Quantitative Evaluation of Crystalline and Amorphous Phases in Clay-Based Cordierite Ceramic

An innovative chemical quantitative mineral analysis (CQMA) was successfully tested on a cordierite-based clay ceramic sample to quantify crystalline and amorphous components. The accuracy of this method was demonstrated on an added module to the CQMA program that used oxide formulas of amorphous phases obtained by energy dispersive X-ray spectroscopy (EDS) microprobe chemical analysis. This CQMA method was tested for three variants calculated using chemical analysis, i.e., X-ray diffraction (XRD) identification of crystalline (cordierite and enstatite) and amorphous phases by scanning electron microscopy (SEM)/EDS texture and microanalyses. The test results from CQMA suggest their application possibilities as well as the limits of their utilization.


Introduction
Clays and clay minerals are used in ceramic industries largely because of their contribution to the plasticity in ceramic mixtures and the density of the body at firing temperatures. Conventional methods for the synthesis of cordierite ceramics include solid-state sintering of individual oxides of the chemical composition of cordierite 2MgO-2Al 2 O 3 -5SiO 2 . The natural raw materials, kaolinite and talc, containing oxides MgO, Al 2 O 3 , and SiO 2 , are often used to fabricate cordierite ceramics [1]. Cordierites have also been sintered from clay mineral mixtures containing vermiculite [2,3]. Cordierite Mg 2 Al 4 Si 5 O 18 rapidly crystallizes from a glass of stoichiometric oxide composition to a well-defined hexagonal crystalline structure [4]. Cordierite ceramics prepared in the laboratories and industry have been found to be strongly dependent on the composition of raw materials and the presence of impurities. Therefore, mullite, corundum, spinel, forsterite, clinoenstatite, and cristobalite secondary crystalline phases are often present together with a glassy phase [5]. The glasses that have been investigated contained substantial amounts of TiO 2 as the nucleating agent [6]. Amorphous phases are commonly found in ceramics [1,3], slags [7,8], fly ash [9,10], cements and concretes [11,12], and their evaluation is performed by various methods. The group of analytical methods that provide very important information about mineral phases includes microscopic methods, the most common of which is electron microscopy [13,14].
Scanning electron microscopy (SEM) enables the characterization of the morphology, shape, size, and particle distribution in materials and moreover the possibility of studying the amorphous phase, cross-section pores, and the computer image analysis [15,16]. For analyses of elemental composition,

