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228
229<div class=WordSection1>
230
231<h1>Stacking Fault Simulations – I</h1>
232
233<p class=MsoNormal>In this exercise you will use GSAS-II to simulate the
234diffraction patterns from faulted diamond. Diamond most commonly has the
235well-known cubic structure with the space group Fd3m and a=3.5668A. The C-atom
236is at 1/8,1/8,1/8 and can be viewed as a cubic stacking of ruffled hexagonal
237nets along the cubic cell 111 diagonal. </p>
238
239<p class=MsoNormal><img width=482 height=361 id="Picture 1"
240src="Stacking%20Faults-I_files/image001.jpg"></p>
241
242<p class=MsoNormal>The structure of lonsdaleite has those layers stacked
243hexagonally and thus a faulted diamond structure may occasionally have
244hexagonal stacked layers instead of all cubic ones. From geometric
245considerations, these planar stacking faults must extend across the entire
246crystal. If there are only a few such faults in a crystal then the diffraction
247pattern will show two cubic diamond patterns in a twin law relationship.
248Otherwise, if there are many such faults then the diffraction pattern will show
249streaks. To simulate the streaks one must first develop a model for the
250hexagonal net of C-atoms and then show how they stack in either the cubic or hexagonal
251forms. GSAS-II uses a suite of subroutines from the DIFFaX program (M.M.J.
252Treacy, J.M. Newsam &amp; M.W. Deem, (1991), Proc. Roy. Soc. Lond. 433A,
253499-520) to calculate the diffraction pattern via a general recursion algorithm
254and a randomized set of stacked layers. NB: this calculation can be quite time
255consuming particularly if unreasonable demands are made on it. </p>
256
257<p class=MsoNormal>If you have not done so already, start GSAS-II.</p>
258
259<h2>Simulation 1. Selected area diffraction for random faults in diamond</h2>
260
261<p class=MsoNormal>To begin we must have a phase to work with. In the main
262GSAS-II data tree menu do <b><span style='font-family:"Calibri",sans-serif'>Data/Add
263new phase</span></b>; a popup window will appear inviting you to name the
264phase. I entered <b><span style='font-family:"Calibri",sans-serif'>‘random
265faults</span></b>’. Then find this phase in the data tree under phases and
266select it; the data window will display the default for the General tab.</p>
267
268<p class=MsoNormal><img width=620 height=334 id="Picture 2"
269src="Stacking%20Faults-I_files/image002.gif"></p>
270
271<p class=MsoNormal>Change the phase type to ‘<b><span style='font-family:"Calibri",sans-serif'>faulted</span></b>’;
272the window will be redrawn and a new tab (‘<b><span style='font-family:"Calibri",sans-serif'>Layers</span></b>’)
273will appear. Select it. Then save the project; I called it ‘<b><span
274style='font-family:"Calibri",sans-serif'>diamond</span></b>’.</p>
275
276<p class=MsoNormal><img width=624 height=370 id="Picture 3"
277src="Stacking%20Faults-I_files/image003.gif"></p>
278
279<p class=MsoNormal>First you need to describe the reference unit cell for the
280stacking model. The cubic/hexagonal stacking in diamond is with layers
281perpendicular to the 111 axis. This will become the new c-axis. The a- &amp;
282b-axes are for the hexagonal net of C-atoms that are stacked in this structure.
