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218<body lang=EN-US link=blue vlink=purple>
219
220<div class=WordSection1>
221
222<h1>Stacking Fault Simulations – II</h1>
223
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
231evidently have stacking faults so that the peaks are displaced, have peculiar
232shapes and are above a varying background. For the exercise we provide a
233laboratory Bragg-Brentano pattern of Keokuk kaolinite and a less ordered one
234from Washington County, Georgia (Clay Minerals Society Standard KGa-1b)
235collected with CuKa radiation on a Bruker instrument and thus in the Bruker RAW
236file format. 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>
239
240<p class=MsoNormal>If you have not done so already, start GSAS-II.</p>
241
242<h2>Part 1. Creating kaolinite layer</h2>
243
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>
255
256<p class=MsoNormal><img width=930 height=500 id="Picture 8"
257src="Stacking%20Faults%20II_files/image001.gif"></p>
258
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>
267
268<p class=MsoNormal><img width=228 height=268 id="Picture 9"
269src="Stacking%20Faults%20II_files/image002.gif"></p>
270
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>
276
277<p class=MsoNormal><img width=479 height=358 id="Picture 10"
278src="Stacking%20Faults%20II_files/image003.jpg"></p>
279
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 double
282click the empty upper left corner box of the table. All atoms will turn green.
283Then do <b><span style='font-family:"Calibri",sans-serif'>Edit/Fill unit cell</span></b>;
284the structure will be redrawn with all atoms that belong in the unit cell.
285Finally, 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>
291
292<p class=MsoNormal><img width=480 height=359 id="Picture 11"
293src="Stacking%20Faults%20II_files/image004.jpg"></p>
294
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
298lattice.</p>
299
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>
308
309<p class=MsoNormal><img width=350 height=339 id="Picture 12"
310src="Stacking%20Faults%20II_files/image005.gif"></p>
311
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 P-1 should
320be used. If you press <b><span style='font-family:"Calibri",sans-serif'>Test</span></b>,
321the new lattice parameters will be shown.</p>
322
323<p class=MsoNormal><img width=350 height=339 id="Picture 13"
324src="Stacking%20Faults%20II_files/image006.gif"></p>
325
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>
333
334<p class=MsoNormal><img width=471 height=352 id="Picture 14"
335src="Stacking%20Faults%20II_files/image007.jpg"></p>
336
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>
356
357<p class=MsoNormal><span style='position:absolute;z-index:251659264;margin-left:
35812px;margin-top:104px;width:356px;height:201px'><img width=356 height=201
359src="Stacking%20Faults%20II_files/image008.gif"></span><img width=477
360height=357 id="Picture 15" src="Stacking%20Faults%20II_files/image009.jpg"></p>
361
362<p class=MsoNormal>I’ll say more about that diagonal line later. This structure
363is now suitable for use in DIFFaX calculations; the cell has a c-axis that is
364perpendicular to the ab plane with a length that is the stacking repeat
365distance. This is a good place to save your project (I called it ‘<b><span
366style='font-family:"Calibri",sans-serif'>kaolinite’</span></b>).</p>
367
368<h2>Part 2. Set up simulation of ideal kaolinite stacking</h2>
369
370<p class=MsoNormal>In this part of the tutorial we’ll create a stacking model
371for Keokuk kaolinite and use DIFFaX to simulate the powder pattern and compare
372it to some real data. To begin we need a new phase that we can declare as
373“faulted’. In the main GSAS-II data tree menu do <b><span style='font-family:
374"Calibri",sans-serif'>Data/Add new phase</span></b>; I named it ‘<b><span
375style='font-family:"Calibri",sans-serif'>Keokuk</span></b>’. The General tab
376for it will immediately appear.</p>
377
378<p class=MsoNormal><img width=930 height=500 id="Picture 17"
379src="Stacking%20Faults%20II_files/image010.gif"></p>
380
381<p class=MsoNormal>Change the <b><span style='font-family:"Calibri",sans-serif'>Phase
382type</span></b> to ‘<b><span style='font-family:"Calibri",sans-serif'>faulted</span></b>’;
383the General tab will be redrawn and a new tab <b><span style='font-family:"Calibri",sans-serif'>‘Layers</span></b>’
384will appear. Select it.</p>
385
386<p class=MsoNormal><img width=817 height=484 id="Picture 18"
387src="Stacking%20Faults%20II_files/image011.gif"></p>
388
389<p class=MsoNormal>We can anticipate (given that kaolinite space group is C1)
390that the <b><span style='font-family:"Calibri",sans-serif'>Diffraction Laue
391symmetry</span></b> is <b><span style='font-family:"Calibri",sans-serif'>-1</span></b>.