Materials and Methods
The cordierite ceramic sample (CCS) was obtained from kaolinite (K) and vermiculite (Ver) with the K/Ver mass ratio of 1:1 in a mixture sintered for 1 h at 1300 • C (more details are in our previous paper [3]). The Ver sample was milled in a cylindrical agate container for 15 min at 550 rpm using an agate planetary mill Fritsch Pulverisette 5, and then was prepared to the fraction <40 µm from sieve. The ceramic K/Ver mixture was homogenously mixed in a bottle at 40 rpm for 1 h (Heidolph Reax overhead shaker, REAX 20/4, Merck Company, Kenilworth, NJ, USA), and then milled for 15 min at 550 rpm in an agate planetary mill Fritsch Pulverisette 5. The mixture sample (3 g) was gently pressed by hand in a porcelain combustion boat, and then sintered in an electrical laboratory furnace LH15/13 for 1 h at 1300 • C. The heating rates were 10 • C/min up to 1000 • C and 2 • C/min until the sintering temperature of 1300 • C was achieved. The sample were left at this temperature for 1 h, and after that it was slowly cooled to room temperature. The ceramic sample for ED-XRF and XRD analysis was ground in a planetary ball mill under the same conditions as the mixture, and then manually pulverized with an agate mortar and pestle.
Kaolinite originates from the kaolin in the Pilsen Basin from locality Chlumčany (supplied by LB Minerals, Ltd., Horní Bříza, Czech Republic) and vermiculite originates from the Paraíba state, northeast region of Brazil (supplied by Grena, a.s., Veselí nad Lužnicí, Czech Republic).
For the SEM and EDS microanalysis study, the cordierite samples with grain size of about 2-5 mm were embedded in epoxy, dry polished, and then were plated with a 35 nm Cr layer by plasma sputtering.
The chemical elemental analysis was performed using the energy dispersive X-ray fluorescence (ED-XRF) spectrometer SPECTRO XEPOS (Spectro Analytical Instruments, Kleve, Germany). Prior to analysis, the measured CCS was finely ground to a particle size below 40 µm. For the XRF analysis, reference samples of metamorphic rocks based on clay minerals were used.
The XRD analyses were carried out on a Rigaku SmartLab diffractometer (RIGAKU, Tokyo, Japan) working in the symmetrical Bragg-Brentano geometry and with the CoKα radiation (λ 1 = 0.178892 nm and λ 2 = 0.179278 nm). The acceleration voltage on the sealed tube was 40 kV, the current was 40 mA. The diffracted intensities were recorded using a one-dimensional (1D) silicon strip detector D/teX Ultra 250 in the 5-80 • 2θ range with a speed of 0.5 • /min and a step size of 0.01 • .
The CQMA method recalculates the percentages of minerals to the percentages of elemental oxides (e.g., SiO 2 , Al 2 O 3 , Fe 2 O 3 , FeO, etc.) and vice versa, i.e., recalculation the percentages of element oxides to percentages of selected minerals ( Figure 1). Selected minerals identified, for example, by XRD or optical methods have to also be characterized by their crystallochemical/oxide formulas [33]. The CQMA program is equipped with a wide database of fixed crystallochemical/oxide formulas (e.g., MgSiO 3 /MgO SiO 2 ) and also formulas that can be modulated via their isomorphic substitution (e.g., micas, montmorillonites, vermiculites, etc.).
Minerals 2020, 10, x FOR PEER REVIEW 3 of 13 Kaolinite originates from the kaolin in the Pilsen Basin from locality Chlumčany (supplied by LB Minerals, Ltd., Horní Bříza, Czech Republic) and vermiculite originates from the Paraíba state, northeast region of Brazil (supplied by Grena, a.s., Veselí nad Lužnicí, Czech Republic).
For the SEM and EDS microanalysis study, the cordierite samples with grain size of about 2-5 mm were embedded in epoxy, dry polished, and then were plated with a 35 nm Cr layer by plasma sputtering.
The chemical elemental analysis was performed using the energy dispersive X-ray fluorescence (ED-XRF) spectrometer SPECTRO XEPOS (Spectro Analytical Instruments, Kleve, Germany). Prior to analysis, the measured CCS was finely ground to a particle size below 40 µm. For the XRF analysis, reference samples of metamorphic rocks based on clay minerals were used.
The XRD analyses were carried out on a Rigaku SmartLab diffractometer (RIGAKU, Tokyo, Japan) working in the symmetrical Bragg-Brentano geometry and with the CoKα radiation (λ1 = 0.178892 nm and λ2 = 0.179278 nm). The acceleration voltage on the sealed tube was 40 kV, the current was 40 mA. The diffracted intensities were recorded using a one-dimensional (1D) silicon strip detector D/teX Ultra 250 in the 5-80° 2θ range with a speed of 0.5°/min and a step size of 0.01°.
The CQMA method recalculates the percentages of minerals to the percentages of elemental oxides (e.g., SiO2, Al2O3, Fe2O3, FeO, etc.) and vice versa, i.e., recalculation the percentages of element oxides to percentages of selected minerals ( Figure 1). Selected minerals identified, for example, by XRD or optical methods have to also be characterized by their crystallochemical/oxide formulas [33]. The CQMA program is equipped with a wide database of fixed crystallochemical/oxide formulas (e.g., MgSiO3/MgO SiO2) and also formulas that can be modulated via their isomorphic substitution (e.g., micas, montmorillonites, vermiculites, etc.). The oxides of elements were calculated from minerals (i.e., analytes ci,calc) according to Equation (1) using the CQMA (option A) as: The oxides of elements were calculated from minerals (i.e., analytes c i,calc ) according to Equation (1) using the CQMA (option A) as: where c i,calc is the calculated i-th element oxide (wt%) of the sample, c i,j is the percentage (wt%) of the i-th element oxide in the j-th mineral phase, w j is the weight fraction of the j-th mineral in the sample, and m is the number of calculated minerals. The weight fraction of the i-th element oxide in the j-th mineral c i,j is calculated from the crystallochemical formula of the j-th mineral.
The calculation of the weight fractions of the j-th mineral (w j ) was calculated by Equation (2) using the CQMA (option B) as: where c i,exp is the i-th element oxide in the sample (wt%) determined by bulk chemical analysis, min is the minimum calculated value of the sum of squares, and n is the number of element oxides in the bulk chemical analysis used for the calculation; condition necessary for the CQMA calculation, n ≥ m. The calculation of the weight fraction (w j ) of the j-th mineral in the sample from Equation (2) is performed using the least squares CQMA method. The feedback calculation of the chemical analysis c i,calc from the calculated minerals w j is then performed from Equation (1). Subsequently, the c i,exp and c i,calc are critically compared using their differences DIFF i = c i,exp − c i,calc . If DIFF i for some i-th element oxides are too high (positive or negative), they can be attributed to some incorrect input data, for example, to the bulk chemical analysis, crystallochemical formula, or identified minerals. After critical evaluation, these data can be reanalyzed or additional data can be added, and then the calculation is repeated. More details about this method and also verification of CQMA calculated data on the data of 6 international standards has already been published and critically evaluated elsewhere [33].
Scanning electron microscopy (SEM) of the samples, monitoring morphology, and rough composition of the determined phases were performed on polished sections using an FEI Quanta-650 FEG autoemission electron microscope (Waltham, MA, USA) from Thermo Fischer Scientific. Photomicrographs were taken using a backscattered electron (BSE) detector (Termo Fischer Scientific, Brno, Czech Republic) in chemical gradient mode.
The chemical composition of the minerals was verified using an EDAX Galaxy energy dispersive spectrometer (Edax Amentek, USA). EDS microanalyses were performed with the correction by external polished microanalysis standards of aluminosilicate minerals by SPI Supplies (USA). Identification of spectral lines was performed by spectral deconvolution using the holographic peak deconvolution function.

