Changeset 2274


Ignore:
Timestamp:
May 15, 2016 3:00:13 PM (6 years ago)
Author:
vondreele
Message:

fix Stacking Faults II.htm

File:
1 edited

Legend:

Unmodified
Added
Removed
  • Tutorials/StackingFaults-II/Stacking Faults II.htm

    r2273 r2274  
    1 <html>
     1<html xmlns:v="urn:schemas-microsoft-com:vml"
     2xmlns:o="urn:schemas-microsoft-com:office:office"
     3xmlns:w="urn:schemas-microsoft-com:office:word"
     4xmlns:m="http://schemas.microsoft.com/office/2004/12/omml"
     5xmlns="http://www.w3.org/TR/REC-html40">
    26
    37<head>
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     10<meta name=Generator content="Microsoft Word 15">
     11<meta name=Originator content="Microsoft Word 15">
     12<link rel=File-List href="Stacking%20Faults%20II_files/filelist.xml">
     13<link rel=Edit-Time-Data href="Stacking%20Faults%20II_files/editdata.mso">
     14<!--[if !mso]>
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     17o\:* {behavior:url(#default#VML);}
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     19.shape {behavior:url(#default#VML);}
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     23<link rel=colorSchemeMapping
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     30  <w:TrackFormatting/>
     31  <w:ValidateAgainstSchemas/>
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     41   <w:SplitPgBreakAndParaMark/>
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     156   Name="List 2"/>
     157  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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     162   Name="List 5"/>
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     168   Name="List Bullet 4"/>
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     175  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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     371  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1"/>
     372  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2"/>
     373  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3"/>
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     375  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading"/>
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     485  <w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
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    215 
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    2211072
    222 <h1>Stacking Fault Simulations – II</h1>
     1073<h1><span style='mso-fareast-font-family:"Times New Roman"'>Stacking Fault
     1074Simulations – II<o:p></o:p></span></h1>
    2231075
    2241076<p class=MsoNormal>In this exercise you will simulate some diffraction patterns
    225 from kaolinite clays. Kaolinite, Al<sub>2</sub>Si<sub>2</sub>O<sub>5</sub>(OH)<sub>4</sub>,
    226 is a 1:1 layer silicate with a single unique sheet with AlO<sub>6</sub>
    227 octahedra on one side and SiO<sub>4</sub> tetrahedra on the other. The layers
    228 stack with an offset to ideally form a triclinic C1 lattice (Bish &amp; Von
     1077from kaolinite clays. Kaolinite, <span class=GramE>Al<sub>2</sub>Si<sub>2</sub>O<sub>5</sub>(</span>OH)<sub>4</sub>,
     1078is a 1:1 layer silicate with a single unique sheet with AlO<sub>6</sub> <span
     1079class=SpellE>octahedra</span> on one side and SiO<sub>4</sub> <span
     1080class=SpellE>tetrahedra</span> on the other. The layers stack with an offset to
     1081ideally form a triclinic C1 lattice (<span class=SpellE>Bish</span> &amp; Von
    2291082Dreele, 1989, Clay &amp; Clay Min. 37, 289-296) for a sample of the most
    2301083ordered form of kaolinite from Keokuk, Iowa. Kaolinites from other locations evidently
     
    2331086Bragg-Brentano pattern of Keokuk kaolinite and a less ordered one from
    2341087Washington County, Georgia (Clay Minerals Society Standard KGa-1b) collected
    235 with CuKa radiation on a Bruker instrument and thus in the Bruker RAW file
    236 format. The KGa-1b sample contains a small amount of anatase (TiO<sub>2</sub>)
    237 and the Keokuk kaolinite has some dickite (different ordered stacking of
    238 kaolinite layers).</p>
     1088with <span class=SpellE>CuKa</span> radiation on a Bruker instrument and thus
     1089in the Bruker RAW file format. The KGa-1b sample contains a small amount of <span
     1090class=SpellE>anatase</span> (TiO<sub>2</sub>) and the Keokuk kaolinite has some
     1091<span class=SpellE>dickite</span> (different ordered stacking of kaolinite
     1092layers).</p>
    2391093
    2401094<p class=MsoNormal>If you have not done so already, start GSAS-II.</p>
    2411095
    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
    245 structure of kaolinite, draw it to see the layer structure and then transform
    246 it into forms suitable for stacking simulations. To begin do <b><span
     1096<h2><span style='mso-fareast-font-family:"Times New Roman"'>Part 1. Creating
     1097kaolinite layer<o:p></o:p></span></h2>
     1098
     1099<p class=MsoNormal>In this initial step we will load from a <span class=SpellE>cif</span>
     1100file the structure of kaolinite, draw it to see the layer structure and then
     1101transform it into forms suitable for stacking simulations. To begin do <b><span
    2471102style='font-family:"Calibri",sans-serif'>Import/Phase/from CIF file</span></b>;
    248 from the file dialog select <b><span style='font-family:"Calibri",sans-serif'>kaolinite.cif</span></b>.
