“No amount of experimentation can ever prove me right;
A single experiment can prove me wrong.” - Albert Einstein
3.1 Green samples preparation
A wet-processed, commercially available plastic porcelain body (Matt and Dave Clays LLC, Alfred, NY) was used for all experiments. This provided a better overall uniformity than might be normally expected in a laboratory-prepared body.
The chemical composition of this body was measured externally (ICP-ES, ACME Analytical Laboratories Ltd., Vancouver, B.C.) and is presented in Table I. The body was used in the as-received form without additional processing.
Table I. Measured Chemistry of the Porcelain Body (wt. %)
The body was extruded into 15 mm rods using a vacuum de-aired piston extruder. The extruded rods were cut into 10 mm thick discs, dried overnight at 110 °C, then ground to a specimen thickness of 7 mm (±0.1 mm) and stored in a drier until heat treatment. The pellet mass was constant at 1.55 grams (±0.05 g) to ensure specimen uniformity. The 7 mm thickness was determined via preliminary experiments to reduce thermal gradients during firing.
3.2 Rapid firing apparatus
Specimens were heat treated at 43 different schedules as listed in Table II.
The heat treatments were performed in a random order. Four samples were fired for each heat treatment condition, with three specimens used for physical properties measurements and Quantitative X-Ray Diffraction. The fourth specimen was retained for microstructural evaluation.
A specially designed rapid-rate vertical tube furnace was used to obtain the heating rates and short hold times. A schematic of the rapid-rate furnace is provided in Figure 7. The furnace is maintained at a constant temperature and the sample is inserted into the furnace via a stepper motor. The furnace temperature
SiO2 Al2O3 Fe2O3 MgO CaO Na2O K2O TiO2
69.97 24.42 0.49 0.41 0.24 0.45 2.36 0.44
17
is maintained using a Silicon Controlled Rectifier (SCR) with a type B thermocouple. The sample temperature is monitored using a type R thermocouple with the specimen temperature used to control the stepper motor via a proportional-integral-differential (PID) feedback-loop so that the specimen temperature is achieved by adjusting the specimen location within the furnace.
With this approach, a maximum heating rate of 1000 K·min-1 can be achieved with an accuracy of ±3 K·min-1.63 The heating rates for this study (5, 20, and 60 K·min-
1) were well within the device capabilities. The furnace temperature was verified using pyrometric temperature check rings (Process Temperature Control Rings (PTCR), Ferro GmbH Performance Pigments and Colors, Gutleutstr, Frankfurt/M, Germany).
For the long dwell times and the fixed heating rates of 5 K·min-1, a standard SiC resistance heated furnace (Carbolite RF1500, Carbolite Limited, Hope Valley, UK) was used. These temperatures were similarly verified.
Table II. Experimental Heat Treatment Parameters Heating Rate
(K·min-1)
Dwell Temperature (°C)
Dwell Time (hours) 5
20 60
1100* 1150*
1200 1250
1300
0.1 0.32 0.20 1.0 3.2 10*
32* 100**
* These samples were only heat treated at a heating rate of 5 K·min-1.
** This sample was only at 1250°C with a rate of 5 K·min-1.
3.3 Fired samples characterization
Apparent bulk density was obtained using an immersion method modified for small specimen size.64 After measurement, the specimens were dried overnight, then crushed to a particle size <10μm. The crushed powder was then dried again prior to measuring the powder density using a pycnometer method (AccuPyc 1330, Helium Pycnometer, Micromeritics Instrument Corp., Norcross,
18
GA, USA) to obtain a true density. This powder was then used for quantitative mineralogy measurements via X-Ray Diffraction. Quantitative X-Ray Diffraction analysis was performed using an internal standard method with 10% (d.w.b.) CaF2. The CaF2 and the specimen powder were mixed for15 minutes using a motorized mortar and pestle. Powder diffraction data was collected (Bruker D2 Phaser, Madison, WI, USA) from 15° to 60° 2θ with CuKα radiation (λ=0.154 nm) at 30kV and 10 mA with a step size of 0.04° and a count time of four seconds. Diffraction patterns were analyzed using commercial software (Jade, v.9, Materials Data Inc., Livermore, CA, USA).
