kaolinite system at high temperature

Available online at www.sciencedirect.com

ScienceDirect Journal of the European Ceramic Society 35 (2015) 1327–1335

Effects of particle size distribution and starting phase composition in Na-feldspar/kaolinite system at high temperature Valeria Diella a,∗ , Ilaria Adamo b , Lucia Pagliari b , Alessandro Pavese a,b , Fernando Francescon c a National Research Council, IDPA, Section of Milan, Via Botticelli 23, I-20133 Milan, Italy Department of Earth Sciences “Ardito Desio”, University of Milan, Via Botticelli 23, 20133 Milan, Italy c Ideal Standard International, C.O.E., Ceramic Process Technology, Via Cavassico Inferiore 160, I-32026 Trichiana, BL, Italy b

Received 5 September 2014; received in revised form 21 October 2014; accepted 30 October 2014 Available online 21 November 2014

Abstract Mullite-glass Gibbs energy of formation (Geff ), micro-texture and phase composition evolution are investigated in the Na-feldspar (F) and kaolinite (K) system, over the 1240–1320 ◦ C interval, as a function of the starting F/K ratio by weight and particle size distribution of F (), using scanning electron microscopy, X-ray diffraction and thermodynamic modeling. Electron microscopy images show that size and aspect ratio of primary and secondary mullite have their largest figures for the smallest and, in general, monotonically increase upon firing temperature. Geff has been modeled by α() × (F/K)2 + β() × F/K + γ() (α, β and γ are linear functions of ). The parameters of such a function have been determined by fitting it to the experimental Geff s, inferred from quantitative phase analysis of X-ray diffraction patterns. Note that we used average Geff -values over the T-range explored because of the modest dependence on temperature shown. We have gathered that (i) F/K affects energetics and mullite content more markedly than does, and (ii) the mullite formation is energetically favored by decreasing F/K and increasing . © 2014 Elsevier Ltd. All rights reserved. Keywords: Feldspar grain size distribution; Feldspar/kaolinite ratio; Phase composition; Mullite-glass Gibbs energies formation

1. Introduction Kaolinite (K) and Na-rich feldspar (F), along with quartz, are the most used raw materials for traditional ceramic manufacturing. Quartz plays the role of a filler to control deformation and shrinkage of the fired bodies, whereas Na-rich feldspar, acting as a flux, is the main responsible during firing for the formation of the quasi-liquid phase that affects the densification process1 and final porosity.2 Moreover, flux interacts with kaolinite, which confers to the body plasticity for shaping and gives mullite + glass on firing,3–5 influencing thereby the micro-structural features and physical properties of the ceramic output.6–8 Mullite morphology and chemical composition depend on the type of clay and feldspar used as raw materials and on the firing

∗

Corresponding author. Tel.: +39 02 50315621; fax: +39 02 503 15597. E-mail address: [email protected] (V. Diella).

http://dx.doi.org/10.1016/j.jeurceramsoc.2014.10.035 0955-2219/© 2014 Elsevier Ltd. All rights reserved.

process. In general, mullite crystals from clay have a cuboidal aspect and are referred to as “primary” mullite, whereas the long needle-shape mullite crystals, related to both feldspar and its interaction with clay, are dubbed “secondary” mullite. Iqbal and Lee4 mention a needle-like third type of mullite, which has an elongation over 20 ␮m. Using energy dispersive X-ray spectroscopy, they observed that the Al2 O3 :SiO2 ratio of cuboidal primary mullite was close to 2:1, versus 3:2 for secondary mullite. However, it is difficult to give precise figures as mullite composition varies over the whole range from 3:2 to 2:1, as a function of the local chemical environment. The results found out in literature are scattered and refer to different and impure systems that are often out of equilibrium. A review on the mulite formation in clays and clay-based vitreous ceramics is presented in Ref. 9. Despite the long known importance of the flux’s particle size distribution for the traditional ceramic reactions, a few works have been found out in literature meant to shed light on how far

