Microstructure of an industrial char by diffraction techniques and Reverse Monte Carlo modelling

Carbon 42 (2004) 2457–2469 www.elsevier.com/locate/carbon

Microstructure of an industrial char by diffraction techniques and Reverse Monte Carlo modelling Tim Petersen *, Irene Yarovsky, Ian Snook, Dougal G. McCulloch, George Opletal Department of Applied Physics, RMIT University, P.O. Box 2476V, Melbourne, Victoria 3001, Australia Received 14 January 2004; accepted 30 April 2004 Available online 26 June 2004

Abstract The disordered microstructure of an industrial carbonaceous char has been characterised using X-ray, neutron and electron diffraction techniques to obtain pair correlation functions. Whilst consistency has been observed between all three techniques, electron diffraction has been found to have advantages by allowing data to be collected over a large range of scattering angles as well as without interference from crystalline regions within the char. Based on the experimentally obtained pair correlation functions, Hybrid Reverse Monte Carlo (HRMC) simulations have also been performed to generate experimentally consistent nanoscale models of the disordered carbonaceous char. The model char structures comprise disordered and buckled graphitic sheets containing a small percentage of interstitial diamond-like atoms between the sheets. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: A. Electron diffraction; B. X-ray diffraction; C. Neutron scattering; D. Coal, Microstructure

1. Introduction Diffraction techniques are most commonly used to deduce the microstructure of highly ordered crystalline materials for which the atomic microstructure may, in some cases, be uniquely determined by crystal symmetries. For materials such as disordered solids and liquids, the greatly diminished atomic order generally yields broad diffraction peaks with fewer features than those of crystalline materials. This loss of detail therefore complicates the interpretation of diffraction patterns from disordered materials. One can however proceed in a similar manner to crystallographic investigations by proposing structural models with corresponding diffraction patterns that can be compared to experimental data to estimate the quality of a given model. Naturally, many models may be consistent with diffraction observations for disordered materials so it is appropriate for disordered solids, in analogy to the study of liquids, to evaluate both theoretical and experimental data statistically. *

Corresponding author. Tel.: +61-3-992-533-97; fax: +61-3-992561-07. E-mail address: [email protected] (T. Petersen). 0008-6223/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2004.04.037

Here we present a computational procedure for producing and evaluating physically realistic microstructural models, which are consistent with experimental diffraction observations. Since the diffraction based modelling approach used in this paper to describe the microstructure of coal derived materials differs considerably from some of the more traditional and other techniques present in the literature, it is pertinent to review some of those methods, with a distinct focus towards the use of diffraction; as will be done in Section 1.1. 1.1. Background Investigations into the microstructure of coal related materials may be considered as extensive as those of carbonaceous materials themselves, since coal represents a naturally abundant and important source of carbon. As would be expected, the techniques used to investigate the microstructure of coal related materials stem from those developed to study disordered carbon in general; dating back to the early work of Franklin [1,2]. A major contribution has been the use of scattering techniques which measure the diffracted intensity IðkÞ. This intensity can be used to obtain the static structure factor SðkÞ

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from which the radial distribution function gðrÞ may be calculated through inversion of the Fourier integral relation between the two: Z 1 SðkÞ ¼ 1 þ 4pq=k rðgðrÞ  1Þ sinðkrÞ dr ð1Þ 0

where the magnitude of the scattering vector k ¼ 4p sinðh=2Þ=k, h is the scattering angle and k is the radiation wavelength. The radial distribution function gives statistical information about the distribution of atoms in space. The key problem, however, is how to interpret this data in terms of the detailed microstructure of the sample. Using Warren’s [3] earlier theoretical description of diffraction from random collections of single layers applied to carbon black, in response to the observation that all of the X-ray diffraction peaks matched the (0 0 l) and (h k 0) reflections from graphite, small vertically aligned stacks of perfectly ordered hexagonal graphite planes where considered by Franklin [1] as the main contributors to the diffracted intensity IðkÞ versus scattering vector k. Within the same paper, Franklin [1] considered a number of possibilities for the observed broadness in the radial distribution function gðrÞ. Contemplating the disorder of aromatic carbon atoms within graphitic sheets, Franklin [1] considered such contributions to the observed broadness in IðkÞ to be small on the basis that a theoretical gðrÞ, which was calculated for a perfect graphite plane with an included artificial damping function, qualitatively matched the experimental gðrÞ. Franklin [1] also considered the possibility of ‘unorganised carbon’, which was said to exist in a purely gas-like state, thus contributing a featureless background to the observed intensity. Although Franklin [1] noted the plausible presence of very small aromatic layers within the diffracting carbonaceous microstructure, the perfect crystallite plane plus gas-like carbon model was chosen as a basis for further investigation. Continuing the ideal crystalline-plane interpretation of disordered carbon, Franklin later [2] applied her analysis techniques to study a number of carbon materials that exhibited X-ray diffraction patterns intermediate to the case where there existed only (h k 0) and (0 0 l) reflections and that of pure crystalline graphite, with complete (h k l) contributions to the intensity. In particular, Franklin [2] investigated the structure of carbon materials with highly ordered crystallites con but taining all c-axis planes separated by 3.44 A, otherwise uncorrelated with each other (turbostratic carbon). For this class of graphitic carbons (which were produced from coke, natural graphite and polymeric chemicals heat treated in the range 1700–3000 °C) the number of parallel c-axis layers per crystallite in such materials were stated to be of the order 30–150, indicating quite ordered structures. These layer sizes were

estimated from the full width at half maximum (FWHM) of the (0 0 2) and (0 0 4) peaks in a manner that is now routinely utilised in the study of the microstructure of graphitic carbon. For example the ‘Lc parameter’, which gives the average length of carbon crystallites along the c-axis direction, may be obtained from the ‘Scherrer equation’, as given by Warren [3,4]: Lc ¼

