Multi-scale quantitative analysis of carbon texture, nanotexture and structure: I. Electron diffraction-based anisotropy measurements

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Multi-scale quantitative analysis of carbon texture, nanotexture and structure: I. Electron diffraction-based anisotropy measurements P.I. Raynal

a,b

, M. Monthioux

a,* ,

O. Dugne

c

a Centre d’Elaboration des Mate´riaux et d’Etudes Structurales (CEMES), UPR-8011 CNRS, University of Toulouse, 29 rue Jeanne Marvig, 31055 Toulouse cedex 4, France b Plateforme des Microscopies – Universite´ Franc¸ois Rabelais et CHRU de Tours, 10 bd Tonnelle´, 37032 Tours cedex, France c CEA, DEN, DTEC, SGCS, LMAC, BP 17171, 30207 Bagnols-sur-Ce`ze cedex, France

A R T I C L E I N F O

A B S T R A C T

Article history:

Transmission electron microscopy is a technique of choice in the study of carbon materials,

Received 15 April 2013

especially graphene-based carbon films, as it provides textural and structural information

Accepted 8 September 2013

at a wide range of scales.

Available online 17 September 2013

The Selected Area (SA) diffraction mode yields valuable data regarding the textural arrangement of the graphene stacks. Specifically, the 002 arcs Opening Angle (OA) quantifies the degree of twist disorientation of the layers, and thus the material anisotropy. Depending on the SA aperture size, regions of interest from typically 0.01 to 10 lm2 can be probed. This work aims to improve on existing methodologies and develop image analysis software tools designed for digital imaging. For easier use, maintenance and portability, these tools are based on the Python programming language. Briefly, the azimuthal intensity profile of the 002 diffraction ring is extracted and fitted by a model based on Gaussian functions, while a fit of the average radial profile provides the offset constant. We show that this single algorithm works for values of OA ranging from less than 25 up to 180. Our method was validated on various pyrolytic carbon samples, specifically the dense, spherulitic deposits in TRISO nuclear fuel particles for 4th generation high temperature reactors.  2013 Elsevier Ltd. All rights reserved.

1.

Introduction

Unlike most crystallized materials, which may be described merely by the atomic positions and crystallite dimensions obtained from X-ray or electron diffraction patterns, graphenebased materials (so-called ‘‘carbon materials’’ in the following) require a multi-scale analysis procedure to characterize the textural, nanotextural, and then structural organization levels. This is because of the specificity of the basic compo-

nent of such carbon materials, graphene, which is capable of bending, bonding, and stacking with others while keeping its foliated nature, thereby generating a large range of materials which are energetically very stable, even when crystallites are nanosized or when graphenes are single. Hence, unless the texture, nanotexture, and structure are all described, the characterization of a carbon material cannot be said to be fully achieved [1]. In this picture, ‘‘structure’’ is used to describe whether the way graphenes are periodically piled

* Corresponding author: Fax: +33 (0) 5 62 25 79 99. E-mail address: [email protected] (M. Monthioux). 0008-6223/$ - see front matter  2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.carbon.2013.09.026

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Fig. 1 – Definition of the Opening Angle (OA): OA is the average of the FWHM, along the diffraction ring (h coordinate), of the 2 . (A colour version of this figure can be viewed online.) two 002 arcs, i.e., OA ¼ FWHM1 þFWHM 2