1328

V. Diella et al. / Journal of the European Ceramic Society 35 (2015) 1327–1335

such an aspect influences the formation of mullite and energetics of the flux-kaolinite system. The role of the particle size of feldspar has hitherto motivated interest to (i) governing the final porosity and stain resistance of porcelain tiles;2 (ii) enhancing the surface properties and chemical corrosion resistance of sanitary glazes;10–12 (iii) understanding its effect on the phase evolution and water absorption of sanitary-ware vitreous bodies.13 The aim of the present paper is to complement the extant ones in literature, contributing to understand how particle size of feldspar, in combination with the feldspar over kaolinite ratio at different firing temperature (T), affects the “kaolinite + feldspar → mullite + glass + H2 O↑” transformation, paying special attention to the resulting phase composition, microstructural features, crystal-phases versus glass-phases equilibrium and related Gibbs energy of formation. In this light, we aim to give a twofold contribution: on one hand, elucidating general aspects of interest to a better comprehension of fundamental traditional ceramic transformations, on the other hand helping to provide a rationale to control and drive technological parameters having a bearing to the industrial ceramic production. Such an investigation is a continuation of our previous study on the Na-feldspar and kaolinite system at high temperature,14 as a function of the kaolinite’s degree of order. In the present study, we choose disordered kaolinite and albite as starting phases, the latter representing a widely used feldspar-based flux in the wholesale industrial practice. Different feldspar over kaolinite ratio values and four particle size distributions of the former have been explored from 1240 to 1320 ◦ C, such as to provide a thermal interval appropriate both for appreciating the temperature effects on the reaction and for covering the firing range used in most traditional ceramic applications. 2. Experimental The kaolinite sample, provided by the international standards KGa-2 (highly disordered specimen, from Warren County, GA, USA) in order to ensure phase and composition purity, bears an estimated density of stacking defects as large as 50%.15,16 Albite (F), from a natural feldspar sample provided by Minerali Industriali S.r.l. (Novara, Italy), has undergone repeated floating cycles to get free of quartz, using amine as a collector. In so doing, the residual quartz at the end of the separation treatment amounts to less than 1%, as proven by X-ray powder diffraction. The chemical composition of the obtained Na-feldspar was determined by an electron microprobe (JEOL JXA-8200) and resulted in Na0.93(2) K0.01(1) Ca0.07(1) Al1.09(2) Si2.91(2) O8 . Twenty different mixtures containing Na-feldspar/kaolinite ratios by weight (F/K), from 0.43 to 1, were prepared and fired at 1240, 1280 and 1320 ◦ C, (for a total of 60 different composition-temperature points), using feldspar milled at four different particle size distributions (the average particle size distribution is hereafter referred to as . : 5, 45, 75, 150 ␮m);

see Table 1. In Fig. 1 the feldspar’s particle size distribution and frequency curves, determined by laser-light scattering using a Mastersizer S of Malvern Instruments Ltd., are reported. Kaolinite and albite were blended together in bi-distilled water for 10 min and thermally treated at 60 ◦ C for 24 h for drying; then cast into 0.5 height and 1 cm diameter cylindrical molds. The dried mixtures were eventually fired in an Elite Thermal System Ltd., BRF14/box furnace at a heating rate of 5 ◦ C/min between 25 and 700 ◦ C, and 3 ◦ C/min from 700 to the three maximum firing temperatures explored. The 1240–1280–1320 ◦ C treatments lasted as long as 2 h, followed by an annealing down to 500 ◦ C (∼−10 ◦ C/min) and then a cooling inside the furnace. From previous tests,14 a firing duration of 2 h allows one to reach quasi-equilibrium conditions in terms of resulting phases; an increase of the heating time does not affect significantly the final phase composition. X-ray powder diffraction (XRPD) data were collected by a PANalytical X’Pert Pro diffractometer, equipped with an X’Celerator detector, using CuKα radiation. The angular range 5–90◦ 2θ was explored with a step scan of 0.02◦ 2θ and a counting time of 30 s per step. The General Structure Analysis System (GSAS) software,17 implementing the Rietveld refinement method, was used to process XRPD data and, according to Gualtieri,18 the addition of 10 wt% NBS-corundum in the fired samples allowed us to quantify the present phases and determine the glass content. Each experiment at a given F/K ratio and temperature value was repeated three times to check reproducibility; the average phase composition are here used, with e.s.d’s ∼0.1 wt%. The micro-structural features for nineteen fired selected bodies were investigated by a Cambridge STEREOSCAN 360 scanning electron microscope (SEM) and semi-quantitative chemical analyses of mullite were performed using the annexed EDS system (ISIS 300 Oxford). We studied the following samples: F/K: 0.43, 0.67 and 1; all the feldspar’s s and firing at 1280 ◦ C (12 specimens); F/K: 0.43, 0.67 and 1; of 150 ␮m and firing at 1240 ◦ C (3 specimens); F/K: 0.43, only; all the feldspar’s s and firing at 1320 ◦ C (4 specimens). The samples were preliminarily etched by a solution of 8 M fluoro-boric acid for 1 h to remove the amorphous phase. ImagePro Plus 4.5 Software, Media Cybernetics Inc., 2001, has been used for the determination of some morphological properties (minimum length and thickness) of primary and secondary mullite, as a function of different conditions of formation. 3. Thermodynamic modeling The thermodynamic model here adopted relies on the one by Adamo et al.,14 which, in turn, uses the general equilibrium relationships according to Denbigh.19 We remind some aspects of the thermodynamic approach followed. A HT-reaction involving kaolinite and feldspar leads to the formation, in general, of

