Mixing function of glass-melting tank is of most important for obtaining high homogeneity of glass. It was assumed that the mixing process developing in glass tank is a kind of diffusion process which is caused by mixing action mainly resulting from thermal and mechanical currents. A fundamental differential equation involving the “mixing diffusion coefficients”, k_x, was proposed for discussing the mixing charater of a given tank.
The numerical value of k_x could be computed by applying a few practical values such as the dimension of tank, the axial mean velocity of glass flow and the time spent till the tracer concentration gets a maximum, T_max, to an equation obtained one of the solutions of the differential equation mentioned above.
Variation of any physical value of glass pulled out during operation is characteristically affected by the values of k_x and pull rate imposed on the tank. Hence, the featuer of the physical value-time curve is characterized by k_x and T_max as the factors dominantly controlling the mixing effect of glass tank, which gives some fruitful suggestions concerning the mixing character of the tank.

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ジルコニア材料を高温で使用するとき, CaOが表面から選択的に蒸発して不安定化され, 表面に応力を生じる. これを明らかにする目的で, ZrO₂-CaO (5-25mole%) 2成分系焼結体 (2,100℃) をタングステン炉の1,900°-2,100℃で7×10^-5mmHgの真空中で加熱し, CaOの蒸発 (ZrO₂は2,100℃で僅か蒸発) を自由蒸発法で測定した. 蒸発による重量減少速度は最初の20分で急激に低下してゆるやかになる. したがってこの方法では蒸気圧を正確に求めることはできなかった. 蒸発後の試料を研摩しながら, 表面のCaを蛍光X線分析により測定して濃度分布を求めた. 表面のCa濃度は時間とともに急激に減少し, 20-60μの深さまで分布が生ずる. 蒸発速度は早く, それが内部から表面へのCaの拡散速度に律速されることが判ったので, この濃度公布からCaの拡散係数を各初期濃度について求め
D_Ca=0.0116exp
[-(82,100-440c)/RT]cm²・sec^-1
を得た. cはCaOのmole%である.

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The thickness ratio of two spinel layers formed by solid state reaction was investigated theoretically by considering each composition of two layers and the diffusion flux of cations through the original reaction interface. The reaction in MgO-Al₂O₃ system was examined under the following conditions; (1) thermodynamic equilibrium prevails at the phase boundaries, (2) spinel of the composition MgAl₂O₄ (=MgO⋅Al₂O₃) is in equilibrium with MgO wheress spinel of the composition Mg_4/(3n+1) Al_8n/(3n+1) O₄ (=MgO⋅nAl₂O₃) is in equilibrium with Al₂O₃, and n is larger than 1.0 because of the large solubility of Al₂O₃ in spinel, (3) the concentrations of Mg²⁺ and Al³⁺ in the spinel layer are linear functions of the distance from the interface, and (4) spinel is formed by interdiffusion of Mg²⁺ and Al³⁺ and the interdiffusion coefficient D is approximately constant in the spinel layer.
As a result of the investigation the thickness ratio, 1: R, was derived as
R=l(Al₂O₃-side)/l(MgO-side)=3(7n+1)/3n+5
The experimental thickness ratios of two spinel layers were compared with theoretical values as a function of temperature as shown in Fig. 4, and is was proved they agreed well. The relation between the rate constant, k(cm²/sec), and the interdiffusion coefficient in the spinel layer, D (cm²/sec), was also investigated and it was derived as
k/D=256(n-1)(3n+1)²/(21n+11)(3n+5)(7n+1)
In case of A_iO_j⋅B_pO_q formation from A_iO_j and B_pO_q the thickness ratio of two layers and the relation between k an D were investigated on the basis of the similar assumption. When the compositions of products on the contact faces with A_iO_j and B_pO_q were expressed by A_mi(j+q)/mj+qB_p(j+q)/mj+qO_j+q(=mA_iO_j⋅B_pO_q) and A_i(j+q)/j+nqB_nq(j+q)/j+nqO_j+q(=A_iO_j⋅nB_pO_q) respectively, they were formulated as follows:
R=l(B_pO_q-side)/l(A_iO_j-side)=q(mnj+2nq+j)/j(mnq+2mj+q)
k/D=16(mn-1)(mj+q)²(nq+j)²/(mnjq+2mj²+2nq²+3jq)(mnq+2mj+q)(mnj+2nq+j)

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In corrosion of mullite or zircon by alkali carbonate, alkali sulfate and alkali chloride vapor, respectively, there were difference to corrosion products and its mechanisms.
The difference was raised from the acid radical components of alkali sulfate and alkali chloride. That is, in the first stage the alkali oxide component (Na₂O or K₂O) reacted with mullite or zircon, and next the acid radical component decomposed these reaction products into glass and the other compounds. Consequently, for example, in corrosion of mullite by sodium carbonate vapor, most corrosion products were carnegieite-sodium aluminate s.s., but in that by sodium sulfate and sodium chloride vapor, respectively, the needlelike crystals of corundum produced remakably with glass.
In the cases of corrosion of mullite by potassium salts vapor and of zircon by sodium salts vapor, there also were similar difference.
Their corrosions by alkali chloride vapor were very analogous to that by alkali sulfate vapor.

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A new predictive densification equation of pressure sintering during final stage is proposed. Geometrical models by which the expressioni isderived are polyhedral space filling bodies, e.g. tetrakaidecahedron and rhombic-dodecahedron, and pores which are surrounded by corners of the bodies.
It is also assumed that the densification occurs by the transport of lattice vacancies from the neighborhood of a pore to adjacent grain boundaries and concentration gradient of the vacancies are simply proportional to compressive stress at flattend contact face of the body.
If the size of contact area can be expressed as a function of porosity, effective stress (σ_e), that is, the compressive stress may be formularized as σ_e=σ_a⋅f(P) where σ_a and f(P) are applied stress and a function of porosity, respectively. From geometrical considerations of the models, a general expression is obtained as,
A=S(1-KP^2/3)
where, A is a size of contact areas per polyhedron, S is a constant equals total surface area of polyhedron at zero porosity, K is also a constant differs in different polyhedron and P is porosity.
Furthermore, this equation can be simplified as,
A′=(1-P)^3/2 when P<0.3,
where A′=(A/SK)-[(1/K)-1.05]
A linear relationship between A and (1-P)^3/2, therefore, would be expected.
Then, effective stress may be given as,
σ_e=σ_a/(1-P)^3/2
It was found the results obtained by Coble and Kingery relating the torsional creep of poly-crystalline alumina to the amount of porosity present, plotted as strain rate versus 1/(1-P)^3/2, a close approximation to a straight line was obtained.
An isothermal densification equation, derived from a combination of Nabarro-Herring diffusional creep equation and the effective stress, is given as,
dρ/dt=10σ_aDΩ/R²kTρ^1/2 or ρ^3/2=30σ_aDΩt/2R²kT+const.
One may predict linear relationship between dρ/dt and ρ^-1/2 as well as ρ^3/2 and t (time).

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