0:89k B0 0 2 cosðh0 0 2 Þ

ð2Þ

where k is the wavelength of the radiation used, B0 0 2 is the FWHM of the graphitic (0 0 2) peak and h0 0 2 is the position of the (0 0 2) peak. Franklin’s [1] unorganised carbon content was later used by Alexander and Sommer [5] as a defining parameter for the microstructure of a form of carbon black. Alexander and Sommer [5] calculated the fraction of unorganised carbon using a theoretical expression for the expected (0 0 2) contribution from an assumed perfect crystallite with a specified number of aromatic layers. Fits to the (0 0 2) peak were optimised by subtracting a constant (from the diffracted intensity IðkÞ), which specified the degree of amorphous carbon, until the peak appeared as symmetrical as possible, whilst decaying to zero either side of the central maximum. Extending the work of Warren [3], a few years after Franklin’s investigations [1,2], Diamond [6] examined the theoretical X-ray diffraction for carbon by applying Warren’s [4] pair distribution function method and the Debye equation [4] for single aromatic sheets. Various sheets having different numbers of atoms were grouped into corresponding classes and the expected X-ray diffraction patterns were calculated. Diamond [6] observed that significant variations in bond lengths within the aromatic planes did not change the calculated patterns by any appreciable amount, presumably since substantial broadening of pair correlation peaks was caused by the small size of the aromatic sheets to begin with. After Diamond [6], Ergun and Tiensuu [7] calculated the pair distribution functions for planes containing different sections of diamond lattices, observing that the diffraction peaks were very close to that of an aromatic system. Based on these observations, Ergun and Tiensuu [7] provided a possible explanation for problems associated with interpreting intensity curves from disordered carbon that had been reported in the literature. Since the calculated tetrahedrally-bonded carbon peaks were found to be quite similar to those from aromatic sheets, Ergun and Tiensuu [7] stated that it was thus difficult to detect the presence of diamond like atoms by diffraction but noted that it was likely such atoms may occur in appreciable quantities in amorphous carbons. Throughout later investigations [8], Ergun also argued against Franklin’s assumption [1] that some carbon atoms necessarily existed in gas-like arrangements.

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Following the work of Diamond [6], Ruland [9] developed a scheme for interpreting intensity curves based on what may be viewed as an early Rietveld [10] scheme to obtain crystallite parameters from very small non-crystalline aromatic carbon polymers. Ruland [9] noted that the ‘unorganised carbon content’ need not relate to gas-like atoms and may be given by disorder within aromatic planes through the inclusion of five membered rings in the atomic network topology, side groups and/or non-carbon side groups. As mentioned by Fischbach [11] in a later review of the relevant literature, Ruland and Ergun et al. further established the inadequacies of simple turbostratic crystallite models, promoting the importance of including defects such as curvature of aromatic planes, holes in the planes and the presence of atoms interstitially located and bonded to the planes. Complementing these ideas, by essentially combining X-ray diffraction with observations from sorption experiments, extensive investigations by Maire and Mering [12] led to the conclusion that between 2% and 10% of carbon atoms in graphitic carbon materials exist in the form of interstitial atoms, strongly bound to the aromatic planes. Using the perfect crystallite approach, yet in opposition to Franklin’s [2] deductions that asymmetries in (0 0 2) peaks arise from dispersions in the degree of ordered crystallites, Yen et al. [13] later proposed that the asymmetry could be used to calculate the ‘degree of aromaticity’. By dividing the (0 0 2) contribution to the diffracted X-ray intensity into two separate symmetrical peaks, Yen et al. [13] suggested that the smaller subsidiary peak to the left of the perfect (0 0 2) peak represented diffraction from carbon that was non-aromatic, such that the ratio of areas between the two peaks could be used to estimate the percentage of aromatic carbon atoms in a given solid. Some experimental and theoretical evidence was provided by considering the diffraction from blends of carbon black and saturated polynuclear aromatic chemicals. This method was more recently used to investigate Australian coals [14] where, whilst the authors noted the assumed simplicity of the structural models, it was concluded that the technique was able to give the maximum amount of structural information from carbonaceous materials using X-ray diffraction in the ‘medium to high angle range’. Also assuming idealised crystallite models, the original methods of Franklin [1,2] were recently applied to estimate the degree of graphitisation for some Pennsylvania anthracites simply by measuring the positions of (0 0 2) peaks [15]. These methods of structure examination are in contrast with earlier coal studies conducted by Girgoriew [16], where the incorporation of diamond-like rings of atoms in addition to sheets of aromatic carbon into coal structure models was required to improve agreement with experimental X-ray diffraction results.