V. Diella et al. / Journal of the European Ceramic Society 35 (2015) 1327–1335

1329

Table 1 Mineralogical composition, Geff values and under saturation index (USI) of our mixtures. (␮m)

F/K

Mixture

Mullite (wt%) 1240 ◦ C

Glass phase (wt%)

Geff (kJ/mol)

USI

Mullite (wt%) 1280 ◦ C

Glass phase (wt%)

Geff (kJ/mol)

USI

Mullite (wt%) 1320 ◦ C

Glass phase (wt%)

Geff (kJ/mol)

USI

5

0.43 0.54 0.67 0.82 1.00

1 1 1 1 1

1 2 3 4 5

38.2 36.8 35.7 31.1 28.8

61.8 63.2 64.3 68.9 71.2

−46.79 −47.64 −49.20 −42.54 −41.03

0.26 0.26 0.25 0.32 0.35

39.7 37.0 36.7 29.4 27.6

60.3 63.0 63.4 70.6 72.4

−51.55 −49.37 −53.07 −39.94 −39.60

0.23 0.26 0.23 0.36 0.37

41.1 38.8 34.1 32.0 30.3

58.9 61.2 65.9 68.0 69.8

−56.81 −55.61 −47.80 −46.89 −46.55

0.21 0.22 0.29 0.30 0.31

45

0.43 0.54 0.67 0.82 1.00

2 2 2 2 2

1 2 3 4 5

39.4 38.2 34.9 29.3 27.9

60.6 61.8 65.1 70.7 72.2

−49.53 −51.15 −47.33 −38.79 −39.02

0.24 0.23 0.27 0.36 0.37

42.0 38.1 35.6 34.2 28.8

58.0 61.9 64.5 65.8 71.2

−58.24 −52.15 −50.14 −51.23 −42.11

0.19 0.23 0.26 0.26 0.35

41.2 36.1 34.3 33.0 28.5

58.8 63.9 65.8 67.1 71.5

−57.11 −48.41 −48.16 −49.14 −42.46

0.20 0.27 0.28 0.28 0.35

75

0.43 0.54 0.67 0.82 1.00

3 3 3 3 3

1 2 3 4 5

44.9 38.0 37.1 31.6 27.9

55.1 62.0 62.9 68.4 72.1

−66.93 −50.66 −52.89 −43.66 −39.13

0.13 0.24 0.22 0.31 0.37

42.6 38.2 36.0 33.4 27.0

57.4 61.8 64.0 66.6 73.0

−59.98 −52.39 −51.26 −49.14 −38.35

0.18 0.23 0.25 0.27 0.39

41.9 38.1 34.7 31.6 28.2

58.1 61.9 65.3 68.4 71.8

−59.32 −53.63 −49.16 −45.80 −41.84

0.19 0.23 0.28 0.31 0.36

150

0.43 0.54 0.67 0.82 1.00

4 4 4 4 4

1 2 3 4 5

46.2 42.1 38.0 34.0 30.2

53.8 57.9 62.0 66.0 69.8

−73.42 −63.17 −55.57 −49.29 −44.19

0.11 0.15 0.21 0.26 0.31

44.9 40.7 35.7 32.5 28.4

55.1 59.3 64.3 67.5 71.6

−68.83 −59.86 −50.63 −46.77 −41.14

0.13 0.18 0.25 0.29 0.36

43.8 40.1 33.2 31.3 27.3

56.2 59.9 66.8 68.7 72.7

−65.96 −59.59 −45.75 −45.11 −40.00

0.15 0.19 0.31 0.32 0.38

mullite, cristobalite and glass. However, if F/K > 0.43, we have observed that cristobalite does not appear and mullite, as suggested by the chemical analyses in EDS-mode, can be considered of the 3:2-type. In such a view, the equilibrium reaction between mullite and glass results therefore in

