Changeset 5027
- Timestamp:
- Sep 17, 2021 1:46:47 PM (17 months ago)
- Location:
- Tutorials/LeBail
- Files:
-
- 17 added
- 11 edited
Legend:
- Unmodified
- Added
- Removed
-
Tutorials/LeBail/LeBailSucrose.fld/filelist.xml
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Tutorials/LeBail/LeBailSucrose.htm
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mso-level-number-position:left; 1073 text-indent:-.25in; 1074 font-family:"Courier New";} 1075 @list l2:level9 1076 {mso-level-number-format:bullet; 1077 mso-level-text:\F0A7; 1078 mso-level-tab-stop:none; 1079 mso-level-number-position:left; 1080 text-indent:-.25in; 1081 font-family:Wingdings;} 1395 1082 ol 1396 1083 {margin-bottom:0in;} … … 1433 1120 Extraction in GSAS-II - Sucrose<o:p></o:p></span></h1> 1434 1121 1435 < P><BL>1436 <LI>Exercise files are found <A href="./data/" 1437 target="_blank">here</a>. The data files are also used in the 3rd 1438 section of the 1439 <a 1440 href="../FitPeaks/Fit%20Peaks.htm#sucrose_peak_fit" 1441 target="_blank">Fit Peaks/Autoindexing tutorial</a>. 1442 </BL></P> 1443 1122 <p class=MsoNormal><BL><span style='font-family:Symbol;mso-ascii-font-family: 1123 "Times New Roman";mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin'>·</span><span 1124 style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin'><span 1125 style='mso-spacerun:yes'> </span>Exercise files are found <a href="data/" 1126 target="_blank">here</a>. The data files are also used in the 3rd section of 1127 the <a href="../FitPeaks/Fit%20Peaks.htm#sucrose_peak_fit" target="_blank">Fit 1128 Peaks/Autoindexing tutorial</a>. <o:p></o:p></span></p> 1129 1130 </BL> 1444 1131 1445 1132 <h1><span style='mso-fareast-font-family:"Times New Roman"'>Background <o:p></o:p></span></h1> 1446 1133 1447 1134 <p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font: 1448 minor-latin'>In a Rietveld fit, a number of different items are fit, potentially 1449 at the same time. These include the lattice parameters, atomic positions and 1450 displacement (aka temperature, <span class=SpellE>U<sub>iso</sub></span> and <span 1451 class=SpellE>U<sub>ij</sub></span>) parameters for one or more phases, as well 1452 as peak shapes parameters either for broadening from either the sample or the instrument 1453 (avoid both together), background fitting terms and one or two correction terms needed to describe 1454 peak shifts due to apparent sample placement. In addition, there could be other 1455 terms needed to describe additional experimental conditions such as for absorption, 1456 preferred orientation or extinction. These parameters can be divided into four 1457 categories: experimental (peak shapes, peak shifts and background), lattice parameters, 1458 structural parameters (atom positions and U values) and intensity correction 1459 terms (absorption, preferred orientation and extinction).<o:p></o:p></span></p> 1135 minor-latin'>In a Rietveld fit, a number of different items are fit, 1136 potentially at the same time. These include the lattice parameters, atomic positions 1137 and displacement (aka temperature, <span class=SpellE>U<sub>iso</sub></span> 1138 and <span class=SpellE>U<sub>ij</sub></span>) parameters for one or more 1139 phases, as well as peak shapes parameters either for broadening from either the 1140 sample or the instrument (avoid doing both together), background fitting terms 1141 and one or two correction terms needed to describe peak shifts due to apparent 1142 sample placement. In addition, there could be other terms needed to describe 1143 additional experimental conditions such as for absorption, preferred 1144 orientation or extinction. These parameters can be divided into four 1145 categories: experimental (peak shapes, peak shifts and background), lattice 1146 parameters, structural parameters (atom positions and U values) and intensity 1147 correction terms (absorption, preferred orientation and extinction).<o:p></o:p></span></p> 1460 1148 1461 1149 <p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font: … … 1463 1151 1464 1152 <p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font: 1465 minor-latin'>In Rietveld, the reflection intensities are generated 1466 from the structural and intensity correction parameters, but 1467 there are two approaches to full-pattern fitting that treat 1468 reflection intensities as arbitrary: (1) Pawley fitting, developed by Stuart Pawley 1469 [Pawley, G. S. (1981). "Unit-Cell Refinement from Powder Diffraction 1470 Scans." Journal of Applied Crystallography 14: 357-361.], where peak 1471 intensities are treated as least-squares variables. (2) Le Bail 1472 fitting, from Armel Le Bail [Le Bail, A. (2005). "Whole powder pattern decomposition methods 1473 and applications: A retrospection." Powder Diffraction 20(4): 316-326.] 1474 The Le Bail approach, demonstrated by this tutorial, takes advantage of the 1475 fact that Hugo Rietveld developed a rather ingenious approach to estimating reflection 1476 i ntensities: the idea behind this is that for every point in a pattern where one1477 or more reflections contribute, one can estimate the relative contribution from 1478 each reflection from the structure factor magnitude, <span class=SpellE>F<sub>calc</sub></span>,1479 from the approximate crystal structure model, adjusted for reflection multiplicity1480 (<i>m</i>) and preferred orientation. Simply apportioning the observed powder 1481 pattern intensities point by point to each reflection provides an estimate for 1482 the observed structure factors, F<sub>obs</sub>. The quality of this estimate1483 improves as the crystal structure model approaches reality. Le Bails method 1484 cleverly appropriates Rietvelds intensity extraction, but assuming the crystal 1485 structure model is unknown, sets all <span class=SpellE>F<sub>calc</sub></span> 1486 values to 1. After the intensity extraction is performed, a set of F<sub>obs</sub> 1487 values is obtained. These initially treat every F<sub>obs</sub>/<i>m</i> ratio 1488 as equivalent and will not be very accurate, but they are much better reflection 1489 estimates than the initial <span class=SpellE>F<sub>calc</sub></span> values (all 1490 unity). The <span class=SpellE>F<sub>calc</sub></span> values are set to the 1491 extracted F<sub>obs</sub> and the Le Bail fit can be repeated, giving even 1492 better intensity estimates. This process is equivalent to a