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244<body lang=EN-US link=blue vlink=purple>
245
246<div class=WordSection1>
247
248<h1>Stacking Fault Simulations – I</h1>
249
250<p class=MsoNormal>In this exercise you will use GSAS-II to simulate the
251diffraction patterns from faulted diamond. Diamond most commonly has the
252well-known cubic structure with the space group Fd3m and a=3.5668A. The C-atom is
253at 1/8,1/8,1/8 and can be viewed as a cubic stacking of ruffled hexagonal nets
254along the cubic cell 111 diagonal. </p>
255
256<p class=MsoNormal><img width=482 height=361
257src="Stacking%20Faults-I_files/image001.jpg"></p>
258
259<p class=MsoNormal>The structure of londsdaleite has those layers stacked
260hexagonally and thus a faulted diamond structure may occasionally have
261hexagonal stacked layers instead of all cubic ones. From geometric
262considerations, these planar stacking faults must extend across the entire
263crystal. If there are only a few such faults in a crystal then the diffraction
264pattern will show two cubic diamond patterns in a twin law relationship.
265Otherwise, if there are many such faults then the diffraction pattern will show
266streaks. To simulate the streaks one must first develop a model for the
267hexagonal net of C-atoms and then show how they stack in either the cubic or
268hexagonal forms. GSAS-II uses a suite of subroutines from the DIFFaX program
269(M.M.J. Treacy, J.M. Newsam &amp; M.W. Deem, (1991), Proc. Roy. Soc. Lond.
270433A, 499-520) to calculate the diffraction pattern via a general recursion
271algorithm and a randomized set of stacked layers. NB: this calculation can be
272quite time consuming particularly if unreasonable demands are made on it. </p>
273
274<p class=MsoNormal>If you have not done so already, start GSAS-II.</p>
275
276<h2>Simulation 1. Selected area diffraction for random faults in diamond</h2>
277
278<p class=MsoNormal>To begin we must have a phase to work with. In the main
279GSAS-II data tree menu do <b><span style='font-family:"Calibri",sans-serif'>Data/Add
280new phase</span></b>; a popup window will appear inviting you to name the
281phase. I entered <b><span style='font-family:"Calibri",sans-serif'>‘random
282faults</span></b>’. Then find this phase in the data tree under phases and
283select it; the data window will display the default for the General tab.</p>
284
285<p class=MsoNormal><img width=620 height=334
286src="Stacking%20Faults-I_files/image002.gif"></p>
287
288<p class=MsoNormal>Change the phase type to ‘<b><span style='font-family:"Calibri",sans-serif'>faulted</span></b>’;
289the window will be redrawn and a new tab (‘<b><span style='font-family:"Calibri",sans-serif'>Layers</span></b>’)
290will appear. Select it. Then save the project; I called it ‘<b><span
291style='font-family:"Calibri",sans-serif'>diamond</span></b>’.</p>
292
293<p class=MsoNormal><img width=624 height=370
294src="Stacking%20Faults-I_files/image003.gif"></p>
295
296<p class=MsoNormal>First you need to describe the reference unit cell for the
297stacking model. The cubic/hexagonal stacking in diamond is with layers
298perpendicular to the 111 axis. This will become the new c-axis. The a- &amp;
299b-axes are for the hexagonal net of C-atoms that are stacked in this structure.
