ペロブスカイト3成分系固溶体の組成変動領域の最小二乗法による決定法

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A method for an estimation of the compositional fluctuation area in ternary solid solution was developed. An elliptic area of the compositional fluctuation which is defined by constants, A, B and φ, was assumed in a ternarydiagram. The maximum and minimum lattice spacings in the assumed area were figured out for several lattice planes. Values of (Δd/d)_i^<cal> fluctuations of the lattice spacings, were calculated from these values. Values of β, which is the net width of the X-ray diffraction peak of the sample, were measured and the values of β cos θ were plotted against sin θ. Theoretically, each plot is on a line whose section at sin θ=0 is fixed by the crystallite size of the sample and whose slope is Δd/d. The section was determined by the least square method using (Δd/d)_i^<cal> estimated from the assumed elliptic area. The Σe_i^2, a sum of squares of the difference between the calculated value of β cos θ and the observed one, was determined. The values of Σe_i^2 were evaluated for various values of A, B and φ systematically. The values of A, B and φ which give the minimum value of Σe_i^2 were finally determined. The area which is settled by the values of A, B and φ determined thus is the compositional fluctuation area. The compositional fluctuation areas such determined agreed with those determined by the method reported previously. By this method, the compositional fluctuation area can be determined without data of diffractions whose dependence of lattice spacing on composition is the same, while it could not be determined by the previous method.
社団法人日本セラミックス協会の論文
1997-05-01

ペロブスカイト3成分系固溶体の組成変動領域の最小二乗法による決定法

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