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Coal Rank and Shape of the small-Angle X-Ray Intensity
Alvise Benedetti, Salvino Ciccariello
To cite this version:
Alvise Benedetti, Salvino Ciccariello. Coal Rank and Shape of the small-Angle X-Ray Intensity.
Journal de Physique III, EDP Sciences, 1996, 6 (11), pp.1479-1487. �10.1051/jp3:1996197�. �jpa- 00249539�
Coal Rank and Shape of the Small-Angle X-Ray Intensity
Alvise Benedetti (~) and Salvino Ciccariello (~,*)
(~) Dipartimento di Chimica-Fisica, Calle Iarga S. Marta DD2137, 30123 Venezia, Italy (~) Dipartimento di Fisica 'G. Galilei'and sez. INFM, via Marzolo 8, 35131 Padova, Italy
(Received 8 February1996, revised 5 July1996, accepted 31 July 1996)
PACS.61.43.Gt Powders, porous materials
PACS.61.10.Eq X-ray scattering (including small-angle scattering) PACS.81.05.Rm Porous materials; granular materials
Abstract. The rank of a natural coal is empirically correlated to the shape of its small-angle X-ray intensity collected with the infinite-slit geometry.
The large variety in the microscopical texture of amorphous materials has been made evi- dent by wide and Small-Angle X-ray Scattering (SAXS) experiments. Considerable efsorts are
nowadays devoted to single out the physical features responsible for such structures as well as to investigate how amorphous' structures change when some external parameters are modified
while materials are prepared. Among amorphous materials, natural coals look particularly interesting. The first important results on coals' structures trace back to Franklin [1] and Hirsch [2]. Since then many investigations on the structure modifications induced by difser- ent thermal processes, as graphitization, pyrolysis, activation and so on (see, e-g-, Perret and Ruland [3], Guet and Tchoubar [4] and references therein), have been carried through. The formation of natural coals from organic materials can be looked at as a similar process occur-
ring in a much softer way but on a much longer time scale. In fact, the rank of a coal, related to the relative abundance of Carbon in comparison to that of Oxigen and Hydrogen present in the coal, generally increases with the ageing duration. (For the difserent terminology as well
as for the difserent ways of determining coals' rank we refer to Lin [5].) I<alliat, Kwak and Schmidt [6] measured the SAXS intensities of a rather large number of natural coals in the attempt of correlating the rank of a coal to the shape of the corresponding scattered intensity
as well as to the relative fractions of micro, meso and macropores, present in the coal [7].
They concluded that the typical behaviours of the pii~-hole intensities (obtained by desmearing
the ones collected with a slit collimation) are those relevant to the fo~r curves shown in their
Figure 2. In particular, curve I is characterized by a rather neat po~ver-law behaviour ii-e- I(h) c~ h~~Ph in the inner h-region [8]. Curve 2 shows a broad shoulder in the h-region where
curve 1 is power behaved. Curve 3 is characterized by a power behaviour in the inner h-region
and by a bump in the outer h-region. Finally, curve 4 differs from curves 1 and 3 in the outer
h-region because there it is higher and nearly constant or smoothly decreasing. Concerning
the coal rank it was found that: curve is typical of lignite and of some sub-bituminous and
high-volatile bituminous coal; curve 2 of sub-bituminous, high-volatile and medium-volatile
(*) Author for correspondence (e-mail: ciccariello@padova.infn.it)
© Les #ditions de Physique 1996
1480 JOURNAL DE PHYSIQUE III N°11
bituminous coals; curve 3 of some medium and low-volatile bituminous coals and, finally, curve
4 of semi-anthracite and anthracite.
According to this correspondence, one would conclude that different coals with the same rank can have differently shaped SAXS intensities and, vice versa, that each of the previous fo~r intensity-shapes does not uniquely determine the rank of the coal. The first part of this
statement is evident. In fact the rank of a coal, being determined by the relative fractions
of Carbon, Hydrogen and Oxygen present in the sample, is mainly related to the average of the electron-density function of the coal, while the scattered intensity, being the Fourier transform of the electron-density autoconvolution, depends on the electron-density function.