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Shi et al. [17] recently extended the crystallographic ‘least-squares’ approach of Ruland [9] for modelling disordered carbon by developing an 11-parameter Rietveld-like [10] computational algorithm for extracting crystallite parameters from experimental X-ray diffraction data. The model of Shi et al. [17] assumes that disordered carbon is comprised of sheets of perfectly ordered aromatic planes, which may be displaced from adjacent planes, only in directions parallel or normal to the planes. Whilst the nearest neighbour distance remains constant within a given plane, entire planes may be stretched in the algorithm of Shi et al. [17], through variation of the in-plane lattice constant, designed to allow further broadening of calculated IðkÞ peaks. In order to account for the possibility of ‘strained regions’ of the hypothesized crystallites, defined by regions of parallel planes with non-graphitic c-axis spacings, Shi et al. [17] describe the normal separation between aromatic planes as involving the crystallographic graphite d0 0 2 spacing, plus a strain parameter. By successively introducing new planes into the crystallite model that are parallel to the original, the strain parameter is enforced through probabilistic selection from a Gaussian distribution for the deviation of the inter-planar separation from the ideal value given by d0 0 2 . After extracting various crystallite parameters from the structural models for the disordered carbon solids investigated, Shi et al. [17] demonstrated good agreement with fitted X-ray diffraction data, although the maximum magnitude of the scattering vector was 1 and the data was not limited to around k ¼ 7:5 A normalised to remove the structure-independent single particle scattering contribution. Although the algorithm of Shi et al. [17] cannot provide features such as interstitial atoms, curvature and defects in aromatic planes, their procedure is notably quite rapid due to the employed simplifications. In a recent investigation of the effect of heat treatment on an Australian char [18], the algorithm of Shi et al. [17] was used to obtain structural parameters. Observing that crystallite parameters were found to increase during heat treatment, it was also shown that the algorithm produced parameters as much as five times larger than those given by the Scherrer equation [4]. Since the algorithm produced reasonable fits to the collected X-ray diffraction data, it was noted that the Scherrer equation may be erroneous for highly disordered carbon with broad diffraction peaks. In a very recent paper however [19], whilst the X-ray diffraction data was again found to fit reasonably well, the same authors found the algorithm of Shi et al. [17] gave incorrect results since, amongst other reasons, some fits resulted in negative values for the fraction of unorganised carbon. Sharma et al. [20] recently used high resolution TEM imaging to ‘directly observe’ the layered structure of

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coals by qualitative visual inspection of graphite-like fringes formed by (0 0 2) contributions to the intensity. In a similar fashion to earlier TEM investigations of carbon soot morphology by Polatas et al. [21], Sharma et al. [22–24] recently continued the imaging analysis to construct a computational procedure for extracting crystallite parameters directly from the images by compressing the image contrast to yield wire frame representations of (0 0 2) fringes from which, amongst other parameters, the number of layers and aromatic layer widths were calculated. Comparison of the same parameters obtained using Scherrer’s equation were reported to give agreement, thereby validating the procedure for highly disordered carbonaceous materials. Noting that other researchers using the algorithm of Shi et al. [17] reported that Scherrer’s equation gave erroneous results for highly disordered carbon materials, there is clearly room for further investigation. It is important to note, however, that similar wire-frame image based methods have also been applied by other groups to extract similar microstructural information for coal related materials [25]. In contrast to the diffraction based approaches for describing coal-related carbonaceous microstructure discussed thus far, many researches to date have alternatively utilised the organic origins of coal as a basis for classification of the microstructure. Arising from differing vegetal sources [26], the structure and properties of the maceral constituents of coal [27] have in particular been investigated in the past. For example, Pergermain’s [28] analyses of six low-rank bitumous coals and their derived chars showed that basic macerals identified within the parent coals can be used explain variations in reactivity, particularly for small sample grain sizes. Lin and Guet [29] also combined X-ray diffraction with maceral classification of chars to study combustion and pyrolysis behaviour in situ, observing that the variation of structural characteristics during heat treatment depend upon maceral composition. The extraction and subsequent investigation of macerals from parent coals thus effectively simplifies attempts to discern links between microstructure and properties for coals such as combustion behaviour, without the requirement to produce detailed molecular models. It is to be noted, however, that other researchers [30] have found inconsistencies between maceral and parent coal relationships, indicating that maceral interactions are important. Invoking dispersion rather than diffraction to deduce structural information, some researchers have recently applied Fourier transform infra red (FTIR) spectroscopy in addition to C13 nuclear magnetic resonance (NMR) to also study the chemical structure [31] of the maceral constituents of coals [32,33]. These types of experiments have also been used to refine models of the macromolecular chemical structure [31] contained within various coal related materials. For example,