300One can also anticipate that the resulting diffraction pattern will have
301hexagonal <b><span style='font-family:"Calibri",sans-serif'>6/mmm</span></b>
302symmetry so first select this from the pull down box neat the top of the page;
303the window will be redrawn.</p>
304
305<p class=MsoNormal><img width=624 height=464
306src="Stacking%20Faults-I_files/image004.gif"></p>
307
308<p class=MsoNormal>The a cell parameter for diamond stacking can be assumed to
309be a<span style='position:relative;top:3pt'><img width=27 height=21
310src="Stacking%20Faults-I_files/image005.gif">&nbsp;= <b><span style='font-family:
311"Calibri",sans-serif'>2.522</span></b> and the c cell parameter is a<span
312style='position:relative;top:3pt'><img width=27 height=21
313src="Stacking%20Faults-I_files/image006.gif">&nbsp;= <b><span style='font-family:
314"Calibri",sans-serif'>2.059</span></b> since there are 3 layers along the 111
315diamond cell diagonal. Enter these in the appropriate places; the cell volume
316will be revised.</p>
317
318<p class=MsoNormal>Now we have to describe the two hexagonal nets that will be
319stacked for either cubic or hexagonal stacking. Select <b><span
320style='font-family:"Calibri",sans-serif'>Add new layer?</span></b> the window
321will be redrawn.</p>
322
323<p class=MsoNormal><img width=624 height=479
324src="Stacking%20Faults-I_files/image007.gif"></p>
325
326<p class=MsoNormal>Name the layer (I chose ‘<b><span style='font-family:"Calibri",sans-serif'>layer
3271</span></b>’) and choose <b><span style='font-family:"Calibri",sans-serif'>‘-1</span></b>’
328for the layer symmetry. The window will be redrawn after changing the name.
329Next, select <b><span style='font-family:"Calibri",sans-serif'>Add atom?</span></b>
330and the window will be redrawn with one line in the layer table.</p>
331
332<p class=MsoNormal><img width=624 height=479
333src="Stacking%20Faults-I_files/image008.gif"></p>
334
335<p class=MsoNormal>To make this a C-atom select the ‘<b><span style='font-family:
336"Calibri",sans-serif'>Unk</span></b>’ under Type with a double click; a
337Periodic table will popup. Select <b><span style='font-family:"Calibri",sans-serif'>C</span></b>;
338the popup will disappear and the window will be redrawn. The coordinates of
339this C-atom in the new stacking unit cell is <b><span style='font-family:"Calibri",sans-serif'>-1/3,-1/6,-1/8</span></b>;
340you may enter these as fractions. Select a table item to complete the entry;
341the window should show the new position.</p>
342
343<p class=MsoNormal><img width=624 height=479
344src="Stacking%20Faults-I_files/image009.gif"></p>
345
346<p class=MsoNormal>You can draw the layer to see what it looks like; select <b><span
347style='font-family:"Calibri",sans-serif'>Draw layer?</span></b> and the drawing
348will appear. </p>
349
350<p class=MsoNormal><img width=486 height=363
351src="Stacking%20Faults-I_files/image010.jpg"></p>
352
353<p class=MsoNormal>A unit cell box is drawn with a 5x5 suite of unit cells; the
354ruffled hexagonal net perpendicular to the c-axis (blue line) is clear.</p>
355
356<p class=MsoNormal>Now we need a second layer; repeat the steps for making a
357layer using <b><span style='font-family:"Calibri",sans-serif'>1/3,1/6,-1/8</span></b>
358for the C-atom position with <b><span style='font-family:"Calibri",sans-serif'>-1</span></b>
359for the layer symmetry. The window should look like this when done.</p>
360
361<p class=MsoNormal><img width=624 height=624
362src="Stacking%20Faults-I_files/image011.gif"></p>
363
364<p class=MsoNormal>I’ve stretched it a bit to show the Layer-Layer transition
365probabilities. Change <b><span style='font-family:"Calibri",sans-serif'>Dz</span></b>
366for each entry to <b><span style='font-family:"Calibri",sans-serif'>1.0</span></b>
