Stacking Fault Simulations – II

In this exercise you will simulate some diffraction patterns from kaolinite clays. Kaolinite, Al2Si2O5(OH)4, is a 1:1 layer silicate with a single unique sheet with AlO6 octahedra on one side and SiO4 tetrahedra on the other. The layers stack with an offset to ideally form a triclinic C1 lattice (Bish & Von Dreele, 1989, Clay & Clay Min. 37, 289-296) for a sample of the most ordered form of kaolinite from Keokuk, Iowa. Kaolinites from other locations evidently have stacking faults so that the peaks are displaced, have peculiar shapes and are above a varying background. For the exercise we provide a laboratory Bragg-Brentano pattern of Keokuk kaolinite and a less ordered one from Washington County, Georgia (Clay Minerals Society Standard KGa-1b) collected with CuKa radiation on a Bruker instrument and thus in the Bruker RAW file format. The KGa-1b sample contains a small amount of anatase (TiO2) and the Keokuk kaolinite has some dickite (different ordered stacking of kaolinite layers).

If you have not done so already, start GSAS-II.

Part 1. Creating kaolinite layer

In this initial step we will load in from a cif file the structure of kaolinite, draw it to see the layer structure and then transform it into forms suitable for stacking simulations. To begin do Import/Phase/from CIF file; from the file dialog select kaolinite.cif. After the “are you sure” popup, there will be another warning you that 4 atom types (‘O-H’) were not recognized chemical element symbols and they were substituted by Xe to make them obvious in the atom list. Press Ok; you are offered a chance to change the phase name, I used ‘kaolinite’. The General tab is displayed (notice the presence of Xe in the element table).

To fix the Xe atoms (they should be O), select Atoms and then double click the Type column heading; a small popup will appear. Select Xe & press Ok; the Xe atoms at the bottom of the atom table will be highlighted. Next select Edit/Modify atom parameters from the Phase Data menu; a new popup will appear.

Select Type & press Ok; a periodic table of the element will appear. Select O from the O-atom pulldown; the structure will be drawn with Al, Si & O atoms only.

To better visualize the stacking layer, select the Draw Atoms tab and then double click the empty upper left corner box of the table. All atoms will turn green. Then do Edit/Fill unit cell; the structure will be redrawn with all atoms that belong in the unit cell. Finally, double click on the Type column heading, select Al & Si (they will turn green) and then do Edit/Fill CN sphere. After a bit of rotating the structure around, the layering along the c-axis (blue line) will be evident.

One can easily see the layer of SiO4 tetrahedra and AlO6 octahedra. Also notice that the next layer (represented by the 4 O atoms at the bottom of the above drawing are offset giving a triclinic lattice.

The stacking fault simulation calculation via DIFFaX routines requires that the stacking layers be defined in a coordinate system that has the stacking direction perpendicular to the stacking plane defined as the c-axis. This requires transformation of the unit cell and atom coordinates; a suitable tool exists in GSAS-II to do this. Select the General tab and do Compute/Transform; a popup window will appear.

Note that this allows one to transform the structure according to a matrix and then shift the resultant positions along some vector and then select those that are unique according to a selected space group. The pulldown gives a selection of commonly used transformations; we want the last one, abc*, which satisfies the stacking fault requirement. Select it; notice that the space group is changed to P1. Leave this as the kaolinite layer has no symmetry; in other circumstances the layer may have an inversion center in which P-1 should be used. If you press Test, the new lattice parameters will be shown.

The a & b axes stay the same, but c is now smaller (the interlayer distance in kaolinite) and a & b = 90 (g is unchanged). Press Ok; a new phase (kaolinite abc*) will be made. Select it from the GSAS-II data tree and then select the Draw Atoms tab to see the result.