European Journal of Mineralogy
 © 2014 E. Schweizerbart'sche Verlagsbuchhandlung Science Publishers
Abstract
The complete knowledge of the porous structure of rocks is necessarily requested for the prediction of the damages induced by salt crystallization. Nevertheless, the geometric description of the porous structure is usually very difficult because of the variability of the size distribution of voids, ranging from nanometers to millimeters, which generally is not accessible by a single methodology. For this reason, a multitechnique approach was used here: the investigation at submicrometric dimensional scale (> 0.004 μm) was carried out by Hg intrusion porosimetry (MIP), whereas the study at the nanoscale required Small Angle Neutron Scattering (SANS) analysis. All the results were interpreted in the framework of a fractal model. The analyses were performed on limestones of different geological formations, cropping out in southeastern Sicily and largely used as building stones in Baroque monuments of the Noto Valley (belonging to the UNESCO Heritage List).
 small angle neutron scattering
 mercury intrusion porosimetry
 petrography
 calcarenites
 fractal dimension
 rock physics
1. Introduction
The study of the degradation attitude of building stones needs the complete knowledge of their composition, structure and texture (Coppola et al., 2002). This kind of research may be preliminary addressed with traditional petrographic techniques such as optical and electronic microscopy and Xray diffraction. Particularly important is the determination of the porosity, in most cases investigated by means of microscopic observations combined with image analysis and porosimetric techniques based on gas adsorption and mercury intrusion. Nevertheless, these methods appear inadequate for the complete modelling of the microstructure of the rock, since they are destructive, measure only the open porosity and explore a limited dimensional range. As a matter of fact, a quantitative description of rock microarchitecture is generally very difficult, given the variability in the dimensional distribution of the voids, ranging over length scales spanning four to five orders of magnitude, i.e. from nanometres to centimetres. In this sense, good results can be in principle achieved by using a multitechnique approach: traditional techniques like mercury intrusion porosimetry are suitable for the investigation of length scales from few nm (about 7 nm) up to ~ 50 μm (Van der Geer et al., 2010), whilst nanometric components need more penetrating techniques such as Small Angle or Ultra Small Angle Neutron Scattering (SANS and USANS, respectively; Antxustegi et al., 1998; Radlinski et al., 2004). This approach has been recently applied to the study of archaeological potteries, furnishing useful results for the determination of production techniques (Barone et al., 2009, 2011).
Based on the aforementioned considerations, this multitechnique investigation is used here for the structural analysis of various typologies of Oligocene to Miocene limestones cropping out in different segments of the Hyblean Plateau, selected among the most largely used in the Baroque buildings of the historical centre of Noto Valley belonging to the UNESCO Heritage List (Anania et al., 2012).
2. Geological setting
The Hyblean Plateau (Fig. 1) represents the foreland of the Apenninic–Maghrebian thrust belt (Ogniben, 1960). The stratigraphic succession is characterised by Mesozoic to Cenozoic carbonatic sequence and by Neogene to Quaternary clastic levels, with volcanic layers interbedded from Trias to PliocenePleistocene (e.g., Grasso & Lentini, 1982; Pedley & Grasso, 1992; Torelli et al., 1998; Guerrera et al., 2012; Barbera et al., 2014). The Cretaceous – Miocene limestones show a deep basin facies in the western sector of the Hyblean Plateau but shallowwater carbonatic sequences in the eastern sector (e.g., Carbone et al., 1982; Grasso et al., 1982). The western sector is characterised by wellexposed late OligoceneMiocene limestone and marly limestone locally impregnated by bitumen which results in a dark colour (i.e., “Ragusa Formation”). The sedimentation continued with the Tortonian marly clay of the “Tellaro Formation” and the heteropical calcarenites of the “Palazzolo Formation”. The latter formation shows two different lithofacies (Carbone et al., 1987; Romeo et al., 1987) consisting of: 1) finegrained grey limestones and soft marly limestones alternating in layers of 20–40 cm; 2) yellowishwhite limestones outcropping in large bank levels.