steepest descents 1493 minimization and it will slowly converge to a self-consistent set of 1494 intensities that will give best possible agreement to the observed 1495 pattern. Note that the apportionment of intensity for reflections that are very 1496 closely overlapped will tend to make their <span class=SpellE>F<sub>calc</sub></span>1497 values approximately equal. (Note that the Pawley approach will tend make <i>m</i>*F<su b>obs</sub>1498 values equal for complete reflection overlap; neither is likely to be accurate.)1499 <o:p></o:p></span></p>1153 minor-latin'>In Rietveld, the reflection intensities are generated from the 1154 structural and intensity correction parameters, but there are two approaches to 1155 full-pattern fitting that treat reflection intensities as arbitrary: (1) Pawley 1156 fitting, developed by Stuart Pawley [Pawley, G. S. (1981). "Unit-Cell 1157 Refinement from Powder Diffraction Scans." Journal of Applied 1158 Crystallography 14: 357-361.], where peak intensities are treated as 1159 least-squares variables. (2) Le Bail fitting, from Armel Le Bail [Le Bail, A. 1160 (2005). "Whole powder pattern decomposition methods and applications: A 1161 retrospection." Powder Diffraction 20(4): 316-326.] The Le Bail approach, 1162 demonstrated by this tutorial, takes advantage of the fact that Hugo Rietveld 1163 developed a rather ingenious approach to estimating reflection intensities: the 1164 idea behind this is that for every point in a pattern where one or more 1165 reflections contribute, one can estimate the relative contribution from each 1166 reflection from the structure factor magnitude, F<sup>2</sup><sub>calc</sub>, 1167 from the approximate crystal structure model, adjusted for reflection 1168 multiplicity (<i>m</i>), preferred orientation and various other geometric 1169 corrections. Simply apportioning the observed powder pattern intensities point 1170 by point to each reflection provides an estimate for the observed structure 1171 factors, F<sup>2</sup><sub>obs</sub>. The quality of this estimate improves as 1172 the crystal structure model approaches reality. Le Bails method cleverly 1173 appropriates Rietvelds intensity extraction, but assuming the crystal 1174 structure model is unknown, sets all F<sup>2</sup><sub>calc</sub> values to an 1175 initial value (e.g. 1.0). After the intensity extraction is performed, a set of 1176 F<sup>2</sup><sub>obs</sub> values is obtained. These initially treat every F<sup>2</sup><sub>obs</sub>/<i>m</i> 1177 ratio as equivalent and will not be very accurate, but they are much better 1178 reflection estimates than the initial F<sup>2</sup><sub>calc</sub> values (all 1179 unity). The F<sup>2</sup><sub>calc</sub> values are set to the extracted F<sup>2</sup><sub>obs</sub> 1180 and the Le Bail fit can be repeated, giving even better intensity estimates. 1181 This process is equivalent to a steepest descents minimization and it will converge 1182 to a self-consistent set of intensities that will give best possible agreement 1183 to the observed pattern. Note that the apportionment of intensity for 1184 reflections that are very closely overlapped will tend to make their F<sup>2</sup><sub>calc</sub> 1185 values approximately equal. (Note that the Pawley approach will tend make <i>m</i>*F<sup>2</sup><sub>obs</sub> 1186 values equal for complete reflection overlap; neither is likely to be 1187 accurate.) <o:p></o:p></span></p> 1500 1188 1501 1189 <p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font: … … 1504 1192 <p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font: 1505 1193 minor-latin'>Note that when either Pawley or Le Bail intensity extraction are 1506 used, all structural and intensity correction parameters no longer affect the intensity1507 computations. Such parameters should not be included in the fit. If included inadvertently, 1508 GSAS-II will usually remove them from the fit along with providing annoying 1509 warning messages, but it is possible that this parameter 1510 removal process could fail and the refinement may not 1511 run properly.</span></p>1194 used, the structural and intensity correction parameters no longer affect the 1195 intensity computations. Such parameters should not be included in the fit as 1196 they will produce singularities in the refinement. If included inadvertently, 1197 GSAS-II will usually remove them from the fit along with providing annoying warning 1198 messages, but it is possible that this parameter removal process could fail and 1199 the refinement may not run properly.</span></p> 1512 1200 1513 1201 <p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font: … … 1515 1203 1516 1204 <p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font: 1517 minor-latin'> 1518 GSAS-II provides two ways to update Le Bail reflection 1519 intensities. The Calculate/"Le Bail fit" menu command will perform 1520 three intensity extraction cycles, but will not change any GSAS-II 1521 parameters. 1522 When the Calculate/Refine menu command is used, 1523 least-squares minimization of experimental 1524 and lattice parameters is alternated with Le Bail fitting. 1525 Note that when first initiating 1526 a Le Bail fit, the reflection intensities are very small 1527 and fitting any lattice or peak width parameters is likely to diverge 1528 and fail. Even background parameters may be affected by poor 1529 reflection intensity estimates. 1530 For this reason, it is best to allow 1531 the reflection intensities to come near convergence using "Le Bail 1532 fit" before refining any parameters with "Refine". Usually, it is only 1533 necessary to do this at the beginning of a fit or if the Le Bail 1534 intensity values are reset (do this by turning the extraction flag off 1535 and then on again), but if parameters change significantly and the Le 1536 Bail intensities are far from optimal, it is an excellent idea to 1537 reconverge them with "Le Bail fit" again. 1538 </p> 1205 minor-latin'>After the LeBail option has been invoked, the Calculate/Refine 1206 menu command will execute a preliminary LeBail only zero cycles refinement in 1207 which only F<sup>2</sup><sub>obs</sub> is adjusted via the LeBail method. It is 1208 cycled 10 times or until a minimum is reached. After that completes, the 1209 Rietveld/LeBail refinement proceeds allowing least-squares minimization of 1210 non-intensity dependent parameters toward a more global fit to the data. 1211 Successive runs allowing other parameters to be varied can then be used to 1212 progressively improve the fit and produce a best estimate of the F<sup>2</sup><sub>obs</sub>.