Accuracy in quantitative phase analysis of mixtures with large amorphous contents. The case of zircon-rich sanitary-ware glazes
The accuracy of quantitative phase analysis (QPA) of samples with dominant amorphous content, reproducing zircon-rich sanitary-ware glazes, has been investigated. X-ray powder diffraction (XRPD) methods were applied using both conventional Cu Kα radiation and high-resolution synchrotron data. In this work, a combination of the reference intensity ratio (RIR) and Rietveld methods was applied to an artificial mixture (90 wt% glass, 10 wt% zircon), taking into account some of the most common effects that may affect the accuracy in amorphous quantification, such as the degree of crystallinity of the phases, microabsorption and sample preparation. Certified NIST SRM 676a (α-Al2O3) [Cline, Von Dreele, Winburn, Stephens & Filliben (2011). Acta Cryst. A67, 357–367] was used to quantify the amorphous content in zircon and in the different internal standards commonly used when a certified standard is not available or not applicable: the results show that all of the phases invariably contain amorphous material in the range 2.0–15.0 wt%. If the amorphous content of the standard is taken into account, the accuracy of the QPA of the artificial mixture is improved. It was observed that the Brindley correction for microabsorption does not significantly improve the results. Care must be applied if grinding time is increased, since this may increase the amorphous content in the sample. Finally, the sensitivity of the RIR–Rietveld method to the addition of a small amount of zircon (∼1 wt%) has been considered, showing that accurate results can be achieved if great care is taken in the sample preparation and refinement strategy.
X-ray powder diffraction is one of the most powerful techniques for quantitative phase analysis (QPA) of polyphasic mixtures (Klug & Alexander, 1974; Zevin & Kimmel, 1995; Madsen & Scarlett, 2008). Different QPA methods are applied: from the classical reference intensity ratio (RIR) method (Chung, 1974a,b) to the Rietveld method (Rietveld, 1969; Hill & Howard, 1987; Bish & Howard, 1988; Bish & Post, 1993). With the Rietveld approach, it is possible to obtain the mass fraction (wi) of each crystalline component (i) in a mixture containing n phases following the equation
where Si is the refined scale factor, Zi is the number of formula units in the unit cell, Mi is the mass of the unit formula and Vi is the unit-cell volume. This method is based on the normalization constraint that the sum of all wi is equal to unity. Hence, the presence of an amorphous fraction cannot be directly evaluated. Even with high-quality data, great attention must be paid to (i) the Rietveld refinement strategy, (ii) microabsorption effects, (iii) the presence of amorphous matter and (iv) the sample preparation strategy.
(i) The guidelines to perform an accurate Rietveld refinement are reported by McCusker et al. (1999) and Hill (1992). A correct background modelling is crucial because its underestimation may result in a strong overestimation of amorphous fraction; as a matter of fact, QPA results can be strongly affected by improper atomic displacement parameters (Gualtieri, 2000) and also by preferred orientation effects (Madsen & Scarlett, 2008). Although some of these problems can be addressed with a careful analysis of the goodness of fit, it is still important to check the physical meaning of the refined parameters.
(ii) X-ray absorption contrast should be carefully taken into account as the accuracy of the QPA results is highly affected by this factor. A number of articles (Brindley, 1945; De Wolff, 1956; Suortti, 1972; Hermann & Ermrich, 1987; Taylor & Matulis, 1991) added pieces of information to the study of this effect. Brindley (1945) provided a correction that requires knowledge of the particle diameter Di and the linear absorption coefficient μi of each phase. This information can thus be used to calculate a correction factor for each phase to be applied to the calculated weight fraction. This method has been successfully adopted by different authors (e.g. De la Torre et al., 2001; Orlhac et al., 2001; Gualtieri et al., 2004; Leinekugel-le-Cocq-Errien et al., 2007; Suzuki-Muresan et al., 2010).
(iii) The presence of an amorphous phase in a mixture must be taken into account. Amorphous phases may be present as an impurity in a crystalline phase, as a surface layer (Cline et al., 2011) or as a result of amorphization during extensive grinding (Zevin & Kimmel, 1995). The application of the Rietveld method permits an estimate of the amorphous content to be obtained if a known amount of internal standard is added to the investigated mixture. The amorphous fraction wA can be calculated according to the following equation:
where WS is the weighed fraction of the internal standard, WM represents the rest of the mixture (i.e. WM = 1 − WS) and w′S is the calculated weight fraction of the internal standard.