The eastern Cenozoic succession begins with the “Monti Climiti Formation” (Burdigalian  Serravallian), which is made by limestone with bioturbation (Melilli Member) and, in its upper part, of algae limestone (Syracuse Member). Tortonian is represented by the reefal limestones with pyroclastic intercalations (i.e., “Carlentini Formation”) followed by Late Tortonian lagoonal limestones (i.e., “Monte Carrubba Formation”).
Pliocene and Quaternary basinal clays and nearshore carbonates as the Panchina Formation outcrop along the margins of the Hyblean Plateau due to its postMiocene uplift and emersion. Coeval volcanic rocks are wellexposed and consist of deposits emplaced both under water and subaerially.
3. Materials and methods
The stone analysed in this experimental study are from some quarries of the Hyblean region, Sicily. Four different samples from lithologically well defined formations have been selected from the Hyblean sedimentary succession. In detail they are:

Ragusa Formation – Burdigalian, this formation is caved in different areas where the stones have specific features: a) Comiso Limestone (labelled as PC) – well lithified whitecream fine grained limestone; b) Modica Limestone (labelled as CTM)  soft, middlefine grained, whitegreyish (fresh cut)/yellowish (outcrop) limestone; c) Ragusa Limestone (labelled as CTR) – middlefine grained, whitegreyish (fresh cut)/whiteyellowish (outcrop) limestone; sometimes this stone is impregnated by bitumen that gives a dark colour, in this case it is locally named Pece Limestone (labelled as PP); d) Scicli Limestone (labelled as CTS) – soft whitegreyish (fresh cut)/pale redyellowish (outcrop) limestone;

Palazzolo Formation – Lower Oligocene – Pliocene, with two varieties: a) Noto yellowish Limestone (labelled as PNG) – soft, fine grained, whiteyellowish (fresh cut)/yellow (outcrop) limestone; b) Noto whitecream Limestone (labelled as PNB) – very soft, fine grained, whitegreyish (fresh cut)/whitecream (outcrop) limestone;

Monti Climiti Formation – Melilli member OligoceneLower Miocene: Melilli white Limestone (labelled as PBM) – fine grained, whiteyellowish limestone;

Pleistocenic Panchina Formation: Giuggiulena Limestone (labelled as GIU): yellowishred calcirudite.
3.1. Smallangle neutron scattering
Although a full discussion of the theory of smallangle neutron scattering is outside the scope of this paper, some basic background is here reported.
In a smallangle neutron scattering experiment (Higgins & Benoit, 1994), the relationship I(Q) of measured scattered intensity, which has dimensions of (length)^{−1} and is normally expressed in units of cm^{−1}, vs. exchanged momentum , where λ is the incident neutron wavelength and θ the scattering angle, is usually expressed as (Teixeira, 1988):
(1)where N_{p} is the number concentration of scattering bodies (given the subscript “p” for “particles”), V_{p} is the volume of one scattering body, (ρ_{p} − ρ_{0}) is the difference in neutron scattering length density (what is more commonly called the contrast K for convenience), P(Q) is a function known as the form or shape factor, S(Q) is the interparticle structure factor, and finally B_{inc} is the (isotropic) incoherent background signal.
The form factor is a function that describes how I(Q) is modulated by interference effects between radiation scattered by different parts of the same scattering body. Consequently it is very dependent on the shape of the scattering body. The general form of P(Q) is given by Van de Hulst’s equation:
(2)where α is a “shape parameter” that might represent a length or a radius of gyration, for example.
The interparticle structure factor S(Q), given by,
(3)is a function that describes how I(Q) is modulated by interference effects between radiation scattered by different scattering bodies. Consequently it is dependent on the degree of local order in the sample, such as might arise in an interacting system, as example.
In petrography, smallangle neutron scattering has been used to demonstrate the fractal character of rocks and determine their fractal dimension (Lucido et al., 1988). Fractals are characterised by selfsimilarity within some spatial range, i.e., the structure is independent on the length scale of observation in that range.