νmu Al4.5 Si1.5 O9.75mu ↔ νAl2 O3 Al2 O3gl + νSiO2 SiO2gl

(1)

where mu = mullite, gl = glass, νmu = 1, νAl2 O3gl = 2.25 and νSiO2gl = 1.5; the subscript gl in the left-hand side member of Eq. (1) means “glass”.

We shall use the notion of chemical potentials that are usually expressed as follows: μj = μj,0 + RT ln(xj ) + RT ln(γj )

(2)

where: μj = is the chemical potential of the jth -component; μj,0 = chemical potential part dependent on pressure and temperature, only; R = gas constant; xj and γ j = molar fraction and activity coefficient of j, respectively. By means of Eqs. (1) and (2), one can derive the relationship beneath νmu μmu = νAl2 O3gl μAl2 O3gl + νSiO2gl μSiO2gl ,

Fig. 1. Grain size distribution and frequency curves of feldspar at 5, 45, 75, and 150 ␮m used for preparation of samples.

(3)

1330

V. Diella et al. / Journal of the European Ceramic Society 35 (2015) 1327–1335

which, after an algebraic manipulation, turns into Kxtal/glass =

xmu νmu xAl2 O3 gl νAl2 O3 gl × xSiO2 gl νSiO2 gl

= exp(−G0 RT ) −

γAl2 O3 gl

γmu νAl2 O3 gl

νmu

× γSiO2 gl νSiO2 gl

= exp(−Geff RT ),

(4)

where: G0 = νmu μmu,0 − νAl2 O3gl μAl2 O3gl,0 − νSiO2gl μSiO2gl,0 ; ␥j ∼ 1 for ideal solid solutions;20,21 Geff represents the “effective” mullite-glass energy of formation and incorporates the two terms in the right-hand side member of Eq. (4). In general, Geff (T, {ξ}, xmu , xAL2 O3gl , xSiO2gl ), where {␰} is a set of variables describing the particle size distributions involved. The constraints due to normalization and F/K-value, namely xmu + xAl2 O3gl + xSiO2gl = 1 and 2.25xmu + xAl2 O3gl 1.5xmu + xSiO2gl

=

2Mfeld + (F/K)Mkao 2Mfeld + 3(F/K)xkao

(Mj is the molar weight of the jth -phase), allow one to reduce the independent composition variables to only one, which we choose to be xmu . As experimentally observed by Adamo et al.,14 xmu and F/K are linearly correlated to one another, which thing leads us to drop the former and retain F/K as the only independent variable associated to the composition of the system. We do not change the kaolinite’s particle size distribution, so that {␰} refers to feldspar’s only. This choice reflects that flux particle size affects final texture more than clay’s does.7,8 Let us take up that {␰} ≡ {pk } where pk is the probability of having a feldspar grain of size sk , and k ranges over N-particle size values. One can reasonably assume that the feldspar’s particle size somehow enters the general transformation in terms of   s 2   4  sk  3 k π δGbulk + 4π δGsurface × pk , (5) k 3 2 2 that is A + B , δGbulk and δGsurface , being bulk and surface average Gibbs energy densities, respectively, thought to as constants for the sake of simplicity. Writing sk = + k and observing that <> = 0, one then has = 3 + <3 > + 3<2 > == 3 × (1 + <3 >/3 + 3<2 >/2 ), and = 2 + <2 > = 2 × (1 + <2 >/). If the s-values are not too dispersed, then one can at a first level of approximation neglect the <2 >/ and <3 >/ terms, so that the expression (5) becomes dependent on only. In full, one has that the mullite-glass energy of formation is a function of T, F/K and , i.e. Geff (T, F/K,).