<o:p></o:p></span></p> 1539 1213 1540 1214 <p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font: … … 1542 1216 1543 1217 <p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font: 1544 minor-latin'> 1545 There are many reasons to use Le Bail fitting. The technique was 1546 developed to obtain a set of reflection intensities for structure 1547 solution. 1548 It can also be used to treat an impurity, where lattice parameters are 1549 known but the structural details are not or for fitting lattice 1550 parameters where likewise the structure is not known. Le Bail fitting is also 1551 useful prior to a structural fit. It allows determination of 1552 reasonable starting values for the 1553 background, peak shapes and unit cell parameters so they can be fixed 1554 until the late stages of the refinement. 1555 Another use is to see when artifacts in the background or peak shapes limit 1556 how well the pattern can be fit. A Le Bail or Pawley fit provides an 1557 estimate for the best possible <span class=SpellE>R<sub>wp</sub></span> and 1558 reduced </span><span lang=EL style='mso-fareast-font-family:Calibri;mso-fareast-theme-font: 1559 minor-latin;mso-ansi-language:EL'>χ</span><sup><span style='mso-fareast-font-family: 1560 Calibri;mso-fareast-theme-font:minor-latin'>2</span></sup><span 1218 minor-latin'>There are many reasons to use Le Bail fitting. The technique was 1219 developed to obtain a set of reflection intensities for structure solution. It 1220 can also be used to treat an impurity, where lattice parameters are known but 1221 the structural details are not or for fitting lattice parameters where likewise 1222 the structure is not known. Le Bail fitting is also useful prior to a 1223 structural fit. It can allow determination of reasonable starting values for 1224 the background, peak shapes and unit cell parameters so they can be fixed until 1225 the late stages of the refinement, although the freedom in peak intensities may 1226 bias some parameters (e.g. background and profile coefficients) if there is a 1227 large number of overlapping reflections. Another use is to see when artifacts 1228 in the background or peak shapes limit how well the pattern can be fit. A Le Bail 1229 or Pawley fit provides an estimate for the best possible <span class=SpellE>R<sub>wp</sub></span> 1230 and reduced </span><span lang=EL style='mso-fareast-font-family:Calibri; 1231 mso-fareast-theme-font:minor-latin;mso-ansi-language:EL'>χ</span><sup><span 1232 style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin'>2</span></sup><span 1561 1233 style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin'> 1562 values that can be expected for a dataset. For complex patterns, where it is difficult1563 to discern where allowed reflections are present, comparison of Le Bail or 1564 Pawley fits can provide insight on extinction conditions. A lower symmetry 1565 s pace group with fewer extinctions should provide a better fit to warrant its1566 consideration.</span></p>1234 values that can be expected for a dataset. For complex patterns, where it is 1235 difficult to discern where allowed reflections are present, comparison of Le 1236 Bail or Pawley fits can provide insight on extinction conditions. A lower 1237 symmetry space group with fewer extinctions should provide a better fit to 1238 warrant its consideration.</span></p> 1567 1239 1568 1240 <p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font: … … 1571 1243 <h1><span style='mso-fareast-font-family:"Times New Roman"'>Prerequisite <o:p></o:p></span></h1> 1572 1244 1573 <p class=MsoNormal>In this exercise you we will use Le Bail fitting to extract approximate1574 reflection intensities. This is similar to what is done in the beginning ofthe1575 Charge Flipping in GSAS-II - sucrose tutorial, which uses Pawley fitting 1576 instead. It follows logically from the third example in the Fit1245 <p class=MsoNormal>In this exercise you we will use Le Bail fitting to extract 1246 approximate reflection intensities. This is similar to what is done in the 1247 beginning of the Charge Flipping in GSAS-II - sucrose tutorial, which instead 1248 uses Pawley fitting. It follows logically from the third example in the Fit 1577 1249 Peaks/Autoindexing in GSAS-II tutorial, from where the sucrose unit cell was 1578 determined. Alternately, a project (<span class=SpellE><span 1579 style='font-family:Courier'>start.gpx</span></span>) file is provided 1580 in the <A href="./data/" target="_blank">exercise files</a> 1581 to start without the previous tutorial.</p> 1582 1583 <p class=MsoNormal><o:p> </o:p></p> 1250 determined. Alternately, a project (<span class=SpellE><span style='font-family: 1251 Courier'>start.gpx</span></span>) file is provided in the <a href="data/" 1252 target="_blank">exercise files</a> to start without the previous tutorial.</p> 1584 1253 1585 1254 <h2>Step 1: Setup for fit</h2> … … 1588 1257 and creating the phase, make the the following changes:</p> 1589 1258 1590 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo 15'><![if !supportLists]><span1259 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span 1591 1260 style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family: 1592 Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> 1593 </span></span></span><![endif]><span dir=LTR></span><b>Controls</b>: Set the Max 1594 cycles value to 5 </p> 1595 1596 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo15'><![if !supportLists]><span 1261 Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> 1262 </span></span></span><![endif]><b>Controls</b>: Set the <b><span 1263 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; 1264 mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Max cycles</span></b> 1265 value to 5 </p> 1266 1267 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span 1597 1268 style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family: 1598 Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> 1599 </span></span></span><![endif]><span dir=LTR></span><b>Limits</b>: Raise the upper 1600 data limit from 8 to 24 degrees</p> 1601 1602 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo15'><![if !supportLists]><span 1269 Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> 1270 </span></span></span><![endif]><b>Limits</b>: Raise the upper data limit from 8 1271 to <b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; 1272 mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>24</span></b> 1273 degrees</p> 1274 1275 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span 1603 1276 style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family: 1604 Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> 1605 </span></span></span><![endif]><span dir=LTR></span><b>Background</b>: Add a background 1606 peak at 5.5 deg with sigma=10,000, set the flag to refine the peak 1607 intensity (window shown in Step 5, below)</p> 1608 1609 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo15'><![if !supportLists]><span 1277 Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> 1278 </span></span></span><![endif]><b>Background</b>: Add a background peak at <b><span 1279 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; 1280 mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>5.5</span></b> 1281 deg with sigma=<b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: 1282 minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>10,000</span></b>, 1283 set the flag to refine the peak intensity. This is to accommodate a broad peak 1284 in the background from the Kapton capillary used to hold the sucrose sample.</p> 1285 1286 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span 1610 1287 style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family: 1611 Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> 1612 </span></span></span><![endif]><span dir=LTR></span><b>Instrument parameters</b>: 1613 Use the Operations<span class=GramE>/</span>Reset profile menu command to 1614 return to the beamline-supplied terms; turn off refinement of all terms</p> 1615 1616 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo15'><![if !supportLists]><span 1288 Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> 1289 </span></span></span><![endif]><b>Instrument parameters</b>: Use the <b><span 1290 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; 1291 mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Operations/Reset 1292 profile</span></b> menu command to return to the beamline-supplied terms; turn 1293 off refinement of all terms</p> 1294 1295 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span 1617 1296 style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family: 1618 Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> 1619 </span></span></span><![endif]><span dir=LTR></span><b>Sample parameters</b>: turn 1620 off refinement of the histogram scale factor</p> 1621 1622 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo15'><![if !supportLists]><span 1297 Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> 1298 </span></span></span><![endif]><b>Sample parameters</b>: turn off refinement of 1299 the <b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; 1300 mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>histogram 1301 scale factor</span></b> and make sure the goniometer radius is <b><span 1302 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; 1303 mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>1000</span></b> 1304 mm.</p> 1305 1306 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span 1623 1307 style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family: 1624 Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> 1625 </span></span></span><![endif]><span dir=LTR></span><b>Phase Sucrose/Data tab</b>: 1626 Use Add powder histograms to link this phase to the powder dataset; set the 1627 refine flag on for the size term and the <span class=SpellE>microstrain</span> 1308 Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> 1309 </span></span></span><![endif]><b>Phase Sucrose/Data tab</b>: Use <b><span 1310 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; 1311 mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Edit phase/Add 1312 powder histograms</span></b> to link this phase to the powder dataset; set the 1313 refine flag on for the <b><span style='font-family:"Calibri",sans-serif; 1314 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font: 1315 minor-latin'>size</span></b> term and the <span class=SpellE><b><span 1316 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; 1317 mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>microstrain</span></b></span> 1628 1318 term. </p> 1629 1319 1630 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo 15'><![if !supportLists]><span1320 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span 1631 1321 style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family: 1632 Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> 1633 </span></span></span><![endif]><span dir=LTR></span><b>Phase Sucrose/Atoms tab</b>: 1634 Use Edit Atoms<span class=GramE>/</span>Append atom menu command to add an 1635 atom to the structure. It does not matter what the atom type is or where it is 1636 located, since the phase structure will not be used in the computation, but one 1637 atom must be present for the phase to be created properly. </p> 1638 1639 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo15'><![if !supportLists]><span 1640 style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family: 1641 Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> 1642 </span></span></span><![endif]><span dir=LTR></span><b>Phase Sucrose/General 1643 tab</b>: Set the Refine the unit cell flag.</p> 1322 Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> 1323 </span></span></span><![endif]><b>Phase Sucrose/General tab</b>: Set the <b><span 1324 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; 1325 mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Refine unit 1326 cell</span></b> flag.</p> 1644 1327 1645 1328 <p class=MsoNormal><o:p> </o:p></p> 1646 1329 1647 1330 <p class=MsoNormal>These changes have been applied to a GSAS-II project file 1648 from the conclusion of the 3rd Example within Fit Peaks/Autoindexing in 1649 GSAS-II and is provided as for this tutorial as file <span class=SpellE><span 1331 from the conclusion of the 3rd Example within <b><span style='font-family: 1332 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: 1333 minor-latin;mso-bidi-theme-font:minor-latin'>Fit Peaks/Autoindexing in GSAS-II</span></b> 1334 tutorial and is provided as for this tutorial as file <span class=SpellE><span 1650 1335 style='font-family:Courier'>start.gpx</span></span>.