(iv) The importance of sample preparation is often undervalued by the operator, although a number of factors may strongly affect the QPA results in terms of both reproducibility and accuracy. A coarse particle size distribution may lead to poor particle statistics. This problem can be partially solved by grinding, but care must be taken in determining an appropriate procedure as too extensive grinding may produce microstrain and possibly amorphization (Zevin & Kimmel, 1995). In this regard, the hardness contrast between the crystalline phases of the mixture and between the mixture itself and the grinding medium should be considered.
Sanitary-ware glazes are obtained after firing of various raw materials (e.g. quartz, feldspar, clays, calcite) together with an opacifier phase that must be added to confer aesthetic properties to the final glazes (Hupa et al., 2005; Casasola et al., 2011). The material obtained consists of an abundant glassy matrix (more than 80 wt%) and at least one crystalline opacifier phase, typically zircon (Rasteiro et al., 2007; Bernasconi et al., 2012). Knowledge of the actual phase composition is important to better understand the technological properties of the glazes, such as rheological behaviour, thermal expansion and optical reflectometry. Although problematic, crystalline phase quantification is now performed with a preliminary calibration based on a single-peak approach (Castilone et al., 1999) or by the application of the RIR–Rietveld method (Schabbach et al., 2007).
The present work is aimed at defining a sample preparation procedure that provides the most accurate QPA results for sanitary-ware glazes using X-ray powder diffraction (XRPD) methods as well as scanning electron microscopy (SEM) and laser scattering.
To quantify the amorphous fraction in a mixture, the use of a fully crystalline internal standard, or an internal standard with a certified amorphous content wOS, is mandatory. In the latter case (most common), equation (2) should be modified by introducing the amorphous fraction in the internal standard, wOS:
If the amorphous fraction in the internal standard is unknown, it should be determined by adding a standard with certified amorphous content and applying equation (3). At the moment, NIST SRM 676a (α-Al2O3) is the most commonly used internal standard because its amorphous content has been accurately quantified to be 0.98 wt% (Cline et al., 2011). However, the use of this standard is not possible when α-Al2O3 is already present in the mixture or when the overall absorption coefficient of the mixture is too different from that of α-Al2O3.
The problem of relative diffraction intensity within mixtures containing phases with different linear absorption coefficients can be circumvented by the application of the Brindley (1945) microabsorption correction. To a first approximation, the Brindley model is valid for the ith phase when μiDi ranges between 0.01 and 0.1 (medium-sized powder range) and if spherical particles are assumed. If μD is lower than 0.01, microabsorption effects are considered to be negligible. If μD is higher than 0.1, the ith phase can be considered as a coarse powder and the model is highly approximate. For example, in a 1:1 binary mixture of corundum (α-Al2O3, μ = 125.4 cm−1) and zircon (ZrSiO4, μ = 379.7 cm−1), zircon, which absorbs more strongly than corundum, will be underestimated if no microabsorption correction is applied. The application of the Brindley correction will be possible (i.e. if μiDi < 0.1) if the zircon mean particle size is up to about 2.5 µm and if the mean corundum particle size is up to about 8 µm.
The RIR–Rietveld method (Gualtieri, 2000; Barbieri et al., 2005), the traditional RIR internal standard method (Chung, 1974a,b) and the Fullpat method (Chipera & Bish, 2002) have been used to perform QPA of an artificial mixture of known composition (90 wt% of glass and 10 wt% of industrial grade zircon). From now on this mixture will be labelled as the `synthetic' mixture.
As mentioned above, NIST SRM 676a (α-Al2O3) is the only standard with a certified amorphous content but it is not recommended to be used when (i) corundum is already present in the investigated sample or (ii) the mixture contains phases with high X-ray linear absorption coefficient. Here, the quantification of amorphous content of a set of different internal standard (see Table 1) was performed. Afterwards, these internal standards were added to the synthetic mixture to investigate their accuracy in the QPA figures. All of the internal standards were used for the application of the RIR–Rietveld and RIR methods, whereas only α-Al2O3 was used for the Fullpat approach.
The effect of grinding was also investigated by comparing the results obtained with zirconia and agate mortars, and by comparing the results obtained after 2, 12 and 22 min of manual grinding.
Finally, laser scattering and SEM measurements were performed as complementary techniques to obtain more information on the particle size distribution (from laser scattering) and on the presence of impurity phases in the standards (from SEM observations and EDS analyses).
