5].
2.2 Methods
XRD was performed on a lab Panalytical X’pert Pro diffractometer with Cu anode (45 kV, 40
mA, λ = 1.54187 Å). Neutron diffraction was performed on 3T2, a high-resolution powder
diffractometer in Laboratoire Léon Brillouin (LLB), Saclay, France, with an incident neutron
wavelength of λ = 1.225 Å. SANS was performed on two spectrometers PAXE and TPA in LLB. The
measurements on PAXE were done with λ = 0.37, 0.6, and 1.7 nm, respectively, covering the Q range
3×10-2 ≤ Q ≤ 5 nm-1 and on TPA with λ = 0.6 nm, covering the Q range 6×10-3 ≤ Q ≤ 1×10-1 nm-1.
SESANS was performed on the dedicated instrument of the Reactor Institute Delft at λ = 0.205 nm,with Δλ/λ = 5% and covered spin-echo length scales from 30 nm to 20 μm. The neutron imaging
measurements took place on the cold neutron facility, ICON, of the Paul Scherrer Institute,
Switzerland. The samples were placed as close as possible to the detector and the spatial resolution of
the images reached ~30 μm.

3.

Results and discussion

3.1 X-ray and neutron diffraction
Fig. 1(a) displays the measured XRD pattern from a virgin IG110 graphite sample (black circles),which is hardly reproduced by the standard Rietveld method and the program GSAS (blue line). Thisis because the inherent disorder, such as the presence of local ABC stacking, the random shift between
adjacent layers and the anisotropic crystallite size cannot be accounted for by a standard Rietveld
refinement. In order to overcome these limitations, it is important to use a model that incorporates the
specific structural particularities of graphite, and includes disorder. Such a refinement program is
CARBONXS, that is based on a model developed by Shi, et al [6]. The model introduces interlayer
spacing fluctuations, characterized by the standard deviation σ around the average value <d002>
besides the average lattice constants <a> and <d002>. It also includes two different characteristic
lengths, one along the c-axis Lc and one in the plane La, to quantify the volumes that scatter coherently
neutron or X-ray beams. In addition, the model quantifies the stacking disorder through twoparameters: PRS, the probability for finding a random shift between adjacent layers; and P3R, theprobability for finding a local ABC stacking sequence. In addition, the program CARBONXS also
includes corrections for the penetration depth of X-rays, the X-ray polarization, the Lorentz factor, apreferred sample orientation and an isotropic Debye-Waller factor.
The red dash line in Fig. 1(a) represents the fit of the measured XRD pattern by CARBONXS,
and illustrates a major improvement as compared with the fit by GSAS. The resulting refinements ofall graphites show that <d002> is an essential indicator of the perfection and graphitization degree ofthe structure. The smaller <d002> implies larger coherent lengths Lc and La, which quantify theextension of the coherent regions and thus the order of the microstructure.
The value of <d002> for nuclear graphites is close to 3.360 Å, which is slightly larger than thevalue for a perfect graphite crystal that amounts to 3.354 Å. This implies that nuclear graphites arehighly disordered, despite their high degree of purity and the fact that they are manufactured in a very
high temperature (2600 ̵ 3000 ºC). In addition, the fits lead to 15-25% random shift PRS and about 7%

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ABC stacking faults P3R, the standard deviation of interlayer spacing fluctuations σ≫<d002>-3.354,
indicating other disorder in the graphite structure, such as dislocations, crosslinks, vacancies andinterstitial defects.

Fig. 1. Measured and calculated X-ray diffraction patterns in log-lin scale for (a) a non-irradiated IG110
graphite sample, and (b) a low dose (2.2 dpa), high temperature (750°C) neutron irradiated graphite
sample. The red lines indicate the refinements based on the program CARBONX and the blue line thestandard Rietveld refinement using the program GSAS.