For surface fractals of surface fractal dimension D_{s} (2 ≤ D_{s} ≤ 3), the scattering law becomes:
(4)Real fractal objects scatter according to Eq. (4) only within a limited Q range, i.e. ξ^{−1} < Q < r_{0} ^{−1}, where r_{0} is the size of single particles in an aggregation process, and ξ the size of the aggregates.
We used the smallangle neutron scattering instrument PAXE at the ORPHEE reactor of the Laboratoire Léon Brillouin (LLB, Saclay, France) (http://wwwllb.cea.fr/spectros/spectro/g54.html). The spectra have been collected using two different configurations: large Q with λ = 6 Å, sampledetector distance = 2 m, collimation = 2 m, and Qrange extending from 5 · 10^{−3} to 2 · 10^{−1} Å^{−1}; and small Q with λ = 15 Å, sampledetector distance = 4.5 m, collimation = 4.5 m, and Qrange extending from 3 · 10^{−3} to 3 · 10^{−2} Å^{−1}. Samples studied were thin sections (thickness < 1 mm), and therefore problems arising from multiple scattering effects are minimised. No appreciable neutron activation of the samples was found after the experiment. By the standard LLB smallangle neutron scattering routines, the twodimensional intensity distributions were corrected for the background and normalized to absolute intensity by measuring the incident beam intensity, the transmission and the thickness of each sample. By integrating the normalized twodimensional intensity distribution with respect to the azimuthal angle, we obtained onedimensional scattering intensity distributions I(Q) expressed as the unit differential crosssection per unit volume of the sample (cm^{−1}).
3.2. Mercury intrusion porosimetry
Porosimetric analysis was carried out with a Thermoquest Pascal 240 macropore unit in order to explore a porosity range ~ 0.0074 μm < r < ~ 15 μm (r being the radius of the pores), and by a Thermoquest Pascal 140 porosimeter instrument in order to investigate a porosity range from ~ 3.8 μm< r < ~ 116 μm.
4. Results
4.1. Optical microscopy
The detailed petrographic description of the limestones samples (studied using a polarizedlight microscope Nikon Eclipse E400POL) are reported in Table 1 and in Fig. 2.
Ragusa Formation: a) The Comiso Limestone –Leonardo Member – presents grain–supported texture with microsparitic and sparitic cement; allochems are mainly formed by Foraminifer debris and subordinately foraminifera, pellets and echinoderms fragments. The porosity is mainly intergranular and intercrystalline and subordinately due to secondary dissolution. According to Dunham (1962) and Folk (1959) it is classified as grainstone or biosparite, respectively (Fig. 2a). b) Modica and Ragusa limestone members also in the Pece variety and Scicli limestones – Irminio Member – are on the whole similar but with small differences in the orthochem abundance. They are classified as packstone or biomicrite and characterised by micrite and grainsupported texture; allochems are formed by fragments of echinoderms, coralline algae, bryozoa and bivalves, other than by foraminifer debris (Fig. 2b, c and d respectively). The intergranular and fossils intragranular porosity is higher than the Comiso limestone. In the case of “Pece Limestone” the porosity is occluded by bitumen (Fig. 2e).
Palazzolo Formation: the Noto limestones are classified as biomicrite or wackestone. The texture is mudsupported with micrite as the exclusive orthochem and foraminifer debris and foraminifera as allochems. The micrite intergranular porosity is high. The petrographic features of the white (PNB; Fig. 2f) and yellowish (PNG; Fig. 2g) variety are very similar. Anania et al. (2012) showed that the main difference is due to the more abundant insoluble clay fraction residue (illite, kaolinite and smectite) in the yellowish variety.
Monti Climiti Formation: the Melilli white limestone (PBM) is classified as biomicrite or wackestone (Fig. 2h). The texture is mudsupported with micrite and allochems formed by foraminifer debris and, in minor amount, fragment of echinoderms, coralline algae and bryozoas. The porosity is mainly intergranular.
Panchina Formation: the Giuggiulena Limestone (GIU) is a biosparite or grainstone formed by abundant coralline algae with sparitic cement (grainsupported texture). The intergranular pore of millimetric dimension are abundant (Fig. 2i).