up within a coherent graphene stack (crystallite) is turbostratic (i.e., with rotational disorder) or build a triperiodic structure (such as in hexagonal or rhombohedral graphite); ‘‘nanotexture’’ is used to describe how more or less extended crystallites are and how far and well crystallites are arranged with respect to each other within areas of similar graphene overall orientation (SGO); ‘‘texture’’ is used to describe the way the various SGOs building the material are displayed with respect to each other [1]. Due to this multi-scale organisation and the large range of dimensions involved, a set of various methods has to be used to describe carbon materials. Among them, transmission electron microscopy is a technique of choice, as its various modes provide (nano)textural and structural information at a wide range of scales, from less than 1 nm to several lm [2,3]. This paper is the first of a series of three, which aims to provide the methodologies to describe carbon materials, and more specifically carbon films and coatings, from the point of view of texture, nanotexture, and structure, by means of selected area electron diffraction (this paper), dark-field imaging, and then lattice fringe imaging. The methodologies will be demonstrated by using a series of pyrolytic carbon (PyC) coatings. PyCs are obtained by chemical vapor deposition (CVD) or infiltration (CVI) from gaseous hydrocarbon precursors [4,5]. They constitute the matrix of many composites (C–C or SiC–C for instance), but they are also used for the protective layers in multi-layer nuclear fuel particles [6–8]. PyC mechanical properties are strongly dependent on their texture, and a determinant parameter is the degree of (an)isotropy of the deposited material. Optical methods are typically used to quantify this parameter and several have been developed [4,9–12], some quite recently [13–15]. But electron diffraction pattern analysis can also been used to assess the degree of anisotropy of PyC texture. In significantly anisotropic carbon materials, the 002 diffraction ring is composed of two arcs, generally symmetrical. The average FWHM of these arcs, or Opening Angle (OA) [11] (Fig. 1), quantifies the degree of twist disorientation of the graphene stacks and is quite useful for assessing the degree of textural organization in PyC [10]. The OA value has been

used recurrently as an anisotropy criterion, as early as the mid-1990s [4,9,16–18], and Bourrat et al. refined the measurement methodology [11,19]. OA measurements have recently seen extensive use in the study of PyC of interest for TRISOtype nuclear fuel [7,20–22]. As selected area electron diffraction (SAED) is able to select electrons diffracted from specific regions of interest, it can thus yield valuable data regarding the textural arrangement of the graphene stacks at various scales. Depending on the projected SA aperture size, areas as small as 0.01 lm2, or as large as 15–20 lm2, can be probed. We present herein the novel methodology we developed and implemented in order to quantify the textural – and structural, in a minor extent – characteristics of carbon materials, in particular the degree of (an)isotropy, based on the analysis of SAED patterns. With respect to the various methods already published also based on SAED patterns analysis, we aimed to propose a single, more versatile procedure likely to be applied to a large range of carbon materials exhibiting a large range of (an)isotropy degrees. Indeed, this is an issue that may not have been sufficiently addressed in previously published works, in particular the problem of the overlap between the two 002 arcs for OA values greater than 65 [19]. Often, this is apparently ignored, even when the investigated sample series exhibit an appreciably wide range of anisotropy [9,18,22], or is overcome by proposing two distinct methods, one for very isotropic materials, another for much more anisotropic materials [19]. The interest of the specific PyC material series which was used to validate our methodology lies in the fact that, although the related PyC coatings are roughly isotropic when considering large size areas, they can be highly anisotropic if considering local areas. Hence, depending on the SA aperture opening used, a wide range of anisotropy could be investigated. Our PyC material series are dense PyC coatings used in TRISO-type nuclear fuel particles [23]. Destined to fourth generation, high temperature reactors, such particles are manufactured using fluidized-bed CVD and their pyrocarbon shows a specific spherulitic texture [6,20,24–27].

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2.

Experimental methods

2.1.

Samples

In order to validate the methodology developed, several test PyC series were analyzed (Table 1). As this methodology has been initially designed for the investigation of the dense PyC layers in TRISO-type nuclear fuel particles, all are samples from fuel or test productions of such particles. Those are small (1 mm) spherical particles, with either an uranium carbide or oxide kernel, or a zirconia kernel, and a multilayer protective coating, deposited through a multi-stage fluidizedbed CVD technique [6,24,25]. The gas precursors consist of C2H2 for the buffer, C3H6 or C2H2/C3H6 for the dense PyC, and CH3SiCl3 (MTS) for the SiC. The coatings are deposited at a temperature of 1300–1400 C for PyC and 1500–1600 C for SiC [26]. Two layers are of particular interest here, the so-called ‘‘outer’’ (OPyC) and ‘‘inner’’ (IPyC) dense pyrocarbon layers. They encase a SiC insulating layer in-between and, for thermomechanical purposes, should be as isotropic as possible [20,26,27]. The deposited carbon exhibits a characteristic spherulitic texture (e.g., Fig. 2), that is to say, an agglomeration of rather large (>200 nm) spherules, which are composed of a relatively thick shell of concentric graphene layers, around one or often several small isotropic cores. It is thus a naturally very heterogeneous material, that can be quite anisotropic locally. All samples were supplied by either the Oak Ridge National Laboratory (ORNL, TN, USA) or the French Commissariat a` l’Energie Atomique (CEA). They were provided as polished half-spheres, without the kernel. AGR-1 and UA19 are American and French reference fuels, respectively. In particular, they exhibit high optical isotropy values. AGR-2 is a more recent nominal French production while PYCASSO 1 is a (single-layer) PyC deposition experiment [14].