367to properly space out the stacked layers. If you select the first box in the
368plot column for layer 1 you will see the two layers stacked but in a way
369reminiscent of how carbon sheets stack in graphite. </p>
370
371<p class=MsoNormal><img width=479 height=358
372src="Stacking%20Faults-I_files/image012.jpg"></p>
373
374<p class=MsoNormal>Clearly not diamond stacking. The table defines how the next
375layer is displaced relative to the reference layer. You can shift this layer by
376using the <b><span style='font-family:"Calibri",sans-serif'>X,Y,Z</span></b>
377&amp; <b><span style='font-family:"Calibri",sans-serif'>shift-X,Y,Z</span></b>
378keys; the plot will be redrawn and the table entry updated each time you shift
379the layer. When you get to the right offset for diamond additional bonds will
380appear connecting the layers together. The correct shift is <b><span
381style='font-family:"Calibri",sans-serif'>Dx=2/3</span></b>, <b><span
382style='font-family:"Calibri",sans-serif'>Dy=1/3</span></b> and <b><span
383style='font-family:"Calibri",sans-serif'>Dz=1.0</span></b> for the layer 1 to
384layer 1 transition and for layer 2 to layer 2 the shifts are <b><span
385style='font-family:"Calibri",sans-serif'>Dx=-2/3</span></b>, <b><span
386style='font-family:"Calibri",sans-serif'>Dy=-1/3</span></b> and <b><span
387style='font-family:"Calibri",sans-serif'>Dz=1.0</span></b>. For the remaining
388layer 1-layer 2 and <i>vice versa</i> transitions <b><span style='font-family:
389"Calibri",sans-serif'>Dx=Dy=0</span></b>. Layer 1 to layer 1 stacking looks
390like.</p>
391
392<p class=MsoNormal><img width=477 height=357
393src="Stacking%20Faults-I_files/image013.jpg"></p>
394
395<p class=MsoNormal>You can explore the result of various stacking sequences in
396the next block of commands; enter <b><span style='font-family:"Calibri",sans-serif'>1
3971 1 1 2 2 2 2</span></b> into the box and press <b><span style='font-family:
398"Calibri",sans-serif'>Enter</span></b>. A plot showing the result of a single
399twin fault will be shown.</p>
400
401<p class=MsoNormal><img width=483 height=361
402src="Stacking%20Faults-I_files/image014.jpg"></p>
403
404<p class=MsoNormal>If you enter 1 2 1 2 1 2 1 2 then the structure of londsdaleite
405will be shown; 1 1 1 1 1 1 or 2 2 2 2 2 2 gives the diamond structure. </p>
406
407<p class=MsoNormal>Finally we must select transition probabilities; they should
408sum to 1.0 for each block. Use <b><span style='font-family:"Calibri",sans-serif'>0.7</span></b>
409for layer 1 to layer 1 and layer 2 to layer 2; the cross terms are then <b><span
410style='font-family:"Calibri",sans-serif'>0.3</span></b> to give</p>
411
412<p class=MsoNormal><img width=624 height=448
413src="Stacking%20Faults-I_files/image015.gif"></p>
414
415<p class=MsoNormal>We are now ready to do a single crystal simulation; select <b><span
416style='font-family:"Calibri",sans-serif'>Operations/Simulate pattern</span></b>
417from the Phase data window menu. A small popup will appear</p>
418
419<p class=MsoNormal><img width=279 height=136
420src="Stacking%20Faults-I_files/image016.gif"></p>
421
422<p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>selected
423area</span></b> for the calculation type; the popup will be redrawn with new
424options.</p>
425
426<p class=MsoNormal><img width=242 height=136
427src="Stacking%20Faults-I_files/image017.gif"></p>
428
429<p class=MsoNormal>To make it interesting select <b><span style='font-family:
430"Calibri",sans-serif'>Max. l index</span></b> of <b><span style='font-family:
431"Calibri",sans-serif'>6</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>.
432Very quickly a new popup will appear letting you know the simulation is
433finished; press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>.