4.2. Mercury intrusion porosimetry
Mercury intrusion porosimetry analysis was carried out on all samples with the exception of the Pece Limestone because, in this case, the presence of bitumen did not permit the complete Hg intrusion and then the correct measurement of the pores structure. With the aim to have a representative picture of the studied rocks porosity, three samples were analysed for each stone typology.
The cumulative volume vs. pore radius plots and relative histograms revealed a polymodal distribution for GIU, PC, CTS and PBM whereas the CTM, CTR, PNB and PNG samples present a unimodal distribution. The cases of PC, PNG, PNB and GIU specimens are shown in Fig. 3, as example, whereas Table 2 reports the average and standarddeviation values of the most important parameters for the description of the porosity for all the investigated samples. The average radius ranges from 0.2 μm to 53.9 μm (Table 2). The lowest value is measured in the fine grained and well cemented PC while the coarsergrained GIU sample presents the largest pore radius. In the same way, the highest value of the total open porosity is measured in the finegrained and uncemented PNG and the lowest is determined in the PC sample, excluding the Giuggiulena Limestone which, even if very porous, presents abundant millimetric pore not revealed in the measure range of the Hg intrusion porosimeter.
Finally, information on the porous structure of the samples can be achieved by analyzing the Hg intrusionextrusion curves. On one side, PC, PNG and PNB (Fig. 4a–c respectively) display subparallel xaxis trend of extrusion curve, because of a not so highly interconnected and tortuous pore structure that allows mercury to be entrapped inside the samples. On the other side, as far as CTR, CTM, CTS, PBM and GIU (the latter reported as example in Fig. 4d) samples are concerned, the subparallel trend in intrusion and extrusion curves demonstrates a more efficiently interconnected and untortuous porous structure.
Taking into account the fractal character of the porous structure of the rocks (Pérez Bernal & Bello, 2001), whose fractal dimension can be considered a characteristic feature of a specific lithotype, in the same way as the frequency distribution of the radius of the pores, we tried to extract the fractal dimensions of the porous surfaces starting from the porosimetric data – with particular reference to the surface fractal model by Friesen & Mikula (1987). According to it, the cumulative intrusion volume derivative with respect to pressure and the surface fractal dimension D_{s} are linked by the relation:
(5)where V_{p} is the cumulative intrusion volume at a given pressure p. By applying the Washburn equation, a similar relation is obtained in terms of the pore diameter:
(6)In this model, the initiator is a unit cube, each face is subdivided into m^{2} small squares, n subsquares are removed with the condition that they do not have common side or square edge. At each square removed, a cube is inserted with its top face missing (Fig. 5). The process is repeated in each cube face and an infinite number of times. In the framework of this model, the dimension D_{s} can be obtained from the slope of the linear fit of the vs. p loglog plot [m^{3}/MPa] vs. [MPa].
An inspection of vs. p loglog plot (Fig. 6) allowed us to distinguish among two characteristic trends: i) for the samples PC, CTS, PBM and GIU three straight lines with different slopes can be recognized, whereas ii) the samples CTR, CTM, PNG and PNB exhibit only two straight lines. The fractal dimensions calculated from each slope (referred to in Table 3 as m_{1}, m_{2}, m_{3}) by means of the Eq. (5) are labelled in Table 3 as D_{s}_{1}, D_{s}_{2}, D_{s}_{3}, respectively. In all samples the D_{s}_{2}, values range between 2 and 3 showing a fractal surface geometry, while D_{s}_{1}, and D_{3}_{s}, values depart from the typical fractal dimension.
Similar trends were reported by Friesen & Mikula (1987) for porosimetric data obtained on coal particles. The deviations from fractal behaviour at low pressures were there explained as due to intergranular porosity while the highpressure features may be ascribed to compressibility effects (Friesen & Mikula 1988).
