Thermal stress and failure of ceramic materials during thermal processes are the important factors for selecting heating or cooling schedules of their uses and manufacturing
In this paper, the authors propose the method for calculating transient thermal stresses in elastic bodies during thermal processes with the schedules of the following type.
(Constant initial temperatures θ_i)→(Heating or cooling at constant rates k)→(Final constant temperatures θ_f)
The bodies were assumed to be spheres, infinite cylinders and infinite plates in shape, respectively. Newton's law was applied for the heat transfer between the surfaces of the bodies and the surrounding mediums.
The calculations were performed with the computer and the maximum thermal stresses at surfaces or at centers of the bodies were shown graphically in dimensionless form. Refering tensile strength and some other physical properties of a brittle material to the figures, one can determine the maximum rate k_max for faultless heating or cooling of the material.

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Studies on crystal growth of wollastonite (β-CaSiO₃) were attempted by slow cooling from NaCl flux.
The solubility of CaSiO₃ in NaCl was very low with 0.09 wt% at 1010°C and 0.42 wt% at 1190°C. The mixtures consisting of the 2-3 wt% of synthetic wollastonite in NaCl of 20-45g, in excess to its solubility, in the Pt crucible were soaked for 0-24 hours at 1080°-1200°C and then cooled to about 800°C with a rate of 5°C per hour.
On crystal growth from above 1125°C, both crystals of pseudowollastonite (α-CaSiO₃) and wollastonite were obtained, the former was stable above 1125°C and the latter was stable below 1125°C.
The wollastonite crystals grown by a soaking at 1200°C for 24 hours were large in size and small by number, for they would have grown from only a few spontaneous nuclei on the upper wall of the crucible. For the soaking at 1150°C, it was found that they were small in size and large by number. These seemed to be formed from much nuclei from the unsolved residues which were excess to its solubility in the bottom of the crucible.
The wollastonite crystals, needle-shaped as large as 6mm in length and 0.3mm in diameter, were grown along b-axis and they took usually single crystal and sometimes twinned crystal.

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The phase equilibrium of 3CoO⋅Al₂O₃⋅3SiO₂-3Y₂O₃⋅5Al₂O₃ system was determined by using the quenching technique and the heating and cooling method. A silicon carbide furnace, a platinum-rhodium strip furnace and a solar furnace were used to heat the specimens. The system 3CoO⋅Al₂O₃⋅3SiO₂-3Y₂O₃⋅5Al₂O₃ is actually a quasi-two component system under the atomospheric pressure, because cobalt garnet is only stable under high pressure [T. Noda and M. Ushio, this journal, 75 125 (1967)]. Mixtures of SiO₂, Al₂O₃, Y₂O₃ and CoO or premelted glass specimens having the compositions of x(3CoO⋅Al₂O₃⋅3SiO₂)+[(1-x)/2] (3Y₂O₃⋅5Al₂O₃), where x was the weight fraction, were kept at temperatures ranging from 1100° to 1900°C for 1-60 hr under the atmospheric pressure and then quenched. The quenched specimens were examined by the X-ray diffraction method and also under a polarizing microscope. Carnet was the only crystalline phase in the quenched specimens of x=0.00-0.30. The lattice constant of the garnets decreased continuously with x, indicating that the continuous solid solution of garnet was formed.
Carnet was formed coexisted with spinel, Y₂O₃-SiO₂ mineral and cristobalite in the specimens of x=0.30-0.41 quenched from temperatures below 1250°C. Garnet and spinel were found in the specimens quenched from temperatures between 1300° and 1500°C. Above 1520°C garnet was the only stable crystalline phase.
In the quenched specimens of x=0.41-0.46, spinel was found to be the only crystalline phase above 1520°C, garnet separated below 1520°C and cristobalite separated below 1300°C. Spinel, garnet and cristobalite coexisted with Y₂O₃-SiO₂ mineral below 1250°C.
In the specimens of x=0.49-0.63 quenched from temperatures below 1270°C spinel, cristobalite, Y₂O₃-SiO₂ mineral and a small amount of unidentified mineral were obtained, but no garnet was found.
In the specimens of x=0.72-0.99 quenched at temperatures below 1270°C, spinel, cristobalite, olivine and a small amount of unidentified mineral were observed. It seemed that spinel, cristobalite, olivine and Y₂O₃-SiO₂ mineral were stable below 1270°C. in the composition range of x=0.49-0.99. Above. 1300°C, spinel was the only crystalline phase, and between 1300°C and 1270°C, spinel and cristobalite coexisted.
In the case of x=1.0, i, e, cobalt garnet composition, spinel, olivine and cristobalite were found to be stable in specimens quenched at temperatures below 1270°C. Above 1270°C olivine disappeared and cristobalite disappeared above 1300°C. Spinel melted at 1424±4°C.
The liquidus temperature increased with the decrease in the fraction of cobalt garnet composition, passing a maximum at 1600°C around x=0.50-0.48, also minimum at 1500°C around x=0.41-0.42, then increased to 1913±15°C of yttrium aluminum garnet.

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The development of enstatite by solid state reaction in mixed powders of forsterite and SiO₂ in various mole ratios at the temperature range 1150°-1350°C and for times up to 580 hrs is followed by quantitative X-ray measurements. Powders are used consisting of coarse (mostly 10μ) particles of one component in a fine-grained (mostly 1μ) matrix of the other component. Although the results are not precisely consistent with a diffusion-controlled mechanism, the rate of reaction is estimated to be about one-third (or even smaller) of that of MgO-SiO₂ reaction.
Studies, using mixed powder, indicate the development of enstatite on the forsterite side as well as on the SiO₂ side, suggesting that one MgO of 2MgO⋅SiO₂ reacts with SiO₂. Mg is believed to be the main diffusing species.
The results of firing in vacuum suggest that the reaction is possibly controlled by the diffusion of Mg ion through the enstatite.
Putting all results obtained by our previous and present works together, the rate of reactions of the systems containing MgO and SiO₂, i.e. MgO-SiO₂, MgO-MgO⋅SiO₂ and 2MgO⋅SiO₂-SiO₂, is conceivable to be controlled by the diffusion of Mg through the reaction product layer (s).

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