283One can also anticipate that the resulting diffraction pattern will have
284hexagonal <b><span style='font-family:"Calibri",sans-serif'>6/mmm</span></b>
285symmetry so first select this from the pull down box neat the top of the page;
286the window will be redrawn.</p>
287
288<p class=MsoNormal><img width=624 height=464 id="Picture 4"
289src="Stacking%20Faults-I_files/image004.gif"></p>
290
291<p class=MsoNormal>The a cell parameter for diamond stacking can be assumed to
292be a<span style='font-size:12.0pt;font-family:"Times New Roman",serif;
293position:relative;top:3.0pt'><img width=27 height=21
294src="Stacking%20Faults-I_files/image005.gif"></span> = <b><span
295style='font-family:"Calibri",sans-serif'>2.522</span></b> and the c cell
296parameter is a<span style='font-size:12.0pt;font-family:"Times New Roman",serif;
297position:relative;top:3.0pt'><img width=27 height=21
298src="Stacking%20Faults-I_files/image006.gif"></span> = <b><span
299style='font-family:"Calibri",sans-serif'>2.059</span></b> since there are 3
300layers along the 111 diamond cell diagonal. Enter these in the appropriate
301places; the cell volume will be revised.</p>
302
303<p class=MsoNormal>Now we have to describe the two hexagonal nets that will be
304stacked for either cubic or hexagonal stacking. Select <b><span
305style='font-family:"Calibri",sans-serif'>Add new layer?</span></b> the window
306will be redrawn.</p>
307
308<p class=MsoNormal><img width=624 height=479 id="Picture 5"
309src="Stacking%20Faults-I_files/image007.gif"></p>
310
311<p class=MsoNormal>Name the layer (I chose ‘<b><span style='font-family:"Calibri",sans-serif'>layer
3121</span></b>’) and choose <b><span style='font-family:"Calibri",sans-serif'>‘-1</span></b>’
313for the layer symmetry. The window will be redrawn after changing the name.
314Next, select <b><span style='font-family:"Calibri",sans-serif'>Add atom?</span></b>
315and the window will be redrawn with one line in the layer table.</p>
316
317<p class=MsoNormal><img width=624 height=479 id="Picture 6"
318src="Stacking%20Faults-I_files/image008.gif"></p>
319
320<p class=MsoNormal>To make this a C-atom select the ‘<b><span style='font-family:
321"Calibri",sans-serif'>Unk</span></b>’ under Type with a double click; a
322Periodic table will popup. Select <b><span style='font-family:"Calibri",sans-serif'>C</span></b>;
323the popup will disappear and the window will be redrawn. The coordinates of
324this 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>;
325you may enter these as fractions. Select a table item to complete the entry;
326the window should show the new position.</p>
327
328<p class=MsoNormal><img width=624 height=479 id="Picture 8"
329src="Stacking%20Faults-I_files/image009.gif"></p>
330
331<p class=MsoNormal>You can draw the layer to see what it looks like; select <b><span
332style='font-family:"Calibri",sans-serif'>Draw layer?</span></b> and the drawing
333will appear. </p>
334
335<p class=MsoNormal><img width=486 height=363 id="Picture 10"
336src="Stacking%20Faults-I_files/image010.jpg"></p>
337
338<p class=MsoNormal>A unit cell box is drawn with a 5x5 suite of unit cells; the
339ruffled hexagonal net perpendicular to the c-axis (blue line) is clear.</p>
340
341<p class=MsoNormal>Now we need a second layer; repeat the steps for making a
342layer using <b><span style='font-family:"Calibri",sans-serif'>1/3,1/6,-1/8</span></b>
343for the C-atom position with <b><span style='font-family:"Calibri",sans-serif'>-1</span></b>
344for the layer symmetry. The window should look like this when done.</p>
345
346<p class=MsoNormal><img width=624 height=624 id="Picture 11"
347src="Stacking%20Faults-I_files/image011.gif"></p>
348
349<p class=MsoNormal>I’ve stretched it a bit to show the Layer-Layer transition
350probabilities. Change <b><span style='font-family:"Calibri",sans-serif'>Dz</span></b>
