jMol series: silicon diffraction

Link here to a generic reciprocal lattice tutor, or trainers specific to srilankite (ZrTi₂O₆) and baddeyelite (ZrO₂).

The left model shows a silicon cluster a few unit-cells across. A "flat Ewald slice" (kinematic electron diffraction pattern) of its corresponding reciprocal lattice is on the right. The bright central spot in the reciprocal space model is the "DC peak" (unscattered beam). Camera constant for the diff pat is 1000 [pmA], 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 1000 to get the corresponding d-spacing in Angstroms. If you prefer to measure from the captured diffraction image in pixels, the camera constant is near 150 [pxA] although it has not been measured carefully.

Challenge: Try capturing a <110> zone diffraction pattern, and indexing the spots in it. This calculator might come in handy if you first type two numbers (e.g. 10 and 100) that multiply to 1000 into the calibration text boxes so that pattern model units substitute for mm.

/---- direct lattice ----/ | \-- reciprocal lattice --\

Below find on the left (using the same diffraction model as that used above) a list of kinematically-allowed diffraction spot types in silicon, in order of decreasing d-spacing. In the center, find a plot of intensity in a powder diffraction pattern, as a function of spatial frequency or scattering angle. On the right, find a list of cross-fringe orientations of "zones", in order of decreasing spot density. All model calculations were done using the algorithms behind our webMathematica atomlist routines linked here.