</p> 1651 1336 1652 <p class=MsoNormal><o:p> </o:p></p>1653 1654 1337 <h2>Step 2: Select Le Bail fitting</h2> 1655 1338 1656 <p class=MsoNormal> <o:p> </o:p></p>1657 1658 <p class=MsoNormal>On the phase Data tab, select the Do new Le Bail extraction 1659 option to put the refinement into Le Bail mode. </p>1339 <p class=MsoNormal>On the phase Data tab, press the <b><span style='font-family: 1340 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: 1341 minor-latin;mso-bidi-theme-font:minor-latin'>Start Le Bail extraction?</span></b> 1342 button to put the refinement into Le Bail mode. </p> 1660 1343 1661 1344 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype … … 1679 1362 <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/> 1680 1363 <o:lock v:ext="edit" aspectratio="t"/> 1681 </v:shapetype><v:shape id="Picture_x0020_50" o:spid="_x0000_i1034" type="#_x0000_t75" 1682 alt="Graphical user interface, text, application Description automatically generated" 1683 style='width:6in;height:229pt;visibility:visible;mso-wrap-style:square'> 1684 <v:imagedata src="LeBailSucrose.fld/image005.png" o:title="Graphical user interface, text, application Description automatically generated"/> 1685 </v:shape><![endif]--><![if !vml]><img border=0 width=432 height=229 1686 src="LeBailSucrose.fld/image005.png" 1687 alt="Graphical user interface, text, application Description automatically generated" 1688 v:shapes="Picture_x0020_50"><![endif]></span></p> 1364 </v:shapetype><v:shape id="Picture_x0020_11" o:spid="_x0000_i1039" type="#_x0000_t75" 1365 alt="GSAS-II project: start.gpx" style='width:432.75pt;height:421.5pt; 1366 visibility:visible;mso-wrap-style:square'> 1367 <v:imagedata src="LeBailSucrose.fld/image001.png" o:title=" start"/> 1368 </v:shape><![endif]--><![if !vml]><img border=0 width=577 height=562 1369 src="LeBailSucrose.fld/image003.png" alt="GSAS-II project: start.gpx" v:shapes="Picture_x0020_11"><![endif]></span></p> 1370 1371 <p class=MsoNormal>The window will be redrawn with all intensity dependent 1372 variables removed from view</p> 1373 1374 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1375 id="Picture_x0020_12" o:spid="_x0000_i1038" type="#_x0000_t75" alt="GSAS-II project: start.gpx" 1376 style='width:435pt;height:325.5pt;visibility:visible;mso-wrap-style:square'> 1377 <v:imagedata src="LeBailSucrose.fld/image004.png" o:title=" start"/> 1378 </v:shape><![endif]--><![if !vml]><img border=0 width=580 height=434 1379 src="LeBailSucrose.fld/image006.png" alt="GSAS-II project: start.gpx" v:shapes="Picture_x0020_12"><![endif]></span></p> 1380 1381 <p class=MsoNormal>and the LeBail button has changed to Stop LeBail 1382 extraction?.</p> 1383 1384 <h2>Step 3: Do the initial Le Bail fit</h2> 1385 1386 <p class=MsoNormal>Do the <b><span style='font-family:"Calibri",sans-serif; 1387 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font: 1388 minor-latin'>Calculate/Refine</span></b> menu command. A popup message will 1389 appear informing you that it will do the initial zero cycle LeBail fit of the 1390 intensities. </p> 1391 1392 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1393 id="Picture_x0020_13" o:spid="_x0000_i1037" type="#_x0000_t75" alt="Le Bail Refinement" 1394 style='width:274.5pt;height:99pt;visibility:visible;mso-wrap-style:square'> 1395 <v:imagedata src="LeBailSucrose.fld/image016.png" o:title="Le Bail Refinement"/> 1396 </v:shape><![endif]--><![if !vml]><img border=0 width=366 height=132 1397 src="LeBailSucrose.fld/image016.png" alt="Le Bail Refinement" v:shapes="Picture_x0020_13"><![endif]></span></p> 1398 1399 <p class=MsoNormal>press <b><span style='font-family:"Calibri",sans-serif; 1400 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font: 1401 minor-latin'>Ok</span></b>. The refinement will proceed and yield <span 1402 class=SpellE>Rwp</span> ~34%. The popup has an Ok and Cancel buttons. The plot 1403 has been updated with this fit. </p> 1404 1405 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1406 id="Picture_x0020_14" o:spid="_x0000_i1036" type="#_x0000_t75" alt="GSAS-II plots: start.gpx" 1407 style='width:501.75pt;height:322.5pt;visibility:visible;mso-wrap-style:square'> 1408 <v:imagedata src="LeBailSucrose.fld/image013.png" o:title=" start"/> 1409 </v:shape><![endif]--><![if !vml]><img border=0 width=669 height=430 1410 src="LeBailSucrose.fld/image007.png" alt="GSAS-II plots: start.gpx" v:shapes="Picture_x0020_14"><![endif]></span></p> 1411 1412 <p class=MsoNormal>You should have a look to be sure that the peaks are in the 1413 right places and that some calculated intensity is present under them. 1414 Otherwise you should press Cancel & adjust things as appropriate (e.g. 1415 lattice parameters). </p> 1689 1416 1690 1417 <p class=MsoNormal><o:p> </o:p></p> 1691 1418 1692 <h2>Step 3: Perform an initial Le Bail-only fit</h2> 1419 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1420 id="Picture_x0020_15" o:spid="_x0000_i1035" type="#_x0000_t75" alt="Le Bail fit: Rwp=34.149" 1421 style='width:274.5pt;height:117pt;visibility:visible;mso-wrap-style:square'> 1422 <v:imagedata src="LeBailSucrose.fld/image027.png" o:title=" Rwp=34"/> 1423 </v:shape><![endif]--><![if !vml]><img border=0 width=366 height=156 1424 src="LeBailSucrose.fld/image027.png" alt="Le Bail fit: Rwp=34.149" v:shapes="Picture_x0020_15"><![endif]></span></p> 1425 1426 <p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif; 1427 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font: 1428 minor-latin'>Ok</span></b> to save this & proceed to the 1<sup>st</sup> 1429 full Rietveld/LeBail refinement. The next refinement will include those 1430 parameters you selected for a full Rietveld/LeBail refinement. The initial 1431 residual should be where the initial LeBail fit finished<span style='mso-no-proof: 1432 yes'>. </span>This will run through five cycles of Rietveld/Le Bail fitting and 1433 the residual will drop to <span class=SpellE>Rwp</span> ~12.6%</p> 1434 1435 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1436 id="Picture_x0020_17" o:spid="_x0000_i1034" type="#_x0000_t75" alt="Refinement results, Rw =12.560" 1437 style='width:274.5pt;height:177.75pt;visibility:visible;mso-wrap-style:square'> 1438 <v:imagedata