434The data window will be redrawn</p>
435
436<p class=MsoNormal><img width=624 height=474
437src="Stacking%20Faults-I_files/image018.gif"></p>
438
439<p class=MsoNormal>At the top is a new item <b><span style='font-family:"Calibri",sans-serif'>Plot
440selected area diffraction?</span></b> Select it and a new plot will appear. The
441intensity scale is adjusted by pressing <b><span style='font-family:"Calibri",sans-serif'>D</span></b>
442(or <b><span style='font-family:"Calibri",sans-serif'>U</span></b>); I got</p>
443
444<p class=MsoNormal><img width=484 height=455
445src="Stacking%20Faults-I_files/image019.gif"></p>
446
447<p class=MsoNormal>The streaking intermixed with sharp spots is clearly obvious
448in this plot. Save this project; you’ll need it for the next simulation.</p>
449
450<h2>Simulation 2. Laboratory powder diffraction simulation for random faults in
451diamond</h2>
452
453<p class=MsoNormal>The setup for a powder pattern simulation is the same as
454above for selected are diffraction with one crucial difference. We need a dummy
455powder pattern to define the simulation limits. Using the same project as
456above, do <b><span style='font-family:"Calibri",sans-serif'>Import/Powder
457data/Simulate a data set</span></b> from the main GSAS-II data tree window. A
458popup will appear requesting the selection of an instrument parameter file;
459here we will use one of the built in defaults. Press <b><span style='font-family:
460"Calibri",sans-serif'>Cancel</span></b> and a new popup will appear offering
461some choices.</p>
462
463<p class=MsoNormal><img width=322 height=268
464src="Stacking%20Faults-I_files/image020.gif"></p>
465
466<p class=MsoNormal>Use the first one for <b><span style='font-family:"Calibri",sans-serif'>CuKa
467lab data</span></b>; a new popup will appear</p>
468
469<p class=MsoNormal><img width=318 height=342
470src="Stacking%20Faults-I_files/image021.gif"></p>
471
472<p class=MsoNormal>Change the end angle to <b><span style='font-family:"Calibri",sans-serif'>150</span></b>
473and the step size to <b><span style='font-family:"Calibri",sans-serif'>0.02</span></b>;
474press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b> and
475choose <b><span style='font-family:"Calibri",sans-serif'>random faults </span></b>(your
476phase name). Notice the small data window lets you know that you can clear the
477observed intensities in the simulation by doing an <b><span style='font-family:
478"Calibri",sans-serif'>Edit range</span></b> (no need to change anything). The
479tree will have a new item <b><span style='font-family:"Calibri",sans-serif'>PWDR
480CW x-ray simulation</span></b>. Select <b><span style='font-family:"Calibri",sans-serif'>Background</span></b>
481&amp; enter <b><span style='font-family:"Calibri",sans-serif'>50</span></b> for
482the 1<sup>st</sup> coefficient. Next select <b><span style='font-family:"Calibri",sans-serif'>Sample
483parameters</span></b> and enter <b><span style='font-family:"Calibri",sans-serif'>1000</span></b>
484for the <b><span style='font-family:"Calibri",sans-serif'>Histogram scale
485factor</span></b> and change the <b><span style='font-family:"Calibri",sans-serif'>Diffractometer
486type</span></b> to <b><span style='font-family:"Calibri",sans-serif'>Bragg-Brentano</span></b>.
487Finally, find your phase (<b><span style='font-family:"Calibri",sans-serif'>random
488faults</span></b>) and select it and then the <b><span style='font-family:"Calibri",sans-serif'>Layers</span></b>
489tab. It should be unchanged from when the selected area simulation was
490finished.</p>
491
492<p class=MsoNormal>To do the simulation do <b><span style='font-family:"Calibri",sans-serif'>Operations/Simulate
493pattern</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>
494from the popup. The calculated pattern will by default be broadened using U, V,
495&amp; W from the Instrument parameters for the chosen powder pattern. Other
496choices use a mean Gaussian broadening (faster) or no broadening (even faster).
