Prospect for application of radial distribution function in coal carbonisation research

Carbonisation is an important way of comprehensive utilisation of coal. In this short contribution, the application of wide angle X-ray scattering (WAXD) and radial distribution function (RDF) in coal carbonisation research is brie ﬂ y reviewed and prospected. General WAXD analysis can only provide basic geometrical structural parameters of crystals in the sample; while RDF derived from WAXD by Fourier transform can give further detailed structural parameters of coordination of atoms in sample. The application of RDF in coal science has been reported in o ﬄ ine static studies, but not in-situ studies. Here, a new ideal to perform in-situ RDF study on coal carbonisation is presented, which is based on a powerful synchrotron radiation platform with a proper detector and a high- temperature furnace. Thus, it is expected to obtain the ﬁ ne dynamic structural evolution characteristics of coal during carbonisation.


Introduction
Coal is a kind of carbonised black solid combustible organic rock formed gradually by the complex biological, chemical and physical changes of ancient plant remains buried underground [1]. It is estimated that the total world reserves amount to around 10 12 tons of coal [2]. Since so much coal exists, this means that the earth has significant coal reserves. These reserves are spread all over the globe. Although the reserves are spread widely, some countries have much more coal than others. Nearly 75% of the world's recoverable coal resources are controlled by five countries [3]: the United States (about 22%), Russia (about 15%), Australia (14%), China (about 13%) and India (about 10%). different final temperatures, carbonisation can be approximately divided into three types: 900-1100°C for high-temperature carbonisation, also namely coking; 700-900°C for medium-temperature carbonisation and 500-600°C for low-temperature carbonisation [1]. Generally, the low-temperature carbonisation produces char with loose structure together with low gas yield and high tar yield; the high-temperature carbonisation produces dense silver-grey coke together with high gas yield and low tar yield; the yield of the medium-temperature carbonisation product is between low-temperature carbonisation and high-temperature carbonisation. Anthracite can be used to make coal gas or directly used as fuel [16,17]. Bitumite is generally used in coking, coal blending, power boiler and gasification industry [18,19]. Lignite is generally used in gasification, liquefaction, power boilers, etc. [20][21][22].
During carbonisation, coal undergoes thermal decomposition, thermal condensation and other physical and chemical changes [23]. The laminates of the hexagonal planar net of carbon atoms form the basis for solid phase residues, while the side chains are broken, resulting in a mixture of liquid, gas and solid. Further heating, decomposition, condensation and other reactions occur, the molecular weight increases and solidification occurs, forming combined char. When the char is further heated, dehydrogenation, aromatisation and other reactions occur. The laminates of the planar net of carbon atoms are further condensed and enlarged. Char tightens and hardens, and cracks to form coke.
Carbonisation is a classic coal conversion way, which has been studied by many researchers [24][25][26][27][28][29][30], but most of the studies are offline static, and the online in-situ dynamic studies are rarely reported [31,32]. The characteristics and mechanism of coal structure change during carbonisation remain to be ambiguous. It is necessary to strengthen the in-situ research on coal carbonisation.

WAXD and RDF
The scientific research on coal carbonisation depends on appropriate characterisation means. Coal and its carbonised solid products are typical carbon materials [31,33,34]. Among a number of means, the wide angle X-ray diffraction (WAXD or XRD) is undoubtedly one of the most powerful means to characterise carbon materials [32,[35][36][37][38]. WAXD is a diffraction experiment that consists of scanning/recording large diffraction angles to cover a wide range of scattering variables down to small d-spacing, which corresponds roughly to the size on the atomic and molecular scale in materials [39]. The graphite-like crystal structure parameters, including the lamellar spacing d 002 , the lamellar stacking height L c and the lamellar lateral size L a , can be directly calculated from the (002) and (100) peaks on WAXD or XRD curve based on the formulae of Bragg (1) [40], Scherrer (2) [41] and Warren (3) [1,42], respectively. (1) where λ is the incident X-ray wavelength; θ 002 and θ 100 , half of the diffraction angle, are the peak positions of (002) peak and (100) peak, respectively; β 002 and β 100 are the full width at half maxima (FWHM) of (002) peak and (100) peak, respectively and K 1 and K 2 are the shape factors, according to Scherrer (K 1 = 0.89) and Warren (K 2 = 1.84) [1,41], respectively. Furthermore, the measured diffraction data can be corrected (i.e. subtraction of background, Compton scattering, multiple scattering, polarisation and absorption) and normalised to obtain the interference function. The Fourier transform of the interference function gives the radial distribution function (RDF) with a spatial resolution inversely proportional to the maximum value of the scattering vector attained in the experiment, as shown in formulae (4)-(8) [43,44].
RDF(r) = 4pr 2 r 0 g(r) = 4pr 2 r 0 + rG(r) where I(q) is the interference function, q is the diffraction/scattering vector, q = 4πsinθ/λ, 2θ is the diffraction/scattering angle, λ is the incident X-ray wavelength; ρ(r) is the number density of the radial distribution of atoms, which represents the average distribution of atomic density on each sphere centred on all atoms with radius r; ρ 0 is the average number density of atoms in the system; G (r) is the reduced radial distribution function, g(r) is the atom-pair distribution function and RDF(r) is the radial distribution function. The RDF(r) gives information about the probability of finding an atom in a spherical shell at a distance r from an arbitrary atom. Successive peaks correspond to the nearest-, the second-, the next-neighbour atomic distribution and so on. Based on the above formulas (4)-(8), the detailed structural information of carbon materials can be derived from the following presentation. The coordination distance r i is the ith peak position on RDF as formula (9) [45]: The coordination number N i is the ith peak area on RDF as formula (10) [46,47]: The aromatic degree f a can be computed from the first coordination distance r 1 on RDF of sample, 0.154 Å of diamond and 0.142 Å of graphite as formula (11) [48]: The short-range ordered domain R s can be identified as the position of |g(r) − 1| ≤ 0.02 at r ≥ R s as formula (12) [48]: The true density d s (g/cm 3 ) can be derived from the slope of G(r) at r→0 as formulas (13) and (14) [49]: where E is the average atomic weight and N A is the Avogadro constant.