src="LeBailSucrose.fld/image028.png" o:title="Refinement results, Rw =12"/> 1439 </v:shape><![endif]--><![if !vml]><img border=0 width=366 height=237 1440 src="LeBailSucrose.fld/image028.png" alt="Refinement results, Rw =12.560" 1441 v:shapes="Picture_x0020_17"><![endif]></span></p> 1442 1443 <p class=MsoNormal>and the fit will be much improved</p> 1444 1445 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1446 id="Picture_x0020_18" o:spid="_x0000_i1033" type="#_x0000_t75" alt="GSAS-II plots: start.gpx" 1447 style='width:7in;height:324pt;visibility:visible;mso-wrap-style:square'> 1448 <v:imagedata src="LeBailSucrose.fld/image029.png" o:title=" start"/> 1449 </v:shape><![endif]--><![if !vml]><img border=0 width=672 height=432 1450 src="LeBailSucrose.fld/image008.png" alt="GSAS-II plots: start.gpx" v:shapes="Picture_x0020_18"><![endif]></span></p> 1451 1452 <p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif; 1453 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font: 1454 minor-latin'>OK</span></b> to accept these results. </p> 1455 1456 <h2>Step 4: Add more parameters</h2> 1457 1458 <p class=MsoNormal>Clearly, further improvement in the fit is desirable. Closely 1459 examining the fit shows issues with background, profile shape and peak 1460 positions.</p> 1461 1462 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1463 id="Picture_x0020_19" o:spid="_x0000_i1032" type="#_x0000_t75" alt="GSAS-II plots: start.gpx" 1464 style='width:501.75pt;height:322.5pt;visibility:visible;mso-wrap-style:square'> 1465 <v:imagedata src="LeBailSucrose.fld/image031.png" o:title=" start"/> 1466 </v:shape><![endif]--><![if !vml]><img border=0 width=669 height=430 1467 src="LeBailSucrose.fld/image009.png" alt="GSAS-II plots: start.gpx" v:shapes="Picture_x0020_19"><![endif]></span><span 1468 style='mso-spacerun:yes'> </span></p> 1469 1470 <p class=MsoNormal>Plotting the (<span class=SpellE>obs-cal</span>)/sigma curve 1471 (press the <b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: 1472 minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>w</span></b> 1473 key) and enlarging it (use the crossed-arrows button and drag the right mouse 1474 button upwards inside the lower box), as shown above, shows that further 1475 background improvement might be expected with more background terms. </p> 1476 1477 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l1 level1 lfo4'><![if !supportLists]><span 1478 style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family: 1479 Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> 1480 </span></span></span><![endif]>Change to use <b><span style='font-family:"Calibri",sans-serif; 1481 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font: 1482 minor-latin'>6</span></b> chebyschev-1 parameters. </p> 1483 1484 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l1 level1 lfo4'><![if !supportLists]><span 1485 style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family: 1486 Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> 1487 </span></span></span><![endif]>Also refine <b><span style='font-family:"Calibri",sans-serif; 1488 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font: 1489 minor-latin'>sig</span></b> and <b><span style='font-family:"Calibri",sans-serif; 1490 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font: 1491 minor-latin'>pos</span></b> for the single background peak. </p> 1492 1493 <p class=MsoNormal>The peak positions are probably offset from a sample 1494 position error (it is almost always present)</p> 1495 1496 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l2 level1 lfo5'><![if !supportLists]><span 1497 style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family: 1498 Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> 1499 </span></span></span><![endif]>Select <b><span style='font-family:"Calibri",sans-serif; 1500 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font: 1501 minor-latin'>Sample X <span class=SpellE>displ</span></span></b> in Sample 1502 Parameters </p> 1503 1504 <p class=MsoNormal>The peak shape shows perhaps (in this case) inadequately 1505 determined instrumental U, V & W parameters</p> 1506 1507 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l2 level1 lfo5'><![if !supportLists]><span 1508 style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family: 1509 Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> 1510 </span></span></span><![endif]>In Instrument Parameters select <b><span 1511 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; 1512 mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>U, V & W</span></b> 1513 for refinement. </p> 1693 1514 1694 1515 <p class=MsoNormal><o:p> </o:p></p> 1695 1516 1696 <p class=MsoNormal>Initiate a fit that improves only the Le Bail intensities 1697 using the Calculate<span class=GramE>/</span>Le Bail fit menu 1698 command. 1699 (Note that control-B is a shortcut for this, except on the Mac where 1700 the shortcut is <span style='font-family:"Cambria Math",serif;mso-fareast-font-family: 1701 "Times New Roman";mso-bidi-font-family:"Cambria Math"'>⌘B).</span></p> 1517 <p class=MsoNormal>Do <b><span style='font-family:"Calibri",sans-serif; 1518 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font: 1519 minor-latin'>Calculate/Refine</span></b>; there will be a high residual for the 1520 initial steps but will quickly settle down to <span class=SpellE>Rwp</span> ~ 1521 6.0%</p> 1522 1523 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1524 id="Picture_x0020_21" o:spid="_x0000_i1031" type="#_x0000_t75" alt="GSAS-II plots: start.gpx" 1525 style='width:7in;height:324pt;visibility:visible;mso-wrap-style:square'> 1526 <v:imagedata src="LeBailSucrose.fld/image033.png" o:title=" start"/> 1527 </v:shape><![endif]--><![if !vml]><img border=0 width=672 height=432 1528 src="LeBailSucrose.fld/image010.png" alt="GSAS-II plots: start.gpx" v:shapes="Picture_x0020_21"><![endif]></span></p> 1529 1530 <p class=MsoNormal>Pretty clearly, this sucrose sample gave an instrumental 1531 profile that was better than what the provided instrument parameter file 1532 indicated</p> 1533 1534 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1535 id="Picture_x0020_22" o:spid="_x0000_i1030" type="#_x0000_t75" alt="GSAS-II plots: start.gpx" 1536 style='width:503.25pt;height:324pt;visibility:visible;mso-wrap-style:square'> 1537 <v:imagedata src="LeBailSucrose.fld/image035.png" o:title=" start"/> 1538 </v:shape><![endif]--><![if !vml]><img border=0 width=671 height=432 1539 src="LeBailSucrose.fld/image011.png" alt="GSAS-II plots: start.gpx" v:shapes="Picture_x0020_22"><![endif]></span></p> 1540 1541 <p class=MsoNormal>The solid line is from the default set of instrument 1542 parameters, the crosses are from the single peak fits done in the peak fitting 1543 tutorial and the dashed curve is from the results of this fit.