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220<div class=WordSection1>
222<h1>Stacking Fault Simulations – II</h1>
224<p class=MsoNormal>In this exercise you will simulate some diffraction patterns
225from kaolinite clays. Kaolinite, Al<sub>2</sub>Si<sub>2</sub>O<sub>5</sub>(OH)<sub>4</sub>,
226is a 1:1 layer silicate with a single unique sheet with AlO<sub>6</sub>
227octahedra on one side and SiO<sub>4</sub> tetrahedra on the other. The layers
228stack with an offset to ideally form a triclinic C1 lattice (Bish &amp; Von
229Dreele, 1989, Clay &amp; Clay Min. 37, 289-296) for a sample of the most
230ordered form of kaolinite from Keokuk, Iowa. Kaolinites from other locations evidently
231have stacking faults so that the peaks are displaced, have peculiar shapes and
232are above a varying background. For the exercise we provide a laboratory
233Bragg-Brentano pattern of Keokuk kaolinite and a less ordered one from
234Washington County, Georgia (Clay Minerals Society Standard KGa-1b) collected
235with CuKa radiation on a Bruker instrument and thus in the Bruker RAW file
236format. The KGa-1b sample contains a small amount of anatase (TiO<sub>2</sub>)
237and the Keokuk kaolinite has some dickite (different ordered stacking of
238kaolinite layers).</p>
240<p class=MsoNormal>If you have not done so already, start GSAS-II.</p>
242<h2>Part 1. Creating kaolinite layer</h2>
244<p class=MsoNormal>In this initial step we will load from a cif file the
245structure of kaolinite, draw it to see the layer structure and then transform
246it into forms suitable for stacking simulations. To begin do <b><span
247style='font-family:"Calibri",sans-serif'>Import/Phase/from CIF file</span></b>;
248from the file dialog select <b><span style='font-family:"Calibri",sans-serif'>kaolinite.cif</span></b>.
249After the “are you sure” popup, there will be another warning you that 4 atom
250types (‘O-H’) were not recognized chemical element symbols and they were
251substituted by Xe to make them obvious in the atom list. Press <b><span
252style='font-family:"Calibri",sans-serif'>Ok</span></b>; you are offered a
253chance to change the phase name, I used ‘<b><span style='font-family:"Calibri",sans-serif'>kaolinite</span></b>’.
254The General tab is displayed (notice the presence of Xe in the element table).</p>
256<p class=MsoNormal><img width=930 height=500 id="Picture 22"
259<p class=MsoNormal>To fix the Xe atoms (they should be O), select <b><span
260style='font-family:"Calibri",sans-serif'>Atoms</span></b> and then double click
261the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b> column
262heading; a small popup will appear. Select <b><span style='font-family:"Calibri",sans-serif'>Xe</span></b>
263&amp; press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
264the Xe atoms at the bottom of the atom table will be highlighted. Next select <b><span
265style='font-family:"Calibri",sans-serif'>Edit/Modify atom parameters</span></b>
266from the Phase Data menu; a new popup will appear.</p>
268<p class=MsoNormal><img width=228 height=268
271<p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>Type</span></b>
272&amp; press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>; a
273periodic table of the element will appear. Select <b><span style='font-family:
274"Calibri",sans-serif'>O</span></b> from the O-atom pulldown; the structure will
275be drawn with Al, Si &amp; O atoms only.</p>
277<p class=MsoNormal><img width=479 height=358
280<p class=MsoNormal>To better visualize the stacking layer, select the <b><span
281style='font-family:"Calibri",sans-serif'>Draw Atoms</span></b> tab and then
282double click the empty upper left corner box of the table. All atoms will turn
283green. Then do <b><span style='font-family:"Calibri",sans-serif'>Edit/Fill unit
