A simplified criterion for the reliability of a powder pattern indexing

Abstract

A figure of merit is defined for an indexing of a given pattern as M20 = Q2o/2gN2o. Here N_,0 is the number of different calculated Q values up to Q20, which is the Q value for the 20th observed and indexed line;is the average discrepancy in Q for these 20 lines. From a number of indexings which have been disproved by single-crystal analysis, the conclusion is drawn that M20 < 6 must give rise to considerable doubt about the result. A number of confirmed indexings shows values of 20-60 for good routine work on pure, well-crystallized samples, and down to 6 for retrievable correct indexings of less accurate data. If the number of unindexed lines below Q20 is not more than two, a value M:0 > 10 guarantees that the indexing is substantially correct.

Theoretical study of a five-coordinated silica polymorph

“…Every peak could then be indexed under this symmetry with a very high figure of merit of 214. 58 The space group was found to be P3 2 21 (No.154) within a tolerance of 0.0038 Å. This is identical to the space group of ␣-quartz.…”

Structure Refinement of the Semiconducting Compound Cu3TaS4from X-Ray Powder Diffraction Data

“…215). The entire powder diffraction dataset of Cu 3 TaS 4 was reviewed by means of the NBS*AIDS program [18] with the following results: a = 5.5149(1) Å, V = 167.73(1) Å 3 , and figures of merit M 20 = 340.6 [19] and F 26 = 190.3 (0.0053, 26) [20]. X-ray powder diffraction data of Cu 3 TaS 4 are given in Table I.…”

Structural exploration on powder diffraction a nice tool for rexamination of phase diagram

“…The solutions determined by both programs are very similar: a= 12.688Å; b= 9.198Å, c= 5.985Å, V= 698.43Å 3 , with a figure of merit M 20 =25.0 [10] and M 20 =85.0 respectively for Treor and Dicvol. The structure solution was determined by Monte Carlo analysis performed by the program Espoir [11] in scratch mode, using only the first 66 peaks.…”

“…As for the La 2 O 3 -MoO 3 phase diagram [4] many reported compositions were not correctly characterized in the La 2 O 3 -WO 3 system [5] (Figure 1). We can mentioned, the doubtful cubic form of La 6 WO 12 [6] and the pseudo pyrochlore of formula La 10 …”