2.2.

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Sample preparation

As a rule, two or three particles from each series were prepared for TEM observation. The hemispherical samples were fixed with wax to a polished Pyrex stub, which was in turn mounted on a tripod; the half-sphere was then polished on diamond polishing disks of diminishing grain size to obtain a cross-section about 10–15 lm-thick. The resulting ring was detached from its mount by dissolution of the wax in acetone, then glued to a single-hole grid and milled to a thickness of

Fig. 2 – Contrasted bright field TEM image of a PyC layer in a TRISO fuel particle, showing the distinctive spherulitic texture.

100 nm by ion beam thinning with a GATAN PIPS (Precision Ion Polishing SystemTM) [28].

2.3.

Diffraction image acquisition

Diffraction pattern images were acquired with a Philips CM20 TEM (operated at 120 kV acceleration voltage) equipped with a 2048 · 2048 CCD camera. Four diffraction images were acquired for each region of interest, using selected area apertures of increasing size: 0.3 lm, 0.9 lm, 1.5 lm, and 4.4 lm (projected aperture diameter in the sample plane). To ensure statistical validity, at least ten series of diffraction patterns were acquired per layer (OPyC and IPyC) for each fuel particle batch [28]. The SAED pattern scale was calibrated using the hk0 diffraction spots of a genuine graphite reference sample (Madagascar graphite). Average d002 and Dd values (see below) were computed from the diffractograms obtained with the widest SA aperture. Tests on a typical sample have verified that these values were not – as expected – sensitive to the SA aperture diameter.

2.4.

Image analysis: technical options

Our objective was to develop new analysis tools meeting the following specification requirements: maximum ease of use and flexibility; ease of maintenance and revision, with transferability to other users; and designed from the outset for use with digital images.

Table 1 – Fuel particle production batches examined. Sample name

Sample description

PyC layers

AGR-1 AGR-1/1800 UA19 AGR-2 PYCASSO 1

Nominal American fuel production Same as above, annealed at 1800 C to simulate compaction Nominal French test production Latest nominal French test production French PyC deposition test production

2 2 2 2 1

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We chose to use open-source software solutions for this development work, namely the Python high-level programming language (http://www.python.org) and the IPython interactive development environment (http://ipython.scipy.org) [29,30]. Python is a very popular open-source multiplatform interpreted language whose clear syntax simplifies code maintenance, and for which scientific and imaging code libraries are available, namely NumPy (http://numpy.scipy.org), SciPy (http://scipy.org), Matplotlib (http://matplotlib.sourceforge.net) and PIL (http://www.pythonware.com/products/pil/) [31,32]. For improved performance, a few computer-intensive routines were re-written in ANSI C and compiled as shared libraries, then called from the main program thanks to the ctypes standard library (http://docs.python.org/library/ ctypes.html).

2.5.

Image analysis: OA measurement

The first step was to develop an algorithm for measuring the OA parameter on digital images produced by our TEM, and generalizable to other instruments. The diffraction image (e.g., Fig. 3) is first converted to polar coordinates to allow straightforward extraction of radial or angular intensity profiles. This requires prior determination of the center of the diffraction pattern. For this purpose, the image is binarized (Fig. 4a) and the average intensity profiles are computed along the x and y axes (Fig. 4b). The asymmetric beam stop extinction results in noncircular profiles; the middle of these profiles yields the pattern center coordinates ðxc ; yc Þ. The polar transform can then be performed (Fig. 5). The next step is to determine the position (r002 ) and width (dr) of the diffraction ring. An average radial intensity profile (i.e., integrated along h) is first computed to obtain an initial estimate of r002 simply by seeking the maximum intensity over a predetermined interval. The angular profile extracted at this position is used to infer the ½h1 ; h2  interval masked by the beam stop near r002 (Fig. 6a), and its intensity value. On the polar image the blanked area is replaced by the average intensity outside the beam stop corrected by an empirical factor (Fig. 6ab). It is then possible to recalculate an extinction-corrected mean radial profile1 (Fig. 7a). The maximum intensity near the initial estimate gives the final r002 value, whereas fitting to a double Lorentzian model (one of which is placed at r ¼ 0 for the central spot) provides dr, defined as the half width at half maximum (HWHM) of the 002 ring radial profile (Fig. 7a). We can now compute the final angular intensity profile for the 002 diffraction ring (Fig. 7b), i.e., the variation in intensity I versus the angle h, averaged along r between r002  dr2 and r002 þ dr2 to improve the signal-to-noise ratio. This profile2 is then fitted to a Gaussian+constant model to obtain OA, the average full width at half maximum (FWHM) of the two arcs.