Three mixtures of NIST SRM 676a (α-Al2O3) and NIST SRM 640c (Si), with proportions (in wt%) of 50:50, 40:60 and 25:75, were prepared to evaluate the amorphous content of standard silicon. Each mixture was collected twice. Silicon was selected as internal standard because its linear absorption coefficient is comparable to that of corundum; moreover, for both phases, μD is in the middle-sized powder range and, consequently, the Brindley model for microabsorption effects can be applied.
The amorphous content of the other standards was quantified by preparing three binary mixtures of each standard with NIST SRM 640c (Si), again with proportions (in wt%) 50:50, 40:60 and 25:75. The same procedure was applied to quantify the amorphous fraction in zircon (ZrSiO4), whose physical properties are reported in Table 1.
A single batch of 20 g of the synthetic mixture has been prepared by weighing 18.0 g of glass [wt% oxides: 66.7 SiO2, 11.9 Al2O3, 13.3 CaO, 2.0 MgO, 2.1 Na2O, 3.3 K2O, 0.7 ZnO, and calculated μ(Cu Kα) = 158 cm−1]. This industrial glass is not entirely amorphous as it contains 3 wt% of quartz (ICSD 67117; Dubrovinskii & Nuzik, 1989), previously calculated by spiking with NIST SRM 676a. This does not alter the results that will be shown, as the crystalline content is fixed and quantified. The mixture was ground for 10 min in an agate mortar and diluted with 2.00 g of industrial grade zircon. After homogenization, aliquots were extracted and spiked with 20 wt% of the different internal standards. This spiking amount was chosen on the basis of the restricted number of phases involved and because it does not significantly reduce the intensity of quartz.
Two batches of each mixture, with the relevant internal standard, were prepared. One was ground in a zirconia mortar and the other was pulverized in an agate mortar. Following 2 min of grinding, enough to homogenize the mixtures rather than reduce the particle size, X-ray powder diffraction data were collected. Subsequently, two consecutive grinding sessions (10 min) were performed, each followed by X-ray powder diffraction data collection.
Finally, each synthetic mixture treated in the zirconia mortar was diluted with a very small amount of zircon (about 1 wt%) to evaluate the sensitivity of the method to very slight changes of composition. These samples are from now on called `added' mixtures. It is important to say that the amount of zircon wZ for each added mixture can be calculated from the equation
where Wsyn and Wadded are the weighed amounts of synthetic and added mixtures, respectively, and wOZ is the amorphous content in zircon. The value 0.1 is the starting weighed amount of zircon in the synthetic mixture. Note that the added zircon amount was not exactly the same in all of the samples and the real weighed quantities have been taken into account in the calculations.
Our synthetic mixtures are composed of a crystalline phase (zircon) and an amorphous phase. The traditional RIR internal standard method (Chung, 1974) requires a coefficient for calculating the zircon amount in each mixture. Hence, a mixture of each internal standard and zircon (1:1 weight ratio) was prepared, ground for 2 min in a zirconia mortar, and measured by X-ray powder diffraction. The powder pattern was used to calculate the coefficient RIRzircon,std (one for each zircon–internal standard pair), included in the following equation for the calculation of the amount of zircon in the synthetic mixture:
where I200,zircon is the integrated area of the 200 peak of zircon, Ihkl,std is the integrated area of a chosen peak of the internal standard (the most intensive non-overlapping peak) and RIRzircon,std is the calculated coefficient.
As far as Fullpat is concerned, a library pattern normalization is required for each phase involved in the mixture. Aldrich annealed α-Al2O3 was used as internal standard for the Fullpat method.