Chemical and X-ray Diffraction (XRD) Phase Analyses
The chemical composition of CCS was obtained using the bulk chemical analysis (ED-XRF) ( Table 1). The concentrations of elements were converted to the concentrations of stoichiometric oxides (wt%); Fe was recalculated to FeIII as Fe 2 O 3 . The chemical analysis (CHA) was completed by XRD identification and quantitative analyses of mineral phases. The XRD pattern of ceramic CCS shows cordierite (PDF card no. 01-082-1884) and enstatite (PDF card no. 00-019-0768) ( Figure 2). An "amorphous" halo from about 20° to 35° (2 θ) of the amorphous phases is marked from the background by the dotted line. The quantitative percentages of cordierite (95 ± 2.5 wt%) and enstatite (5 ± 2.5 wt%) were calculated by using the reference intensity ratio (RIR) method from the not overlapping diffractions [34]. The crystallochemical formulas of cordierite Ca0.10Mg1.90Fe(III)0.40Al3.60Si5.00O18.00 and enstatite MgSiO3 were selected from our previous work [3] and are similar to those reported by Balassone et al. [35].

Scanning Electron Microscopy (SEM)
The CCS morphology was studied by scanning electron microscopy (SEM), as shown in Figure  3. At this lower magnification (1600×) pseudohexagonal crystals of cordierite (phase I) can be well differentiated from an amorphous matter (III) that consists of two different phases, III/1 and III/2 ( Figure 3a). Enstatite identified using XRD pattern may correspond to the phase II with needle habitus (ei, enstatite inclusion) in Figure 3b.
The crystalline enstatites occur in pseudohexagonal crystals of cordierite I and in amorphous phase III/1 but are not observed in phase III/2 ( Figure 3b). Phases I and III/2 are encapsulated in the phase III/1 around them. Except for enstatite inclusions (ei), other small glassy inclusions (oi) occur, namely, in amorphous phase III/1 but not observed in phase III/2. The chemical composition of both types of these inclusions and their identification by EDS is rather complicated (Figure 3b). This is because at least one of the dimensions of these inclusions is smaller than 1-2 µm, while the emitted ray of EDS is simultaneously analyzing the surrounding area of the observed objects with diameter of about 5 µm (Figure 3b). An "amorphous" halo from about 20 • to 35 • (2 θ) of the amorphous phases is marked from the background by the dotted line. The quantitative percentages of cordierite (95 ± 2.5 wt%) and enstatite (5 ± 2.5 wt%) were calculated by using the reference intensity ratio (RIR) method from the not overlapping diffractions [34]. The crystallochemical formulas of cordierite Ca 0.10 Mg 1.90 Fe(III) 0.40 Al 3.60 Si 5.00 O 18.00 and enstatite MgSiO 3 were selected from our previous work [3] and are similar to those reported by Balassone et al. [35].