497The only choice for the pattern is given in the next popup; press <b><span
498style='font-family:"Calibri",sans-serif'>Ok</span></b> and the simulation will
499proceed. After a few seconds a small popup will appear letting you know it is
500done; press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b> and
501the powder pattern will be displayed with the result. On the plot press the ‘<b><span
502style='font-family:"Calibri",sans-serif'>+</span></b>’ key to suppress the ‘+’
503marks. The plot should look like: I’ve expanded the scale to show the
504interesting stuff around each peak.</p>
505
506<p class=MsoNormal><img width=624 height=587
507src="Stacking%20Faults-I_files/image022.gif"></p>
508
509<p class=MsoNormal>The blue line is a simulated observed pattern with imposed
510Poisson noise, the red line is the calculated background and the green curve is
511the smooth calculated pattern. A difference curve is also shown. You can play
512with changing the transition probabilities and/or the layer offsets to see what
513effect these have on the pattern; changing these will change the calculated
514pattern unless you reset the dummy profile as noted above.</p>
515
516<h2>Simulation 3. Sequential parameter change</h2>
517
518<p class=MsoNormal>A perhaps useful means of exploring the effects of changing
519stacking parameters is doing a sequence of simulations varying one parameter
520over a range. To try this out do <b><span style='font-family:"Calibri",sans-serif'>Operations/Sequence
521simulations</span></b> from the Layers menu; a popup will appear</p>
522
523<p class=MsoNormal><img width=279 height=191
524src="Stacking%20Faults-I_files/image023.gif"></p>
525
526<p class=MsoNormal>Here you select the parameter, range and number of steps
527(both ends will be used). From the <b><span style='font-family:"Calibri",sans-serif'>Select
528parameter</span></b> pulldown choose <b><span style='font-family:"Calibri",sans-serif'>TransP;0;0</span></b>;
529this is the layer 1 to layer 1 transition probability. Then change the no.
530steps to <b><span style='font-family:"Calibri",sans-serif'>10</span></b> (11 will
531be calculated). We have the same choices for instrument broadening as above;
532use the default. Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
533the next popup allows selection of a powder pattern (e.g. for comparison and
534the range for the calculation). Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>
535for this one; the sequential simulation will proceed. The console displays
536progress and the transition matrix for each step. A popup will appear when the
537sequence is finished after several seconds. Notice that the matrix is not
538symmetric so that layer1 to layer 1 probability is not the same as layer 2 to
539layer 2 at each step in the simulation. We can force this by selecting <b><span
540style='font-family:"Calibri",sans-serif'>Symmetric probabilities?</span></b> on
541the Layers page. Do this and repeat the sequential simulation as above. Now the
542matrices are symmetric as one could expect. When the simulation is finished,
543select the <b><span style='font-family:"Calibri",sans-serif'>Plot sequential
544result?</span></b> box; a new plot will appear.</p>
545
546<p class=MsoNormal><img width=624 height=535
547src="Stacking%20Faults-I_files/image024.gif"></p>
548
549<p class=MsoNormal>This is a multiline plot; you can shift the lines with the <b><span
550style='font-family:"Calibri",sans-serif'>U,D,L,R</span></b> keys (<b><span
551style='font-family:"Calibri",sans-serif'>O</span></b> resets offsets to zero).
552I’ve done this for the next plot.</p>
553
554<p class=MsoNormal><img width=624 height=535
555src="Stacking%20Faults-I_files/image025.gif"></p>
556
557<p class=MsoNormal>The first blue line is for pure hexagonal londsdaleite stacking
558and the last magenta line is for pure cubic diamond stacking. You can see how
559some lines quickly vanish with the introduction of stacking faults while other
560persist across the entire sequence. This is a good place to save your project
561file; the sequential result will be included.</p>
562
563<h2>Simulation 4. Modelling clustering in diamond</h2>
564
565<p class=MsoNormal>In this simulation we will explore the possibility that the
566stacking history affects the probability of a fault. In the case of diamond, a
567fault to form londsdaleite could be followed by similar layers until a lower
568probability fault converts the structure back to diamond. The crystal then has
569blocks of diamond structure interleaved with blocks of londsdaleite. This is
570best done in a new phase so we don’t mess up the above simulations, but most of
571the data in the current phase is useful for the cluster model. The easiest way
572is to import the new phase from the current project. <b><span style='font-family:
573"Calibri",sans-serif'>Do Import/Phase/from GSAS-II gpx file</span></b> from the
574main GSAS-II data tree menu. A file selection dialog box will appear; select
575the current project file (<b><span style='font-family:"Calibri",sans-serif'>diamond.gpx</span></b>)
576and press <b><span style='font-family:"Calibri",sans-serif'>Open</span></b>. A