351for each entry to <b><span style='font-family:"Calibri",sans-serif'>1.0</span></b>
352to properly space out the stacked layers. If you select the first box in the
353plot column for layer 1 you will see the two layers stacked but in a way
354reminiscent of how carbon sheets stack in graphite. </p>
355
356<p class=MsoNormal><img width=479 height=358 id="Picture 12"
357src="Stacking%20Faults-I_files/image012.jpg"></p>
358
359<p class=MsoNormal>Clearly not diamond stacking. The table defines how the next
360layer is displaced relative to the reference layer. You can shift this layer by
361using the <b><span style='font-family:"Calibri",sans-serif'>X,Y,Z</span></b>
362&amp; <b><span style='font-family:"Calibri",sans-serif'>shift-X,Y,Z</span></b>
363keys; the plot will be redrawn and the table entry updated each time you shift
364the layer. When you get to the right offset for diamond additional bonds will
365appear connecting the layers together. The correct shift is <b><span
366style='font-family:"Calibri",sans-serif'>Dx=2/3</span></b>, <b><span
367style='font-family:"Calibri",sans-serif'>Dy=1/3</span></b> and <b><span
368style='font-family:"Calibri",sans-serif'>Dz=1.0</span></b> for the layer 1 to
369layer 1 transition and for layer 2 to layer 2 the shifts are <b><span
370style='font-family:"Calibri",sans-serif'>Dx=-2/3</span></b>, <b><span
371style='font-family:"Calibri",sans-serif'>Dy=-1/3</span></b> and <b><span
372style='font-family:"Calibri",sans-serif'>Dz=1.0</span></b>. For the remaining
373layer 1-layer 2 and <i>vice versa</i> transitions <b><span style='font-family:
374"Calibri",sans-serif'>Dx=Dy=0</span></b>. Layer 1 to layer 1 stacking looks
375like.</p>
376
377<p class=MsoNormal><img width=477 height=357 id="Picture 13"
378src="Stacking%20Faults-I_files/image013.jpg"></p>
379
380<p class=MsoNormal>You can explore the result of various stacking sequences in
381the next block of commands; enter <b><span style='font-family:"Calibri",sans-serif'>1
3821 1 1 2 2 2 2</span></b> into the box and press <b><span style='font-family:
383"Calibri",sans-serif'>Enter</span></b>. A plot showing the result of a single
384twin fault will be shown.</p>
385
386<p class=MsoNormal><img width=483 height=361 id="Picture 14"
387src="Stacking%20Faults-I_files/image014.jpg"></p>
388
389<p class=MsoNormal>If you enter 1 2 1 2 1 2 1 2 then the structure of
390lonsdaleite will be shown; 1 1 1 1 1 1 or 2 2 2 2 2 2 gives the diamond
391structure. </p>
392
393<p class=MsoNormal>Finally we must select transition probabilities; they should
394sum to 1.0 for each block. Use <b><span style='font-family:"Calibri",sans-serif'>0.7</span></b>
395for layer 1 to layer 1 and layer 2 to layer 2; the cross terms are then <b><span
396style='font-family:"Calibri",sans-serif'>0.3</span></b> to give</p>
397
398<p class=MsoNormal><img width=624 height=448
399src="Stacking%20Faults-I_files/image015.gif"></p>
400
401<p class=MsoNormal>We are now ready to do a single crystal simulation; select <b><span
402style='font-family:"Calibri",sans-serif'>Operations/Simulate pattern</span></b>
403from the Phase data window menu. A small popup will appear</p>
404
405<p class=MsoNormal><img width=279 height=136
406src="Stacking%20Faults-I_files/image016.gif"></p>
407
408<p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>selected
409area</span></b> for the calculation type; the popup will be redrawn with new
410options.</p>
411
412<p class=MsoNormal><img width=242 height=136 id="Picture 15"
413src="Stacking%20Faults-I_files/image017.gif"></p>
414
415<p class=MsoNormal>To make it interesting select <b><span style='font-family:
416"Calibri",sans-serif'>Max. l index</span></b> of <b><span style='font-family:
417"Calibri",sans-serif'>6</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>.
418Very quickly a new popup will appear letting you know the simulation is
419finished; press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>.