Scanning Electron Microscopy (SEM)
The CCS morphology was studied by scanning electron microscopy (SEM), as shown in Figure 3. At this lower magnification (1600×) pseudohexagonal crystals of cordierite (phase I) can be well differentiated from an amorphous matter (III) that consists of two different phases, III/1 and III/2 ( Figure 3a). Enstatite identified using XRD pattern may correspond to the phase II with needle habitus (ei, enstatite inclusion) in Figure 3b.
The crystalline enstatites occur in pseudohexagonal crystals of cordierite I and in amorphous phase III/1 but are not observed in phase III/2 ( Figure 3b). Phases I and III/2 are encapsulated in the phase III/1 around them. Except for enstatite inclusions (ei), other small glassy inclusions (oi) occur, namely, in amorphous phase III/1 but not observed in phase III/2. The chemical composition of both types of these inclusions and their identification by EDS is rather complicated (Figure 3b). This is because at least one of the dimensions of these inclusions is smaller than 1-2 µm, while the emitted ray of EDS is simultaneously analyzing the surrounding area of the observed objects with diameter of about 5 µm (Figure 3b).

X-ray Energy Dispersive Spectroscopy (EDS) and Calculated Oxide Formula Coefficients
The SEM observations confirmed that the highest percentage relates to cordierite (Phase I), followed by the amorphous phases III/1 and III/2 (Figure 3a). The microanalysis of these phases was obtained by energy dispersive X-ray apectroscopy (EDS) on 10 samples of cordierite (phase I) and 10 samples of amorphous phase III/1. From amorphous phase III/2, only seven analyses were performed with the view of lower % representation. Positions/locations of these microanalyses conducted are depicted in Figure 3a and their calculated average values of and standard deviations si are listed ( Table 2).
While amorphous phase III/1 is nearly homogeneous in terms of bulk chemical composition, amorphous phase (III/2) is heterogeneous corresponding higher standard deviations . The chemical microanalyses of phases I, III/1, and III/2 are contaminated by inclusions of other phases marked as ei in phase I, ei and oi in phase III/1, and ei inclusion in phase III/2 (Figure 3a,b). The proportion of these other phases can hardly be estimated; nevertheless, it can be deduced that the chemical analyses do not correspond with the pure phases of cordierite and amorphous phases III/1 and III/2 without inclusions ( Table 2).  Figure 3a); ci,cord and ci,enst, oxide percentage

X-ray Energy Dispersive Spectroscopy (EDS) and Calculated Oxide Formula Coefficients
The SEM observations confirmed that the highest percentage relates to cordierite (Phase I), followed by the amorphous phases III/1 and III/2 (Figure 3a). The microanalysis of these phases was obtained by energy dispersive X-ray apectroscopy (EDS) on 10 samples of cordierite (phase I) and 10 samples of amorphous phase III/1. From amorphous phase III/2, only seven analyses were performed with the view of lower % representation. Positions/locations of these microanalyses conducted are depicted in Figure 3a and their calculated average values of c i and standard deviations s i are listed (Table 2). Table 2. Microprobe analyses of elemental oxides determined by energy dispersive X-ray spectroscopy (EDS) and calculated oxide formula coefficient (OFC i ).  While amorphous phase III/1 is nearly homogeneous in terms of bulk chemical composition, amorphous phase (III/2) is heterogeneous corresponding higher standard deviations s i . The chemical microanalyses of phases I, III/1, and III/2 are contaminated by inclusions of other phases marked as ei in phase I, ei and oi in phase III/1, and ei inclusion in phase III/2 (Figure 3a,b). The proportion of these other phases can hardly be estimated; nevertheless, it can be deduced that the chemical analyses do not correspond with the pure phases of cordierite and amorphous phases III/1 and III/2 without inclusions ( Table 2).

Oxides
For the relevant i-th oxides of phases I, III/1, and III/2, c i values were used for the calculation of their oxide formula coefficient (OFC i ) using Equations (3) and (4) as follows: where f SiO2 is correction factor used for the recalculation of all i-th OFC i values to the relation to value OFC SiO2 = 10.00 for each phase (If any number instead of constant 10.00 is used, then the i-th oxides of the elements will preserve the same ratio with each other and the final calculation of the crystalline or amorphous percentages calculated by CQMA will not be affected);  Table 2).
The comparison of cordierite oxides (c i and c i,cord ) indicates a very good agreement. Microanalyses (c i ) of amorphous phases III/1 and III/2 as compared with the c i,enst of enstatite are different. Nevertheless, the chemical composition of III/2 phase is closer to enstatite due to their high % of MgO. However, high standard deviations, s i , signalize high heterogeneity and enstatite cannot be assumed. Therefore, for III/1 amorphous phase the calculation of c i,enst was not necessary.
The concentrations of elemental oxide maps are collected by SEM/EDS system (Figure 4). The distributions of cordierite I, as well as amorphous phases III/1 and III/2 are shown on the photo (see left side of this figure). The resolution of element oxide concentrations in the phases can be found according to the intensity of their coloration. A higher intensity (lighter color) corresponds to higher contents of the element. The results are summarized in the following points: OFC for individual phases I, III/2, and III/1 were compiled from their OFC i data (Table 3). The results in Figure 4 agree well with the determined % contents of individual oxides of elements (c i ) in Table 2. The results in Figure 4 agree well with the determined % contents of individual oxides of elements ( ) in Table 2.