In our limestones, the low pressure deviation from fractal geometry (as indicated by the behaviour of D_{s}_{1}) is observable in the samples (PC, CTS, PBM and GIU) characterised by polymodal distribution and a relative maximum with radius bigger than the main porosity. This behaviour is particularly evident in the GIU limestone in which the large pores are predominant. In the PC samples, the observed D_{s}_{1} value is interpretable as due to diagenetic dissolution pores. On the contrary, the samples with unimodal porosimetric distribution (such as for example CTM, CTR, PNB and PNG) do not present or have a little lowpressure deviation.
The highpressure deviation from fractal geometry is observed in all the samples, supporting the hypothesis of compressibility effects. However, the presence of clay minerals may influence this behaviour as suggested by the strong positive slope of the highpressure straight line observed in the Noto yellowish limestone (PNG) characterised by abundant insoluble residue (Anania et al., 2012).
4.3. Smallangle neutron scattering measurements
The loglog plot of the scattered intensity I(Q) is shown for GIU (Fig. 7a) and PNG (Fig. 7b) specimens, as example. Making reference to an empirical approach (Beaucage, 1995), already successfully applied for a variety of similar systems (Botti et al., 2006; Barone et al., 2009, 2011), the fitting law for I(Q) has been described as the sum of two independent contributions coming from mesoscopic units with different dimensions and geometries. On one side, “small” units, i.e. minerals crystallites or aggregates, accessible in the investigated Qrange, will contribute to the scattering by means of a Guinier law (Guinier et al., 1955): . The Guinier law, for isolated particles, in the range where QR <<1, if R is the particle radius, relates the intensity scattered in the near vicinity of the mean beam to the radius of gyration of the particle R_{g}. On the other side, “big” units, i.e. voids/mineral aggregates, having sizes out from the experimental range and, hence, only surface accessible, will scatter according to a power law.
In this way, the I(Q) function can be expressed as:
(7)In the above expression, the factors C_{1}and C_{2} are free parameters containing the relative intensity of the Guinier’s and power law. The radius of gyration R_{g} and the exponent α = 6 − D_{s} are also free parameters, and account for the mean size of newly formed mineral crystallites and the roughness of the voids/mineral aggregates, respectively. According to the fractal model, 2 < D_{s} < 3, so implying 3 < α <4. The twodimensional Euclidean exponent D_{s} = 2 (and hence α = 4) is restored for particles with sharp interfaces.
The values of α, D_{s} and R_{g} for all the investigated samples are reported in Table 4.
The values obtained for the fractal exponent α turned out in all cases between 3 and 4, in agreement with the fractal surface model according to other literature observation on the fractal geometry of the sedimentary rocks porosity (Radlinski et al., 2004).
At large Q values the scattering from all samples, as expressed by C_{2}Q^{−}^{α}, has been compared with the Q^{−4} dependence of Porod’s law, I(Q) = 2πK^{2}SQ^{−4}, S being the total area of the interfaces per unit volume of sample. The contrast K has been preliminary evaluated from the quantitative chemical composition of the samples, as given by Xray fluorescence (XRF) measurements not reported here. We choose two values, Q_{1} = 0.04 Å^{−1} and Q_{2} = 0.18 Å^{−1}, within the fractal domain, so obtaining C_{2}Q_{1}^{−}^{α} = 2πK^{2}S_{Q}_{1}Q_{1}^{−4} and C_{2}Q_{2}^{−}^{α} = 2πK^{2}S_{Q}_{2}Q_{2}^{−4}. The C_{2}, K^{2}, S_{Q}_{1} and S_{Q}_{2} values are reported in Table 5, S_{Q}_{1} and S_{Q}_{2} are two evaluations of the same interface area measured with 1/Q_{1} and 1/Q_{2} gauges.
Starting from the S_{Q}_{1} values, we also made a rough estimation of the average radius r of the objects constituting the population of “big” mesoscopic units (voids/minerals aggregates). Assuming each sample formed by n spherical grains of total volume V_{t} and total surface area S_{t}, indicating with ρ_{app} (apparent density) and ρ_{bulk} (bulk density) the density, respectively, of the calcarenites and of the corresponding bulk materials, then:
(8)The so obtained r data are reported in Table 5. In the case of PP specimen, r has not been evaluated, ρ_{app} and ρ_{bulk} being unknown.