420The data window will be redrawn</p>
421
422<p class=MsoNormal><img width=624 height=474 id="Picture 16"
423src="Stacking%20Faults-I_files/image018.gif"></p>
424
425<p class=MsoNormal>At the top is a new item <b><span style='font-family:"Calibri",sans-serif'>Plot
426selected area diffraction?</span></b> Select it and a new plot will appear. The
427intensity scale is adjusted by pressing <b><span style='font-family:"Calibri",sans-serif'>D</span></b>
428(or <b><span style='font-family:"Calibri",sans-serif'>U</span></b>); I got</p>
429
430<p class=MsoNormal><img width=484 height=455 id="Picture 17"
431src="Stacking%20Faults-I_files/image019.gif"></p>
432
433<p class=MsoNormal>The streaking intermixed with sharp spots is clearly obvious
434in this plot. Save this project; you’ll need it for the next simulation.</p>
435
436<h2>Simulation 2. Laboratory powder diffraction simulation for random faults in
437diamond</h2>
438
439<p class=MsoNormal>The setup for a powder pattern simulation is the same as
440above for selected are diffraction with one crucial difference. We need a dummy
441powder pattern to define the simulation limits. Using the same project as
442above, do <b><span style='font-family:"Calibri",sans-serif'>Import/Powder
443data/Simulate a data set</span></b> from the main GSAS-II data tree window. A
444popup will appear requesting the selection of an instrument parameter file;
445here we will use one of the built in defaults. Press <b><span style='font-family:
446"Calibri",sans-serif'>Cancel</span></b> and a new popup will appear offering
447some choices.</p>
448
449<p class=MsoNormal><img width=322 height=268 id="Picture 18"
450src="Stacking%20Faults-I_files/image020.gif"></p>
451
452<p class=MsoNormal>Use the first one for <b><span style='font-family:"Calibri",sans-serif'>CuKa
453lab data</span></b>; a new popup will appear</p>
454
455<p class=MsoNormal><img width=318 height=342 id="Picture 19"
456src="Stacking%20Faults-I_files/image021.gif"></p>
457
458<p class=MsoNormal>Change the end angle to <b><span style='font-family:"Calibri",sans-serif'>150</span></b>
459and the step size to <b><span style='font-family:"Calibri",sans-serif'>0.02</span></b>;
460press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b> and
461choose <b><span style='font-family:"Calibri",sans-serif'>random faults </span></b>(your
462phase name). Notice the small data window lets you know that you can clear the
463observed intensities in the simulation by doing an <b><span style='font-family:
464"Calibri",sans-serif'>Edit range</span></b> (no need to change anything). The
465tree will have a new item <b><span style='font-family:"Calibri",sans-serif'>PWDR
466CW x-ray simulation</span></b>. Select <b><span style='font-family:"Calibri",sans-serif'>Background</span></b>
467&amp; enter <b><span style='font-family:"Calibri",sans-serif'>50</span></b> for
468the 1<sup>st</sup> coefficient. Next select <b><span style='font-family:"Calibri",sans-serif'>Sample
469parameters</span></b> and enter <b><span style='font-family:"Calibri",sans-serif'>1000</span></b>
470for the <b><span style='font-family:"Calibri",sans-serif'>Histogram scale
471factor</span></b> and change the <b><span style='font-family:"Calibri",sans-serif'>Diffractometer
472type</span></b> to <b><span style='font-family:"Calibri",sans-serif'>Bragg-Brentano</span></b>.
473Finally, find your phase (<b><span style='font-family:"Calibri",sans-serif'>random
474faults</span></b>) and select it and then the <b><span style='font-family:"Calibri",sans-serif'>Layers</span></b>
475tab. It should be unchanged from when the selected area simulation was
476finished.</p>
477
478<p class=MsoNormal>To do the simulation 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>
480from the popup. The calculated pattern will by default be broadened using U, V,
481&amp; W from the Instrument parameters for the chosen powder pattern. Other
482choices use a mean Gaussian broadening (faster) or no broadening (even faster).
