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226<div class=WordSection1>
228<h1>Stacking Fault Simulations – II</h1>
230<p class=MsoNormal>In this exercise and the next you will simulate some
231diffraction patterns from kaolinite clays. Kaolinite, Al<sub>2</sub>Si<sub>2</sub>O<sub>5</sub>(OH)<sub>4</sub>,
232is a 1:1 layer silicate with a single unique sheet with AlO<sub>6</sub>
233octahedra on one side and SiO<sub>4</sub> tetrahedra on the other. The layers
234stack with an offset to ideally form a triclinic C1 lattice (Bish &amp; Von
235Dreele, 1989, Clay &amp; Clay Min. 37, 289-296) for a sample of the most
236ordered form of kaolinite from Keokuk, Iowa. Kaolinites from other locations
237evidently have stacking faults so that the peaks are displaced, have peculiar
238shapes and are above a varying background. For the exercise we provide a
239laboratory Bragg-Brentano pattern of Keokuk kaolinite collected with CuKa
240radiation on a Bruker instrument and thus in the Bruker RAW file format. The
241Keokuk kaolinite has some dickite (different ordered stacking of kaolinite
242layers). The next exercise Stacking Faults-III) covers a simple simulation of a
243faulted kaolinite from Georgia.</p>
245<p class=MsoNormal>If you have not done so already, start GSAS-II.</p>
247<h2>Part 1. Creating kaolinite layer</h2>
249<p class=MsoNormal>In this initial step we will load from a cif file the
250structure of kaolinite, draw it to see the layer structure and then transform
251it into forms suitable for stacking simulations. To begin do <b><span
252style='font-family:"Calibri",sans-serif'>Import/Phase/from CIF file</span></b>;
253from the file dialog select <b><span style='font-family:"Calibri",sans-serif'>kaolinite.cif</span></b>.
254After the “are you sure” popup, there will be another warning you that 4 atom
255types (‘O-H’) were not recognized chemical element symbols and they were
256substituted by Xe to make them obvious in the atom list. Press <b><span
257style='font-family:"Calibri",sans-serif'>Ok</span></b>; you are offered a
258chance to change the phase name, I used ‘<b><span style='font-family:"Calibri",sans-serif'>kaolinite</span></b>’.
259The General tab is displayed (notice the presence of Xe in the element table).</p>
261<p class=MsoNormal><img width=930 height=500
264<p class=MsoNormal>To fix the Xe atoms (they should be O), select <b><span
265style='font-family:"Calibri",sans-serif'>Atoms</span></b> and then double click
266the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b> column
267heading; a small popup will appear. Select <b><span style='font-family:"Calibri",sans-serif'>Xe</span></b>
268&amp; press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
269the Xe atoms at the bottom of the atom table will be highlighted. Next select <b><span
270style='font-family:"Calibri",sans-serif'>Edit/Modify atom parameters</span></b>
271from the Phase Data menu; a new popup will appear. Select <b><span
272style='font-family:"Calibri",sans-serif'>Type</span></b> &amp; press <b><span
273style='font-family:"Calibri",sans-serif'>Ok</span></b>; a periodic table of the
274element will appear. Select <b><span style='font-family:"Calibri",sans-serif'>O</span></b>
275from the O-atom pulldown; the structure will be drawn with Al, Si &amp; O atoms
278<p class=MsoNormal><img width=479 height=358
281<p class=MsoNormal>To better visualize the stacking layer, select the <b><span
282style='font-family:"Calibri",sans-serif'>Draw Atoms</span></b> tab and then
283double click the empty upper left corner box of the table. All atoms will turn
284green. Then do <b><span style='font-family:"Calibri",sans-serif'>Edit/Fill unit
285cell</span></b>; the structure will be redrawn with all atoms that belong in
286the unit cell. Finally, double click on the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b>
287column heading, select <b><span style='font-family:"Calibri",sans-serif'>Al</span></b>
288&amp; <b><span style='font-family:"Calibri",sans-serif'>Si</span></b> (they
289will turn green) and then do <b><span style='font-family:"Calibri",sans-serif'>Edit/Fill
290CN sphere</span></b>. After a bit of rotating the structure around, the
291layering along the c-axis (blue line) will be evident.</p>
293<p class=MsoNormal><img width=480 height=359
296<p class=MsoNormal>One can easily see the layer of SiO<sub>4</sub> tetrahedra
297and AlO<sub>6</sub> octahedra. Also notice that the next layer (represented by
298the 4 O atoms at the bottom of the above drawing are offset giving a triclinic
301<p class=MsoNormal>The stacking fault simulation calculation via DIFFaX
302routines requires that the stacking layers be defined in a coordinate system
303that has the stacking direction perpendicular to the stacking plane defined as
304the c-axis. This requires transformation of the unit cell and atom coordinates;