Figure 7. A schematic diagram of the rapid-rate furnace constructed at Alfred University. The specimen temperature was monitored via a separate thermocouple and adjusted via a stepper-motor with a feedback loop.
Three non-overlapping peaks were selected for each mineral phase as listed in Table III. A calibration curve was developed using the peak areas of three
19
peaks for each mineral phase compared to obtain a peak area ratio to three CaF2
peaks (additive). This method is described elsewhere.16 (No cristobalite was observed in any of the samples, potentially attesting to the quality of mixing22).
Samples heat treated below 1200°C contained residual potassium feldspar (microcline), but the amounts were not determined.
Table III. Diffraction Peaks and Measurement Reliability for Quantitative Analysis via XRD 16
Mineral phase Diffraction peaks for analysis Reliability (wt. %)*
Mullite Quartz CaF2
(001) (220) (121) (110) (111) (112) (111) (220) (331)
±2%
±3%
* The reliability is relative to the measured value, not absolute.
3.4 Microstructure analysis
The remaining fired samples from different firing conditions were ground on silicon carbide paper and then polished using 6, 3 and 1 micron diamond pastes and etched with 20% HF at 0 °C (temperature controlled via a water bath) for 10 seconds, then microstructurally examined using a scanning electron microscopy (FEI, Quanta 200F, OR, USA). The thickness of the quartz dissolution rim was also graphically determined by computer software (Analyzing Digital Images, The Regents of the University of California, CA, USA).
3.5 Mullite crystallite size calculated by Debye-Scherrer’s equation The mullite crystallite size was evaluated from line profile analysis of the 110 reflection. All the observed XRD peaks were approximated by using the Pearson VII functions in commercial software as previously mentioned (Jade, v.9, Materials Data Inc. Livermore, CA, USA). The Debye-Scherrer’s equation was employed to evaluate the mullite crystallite coarsening. The Scherrer’s constant K=0.94 was used. Therefore, in this case the Debye-Scherrer’s equation was given as below:
20 𝐿(110)= 0.94𝜆
(𝐵 𝑐𝑜𝑠 𝜃) (8)
Where B is Full Width Half Maximum of the diffraction peak, L is the thickness of crystal grain (nm), θ is the diffraction angle from X-ray diffractometer, λ is wavelength of the incident X-ray.
21
IV. RESULTS AND DISSCUSSION
“Science knows no country, because knowledge belongs to humanity, and is the torch which illuminates the world. Science is the highest personification of the nation because that nation will remain the first which
carries the furthest the works of thought and intelligence” - Louis Pasteur
4.1 Mineralogy
4.1.1 Feldspar reaction
Microcline (K-Feldspar) forms a eutectic melt with amorphous silica from the clay relics at 990°C.65 The dissolution of feldspar into the eutectic melt is not complete, however, until above 1150°C, as shown in Figure 8. This is consistent with previous work that reported of feldspar reaction completion by 1160°C.66 Based on the proposed concept of the glass formation boundary, the availability of alumina for mullite formation is limited by the solubility of alumina into the glass phase, and the amount of alumina dissolved into the glass is coupled to flux level (alkali and alkaline earth oxides; R2O + RO) in the glass.8, 16, 22
Measurements show the molar ratio of alumina: flux is 1.19 (±0.1):1.0, or 1.19 moles of alumina per mole of flux. Excess alumina, i.e., that above the solubility limit of alumina in the glass, is the only alumina available for mullite formation in a typical triaxial porcelain. Unreacted feldspar reduces both the amount of alkali and the amount of alumina for glass formation. The presence of unreacted feldspar therefore complicates the quantitative mineralogy analysis of a porcelain heat treated at or below 1150°C; therefore only data obtained at 1200°C or higher will be evaluated here.
4.1.2 Mullite formation
The mullite level (weight %) in the 43 samples heat treated above 1200°C was 25.8% (±0.4%). The data as a function of dwell time are presented in Figure 9. The data indicates that the mullite level is independent of temperature, dwell time, and heating rate, consistent with some previous works,15, 16 but not with all.8,
21, 42 Inconsistencies with other published work can be attributed to using the peak height instead of peak areas in quantitative analysis, as is addressed elsewhere.67
22
The amount of mullite expected to form based on the glass formation boundary is 26.1% (±0.3%), therefore the measured values are within the range of the predicted levels.