483The only choice for the pattern is given in the next popup; press <b><span
484style='font-family:"Calibri",sans-serif'>Ok</span></b> and the simulation will
485proceed. After a few seconds a small popup will appear letting you know it is
486done; press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b> and
487the powder pattern will be displayed with the result. On the plot press the ‘<b><span
488style='font-family:"Calibri",sans-serif'>+</span></b>’ key to suppress the ‘+’
489marks. The plot should look like: I’ve expanded the scale to show the
490interesting stuff around each peak.</p>
491
492<p class=MsoNormal><img width=624 height=587 id="Picture 20"
493src="Stacking%20Faults-I_files/image022.gif"></p>
494
495<p class=MsoNormal>The blue line is a simulated observed pattern with imposed
496Poisson noise, the red line is the calculated background and the green curve is
497the smooth calculated pattern. A difference curve is also shown. You can play
498with changing the transition probabilities and/or the layer offsets to see what
499effect these have on the pattern; changing these will change the calculated
500pattern unless you reset the dummy profile as noted above.</p>
501
502<h2>Simulation 3. Sequential parameter change</h2>
503
504<p class=MsoNormal>A perhaps useful means of exploring the effects of changing
505stacking parameters is doing a sequence of simulations varying one parameter
506over a range. To try this out do Operations/Sequence simulations from the
507Layers menu; a popup will appear</p>
508
509<p class=MsoNormal><img width=279 height=191 id="Picture 21"
510src="Stacking%20Faults-I_files/image023.gif"></p>
511
512<p class=MsoNormal>Here you select the parameter, range and number of steps
513(both ends will be used). From the <b><span style='font-family:"Calibri",sans-serif'>Select
514parameter</span></b> pulldown choose <b><span style='font-family:"Calibri",sans-serif'>TransP;0;0</span></b>;
515this is the layer 1 to layer 1 transition probability. Then change the no.
516steps to <b><span style='font-family:"Calibri",sans-serif'>10</span></b> (11
517will be calculated). We have the same choices for instrument broadening as
518above; use the default. Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
519the next popup allows selection of a powder pattern (e.g. for comparison and
520the range for the calculation). Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>
521for this one; the sequential simulation will proceed. The console displays
522progress and the transition matrix for each step. A popup will appear when the
523sequence is finished after several seconds. Notice that the matrix is not
524symmetric so that layer1 to layer 1 probability is not the same as layer 2 to
525layer 2 at each step in the simulation. We can force this by selecting <b><span
526style='font-family:"Calibri",sans-serif'>Symmetric probabilities?</span></b> on
527the Layers page. Do this and repeat the sequential simulation as above. Now the
528matrices are symmetric as one could expect. When the simulation is finished,
529select the <b><span style='font-family:"Calibri",sans-serif'>Plot sequential
530result?</span></b> box; a new plot will appear.</p>
531
532<p class=MsoNormal><img width=624 height=535 id="Picture 22"
533src="Stacking%20Faults-I_files/image024.gif"></p>
534
535<p class=MsoNormal>This is a multiline plot; you can shift the lines with the <b><span
536style='font-family:"Calibri",sans-serif'>U,D,L,R</span></b> keys (<b><span
537style='font-family:"Calibri",sans-serif'>O</span></b> resets offsets to zero).
538I’ve done this for the next plot.</p>
539
540<p class=MsoNormal><img width=624 height=535 id="Picture 23"
541src="Stacking%20Faults-I_files/image025.gif"></p>
542
543<p class=MsoNormal>The first blue line is for pure hexagonal lonsdaleite
544stacking and the last magenta line is for pure cubic diamond stacking. You can see
545how some lines quickly vanish with the introduction of stacking faults while
546other persist across the entire sequence. This is a good place to save your
547project file; the sequential result will be included.</p>
548
549<h2>Simulation 4. Modelling clustering in diamond</h2>
550
551<p class=MsoNormal>In this simulation we will explore the possibility that the
552stacking history affects the probability of a fault. In the case of diamond, a
553fault to form lonsdaleite could be followed by similar layers until a lower
554probability fault converts the structure back to diamond. The crystal then has
555blocks of diamond structure interleaved with blocks of lonsdaleite. This is
556best done in a new phase so we don’t mess up the above simulations, but most of
557the data in the current phase is useful for the cluster model. The easiest way
558is to import the new phase from the current project. <b><span style='font-family:
559"Calibri",sans-serif'>Do Import/Phase/from GSAS-II gpx file</span></b> from the
560main GSAS-II data tree menu. A file selection dialog box will appear; select
561the current project file (<b><span style='font-family:"Calibri",sans-serif'>diamond.gpx</span></b>)
562and press <b><span style='font-family:"Calibri",sans-serif'>Open</span></b>. A