Mathews et al. [34] combined information obtained from C13 NMR experiments and a range of other analyses to guide the construction of three dimensional models for the structure of particular coal macerals, which were then refined using force-field based energy minimisation procedures in a similar nature to the structural modelling work of Carlson [35]. As another example, using FTIR spectroscopy, Jones et al. [36] determined the aromaticity of carbon networks as well as the concentrations of aromatic to aliphatic hydrogen and carbon atoms within particular bitumous coal and char samples. In conjunction with elemental analysis, this information was used to construct microstructural molecular-fragment models of the samples. Using a commercial molecular modeling package to minimise the energy of the model structures, estimations of pore sizes were then taken by noting distances between structurally optimised fragments. Modelling of porous structure is clearly also important, as exemplified by the recent publication of Snook et al. [37], where a detailed combination of small angle neutron scattering (SANS) and gas absorption experiments were used to measure the porous properties of industrially important coal chars. Combining porosity with microstructure in carbonaceous models is rather complicated however, as recently discussed by Acharya et al. [38] and Petkov et al. [39]. In light of the existence of well known carbonaceous fullerenes, the interplay of microstructure and porosity can be varied and complex for carbon based materials [40]. For example, such exotic structures as negatively curved minimal surfaces decorated by aromatic carbon networks have been found to be physically plausible for materials comprised of carbon alone [41–52]. Indeed, atomic structures of the form proposed by Jenkins and Kawamura [53] for glassy carbon, where pores result from interwoven graphitic microstructure, are still yet to be fully realised. Hence, for structural modelling of coal related materials such as chars, it is clear that the inclusion of porosity for modelling both meso and microstructure simultaneously is a very complex issue and, as such, will be considered outside the scope of this paper, which is to be defined in the next section. 1.2. Aims of this investigation In this paper, we apply Warren’s [4] distribution function concepts to quantitatively measure microstructural pair correlations from an industrial char using X-ray, neutron and our recently developed (to be published) electron diffraction techniques, which are based on the techniques of Cockayne and McKenzie [54]. The char sample was provided by BlueScope Steel (formerly BHP Steel), motivated by the need to further understand possible links between the microstructure of coal-derived carbonaceous materials and their dissolution in

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iron, which is important for iron making technologies. As desired by BlueScope Steel, the nature and origin of the char for this particular study will not be revealed and simply referred to as ‘char X ’. In contrast to some of the more traditional studies outlined in the previous section, the methods used to interpret the char X diffraction data in this paper will not largely depend upon crystallographic reasoning; making as few assumptions as possible regarding the dense carbonaceous microstructure. The focus of this paper is to describe procedures for statistically characterising the dense carbonaceous microstructure of an industrial char at the level of atomic pair correlations. Procedures for characterising the microstructure of char X using electron diffraction data for quantitative analysis will be outlined and information beyond that which can be deduced from inspection of diffraction patterns alone will also be presented. Our theoretical approach is based upon the ‘Reverse Monte Carlo’ (RMC) computational technique of McGreevy and Pusztai [55], which produces configurations of atomic models statistically consistent with experimental observations and may be considered similar to the work of Shi et al. [17] in this regard. However, we have recently enhanced the existing RMC algorithm for disordered carbons and, as with our previous work [56,57], the focus here will involve small scale statistical measures of disordered char structure such as atomic coordination number distributions, bond angle distribution functions and atomic network ring statistics. We will demonstrate that our approach permits a description of disordered graphitic microstructure in a physically motivated and experimentally consistent manner. It should also be noted that, in principle, larger scale features such as average crystallite lengths and porosity could indeed be modelled using the procedures discussed here but would however require additional experimental information such as small angle neutron [37] or X-ray scattering (SANS or SAXS) to provide sufficient structural consistency across a range of characteristic length scales.

2. Experimental techniques 2.1. Neutron, X-ray and electron diffraction of an industrial coal char Electron diffraction was chosen as the primary tool for analysis to allow data from the disordered carbon in char X to be collected without interference from crystalline regions as well as to provide information over a wide range of scattering angles, which is important for accurate inversion of gðrÞ from Eq. (1). It is generally not customary to use more than one type of diffraction technique to investigate a material of interest however, since neutron and X-ray diffraction probe regions of

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material many orders larger than that of electron diffraction, by comparison, these techniques enable an assessment of the degree of homogeneity of char X . Of equal importance, comparison with neutron and X-ray data also provides a measure for the validity of the single scattering assumption (which is used to derive Eq. (1)) for the electron diffraction data which is not always justified, on account of the much stronger interaction of electrons with matter [58]. Extraction of SðkÞ from IðkÞ involves removal of experimental artefacts not associated with the microstructure of the material of interest. Such complications vary depending upon both the type of radiation used to probe a given sample and the particular experimental arrangement used in a given experiment. Some explanation of various experimental data corrections used in our diffraction measurements is therefore required, as outlined in the following three sections. 2.1.1. Neutron diffraction The shortest neutron wavelength available corresponding to the (3 3 5) reflection from the germanium crystal monochromator on the medium resolution powder diffractometer (MRPD) at the Australian Nuclear Science and Technology Organisation (ANSTO) Lucas Heights, Australia, was used to extend the neutron diffraction data for char X to the largest possible 1 . Scattering magnitude of scattering vector k  11 A angles were calibrated using Rietveld analysis [10] for the diffracted intensities collected from a solid rutilephase poly-crystalline Titanium-Oxide (TiO2 ) sample under the same experimental conditions. After calibration of the scattering angles, the neutron data was then normalised using the method of North et al. [59]. Geometric absorption corrections given by Paalman and Pings [60] were neglected in addition to Placzek corrections [59], which would account for the, assumed small or at least isotropic, inelastic scattering contribution. Due to the comparatively small incoherent scattering factor for carbon, the only other physical correction to be applied was for the presence of hydrogen which was assumed to contribute no more than a linear k-dependent slope to the intensity data [61]. Backgrounds were measured in situ using an empty vanadium can identical to those used to hold the sample and were subsequently subtracted from the diffracted intensity. Finally, in accordance with the method of North et al. [59], the instrumental response function was accounted for by dividing the experimental data by that obtained from a cylinder of solid vanadium of similar geometry as the experimental sample under the same experimental conditions. 2.1.2. X-ray diffraction Exactly the same char X powder sample used in the neutron scattering experiments was analysed in a Bruker