The neutron irradiation effects on graphite structure have been investigated in the same way [7].
Fig. 1(b) depicts the measured XRD pattern of a neutron irradiated (750 ºC, 2.2 dpa) graphite sample
from INNOGRAPH and the fit by CARBONXS. The refinement shows that irradiation does not affectthe lattice constant <a> but increases <d002> by ~0.5%, which seems to approache saturation at ~2.2
dpa. The increase of <d002> is attributed to interstitial faults caused by atom displacements during
irradiation. Furthermore, neutron irradiation deteriorates the stacking of layers within the coherent
regions as indicated by the increase of PRS and the decrease of P3R. In addition, La decreases
continuously up to a dose of ~1.5 dpa, indicating induced in-plane defects, as well as the breaking,bending and displacement of the basal planes. On the other hand, the relative changes of <d002> andLc up to a dose of ~1.5 dpa indicate that, along the c-axis, the number of layers in the coherent regions
slightly increases, which may be due to (1) the formation of interstitial dislocation loops and/or (2) the
closing of micro-cracks between slightly disoriented coherent regions. This effect is revered for higher
irradiation doses, and for ~1.5 to ~2.2 dpa, Lc decreases significantly, which indicates thefragmentation of the coherent regions into smaller ones. These results are in qualitative agreementwith previous observations from electron microscopy [8].
Neutron diffraction experiments have been performed on virgin graphites in order to complement
and validate the XRD results. In fact, compared to X-rays, neutrons do not suffer from beamabsorption or the Kβ contamination of the main Kα wavelength produced by the Cu anode of alab-based X-ray diffractometer. For this reason, it was expected that neutron diffraction would provide“cleaner” patterns that would be better suited for a direct comparison with models. Indeed, the Bragg
peaks of the neutron diffraction patterns are more symmetric than those produced by XRD, and can beperfectly accounted for by the CARBONXS program, which has been adapted to neutron diffraction
by also including the instrumental resolution of a neutron diffractometer, as shown in Fig. 2. Neutron
and X-Rays lead to slightly different values for the refined parameters, in particular for the coherent
lengths, but with the same trends. On the basis of these results, we recommend that the structuralmodel and the refinement program CARBONXS is applied for analyzing XRD patterns of graphites
irradiated under other conditions as well.

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Fig. 2. Measured (black circles) and calculated by the program CARBONX (red lines) neutron (a-c) and
X-ray (d-f) diffraction patterns for a PGA graphite sample at selected regions revealing the shapes of thepeaks and the fitting details.

3.2 Neutron scattering and imaging
As previously mentioned, the structure of graphite has been investigated from the micro to themacro length scales by combining SANS, spin echo SANS (SESANS) and neutron imaging. In thesemeasurements, the contrast arises from the difference in the neutron scattering/absorption crosssection between the pores (cracks) and the carbon matrix.
Fig. 3(a) shows the resulting absolute scattering cross section of a PGA graphite sample and forthe indicated different instrument and neutron wavelengths. The data follow a power law I(Q)∝Q-βwith β = 3.45. The deviations at high-Qs are attributed to a (spin-incoherent) background and at low Q
region to multiple scattering. Fig. 3(b) shows that the SESANS polarization, decreases continuously
as a function of the spin-echo length z, indicating that inhomogeneities extend from the SANS region
to ~10 μm. Fig. 3(c) shows the pores observed by neutron imaging, which for the sake of clarity havebeen labelled with different colors. A 2D Fourier transform of the image leads to the 1D scattering
curve shown in Fig. 3(d), which leads to another power law I(Q)∝Q-β with β = 2.44.
The power law behavior found by SANS and neutron imaging indicates a fractal structure of thepores. It is expected that for a surface fractal: I(Q)∝Q-(6-Ds), and for a mass fractal: I(Q)∝Q-Dm, where
Ds and Dm are the surface and mass fractal dimensions respectively, which both take values smaller
than 3 [9, 10]. Consequently, the power laws indicate a surface fractal with Ds = 2.55 at the Q’s
probed by SANS and a mass fractal with Dm = 2.56  Ds at the Q’s probed by neutron imaging.
For a quantitative interpretation of these experimental findings a fractal model has been
introduced that is able to fit the data obtained by all techniques. To be specific, the pore structure
consists of a network of pore clusters with many pore-building blocks characterized by the massfractal dimension Dm at length scales larger than the size of the primary block. Moreover, the porebuilding blocks are bounded by rough surfaces with fractal morphology, characterized by the surface
fractal dimension Ds. In this case, the scattering cross section I(Q) reflects the fractal properties of thestructure and it can be written as [11]:I (Q)  B  P(Q)  S (Q)(1)