305a suitable tool exists in GSAS-II to do this. Select the <b><span
306style='font-family:"Calibri",sans-serif'>General</span></b> tab and do <b><span
307style='font-family:"Calibri",sans-serif'>Compute/Transform</span></b>; a popup
308window will appear.</p>
310<p class=MsoNormal><img width=350 height=339
313<p class=MsoNormal>Note that this allows one to transform the structure
314according to a matrix and then shift the resultant positions along some vector
315and then select those that are unique according to a selected space group. The
316pulldown gives a selection of commonly used transformations; we want the last
317one, <b><span style='font-family:"Calibri",sans-serif'>abc*</span></b>, which
318satisfies the stacking fault requirement. Select it; notice that the space
319group is changed to P1. Leave this as the kaolinite layer has no symmetry; in
320other circumstances the layer may have an inversion center in which case P-1
321should be used. If you press <b><span style='font-family:"Calibri",sans-serif'>Test</span></b>,
322the new lattice parameters will be shown.</p>
324<p class=MsoNormal><img width=350 height=339
327<p class=MsoNormal>The a &amp; b axes stay the same, but c is now smaller (the
328interlayer distance in kaolinite) and <span style='font-family:Symbol'>a</span>
329&amp; <span style='font-family:Symbol'>b</span> = 90 (<span style='font-family:
330Symbol'>g</span> is unchanged). Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
331a new phase (kaolinite abc*) will be made and its General tab will be shown
332immediately. Select the <b><span style='font-family:"Calibri",sans-serif'>Draw
333Atoms</span></b> tab to see the resulting structure.</p>
335<p class=MsoNormal><img width=471 height=352
338<p class=MsoNormal>To see what this layer looks like with more of it drawn, you
339can add more unit cells to the drawing; select all the atoms by double clicking
340the upper left empty box of the Draw atoms table. Do <b><span style='font-family:
341"Calibri",sans-serif'>Edit/Add atoms</span></b> and <b><span style='font-family:
342"Calibri",sans-serif'>increment</span></b> the 1<sup>st</sup> <b><span
343style='font-family:"Calibri",sans-serif'>Choose unit cel</span></b>l and press <b><span
344style='font-family:"Calibri",sans-serif'>Ok</span></b>; this will add one unit
345cell along x. Now select all the atoms again, do <b><span style='font-family:
346"Calibri",sans-serif'>Edit/Add atoms</span></b> and now <b><span
347style='font-family:"Calibri",sans-serif'>decrement</span></b> the 1<sup>st</sup>
348<b><span style='font-family:"Calibri",sans-serif'>Choose unit cell</span></b>.
349Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>; the
350drawing will now be 3 unit cells wide along x. Repeat this once more <b><span
351style='font-family:"Calibri",sans-serif'>decrementing</span></b> the 2<sup>nd</sup>
352<b><span style='font-family:"Calibri",sans-serif'>Choose unit cell</span></b>
353to give a 3x2 unit cell block of atoms. Double click the <b><span
354style='font-family:"Calibri",sans-serif'>Style</span></b> column heading and
355select <b><span style='font-family:"Calibri",sans-serif'>Balls and sticks</span></b>;
356the drawing should look like (after some zooming/shifting/rotation).</p>
358<p class=MsoNormal><img width=477 height=357
361<p class=MsoNormal>This structure is now suitable for use in DIFFaX
362calculations; the cell has a c-axis that is perpendicular to the ab plane with
363a length that is the stacking repeat distance. This is a good place to save
364your project (I called it ‘<b><span style='font-family:"Calibri",sans-serif'>kaolinite’</span></b>).</p>
366<h2>Part 2. Set up simulation of ideal kaolinite stacking</h2>
368<p class=MsoNormal>In this part of the tutorial we’ll create a stacking model
369for Keokuk kaolinite and use DIFFaX to simulate the powder pattern and compare
370it to some real data. To begin we need a new phase that we can declare as
371“faulted’. In the main GSAS-II data tree menu do <b><span style='font-family:
372"Calibri",sans-serif'>Data/Add new phase</span></b>; I named it ‘<b><span
373style='font-family:"Calibri",sans-serif'>Keokuk</span></b>’. The General tab
374for it will immediately appear.</p>
376<p class=MsoNormal><img width=930 height=500
379<p class=MsoNormal>Change the <b><span style='font-family:"Calibri",sans-serif'>Phase
380type</span></b> to ‘<b><span style='font-family:"Calibri",sans-serif'>faulted</span></b>’;
381the General tab will be redrawn and a new tab <b><span style='font-family:"Calibri",sans-serif'>‘Layers</span></b>’
382will appear. Select it.</p>
384<p class=MsoNormal><img width=817 height=484
387<p class=MsoNormal>We can anticipate (given that kaolinite space group is C1)
388that the <b><span style='font-family:"Calibri",sans-serif'>Diffraction Laue
389symmetry</span></b> is <b><span style='font-family:"Calibri",sans-serif'>-1</span></b>.