284cell</span></b>; the structure will be redrawn with all atoms that belong in
285the unit cell. Finally, double click on the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b>
286column heading, select <b><span style='font-family:"Calibri",sans-serif'>Al</span></b>
287&amp; <b><span style='font-family:"Calibri",sans-serif'>Si</span></b> (they
288will turn green) and then do <b><span style='font-family:"Calibri",sans-serif'>Edit/Fill
289CN sphere</span></b>. After a bit of rotating the structure around, the
290layering along the c-axis (blue line) will be evident.</p>
292<p class=MsoNormal><img width=480 height=359
295<p class=MsoNormal>One can easily see the layer of SiO<sub>4</sub> tetrahedra
296and AlO<sub>6</sub> octahedra. Also notice that the next layer (represented by
297the 4 O atoms at the bottom of the above drawing are offset giving a triclinic
300<p class=MsoNormal>The stacking fault simulation calculation via DIFFaX
301routines requires that the stacking layers be defined in a coordinate system
302that has the stacking direction perpendicular to the stacking plane defined as
303the c-axis. This requires transformation of the unit cell and atom coordinates;
304a suitable tool exists in GSAS-II to do this. Select the <b><span
305style='font-family:"Calibri",sans-serif'>General</span></b> tab and do <b><span
306style='font-family:"Calibri",sans-serif'>Compute/Transform</span></b>; a popup
307window will appear.</p>
309<p class=MsoNormal><img width=350 height=339
312<p class=MsoNormal>Note that this allows one to transform the structure
313according to a matrix and then shift the resultant positions along some vector
314and then select those that are unique according to a selected space group. The
315pulldown gives a selection of commonly used transformations; we want the last
316one, <b><span style='font-family:"Calibri",sans-serif'>abc*</span></b>, which
317satisfies the stacking fault requirement. Select it; notice that the space
318group is changed to P1. Leave this as the kaolinite layer has no symmetry; in
319other circumstances the layer may have an inversion center in which case P-1
320should be used. If you press <b><span style='font-family:"Calibri",sans-serif'>Test</span></b>,
321the new lattice parameters will be shown.</p>
323<p class=MsoNormal><img width=350 height=339
326<p class=MsoNormal>The a &amp; b axes stay the same, but c is now smaller (the
327interlayer distance in kaolinite) and <span style='font-family:Symbol'>a</span>
328&amp; <span style='font-family:Symbol'>b</span> = 90 (<span style='font-family:
329Symbol'>g</span> is unchanged). Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
330a new phase (kaolinite abc*) will be made and its General tab will be shown
331immediately. Select the <b><span style='font-family:"Calibri",sans-serif'>Draw
332Atoms</span></b> tab to see the resulting structure.</p>
334<p class=MsoNormal><img width=471 height=352
337<p class=MsoNormal>To see what this layer looks like with more of it drawn, you
338can add more unit cells to the drawing; select all the atoms by double clicking
339the upper left empty box of the Draw atoms table. Do <b><span style='font-family:
340"Calibri",sans-serif'>Edit/Add atoms</span></b> and <b><span style='font-family:
341"Calibri",sans-serif'>increment</span></b> the 1<sup>st</sup> <b><span
342style='font-family:"Calibri",sans-serif'>Choose unit cel</span></b>l and press <b><span
343style='font-family:"Calibri",sans-serif'>Ok</span></b>; this will add one unit
344cell along x. Now select all the atoms again, do <b><span style='font-family:
345"Calibri",sans-serif'>Edit/Add atoms</span></b> and now <b><span
346style='font-family:"Calibri",sans-serif'>decrement</span></b> the 1<sup>st</sup>
347<b><span style='font-family:"Calibri",sans-serif'>Choose unit cell</span></b>.
348Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>; the
349drawing will now be 3 unit cells wide along x. Repeat this once more <b><span
350style='font-family:"Calibri",sans-serif'>decrementing</span></b> the 2<sup>nd</sup>
351<b><span style='font-family:"Calibri",sans-serif'>Choose unit cell</span></b>
352to give a 3x2 unit cell block of atoms. Double click the <b><span
353style='font-family:"Calibri",sans-serif'>Style</span></b> column heading and
354select <b><span style='font-family:"Calibri",sans-serif'>Balls and sticks</span></b>;
355the drawing should look like (after some zooming/shifting/rotation).</p>
357<p class=MsoNormal><span style='position:absolute;z-index:251659264'><img
358width=477 height=357 src="Stacking%20Faults%20II_files/image009.jpg"></p>
360<p class=MsoNormal>This structure is now suitable for use in DIFFaX
361calculations; the cell has a c-axis that is perpendicular to the ab plane with a
362length that is the stacking repeat distance. This is a good place to save your
363project (I called it ‘<b><span style='font-family:"Calibri",sans-serif'>kaolinite’</span></b>).</p>
365<h2>Part 2. Set up simulation of ideal kaolinite stacking</h2>
367<p class=MsoNormal>In this part of the tutorial we’ll create a stacking model
368for Keokuk kaolinite and use DIFFaX to simulate the powder pattern and compare
369it to some real data. To begin we need a new phase that we can declare as
370“faulted’. In the main GSAS-II data tree menu do <b><span style='font-family:
371"Calibri",sans-serif'>Data/Add new phase</span></b>; I named it ‘<b><span
372style='font-family:"Calibri",sans-serif'>Keokuk</span></b>’. The General tab
373for it will immediately appear.</p>
375<p class=MsoNormal><img width=930 height=500
378<p class=MsoNormal>Change the <b><span style='font-family:"Calibri",sans-serif'>Phase
379type</span></b> to ‘<b><span style='font-family:"Calibri",sans-serif'>faulted</span></b>’;
380the General tab will be redrawn and a new tab <b><span style='font-family:"Calibri",sans-serif'>‘Layers</span></b>’
381will appear. Select it.</p>
383<p class=MsoNormal><img width=817 height=484
386<p class=MsoNormal>We can anticipate (given that kaolinite space group is C1)
387that the <b><span style='font-family:"Calibri",sans-serif'>Diffraction Laue
388symmetry</span></b> is <b><span style='font-family:"Calibri",sans-serif'>-1</span></b>.
389We can enter by hand the lattice parameters from the kaolinite abc* phase but
390an easier method is available. Do <b><span style='font-family:"Calibri",sans-serif'>Operations/Copy
391phase cell</span></b>; a file selection dialog will appear for your current
392directory and the file <b><span style='font-family:"Calibri",sans-serif'>kaolinite.gpx</span></b>
393should be there. Select it; a small popup will appear listing the available
394phases. Choose ‘<b><span style='font-family:"Calibri",sans-serif'>kaolinite
395abc*</span></b>’ and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
396the Layers window will be redrawn with the new lattice parameters.</p>
398<p class=MsoNormal><img width=829 height=484
401<p class=MsoNormal>Next, you need to define the layer. As it would be very
402tedious to enter 24 atoms by hand, the alternative is to get them from the
403previously created kaolinite abc* phase. Select the <b><span style='font-family:
404"Calibri",sans-serif'>Import new layer</span></b> box; the file dialog with <b><span
405style='font-family:"Calibri",sans-serif'>kaolinite.gpx</span></b> will appear.
406Select the file and press <b><span style='font-family:"Calibri",sans-serif'>Open</span></b>;
407again a small popup with two phases listed will appear. Again select <b><span
408style='font-family:"Calibri",sans-serif'>kaolinite abc*</span></b> and press <b><span
409style='font-family:"Calibri",sans-serif'>Ok</span></b>; the Layers page will be
410redrawn with a layer (named kaolinite) will be filled out.</p>
412<p class=MsoNormal><img width=829 height=500
415<p class=MsoNormal>If you move down to the bottom of the page (if there isn’t a
416scroll bar, just grab an edge of the window &amp; shift it slightly) to find
417the one line <b><span style='font-family:"Calibri",sans-serif'>Layer-Layer
418Transition probabilities</span></b>. Change <b><span style='font-family:"Calibri",sans-serif'>Dz=1.0</span></b>
419and press the plot box; the drawing will show a layer of kaolinite stacked
420directly above another one.</p>