</p> 1544 1545 <h2>Step 5: Explore peak shape terms</h2> 1546 1547 <p class=MsoNormal>At this point the fit is still poorer than what would be 1548 expected based on counting statistics (which would yield a reduced <span 1549 lang=EL style='mso-ansi-language:EL'>χ</span><sup>2</sup> value close to 1.) 1550 Looking closely at the data and computed pattern, as shown below for example, 1551 leads one to believe that the profile is still not being well-fit.</p> 1552 1553 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1554 id="Picture_x0020_23" o:spid="_x0000_i1029" type="#_x0000_t75" alt="GSAS-II plots: start.gpx" 1555 style='width:503.25pt;height:324pt;visibility:visible;mso-wrap-style:square'> 1556 <v:imagedata src="LeBailSucrose.fld/image037.png" o:title=" start"/> 1557 </v:shape><![endif]--><![if !vml]><img border=0 width=671 height=432 1558 src="LeBailSucrose.fld/image012.png" alt="GSAS-II plots: start.gpx" v:shapes="Picture_x0020_23"><![endif]></span></p> 1559 1560 <p class=MsoNormal>A Le Bail fit provides a good way to explore different peak 1561 shape broadening options. Moreover, if the intended use of the extracted 1562 structure factors is structure solution, then one wants the best LeBail fit 1563 possible. Investigation of a number of models for anisotropic peak broadening 1564 finds that the <span class=SpellE>R<sub>wp</sub></span> can be reduced to 5.23%, 1565 through use of the Popa/Stephens model for <span class=SpellE>microstrain</span> 1566 (refining 9 terms in the generalized mustrain model), with a plausible <span 1567 class=SpellE>microstrain</span> directional plot, as below. A fit that uses 1568 fewer terms that is almost as good uses uniaxial crystallite domain size 1569 broadening along the 010 axis and uniaxial <span class=SpellE>microstrain</span> 1570 broadening along the 010 axis, my residual was <span class=SpellE>R<sub>wp</sub></span> 1571 = 5.38%. This adds 2 only parameters. We will continue with the isotropic size 1572 and generalized mustrain models; my final <span class=SpellE>R<sub>wp</sub></span> 1573 after several sets of LeBail/Rietveld refinement was <span class=SpellE>R<sub>wp</sub></span> 1574 = 5.197%.</p> 1702 1575 1703 1576 <p class=MsoNormal><o:p> </o:p></p> 1704 1577 1578 <p class=MsoNormal><b><i>The important result here is that this sample exhibit 1579 non-ideal broadening artifacts. This could be due to milling of the sucrose 1580 during manufacture creating defects that cannot be well-fit with a conventional 1581 peak shape. From this fit, it is now clear that best possible fit to be 1582 expected from any structural model will have a <span class=SpellE>R<sub>wp</sub></span> 1583 on the order of 5% and a reduced </i></b><b><i><span lang=EL style='mso-ansi-language: 1584 EL'>χ</span><sup>2</sup> value on the order of 1.5, since no crystal 1585 structure model could give a better intensity fit than a Le Bail or Pawley fit. 1586 <o:p></o:p></i></b></p> 1587 1705 1588 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1706 id="Picture_x0020_44" o:spid="_x0000_i1033" type="#_x0000_t75" alt="Graphical user interface, text, application, chat or text message Description automatically generated" 1707 style='width:279pt;height:147pt;visibility:visible;mso-wrap-style:square'> 1708 <v:imagedata src="LeBailSucrose.fld/image002.png" o:title="Graphical user interface, text, application, chat or text message Description automatically generated"/> 1709 </v:shape><![endif]--><![if !vml]><img border=0 width=279 height=147 1710 src="LeBailSucrose.fld/image002.png" 1711 alt="Graphical user interface, text, application, chat or text message Description automatically generated" 1712 v:shapes="Picture_x0020_44"><![endif]></span></p> 1589 id="Picture_x0020_24" o:spid="_x0000_i1028" type="#_x0000_t75" alt="GSAS-II plots: start.gpx" 1590 style='width:505.5pt;height:510.75pt;visibility:visible;mso-wrap-style:square'> 1591 <v:imagedata src="LeBailSucrose.fld/image015.png" o:title=" start"/> 1592 </v:shape><![endif]--><![if !vml]><img border=0 width=674 height=681 1593 src="LeBailSucrose.fld/image017.png" alt="GSAS-II plots: start.gpx" v:shapes="Picture_x0020_24"><![endif]></span></p> 1594 1595 <h2>Step 6. Resetting the LeBail extracted intensities</h2> 1596 1597 <p class=MsoNormal>A perhaps further improvement in the extracted structure factors 1598 with the aim of using then in structure solution can be obtained by 1599 reinitializing the LeBail extraction using the now better parameter set. Go to 1600 the Data tab.</p> 1601 1602 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1603 id="Picture_x0020_25" o:spid="_x0000_i1027" type="#_x0000_t75" alt="GSAS-II project: start.gpx" 1604 style='width:508.5pt;height:430.5pt;visibility:visible;mso-wrap-style:square'> 1605 <v:imagedata src="LeBailSucrose.fld/image018.png" o:title=" start"/> 1606 </v:shape><![endif]--><![if !vml]><img border=0 width=678 height=574 1607 src="LeBailSucrose.fld/image019.png" alt="GSAS-II project: start.gpx" v:shapes="Picture_x0020_25"><![endif]></span></p> 1608 1609 <p class=MsoNormal>Notice the message on the righthand status line; to reset 1610 the LeBail intensities, cycle the Le Bail button. Press <b><span 1611 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; 1612 mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Stop Le Bail 1613 extraction</span></b> (NB: this will set the refinement into normal Rietveld mode 1614 impossible because the model contains no atoms!). The window will be redrawn 1615 to include the intensity dependent parameters. Now press it again (<b><span 1616 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; 1617 mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Start Le bail 1618 extraction?</span></b>). The window will be redrawn again. The next refinement 1619 will start with new initial structure factor values (=1.0) and will do the 1620 preliminary zero cycle Le Bail refinement. You may leave the refinement 1621 parameters alone. The refinement will start out high (Rwp~67%) but will quickly 1622 drop to ~5.7% because all the other parameters are near their optimal values.