Fig. 2. Rietveld refinement of the X-ray powder diffraction pattern of the sample 1 3 fired at 1280 ◦ C. The lower pattern represents the residual between the calculated and experimental curves.

of the explored temperatures. Given that we aim at bringing to light effects due to , Geff (T, F/K,) is replaced by its average over T, i.e.      F F Geff = Geff T, , < s > ,< s > K K T   1 = T   T max F × Geff T, , < s > dT. K T min If Geff (F/K,)T , in turn, is Taylor expanded as a function of F/K, treating as a parameter, one obtains  Geff



F ,< s > K

= T



 j

a(< s >)j ×

F K

j ,

(6)

and then α(< s >)j =



aj,k × < s>k .

(7)

k

The order of the expansions (6) and (7) is fixed as a function of their actual ability to fit the experimental data, as it will be discussed below. Although such an approach is heuristic, we have found out it to be the only one reliable as F/K and correlate with one another, the former being in part dependent on given that the feldspar content by weight is naturally related to 3 × ρfeldspar , ρfeldspar = density of feldspar. The notion of “under-saturation index”, defined in Adamo et al.14 and resulting in xmu , xmu + xAl2 O3gl /2.25

4. Parametrization of the energy of formation

USI = 1 −

Preliminary observations have shown that Geff (T, F/K,) ranges over an interval as large as 10 kJ/mol, only, as a function

is here used to quantify the tendency of the available Al2 O3 to contribute to the formation of mullite.

(8)

V. Diella et al. / Journal of the European Ceramic Society 35 (2015) 1327–1335

1331

Fig. 3. Mullite content as a function of feldspar and F/K ratio at different temperatures.

5. Results and discussion 5.1. Phase evolution Table 1 shows the mineralogical compositions of the mixtures after heating at 1240–1280–1320 ◦ C for 2 h, and containing

feldspar with and F/K ranging from 5 to 150 ␮m, and from 0.43 to 1, respectively. The figures of merit for the Rietveld refinements lie in the intervals Rp = 0.046–0.052, Rwp = 0.062–0.069 and χ2 = 1.02–1.28. For F/K > 0.43, cristobalite is absent, as stated above, and the only occurring crystalline phase is mullite, along with glass.

Fig. 4. Secondary electron images showing primary mullite microstructural features of (a) 1 1, (b) 4 1, (c) 1 3, (d) 4 5, after firing at 1280 ◦ C.

1332

V. Diella et al. / Journal of the European Ceramic Society 35 (2015) 1327–1335

Fig. 5. Secondary electron images showing secondary mullite microstructural features in sample 4 1 at (a) 1240 ◦ C, (b) 1280 ◦ C and (c) 1320 ◦ C.

In Fig. 2 an example of XRD pattern among those used to quantify the phase composition is shown. In Fig. 3a,b the trends of mullite as a function of F/K at different , and as a function of at different F/K, are displayed. First of all, one qualitatively gathers that the mullite contents by percentage, χ(T, F/K,)mu , increase upon decreasing F/K and increasing , and do not exhibit any relevant dependence on temperature. We here introduce χ()F/K mu = )mu / d(F/K)>T , namely the slope of χ(T, F/K,)mu as a function of F/K, averaged over the explored temperature range and for a given . Using linear interpolations in F/K, we have found χ()F/K mu -values of −20(±3), −21(±3), −26(±3) and −28(±3) for 5, 45, 75, and 150 ␮m, respectively. Such results show that: χ()F/K mu < 0 for any , which thing hints at a tendency to disfavor formation of mullite upon increasing F/K;7

although χ()F/K mu has values scattered within 3σ from each other, yet the absolute value of χ()F/K mu increases as a function of , pointing to that the larger , the more quickly mullite decreases as a function of F/K. If one analyses χ(F/K) mu = )mu / d()>T , corresponding to the slope of χ(T, F/K,)mu as a function of at given F/K and averaged over T, then the following χ(F/K) mu -values are obtained: 0.038(±7), 0.025(±7), 0.003(±5), 0.011(±1) and −0.001(±6) ␮m−1 , for F/K of 0.43, 0.54, 0.67, 0.82 and 1, respectively. Taking the grand-averages of χ()F/K mu and χ(F/K) mu , i.e. <χ()F/K mu > = −23.8 and <χ(F/K) mu > = −1 0.015 ␮m respectively, one can state that a 1% change of the mullite content is achievable by either a -variation of ≈67 ␮m or a F/K-variation of ≈0.04, corresponding to some 50% and 6% of the and F/K ranges explored. In this view, altogether F/K seems to more effectively affect the mullite content than does.