    249 After the “are you sure” popup, there will be another warning you that 4 atom
    250 types (‘O-H’) were not recognized chemical element symbols and they were
    251 substituted by Xe to make them obvious in the atom list. Press <b><span
     1103from the file dialog select <span class=SpellE><b><span style='font-family:
     1104"Calibri",sans-serif'>kaolinite.cif</span></b></span>. After the “are you sure”
     1105popup, there will be another warning you that 4 atom types (‘O-H’) were not
     1106recognized chemical element symbols and they were substituted by <span
     1107class=SpellE>Xe</span> to make them obvious in the atom list. Press <b><span
    2521108style='font-family:"Calibri",sans-serif'>Ok</span></b>; you are offered a
    2531109chance to change the phase name, I used ‘<b><span style='font-family:"Calibri",sans-serif'>kaolinite</span></b>’.
    254 The 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 22"
    257 src="Stacking%20Faults%20II_files/image001.gif"></p>
    258 
    259 <p class=MsoNormal>To fix the Xe atoms (they should be O), select <b><span
    260 style='font-family:"Calibri",sans-serif'>Atoms</span></b> and then double click
    261 the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b> column
    262 heading; 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>;
    264 the Xe atoms at the bottom of the atom table will be highlighted. Next select <b><span
     1110The General tab is displayed (notice the presence of <span class=SpellE>Xe</span>
     1111in the element table).</p>
     1112
     1113<p class=MsoNormal><span style='mso-no-proof:yes'><img width=930 height=500
     1114id="_x0000_i1043" src="Stacking%20Faults%20II_files/image001.gif"></span></p>
     1115
     1116<p class=MsoNormal>To fix the <span class=SpellE>Xe</span> atoms (they should
     1117be O), select <b><span style='font-family:"Calibri",sans-serif'>Atoms</span></b>
     1118and then double click the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b>
     1119column heading; a small popup will appear. Select <span class=SpellE><b><span
     1120style='font-family:"Calibri",sans-serif'>Xe</span></b></span> &amp; press <b><span
     1121style='font-family:"Calibri",sans-serif'>Ok</span></b>; the <span class=SpellE>Xe</span>
     1122atoms at the bottom of the atom table will be highlighted. Next select <b><span
    2651123style='font-family:"Calibri",sans-serif'>Edit/Modify atom parameters</span></b>
    266 from the Phase Data menu; a new popup will appear.</p>
    267 
    268 <p class=MsoNormal><img width=228 height=268
    269 src="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
    273 periodic 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
    275 be drawn with Al, Si &amp; O atoms only.</p>
    276 
    277 <p class=MsoNormal><img width=479 height=358
    278 src="Stacking%20Faults%20II_files/image003.jpg"></p>
     1124from the Phase Data menu; a new popup will appear. Select <b><span
     1125style='font-family:"Calibri",sans-serif'>Type</span></b> &amp; press <b><span
     1126style='font-family:"Calibri",sans-serif'>Ok</span></b>; a periodic table of the
     1127element will appear. Select <b><span style='font-family:"Calibri",sans-serif'>O</span></b>
     1128from the O-atom pulldown; the structure will be drawn with Al, Si &amp; O atoms
     1129only.</p>
     1130
     1131<p class=MsoNormal><span style='mso-no-proof:yes'><img width=479 height=358
     1132id="_x0000_i1042" src="Stacking%20Faults%20II_files/image003.jpg"></span></p>
    2791133
    2801134<p class=MsoNormal>To better visualize the stacking layer, select the <b><span
     
    2901144layering along the c-axis (blue line) will be evident.</p>
    2911145
    292 <p class=MsoNormal><img width=480 height=359
    293 src="Stacking%20Faults%20II_files/image004.jpg"></p>
    294 
    295 <p class=MsoNormal>One can easily see the layer of SiO<sub>4</sub> tetrahedra
    296 and AlO<sub>6</sub> octahedra. Also notice that the next layer (represented by
    297 the 4 O atoms at the bottom of the above drawing are offset giving a triclinic
    298 lattice.</p>
    299 
    300 <p class=MsoNormal>The stacking fault simulation calculation via DIFFaX
    301 routines requires that the stacking layers be defined in a coordinate system