563small popup will appear confirming your choice; press <b><span
564style='font-family:"Calibri",sans-serif'>Yes</span></b>. The next popup offers
565the change to name the phase, I chose <b><span style='font-family:"Calibri",sans-serif'>clustered</span></b>
566for the name. Next select the PWDR data set to be linked to this phase. The
567General tab for the new phase will appear.</p>
568
569<p class=MsoNormal><img width=624 height=336 id="Picture 24"
570src="Stacking%20Faults-I_files/image026.gif"></p>
571
572<p class=MsoNormal>Notice that the Phase type is faulted and that Layers is one
573of the tabs; select it.</p>
574
575<p class=MsoNormal><img width=624 height=474 id="Picture 26"
576src="Stacking%20Faults-I_files/image027.gif"></p>
577
578<p class=MsoNormal>This is all the same information as for the random faults
579phase. To simulate clustering we need two new layers which are the same as
580these two listed here. Do <b><span style='font-family:"Calibri",sans-serif'>Add
581new layer?</span></b> twice so two new layers appear. Name them <b><span
582style='font-family:"Calibri",sans-serif'>layer 3</span></b> and <b><span
583style='font-family:"Calibri",sans-serif'>layer 4</span></b>. Make layer 3 <b><span
584style='font-family:"Calibri",sans-serif'>Same as layer</span></b> 1 (select
585from the pull down) and layer 4 <b><span style='font-family:"Calibri",sans-serif'>Same
586as layer 2</span></b>. Each time the window is redrawn so that the transition
587probability tables reflect these changes. You should also change the <b><span
588style='font-family:"Calibri",sans-serif'>Diffraction Laue symmetry</span></b>
589to <b><span style='font-family:"Calibri",sans-serif'>-3m</span></b>. When you
590are done the upper part of the Layers window should look like.</p>
591
592<p class=MsoNormal>&nbsp;</p>
593
594<p class=MsoNormal>&nbsp;</p>
595
596<p class=MsoNormal><img width=624 height=474 id="Picture 28"
597src="Stacking%20Faults-I_files/image028.gif"></p>
598
599<p class=MsoNormal>&nbsp;</p>
600
601<p class=MsoNormal>The transition vectors for the cluster model are similar to
602the random faults model, i.e. layer 1-1 and layer 3-1 transitions are <b><span
603style='font-family:"Calibri",sans-serif'>2/3,1/3,1</span></b> for Dx, Dy &amp;
604Dz, layer, and layer 2-4 and 4-4 transitions are <b><span style='font-family:
605"Calibri",sans-serif'>-2/3,-1/3,1</span></b> for Dx, Dy &amp; Dz. All the rest
606are <b><span style='font-family:"Calibri",sans-serif'>0,0,1</span></b> for
607Dx,,Dy &amp; Dz. The probabilities can best be seen from the following array</p>
608
609<p class=MsoNormal>&nbsp;</p>
610
611<table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
612 style='border-collapse:collapse;border:none'>
613 <tr style='height:21.45pt'>
614  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
615  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
616  <p class=MsoNormal>Layer</p>
617  </td>
618  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
619  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
620  <p class=MsoNormal>1</p>
621  </td>
622  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
623  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
624  <p class=MsoNormal>2</p>
625  </td>
626  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
627  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
628  <p class=MsoNormal>3</p>
629  </td>
630  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
631  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
632  <p class=MsoNormal>4</p>
633  </td>
634 </tr>
635 <tr style='height:21.45pt'>
636  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
637  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
638  <p class=MsoNormal>1</p>
639  </td>
640  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
641  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
642  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
643  <p class=MsoNormal>CS</p>
644  </td>
645  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
646  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
647  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
648  <p class=MsoNormal>CF</p>
649  </td>
650  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
651  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
652  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
653  <p class=MsoNormal>x</p>
654  </td>
655  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
656  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
657  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
658  <p class=MsoNormal>x</p>
659  </td>
660 </tr>
661 <tr style='height:21.45pt'>
662  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
663  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
664  <p class=MsoNormal>2</p>
665  </td>
666  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
667  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
668  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
669  <p class=MsoNormal>x</p>
670  </td>
671  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
672  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
673  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