577small popup will appear confirming your choice; press <b><span
578style='font-family:"Calibri",sans-serif'>Yes</span></b>. The next popup offers
579the change to name the phase, I chose <b><span style='font-family:"Calibri",sans-serif'>clustered</span></b>
580for the name. Next select the PWDR data set to be linked to this phase. The
581General tab for the new phase will appear.</p>
582
583<p class=MsoNormal><img width=624 height=336
584src="Stacking%20Faults-I_files/image026.gif"></p>
585
586<p class=MsoNormal>Notice that the Phase type is faulted and that Layers is one
587of the tabs; select it.</p>
588
589<p class=MsoNormal><img width=624 height=474
590src="Stacking%20Faults-I_files/image027.gif"></p>
591
592<p class=MsoNormal>This is all the same information as for the random faults
593phase. To simulate clustering we need two new layers which are the same as
594these two listed here. Do <b><span style='font-family:"Calibri",sans-serif'>Add
595new layer?</span></b> twice so two new layers appear. Name them <b><span
596style='font-family:"Calibri",sans-serif'>layer 3</span></b> and <b><span
597style='font-family:"Calibri",sans-serif'>layer 4</span></b>. Make layer 3 <b><span
598style='font-family:"Calibri",sans-serif'>Same as layer</span></b> 1 (select
599from the pull down) and layer 4 <b><span style='font-family:"Calibri",sans-serif'>Same
600as layer 2</span></b>. Each time the window is redrawn so that the transition
601probability tables reflect these changes. You should also change the <b><span
602style='font-family:"Calibri",sans-serif'>Diffraction Laue symmetry</span></b>
603to <b><span style='font-family:"Calibri",sans-serif'>-3m</span></b>. When you
604are done the upper part of the Layers window should look like.</p>
605
606<p class=MsoNormal>&nbsp;</p>
607
608<p class=MsoNormal>&nbsp;</p>
609
610<p class=MsoNormal><img width=624 height=474
611src="Stacking%20Faults-I_files/image028.gif"></p>
612
613<p class=MsoNormal>&nbsp;</p>
614
615<p class=MsoNormal>The transition vectors for the cluster model are similar to
616the random faults model, i.e. layer 1-1 and layer 3-1 transitions are <b><span
617style='font-family:"Calibri",sans-serif'>2/3,1/3,1</span></b> for Dx, Dy &amp;
618Dz, layer, and layer 2-4 and 4-4 transitions are <b><span style='font-family:
619"Calibri",sans-serif'>-2/3,-1/3,1</span></b> for Dx, Dy &amp; Dz. All the rest
620are <b><span style='font-family:"Calibri",sans-serif'>0,0,1</span></b> for
621Dx,,Dy &amp; Dz. The probabilities can best be seen from the following array</p>
622
623<p class=MsoNormal>&nbsp;</p>
624
625<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
626 style='border-collapse:collapse'>
627 <tr style='height:21.45pt'>
628  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
629  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
630  <p class=MsoNormal>Layer</p>
631  </td>
632  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
633  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
634  <p class=MsoNormal>1</p>
635  </td>
636  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
637  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
638  <p class=MsoNormal>2</p>
639  </td>
640  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
641  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
642  <p class=MsoNormal>3</p>
643  </td>
644  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
645  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
646  <p class=MsoNormal>4</p>
647  </td>
648 </tr>
649 <tr style='height:21.45pt'>
650  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
651  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
652  <p class=MsoNormal>1</p>
653  </td>
654  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
655  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
656  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
657  <p class=MsoNormal>CS</p>
658  </td>
659  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
660  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
661  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
662  <p class=MsoNormal>CF</p>
663  </td>
664  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
665  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
666  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
667  <p class=MsoNormal>x</p>
668  </td>
669  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
670  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
671  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
672  <p class=MsoNormal>x</p>
673  </td>
674 </tr>
675 <tr style='height:21.45pt'>
676  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
677  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
678  <p class=MsoNormal>2</p>
679  </td>
680  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
681  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
682  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
683  <p class=MsoNormal>x</p>
684  </td>
685  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
686  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
687  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