2 Theta
26.0 26.5 27.0 27.5 28.0 28.5 29.0
Relative Intensity (a.u)
Figure 8. X-ray diffraction pattern for porcelain samples heat treated from 1050°C to 1150°C showing residual microcline up to 1150°C but not present at 1200°C. (Heat treatment conditions: 5K/min; dwell time of one hour.)
Microcline
1050°C 1150°C
1100°C 1200°C
Fluorite
Quartz
Mullite
23
Dwell time (hour)
0.1 1 10 100
Mullite, wt. %
24 25 26 27 28
Dwell time (hour)
0.1 1 10 100
Mullite, %wt.
24 25 26 27 28
Figure 9. The amount of mullite (wt. %) (a) as a function of heating rate, dwell time and temperature with ±2 wt. % reliability (presented by dash lines). (The heating rate presented by; the fill of the symbol: solid fill, 5 K•min-1, grey fill, 20 K•min-1; and no fill, 60 K•min-1.), (b) The average mullite content calculated from samples fired at a given dwell time but different heating rates and temperatures.
(a)
(b)
1200 ˚C 1250 ˚C 1300 ˚C
24 4.1.3 Mullite crystallite size
A previous study was done by Juthapakdeepasert that proposed mullite crystallite orientated in the [110] plane coarsens as a function of temperature and dwell time.4 However, it was not reported whether the mullite crystallite size coarsened due to the effect of heating rate.Therefore, this study investigated the effect of the temperature, dwell time and heating rate on mullite crystallite coarsening.
Figure 10 and 11 show the plot of mullite crystallite size as a function of temperature, dwell time and heating rate. It was observed that temperature and dwell time are the major contributor to the mullite crystallite size coarsening compared to the heating rate.
A statistical analysis was performed to confirm the effect of temperature, dwell time, and heating rate. The analysis results reveal that the mullite crystallite size is statistically affected by the three factors. (The detail of statistical analysis results is presented in the appendix).
The contribution of heating rate, however, was small and was therefore omitted in the empirical model, so the model only addressed the roles of temperature and dwell time. As shown in Figure 11, the slopes and intercepts values of the three regression lines were calculated and used to create the model.
The three regression equations are shown in Table IV.
Table IV. The Mullite Crystallite Size as a Function of Temperature and Dwell time Temperature (°C) Slope (x·log(t)) Intercept r2
1200 7.858 +33.35 0.982
1250 7.430 +39.75 0.995
1300 7.854 +45.56 0.992
25
The relationship of mullite crystallite size (L) as a function of temperature (T, °C) and time (t, hours) can be expressed by the given equation:
𝐿(110) = {7.71 ∗ 𝐿𝑂𝐺(𝑡)} + {((0.1168 ∗ 𝑇) − 106.54)} (9)
Figure 12 is a comparison of the predicted mullite crystallite size to the measured one, showing an excellent correlation (r2 = 0.993).
Figure 13 is a contour plot showing the relationship of temperature and time (on a log basis) for Lnm allowing the mullite crystallite size to be predicted from any firing conditions. Generally, the mullite crystallite size increases with increases in temperatures at given dwell time with constant rate.
Dwell time (hour)
0.01 0.1 1 10 100
Mullite crystallite size (nm)
20 25 30 35 40 45 50 55 60
Figure 10. Mullite crystallite size measured using X-ray line broadening for porcelain samples as a function of firing temperature, dwell time, and heating rates. (The heating rates are presented by the fill of the symbol:
solid fill, 5 K•min-1; grey fill, 20 K•min-1, and no fill, 60 K•min-1).
1200 ˚C 1250 ˚C 1300 ˚C
5 K•min-1 20 K•min-1 60 K•min-1
26
Dwell time (hour)
0.1 1 10 100
Mullite thickness, nm
20 30 40 50 60
Figure 11. Mullite crystallite size thickness measured using X-ray line broadening for porcelain samples as a function of firing temperatures and dwell times regardless of heating rate. (The regression equations are presented in Table IV).