    302 that has the stacking direction perpendicular to the stacking plane defined as
    303 the c-axis. This requires transformation of the unit cell and atom coordinates;
    304 a suitable tool exists in GSAS-II to do this. Select the <b><span
    305 style='font-family:"Calibri",sans-serif'>General</span></b> tab and do <b><span
    306 style='font-family:"Calibri",sans-serif'>Compute/Transform</span></b>; a popup
    307 window will appear.</p>
    308 
    309 <p class=MsoNormal><img width=350 height=339
    310 src="Stacking%20Faults%20II_files/image005.gif"></p>
     1146<p class=MsoNormal><span style='mso-no-proof:yes'><img width=480 height=359
     1147id="_x0000_i1041" src="Stacking%20Faults%20II_files/image004.jpg"></span></p>
     1148
     1149<p class=MsoNormal>One can easily see the layer of SiO<sub>4</sub> <span
     1150class=SpellE>tetrahedra</span> and AlO<sub>6</sub> <span class=SpellE>octahedra</span>.
     1151Also notice that the next layer (represented by the 4 O atoms at the bottom of
     1152the above drawing are offset giving a triclinic lattice.</p>
     1153
     1154<p class=MsoNormal>The stacking fault simulation calculation via <span
     1155class=SpellE>DIFFaX</span> routines requires that the stacking layers be defined
     1156in a coordinate system that has the stacking direction perpendicular to the
     1157stacking plane defined as the c-axis. This requires transformation of the unit
     1158cell and atom coordinates; a suitable tool exists in GSAS-II to do this. Select
     1159the <b><span style='font-family:"Calibri",sans-serif'>General</span></b> tab and
     1160do <b><span style='font-family:"Calibri",sans-serif'>Compute/Transform</span></b>;
     1161a popup window will appear.</p>
     1162
     1163<p class=MsoNormal><span style='mso-no-proof:yes'><img width=350 height=339
     1164id="_x0000_i1040" src="Stacking%20Faults%20II_files/image005.gif"></span></p>
    3111165
    3121166<p class=MsoNormal>Note that this allows one to transform the structure
     
    3141168and then select those that are unique according to a selected space group. The
    3151169pulldown gives a selection of commonly used transformations; we want the last
    316 one, <b><span style='font-family:"Calibri",sans-serif'>abc*</span></b>, which
    317 satisfies the stacking fault requirement. Select it; notice that the space
    318 group is changed to P1. Leave this as the kaolinite layer has no symmetry; in
    319 other circumstances the layer may have an inversion center in which case P-1
    320 should be used. If you press <b><span style='font-family:"Calibri",sans-serif'>Test</span></b>,
     1170one, <span class=SpellE><span class=GramE><b><span style='font-family:"Calibri",sans-serif'>abc</span></b></span></span><b><span
     1171style='font-family:"Calibri",sans-serif'>*</span></b>, which satisfies the
     1172stacking fault requirement. Select it; notice that the space group is changed
     1173to P1. Leave this as the kaolinite layer has no symmetry; in other
     1174circumstances the layer may have an inversion center in which case P-1 should
     1175be used. If you press <b><span style='font-family:"Calibri",sans-serif'>Test</span></b>,
    3211176the new lattice parameters will be shown.</p>
    3221177
    323 <p class=MsoNormal><img width=350 height=339
    324 src="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
    327 interlayer 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:
    329 Symbol'>g</span> is unchanged). Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
    330 a new phase (kaolinite abc*) will be made and its General tab will be shown
    331 immediately. Select the <b><span style='font-family:"Calibri",sans-serif'>Draw
     1178<p class=MsoNormal><span style='mso-no-proof:yes'><img width=350 height=339
     1179id="_x0000_i1039" src="Stacking%20Faults%20II_files/image006.gif"></span></p>
     1180
     1181<p class=MsoNormal><span class=GramE>The a</span> &amp; b axes stay the same,
     1182but c is now smaller (the interlayer distance in kaolinite) and <span
     1183style='font-family:Symbol'>a</span> &amp; <span style='font-family:Symbol'>b</span>
     1184= 90 (<span style='font-family:Symbol'>g</span> is unchanged). Press <b><span
     1185style='font-family:"Calibri",sans-serif'>Ok</span></b>; a new phase (kaolinite <span