Status and prospect of RDF in coal carbonisation research
It is well known that WAXD or XRD is the classical and routine means for characterisation of coal [32,[50][51][52] char [53,54] and coke [55,56] and the main structural information are d 002 , L a and L c . Most of the studies based on WAXD or XRD are static and offline, while the in-situ dynamic studies on coal carbonisation are few [32]. The RDF has been scarcely applied in the static offline studies on raw coal [57,58], char and coke [59], but not been applied in the dynamic in-situ study on coal conversion. This is mainly due to the lack of suitable furnace and detector. The furnace needs to provide both a high temperature (∼1000°C) and a wide diffraction angle range (usually greater than 90°). The detector needs to be large enough to receive the diffraction/scattered signals covering the full angular range at each exposure. It also requires that the incoming X-rays be strong enough to shorten exposure time. These requirements are often difficult to obtain and limit the use of RDF for in-situ study. As well known, the skeletons of coal and their carbonised solid products are composed of graphite-like ordered and amorphous structures. The size and condensation degree of ordered domain are different with different coal ranks and carbonisation temperatures. In fact, no matter what kind of coal and how high temperature of carbonisation, RDF can be used to study the change of the skeleton carbon structure, especially the coordination of the carbon atoms with temperature, which is just the valuable information to reveal the detailed structural evolution of coal during carbonisation from the atomic level. Fortunately, with the development of science and technology, the above difficulties have been gradually overcome. The first is the development of synchrotron radiation facilities, which provide a powerful scientific platform for the study of the matter structure [35,[60][61][62]. Synchrotron radiation has many advantages such as high intensity and good collimation. Using synchrotron radiation as the X-ray probe of WAXS largely reduces the exposure time and is especially suitable for in-situ dynamic research [35]. In recent years, the wider-angle arc detectors, such as Mythen detector [63], have been equipped at synchrotron radiation experimental stations (such as 4B9A diffraction station and 1W2B biomacromolecule station (Figure 1) at the Beijing Synchrotron Radiation Facility (BSRF)), enabling collect the whole WAXD signals (0∼140°or so) at one time. In addition, the high-temperature furnaces suitable for synchrotron radiation instruments have been developed and applied [31,32,64,65]. We are developing a small furnace for carbonisation of coal in inert gas (such as nitrogen) with a maximum temperature of 1000°C and a special light outlet with a maximum angle (2θ) of 140°and a highest heating speed of 20°C/min ( Figure 2). The sample is situated at the centre of the furnace in a tilted attitude enabling the WAXS can be measured in a transmission mode. The sample atmosphere can be air or inert gas. The device is heated at the centre of the sample by the ring field heating method to ensure uniform temperature of the sample. The heating process can be controlled programmatically. The furnace shell is cooled by circulating water. The slits of light outlet are sealed by a piece of nonopaque film to keep temperature. It has the characteristics of small volume (diameter of about 120 mm and thickness of about 80 mm), simple structure, high thermal efficiency and low heat consumption. These developments will provide well conditions for the in-situ study on coal carbonisation at the synchrotron radiation platform. If such research can be carried out (sketched in Figure 3), the dynamic in-situ change of fine structure of carbon skeleton in coal will be obtained, which might be referable and helpful for further understanding and development of coal carbonisation.

Summary
Coal is an important energy and chemical raw material. Carbonisation is one of the main ways to achieve comprehensive utilisation of coal, in which coal undergoes thermal decomposition to release gas and tar, and thermal polycondensation to form char and coke or residue carbon. Both the raw coal and its carbonised solid products have typical structural characteristics of long-range amorphous disorder and short-range graphite-like order, making them particularly suitable to be characterised by RDF, which are derived from the special WAXD of the sample. The general WAXD or XRD can only give the basic geometric parameters of graphite-like crystals, while the RDF can detect the fine structural information as coordination of carbon atoms in the skeleton of the sample. In particular, based on a proper detector with wide angle coverage and a proper furnace with wide angle and high temperature at synchrotron radiation platform, the RDF study on carbonisation of coal is expected to be carried out in-situ, which will be helpful for deep understanding of the characteristics and mechanism of coal carbonisation.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Notes on contributors
Xiaoxia Shang is engaged in coal, char and coke.
Meijun Wang, Liping Chang and Yanfeng Shen are engaged in coal chemical industry.
Zhihong Li is engaged in SAXS and WAXS.