Calculation of Minerals Percentages Using CQMA (Option B)
The CQMA program (option B) for the calculation of mineral percentages of analyzed sample used the following input data: (a) bulk chemical analysis (Table 1), (b) identified crystalline minerals by XRD, and (c) their crystallochemical formula obtained from XRD database or from compiled oxide element formula obtained using the microanalysis of analyzed sample ( Table 3). The CQMA calculations were performed for the following different Variants 1-3:

Variant 1
Crystallochemical/oxide formulas were the following: For variant 1 and the following variant 2 the crystallochemical formulas for cordierite and enstatite have already been given and discussed in Section 3.1. From bulk chemical analysis (Table 1) all percentages of Al2O3, Fe2O3, CaO, MgO, and part of SiO2 were included in identified crystalline phases (cordierite and enstatite), while the surplus of SiO2 (7.56%) and all percentages of TiO2 (0.81%), Na2O (0.21%), and K2O (2.09%) were included in non-crystalline phase. For this purpose, the calculation by CQMA (option B) was used and maximal possible percentages of crystalline minerals (89.0%) and minimal percentages of amorphous phase (10.7%) were obtained. Then, the percentages of element oxides obtained from non-crystalline phase were recalculated to the oxide formula 10.0SiO2 0.81TiO2 0.27Na2O 1.72 K2O.

Variant 2
Crystallochemical/oxide formulas were the following:

Calculation of Minerals Percentages Using CQMA (Option B)
The CQMA program (option B) for the calculation of mineral percentages of analyzed sample used the following input data: (a) bulk chemical analysis (Table 1), (b) identified crystalline minerals by XRD, and (c) their crystallochemical formula obtained from XRD database or from compiled oxide element formula obtained using the microanalysis of analyzed sample ( Table 3). The CQMA calculations were performed for the following different Variants 1-3:

Variant 1
Crystallochemical/oxide formulas were the following: For variant 1 and the following variant 2 the crystallochemical formulas for cordierite and enstatite have already been given and discussed in Section 3.1. From bulk chemical analysis (Table 1) all percentages of Al 2 O 3 , Fe 2 O 3 , CaO, MgO, and part of SiO 2 were included in identified crystalline phases (cordierite and enstatite), while the surplus of SiO 2 (7.56%) and all percentages of TiO 2 (0.81%), Na 2 O (0.21%), and K 2 O (2.09%) were included in non-crystalline phase. For this purpose, the calculation by CQMA (option B) was used and maximal possible percentages of crystalline minerals (89.0%) and minimal percentages of amorphous phase (10.7%) were obtained. Then, the percentages of element oxides obtained from non-crystalline phase were recalculated to the oxide formula 10.0SiO 2 0.81TiO 2 0.27Na 2  For the variant 2, the crystallochemical formulas of cordierite and enstatite from variant 1 were used. In addition to this, for the calculation of amorphous phase III/1 and the other amorphous phase III/2, the compiled OFC were used (Table 3).
Calculated results from XRD analysis and variants 1-3 of CQMA (option B) are given in Table 4 and graphically shown in Figure 5. For the variant 2, the crystallochemical formulas of cordierite and enstatite from variant 1 were used. In addition to this, for the calculation of amorphous phase III/1 and the other amorphous phase III/2, the compiled OFC were used (Table 3).
Calculated results from XRD analysis and variants 1-3 of CQMA (option B) are given in Table 4 and graphically shown in Figure 5.

Discussion
Results of variant 1 can be considered to be indicative, showing a relation with the total maximal content of both crystalline phases (cordierite and enstatite) and minimum content of total amorphous phase, which is afterwards documented by percentages of phase contents calculated from variant 2 and variant 3.
Unlike variants 1 and 3, variant 2 enables use of two OFC phase formulas III/1 and III/2 calculated from averages of microanalyses ( Table 2). The OFC formulas used for the calculation of both amorphous phases III/1 and III/2 are given in Table 3. The added amorphous phase III/2 shows that this phase (unlike amorphous phase III/1) is very heterogeneous and is characterized for some elemental oxides (e.g., Al2O3 and MgO) by high standard deviations (Table 2). Calculated percentages of phases I, II, III/1, and III/2 (Table 4) are in a good agreement with compared phases in Figure 3a,b.