Selecting a model In a previously published method (ANADIF software [26,28], based on [19]), the direct method operates in a similar manner

1 2

Excluding ½h1 ; h2 . Offset along h so the maxima occur at about 90 and 270.

Fig. 3 – Raw electron diffraction diagram for a pyrocarbon sample (UA19 sample, OPyC layer; 0.3 lm aperture).

but is valid only for OA < 65. At higher values OA is systematically underestimated due to the overlap between the two arcs. To avoid this limitation, and to use a single algorithm over the full OA variation range, we devised a more suitable model. The basic fit model is f ðhÞ ¼ C þ g1 ðhÞ þ g2 ðhÞ, where C is an offset constant and g1 and g2 are two Gaussian functions. To allow for the periodicity of the angular profile (defined modulo 360), we used a model with six Gaussian peaks (Fig. 8): f ðhÞ ¼ K þ g1a ðhÞ þ g2a ðhÞ þ g1b ðhÞ þ g2b ðhÞ þ g1c ðhÞ þ g2c ðhÞ

ð1Þ 

where: K is the offset constant, g1b ðhÞ ¼ g1a ðh  360 Þ and g2b ðhÞ¼g1a ðhþ360 Þ;g1c ðhÞ¼g1a ðhþ360 Þ and g2c ðhÞ¼g2a ðh360 Þ. The profiles between 0 and 360 are transposed on either side of the interval (first and second neighbours) so the contribution of one arc to the intensity profile of the other arc can be taken into account, even for high OA values. In addition, instead of allowing the offset constant to ‘‘float’’ freely, we sought to give it a more physical significance. We therefore set it to the value of the mean intensity of the central spot ‘‘beneath’’ the 002 diffraction ring. K002 is defined as the mean intensity of the corrected background fit between r002  dr2 and r002 þ dr2 . Fig. 9 shows three examples of angular profile fits for increasing OA values. In the case of narrow arcs (Fig. 9a) both models give comparable results; the offset values (horizontal dash-dot lines) are indistinguishable. Conversely, in Fig. 9b the difference between K002 (short green dashes) and a free-floating constant (long blue dashed) is very significant and the OA value is substantially greater for the sixGaussian model. The difference between both models is even more pronounced for an isotropic diffraction pattern (Fig. 9c). Therefore, the validity of our method over a wide range of OA values (25–180) is confirmed; in contrast, the simple, direct method (2-Gaussian fit) tends to ‘‘saturate’’ at 100 and is thus unsuitable for high OA values, which are underestimated [19,28].

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Fig. 4 – Diffraction image analysis procedure (1): determination of the center of the diffraction pattern. The image is first binarized (a) and then integrated intensity profiles are computed (b); the edges of the x (top) and y (bottom) profiles are defined as the points where the intensity reaches a threshold value (horizontal dashed red lines), and allow to fix the pattern center position ðxc ; yc Þ (vertical dash-dot red lines). (A colour version of this figure can be viewed online.)

Fig. 5 – Diffraction image analysis procedure (2): polar transform. Based on the pattern center determined previously (cross), the original image (left) is transposed into polar coordinates (right), i.e., ðx; yÞ7!ðr; hÞ. (A colour version of this figure can be viewed online.)

2.6.

