A note on mean distances, (R)over-bar[MO6], in substituted polyhedra, [(M1-xMx′)O6], in the crystal structures of oxygen based solid solutions:: local versus crystal averaging methods

Structure determination or refinement by diffraction methods on solid solutions containing more than one type of central ion in certain polyhedra of their crystal structures, e.g. (M1-xMx')O-6 octahedra, yield crystal-averaged mean distances (R) over bar ((M1-xMx')-O) depending on the site fraction x(M'i) of the substituting metal ion M', which are equal or close to the interpolations between the mean distances in the respective end member polyhedra. However, such results represent virtual crystal approximations as they imply that no structural relaxation occurs to balance the different sizes of M and M'. Another extreme would be the hard sphere model, implying full structural relaxation. in this case, (R) over bar (M-O) and (R) over bar (M'-O) retain the end member values independent of x(M'i), and the results of the virtual crystal approximation obtained by diffraction methods, are to be interpreted as fractional distance sums x(M') * (R) over bar (M-O) + (1 - x(M')) * (R) over bar (M-O) The real local situation is expected between these extremes, though the crystal averaging diffraction methods of structure research do not see that. This paper shows that the required local polyhedral distances in solid solutions in the case of substitutive 3d(N) transition metal ions, may be obtained by evaluating their crystal field parameters 10 Dq as extracted from their dd-transitions in electronic absorption spectra of the respective crystals. For this purpose, 10 Dq(xM') at a site fraction x(M'i) is to be extracted from measured spectra and reference values of (10 Dq(M'i))(x=1) and ((R) over bar ((M'-O)i))(x=1) in the M'-bearing end member of the solid solution series have to be known or measured. The evaluation of single crystal electronic spectra as well as of refinements of data from X-ray diffraction on crystals of a number of different 3d(N)-ion bearing solid solution series as viridine, piemontite, (Ni,Mg)-olivine, rubies, (Fe,Mg)-chloritoid, prove that in all these cases R(M'-O)i strongly deviates from the virtual crystal approximation towards the fully relaxed situation of the real crystal. The lattice relaxations for infinite dilution, i.e. lim x(M'i) --> 0, in corundum, andalusite, Mg-chloritoid and olivine are appreciable but do not strongly differ from each other, 0.52 < <epsilon> < 0.76. That the relaxation in corundum (ruby) is also in this range indicates that there is no strong compression of Cr3+-ions substituting for Al in this "hard structure".