390We can enter by hand the lattice parameters from the kaolinite abc* phase but
391an easier method is available. Do <b><span style='font-family:"Calibri",sans-serif'>Operations/Copy
392phase cell</span></b>; a file selection dialog will appear for your current
393directory and the file <b><span style='font-family:"Calibri",sans-serif'>kaolinite.gpx</span></b>
394should be there. Select it; a small popup will appear listing the available
395phases. Choose ‘<b><span style='font-family:"Calibri",sans-serif'>kaolinite
396abc*</span></b>’ and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
397the Layers window will be redrawn with the new lattice parameters.</p>
399<p class=MsoNormal><img width=829 height=484
402<p class=MsoNormal>Next, you need to define the layer. As it would be very
403tedious to enter 24 atoms by hand, the alternative is to get them from the
404previously created kaolinite abc* phase. Select the <b><span style='font-family:
405"Calibri",sans-serif'>Import new layer</span></b> box; the file dialog with <b><span
406style='font-family:"Calibri",sans-serif'>kaolinite.gpx</span></b> will appear.
407Select the file and press <b><span style='font-family:"Calibri",sans-serif'>Open</span></b>;
408again a small popup with two phases listed will appear. Again select <b><span
409style='font-family:"Calibri",sans-serif'>kaolinite abc*</span></b> and press <b><span
410style='font-family:"Calibri",sans-serif'>Ok</span></b>; the Layers page will be
411redrawn with a layer (named kaolinite) will be filled out.</p>
413<p class=MsoNormal><img width=829 height=500
416<p class=MsoNormal>If you move down to the bottom of the page (if there isn’t a
417scroll bar, just grab an edge of the window &amp; shift it slightly) to find
418the one line <b><span style='font-family:"Calibri",sans-serif'>Layer-Layer
419Transition probabilities</span></b>. Change <b><span style='font-family:"Calibri",sans-serif'>Dz=1.0</span></b>
420and press the plot box; the drawing will show a layer of kaolinite stacked
421directly above another one.</p>
423<p class=MsoNormal><img width=480 height=359
426<p class=MsoNormal>Compare that to the stacking in kaolinite.</p>
428<p class=MsoNormal><img width=480 height=359
431<p class=MsoNormal>Notice the effect of the offset. The 1<sup>st</sup> row of
432SiO<sub>4</sub> tetrahedra are positioned directly above the AlO<sub>6</sub>
433octahedra in the real structure but not in the vertically stacked structure. We
434can use a bit of simple geometry to work out what the offset is but first let
435us see what happens in the simulation and how it compares to real data.</p>
437<h2>Step 3. Import Keokuk kaolinite data and do 1<sup>st</sup> simulation</h2>
439<p class=MsoNormal>First we need to import the Keokuk kaolinite powder data; do
440<b><span style='font-family:"Calibri",sans-serif'>Import/Powder Data/from
441Bruker RAW file</span></b>. Select <b><span style='font-family:"Calibri",sans-serif'>Keokuk
442kaolinite.RAW</span></b> from the file dialog box; press <b><span
443style='font-family:"Calibri",sans-serif'>Yes</span></b> in the next popup. A
444new file dialog appears requesting an instrument parameter file; we will use an
445internal default instead. Press <b><span style='font-family:"Calibri",sans-serif'>Cancel</span></b>
446and select <b><span style='font-family:"Calibri",sans-serif'>Defaults for CuKa
447lab data</span></b> from the next popup. This process will repeat since the RAW
448file contains two scans. In the next popup, select only <b><span
449style='font-family:"Calibri",sans-serif'>kaolinite abc*</span></b>. There will
450be two PWDR scans in the GSAS-II data tree; one covers 2<span style='font-family:
451Symbol'>Q</span>= 10-90<span style='font-family:"Calibri",sans-serif'>°</span>
452and the other covers 2<span style='font-family:Symbol'>Q</span>=80-150°. Only
453the lower part of the first one is going to be used in our simulation work as the
454calculations become very time consuming for complex structures and high angle
455data. Select <b><span style='font-family:"Calibri",sans-serif'>PWDR Keokuk
456kaolinite.RAW Scan 1</span></b> from the GSAS-II data tree make sure it