Since different electron-density functions can have the same average value, it is evident that coals with the same rank can have difserently shaped intensities. Nonetheless, it is sensible that the rank of a coal may be determined from the scattered intensity. With some optimism, in fact, the scattered intensity determines the sample's electron-density function which, after
being averaged, will determine the coal's rank. (In passing, it is noted that the knowledge of the electron-density function yields that of the micro, meso and macropores. See Fig. 2 of Ref.
[9].) This conclusion clearly disagrees with the second part of the previous statement. But it is fairly evident that the inconsistency stems from the fact that only fo~r intensity shapes have
been considered. On the contrary, accounting for more distinctive characters of the observed intensities, it appears reasonable that the coal rank can be determined by some features of the
resulting shapes.
The aim of this note is to point out a possible way for determining coals' rank from the behaviour of the corresponding small-angle X-ray intensities, collected with the most convenient
(and most common) geometry, namely the ii~jii~ite-slit one.
Figure 1 shows the SAXS intensities relevant to a set of15 coals. The intensities have been measured, with the 'infinite-slit' geometry, by a Kratky camera equipped with a step
scanner detector. CuKoNi-filtered radiation has been used. The further operative conditions
are those specified in an earlier paper by Benedetti, Ciccariello and Fagherazzi [10]. The coal samples have been heated at 100 °C for 2 h and the measurements have been done under
a mild vacuum. The sample holders, with Mylar windows, were 1 mm thick. The shown
intensities have been corrected for background and absorption and are reported in counts s~~.
In order to avoid the figure's overcrowding, each intensity has been multiplied by 10° with
a = 0,1,1.5, 2.3, 2.9, 3.7, 4.3, 4.8, 5.3, 5.8 and so on, starting from the bottom.
The shown intensities refer to coals whose rank increases from the bottom towards the top.
The coal samples considered are:
a) humus of the holocene (from the Rhine region near Bonn, Germany),
b) peat of the upper pleistocene (from Steinhuder Meer, Lower Saxony, Germany),
c) sub-bituminous of the lower miocene (from Knapsack near Cologne, Germany), d) sub-bituminous B (from Sulcis, Sardinia, Italy),
e) sub-bituminous A (from the french seam of Gardanne),
f) high-volatile bituminous A of the upper carboniferous (from Ewald, Ruhr, Germany), g) high-volatile bituminous A (from the seam of Vouters, France),
h) high-volatile bituminous A (from the french seam of Gironville at a depth of 2500 m), I) high-volatile bituminous A (from the french seam of MAricourt),
j) low-volatile bituminous (from the french seam of Escarpelle),
k) semi-anthracite (from the french seam of Gironville at the depth of 4400 m), I) semi-anthracite (UA2, from Spain),
m) semi-anthracite (from the belgian seam of Bligny, near LiAge),
n) anthracite (from the french seam of Gironville at the depth of 5000 m) and
o) anthracite (from the french seam of La Mire) ill].
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1482 JOURNAL DE PHYSIQUE III N°11
Quite interestingly, most of the features, pointed out by Kalliat, Kwak and Schmidt [6]
(IIKS) for the pin-hole intensities that they reported, are to a large extent observable in the slit-intensities shown in Figure 1, despite the different collimation of the latter. In particular,
curves a, b, c and d correspond to curve of KKS, curve e corresponds to curve 2 of IIKS
and curves n and o correspond to curve 4 of KKS. Curves I and m, presenting a vestige of a
bump in the region h m 0.25 I ~, might correspond to shape 3 of KKS. But, the KITS shape
to be assigned to each of the remaining intensities is by no way evident, if the coal rank is not known.
Figure 1, howei~er, makes it clear that, as the coal rank increases,
I) the elbow, present in each intensity, generally shifts towards smaller h values, (this fact is made evident by the broken line roughly locating the elbow positions), and
it) the outer part of the SAXS intensity is at first concave toward the top (see curves a. b
and c), then its outermost part tends to flatten id, e and f) and to develop a concavity to~vards the bottom, while the resulting ki~ee moves towards smaller h's (g-o).
On the basis of these two features, the correspondence between the slit-intensity shape and the coal rank becomes practically unique. It is stressed that both feature I) and feature it)
must be taken into account in order to determine the rank of a coal. Indeed, the position of the only elbol~> is not sufficient, as it happens for coals b and g. For these coals the elbol~<s'
positions appear to be smaller than those of c and h. On the basis of I) it would be concluded that the ranks of b and g are greater than those of c and h. In reality, the contrary holds true.