422<p class=MsoNormal><img width=480 height=359
425<p class=MsoNormal>Compare that to the stacking in kaolinite.</p>
427<p class=MsoNormal><img width=480 height=359
430<p class=MsoNormal>Notice the effect of the offset. The 1<sup>st</sup> row of
431SiO<sub>4</sub> tetrahedra are positioned directly above the AlO<sub>6</sub>
432octahedra in the real structure but not in the vertically stacked structure. We
433can use a bit of simple geometry to work out what the offset is but first let
434us see what happens in the simulation and how it compares to real data.</p>
436<h2>Step 3. Import Keokuk kaolinite data and do 1<sup>st</sup> simulation</h2>
438<p class=MsoNormal>First we need to import the Keokuk kaolinite powder data; do
439<b><span style='font-family:"Calibri",sans-serif'>Import/Powder Data/from
440Bruker RAW file</span></b>. Select <b><span style='font-family:"Calibri",sans-serif'>Keokuk
441kaolinite.RAW</span></b> from the file dialog box; press <b><span
442style='font-family:"Calibri",sans-serif'>Yes</span></b> in the next popup. A
443new file dialog appears requesting an instrument parameter file; we will use an
444internal default instead. Press <b><span style='font-family:"Calibri",sans-serif'>Cancel</span></b>
445and select <b><span style='font-family:"Calibri",sans-serif'>Defaults for CuKa
446lab data</span></b> from the next popup. This process will repeat since the RAW
447file contains two scans. In the next popup, select only <b><span
448style='font-family:"Calibri",sans-serif'>kaolinite abc*</span></b>. There will
449be two PWDR scans in the GSAS-II data tree; one covers 2<span style='font-family:
450Symbol'>Q</span>= 10-90<span style='font-family:"Calibri",sans-serif'>°</span>
451and the other covers 2<span style='font-family:Symbol'>Q</span>=80-150°. Only
452the lower part of the first one is going to be used in our simulation work as
453the calculations become very time consuming for complex structures and high
454angle data. Select <b><span style='font-family:"Calibri",sans-serif'>PWDR
455Keokuk kaolinite.RAW Scan 1</span></b> from the GSAS-II data tree make sure it
456expands; its plot will also show.</p>
458<p class=MsoNormal><img width=700 height=600
461<p class=MsoNormal>Go to <b><span style='font-family:"Calibri",sans-serif'>Limits</span></b>
462and set <b><span style='font-family:"Calibri",sans-serif'>Tmax</span></b> to <b><span
463style='font-family:"Calibri",sans-serif'>52.0</span></b>; that puts the upper
464limit in a relatively clear part of the pattern. Then go to Background and set
465the 1<sup>st</sup> coefficient to 20 (approximately the background at 2Q=18).
466Next go to <b><span style='font-family:"Calibri",sans-serif'>Sample parameters</span></b>
467and set the <b><span style='font-family:"Calibri",sans-serif'>Histogram scale</span></b>
468to something reasonable (I chose <b><span style='font-family:"Calibri",sans-serif'>20.0</span></b>)
469and make sure the <b><span style='font-family:"Calibri",sans-serif'>Diffractometer
470type is Bragg-Brentano</span></b>.</p>
472<p class=MsoNormal>Now we are ready for our 1<sup>st</sup> kaolinite
473simulation. Go to <b><span style='font-family:"Calibri",sans-serif'>Phases/Keokuk</span></b>
474and select the <b><span style='font-family:"Calibri",sans-serif'>Layers</span></b>
475tab. Do <b><span style='font-family:"Calibri",sans-serif'>Operations/Simulate
476pattern</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>
477in the popup. Select the <b><span style='font-family:"Calibri",sans-serif'>Scan
4781</span></b> pattern and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
479the simulation will finish quickly (press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>)
480and the new plot will be displayed (I’ve zoomed in a bit).</p>
482<p class=MsoNormal><img width=700 height=600
485<p class=MsoNormal>As you can see the simulation (green curve) does not fit the
486data (blue crosses) at all mostly due to the incorrect layer offset although
487the 1<sup>st</sup> peak seems to be positioned correctly. To work out the
488offset consider the drawing of kaolinite.</p>
490<p class=MsoNormal><span style='position:absolute;z-index:251661312'><span
491style='position:absolute;z-index:251660288'><img width=480 height=338
492id="Picture 23" src="Stacking%20Faults%20II_files/image002.gif"></p>
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 part of the exercise.</p>
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