K. Kakegawa et al., DETERMINATION OF THE COMPOSITIONAL FLUCTU ATION AREA IN TERNARY PEROVSKITE SOLID-SOLUTIONS USING LEAST-SQUARE METHOD, Nippon Seramikkusu Kyokai gakujutsu ronbunshi, 105(5), 1997, pp. 418-423
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.