On the Thickness Ratio of Two Spinel Layers Formed by Solid State Reaction

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 Mg4/(3n+1) Al8n/(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 asR=l(Al2O3-side)/l(MgO-side)=3(7n+1)/3n+5The 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 ask/D=256(n-1)(3n+1)2/(21n+11)(3n+5)(7n+1)In case of AiOj⋅BpOq formation from AiOj and BpOq 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 AiOj and BpOq were expressed by Ami(j+q)/mj+qBp(j+q)/mj+qOj+q(=mAiOj⋅BpOq) and Ai(j+q)/j+nqBnq(j+q)/j+nqOj+q(=AiOj⋅nBpOq) respectively, they were formulated as follows:R=l(BpOq-side)/l(AiOj-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)