Discussion
Results of variant 1 can be considered to be indicative, showing a relation with the total maximal content of both crystalline phases (cordierite and enstatite) and minimum content of total amorphous phase, which is afterwards documented by percentages of phase contents calculated from variant 2 and variant 3.
Unlike variants 1 and 3, variant 2 enables use of two OFC phase formulas III/1 and III/2 calculated from averages of microanalyses ( Table 2). The OFC formulas used for the calculation of both amorphous phases III/1 and III/2 are given in Table 3. The added amorphous phase III/2 shows that this phase (unlike amorphous phase III/1) is very heterogeneous and is characterized for some elemental oxides (e.g., Al 2 O 3 and MgO) by high standard deviations (Table 2). Calculated percentages of phases I, II, III/1, and III/2 (Table 4) are in a good agreement with compared phases in Figure 3a,b. Phase II (enstatite) was identified only by XRD and in Figure 3b was denoted as inclusion (ei) in all phases of the analyzed sample.
In variant 3, the same OFC phase formula of amorphous phases III/1 was used for the calculation of phases, similar to the case of the previous variant 2. For cordierite (I), the OFC formula (Table 3) partially includes the inclusions of crystalline enstatite (ei). The differences between OFC formula of cordierite I, containing enstatite inclusions 10.0SiO 2  The sum of percentage crystalline phases determined in variant 2 (cordierite and enstatite) is almost the same as the content of cordierite 1 (phase I) in variant 3 (Table 4). This fact is due to the simple OFC formulas of cordierite and enstatite identified by XRD PDF cards and used for variant 2, while cordierite variant 3 with enstatite inclusion was calculated according to the OFC formula in Table 3. Of course, then, the sum percentages of amorphous phase III/1 and III/2 for variant 2 and variant 3 are also the same (Table 4). Due to the heterogeneous character of III/2 phase and their higher percentages in variant 3, it is probable that this analysis is burdened by bigger errors.
CQMA (option B) is proposed as an optimized method with the aim to approximate the calculated chemical analysis (c i,calc ) from the concentrations of crystalline and amorphous phases to bulk chemical analysis (c i,exp ) of analyzed sample. The results of chemical analyses (Table 5) show this trend in all three variants 1-3. Moreover, sumDiff 2 (5) is calculated during the calculation of mineral contents as a control:  The sumDiff 2 values exceeding ca. 2.0 indicate that the calculation is not fully correct or not complete, i.e., that some minor phase is not included in the calculation. More details (critical evaluation and comparison of the CQMA and QXRD-Rietveld methods of mineral phases can be found in the previous study [33]).

Conclusions
An innovative method based on chemical quantitative phase analysis (CQMA) was developed for the quantitative calculation of crystalline and amorphous phases for materials with simple mineral compositions. The CQMA method was tested (three different variants) on the cordierite ceramic sample CCS, prepared from a mixture of kaolinite and vermiculite at a temperature of 1300 • C. The analytical re-examination of all three variants was based on XRF chemical analysis and XRD identification of crystalline (cordierite and enstatite) and amorphous phases, with the addition of SEM/EDS for texture and microanalyses and CQMA for calculation of quantitative phase analyses.
Variant 1 calculated the maximal percentages of crystalline cordierite and enstatite and minimal amorphous phase in which Ti, Ca, K, and Na were fully fixed. Variant 2 calculated identified amorphous phases (the first III/1 with chemically homogeneous composition and the second III/2 with chemically heterogeneous one). Both their OFC were calculated from average microanalyses determined by EDS and from XRD PDF data of crystalline cordierite and enstatite. Variant 3 originated from the occurrence of dominant cordierite (I) containing inclusion of enstatite II and two amorphous phases III/1 and III/2 whose OFC were, similar to the case of variant 2, calculated from average microanalyses.
All quantitative data for three variants were finally recalculated using CQMA (option B) optimization method and a good agreement and logic relationship were revealed between their calculated contents. The results lead to the conclusion that CQMA method can also be successfully used in combination with SEM/EDS to calculate quantitative phase analysis for minerals containing chemically homogeneous amorphous phase whose crystallochemical/oxidic formula can reliably be determined.