Fig. 6. Secondary electron images showing secondary mullite microstructural features in samples (a) 1 3 an (b) 4 3 at 1280 ◦ C.

V. Diella et al. / Journal of the European Ceramic Society 35 (2015) 1327–1335

1333

Fig. 7. Coefficients of the α, β, γ-function, according to Eqs. (10a)–(10c).

5.2. Microstructural features The primary mullite exhibits a stocky aspect and its crystals as large as 0.3–0.6 ␮m in length and ∼0.1 ␮m in thickness, corresponding to an aspect ratio ranging from 3:1 to 6:1, the highest figure for the samples that have been treated at 1320 ◦ C. The grain size of feldspar and the F/K ratio in the mixture influence the sizes of the primary mullite, which turns out bigger upon

Fig. 9. f (ζ, ζ min ) as a function of ζ, at different feldspar .

decreasing (compare the cases of ∼5 and ∼150 ␮m, corresponding to Fig. 4 a and b) and F/K (see Fig. 4 a and c); at F/K > 0.43 somewhat of a “saturation” is reached, and the mullite’s morphology seems practically independent of and F/K (no substantial difference is visible in Fig. 4 c and d). Needle-shaped crystals, referred to as secondary mullite, show, in general, minimum length and thickness ranging over the intervals 1–5 and 0.1–0.5 ␮m, respectively. The average aspect ratio over all our samples is 16:1, and it decreases down to 7:1 in those specimens treated at the highest temperature explored. This hints that high temperature favors a growth that develops not only in length, but also transversally. Figure 5 displays such an effect: the sample treated at 1320 ◦ C exhibits bigger massive crystals (minimum length between 3 and 3.6 ␮m) than specimens’ heated at 1240 and 1280 ◦ C. As already seen for primary mullite, the size of the secondary mullite increases upon decreasing . For example, at 1280 ◦ C and F/K = 0.67, using ∼5 ␮m, the average values of minimum length and thickness are of 4.4 and 0.3 ␮m (Fig. 6a), respectively. Such figures are definitely greater than those of the mullite from ∼150 ␮m, which Exhibits 1.9 ␮m and 0.2 ␮m, respectively, on the average (Fig. 6b). The F/K ratio, in turn, does not seem to relevantly influence the crystal size of secondary mullite, but a slight tendency to favor bigger crystals’ development upon increasing F/K. Semi-quantitative chemical analyses, performed by an EDS spectrometer, have allowed us to determine that cuboidal mullite prevalently shows a 3:2 composition. A comparison with the needle-like crystals proves they tend to bear lower Al and higher Si contents, i.e. somewhat halfway between 3:2 and 2:1mullite types, though their small width is a serious hindrance to attaining precise compositions. 5.3. Mullite-glass Gibbs energy of formation

Fig. 8. Geff at different F/K ratio and feldspar .

Table 1 reports phase compositions and mullite-glass Gibbs energy of formation values determined by Eq. (4), i.e. Geff (T, F/K,)exp , as a function of T, F/K, and .

1334

V. Diella et al. / Journal of the European Ceramic Society 35 (2015) 1327–1335

Fig. 10. (a) USI (under-saturation index) as a function of F/K and (b) Geff determined by quantitative phase analysis as a function of USI.

We used the model discussed in Section 4 to interpolate the experimental data. First, Geff (T, F/K,) has been analyzed as a function of F/K only, treating as a parameter and using the series (6). Then, the expansions (7) has been fitted to the coefficients of the series (6), determined as a function of . We have observed that (6) and (7) may be truncated at the second and first order, respectively. In so doing, we have in full    2 F F Geff = α(< s >) × + β(< s >) ,< s > K K T   F × (9) + γ(< s >) K and α(< s >) = α0 + α1 × < s >

(10a)

β(< s >) = β0 + β1 × < s >

(10b)

γ(< s >) = γ0 + γ1 × < s > .