     1186class=SpellE><span class=GramE>abc</span></span>*) will be made and its General
     1187tab will be shown immediately. Select the <b><span style='font-family:"Calibri",sans-serif'>Draw
    3321188Atoms</span></b> tab to see the resulting structure.</p>
    3331189
    334 <p class=MsoNormal><img width=471 height=352
    335 src="Stacking%20Faults%20II_files/image007.jpg"></p>
     1190<p class=MsoNormal><span style='mso-no-proof:yes'><img width=471 height=352
     1191id="_x0000_i1038" src="Stacking%20Faults%20II_files/image007.jpg"></span></p>
    3361192
    3371193<p class=MsoNormal>To see what this layer looks like with more of it drawn, you
     
    3531209style='font-family:"Calibri",sans-serif'>Style</span></b> column heading and
    3541210select <b><span style='font-family:"Calibri",sans-serif'>Balls and sticks</span></b>;
    355 the drawing should look like (after some zooming/shifting/rotation).</p>
    356 
    357 <p class=MsoNormal><span style='position:absolute;z-index:251659264'><img
    358 width=477 height=357 src="Stacking%20Faults%20II_files/image009.jpg"></p>
    359 
    360 <p class=MsoNormal>This structure is now suitable for use in DIFFaX
    361 calculations; the cell has a c-axis that is perpendicular to the ab plane with a
    362 length that is the stacking repeat distance. This is a good place to save your
    363 project (I called it ‘<b><span style='font-family:"Calibri",sans-serif'>kaolinite’</span></b>).</p>
    364 
    365 <h2>Part 2. Set up simulation of ideal kaolinite stacking</h2>
     1211the drawing should look like (after some zooming/shifting/rotation).<o:p></o:p></p>
     1212
     1213<p class=MsoNormal><span style='mso-no-proof:yes'><img width=477 height=357 id="_x0000_i1037"
     1214src="Stacking%20Faults%20II_files/image009.jpg"></span></p>
     1215
     1216<p class=MsoNormal>This structure is now suitable for use in <span
     1217class=SpellE>DIFFaX</span> calculations; the cell has a c-axis that is
     1218perpendicular to the ab plane with a length that is the stacking repeat
     1219distance. This is a good place to save your project (I called it ‘<b><span
     1220style='font-family:"Calibri",sans-serif'>kaolinite’</span></b>).</p>
     1221
     1222<h2><span style='mso-fareast-font-family:"Times New Roman"'>Part 2. Set up
     1223simulation of ideal kaolinite stacking<o:p></o:p></span></h2>
    3661224
    3671225<p class=MsoNormal>In this part of the tutorial we’ll create a stacking model
    368 for Keokuk kaolinite and use DIFFaX to simulate the powder pattern and compare
    369 it 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
    372 style='font-family:"Calibri",sans-serif'>Keokuk</span></b>’. The General tab
    373 for it will immediately appear.</p>
    374 
    375 <p class=MsoNormal><img width=930 height=500
    376 src="Stacking%20Faults%20II_files/image010.gif"></p>
     1226for Keokuk kaolinite and use <span class=SpellE>DIFFaX</span> to simulate the
     1227powder pattern and compare it to some real data. To begin we need a new phase
     1228that we can declare as “faulted’. In the main GSAS-II data tree menu do <b><span
     1229style='font-family:"Calibri",sans-serif'>Data/Add new phase</span></b>; I named
     1230it ‘<b><span style='font-family:"Calibri",sans-serif'>Keokuk</span></b>’. The
     1231General tab for it will immediately appear.</p>
     1232
     1233<p class=MsoNormal><span style='mso-no-proof:yes'><img width=930 height=500
     1234id="_x0000_i1036" src="Stacking%20Faults%20II_files/image010.gif"></span></p>
    3771235
    3781236<p class=MsoNormal>Change the <b><span style='font-family:"Calibri",sans-serif'>Phase
     
    3811239will appear. Select it.</p>
    3821240
    383 <p class=MsoNormal><img width=817 height=484
    384 src="Stacking%20Faults%20II_files/image011.gif"></p>
     1241<p class=MsoNormal><span style='mso-no-proof:yes'><img width=817 height=484
     1242id="_x0000_i1035" src="Stacking%20Faults%20II_files/image011.gif"></span></p>
    3851243
    3861244<p class=MsoNormal>We can anticipate (given that kaolinite space group is C1)
    3871245that the <b><span style='font-family:"Calibri",sans-serif'>Diffraction Laue
    3881246symmetry</span></b> is <b><span style='font-family:"Calibri",sans-serif'>-1</span></b>.