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XD8 Advance X-ray Diffractometer. Whilst divergence slits normally used to improve the angular resolution of sharply diffracting materials were widened to improve signal to noise ratio at high scattering angles, the maximum value of the scattering vector k was set by instrumental limitations. Like the neutron diffraction MRPD instrument, the detection angle was limited by physical constraints, with a maximum collection angle 1 using Cu Ka X-rays). of 150 degrees (giving k  7:0 A To further improve data quality at the largest scattering angles, angular resolution was also sacrificed by deselecting both the graphite monochromator and Cu Kb filter. For the cylindrical flat reflection geometry used in the X-ray experiments here, an analytic form of geometrical absorption correction factors given by Paalman and Pings [60] were necessarily estimated. Inelastic recoil corrections, background and air scatter (with appropriate geometric factors), absorption and incoherent scattering factors were also accounted for. Ergun’s [7,8] graphical method for removing the ambiguity of determining normalisation parameters was not able to be realised due to limitations in the maximum angle of collection but nonetheless proved useful for obtaining first estimates of normalisation parameters. These parameters, along with the background correction, were then refined by comparison with the neutron diffraction data, so as to achieve consistency between the two. For removal of the single particle contribution to IðkÞ, the X-ray form factor for carbon was obtained from International Tables for X-ray Crystallography [62], with dispersion corrections neglected.

to be (effectively) elastic. In order to obtain higher quality data at larger scattering angles, three partially overlapping diffraction patterns were ‘spliced’ together with our developed analysis software, which will be described in a future publication. This allowed the collection of the diffracted intensity to large scattering an1 ), which are (crucially) required to gles (k  24 A improve the quality of the derived radial distribution function gðrÞ. Observed scattering angles were calibrated using known peaks from a polycrystalline aluminium sample collected under the same conditions as char X . Slowly varying background artefacts, most likely caused by small contributions from multiple scattering, were removed by simply obtaining gðrÞ from SðkÞ, setting to zero any unphysical oscillations in gðrÞ preceding the first nearest neighbour peak (located  and then transforming gðrÞ back to about r ¼ 1:42A) SðkÞ. In accordance with our previous work on glassy carbon [57], which has a bulk density differing greatly from the microstructural density, the matching of positions of the broad peaks in the measured SðkÞ data for char X to that of the (h k 0) and (0 0 l) contributions from graphite was used to postulate a network density equal to that of graphite. In order to provide some estimate of the nature of the char X microstructure in comparison to that of other carbonaceous materials, some high resolution TEM images were acquired from char X in addition to a previously investigated [57,63] V25 glassy carbon sample.

2.1.3. Electron diffraction TEM samples were prepared using ultramicrotomy. Since the char was supplied in powdered form, it was necessary to use a hand-operated hydraulic press to compress the char powder into a cylindrical pellet. Fragments of the compressed char were then immersed in epoxy resin, which was then thinly sliced with a diamond knife in an ultra-microtome. It is possible to detect compositional heterogeneities throughout a TEM investigation, using spectroscopy based techniques, however it was reasoned that the majority of mineral inclusions would exist in crystalline form, so that regions containing disordered carbon were selected by simply examining familiar peaks in (in situ) electronically collected diffraction patterns. Choosing specific areas that yielded isotropic diffraction patterns, devoid of any bright crystalline features, two dimensional energy filtered electron diffraction patterns were collected using a Gatan Imaging Filter (GIF 2000) system on a JOEL 2010 TEM operating at 200 kV. Energy filtering was performed with the GIF 2000 instrument to collect only those electrons that suffered negligible energy loss; considered

3. Simulation techniques 3.1. Reverse Monte Carlo modelling Given a configuration of points representing atoms in a simulation, gðrÞ may be calculated in a routine, intuitive and reasonably rapid manner. The fast Fourier transform can also be used to efficiently calculate the corresponding SðkÞ for a frozen assembly of atomic positions using Eq. (1). These two facts are central to the RMC algorithm of McGreevy and Pusztai [55], which seeks to minimise the ‘least-squares’ difference between a simulated static structure factor and that from experiment. In principle, any experimental or physically motivated function which may be calculated from the positions of an assembly of atoms may be used within the RMC procedure to produce model atomic structures consistent with experimental observations. Recent work by O’Malley et al. [63] has shown that the inclusion of a constraint, which biases the RMC algorithm to produce desired proportions of experimentally determined atomic coordination fractions, improves the microstructural description of glassy carbon materials.

