Some statistical results for structures with pseudosymmetry

Abstract

The values of the second, third and fourth-order moments of the normalized intensity z and the maximum probable values of two types of discrepancy index, namely RB and R2, are worked out for various types of pseudosymmetric structures considered by

Effects of misplaced atoms on the residualR2in space groups of higher symmetry

“…one thus takes into account the actual average of the calculated intensity for the atoms whose positions are supposed known, and the average to be expected on statistical grounds for the atoms whose positions are unknown. The procedure of Parthasarathi & Parthasarathy (1975), following Srinivasan & Ramachandran (1965), goes some way towards this, but is not identical with it. Refining the scaling factor by least squares would seem to be unjustifiable, since the value obtained is known to be biased by 'defects in the model', which missing or misplaced atoms certainly are.…”

“…A recent paper by Parthasarathi & Parthasarathy (1975) appears at first sight to be dealing with the same questions, but there are two important differences. First, they use a scaling factor that makes the average intensity for a partial structure equal to the average value for the full structure when some of the atoms are omitted because, for example, their positions are unknown.…”

Discrepancy indices for use in crystal structure analysis. III. A theoretical comparison of the normalized indices

“…:I: A recent study of the 8R,(I) index for structures with heavy atoms has shown that this R index could have a larger value for the NC case than for the C case under certain circumstances (for details see the last paragraph in Parthasarathi & Parthasarathy, 1975).…”