    389 We can enter by hand the lattice parameters from the kaolinite abc* phase but
    390 an easier method is available. Do <b><span style='font-family:"Calibri",sans-serif'>Operations/Copy
     1247We can enter by hand the lattice parameters from the kaolinite <span
     1248class=SpellE><span class=GramE>abc</span></span>* phase but an easier method is
     1249available. Do <b><span style='font-family:"Calibri",sans-serif'>Operations/Copy
    3911250phase cell</span></b>; a file selection dialog will appear for your current
    392 directory and the file <b><span style='font-family:"Calibri",sans-serif'>kaolinite.gpx</span></b>
     1251directory and the file <span class=SpellE><b><span style='font-family:"Calibri",sans-serif'>kaolinite.gpx</span></b></span>
    3931252should be there. Select it; a small popup will appear listing the available
    394 phases. Choose ‘<b><span style='font-family:"Calibri",sans-serif'>kaolinite
    395 abc*</span></b>’ and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
    396 the Layers window will be redrawn with the new lattice parameters.</p>
    397 
    398 <p class=MsoNormal><img width=829 height=484
    399 src="Stacking%20Faults%20II_files/image012.gif"></p>
     1253phases. Choose ‘<b><span style='font-family:"Calibri",sans-serif'>kaolinite <span
     1254class=SpellE><span class=GramE>abc</span></span>*</span></b>’ and press <b><span
     1255style='font-family:"Calibri",sans-serif'>Ok</span></b>; the Layers window will
     1256be redrawn with the new lattice parameters.</p>
     1257
     1258<p class=MsoNormal><span style='mso-no-proof:yes'><img width=829 height=484
     1259id="_x0000_i1034" src="Stacking%20Faults%20II_files/image012.gif"></span></p>
    4001260
    4011261<p class=MsoNormal>Next, you need to define the layer. As it would be very
    402 tedious to enter 24 atoms by hand, the alternative is to get them from the
    403 previously 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
    405 style='font-family:"Calibri",sans-serif'>kaolinite.gpx</span></b> will appear.
    406 Select the file and press <b><span style='font-family:"Calibri",sans-serif'>Open</span></b>;
     1262tedious to enter 24 atoms by hand, the alternative is to get them from the previously
     1263created kaolinite <span class=SpellE><span class=GramE>abc</span></span>*
     1264phase. Select the <b><span style='font-family:"Calibri",sans-serif'>Import new
     1265layer</span></b> box; the file dialog with <span class=SpellE><b><span
     1266style='font-family:"Calibri",sans-serif'>kaolinite.gpx</span></b></span> will
     1267appear. Select the file and press <b><span style='font-family:"Calibri",sans-serif'>Open</span></b>;
    4071268again a small popup with two phases listed will appear. Again select <b><span
    408 style='font-family:"Calibri",sans-serif'>kaolinite abc*</span></b> and press <b><span
    409 style='font-family:"Calibri",sans-serif'>Ok</span></b>; the Layers page will be
    410 redrawn with a layer (named kaolinite) will be filled out.</p>
    411 
    412 <p class=MsoNormal><img width=829 height=500
    413 src="Stacking%20Faults%20II_files/image013.gif"></p>
     1269style='font-family:"Calibri",sans-serif'>kaolinite <span class=SpellE><span
     1270class=GramE>abc</span></span>*</span></b> and press <b><span style='font-family:
     1271"Calibri",sans-serif'>Ok</span></b>; the Layers page will be redrawn with a
     1272layer (named kaolinite) will be filled out.</p>
     1273
     1274<p class=MsoNormal><span style='mso-no-proof:yes'><img width=829 height=500
     1275id="_x0000_i1033" src="Stacking%20Faults%20II_files/image013.gif"></span></p>
    4141276
    4151277<p class=MsoNormal>If you move down to the bottom of the page (if there isn’t a
    4161278scroll bar, just grab an edge of the window &amp; shift it slightly) to find
    4171279the one line <b><span style='font-family:"Calibri",sans-serif'>Layer-Layer
    418 Transition probabilities</span></b>. Change <b><span style='font-family:"Calibri",sans-serif'>Dz=1.0</span></b>
    419 and press the plot box; the drawing will show a layer of kaolinite stacked
    420 directly above another one.</p>
    421 
    422 <p class=MsoNormal><img width=480 height=359
    423 src="Stacking%20Faults%20II_files/image014.jpg"></p>