In order to avoid this contradiction, feature it) has to be taken into account. From the figure
it appears evident that intensities b and g respectively increase more quickly than c and h in
the outer h-region. As a thumb rule, in such cases the coal rank must be taken smaller than
the value suggested by the elbow position. In conclusion, the suggested qualitative recipe for
determining the rank of a coal from the corresponding X-ray slit intensity is as follows: first the elbow position of the observed slit intensity is compared with those of Figure 1. In this way t~vo intensities are singled out, namely, those having their elbow positions immediately
on the left and on the right of the observed one. Denote the two intensities by A and B, and let C denote the next intensity at the bottom of B in the figure. The coal's sought for rank
generally is in between that of B and that of A. However, it is equal to that of C when the outer part of the considered intensity increases more quickly than that of B.
According to this empirical suggestion, the coal rank is determined by the shape of the slit- intensity in the tail region 0.05 < h < 0.4 I T~vo remarks
appear not useless now. First, the recipe just suggested can easily be used, because slit-intensities are very easily, quickly and accurately measurable, particularly in the tail region (with a step-scanner detector). Second, it is natural to ~v.onder whether a similar correlation exists between the rank and the pin-hole intensity shapes. In our opinion, this should happen. But in order to find it it is necessarj~ to
accurately measure the intensities with the pin-hole collimation and not simply to use those obtained by desmearing the slit-ones, owing to the fact that the desmearing usually yields large
errors in the tail region, particularly when no Porod behaviour is observed (or, in other words,
when no model-independent information on the intensity behaviour at large h's is available)
as it happens in the case of coals. However, the recipe we have suggested above suffers the limitation of having a qualitative nature only. Before attempting a quantitative formulation,
we would like to stress two experimental results supporting, in our opinion, the point of view that the information on the coal rank is really related to the changes in the intensity shapes
described at items I) and 11).
It is known that [12] coals consist of different macerals which are grouped into three main classes: the vitrinite, the inertinite and the exinite. The first two macerals are much richer in aromatic carbons than the last one containing, on the contrary, more aliphatic carbon.
Furthermore, the higher the coal rank the higher is its vitrinite content. The SAXS pin-hole
intensities of the former three macerals were measured by Lin and Guet [13j and are shown in Figure 10 of their paper. From this figure it appears evident that the elbow position of
the vitrinite is smaller than the exinite's one which, in turns, is smaller than that of the inertinite. We found that the same behaviour takes place for the slit intensities obtained by convoluting the former pin-hole intensities with an infinite slit. We also tried to reproduce
the intensity of a natural coal by taking the most suitable linear combination (with positive coefficients) of the three maceral intensities with no success. This means that interference
efsects related to the actual geometrical configurations of the macerals inside the coals are not
negligible. Nonetheless, it is reasonable to expect that, as the coal rank increases, the coal intensity approaches to that of the vitrinite, since this maceral becomes the dominant one.
This fact supports our claim that the smaller the elbow position the higher the coal rank.
The second experimental result supporting our claim is the SAXS behaviour of a natural coal which has undergone an extraction process by a fluid. These interesting experiments have
recently been performed by Nemmers, Horne and Bale [14]. Their Figure 1 reports the pii~- hole SAXS intensities of a sub-bituminous coal before and after the extraction process. The
figure shows that, after extracting some of the coal material, the intensity increases in the region h m 0.1 i~~ It is reasonable that the extraction
process takes away mainly the most volatile components of the coal, I.e. those corresponding to the exinite, so that the extraction
process amounts to increase the coal rank. Quite interestingly, the changes in the intensity shapes observable in Nemmers et al.'s figures are similar to those described above at items I) and it). In fact, as the extraction process goes on, the elbow moves at smaller h-values and
simultaneously "plateaux" similar to those of intensities h-o of Figure I are formed (see Figs.
1, 2 and 4 of Ref. [14]).