 002 and Dd measurement d

In addition to OA, which is a texture parameter, the SAED pattern also yields structural information, namely the average  002 and the radial FWHM of the 002 inter-graphene spacing d  arc Dd. d002 is a criterion that relates to increasing carbon structuration in the path toward reaching the graphite struc002 reaches the lowest value of 0.335 nm). Dd ture (for which d mostly relates to the average number of graphenes stacked within the crystallites, i.e., it is inversely proportional to Lc , the coherent domain size along the c axis (i.e., perpendicular to the graphene planes) [3,33]. However, strictly speaking, Dd is somewhat also related to the dispersion of intergraphene spacing values. It is known, from the overall knowledge gathered about the carbonisation processes, that both criteria decreases as the structuration increases. 002 and Dd are easily computed from the r002 and dr paramd eters of the average radial profile fit:

002 ¼ 1 d r002 dd ¼ 

dr 2dr ) Dd ’ 2 r2 r002

002-Ring radial profile model As the estimation of d002 and Dd directly depends on that of r002 and dr, we tried to optimize the quality of the fit of the 002-ring average radial profile. A quite significant improvement is observed, with the addition of a single free parameter, when one replaces the usual lorentzian 002 peak by a Breit–Wigner–Fano (BWF) profile (e.g., Fig. 10). The BWF profile is a lorentzian-like asymmetric function (Eq. 2), equivalent to a lorentzian peak when parameter Q ! 1. h i2 oÞ 1 þ 2 ðrr QC fBWF ðrÞ ¼ Io ð2Þ h i2 oÞ 1 þ 2 ðrr C

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Fig. 6 – Diffraction image analysis procedure (3): after the initial estimate of r002 , a preliminary angular profile is extracted (a) and used to determine the ½h1 ; h2  interval covered by the beam stop (in red); a beam stop correction is then applied (b) prior to computing the mean radial profile (Fig. 7a). (A colour version of this figure can be viewed online.)

Fig. 7 – Diffraction image analysis procedure (4): the mean radial profile (a) is fitted in order to determine the position (r002 ) and width (dr) of the 002 ring, and then to estimate the contribution of the central spot ‘‘beneath’’ the ring (K002 ); the angular profile is then extracted and fitted to the selected model (b) to determine OA. (Blue dashed line: data fit, magenta dash-dotted line: background component, red dotted line: 002-ring component.) (A colour version of this figure can be viewed online.)

Position of the maximum, peak intensity and width are given by:     1 þ Q12 C 1  ¼ 2dr rmax ¼ ro þ ; Imax ¼ Io 1 þ 2 ; FWHM ¼ C  2Q Q 1  12 Q

This model was subsequently used for all 002 ring radial profile fits.

3.

Results

3.1.

Texture

The Opening Angle measurements results obtained from the diffractograms of our various samples are displayed in Fig. 11, as the variation of OA with the (projected) Selected Area aperture diameter. The OA value increases along with SA for all sample series, converging rather quickly towards 180 (or 160 in the case of PYCASSO 1). Indeed, while a small aperture probes the PyC

Fig. 8 – Model for the fit of the 002-ring angular profile. Additional Gaussian profiles allow to take into account the overlap of wider 002 arcs. (A colour version of this figure can be viewed online.)

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Fig. 10 – Example of data fit of an 002 diffraction ring average profile (a), and associated residuals (b), using either a lorentzian profile (green dots) or a BWF profile (blue dashes/ squares). The fit is much better with the latter model (v2BWF =v2lorentz: ’ 0:13 in this case). (A colour version of this figure can be viewed online.)

Fig. 9 – OA measurement examples using the standard 2Gaussian model and our 6-Gaussian model (green dashed line and blue long-dash line, resp.; horizontal lines materialize the fit constants). The values found are: (a) OA2g = 61, OA6g = 62; (b) OA2g = 94, OA6g = 129; (c) OA2g = 93, OA6g = 177. The inset in (c) is a magnified version of the profile above it. (A colour version of this figure can be viewed online.)

local texture, the sampled area increases rapidly with the SA aperture and soon the overall, isotropic texture is observed. In addition, we note that the PyC in PYCASSO 1 is markedly less isotropic than in the other French samples, at all scales, with a wider dispersion in values (Fig. 11b).