     1280Transition probabilities</span></b>. Change <span class=SpellE><b><span
     1281style='font-family:"Calibri",sans-serif'>Dz</span></b></span><b><span
     1282style='font-family:"Calibri",sans-serif'>=1.0</span></b> and press the plot
     1283box; the drawing will show a layer of kaolinite stacked directly above another
     1284one.</p>
     1285
     1286<p class=MsoNormal><span style='mso-no-proof:yes'><img width=480 height=359
     1287id="_x0000_i1032" src="Stacking%20Faults%20II_files/image014.jpg"></span></p>
    4241288
    4251289<p class=MsoNormal>Compare that to the stacking in kaolinite.</p>
    4261290
    427 <p class=MsoNormal><img width=480 height=359
    428 src="Stacking%20Faults%20II_files/image015.jpg"></p>
     1291<p class=MsoNormal><span style='mso-no-proof:yes'><img width=480 height=359
     1292id="_x0000_i1031" src="Stacking%20Faults%20II_files/image015.jpg"></span></p>
    4291293
    4301294<p class=MsoNormal>Notice the effect of the offset. The 1<sup>st</sup> row of
    431 SiO<sub>4</sub> tetrahedra are positioned directly above the AlO<sub>6</sub>
    432 octahedra in the real structure but not in the vertically stacked structure. We
    433 can use a bit of simple geometry to work out what the offset is but first let
    434 us see what happens in the simulation and how it compares to real data.</p>
    435 
    436 <h2>Step 3. Import Keokuk kaolinite data and do 1<sup>st</sup> simulation</h2>
     1295SiO<sub>4</sub> <span class=SpellE>tetrahedra</span> are positioned directly
     1296above the AlO<sub>6</sub> <span class=SpellE>octahedra</span> in the real
     1297structure but not in the vertically stacked structure. We can use a bit of
     1298simple geometry to work out what the offset is but first let us see what
     1299happens in the simulation and how it compares to real data.</p>
     1300
     1301<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 3. Import
     1302Keokuk kaolinite data and do 1<sup>st</sup> simulation<o:p></o:p></span></h2>
    4371303
    4381304<p class=MsoNormal>First we need to import the Keokuk kaolinite powder data; do
    4391305<b><span style='font-family:"Calibri",sans-serif'>Import/Powder Data/from
    4401306Bruker RAW file</span></b>. Select <b><span style='font-family:"Calibri",sans-serif'>Keokuk
    441 kaolinite.RAW</span></b> from the file dialog box; press <b><span
    442 style='font-family:"Calibri",sans-serif'>Yes</span></b> in the next popup. A
    443 new file dialog appears requesting an instrument parameter file; we will use an
    444 internal default instead. Press <b><span style='font-family:"Calibri",sans-serif'>Cancel</span></b>
    445 and select <b><span style='font-family:"Calibri",sans-serif'>Defaults for CuKa
    446 lab data</span></b> from the next popup. This process will repeat since the RAW
    447 file contains two scans. In the next popup, select only <b><span
    448 style='font-family:"Calibri",sans-serif'>kaolinite abc*</span></b>. There will
     1307<span class=SpellE>kaolinite.RAW</span></span></b> from the file dialog box;
     1308press <span class=GramE><b><span style='font-family:"Calibri",sans-serif'>Yes</span></b></span>
     1309in the next popup. A new file dialog appears requesting an instrument parameter
     1310file; we will use an internal default instead. Press <b><span style='font-family:
     1311"Calibri",sans-serif'>Cancel</span></b> and select <b><span style='font-family:
     1312"Calibri",sans-serif'>Defaults for <span class=SpellE>CuKa</span> lab data</span></b>
     1313from the next popup. This process will repeat since the RAW file contains two
     1314scans. In the next popup, select only <b><span style='font-family:"Calibri",sans-serif'>kaolinite
     1315<span class=SpellE><span class=GramE>abc</span></span>*</span></b>. There will
    4491316be two PWDR scans in the GSAS-II data tree; one covers 2<span style='font-family:
    4501317Symbol'>Q</span>= 10-90<span style='font-family:"Calibri",sans-serif'>°</span>
     
    4531320the calculations become very time consuming for complex structures and high
    4541321angle data. Select <b><span style='font-family:"Calibri",sans-serif'>PWDR
    455 Keokuk kaolinite.RAW Scan 1</span></b> from the GSAS-II data tree make sure it