392We can enter by hand the lattice parameters from the kaolinite abc* phase but
393an easier method is available. Do <b><span style='font-family:"Calibri",sans-serif'>Operations/Copy
394phase cell</span></b>; a file selection dialog will appear for your current
395directory and the file <b><span style='font-family:"Calibri",sans-serif'>kaolinite.gpx</span></b>
396should be there. Select it; a small popup will appear listing the available
397phases. Choose ‘<b><span style='font-family:"Calibri",sans-serif'>kaolinite
398abc*</span></b>’ and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
399the Layers window will be redrawn with the new lattice parameters.</p>
400
401<p class=MsoNormal><img width=829 height=484 id="Picture 19"
402src="Stacking%20Faults%20II_files/image012.gif"></p>
403
404<p class=MsoNormal>Next, you need to define the layer. As it would be very
405tedious to enter 24 atoms by hand, the alternative is to get them from the
406previously created kaolinite abc* phase. Select the <b><span style='font-family:
407"Calibri",sans-serif'>Import new layer</span></b> box; the file dialog with <b><span
408style='font-family:"Calibri",sans-serif'>kaolinite.gpx</span></b> will appear.
409Select the file and press <b><span style='font-family:"Calibri",sans-serif'>Open</span></b>;
410again a small popup with two phases listed will appear. Again select <b><span
411style='font-family:"Calibri",sans-serif'>kaolinite abc*</span></b> and press <b><span
412style='font-family:"Calibri",sans-serif'>Ok</span></b>; the Layers page will be
413redrawn with a layer (named kaolinite) will be filled out.</p>
414
415<p class=MsoNormal><img width=829 height=500 id="Picture 20"
416src="Stacking%20Faults%20II_files/image013.gif"></p>
417
418<p class=MsoNormal>If you move down to the bottom of the page (if there isn’t a
419scroll bar, just grab an edge of the window &amp; shift it slightly) to find
420the one line <b><span style='font-family:"Calibri",sans-serif'>Layer-Layer
421Transition probabilities</span></b>. Change <b><span style='font-family:"Calibri",sans-serif'>Dz=1.0</span></b>
422and press the plot box; the drawing will show a layer of kaolinite stacked
423directly above another one.</p>
424
425<p class=MsoNormal><img width=480 height=359 id="Picture 24"
426src="Stacking%20Faults%20II_files/image014.jpg"></p>
427
428<p class=MsoNormal>Compare that to the stacking in kaolinite.</p>
429
430<p class=MsoNormal><img width=480 height=359 id="Picture 26"
431src="Stacking%20Faults%20II_files/image015.jpg"></p>
432
433<p class=MsoNormal>Notice the effect of the offset. The 1<sup>st</sup> row of
434SiO<sub>4</sub> tetrahedra are positioned directly above the AlO<sub>6</sub>
435octahedra in the real structure but not in the vertically stacked structure. We
436can use a bit of simple geometry to work out what the offset is but first let
437us see what happens in the simulation and how it compares to real data.</p>
438
439<h2>Step 3. Import Keokuk kaolinite data and do 1<sup>st</sup> simulation</h2>
440
441<p class=MsoNormal>First we need to import the Keokuk kaolinite powder data; do
442<b><span style='font-family:"Calibri",sans-serif'>Import/Powder Data/from
443Bruker RAW file</span></b>. Select <b><span style='font-family:"Calibri",sans-serif'>Keokuk
444kaolinite.RAW</span></b> from the file dialog box; press <b><span
445style='font-family:"Calibri",sans-serif'>Yes</span></b> in the next popup. A
446new file dialog appears requesting an instrument parameter file; we will use an
447internal default instead. Press <b><span style='font-family:"Calibri",sans-serif'>Cancel</span></b>
448and select <b><span style='font-family:"Calibri",sans-serif'>Defaults for CuKa
449lab data</span></b> from the next popup. This process will repeat since the RAW
450file contains two scans. In the next popup, select only <b><span
451style='font-family:"Calibri",sans-serif'>kaolinite abc*</span></b>. There will
452be two PWDR scans in the GSAS-II data tree; one covers 2<span style='font-family:
453Symbol'>Q</span>= 10-90<span style='font-family:"Calibri",sans-serif'>°</span>
454and the other covers 2<span style='font-family:Symbol'>Q</span>=80-150°. Only
455the lower part of the first one is going to be used in our simulation work as
456the calculations become very time consuming for complex structures and high
457angle data. Select <b><span style='font-family:"Calibri",sans-serif'>PWDR
458Keokuk kaolinite.RAW Scan 1</span></b> from the GSAS-II data tree make sure it
459expands; its plot will also show.</p>
460
461<p class=MsoNormal><img width=700 height=600 id="Picture 27"
462src="Stacking%20Faults%20II_files/image016.gif"></p>
463
464<p class=MsoNormal>Go to <b><span style='font-family:"Calibri",sans-serif'>Limits</span></b>
465and set <b><span style='font-family:"Calibri",sans-serif'>Tmax</span></b> to <b><span
466style='font-family:"Calibri",sans-serif'>52.0</span></b>; that puts the upper
467limit in a relatively clear part of the pattern. Then go to Background and set
468the 1<sup>st</sup> coefficient to 20 (approximately the background at 2Q=18).