457expands; its plot will also show.</p>
459<p class=MsoNormal><img width=700 height=600
462<p class=MsoNormal>Go to <b><span style='font-family:"Calibri",sans-serif'>Limits</span></b>
463and set <b><span style='font-family:"Calibri",sans-serif'>Tmax</span></b> to <b><span
464style='font-family:"Calibri",sans-serif'>52.0</span></b>; that puts the upper limit
465in a relatively clear part of the pattern. Then go to Background and set the 1<sup>st</sup>
466coefficient to 20 (approximately the background at 2Q=18). Next go to <b><span
467style='font-family:"Calibri",sans-serif'>Sample parameters</span></b> and set
468the <b><span style='font-family:"Calibri",sans-serif'>Histogram scale</span></b>
469to something reasonable (I chose <b><span style='font-family:"Calibri",sans-serif'>20.0</span></b>)
470and make sure the <b><span style='font-family:"Calibri",sans-serif'>Diffractometer
471type is Bragg-Brentano</span></b>.</p>
473<p class=MsoNormal>Now we are ready for our 1<sup>st</sup> kaolinite
474simulation. Go to <b><span style='font-family:"Calibri",sans-serif'>Phases/Keokuk</span></b>
475and select the <b><span style='font-family:"Calibri",sans-serif'>Layers</span></b>
476tab. Do <b><span style='font-family:"Calibri",sans-serif'>Operations/Simulate
477pattern</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>
478in the popup. Select the <b><span style='font-family:"Calibri",sans-serif'>Scan
4791</span></b> pattern and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
480the simulation will finish quickly (press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>)
481and the new plot will be displayed (I’ve zoomed in a bit).</p>
483<p class=MsoNormal><img width=700 height=600
486<p class=MsoNormal>As you can see the simulation (green curve) does not fit the
487data (blue crosses) at all mostly due to the incorrect layer offset although
488the 1<sup>st</sup> peak seems to be positioned correctly. To work out the
489offset consider the drawing of kaolinite.</p>
491<p class=MsoNormal><img width=480 height=338
494<p class=MsoNormal>The offset Dx is given by the blue arrow in the above
495drawing of kaolinite and is in fractional coordinates. Geometry gives</p>
497<p class=MsoNormal><span style='position:relative;top:3pt'><img width=106
498height=26 src="Stacking%20Faults%20II_files/image021.gif">&nbsp;Or in this case
499<b><span style='font-family:"Calibri",sans-serif'>-0.368</span></b>. Set <b><span
500style='font-family:"Calibri",sans-serif'>Dx</span></b> to this value &amp;
501repeat simulation.</p>
503<p class=MsoNormal><img width=700 height=600
506<p class=MsoNormal>There is some improvement but some parts are not very well
507represented. Recall from the triclinic kaolinite lattice parameters that <span
508style='font-family:Symbol'>a</span> was 91.7°; that will produce a small offset
509in Dy. Using the same kind of geometry math gives <b><span style='font-family:
510"Calibri",sans-serif'>Dy=-0.0246</span></b>. Enter this value &amp; repeat the
511simulation again. This gives a much better fit to the observed pattern, but the
512simulated peaks are too sharp; this can be fixed by changing the U,V,W
513Instrument parameters. I’d just set <b><span style='font-family:"Calibri",sans-serif'>W=40</span></b>
514and the <b><span style='font-family:"Calibri",sans-serif'>Histogram scale</span></b>
515(in <b><span style='font-family:"Calibri",sans-serif'>Sample parameters</span></b>)
516to <b><span style='font-family:"Calibri",sans-serif'>40</span></b> and try
519<p class=MsoNormal><img width=700 height=600
522<p class=MsoNormal>That is a pretty good fit for a stacking simulation. By
523further hand tweaking of the parameters one can further improve the simulation
524but based on what we see here we do have the right description of stacking in
525Keokuk kaolinite. Doing sequence simulations varying each parameter over a
526small range can be used to help with optimization, but in this case it would be
527far easier to do a Rietveld refinement for this well ordered kaolinite. Save
528your project as you will need it for the next exercise (Stacking Faults-III).</p>
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