    456 expands; its plot will also show.</p>
    457 
    458 <p class=MsoNormal><img width=700 height=600
    459 src="Stacking%20Faults%20II_files/image016.gif"></p>
     1322Keokuk <span class=SpellE>kaolinite.RAW</span> Scan 1</span></b> from the
     1323GSAS-II data tree make sure it expands; its plot will also show.</p>
     1324
     1325<p class=MsoNormal><span style='mso-no-proof:yes'><img width=700 height=600
     1326id="_x0000_i1030" src="Stacking%20Faults%20II_files/image016.gif"></span></p>
    4601327
    4611328<p class=MsoNormal>Go to <b><span style='font-family:"Calibri",sans-serif'>Limits</span></b>
    462 and set <b><span style='font-family:"Calibri",sans-serif'>Tmax</span></b> to <b><span
    463 style='font-family:"Calibri",sans-serif'>52.0</span></b>; that puts the upper
    464 limit in a relatively clear part of the pattern. Then go to Background and set
    465 the 1<sup>st</sup> coefficient to 20 (approximately the background at 2Q=18).
    466 Next go to <b><span style='font-family:"Calibri",sans-serif'>Sample parameters</span></b>
    467 and set the <b><span style='font-family:"Calibri",sans-serif'>Histogram scale</span></b>
    468 to something reasonable (I chose <b><span style='font-family:"Calibri",sans-serif'>20.0</span></b>)
    469 and make sure the <b><span style='font-family:"Calibri",sans-serif'>Diffractometer
    470 type is Bragg-Brentano</span></b>.</p>
     1329and set <span class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Tmax</span></b></span>
     1330to <b><span style='font-family:"Calibri",sans-serif'>52.0</span></b>; that puts
     1331the upper limit in a relatively clear part of the pattern. Then go to
     1332Background and set the 1<sup>st</sup> coefficient to 20 (approximately the
     1333background at 2Q=18). Next go to <b><span style='font-family:"Calibri",sans-serif'>Sample
     1334parameters</span></b> and set the <b><span style='font-family:"Calibri",sans-serif'>Histogram
     1335scale</span></b> to something reasonable (I chose <b><span style='font-family:
     1336"Calibri",sans-serif'>20.0</span></b>) and make sure the <b><span
     1337style='font-family:"Calibri",sans-serif'>Diffractometer type is Bragg-Brentano</span></b>.</p>
    4711338
    4721339<p class=MsoNormal>Now we are ready for our 1<sup>st</sup> kaolinite
     
    4801347and the new plot will be displayed (I’ve zoomed in a bit).</p>
    4811348
    482 <p class=MsoNormal><img width=700 height=600
    483 src="Stacking%20Faults%20II_files/image017.gif">.</p>
     1349<p class=MsoNormal><span style='mso-no-proof:yes'><img width=700 height=600
     1350id="_x0000_i1029" src="Stacking%20Faults%20II_files/image017.gif"></span>.</p>
    4841351
    4851352<p class=MsoNormal>As you can see the simulation (green curve) does not fit the
    4861353data (blue crosses) at all mostly due to the incorrect layer offset although
    4871354the 1<sup>st</sup> peak seems to be positioned correctly. To work out the
    488 offset consider the drawing of kaolinite.</p>
    489 
    490 <p class=MsoNormal><span style='position:absolute;z-index:251661312'><span
    491 style='position:absolute;z-index:251660288'><img width=480 height=338
    492 id="Picture 23" src="Stacking%20Faults%20II_files/image002.gif"></p>
    493 
    494 <p class=MsoNormal>The offset Dx is given by the blue arrow in the above
    495 drawing of kaolinite and is in fractional coordinates. Geometry gives</p>
    496 
    497 <p class=MsoNormal><span style='position:relative;top:3pt'><img width=106
    498 height=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
    500 style='font-family:"Calibri",sans-serif'>Dx</span></b> to this value &amp;
    501 repeat simulation.</p>
    502 
    503 <p class=MsoNormal><img width=700 height=600
    504 src="Stacking%20Faults%20II_files/image022.gif"></p>
     1355offset consider the drawing of kaolinite.<o:p></o:p></p>
     1356
     1357<p class=MsoNormal><span style='mso-no-proof:yes'><img width=480 height=338 id="_x0000_i1028"
     1358src="Stacking%20Faults%20II_files/image002.gif"></span></p>
     1359
     1360<p class=MsoNormal>The offset <span class=SpellE>Dx</span> is given by the blue
     1361arrow in the above drawing of kaolinite and is in fractional coordinates.