B  D  2V p  D  2 4 l 3 / 3

S (Q)  1 ,

P (Q)  (1  Q 2l 2 )( Ds 6)/ 2

Dm ( Dm  1)
1 (1 Dm )/2(1 )
 sin[( Dm  1) arctan(Q )]Dm(2Ql )(Q ) 2

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,
(2)

Z. Zhou, et al./ Title of the Paper

Here B is a pre-factor determined by ϕD the porosity, 2 is the neutron scattering length density
contrast between the carbon matrix and the pores, and Vp the volume of a primary pore building block.
P(Q) is the form factor characterizing the morphology/shape of the pores, and S(Q) is the structural
factor characterizing the correlations between the pores. The characteristic length l marks the
cross-over between mass and surface fractal scattering, and is proposed to be the cross-over between
cracks (small and in the filler particles) and micro-pores (formed by gas evolution during
manufacturing). The length ξ is a cut-off length indicating the average diameter for the pore clusters.

Fig. 3. Measurements results of several neutron-based techniques on a PGA graphite sample: (a)absolute scattering cross section from SANS measurement for the indicated different instrument andneutron wavelengths; (b) normalized SESANS polarization as a function of spin-echo length; (c) neutrontransmission image where pores are labelled with different colors; (d) 1D scattering curve obtained from
2D Fourier transform on the original gray scale image of (c). The red lines are corresponding to fractal
model, which is representing by eq. (1)-(3)In order to fit all experimental data by this simple model, Ds was fixed to the value derived fromthe power law of the SANS patterns whereas Dm and ξ were fixed to the values obtained from the fitsof the curves derived by 2D-Fourier transforming the neutron images. As for all graphites Dm  Ds, forthe sake of simplicity we assumed Dm = Ds. At last, the parameter l was determined by fitting
SESANS data, which was achieved by numerically Hankel transforming Eq. (1-2) to calculate
SESANS polarization through the relation:PS ( z )  exp[t  2 (G( z )  G(0)) / 2 ] with G( z )   J 0 (Qz ) I (Q)QdQ(3)0where  is the neutron wavelength, t is the sample thickness, J0 is a zero-order Bessel function of thefirst kind, and PS (z) the measured SESANS polarization.

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Table 1 Fitting parameters of the fractal model assuming Dm = Ds
SANSImagingSESANS
SampleDs = Dm (fixed)ξ [μm] (fitted)
l [μm] (fitted)
PGA1
3.45 (1)18.9 (4)2.27 (10)PGA2
3.43 (1)17.0 (5)2.64 (25)RID
3.45 (1)18.7 (4)1.87 (6)In Fig.3 (a), (b) and (d), the red lines correspond to the fits of SANS, SESANS and neutron
imaging data to the fractal model, respectively, using the parameters listed in Table 1. The high qualityof the fits and the consistent parameter set reveal a global picture of the fractal microstructure ofgraphite over an extraordinary large range of length scales of 6 orders of magnitude (-0.6 nm ≤ 2π/Q ≤0.6 mm). In this study, two characteristic lengths l and ξ have been identified. The cut-off lengths ξare more or less the same for all samples, which could be due to the fact that both PGA and RID aremade out of petroleum coke. On the other hand, l varies more from one sample to another. Thisparameter might indeed be more closely linked to the particularities of the microstructure as it might
originate from the surface fractal scattering of Mrozowski cracks. In addition, the measured surface
and mass fractal dimensions are very similar for all samples and they all are very close to 2.5, a value
found for percolating clusters and fractured ranked surfaces in 3D [12, 13].
It has been shown that surface fractality disappears whereas the mass fractal dimension decreases
under neutron irradiation [14]. These effects should be easily followed by neutron scattering andimaging techniques in combination with the data analysis strategy described above. These studies
would lead to a more quantitative investigation of irradiation damage and/or oxidation effects on the
structural changes of graphites.