469Next go to <b><span style='font-family:"Calibri",sans-serif'>Sample parameters</span></b>
470and set the <b><span style='font-family:"Calibri",sans-serif'>Histogram scale</span></b>
471to something reasonable (I chose <b><span style='font-family:"Calibri",sans-serif'>20.0</span></b>)
472and make sure the <b><span style='font-family:"Calibri",sans-serif'>Diffractometer
473type is Bragg-Brentano</span></b>.</p>
474
475<p class=MsoNormal>Now we are ready for our 1<sup>st</sup> kaolinite
476simulation. Go to <b><span style='font-family:"Calibri",sans-serif'>Phases/Keokuk</span></b>
477and select the <b><span style='font-family:"Calibri",sans-serif'>Layers</span></b>
478tab. Do <b><span style='font-family:"Calibri",sans-serif'>Operations/Simulate
479pattern</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>
480in the popup. Select the <b><span style='font-family:"Calibri",sans-serif'>Scan
4811</span></b> pattern and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
482the simulation will finish quickly (press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>)
483and the new plot will be displayed (I’ve zoomed in a bit).</p>
484
485<p class=MsoNormal><img width=700 height=600 id="Picture 29"
486src="Stacking%20Faults%20II_files/image017.gif">.</p>
487
488<p class=MsoNormal>As you can see the simulation (green curve) does not fit the
489data (blue crosses) at all mostly due to the incorrect layer offset although
490the 1<sup>st</sup> peak seems to be positioned correctly. To work out the
491offset consider the drawing of kaolinite.</p>
492
493<p class=MsoNormal><span style='position:absolute;z-index:251661312;margin-left:
494104px;margin-top:123px;width:46px;height:22px'><img width=46 height=22
495src="Stacking%20Faults%20II_files/image018.gif"></span><span style='position:
496absolute;z-index:251660288;margin-left:153px;margin-top:135px;width:3px;
497height:199px'><img width=3 height=199
498src="Stacking%20Faults%20II_files/image019.gif"></span><img width=481
499height=360 id="Picture 30" src="Stacking%20Faults%20II_files/image020.jpg"></p>
500
501<p class=MsoNormal>The offset Dx is given by the blue arrow in the above
502drawing of kaolinite and is in fractional coordinates. Geometry gives</p>
503
504<p class=MsoNormal><span
505style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
506top:3.0pt'><img width=106 height=26
507src="Stacking%20Faults%20II_files/image021.gif"></span> Or in this case <b><span
508style='font-family:"Calibri",sans-serif'>-0.368</span></b>. Set <b><span
509style='font-family:"Calibri",sans-serif'>Dx</span></b> to this value &amp;
510repeat simulation.</p>
511
512<p class=MsoNormal><img width=700 height=600 id="Picture 33"
513src="Stacking%20Faults%20II_files/image022.gif"></p>
514
515<p class=MsoNormal>There is some improvement but some parts are not very well
516represented. Recall from the triclinic kaolinite lattice parameters that <span
517style='font-family:Symbol'>a</span> was 91.7°; that will produce a small offset
518in Dy. Using the same kind of geometry math gives <b><span style='font-family:
519"Calibri",sans-serif'>Dy=-0.0246</span></b>. Enter this value &amp; repeat the
520simulation again. This gives a much better fit to the observed pattern, but the
521simulated peaks are too sharp; this can be fixed by changing the U,V,W
522Instrument parameters. I’d just set <b><span style='font-family:"Calibri",sans-serif'>W=40</span></b>
523and the <b><span style='font-family:"Calibri",sans-serif'>Histogram scale</span></b>
524(in <b><span style='font-family:"Calibri",sans-serif'>Sample parameters</span></b>)
525to <b><span style='font-family:"Calibri",sans-serif'>40</span></b> and try
526again.</p>
527
528<p class=MsoNormal><img width=700 height=600 id="Picture 34"
529src="Stacking%20Faults%20II_files/image023.gif"></p>
530
531<p class=MsoNormal>That is a pretty good fit for a stacking simulation. By
532further hand tweaking of the parameters one can further improve the simulation
533but based on what we see here we do have the right description of stacking in
534Keokuk kaolinite. Save your project as you will need it for the next part of
535the exercise.</p>
536
537</div>
538
539</body>
540
541</html>
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