     1362Geometry gives<o:p></o:p></p>
     1363
     1364<p class=MsoNormal><span style='position:relative;top:3pt'><span
     1365style='mso-no-proof:yes'><img width=106 height=26 id="_x0000_i1027"
     1366src="Stacking%20Faults%20II_files/image021.gif"></span>&nbsp;Or in this case <b><span
     1367style='font-family:"Calibri",sans-serif'>-0.368</span></b>. Set <span
     1368class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Dx</span></b></span>
     1369to this value &amp; repeat simulation.</p>
     1370
     1371<p class=MsoNormal><span style='mso-no-proof:yes'><img width=700 height=600
     1372id="_x0000_i1026" src="Stacking%20Faults%20II_files/image022.gif"></span></p>
    5051373
    5061374<p class=MsoNormal>There is some improvement but some parts are not very well
    5071375represented. Recall from the triclinic kaolinite lattice parameters that <span
    5081376style='font-family:Symbol'>a</span> was 91.7°; that will produce a small offset
    509 in 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
    511 simulation again. This gives a much better fit to the observed pattern, but the
    512 simulated peaks are too sharp; this can be fixed by changing the U,V,W
    513 Instrument parameters. I’d just set <b><span style='font-family:"Calibri",sans-serif'>W=40</span></b>
    514 and 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>)
    516 to <b><span style='font-family:"Calibri",sans-serif'>40</span></b> and try
    517 again.</p>
    518 
    519 <p class=MsoNormal><img width=700 height=600
    520 src="Stacking%20Faults%20II_files/image023.gif"></p>
     1377in Dy. Using the same kind of geometry math gives <span class=SpellE><b><span
     1378style='font-family:"Calibri",sans-serif'>Dy</span></b></span><b><span
     1379style='font-family:"Calibri",sans-serif'>=-0.0246</span></b>. Enter this value
     1380&amp; repeat the simulation again. This gives a much better fit to the observed
     1381pattern, but the simulated peaks are too sharp; this can be fixed by changing
     1382the U<span class=GramE>,V,W</span> Instrument parameters. I’d just set <b><span
     1383style='font-family:"Calibri",sans-serif'>W=40</span></b> and the <b><span
     1384style='font-family:"Calibri",sans-serif'>Histogram scale</span></b> (in <b><span
     1385style='font-family:"Calibri",sans-serif'>Sample parameters</span></b>) to <b><span
     1386style='font-family:"Calibri",sans-serif'>40</span></b> and try again.</p>
     1387
     1388<p class=MsoNormal><span style='mso-no-proof:yes'><img width=700 height=600
     1389id="_x0000_i1025" src="Stacking%20Faults%20II_files/image023.gif"></span></p>
    5211390
    5221391<p class=MsoNormal>That is a pretty good fit for a stacking simulation. By
     
    5261395small range can be used to help with optimization, but in this case it would be
    5271396far easier to do a Rietveld refinement for this well ordered kaolinite. Save
    528 your project as you will need it for the next part of the exercise.</p>
    529 
    530 </span></span></span></div>
    531 
     1397your project as you will need it for the next part of the exercise.<o:p></o:p></p>
     1398
     1399</span></div>
     1400
     1401</span></span></span>
    5321402</body>
    5331403
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