The exposed closed pores can be found on the surface of particles after passing through 40 and 140 mesh sieves with mesh sizes of 425 and 105 μm, respectively. The predicted porcelain body mineralogy shows good correlation compared to QXRD mineralogy (A) with an overall. Compared to measured mineralogy via QXRD, the predicted mullite level is higher and the corundum level is lower.
This thesis proposes that quantitative mineralogy can be reasonably predicted from easily measured material properties (such as density and coefficient of thermal expansion) using a volume-based rule of mixtures (ROM). Obtaining the mineralogy of a two-component system is easy from a single property, but obtaining the mineralogy of a three-component system requires two measurements of the properties. The predicted mineralogy was compared with results obtained using QXRD via an internal standard method.
It is proposed that this approach can predict the mineralogy of systems composed of more than three components (n=3) using n-1 measured properties or constraints (such as chemistry).
INTRODUCTION
BACKGROUND
Rule of Mixture
Mineralogy predicted by two measured properties
From the above three equations, the volume fraction of each phase can be calculated using Cramer's rule:8.
Mineralogy predicted by one measured property with starting
As shown in the triaxial diagram (Figure 7), the result is the point of intersection between the measured properties. On the other hand, compared to the stoichiometric starting chemistry, the final mineralogy of the C component and excess B can be formed by the reaction of a smaller amount of the A phase as starting material. The parameter 𝑎 is the number between 0 and 1, which represents the mineralogy of the initial and final mineralogy.
As a first theory, the measured characteristic can be plotted as a linear line on the ternary diagram. Parameter 𝑏 is the number between 0 and 1, representing the different mineralogy with the same property. The mineralogy of the material can be fixed at one point which is the intersection of the chemistry constraint and measured property (Figure 8).
Properties
In this approach, slip casting is used to prepare a green body, where each component can be oriented randomly in the sample. The requirements of these two properties in the ROM approach are listed in Table II.
Experimental approach
EXPERIMENTAL PROCEDURE
Raw Materials Selection and Chemical Composition
This simple reaction follows that one mole of each alumina and magnesium oxide can synthesize one mole of spinel. The final mineralogy of this spinel synthesis can be calculated as 16.28% excess magnesium oxide with 83.72% spinel. The results of the chemical analysis measured for all the raw materials used are listed in Table IV.
All samples were prepared by slip casting in gypsum molds and fired in air in a MoSi2 furnace (DT-31-RS-14, Deltech Inc., Denver, CO, USA) at a heating rate of 5K/min with one hour attitude. the time.
Analyses
Helium pycnometer
Dilatometer
X-ray Diffraction
RESULT AND DISCUSSION
Porcelain
Consequently, clays such as kaolinite (Al2O3·2SiO2·2H2O) are among the starting materials commonly used in mullite. Measured density may be lower from testing larger particles with closed porosity inside, which increases the volume of the sample. The linear thermal expansion is calculated by fitting a linear trend line to the percentage linear expansion with temperature plot from 200oC to 500oC range for all samples.
The linear thermal expansion of a porcelain body (Figure 14) increased suddenly due to the α-β quartz inversion at 573oC. Comparison of the total area of the peaks for each phase with that of the CaF2 standard gives the volume percentage of that phase in the body. In these equations, y is the peak area of the phase divided by the peak area of the standard and x is the volume percentage of the phase.
The composition of the glass phase (in the porcelain/mill system) and the spinel phase (in the spinel system) are obtained from the balance of the other two phases. The properties of a porcelain body follow the requirements for the ROM approach, which density and C.T.E. Mineralogy of porcelain samples fired from 1200oC to 1500oC. Measured and calculated densities and C.T.E. based on mineralogy analyzed by QXRD) are shown in Figure 17 and 18 as a function of temperature.
The cross between density (solid blue line) and C.T.E. pink dashed line) is the predicted mineralogy by volume. The mineralogy obtained by QXRD and the ROM approach on a mass fraction basis is shown in the ternary diagram (Figure 20A). The mineralogy predicted for the porcelain body shows good correlation compared to the QXRD mineralogy (A) with an overall correlation coefficient r B .