(10c)

In Fig. 7 we report measured α(), β() and γ(), which display linear trends within experimental uncertainties. The following values have been obtained for the parameters of Eqs. (10a)–(10c): α0 = −4(±1) kJ/mol, α1 = 1(±0.1) kJ/mol/␮m, β0 = 14(±6) kJ/mol, β1 = −0.6(±0.1) kJ/mol/␮m, γ 0 = −51(±5) kJ/mol and γ 1 = −0.5(±0.1)kJ/mol/␮m. In Fig. 8 Geff (F/K,)T calc and Geff (F/K,)T exp are shown as a function of F/K (a) and (b). The average discrepancy between theoretical values and observations results about 2%. Geff (F/K,)T spans an interval from 40 to 70 kJ/mol as a function of F/K, and exhibits values approaching each other upon increasing F/K (the curves intersect each other at F/K∼0.8). If F/K > 0.8 the trends flatten and give energy values corresponding to conditions which are more favorable to formation of glass than mullite. At small F/K, Geff (F/K, )T decreases upon increasing , shifting the equilibrium toward the left-hand side member of Eq. (1), i.e. mullite. Geff (F/K, )T shows a linear trend as a function of , as expected from Eqs. (10a)–(10c), and ostensibly proves that particle size is relevant for comparatively small F/K values, whereas it becomes quasi-immaterial at F/K approaching unity.

To better evidence the dependence of energy of formation on F/K and , we introduce the function ζmin +ζ 1 × f (ζ; ζmin ; < s >) = Geff (ζ, < s >)T dζ ζ ζmin where ζ = F/K and ζ is the width of the integration interval from ζ min . f (ζ;ζ min ; ) reduces oscillations due to uncertainties over F/K and provides average energies of formation that maximize the differences owing to . Fig. 9 shows that the smaller , the more f(ζ;ζ min ; ) is sensitive to the feldspar size. If one averages over the whole F/K-interval explored, the f(ζ;ζ min ; )-values are spread over a range as large as 10 kJ/mol, whereas for small ζs the figures are dispersed over a some 20 kJ/mol interval. The averages on temperature of the USIs, shown in Fig. 10 a, exhibit generally increasing trends versus F/K, common to all the samples investigated regardless of , i.e. a decrease of bent to form mullite. For F/K < 0.6, USI exhibits a dependence on , which disappears at larger feldspar contents.4,22 Fig. 10 b displays the correlation between Geff (F/K,)T exp , and USI: the larger USI the larger Geff (F/K,)T exp , because of a shift of equilibrium toward the Al2 O3 –SiO2 glass phases. For small USI-values, only, it is possible to discriminate the effect of on energy. A linear relationship holds between Geff (F/K,)T exp , and USI, with a slope of 119 (±7) kJ/mol. 6. Conclusions The binary system Na-feldspar-kaolinite has here been studied to bring to light the dependence of mullite content, its microstructures and mullite-glass Gibbs energy of formation on T, F/K and . The content of mullite ranges between 27 and 46 wt% and decreases in favor of glass when the F/K ratio increases (χ()F/K mu < 0 for any ; average value over the explored -range, i.e. <χ()F/K mu >, equal to −23.8), in keeping with Adamo et al.14 The particle size of the starting feldspar affects the formation of mullite so that, on the average, the smaller , the more the equilibrium shifts toward the amorphous phase (χ(F/K) mu > 0 for any F/K, but F/K = 1; mean value over the explored F/K-range, i.e. <χ(F/K) mu >, equal to 0.015 ␮m−1 ).

