THE DETERMINATION OF UNIT-CELL PARAMETERS FROM BRAGG REFLECTION DATA USING A STANDARD REFERENCE MATERIAL BUT WITHOUT A CALIBRATION CURVE

The procedure for determining unit-cell parameters from Bragg reflecti on data, using a standard reference material but without a calibration curve, is described. In this procedure, the observation equations for both the sample to be measured (SMP) and a standard reference materia l (SRM) are solved simultaneously and the unit-cell parameters and a f orm of error function are determined during the least-squares calculat ion. The theory, which was first proposed as a linear least-squares pr ocedure [Toraya & Kitamura (I 990). J. Appl. Cryst. 23, 282-285], has been extended to create a nonlinear least-squares procedure. The proce dure can be used in two different ways. In one approach, the unit-cell parameters of the SMP and the parameters in the error function are re fined while the unit-cell parameters of the SRM are fixed during the l east-squares calculation. This procedure requires knowledge of the wav elength but it gives a stable solution and the tangent term in the err or function gives a perfect correction for the error in wavelength. In the other approach, the unit-cell parameters of both the SMP and the SRM are refined, together with the parameters in the error function. T he procedure does not require knowledge of the wavelength. The solutio n, however, became unstable when the correlation was strong between th e unit-cell parameters and the error function and careful selection of the error function was required. The first approach gave the same res ult as the second and is, therefore, more practical to use. Since the form of the angle-dependent error function is determined using reflect ion data from both the SMP and the SRM, just one or two reflections fr om the SRM were enough for the correction of systematic error. The pro cedure, coupled with high-precision reflection data, can determine acc urately the unit-cell parameters in a routine analysis.