Over-grinding may produce amorphization of crystalline powders (Bish & Post, 1993; Zevin & Kimmel, 1995). In a mixture in which each ith phase is characterized by a different particle size distribution (PSDi), the cumulative particle size distribution (CPSD) can be calculated from the single PSDi and the relative ith volume fractions (Xi) following
If there exists an ith phase (i.e. dashed line in Fig. 1, upper part) characterized by a PSD with a particle diameter much larger than that of all the others (i.e. continuous and dotted lines in Fig. 1, upper part, which are referred to as the jth and kth phases, respectively), the effect of grinding on this ith phase may be evaluated in the d1–d2 region, where d1 is the maximum particle diameter among all the other phases and d2 is the maximum particle diameter of the ith phase. This is possible by grinding the sample for t1 and t2 (where t2 represents a time longer than t1) and by subtracting, in the d1–d2 range, its CPSD measured after t2 from its CPSD measured after t1. The area that in Fig. 1 (lower part) corresponds to the difference between the horizontal-line-filled area and the vertical-line-filled area equates to the volume loss in the d1–d2 region, from t1 to t2, of the ith phase. As an example, (i) if one is dealing with a mixture with a starting maximum particle diameter of 5 and 10 µm for the jth and kth phases, respectively, and a starting maximum particle diameter for the ith phase of 20 µm, and (ii) if the CPSD of the mixture is known before and after 10 min of grinding, it is possible to obtain the volume loss of the ith phase, in the 10–20 µm range, from the 0–10 min range.
Samples were analysed using an X'Pert Pro PANalytical diffractometer with a θ–2θ geometry and equipped with a real time multiple strip (RTMS) detector. To refine the structure of each phase, a diffraction pattern of each pure phase was collected in the range 5–140° 2θ, with a counting time of 50 s per step and a step size of 0.008° 2θ. Experimental data of all the samples described in §2.1 were collected in the angular range 5–80° 2θ with a counting time of 50 s and a step size of about 0.017° 2θ. A sample spinner was used during the data collection to improve particle statistics. Each powder mixture was remounted and collected again to check for reproducibility.
To crosscheck the results obtained with copper radiation, one composition for each binary mixture was measured at the ID31 beamline at the European Synchrotron Radiation Facility (Grenoble, France) to exploit the use of short-wavelength radiation (0.354191 Å) and the high brilliance of the photon flux. Such experiments, performed in transmission mode with a boron glass capillary, offer a number of advantages over data collected with a conventional instrument: (i) minimization of microabsorption and primary extinction effects (Sabine, 1988); (ii) a higher possibility to detect minor phases; (iii) a wider investigated d-spacing range (dmin was 0.68 Å instead of 1.2 Å); (iv) high instrumental resolution (Fitch, 2004). For all the internal standards whose amorphous content had to be determined, one of the three different compositions described in §2.1.1 was collected at ID31. Each added mixture with different internal standard was also collected at the ID31.
Laser scattering measurements were performed with a Malvern Mastersizer 2000 in humid conditions. The experiment provides particle size distributions in the range 0.02–2000 µm by measuring the intensity of the light scattered when the laser beam passes through the dispersed sample. Such analyses have been performed on (i) phases without a certified particle size distribution (i.e. annealed Aldrich corundum and industrial grade zircon), so that the Brindley correction could be applied, and (ii) some selected synthetic mixtures with different internal standard, grinding time and mortar, to evaluate the effect of these parameters on the final particle size distribution.
Selected samples were also analysed using a Cambridge Stereoscan 360 scanning electron microscope to investigate the presence of impurities by means of backscattered electron images at different magnification levels.
2.4. Rietveld refinement strategy
All Rietveld refinements were performed using the GSAS package (Larson & Von Dreele, 2004) and its graphical interface EXPGUI (Toby, 2001). Structure refinements of each crystalline phase (reference ICDS structure as shown in Table 1) were performed to obtain a reliable structure model to be used in the quantitative analysis (details of the refined structures are available from the IUCr electronic archives as supplementary data1). For each phase, scale factor, cell parameters, displacement parameters, atomic coordinates and pseudo-Voigt profile function coefficients were refined; zero shift was corrected and instrumental background modelled with a Chebychev polynomial function with a variable number of terms.
The amorphous content in the crystalline phases was determined using Cu-anode data, by refining the scale factor, cell parameters and pseudo-Voigt profile function coefficients for each phase. Background and instrumental zero were also refined. In the case of NIST SRM 640c (111) plane, preferred orientation and primary extinction were refined using the March model (Dollase, 1986) and Sabine formalism (Sabine, 1988), respectively. The latter effect was considered because of the low density of defects of NIST SRM 640c and the low energetic source, in agreement with Cline et al. (2011). The same refinement strategy was used for synchrotron data but without correcting for preferred orientation and primary extinction, as these phenomena were minimized owing to the Debye–Scherrer capillary geometry and the high-energy beam, respectively.