674  <p class=MsoNormal>x</p>
675  </td>
676  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
677  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
678  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
679  <p class=MsoNormal>HS</p>
680  </td>
681  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
682  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
683  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
684  <p class=MsoNormal>HF</p>
685  </td>
686 </tr>
687 <tr style='height:21.45pt'>
688  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
689  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
690  <p class=MsoNormal>3</p>
691  </td>
692  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
693  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
694  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
695  <p class=MsoNormal>HF</p>
696  </td>
697  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
698  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
699  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
700  <p class=MsoNormal>HS</p>
701  </td>
702  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
703  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
704  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
705  <p class=MsoNormal>x</p>
706  </td>
707  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
708  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
709  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
710  <p class=MsoNormal>x</p>
711  </td>
712 </tr>
713 <tr style='height:21.45pt'>
714  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
715  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
716  <p class=MsoNormal>4</p>
717  </td>
718  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
719  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
720  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
721  <p class=MsoNormal>x</p>
722  </td>
723  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
724  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
725  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
726  <p class=MsoNormal>x</p>
727  </td>
728  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
729  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
730  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
731  <p class=MsoNormal>CF</p>
732  </td>
733  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
734  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
735  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
736  <p class=MsoNormal>CS</p>
737  </td>
738 </tr>
739</table>
740
741<p class=MsoNormal>Where CS – cubic stacking, CF – cubic fault, HS – hexagonal
742stacking, HF – hexagonal fault and x – not allowed. A suitable model might be
743CS = <b><span style='font-family:"Calibri",sans-serif'>0.9</span></b>, CF = <b><span
744style='font-family:"Calibri",sans-serif'>0.1</span></b>, HS = <b><span
745style='font-family:"Calibri",sans-serif'>0.8</span></b> and HF = <b><span
746style='font-family:"Calibri",sans-serif'>0.2</span></b>. This will give more
747and thicker cubic blocks than hexagonal ones. Set these values and the
748Transition tables should look like</p>
749
750<p class=MsoNormal><img width=624 height=620 id="Picture 29"
751src="Stacking%20Faults-I_files/image029.gif"></p>
752
753<p class=MsoNormal>Before doing the simulation we need to clear away the old
754one; select the <b><span style='font-family:"Calibri",sans-serif'>PWDR</span></b>
755entry from the GSAS-II data tree and then select <b><span style='font-family:
756"Calibri",sans-serif'>Edit range</span></b> from the data window. Don’t change
757anything, just press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
758this will clear the previous simulation. Then return to the clustered phase
759Layers tab. Do <b><span style='font-family:"Calibri",sans-serif'>Operations/Simulate
760pattern</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>
761twice. The simulation will require some seconds to finish; the powder profile
762will look like</p>
763
764<p class=MsoNormal><img width=624 height=535 id="Picture 30"
765src="Stacking%20Faults-I_files/image030.gif"></p>
766
767<p class=MsoNormal>Again, I have used ‘<b><span style='font-family:"Calibri",sans-serif'>+</span></b>’
768and zoomed in to show the interesting part of the pattern. </p>
769
770<p class=MsoNormal>As additional work you can do sequential simulations to
771explore the effect of changing probabilities. Try varying <b><span
772style='font-family:"Calibri",sans-serif'>TransP;0;0</span></b>, i.e. layer 1 –
773layer 1 (CS) transition probability and <b><span style='font-family:"Calibri",sans-serif'>TransP;2;1</span></b>,
774i.e. layer 3 – layer – 2 (HS) transition probability. Be sure the <b><span
775style='font-family:"Calibri",sans-serif'>Symmetric probabilities</span></b> box
776is checked otherwise you’ll get nonsense. This ends this stacking fault
777tutorial; the next one involves using kaolinite layers to simulate diffraction
778patterns from kaolinite clays.</p>
779
780</div>
781
782</body>
783
784</html>
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