5. Discussion
Of particular interest in our analytical approach is the comparison between the pore structure as obtained by Hg intrusion porosimetry and smallangle neutron scattering analyses.
The average pore radii as obtained by Hg intrusion porosimetry in the studied limestones turned out to be systematically of one or two orders of magnitude larger than those extracted by neutron scattering. On the contrary, the S_{Q}_{1} values of the interfaces area per unit volume resulting from neutron scattering (Table 5) are comparable with the S_{Hg} average total surface area of the pores per unit volume obtained by Hg intrusion porosimetry (Table 2). The reason of these contrasting results regarding the pore radius and the total surface can be ascribed to the fact that S_{Q}_{1} was directly obtained from the spectra by a comparison with Porod’s law, whereas r was indirectly estimated by the aforementioned assumption summarized in Eq. 8. The reasons for the observed differences between smallangle neutron scattering and Hg intrusion porosimeter measurements can be found taking into account that closed pores can be accessed by smallangle neutron scattering and not by Hg intrusion porosimetry. The latter method probes pores with sizes ≥ 50 Å, whereas S_{Q}_{1} and, consequently, r were obtained starting from the fractal surface exponent α which was referred to the “big” units, whose size was out of the experimental window, i.e. ≥1/Q_{min} ~ 330 Å. Furthermore, we assumed spherical grains for the calculation of r from neutronscattering data, whereas Hg injection porosimetry probes cylindrical pores.
By applying the fractal geometry, it is possible to overcome part of this limitation in the comparison of the pore structure as obtained by the two methods. The fractaldimension D_{s}_{2} values obtained from the vs. p diagram resulting from Hg porosimetry are indicative of fractal geometry, and are comparable with the D_{s} exponent given by smallangle neutron scattering for most of the analysed samples (Fig. 8). This result, even if it needs further analyses, appear particularly interesting, since it permits to apply the fractal geometry concept, at least for the investigated limestones, to a wider range of pore sizes.
Regarding the significance of the fractal dimension in terms of petrographic features, the higher D values are observable in the Comiso Limestone. In this case the fractal dimension is probably due to the sparite and microsparite cement and to the allochems fine grain size. On the contrary, the Noto Limestones (PNG and PNB) and the Melilli Limestone (PBM), characterized by mudsupported texture and allochems fine granulometry, present lower D values.
The other studied limestones belonging to the Ragusa Formation (CTM, CTR and CTS) and to the Panchina Formation (GIU) have grainsupported texture characterised by coarser allochems and sparite (GIU) or micrite (CTM, CTR and CTS) orthochems. In these cases, the D values are variable but, except for the Scicli Limestone, intermediate between the first two cases.
6. Conclusions
In this work, it has been recognized that the porous structure of the studied limestones exhibits a fractal geometry and that the fractal dimension can be used as a descriptor of the pore surface.
The fractal dimension D_{s}_{2} has been calculated from Hg intrusion porosimetry data by using the Friesen & Mikula method, describing the porous structure at length scales extending from few nm up to ~ 50 μm. For the complete modelling of the microstructure of the rock, nanometric components have been investigated by smallangle neutron scattering, yielding a fractal dimension D_{s}. Worth of note is that the fractal dimension obtained with the two methods in different length scales are correlated and comparable.
Taking in account the petrographic features, this first approach to the problems seems to indicate the relationship between the fractal dimension and the structure and texture of the limestone, such as sparite and micrite matrix and abundance and dimension of allochems. However, this topic need further study based on a wider limestone selection.
The obtained results, according to the existing literature on fractal geometry of the porosity of sedimentary rocks, show the efficiency of this multitechnique approach for the complete description of the porous structure of calcarenites, opening a new overview on diagnostic parameters useful for the characterization of building stones.
Acknowledgements
The authors thank three anonymous official peer reviewers for their criticisms and suggestions which greatly improved the original manuscript.
 Received 23 April 2013.
 Modified version received 22 July 2013.
 Accepted 14 October 2013.