Mullite crystallite size, nm- Experiment
20 25 30 35 40 45 50 55 60
Mullite crystallite size, nm- Calculation
20 30 40 50 60
Figure 12. The mullite crystallite size—comparison of model and experimental data. The solid line is the regression line and the dash lines represent 95 % confident interval.
1200 ˚C 1250 ˚C 1300 ˚C
r² = 0.993
1200 ˚C 1250 ˚C 1300 ˚C
27
Temperature (oC)
1200 1220 1240 1260 1280 1300
Dwell time (hour)
0.1 1 10
100 60
55 55
50 50
50 50
45
45
45
45 40
40
40
40 35
35
35 30
30
Figure 13. A contour map of mullite crystallite size for a broad range of heat treatment conditions.
28 4.1.4 Quartz dissolution
Unlike mullite crystallization, which is independent of temperature, time, and heating rate. Quartz dissolution increases linearly with temperature and with a log- time dependence (Figure 14). Quartz dissolution, however, was statistically independent of the heating rate. The regression data is presented in Table V were used to generate an empirical model to predict residual quartz level in this porcelain body as a function of temperature and time. From the data collected, increasing the dwell temperature by 50K at fixed dwell time resulted in an increase in quartz dissolution by 3.0 wt. % (±0.4%).
Table V. The Quartz Dissolution Kinetics as a Function of Dwell Time Temperature (°C) Slope (x·log(t)) Intercept r2
1200 -5.534 +25.109 0.9934
1250 -5.659 +22.163 0.9904
1300 -5.824 +19.216 0.9971
The relationship of undissolved quartz (QUD) as a function of temperature (T, °C) and time (t, hours) is given by:
𝑄𝑈𝐷 = {((0.0029 ∗ 𝑇) + 2.05) ∗ 𝐿𝑂𝐺(𝑡)} + {((0.0589 ∗ 𝑇) − 60.44)} (10)
Moreover, based on the data and the model, quartz dissolution clearly exhibits a log-time dependence where a 10x increase in dwell time dissolved the same amount of quartz at 100K temperature decrease. Figure 15 is a comparison of predicted QUD to measured QUD showing excellent correlation and Figure 16 is a contour plot showing the relationship of temperature and time (on a log basis) for QUD allowing the residual quartz content to be predicted from any firing conditions. Generally, the quartz dissolution level decreases with increases in temperatures at given dwell time with constant rate.
29
Dwell time (hour)
0.1 1 10 100
Undissolved Quartz,%wt.
5 10 15 20 25 30 35
Figure 14. The quartz dissolution kinetics as a function of temperature, log- dwell time, (a) average value regardless the effect of heating rate, (b) showing the scattered data as a function of the heating rate. (The heating rates are presented by the fill of the symbol: solid fill, 5 K•min-1; grey fill, 20 K•min-1, and no fill, 60 K•min-1). (The regression equations are presented in Table V).
Dwell time (hour)
0.1 1 10
Undissolved Quartz, Wt. %
20 22 24 26 28 30 32
(a)
(b)
1200 ˚C 1250 ˚C 1300 ˚C
1200 ˚C 1250 ˚C 1300 ˚C
30
Undissolved Quartz (wt. %)-Measured
5 10 15 20 25 30 35
Undissolved Quartz (wt. %)-calculated
5 10 15 20 25 30 35
Figure 15. The quartz dissolution level—comparison of model and experimental data. The solid line is the regression line and the dash lines represent 95 % confident interval.
r2 = 0.995
1200 ˚C 1250 ˚C 1300 ˚C
31
Temperature (oC)
1200 1220 1240 1260 1280 1300
Dwell time (hour)
0.1 1 10 100
10 10
15
15
15
20 15
20
20
25 20
25
25
30 25
Figure 16. A contour map of residual quartz level (QUD) for a broad range of heat treatment conditions.
32 4.1.5 Silica level in the glass phase
The silica level dissolved in the glass phase (SiO2, UMF) was determined by using quantitative XRD results. The total amount of silica, obtained from ICP data, was subtracted out by silica in the forms of mullite and undissolved quartz.
All calculation was based on the assumption that only 3:2 mullite (3Al2O3.2SiO2) is formed. Table VI provides the steps involved in calculation of the silica level in the glass phase.
