Aggregate Feff calculation

If crystal data has two or more inequivalent sites occupied by the same kind of atom, some additional functionality is enabled when one of the inequivalent sites is selected as the absorber. As you can see in the following screenshot, the “Aggregate” button is available, as are controls for setting the fuzzy degeneracy parameters.

Crystal data for CaZrTi₂O₇ with a Ti atom selected, enabling the aggregate calculation controls.

In the aggregate FEFF calculation, the path finder is run for each inequivalent position containing the same central atom. The path lists are merged together, weighted by fractional population of the site in the unit cell, before running the check for fuzzy degeneracy. The weighting by population fraction means that a bin of paths can be occupied by a non-integer number of atoms.

In the example of CaZrTi₂O₇, there are three Ti sites. The are 8 Ti1 atoms in the unit cell and 4 each of Ti2 and Ti3. Thus half the Ti atoms are from site 1 and a quarter each from sites 2 and 3. Each Ti site is surrounded by 6 oxygen atoms at a variety of distances. Ti1 has O atoms at 1.843 Å, 1.880 Å, 1.927 Å, 1.987 Å, 2.0007 Å, and 2.023 Å. Ti2 has 2 O atoms at each of 1.786 Å, 2.050 Å, 2.498 Å. Ti3 has 2 O atoms at each of 1.975 Å, 1.877 Å, 1.975 Å. In short, the Ti K edge of CaZrTi₂O₇ is a mess!

Using a bin size of 0.1 Å and combining the three sites together weighted by their fractional populations in the unit cell, we end up with 4 distances. There are 2.5 O atoms at 1.852 Å, 2.5 O atoms at 1.984 Å, 0.5 O atoms at 2.050 Å, and 0.5 O atoms at 2.498 Å.

Instead of having to parameterize 12 different Ti-O distances, keeping track of fractional populations when parameterizing the S²₀ values for each path, the aggregate FEFF calculation requires managing only 4 paths.

For a complete discussion of the the aggregate FEFF calculation, see B. Ravel, J. Synchrotron Radiat., 21, (2014) p. 1269-1274 (DOI: 10.1107/S1600577514014982)