DETERMINATION OF THE COMPOSITIONAL FLUCTU ATION AREA IN TERNARY PEROVSKITE SOLID-SOLUTIONS USING LEAST-SQUARE METHOD

A method for an estimation of the compositional fluctuation area in te rnary solid solutions was developed. An elliptic area of the compositi onal fluctuation which is defined by constants, A, B and phi, was assu med in a ternary diagram. The maximum and minimum lattice spacings in the assumed area were figured out for several lattice planes. Values o f (Delta d/d)(i)(cal), fluctuations of the lattice spacings, were calc ulated from these values. Values of beta, which is the net width of th e X-ray diffraction peak of the sample. were measured and the values o f beta cos theta were plotted against sin theta. Theoretically, each p lot is on a line whose section at sin theta=0 is fixed by the crystall ite size of the sample and whose slope is Delta d/d. The section was d etermined bq the least square method using (Delta d/d)(i)(cal) estimat ed from the assumed elliptic area. Then Sigma e(i)(2), a sum of square s of the difference between the calculated value of beta cos theta and the observed one. was determined. The values of Sigma e(i)(2) were ev aluated for various values of A, B and phi systematically. The values of A, B and phi which give the minimum value of Sigma e(i)(2) were fin ally determined. The area which is settled by the values of A, B and p hi determined thus is the compositional fluctuation area. The composit ional fluctuation areas such determined agreed with those determined b y the method reported previously, By this method, the compositional fl uctuation area can be determined without data of diffractions whose de pendence of lattice spacing on composition is the same, while it could not be determined by the previous method.