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Extending on the work of O’Malley et al. [63], we have recently incorporated the environment dependent interaction potential (EDIP), which was developed by Marks [64] for carbon, into the algorithm; thereby combining Metropolis Monte Carlo methods with those of RMC. As described in our previous publications [56,57], the current hybrid algorithm, which will be referred to here as ‘HRMC’, allows the EDIP energy of structures to be minimised whilst also maintaining statistical agreement with experimental observations, thereby improving the physical nature of the atomic configurations produced for carbonaceous materials. Control over the discrepancy between experiment and calculated diffraction data is achieved through an experimental error weighting function rðkÞ, whilst the EDIP energy is simultaneously weighted by a Boltzmann factor kT , where T is the temperature of the system. For the purposes of the HRMC modelling presented here, these two factors may be considered as simply relative weights of the importance given to either the degree of experimental consistency or that of the minimisation of energy and, optimally, both.

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4. Results 4.1. Qualitative TEM analysis Fig. 1 displays a typical diffraction pattern segment from a region in char X , assumed to contain mineral inclusions or at least highly ordered components of the microstructure, unsuitable for distribution function analysis. The central spot of the poly-crystalline pattern is located at the bottom left corner of the picture and was not recorded so as to prevent damage to the CCD array. Fig. 2(a) shows a high resolution TEM image of char X . Most areas of the sectioned char X such as the one shown in Fig. 2(a) appeared qualitatively similar, indicating a high degree of disorder as also evident from the broadness of the diffraction patterns collected from similar areas. For comparison, results from glassy carbon heat treated to 2500 °C in Fig. 2(b) show a pronounced degree of ordering suggested by the alignment of sets of (0 0 2) fringes in this image. 4.2. Pair distribution function analysis

3.1.1. Simulation details Guided by the Hybrid Reverse Monte Carlo (HRMC) investigations of glassy carbon reported in previous work [57,63], 1296 unique atoms were chosen for HRMC simulations of char X , due to the lack of features in the experimentally determined (using elec Beginning with a tron diffraction) gðrÞ beyond r  10 A. dense graphite lattice as a reasonable initial structure, this precise number of atoms was calculated by assuming a graphite network density and choosing conventional cell parameters of nearly equal dimension for  Y ¼ efficient modelling of gðrÞ given by: X ¼ 22:14 A,  Z ¼ 20:13 A;  where the Z axis corresponds to 25:57 A, the graphitic c-axis. Although the bulk density of the char certainly differed from this value (due to porosity), in the electron diffraction experiments, the length scale probed (dictated by the range of the scatting vector k) ensured sampling of only the dense local microstructure of the disordered carbonaceous region of the char. The constructed cell was then infinitely repeated throughout space using standard periodic boundary conditions. Thus, as stated earlier, the simulation was designed only to model the dense local atomic microstructure of char X and not larger scale features such as crystallite parameters or porosity. After six trial simulations using graphite initial lattices and different temperature weighting factors for the EDIP energy constraint, T ¼ 500 K was found to give the largest possible weighting of the EDIP energy term, whilst maintaining close agreement with experimental diffraction data with a constant experimental error weighting of rðkÞ ¼ 0:02.

After applying previously described corrections to the X-ray, neutron and electron diffraction IðkÞ data sets, the SðkÞ results from each method can be quantitatively compared, as shown in Fig. 5. Consistency of the SðkÞ functions obtained using three different radiations, can be clearly seen from Fig. 3 although peaks in the X-ray and neutron diffraction results due to mineral inclusions obscure the agreement to an extent. The absence of such sharp features in the electron diffraction data is because the analysis of very small regions enabled the disordered carbonaceous structure to be probed directly. The reasonable

Fig. 1. Sharp spots and rings in the diffraction pattern were used to detect regions containing significant crystalline material, thereby identifying areas that would be unsuitable for analysis.

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Fig. 2. (a) High resolution TEM image of char X . (b) High resolution TEM image of glassy carbon heat treated to 2500 °C. In (b) large correlations between (0 0 2) contributions to the observed intensity can be observed.

Fig. 3. The static structure factors for the broad diffracting disordered carbon contained in char X , using three different incident radiation sources. Satisfactory agreement is seen between all three, suggesting a certain degree of homogeneity in the disordered carbon pair correlated structure for char X .

agreement between all three SðkÞ data sets indicates that the pair correlated structure for the disordered carbon in char X is relatively homogenous, since the scattering volumes between each technique vary by many orders of magnitude [58]. Notwithstanding that the broader (0 0 2) peak in the electron diffraction data is most likely due to multiple scattering, the seeming homogeneity given by Fig. 3 serves to indicate that the application of RMC techniques to represent the statistical pair correlated structure for char X should give an indication of the average microstructure of the disordered carbon within char X . Naturally, microstructure heterogeneities could actually be accounted for by combining electron diffraction data from several contrasting regions of sample with respective HRMC simulations, a possibility unique to electron diffraction. The electron diffraction data also shows significant detail out to approximately twice the k range spanned by the neutron data. Assuming an atomic network density equal to that of graphite, the electron diffraction static structure factor in Fig. 3 was Fourier inverted to give the corresponding radial distribution function gðrÞ, as shown in Fig. 4.