688  <p class=MsoNormal>x</p>
689  </td>
690  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
691  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
692  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
693  <p class=MsoNormal>HS</p>
694  </td>
695  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
696  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
697  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
698  <p class=MsoNormal>HF</p>
699  </td>
700 </tr>
701 <tr style='height:21.45pt'>
702  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
703  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
704  <p class=MsoNormal>3</p>
705  </td>
706  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
707  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
708  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
709  <p class=MsoNormal>HF</p>
710  </td>
711  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
712  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
713  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
714  <p class=MsoNormal>HS</p>
715  </td>
716  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
717  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
718  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
719  <p class=MsoNormal>x</p>
720  </td>
721  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
722  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
723  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
724  <p class=MsoNormal>x</p>
725  </td>
726 </tr>
727 <tr style='height:21.45pt'>
728  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
729  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
730  <p class=MsoNormal>4</p>
731  </td>
732  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
733  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
734  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
735  <p class=MsoNormal>x</p>
736  </td>
737  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
738  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
739  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
740  <p class=MsoNormal>x</p>
741  </td>
742  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
743  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
744  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
745  <p class=MsoNormal>CF</p>
746  </td>
747  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
748  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
749  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
750  <p class=MsoNormal>CS</p>
751  </td>
752 </tr>
753</table>
754
755<p class=MsoNormal>Where CS – cubic stacking, CF – cubic fault, HS – hexagonal
756stacking, HF – hexagonal fault and x – not allowed. A suitable model might be
757CS = <b><span style='font-family:"Calibri",sans-serif'>0.9</span></b>, CF = <b><span
758style='font-family:"Calibri",sans-serif'>0.1</span></b>, HS = <b><span
759style='font-family:"Calibri",sans-serif'>0.8</span></b> and HF = <b><span
760style='font-family:"Calibri",sans-serif'>0.2</span></b>. This will give more
761and thicker cubic blocks than hexagonal ones. Set these values and the
762Transition tables should look like</p>
763
764<p class=MsoNormal><img width=624 height=620
765src="Stacking%20Faults-I_files/image029.gif"></p>
766
767<p class=MsoNormal>Before doing the simulation we need to clear away the old
768one; select the <b><span style='font-family:"Calibri",sans-serif'>PWDR</span></b>
769entry from the GSAS-II data tree and then select <b><span style='font-family:
770"Calibri",sans-serif'>Edit range</span></b> from the data window. Don’t change
771anything, just press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
772this will clear the previous simulation. Then return to the clustered phase
773Layers tab. Do <b><span style='font-family:"Calibri",sans-serif'>Operations/Simulate
774pattern</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>
775twice. The simulation will require some seconds to finish; the powder profile
776will look like</p>
777
778<p class=MsoNormal><img width=624 height=535
779src="Stacking%20Faults-I_files/image030.gif"></p>
780
781<p class=MsoNormal>Again, I have used ‘<b><span style='font-family:"Calibri",sans-serif'>+</span></b>’
782and zoomed in to show the interesting part of the pattern. </p>
783
784<p class=MsoNormal>As additional work you can do sequential simulations to
785explore the effect of changing probabilities. Try varying <b><span
786style='font-family:"Calibri",sans-serif'>TransP;0;0</span></b>, i.e. layer 1 –
787layer 1 (CS) transition probability and <b><span style='font-family:"Calibri",sans-serif'>TransP;2;1</span></b>,
788i.e. layer 3 – layer – 2 (HS) transition probability. Be sure the <b><span
789style='font-family:"Calibri",sans-serif'>Symmetric probabilities</span></b> box
790is checked otherwise you’ll get nonsense. This ends this stacking fault
791tutorial; the next one involves using kaolinite layers to simulate diffraction
792patterns from kaolinite clays.</p>
793
794</div>
795
796</body>
797
798</html>
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