In the last step, the Rietveld refinement of synthetic mixtures with different internal standards was performed. The presence of a background bump in the range 10–30° 2θ due to the amorphous phase required the use of 14 terms in the Chebychev polynomial function. For each phase, scale factor, cell parameters and profile coefficients of the pseudo-Voigt function were refined. The instrumental zero was also refined. The same Rietveld refinement strategy was applied to the added mixtures collected with the in-house instrument and the ID31 diffractometer.
Certified NIST SRM 676a was used to determine the sample purity of NIST SRM 640c. The results of the data collected with the Cu anode revealed the presence of amorphous material in NIST SRM 640c, quantified to 7.04 [±1.98] wt% if the Brindley correction is not applied and 6.95 [±1.98] wt% if the Brindley correction is applied. The number in square brackets represents the standard deviation of six amorphous evaluations for the mixture NIST SRM 676a–NIST SRM 640c (three binary ratios, each evaluated twice, as described in §2.1.1). In the case of ID31 data, the amorphous content in NIST SRM 640c amounts to 8.42 (22) wt% if the Brindley correction is not applied and 8.40 (22) wt% if the Brindley correction is applied. For these data, the numbers in parentheses are obtained from the least-squares procedure and refer to the least-significant digits. The purity of NIST SRM 640c, traced back to NIST SRM 676a, can be used to certify the purity of industrial grade zircon and internal standards. It is important to say that no increasing (or decreasing) trend of amorphous content in NIST SRM 640c occurred for the three different compositions. Detailed results are shown in the top part of Table 2.
For each phase, the Brindley correction is valid because the related μiDi value falls in the medium powder range (0.01–0.1). The only exception is annealed Aldrich α-Al2O3 for which the correction is an approximation (μiDi is in the lower part of the range, but very close to it). Moreover, the small diameter of the particles minimizes the (μi – μmixture) Ri values, with corresponding τ values (as defined by Brindley, 1945) given in Table 2. Consequently, the differences between calculated amorphous content with and without the application of the Brindley correction are negligible, even for NIST SRM 674a (TiO2) and NIST SRM 674a (α-Cr2O3), which have the highest linear absorption coefficients. A relevant amorphous fraction was also detected in zircon. Hence, the expected zircon content in the synthetic mixture must be rescaled with respect to the starting weighed amount (i.e. 10 wt%). For each crystalline phase, the amorphous content calculated from the Cu-anode data was compared with the results obtained using the ID31 data. The calculated figures confirm that a nonnegligible amorphous amount is present in all the internal standards and zircon (see bottom part of Table 2). The differences in the amorphous content of the various standards obtained with Cu-anode and ID31 data are due to the presence of preferred orientation of the (111) planes of silicon crystals when collected in reflection mode. In fact, with Bragg–Brentano geometry, preferred orientation on silicon (111) is nonnegligible and has to be refined (as described in the Rietveld refinement strategy): however, the preferred orientation and weight fraction of silicon are highly correlated. For this reason, the weight fraction of silicon in the mixtures tends to be overestimated and influences all the other amorphous quantification, both in the standards and in the samples.
Amorphous quantification with Cu-anode data is also strongly affected by primary extinction. In fact, if this effect is neglected, we have calculated that the amorphous content of NIST SRM 640c shifts to about 11.0 wt%. Consequently, the amorphous content in the other standards is also quite different. At the moment, the only certified standard is NIST SRM 676a, whose certification involved the refinement of the primary extinction effect on silicon powder, due to its high crystallinity (Cline et al., 2011). For this reason, primary extinction correction was allowed in our refinements, in order to make proper use of the quantification results obtained by Cline et al. (2011).
SRM 674a (α-Cr2O3) turns out to be the internal standard with the highest amorphous fraction. To crosscheck the results, SEM observations have been performed. Evidence of a possible amorphous phase with a `spider-web'-like habit, chemically and morphologically different from α-Cr2O3, has been found (see Fig. 2). This phase contains sulfur, indicating that it may be a sub-product of the synthesis used to prepare this material (Anger et al., 2005).
In the case of SRM 674a (ZnO), also characterized by an amorphous content greater than 10 wt%, weak peaks of zinc sulfides have been observed and identified as sub-products during the process of synthesis of zincite.
