The modulated structure of intermediate plagioclase feldspar CaxNa1−xAl1+xSi3−xO8

The modulated structure of labradorite (An52) has been refined within the harmonic approximation using the intensity data collected by Klein [Horst, Tagai, Korekawa & Jagodzinski (1981 ). Z. Kristallogr. 157, 233-250]. The analysis is based on the fourdimensional triclinic space group with centering translations which is group-theoretically equivalent to PP~. The restricted least-squares method with two kinds of penalty functions has been employed to keep the occupation probability and the bond lengths within crystal-chemically reasonable ranges. This method gave smooth convergence of the R factors from 0-207 to 0.065 for 1633 observed main (a) and from 0-83 to 0.094 for 3102 observed e~-satellite reflections after 18 cycles. The average bond distances between the tetrahedral A1/Si and four neighboring O atoms show distinct periodic substitutions of A1 and Si, while the substitutional modulation of the Ca/Na site is weak. These results are consistent with the model proposed by Kitamura & Morimoto [Phys. Chem. Miner. (1977), 1, 199-212]. With the anharmonic terms taken into account, a reasonable interpretation of the diffraction aspect of the higher-order satellite reflections has been made by the present structure determination and the phase fluctuation of the modulation waves, which is important in evaluation of the higher-order satellite intensity. The present results indicate that the most probable structure of labradorite is a modulated structure with albite-like (An2o) and anorthite-like (Anso) regions. The anorthite-like regions in an antiphase relation are coherently separated by the albite-like regions.