V. Diella et al. / Journal of the European Ceramic Society 35 (2015) 1327–1335

A comparison between <χ()F/K mu > and <χ(F/K) mu > suggests that and F/K influence the formation of mullite at very different rates: a 1% change of the mullite content is achieved by shifts of and F/K corresponding to some 6 and 50% of their investigated ranges, respectively. influences the morphology of primary and secondary mullite. At given F/K, we observe that small s tend to give bigger mullite crystals than large s. We hypothesize that small s make feldspar very reactive and ready to dissolve, but offer also large surfaces from which secondary mullite may nucleate. Although such mechanisms vie with one another, dissolution of feldspar provides the system with a chemical supply to make developed secondary mullite grow more. Geff (F/K,)T has been parametrized as a second order polynomial in F/K, whose coefficients are linear function of . The Geff (F/K, )T curves tend to converge at large F/K values, i.e. above 0.6, whereas marked differences are visible for small F/Ks. Large s affect Geff (F/K,)T more markedly than small feldspar sizes, the latter giving quasi-linear Gibbs energy of formation versus F/K trends (Fig. 9). Therefore a combination of large flux particle size with small F/K ratios allows one to promote formation of mullite via a lowering of Geff (F/K,)T . References 1. Das SK, Dana K. Differences in densification behaviour of K- and Na-feldspar-containing porcelain bodies. Thermochim Acta 2003;406: 199–206. 2. Alves HJ, Melchiades FG, Boschi AO. Effect of feldspar size on the porous microstructure and stain resistance of polished tiles. J Eur Ceram Soc 2012;32:2095–102. 3. Carty WM, Senapati U. Porcelain – raw materials, processing, phase evolution and mechanical behavior. J Am Ceram Soc 1998;81: 3–20. 4. Iqbal Y, Lee WE. Microstructural evolution in triaxial porcelain. J Am Ceram Soc 2000;83:3121–7. 5. Martín-Márquez J, Rincón JMA, Romero M. Mullite development on firing in porcelain stoneware bodies. J Eur Ceram Soc 2010;30:1599–607. 6. Tarvornpanich T, Souza GP, Lee WE. Microstructural evolution in claybased ceramics II: ternary and quaternary mixtures of clay, flux, and quartz filler. J Am Ceram Soc 2008;91:2272–80.

1335

7. De Noni Jr A, Hotza D, Soler VC, Vilches ES. Influence of composition on mechanical behaviour of porcelain tile. Part I: Microstructural variation and developed phases after firing. Mater Sci Eng 2010;527:1730–5. 8. Pagani A, Francescon F, Pavese A, Diella V. Sanitary-ware vitreous body characterization method by optical microscopy, elemental maps, image processing and X-ray powder diffraction. J Eur Soc Ceram 2010;30:1267–75. 9. Lee WE, Souza GP, McConville CJ, Tarvornpanich T, Iqbal Y. Mullite formation in clay and clay-derived vitreous ceramics. J Eur Ceram Soc 2008;28:465–71. 10. Bernardin AN. The influence of particle size distribution on the surface appearance of glaze. Dyes Pigments 2011;80:121–4. 11. Partyka J, Lis J. The influence of the grain size distribution of raw materials on the selected surface properties of sanitary ware. Ceram Int 2011;37:1285–92. 12. Partyka J, Lis J. Chemical corrosion of sanitary glazes of variable grain size composition in acid and basic aqueous solution media. Ceram Int 2012;38:553–60. 13. Bernasconi A, Marinoni N, Pavese A, Francescon F, Young K. Feldspar and firing cycle effects on the evolution of sanitary-ware vitreous body. Ceram Int 2014;40:6389–98. 14. Adamo I, Diella V, Pavese A, Vignola P, Francescon F. Na-feldspar (F) and kaolinite (K) system at high temperature: resulting phase composition, micro-structural features and mullite-glass Gibbs energy of formation, as a function of F/K ratio and kaolinite crystallinity. J Eur Ceram Soc 2013;33:3387–95. 15. Artioli G, Bellotto M, Gualtieri A, Pavese A. Nature of structural disorder in natural kaolinites: a new model based on computer simulation of powder diffraction data and electrostatic energy calculation. Clays Clay Miner 1995;43:438–45. 16. Bellotto M, Gualtieri A, Artioli G, Clark SM. Kinetic study of the kaolinitemullite reaction sequence. Part I: Kaolinite dehydroxylation. Phys Chem Mineral 1995;22:207–14. 17. Larson C, Von Dreele RB. General structure analysis system (GSAS) LAUR Rep. 86-748. Los Alamos: Los Alamos Natl Lab; 1994. 18. Gualtieri A. Accuracy of XRPD QPA using the combined Rietveld-RIR method. J Appl Crystallogr 2000;33:267–78. 19. Denbigh K. The principles of chemical equilibrium. Cambridge University Press; 1981. 20. McMillan WG, Mayer JE. The statistical thermodynamics of multicomponent systems. J Chem Phys 1945;13:276–305. 21. Acree WEJr, Zvaigzne AI. Thermodynamic properties of non-electrolyte solutions: Part 4. Estimation and mathematical representation of solute activity coefficients and solubilities in binary solvents using the NIBS and modified Wilson equations. Thermochim Acta 1991;178:151–67. 22. Wang H, Li C, Peng Z, Zhang S. Characterization and thermal behavior of kaolin. J Therm Anal Calorim 2011;105:157–60.