The results of the Rietveld refinements of the synthetic mixtures with different internal standards obtained with Cu-anode data can be later corrected for microabsorption effects and for the amorphous content of the internal standards, by means of equation (3). Note that the rather large content of amorphous phase in zircon (ranging from about 10 wt% for ID31 data, with negligible microabsorption effect, to about 15 wt% for Cu-anode data, with more evident microabsorption effect) must be considered. The first and second lines in Table 3 show the calculated zircon content obtained considering Cu-anode and ID31 amorphous content determinations and by applying, in both cases, the Brindley correction. If Cu-anode amorphous determinations (first line in Table 3) are considered, NIST SRM 676a and NIST SRM 674a (ZnO) provide the most accurate zircon quantification, whereas the other three standards result in a zircon overestimation that ranges from 0.41 to 0.97 wt%. In the case of ID31 amorphous determinations (second line in Table 3), zircon tends to be underestimated with respect to the expected figure (9.03 wt%).
It should be remarked that the use of Aldrich annealed α-Al2O3 produces a zircon overestimation with both wavelengths, presumably because the Brindley correction in this case is only approximated.
The third line in Table 3 reports the values of zircon content that would be obtained if the corrections for the amorphous content in zircon (and the standards) were not taken into account. Oddly, the results seem to be accurate for all the internal standards except for NIST SRM 676a (zircon underestimation up to 1.3 wt%), the elected standard for amorphous evaluation.
As discussed in §2.1.3, each internal standard was mixed with zircon in equal amounts to obtain the reference intensity ratio coefficient. All the coefficients were introduced in equation (5) and the resulting zircon amounts in the synthetic mixture are summarized in Table 4. The diffraction patterns used for these calculations are the very same as were used for the previous Rietveld refinements.
The results are more scattered and less accurate, if compared with those obtained with the RIR–Rietveld method. The RIR method is not biased by the linear absorption coefficient of the mixture μm, so the scatter of the results should be attributed to other sources of bias: for example, to the presence of an abundant amorphous fraction in ZnO, TiO2 and α-Cr2O3, or merely to the lower accuracy of the method owing to the single-peak approach.
As far as the Fullpat method is concerned, this approach has been applied only to annealed Aldrich α-Al2O3. After the classical library pattern normalization of the zircon (on the 012 peak of corundum), the amorphous phase was treated as a conventional phase in the software procedure (normalized on the 014 peak of corundum). The final results (bottom line of Table 4), show an overestimation (1.5 wt%) of the zircon content. It is important to say that the Fullpat approach, whose accuracy depends upon the closeness of the assumed FWHM of the library pattern with respect to the observed ones, can be more tricky to apply to the real case of sanitary-ware glazes. In fact, the starting mixture is heated at about 1473 K, causing annealing of the original zircon and a consequent decrease in its FWHM. The use of calcined zircon in the Fullpat library might be of great help.
As previously mentioned in §2.1.2, bias introduced by the use of different mortars and different grinding times has been considered. Over-grinding can affect the quality of the diffraction pattern to the extent that it may no longer be representative of the original sample. In the present work a significant difference has been observed when using a zirconia mortar in place of a common agate mortar. Because of its low porosity, hardness, inertness and high density, a zirconia mortar is considered ideal to grind hard materials and minimize contamination. Nevertheless, agate mortars are generally used in research and industrial laboratories, being relatively harder and less porous than the more economical porcelain mortar. Again the difference in hardness between the particles involved in the mixture and between them and the mortar could influence the grinding efficiency.
The effect of the nature of the mortar and grinding time on QPA was evaluated by the RIR–Rietveld and traditional RIR methods and by looking at the peak broadening in terms of FWHM, whose values were extracted by means of the X'Pert High Score Plus software (PANalytical, 2004). If grinding time is increased, the zircon content decreases for both methods of analysis. This effect is more evident in the case of samples ground using a zirconia mortar than samples ground using an agate mortar. In addition, regardless of the internal standard used, samples ground in an agate mortar exhibit a zircon underestimation with respect to the samples ground in a zirconia mortar (see Fig. 3). Considering equation (3), a decreasing trend of zircon content with grinding may be explained by (i) a loss of zircon, (ii) contamination of the internal standard and (iii) zircon amorphization. A contamination of the internal standard is implausible, whereas the two other options are likely. Although it is hard to explain, the observed loss of zircon in the different cases is attested by the decreasing trends of zircon content observed with both RIR–Rietveld and traditional RIR methods.