Mullite
The mullite phase cannot be found in the XRD pattern below the synthesis temperatures for the AC and AS routes. The QXRD mineralogy for mullite samples in the temperature range 1200oC- 1500oC is shown in Figure 23. The amount of glass phase is balanced by the difference of fractions of mullite and corundum phases.
The predicted mineralogy in the 1250oC-1350oC temperature range cannot be found (no crossover) from the ROM calculation (Figure 26). To understand the problem of mullite samples under this temperature range, the XRD pattern (Figure 27) is examined to find any impurities contained in the mullite samples. The small amount of cristobalite is found in all three initial compositions under this temperature range, which also exists in previous works.24,29 The cristobalite phase exists from 1250oC and disappears at 1400oC (Figure 28) due to the reaction with corundum.
The density value of cristobalite (2.32 g/cm3) is slightly lower than the glass phase (2.39 g/cm3), so limited error is generated. After including this unexpected phase in the ROM calculation for density and C.T.E., the offset values between measured and calculated can be corrected (Figures 29 and 30). Below the temperature range where cristobalite is present, the mineralogy is no longer three components, but four components.
In conclusion, if the mineralogy cannot be predicted through the ROM approach, it may be that the mineral phase of the impurity contributes to the measured properties. Measured and predicted clay–alumina reaction mineralogy in a mass-based ternary diagram (A) and comparison (B). From previous research, the coefficient of thermal expansion of glass decreases with increasing molar percentage of silica and alumina (Figure The molar percentage of silica and alumina of the glass phase are similar for porcelain (94.0%) and mullite (97.0%) bodies in this study.
The large difference in elastic modulus between the components can also be a problem, but it is assumed that it contributes to the small impact after C.T.E.
Spinel
The mineralogy of spinel synthesis via the reaction of aluminum and magnesium oxide can be analyzed by QXRD (Figure 37). At 1600oC the synthesis reaction is almost complete and the main phases in the sample are spinel and excess magnesium oxide. The aluminum and magnesium oxide compounds are reduced with increasing temperature to synthesize spinel.
The mineralogy of the spinel sample predicted by this ROM approach is shown in Figure 40 with a correlation coefficient of 0.927. The spinel system is a promising experiment for this approach because the mineralogy can also be obtained from its chemical constraint with only one measured property. The formation of magnesium aluminate spinel can be synthesized by a simple chemical reaction of magnesium oxide with calcined alumina (Equation 18).
With higher or lower Al2O3/MgO ratio than starting chemistry, the final products may be spinel with excess alumina or magnesium oxide. Therefore, it may be possible to determine the mineralogy of C.T.E. or density) measurements in conjunction with the chemistry, thus eliminating the need for additional property measurements. Using measured density values with starting chemistry (40 wt% magnesium oxide- 60 wt% alumina), the mineralogy can be predicted on the ternary lattice diagram (Figure 42A) compared to the QXRD analysis on a mass fraction basis.
The accuracy of this ROM approach drops significantly under these circumstances because a small difference in measured C.T.E. values can remarkably change the predicted mineralogy. The grids formed by chemical constraints and C.T.E. values increasing consistently, which disobeys the second requirement of the ROM approach. The mineralogy calculated via chemistry and C.T.E. in the spinel system is not taken into account as it does not comply with the second requirement of this approach.
The chemistry constraint can be used in predicting mineralogy, but it must also meet the above requirements. Other three-component materials, such as the Ca2SiO4 and PbTiO3 systems, can also be analyzed via this ROM approach from either two measured properties or one property with the initial chemistry. Conceptually, it should be possible to apply this technique to systems consisting of more than three components, but it may be necessary to include a third parameter, such as the onset of chemistry in a simple density reaction and C.T.E.
For example, the elastic modulus (E) can be corrected if the volume of porosity in the sample can be measured (Equation 20). The measurement error also affects the prediction result; with a higher measurement reliability, the standard deviation of the predicted mineralogy will be lower.