As the intermediate apertures are uncertain in terms of sampling area with respect to the spherule size (typically 400 nm [28]), and would be rather more delicate to interpret, we chose to limit our analysis of the OA measurements to the smallest (i.e., 0.1 lm2) and largest (i.e., 15 lm2, the one most comparable to optical techniques) scales (Fig. 12). Moreover, as the OA values for each sample exhibit substantial dispersions (i.e., large standard deviations), we checked the statistical significance of the observed differences between samples using the Mann–Whitney U test (this test provides the probability parameter p, whose value is as lower as the difference observed is more significant). We first looked for differences between the two dense PyC layers, OPyC and IPyC, in the various samples. A partial annealing of the IPyC layer is indeed expected when the SiC layer is deposited at a higher temperature, and then when the OPyC is deposited. Heat treatment is well known to remove plane defects and increase anisotropy. The OPyC layer, being deposited last (in the same conditions as IPyC), would not experience similar thermal effects. However, for these sample series, the OA measurements proved ambiguous. In AGR-1, for the smallest aperture (Fig. 12a), there is no real statistical difference between OPyC and IPyC (p ¼ 0:3), even though the OPyC average OA is slightly greater. At the widest aperture (Fig. 12b), the difference between OPyC and IPyC is no more significant. Even more so, in the annealed

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Fig. 12 – Opening Angle at smallest (a) and widest SA (b) apertures for all samples (mean 1r). (A colour version of this figure can be viewed online.)

Fig. 11 – Variation of the Opening Angle with Selected Area aperture (diameter as projected in sample plane) for the US (a) and French (b) PyC samples (symbols: mean values, bars: 1r). Expectedly, OA increases with SA and reaches 180 for the wider apertures. (A colour version of this figure can be viewed online.)

AGR-1/1800 sample (at both scales), the differences between OPyC and IPyC are not significant (p > 0:6). In the French reference samples, at the smallest SA aperture (Fig. 12a), although the average OA value is lower for IPyC than for OPyC in both UA19 and AGR-2, the differences do not appear actually significant (p  0:1). No difference between OPyC and IPyC in this samples is apparent at the widest aperture (Fig. 12b), i.e., at the lm scale. Annealing the AGR-1 particles at 1800 C somewhat impacts the OA value as measured with the smallest aperture (Fig. 12a): the OPyC layer might be more anisotropic than in the non-heated sample series, with limited confidence (p ¼ 0:1). Conversely, the annealed IPyC layer does not differ from that of the ‘‘raw’’ sample, likely as it has already experienced a significant heat treatment. At the largest scale (Fig. 12b), no significant difference is observed in OPyC and IPyC before and after annealing. However, if one does not differentiate between OPyC and IPyC OA values, the AGR-1/1800 sample might exhibit a more anisotropic texture overall than the untreated AGR-1 (p ¼ 0:1). This hints that, in spite of somewhat disappointing results at first, the OA distribution may be more reliably discriminant

when considering whole sample series instead of PyC layers, especially with the widest SA aperture (i.e., at a wider scale, Fig. 12b). Statistical tests confirm this hypothesis. The difference between AGR-2 and AGR-1 is established with a high degree of confidence (p ¼ 0:003), as between AGR-2 and UA19 (p ¼ 0:005). Conversely, the properties of AGR-1 and UA19 are identical (p > 0:95). Any doubt about the specificity of PYCASSO 1 (which already exhibits the lowest OA values and highest dispersions) is also removed, with p values < 0:01 when compared to AGR-2 and < 0:002 when compared to AGR-1 and UA19.

3.2.

Structure

As explained in Section 2.6, our algorithm also yields the aver002 and the spacing dispersion Dd age inter-graphene spacing d (Fig. 13), which both provide structural information and trace what could be called the ‘‘degree of maturity’’ of a carbon material [33,3]. Correspondingly, the variations of these parameters along a sample series are strongly dependent upon its thermal his002 value is found in tory. In AGR-1 for instance, the highest d the OPyC of the untreated sample, then progressively decreases, converging down to the annealed IPyC value (Fig. 13a). The Dd value follows a parallel trend. Actually, for all samples, both parameters exhibit a rather strong correlation (Fig. 14). 002 remain independent It is worth noting that OA and d 002 (Fig. 15), OA values do parameters. When plotted against d

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Fig. 15 – Variation of Opening Angle (at widest SA aperture)  002 (symbols as in Fig. 11). (A with mean interlayer spacing d colour version of this figure can be viewed online.)

4.

 002 (a) and Dd parameter Fig. 13 – Mean interlayer spacing d (b) for all samples (mean 1r). (A colour version of this figure can be viewed online.)