Fig. 4 indicates that the char X microstructure is more disordered than that of the glassy carbon material studied in our previous work [57,63], with significant  Small deviapair correlations extending to only 7 A. tions in the left hand side of the first nearest neighbour peaks in Fig. 4 were caused by termination of the SðkÞ at the maximum collected value of k and were minimised by application of an artificial temperature factor [1,4]. 4.3. Hybrid Reverse Monte Carlo simulations Following equilibration of the total error in the HRMC algorithm over 2 million Monte Carlo steps using the chosen weighting parameters with SðkÞ, gðrÞ and EDIP constraints switched on throughout the entire simulation, another 400 000 steps were run to collect statistics for the char X microstructure configurations. The modelled gðrÞ and SðkÞ functions are shown in Figs. 5 and 6. As observed in HRMC simulations of glassy carbon in previous work [57], the HRMC algorithm had difficulty modelling the region between the first and second

T. Petersen et al. / Carbon 42 (2004) 2457–2469 3.5 3

glassy carbon (O'Malley et al [37])

2.5

char X

g(r)

2 1.5 1 0.5 0 0

2

4 6 pair separation distance r (Å)

8

10

Fig. 4. Radial distribution function obtained from char X using energy-filtered electron diffraction compared to the glassy carbon gðrÞ which was investigated by O’Malley et al. [63] and more recently by the present authors [57].

3

2

HRMC

g(r)

EXP.

1

0 0

2

4

6

8

10

pair separation r (Å)

Fig. 5. Comparison between the HRMC calculated and experimental gðrÞ for char X .

2 1.8 1.6

HRMC

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EXP

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bonded atoms. In a similar manner, the asymmetric broadness of the left hand side of the first nearest neighbour peak was also unable to be reproduced since this feature, as well as (to an extent) the filling of the first minimum in the experimental gðrÞ, are both due to limitations in the range of k over which quality IðkÞ data were collected in the TEM. As expected, the small angle features in the theoretical SðkÞ in Fig. 6 also show discrepancy due to the use of dense atomic configurations that do not model larger scale features. However, the previous analysis of the X-ray and neutron SðkÞ data also suggests that perhaps multiple scattering in the experimental electron diffraction SðkÞ also contributes to some systematic error at small k. Despite these differences, both gðrÞ and SðkÞ HRMC models of the experimental data are still quite reasonable. Fig. 7 gives the coordination distribution statistics for char X , showing a high degree of sp2 hybridised carbon atoms corresponding to around 77% three-fold coordinated atoms. Four-fold coordinated atoms are due to the presence of tetrahedrally-bonded diamond like atoms, whilst the large percentage of sp hybridised atoms indicates significant stretches in bond lengths, associated with defects within the disordered graphite like layers for the char X microstructure. The small percentage of singly coordinated atoms is likely due to systematic errors in the experimental data. Fig. 8 shows the corresponding bond angle distribution functions BðhÞ for bonds containing two, three and four-fold coordinated atoms at the vertices of the bonds; where the sub-distributions have been normalised so that they all sum to give the total BðhÞ. The sub-distributions for each coordination type are found to be quite distinct, indicating that inclusion of the EDIP energy weighting enforces particular bonding configurations to assume physical arrangements. The physical soundness of the generated microstructures is supported by the observation that the three-fold coordinated BðhÞ has maximum at 120°, whilst the tetrahedral bonds are

1

80

0.8

70

0.6 0.4 0.2 0 0

5

10

15

20

-1

k (Å )

Fig. 6. Modelled experimental SðkÞ for the HRMC simulation of char X compared with that from experiment. Discrepancies in the peaks at small values of k are due to the fixed unit cell boundaries employed.

% of coordinated atoms

S(k)

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60

HRMC

50 40 30 20 10 0 0

1

2

3

4

5

Coordination number

nearest neighbour distances in the experimental char X gðrÞ shown in Fig. 5, due to the influence of the EDIP potential enforcing physically reasonable distances upon

Fig. 7. Coordination statistics for the HRMC char X simulation. The small percentage of 1-fold coordinated atoms is likely the result of uncertainties in the experimental data.