Finally, a possible way for making the aforesaid qualitative recipe quantitative is now re-
ported. Curves h-o suggest that the coal rank could be related to the positions of the curves' flex points. These are determined as the solutions of
Since curves a-e show no bending towards the bottom, it is assumed that this bending takes place in the unexplored region of the larger h's. An accurate parameterization of each observed
intensity becomes unavoidable in order to extrapolate the intensity in the unexplored momen-
tum transfer range as well as to obtain an expression of the second derivative, present on the left side of ii), sufficiently smooth to make the search ofthe roots of equation (1) reliable. The
shapes of curves h-o suggest the parameterization
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= Pmlf) + ~ zmf~, 12)
with ( e log(h/ho) and ho> go> xi,z2,
..,
zM unknown parameters to be determined by best-
fitting the intensities to (2). Equation (I) amounts to require
Pf~if)
= 0, (3)
1484 JOURNAL DE PHYSIQUE III N°11
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Fig. 2. The continuous and the broken lines represent the intensities obtained by best-fitting the
experimental ones (given by the symbols) to equation (2) with M
= 5
where superscript 2 denotes the second derivative. Since equation (2) can be written as
h xl+x2~+...+X3f~~' ~
~~~~ ~ £~ , ~~~
with C e 10~°
= J(ho), it results J(h) m C())~i in the region h m ho- Thus, by setting ho = 0.01 i~~, it
may be expected xi * -lfsi, because an approximate power-law behaviour is always observed in the region ho * 0.01 i~~ (It is reminded that the ~sj-values
are related to the ~ph's, I-e- those obtained from the pin-hole intensities, by ~sj = ~ph -1.) [15]. In this way, the parameters to be determined by best-fitting the observed intensities to (2) are
xi, ..,xM. But for coal e, the best-fits turned out to be satisfactory with M = 3. For curve e,
Table I. The lst col~mi~ lists the coal samples. The 2i~d col~mi~ reports the ezpoi~ei~t xi of
the power-law behavio~r obeyedby the correspoi~dii~g slit-ii~tei~sities ii~ the regioi~ h m 0.01 Ji~~
The third col~mi~ glues the relevant average flex positioi~s (in /~~) which appear to decrease
monotono~sly as the coal rank increases. Both xi and (hfix) have been obtained by best-fitting eq~ation (2), with M
= 5, to the observed intensities
Sample xi
o) -2.9 0.076
n) -3.1 0.092
m) -3.0 0.093
1) -3.0 0.102
k) -2.9 0.103
j) -2.7 0.104
I) -2.7 0.110
h) -2.9 0.122
g) -2.9 0.133
f) -2.5 0.144
e) -2.1 0.192
d) -2A 0.302
c) -3.0 0.336
b -3.1 0.348
-2.9 0.499
the small shoulder in the region h m 0.04 i~~ required five parameters, I.e. M
= 5. Then, for
homogeneity, all the coal fits were performed with M
= 5. Figure 2 shows the final agreement achieved in the most typical cases. (In particular, the top curve is the one relevant to the worst
fit.) The results for xi and (hflx) are reported in Table I. When more than one flex has been
found, (hflx) has been taken equal to the arithmetic mean of the two flex lying in the region
h > 0.04 I ~~ The numerical uncertainty on the xi-values is roughly 10%, that of (hflx)
is 15% for samples I-o, 30% for a-d, f, g and 50% for e. These uncertainties were estimated
by comparing the xi and (hflx) values relevant to the fit with M
= 3 and M
= 5. On the
one hand, the xi-values (decreased by I, owing to the difserent collimation geometry) compare favorably with those obtained by Auvray, Cotton and Papoular [16], except for coals g and j.
On the other hand, (hflx) decreases monotoi~ically as the coal rank increases and thus (hflx)
can be considered as a measure of the coal rank.
Acknowledgments
We are pleased to thank once more Dr.s L. Auvray, J-P- Cotton and R. Papoular for having kindly provided us both with their samples and with some of their neutron scattering intensities.
We are also grateful to Professor H. Brufliberger and Dr. P. Vyskocil for having kindly measured the SAXS intensities of samples e, and o with the pin-hole camera at the ETH in Zurich,
and to Dr. V. Di Noto for some analyses on the coals' composition. Finally, we thank Mr. L.
Bertoldo for experimental help.
Financial supports from "Fondi 40% and 60% MURST" are acknowledged.