Fig. 14 – Variation of Dd parameter with mean interlayer  002 (symbols as in Fig. 11). (A colour version of this spacing d figure can be viewed online.)

not exhibit any obvious trend. What is more, the test sample PYCASSO 1 remains clearly apart from the other sample ser002 values ies, with both the lowest OA value and the highest d (i.e., the lowest structural maturity). In other words, we are able, through our analysis of the SAED patterns, to extract 002 ; Dd) independent textural (OA) and structural (d information.

Discussion

In this work, we have developed and validated on samples of multi-layer nuclear fuel particles an original methodology for extracting textural and structural data from SAED patterns, namely the Opening Angle of the 002 diffraction ring [11]. We were able to use a single algorithm to directly measure the OA values, taking into account the overlap between the two 002 arcs. This is an improvement over previous works (such as the ANADIF software [19]), where the direct method could only be used provided there was no overlap (OA K 65), and where an indirect method, relying upon a (materialdependent) calibration curve, was used beyond this OA value. In addition, we were able to detect significant differences between a priori quite similar samples (e.g., the French productions UA19, AGR-2 and PYCASSO 1, Fig. 12), that is to say dense, quasi-isotropic and produced in analogous synthesis conditions. The OA measurements results are also compatible with the known thermal history of the samples (heating of the IPyC layer during SiC layer deposition, and, as the case may be, annealing at 1800 C). The isotropy variation with heat-treatment is also consistent with previous optical measurements [13]. Finally, the simultaneous extraction of independent, com002 ; Dd) from the same data plementary structural data (d set allowed us to optimize data analysis and reveal the atypical behavior of a sample such as PYCASSO 1. It is evident, from our data, that the choice of the SA aperture size matters with respect to the OA value (Fig. 11). There is some discrepancy in the literature regarding the choice of the aperture size: rather large for Reznik and Hu¨ttinger (2.5 lm2, i.e., 1.8 lm in diameter) [10], or quite small for Meadows et al. (200 nm) [22], for instance. Some authors do not actually indicate this value. While this may not be of the greatest concern in very anisotropic, homogeneous samples (e.g., laminar PyCs), the aperture size becomes much more significant with samples exhibiting a more complex texture, such as the fluidized-bed CVD-deposited dense pyrocarbons studied herein.

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Indeed, we verified that OA values predictably increase with SA, tending quickly towards isotropy (180, Fig. 11). This is consistent with the known spherulitic texture of such pyrocarbons [26]: locally, in a portion of a spherule shell for instance, the graphene layers exhibit a significant preferred orientation ; on the other hand, as the sampled area increases, more and more spherules are integrated and the graphene plane orientation distribution averages out towards isotropy. Such behavior has previously been observed on comparable samples [21,22], albeit with more conical than spherulitic growth patterns. Therefore care should be taken when characterizing the texture of the pyrocarbon as to which scale is being considered. Using the terminology proposed by Reznik and Hu¨ttinger [10], PyC in our samples would be considered ‘‘mediumtextured’’ locally, but ‘‘low-textured’’ or ‘‘isotropic’’ overall, based only on its OA value.

5.

Conclusion

This work was aimed at developing new or improved methodologies for the quantitative characterization of pyrolytic carbon texture using transmission electron microscopy. We have shown that a single algorithm is able to extract the Opening Angle of the 002 arcs from SAED patterns on the whole OA variation range (25–180). We were thus able to perform reliable (an)isotropy measurements on various fluidized bed CVD-deposited, spherulitic pyrocarbon samples from HTR nuclear fuel particles, consistently with previous studies. These tools are to be complemented by dark field and 002lattice fringe image analysis in a multi-scale strategy, that will be presented in forthcoming papers. It is believed that the methodology is applicable to other kinds of pyrocarbon materials such as laminar ones, and beyond them, to a wider variety of carbon materials.

Acknowledgements The research was done under an AREVA NP and CEA (DEN, DMN, SEMI Saclay) co-sponsored budget. The authors wish to thank specifically F. Charollais and J.-M. Moulinier (CEA, DEN, DEC, SPUA, Cadarache) on the one hand, and J. Hunn (ORNL/DOE) on the other hand, for providing the samples. This work was done under the overall framework of the INERI project 2006-003-F. The authors also thank G. Vignoles (LCTS, Bordeaux) for several fruitful discussions and providing access to the ANADIF software, as well as A. Le Gouge (CIC-INSERM 202, CHRU de Tours), for her advice on the use of statistical tests.

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