Table VI. Steps Involved in the Silica Level in the Glass Phase Calculation of the Porcelain Sample* Fired in 1200°C, 3.2 Hours of Dwell Time Regardless of Heating Rate
Items SiO2 Al2O3 Fe2O3 MgO CaO Na2O K2O TiO2
Molecular Wt. 60.09 101.9 159.7 40.30 56.08 61.98 94.20 80.90 Wt. % oxides in
the body (ICP) 69.97 24.42 0.49 0.41 0.24 0.45 2.36 0.44 Wt. % oxides in
crystalline forms**
30.33 18.62 - - - -
Proportion of oxide in glass phase
39.64 5.80 0.49 0.41 0.24 0.45 2.36 0.44 Moles of oxide
in glass phase 0.660 0.057 0.047
UMF of glass
phase 14.11 1.22 1.00
* The porcelain sample composed of 25.94 % mullite, 23.02 % undissolved, and 51.04% glass.
** Mullite composed of 71.79% of Al2O3 and 28.21% SiO2 (wt. %). Therefore, 25.94 wt. % Mullite composed of 18.62% Al2O3 and 7.31% SiO2. The total silica in the crystalline form is the summation of % silica in mullite and undissolved quartz.
It can be seen from Table VI that subtraction of alumina and silica presented in the crystalline forms (mullite and undissolved quartz) gives the level of silica and alumina in the glass phase which is then converted to moles.
Normalizing the moles of each oxide with the sum of moles of flux gives the UMF of the glass phase.
33
The silica level in the glass phase (SiO2, UMF) result was used to establish a model. The three regression lines were plotted (as presented in Figure 17). Their slopes and intercepts were used to create the model. The three regression equations are shown here:
Table VII. Silica Level into the Glass Phase as a Function of Temperature and Time
Temperature (°C) Slope (x·log(t)) Intercept r2
1200 1.975 +13.37 0.992
1250 2.000 +14.42 0.992
1300 2.038 +15.47 0.997
The relationship of silica level in the glass phase (SiO2, UMF) as a function of temperature (T, °C) and time (t, hours) can be expressed by the given equation:
𝑆𝑖𝑂2,𝑈𝑀𝐹 = {((−0.00063 ∗ 𝑇) + 1.22) ∗ 𝐿𝑂𝐺(𝑡)} + {((0.021 ∗ 𝑇) − 11.83)} (11)
Figure 18 is a comparison of predicted QD to measured QD showing excellent correlation with r² = 0.999.
Figure 19 is a contour plot showing the relationship of temperature and time (on a log basis) for 𝑆𝑖𝑂2,𝑈𝑀𝐹 allowing the silica in glass phase to be predicted from any firing conditions. Generally, the silica level increases with increases in temperatures at given dwell time with constant rate.
34
Dwell time (hour)
0.1 1 10 100
Silica in glass phase, UMF
10 12 14 16 18 20
Figure 17. Silica level in the glass phase (UMF) of porcelain samples fired at different temperatures, dwell times, and heating rates. (The regression equations are presented in Table VII).
Silica in the glass phase, UMF-Experiment
11 12 13 14 15 16 17 18 19
Silica in the glass phase, UMF-Calculated
10 12 14 16 18 20
Figure 18. The quartz dissolution level—comparison of model and experimental data. The solid line is the regression line and the dash lines represent 95 % confident interval.
r² = 0.999
1200 ˚C 1250 ˚C 1300 ˚C
1200 ˚C 1250 ˚C 1300 ˚C
35
Temperature (oC)
1200 1220 1240 1260 1280 1300
Dwell time (hour)
0.1 1 10 100
19
18 18
18 17
17
17
17 16
16
16
16 15
15
15
15 14
14
14
14 13
13
12 13
Figure 19. A contour map of silica level dissolved in the glass phase (𝑆𝑖𝑂2,𝑈𝑀𝐹) for a broad range of heat treatment conditions.