4.

Conclusion

In summary, we have presented the combination of several X-ray and neutron techniques, which
provides new insights in the structural properties of graphite. The methodology used in this work is
promising for investigating irradiated graphites and will certainly lead to a better understanding of thestructural changes and the resulting modifications of the physical properties under irradiation. In
addition, the approach can be applied to the investigation of other complex systems with a hierarchyof length scales such as biological materials, concrete and rocks, materials for CO2 sequestration, Li
batteries, fuel cells or solar cells.

References[1] B. Kelly, B. Marsden, K. Hall, D. Martin, A. Harper, A. Blanchard: “Irradiation damage in graphite due tofast neutrons in fission and fusion systems”, IAEA Tecdoc 2000; 1154.
[2] R. H. Telling, M. I. Heggie: “Radiation defects in graphite”, Philosophical Magazine, Vol. 87, No. 31, pp.
4797–4846 (2007).
[3] Z. Zhou, W. G. Bouwman, H. Schut, C. Pappas: “Interpretation of X-ray diffraction patterns of (nuclear)graphite”, Carbon, Vol. 69, pp. 17–24 (2014).
[4] Z. Zhou, W. G. Bouwman, H. Schut, S. Desert, J. Jestin, S. Hartmann, C. Pappas: “From nanopores tomacropores: Fractal morphology of graphite”, Carbon, Vol. 96, pp. 541–547 (2016).
[5] M. Heijna: “The innograph-1c low dose irradiation experiment: extending the HTR graphite materials
properties curves at 750 °C”. Presentation at the 15th International Nuclear Graphite Specialists Meeting,Hangzhou, China (2014).
[6] H. Shi, J. N. Reimers, J. R. Dahn: “Structure-refinement program for disordered carbons”, Journal ofApplied Crystallography, Vol. 26, pp. 827–836 (1993).
[7] Z. Zhou, W.G. Bouwman, H. Schut, T.O. van Staveren, M.C.R. Heijna, C. Pappas: “Influence of neutron
irradiation on the microstructure of nuclear graphite: An X-ray diffraction study”. Journal of Nuclear
Materials Vol 487, 323–330 (2017).
[8] C. Karthik, J. Kane, D. P. Butt, W. E. Windes, R. Ubic: “In situ transmission electron microscopy ofelectron-beam induced damage process in nuclear grade graphite”. Journal of Nuclear Materials, Vol. 412,
pp. 321–326 (2011)[9] H. D. Bale, P. W. Schmidt: “Small-angle x-ray-scattering investigation of sub-microscopic porosity withfractal properties”, Phys. Rev. Lett. Vol. 53, No. 6, pp. 596-599 (1984).
[10] J. Teixeira: “Small-angle scattering by fractal systems”, J. Appl. Crystallogr. Vol. 21 pp. 781-785 (1988).
[11] H. W. Wang, L. M. Anovitz, A. Burg, D. R. Cole, L. F. Allard, A. J. Jackson, A. G. Stack, G. Rother:“Multi-scale characterization of pore evolution in a combustion metamorphic complex, Hatrurim basin,
Israel: Combining (ultra) small-angle neutron scattering and image analysis”, Geochimca et Cosmochimica

143

Z. Zhou, et al./ Title of the Paper
Acta, Vol. 121, pp. 339-362 (2013).
[12] S. C. van der Marck: “Percolation thresholds and universal formulas”, Physical Review E, Vol. 55, No. 2,
pp. 1514-1517 (1997).
[13] K. J. Schrenk, N. A. M. Araujo, J. S. Andrade, H. J. Herrmann: “Fracturing ranked surfaces”, Scientific
Reports, 2 (2012)[14] Z. Mileeva, D. K. Ross, S. M. King: “A study of the porosity of nuclear graphite using small-angle neutron
scattering”, Carbon, Vol. 64, pp. 20–26 (2013)144