Space group ambiguities

Space group ambiguity Sometimes more than one space group fits a given set of systematic absences in intensity. In such a case, other physical methods have to be used to establish the true space group. 

Unfortunately it is not always possible to characterize a space group unequivocally by systematic absences two or more space groups may have the same systematic absences, leading to space group ambiguities. Often these are cases where one space group is centrosymmetric and the other is noncentrosymmetric. Alternative methods of symmetry assign-... 

A space group ambiguity is resolved by intensity statistics alone. 

Fig. 20. The use of svsematic absences in X-ray diffraction patterns to determine the space group of the crystal. (a)F2l212] /tAO,(b)Ml, (c)/222or/2,2121, hk O, and (d)Ml. In the second case there is a space-group ambiguity.

P. Thompson and N. Grimes. Multiple diffraction in spinel and the space group ambiguity. J. Appl. Cryst., 10 369-371, 1977. 

One complication occurs with polar space groups, where all the possibilities must be tried in the TF. If there is an ambiguity in the extinctions, for instance in the Laue group Pmmm, again all possibilities must be searched. This is usually done T>y hand, going through all different possibilities one by one. 

Interesting ternary chalcogenides have been prepared employing electrochemical methods via anodic dissolution of copper or silver electrodes at low temperatures. For example, the series of KCu - S4 (0 < x < 0.34) was prepared in an ethylenediamine solution of polysulfide K2S (x = 5, 6) electrolytes. Single crystal stmcture analysis confirmed the once ambiguous space group of these compounds and showed that the KCU7S4 phase which exhibits an unusual insulator-to-metal transition is non-stoichiometric. The stmcture... 

These two space groups also have the same extinctions, and the situation is similar to the Cc-C2/c ambiguity. Although more examples might be found by a literature search based on the tables of Nowacki,45 only three are given below. 

Models of Ni-Fe sulfide were constructed as cut offs from the crystal structure of violarite [110] with space group Fd-3m and cubical unit cell with the parameters a = b = c = 9.465 A. Due to total structural changes caused by the optimization the original model was modified, its size was decreased by removal of the ambiguous part. The new model consists of one Fe, one Ni atom, and six sulfur atoms. Dangling bonds that occur on four sulfur atoms were saturated by the hydrogen atoms to ensure the electroneutrality of the entire system. 

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