4.1.6 Mullite crystallite coarsening versus glass chemistry
Figure 20 presents a contour map of the mean mullite crystallite size and silica level (on a molar ratio basis) in the glass phase as a function of temperature and dwell time. The contour plot demonstrates that the two processes have different kinetics. This should be expected based on the underlying mechanisms for quartz dissolution (Si4+ diffusion, since quartz dissolution is a diffusion- controlled process 68) and mullite crystallite coarsening is controlled by the diffusion of Al3+. This plot indicates that it should be possible to uniquely determine the firing conditions of a porcelain sample by measuring the mullite crystallite size (via X-ray line broadening) and the chemistry of the glass phase.
36
Temperature (oC)
1200 1220 1240 1260 1280 1300
Dwell time (hour)
0.1 1 10 100
55 55
50 50
50 50
45
45
45
45 40
40
40
40 35
35
35 30
30
18
17 17
17 16
16
16
16 15
15
15
15 14
14
14
14 13
13
12 13
Figure 20. The contour plot showing the mean mullite crystallite coarsening and silica dissolved into the glass as a function of temperature, and dwell time. The slopes present the difference of diffusion kinetics of both processes.
4.2 Validation of the glass formation boundary
It has been demonstrated that the glass formation boundary is applicable for the commercial porcelain body fired over the industrial firing temperature range of about 1200-1400ºC. It was also observed in this study as well. The level of alumina dissolved into the glass phase is shown in the K2O-Al2O3-SiO2 ternary phase diagram.
Figure 21 shows a plot of the amount of alumina dissolved in the glass phase which was calculated by subtracting out the amount of alumina that was used to form mullite. The Al2O3 :( R2O+RO) molar ratio for this work remained constant at 1.24(±0.06) alumina over the temperature range 1200-1300 °C.
Silica in the glass phase (UMF) Mullite crystallite size (nm)
37
However, it was slightly different compared to the glass formation boundary which was previously proposed of 1.19(±0.1).8
Mullite
0 10 20 30 40 50 60 70 80 90 100
Quartz
0 10 20 30 40 50 60 70 80 90 100
Leucite
0
10
20
30
40
50
60
70
80
90
100
Figure 21. Glass formation boundary on the typical porcelain composition region of the K2O-Al2O3-SiO2 ternary phase diagram—from this experiment.
Figure 21, moreover, presents the effect of the temperature, dwell time, and heating rate. It can be seen that the glass formation boundary is independent of temperature, dwell time, and heating rate over the temperature range of 1200- 1300 °C.
Meta-Kaolin Mullite Phase Field
K-Spar
Cristobalite-Tridymite-Mullite Invariant Point
1200 ˚C 1250 ˚C 1300 ˚C
38 4.3 Densification
4.3.1 Skeletal or “True” Density
In order to evaluate the densification behavior and to determine the density of the glass phase and compare the results directly to the mineralogy, samples were crushed to a fine particle size then measured using a pycnometer method.
Crushing the sample would ideally eliminate any closed porosity, commonly present in all sintered porcelain bodies as full density is reached. As the amount of mullite is constant, the true density decreases slightly with increasing temperature and time due to the dissolution of quartz into the glass phase due to the density difference between quartz and glass. Previous work reported a glass density of 2.37 ±0.02 g·cm-3.69 Once feldspar reaction and mullite formation are complete, observed in this study to be above 1200°C, the true density would be expected to be nearly constant but decrease with quartz dissolution.
Figure 22 shows the change in true density as a function of dwell time for the different dwell temperatures and heating rates. This shows that density does decrease with increasing quartz dissolution (both via dwell temperature and time), and that the decrease is not insignificant. Statistical analysis supports the conclusion that true density is independent of heating rate over the range of this study.
4.3.2 Calculated Density Based on Mineralogy
The rule of mixtures, using weight percent and specific volume, was used to calculate the density based on the mineralogy. In addition, with the quartz dissolution data, the density of the glass phase can be calculated by comparing the calculated density with the true density data. Figure 23 presents the glass phase density as a function of dwell time for the different dwell temperatures and heating rates showing that the glass phase density is constant at 2.36 (±0.02) g·cm-3 which is in excellent agreement with the previously reported value of 2.37 (±0.02) g·cm-3.
Moreover, the rule of mixture was also used to calculate the density of porcelain samples. For example, a sample heat treated at 1250°C for 3.2 hours at a heating rate of 20 K·min-1 was composed of 25.3% mullite, 20.5% quartz, and