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Number of rings per atom

0.06

total

0.04

B(θ)

2-fold coordinated centres 3-fold coordinated centres 4-fold coordinated centres

0.02

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HRMC

0.25 0.2 0.15 0.1 0.05 0 3

0 0

20

40

60

80

100

120

140

160

180

200

θ (degrees)

Fig. 8. Coordination-centre resolved bond angle distributions from the HRMC simulations of char X .

centred around h ¼ 110°. Two-fold coordinated atom bond centres are seen to involve a wide range of bond angles, peaked vaguely near h ¼ 120° and extending up to h ¼ 180°. This slight peak in the two-fold coordinated bond angles at h ¼ 120° suggests that such bonds are responsible for disorder within the disordered graphitic planes, as will be confirmed by ‘snapshots’ of atomic configurations of the microstructure in later figures. Rings statistics for the char X microstructures defined by Franzblau’s [65] shortest path criterion were created using numerical routines of O’Malley et al. [63], and are shown in Fig. 9. Large numbers of six rings per atom in Fig. 9 correlate with the statistical distribution functions in Figs. 7 and 8 and relate to dominant hexagonal configurations of atoms within the disordered graphitic planes for char X . Given that the statistical bond lengths and angles were observed to be well defined, the smaller

4

5

6

7

8

Number of atoms in ring

Fig. 9. Ring statistics from the HRMC simulations of char X . Five and seven membered rings indicate departures from planarity in the disordered (0 0 2) planes, as does the significant presence of eight membered rings, which indicate large holes in the (0 0 2) layers.

and larger numbers of rings per atom in Fig. 9 suggest significant departures from planarity of the (0 0 2) graphitic sheets, where the eight membered rings correspond to large defects within the layers. Figs. 10–12 display various representations of the simulated char X microstructure where in all pictures dark atoms identify two-fold coordinated atoms, white atoms identify three-fold coordinated atoms, whilst light grey atoms correspond to four-fold coordinated (diamond-like) atoms. Fig. 10 clearly shows that diamondlike atoms are located interstitial to the disordered (0 0 2) planes. Most two-fold coordinated atoms are also observed to lie within the planes. Fig. 11 gives a clearer view of internal section of the char X microstructure, where curvature or buckling in the planes is noticeable. Fig. 12 displays one of the disordered (0 0 2) planes,

Fig. 10. Side view of an atomic configuration that was generated during the equilibrated stage of the HRMC calculations for char X .

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Fig. 11. Internal view of an atomic configuration that was generated during the equilibrated stage of the HRMC calculations for char X . Some bonds into and out of the page are not shown.

Fig. 12. Planar view of a disordered (0 0 2) plane that was generated during the equilibrated stage of the HRMC calculations for char X . Due to the buckling of the plane, some bonds into and out of the page are not shown.

where large ‘‘holes’’ in the plane are visualisation artefacts which are caused by atoms lying outside the cross-section as a result of buckling of the plane. In accordance with indications from previous literature [7– 9,11,12], it is evident that the diamond-like atoms are grafted to the hexagonal planes. Two-fold coordinated atoms are confirmed to be associated with large ring defects in the (0 0 2) planes, involving wider bond angles than those of the three-fold coordinated atoms.

5. Conclusion We have experimentally characterised the microstructure of an industrial disordered carbonaceous char (char X ) using three different radiation source diffraction techniques and generated a model of the char in atomic detail, statistically consistent with the experimental data from the carbonaceous region of the sample. Static structure factors of char X obtained from each of the

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three diffraction techniques showed consistency, indicating reliability in the resulting static structure factor SðkÞ. In particular, the electron diffraction SðkÞ was measured over a large range of scattering angles and was devoid of any features attributable to crystalline regions of the industrial char. Agreement between broad features in all diffraction data sets indicated that the disordered carbonaceous microstructure of char X must be reasonably homogenous. Therefore, it is reasonable to assume that the Hybrid Reverse Monte Carlo (HRMC) modelling presented here and the resulting characteristic distribution functions suitably describe the disordered carbonaceous parts of the dense char X microstructure. Ring statistics, coordination distributions and bond angle distribution functions all indicated that the modelled char X microstructure statistically exhibits disordered graphitic features, with a distinct contribution from a small percentage of diamond-like, four-fold coordinated, atoms. Extension to the work reported here will include future investigations by collecting diffraction data over an even larger range of scattering angles from more regions of the sample, whilst the incorporation of information from small angle scattering experiments would also allow, within the framework described here, modelling of larger scale features such as crystallite parameters and micropores. The use of spectroscopic techniques such as electron energy loss spectroscopy (EELS) [66] would also allow the detection of elements that may be present within the disordered carbonaceous microstructure.

Acknowledgements Blue Scope Steel (formerly BHP Steel) and, specifically, Dr. Paul Zulli, is acknowledged for motivation of this work and for providing both financial support to one of the authors (TP) and the char sample. The Victorian Partnership for Advanced Computing (VPAC) provided computer time for performing the HRMC simulations and the Australian Nuclear Science and Technology Organisation (ANSTO) granted instrument time and technical support for performing neutron diffraction experiments and are thanked for their kind assistance. The authors would like to thank Dr. Nigel Marks of the Department of Applied Physics, School of Physics (A28), University of Sydney, NSW 2006, Australia for the use of his carbon EDIP. Furthermore, the authors would like to thank Dr. Brendan O’Malley, Unilever R&D Port Sunlight, Bebington, Wirral, UK for the use of his ring statistics codes and his significant involvement with the development of the simulation code. Finally, Dr I. Burgar, CSIRO Manufacturing Science and Technology Melbourne, VIC, is thanked for assistance with compressing the powdered char.

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