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24 European Crystallographic Meeting, ECM24, Marrakech, 2007 Page s77 Acta Cryst. (2007). A63, s77 average structure reveals the distribution of the ions as described by the probability density function, which can be obtained either by Fourier transformation of the Debye Waller factor (including anharmonic terms [1]) or by Fourier methods. The former is more appropriate for interstitial diffusion processes, i.e. when the migration of the ions proceeds directly to adjacent vacant sites. In this case a continuous density is found directly representing the diffusion pathway. Moreover, by applying Boltzmann statistics effective single particle potentials can be derived containing the potential barriers to migration which can be compared with otherwise measured activation energies. On the other hand, if interstitialcy (exchange) processes prevail, it is more meaningful to analyse difference Fourier maps and/or to introduce additional (metastable) positions. All this will be illustrated by various examples. For fluorite like ZrO2 doped with cations and anions (e.g. Sc and N [2]) one generally finds anion diffusion pathways directly through an edge of the surrounding cation tetrahedron along to a neighbouring site. Derived activation energies agree with those obtained from conductivity measurements showing that no additional energy is needed for the creation of defects. By comparing samples with and without N it is possible to derive separate activation energies for O and N. In perovskite like LaGaO3 doped with Mg and Sr the pathways are curved. These and the corresponding potentials are significantly altered when measured under electric fields [3] or microwave irradiation [4]. An example of interstitialcy diffusion is provided by mayenite (Ca12Al14O33) [5]. Its structure may be described as a calciumaluminate framework containing 32 of the 33 O atoms, while the remaining “free” oxygen statistically occupies 1/6 of larger cages in the structure. In spite of the presence of vacancies and rather large openings between adjacent cages no continuous density was found, therewith ruling out interstitial diffusion (probably because of too long jump distances). On the other hand, difference Fourier maps revealed various other weakly occupied positions which can be related to an exchange process with particular framework O. Moreover, each jump process is connected with a relaxation of Ca, i.e. there is considerable interaction with the framework. Interestingly, the mechanism is different when the “free” O is replaced by N, i.e. nitrogen shows the interstitial type of diffusion within the same framework.

Remarkable microstructure evolution in biogenic crystals upon mild annealing