The effect of zircon underestimation is also visible by comparing the diffraction patterns of the synthetic mixture with Aldrich annealed α-Al2O3 (i.e. one of the standards in which zircon strongly decreases) as a function of grinding time (see Fig. 4, left side). The intensity of the zircon 002 peak, located at about 27° 2θ, significantly decreases, while the intensity of the corundum 012 peak, located at about 24° 2θ, does not. Similar effects are observed when comparing the same zircon peak in all the other synthetic mixtures with different internal standards.
Grinding influences the diffraction pattern also in terms of peak broadening. Looking at the zircon 002 peak, a slight increase of the FWHM (between 0.006 and 0.009° 2θ) has been observed, although it does not seem to be correlated to the zircon underestimation or the hardness of the internal standard. On the other hand, the FWHM of the internal standard peaks is strongly influenced by the hardness of the standard itself: NIST SRM 674a (ZnO), which is characterized by the lowest hardness value, exhibits a greater broadening of the peaks (see Fig. 4, right side), whilst the standards with greater hardness are less affected by this phenomenon. Fig. 5 (left side) highlights this effect when both agate and zirconia mortars are used.
Finally, the effect of grinding time on glass particle size has been measured following the method described in §2.2. If the particle size range 19–136 µm is considered, it was observed that the greater the hardness of the internal standard used, the finer the particle size of the glass phase that is obtained. As a matter of fact, in the case of NIST SRM 676a (the standard with the highest Mohs scale value, i.e. 9), the resulting loss of glass fraction from 2 to 22 min is 16.3%. On the other hand, NIST SRM 674a ZnO (the standard with the lowest Mohs scale value, i.e. 4–4.5), undergoes a resultant loss of glass volume from 2 to 22 min of only 6.7%. If all the standards are considered, the trend is first order (right side of Fig. 5).
The decreasing trend in zircon content observed in the results presented in §3.4 is evidence of the sensitivity of Rietveld and traditional RIR to small differences in zircon content, even if it is hard to explain. To shed light on this issue, the effect of dilution of all synthetic mixtures with zircon was evaluated. For each added mixture, the expected zircon amount was calculated following equation (4) but replacing the 0.1 value with the zircon amounts calculated in §3.4 (i.e. after grinding for 22 min in a zirconia mortar). The results obtained are shown in Fig. 6. Discrepancies between expected zircon and calculated zircon content were interpreted in terms of (i) Cu-anode data on added mixtures with a correction for amorphous determinations based on Cu-anode data (black circles); (ii) Cu-anode data on added mixtures with a correction for amorphous determinations based on ID31 data (white circles); and (iii) ID31 data on added mixtures with a correction for amorphous determinations based on ID31 data (black triangles). In all three cases, good agreement is observed between the expected and the calculated zircon content. Results obtained with Cu-anode data and corrected for amorphous determination based on Cu-anode data (black circles) are less scattered and closer to the expected value, estimated with equation (4) (ideal null discrepancy), than the other two data sets. Thus, for these artificial sanitary-glaze mixtures, if appropriate corrections are considered, Cu-anode data can also provide accurate results.
All the internal standards and the industrial grade zircon contain a non-negligible amount of amorphous phase. QPA of the synthetic mixture is accurate despite the nature of the internal standards used. The accuracy of the obtained figures is favoured by the small particle size of involved phases, which minimizes the microabsorption effect, and by the application of an equation [equation (3)] that corrects the results for the amorphous phase of the standards. However, it was observed that the most accurate QPA was obtained with NIST SRM 676a and NIST SRM 674a (ZnO). Care must be taken in the sample preparation procedure; in particular, the use of a zirconia mortar and `reasonable' grinding times are of great importance, allowing zircon underestimation and significant peak broadening to be avoided.
If faster zircon quantification is required, traditional RIR and Fullpat approaches can be applied with reasonable accuracy. They also preserve a good sensitivity to small zircon variations if grinding time is increased.
Finally, the comparison between Cu-anode and ID31 results on added mixtures are very close, pointing out that an accurate QPA can be accomplished also with conventional laboratory-based X-ray diffraction facilities.
The authors would like to thank the Ideal Standard laboratory of Trichiana (Italy) for providing the raw materials (zircon and glass) that were used to prepare the synthetic mixture, Dr Miriam Hanuskova for laser scattering measurements and Dr Ryan Winburn for a brief but very fruitful e-mail correspondence. The European Synchrotron Radiation Facility (ESRF) is acknowledged for beamtime of experiment HS4665 at ID31. Two anonymous referees are thanked, as they helped improve the paper.
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