jMol series: srilankite diffraction

[larger] [live3d] diffraction: [ZrTi2O6] [Zr2Ti4O12] [ZrO2] [ZrTiO4] [Zr2Ti2O8]

The left model shows a 2 nm diameter ZrTi2O6 cluster. A "flat Ewald slice" (kinematical electron diffraction pattern) of its reciprocal lattice is on the right. Javascript controls allow you to reorient the cluster at will. The bright central spot in the reciprocal space model is the "DC peak" (unscattered beam). Both {200} reciprocal-lattice spots are colored red, the {020} spots green, and the {002} spots blue. Following this theme, we'll also make the four {110} spots yellow, the {022} spots cyan, and the {202} spots magenta. Camera constant for the diff pat is 10000 [pmÅ], meaning that you divide the spot measurement in pm (pattern model units obtained by double-clicking spot pairs with ZOLZ toggled to show the full reciprocal lattice) into 10000 to get the corresponding d-spacing in Ångstroms. This calculator might help if you first type 100 into each of the calibration text boxes so that pattern model units substitute for mm. If you instead measure in pixels from a captured diffraction image, the camera constant is around 150 [pxÅ].

|\-- field width ~20Å --\/----- direct lattice -----/|\--- reciprocal lattice ---\/-- field width ~2/Å --/|
main axis: ; 2nd axis: ; rotate

direct space: ; reciprocal space:
In the experimental patterns for comparison above, the bright "4th spots" are separated in those streaked vertical columns by the reciprocal of a d-spacing near 2.7 Angstroms. The field width (around 2 reciprocal Angstroms) and camera constants are approximately those of the diffraction window on the right side of the interactive model. The question is: Can these patterns be: (i) indexed against the above srilankite structure (which assumes Zr/Ti substitutions are random), and (ii) explained by superlattice ordering between Zr and Ti sites? For example, how about a <201> zone (g020 and g102) for the first image, and a <101> zone (g020 and g202) for the second? If this is plausible, then what arrangement of Zr atoms would give rise to the observed superlattice spots?
Below find a powder pattern generated using the same diffraction model.

At the left and right, respectively, you'll find an attempt at listing zones in order of decreasing spot density, and spacings in order of decreasing d-value from that same model. The zone routine still needs work (esp. the interspot angle), although the d-value lists seem reasonable so far. All model elements have been calculated, with help from routines like those that power the webMathematica atomlist program linked here, using lattice parameters {a,b,c,α,β,γ} of {4.706Å, 5.553Å, 5.024Å, π/2, π/2, π/2} and these twelve fractional atom coordinates: {{0, 0.1837, 0.25, Ti/Zr}, {0.2729, 0.389, 0.4225, O}, {0.5, 0.3163, 0.75, Ti/Zr}, {0.227, 0.111, 0.9225, O}, {0.7729, 0.111, 0.5775, O}, {0.7271, 0.389, 0.0775, O}, {0, 0.8163, 0.75, Ti/Zr}, {0.727, 0.611, 0.5775, O}, {0.5, 0.6837, 0.25, Ti/Zr}, {0.7729, 0.889, 0.0775, O}, {0.2271, 0.889, 0.4225, O}, {0.2729, 0.611, 0.9225, O}}. Superlattice models, of course, will require a bigger unit cell.

Diffraction patterns from other molecules may be examined here, here, here, here, and here.