</p> 1623 1624 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1625 id="Picture_x0020_26" o:spid="_x0000_i1026" type="#_x0000_t75" alt="Le Bail fit: Rwp=5.756" 1626 style='width:274.5pt;height:117pt;visibility:visible;mso-wrap-style:square'> 1627 <v:imagedata src="LeBailSucrose.fld/image020.png" o:title=" Rwp=5"/> 1628 </v:shape><![endif]--><![if !vml]><img border=0 width=366 height=156 1629 src="LeBailSucrose.fld/image020.png" alt="Le Bail fit: Rwp=5.756" v:shapes="Picture_x0020_26"><![endif]></span></p> 1630 1631 <p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif; 1632 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font: 1633 minor-latin'>OK</span></b> to continue with the Rietveld/LeBail part of the 1634 refinement; a popup will show the status of this part.</p> 1635 1636 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1637 id="Picture_x0020_27" o:spid="_x0000_i1025" type="#_x0000_t75" alt="Refinement results, Rw =5.469" 1638 style='width:274.5pt;height:177.75pt;visibility:visible;mso-wrap-style:square'> 1639 <v:imagedata src="LeBailSucrose.fld/image021.png" o:title="Refinement results, Rw =5"/> 1640 </v:shape><![endif]--><![if !vml]><img border=0 width=366 height=237 1641 src="LeBailSucrose.fld/image021.png" alt="Refinement results, Rw =5.469" 1642 v:shapes="Picture_x0020_27"><![endif]></span></p> 1643 1644 <p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif; 1645 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font: 1646 minor-latin'>OK</span></b>. Set the number of cycles to <b><span 1647 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; 1648 mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>20</span></b> 1649 and repeat <b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: 1650 minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Calculate/Refine</span></b> 1651 until the fit has converged (it may take several repeats as this part of a Le 1652 Bail refinement does converge slowly). I got <span class=SpellE>Rwp</span> = 1653 5.26% when I quit recycling the refinement. You can now use these extracted 1654 intensities to see if they can be used for a charge flipping structure solution 1655 (I did get it to work once otherwise many failures).</p> 1713 1656 1714 1657 <p class=MsoNormal><o:p> </o:p></p> 1715 1658 1716 <p class=MsoNormal>This will run through three cycles of Le Bail1717 fitting. <B><I>This will only optimize the intensities of reflections. No1718 other parameter values will be optimized until Step 5, when a least1719 squares fit is done.</I></B>1720 After one use, a fairly reasonable fit is obtained, as shown below. </p>1721 1722 <p class=MsoNormal><o:p> </o:p></p>1723 1724 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape1725 id="Picture_x0020_52" o:spid="_x0000_i1032" type="#_x0000_t75" alt="Graphical user interface Description automatically generated"1726 style='width:8in;height:378pt;visibility:visible;mso-wrap-style:square'>1727 <v:imagedata src="LeBailSucrose.fld/image006.png" o:title="Graphical user interface Description automatically generated"/>1728 </v:shape><![endif]--><![if !vml]><img border=0 width=576 height=3781729 src="LeBailSucrose.fld/image006.png"1730 alt="Graphical user interface Description automatically generated"1731 v:shapes="Picture_x0020_52"><![endif]></span></p>1732 1733 <p class=MsoNormal>Press OK to accept these results. </p>1734 1735 <p class=MsoNormal><o:p> </o:p></p>1736 1737 <h2>Step 4: Perform additional Le Bail-only fits</h2>1738 1739 <p class=MsoNormal>The Le Bail intensities can be further fit using the Calculate<span1740 class=GramE>/</span>Le Bail fit menu command again. The fit improves very1741 slightly, as shown below. </p>1742 1743 <p class=MsoNormal><o:p> </o:p></p>1744 1745 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape1746 id="Picture_x0020_53" o:spid="_x0000_i1031" type="#_x0000_t75" alt="Graphical user interface, timeline Description automatically generated"1747 style='width:8in;height:376pt;visibility:visible;mso-wrap-style:square'>1748 <v:imagedata src="LeBailSucrose.fld/image007.png" o:title="Graphical user interface, timeline Description automatically generated"/>1749 </v:shape><![endif]--><![if !vml]><img border=0 width=576 height=3761750 src="LeBailSucrose.fld/image007.png"1751 alt="Graphical user interface, timeline Description automatically generated"1752 v:shapes="Picture_x0020_53"><![endif]></span></p>1753 1754 <p class=MsoNormal><o:p> </o:p></p>1755 1756 <p class=MsoNormal>Since the improvement is so small, there is little value in running1757 this again (though there is also no harm in doing this). In other projects, it may1758 be necessary to perform this step more than twice before the fit no longer1759 improves significantly. Here, any improvement to the fit will require1760 refinement of the1761 the <span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin'>experimental1762 and lattice parameters, which is done via least-squares fitting. </span></p>1763 1764 <h2>Step 5: Combined Le Bail/Least Squares fit</h2>1765 1766 <p class=MsoNormal><span style='mso-ascii-font-family:"Times New Roman";1767 mso-ascii-theme-font:major-bidi;mso-hansi-font-family:"Times New Roman";1768 mso-hansi-theme-font:major-bidi;mso-bidi-font-family:"Times New Roman";1769 mso-bidi-theme-font:major-bidi'>In the instructions for Step 1, refinement1770 flags were set for three background terms, the intensity value for a single background1771 peak, a sample broadening term and a <span class=SpellE>microstrain</span>1772 broadening term plus four lattice parameters (10 parameters in total). This can1773 be verified using the Calculate<span class=GramE>/</span>View LS parameters menu1774 command (shortcut: control-L or </span><span style='font-family:"Cambria Math",serif;1775 mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Cambria Math"'>⌘</span><span1776 style='mso-ascii-font-family:"Times New Roman";mso-ascii-theme-font:major-bidi;1777 mso-fareast-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman";1778 mso-hansi-theme-font:major-bidi;mso-bidi-font-family:"Times New Roman";1779 mso-bidi-theme-font:major-bidi'>L). <o:p></o:p></span></p>1780 1781 <p class=MsoNormal><span style='mso-ascii-font-family:"Times New Roman";1782 mso-ascii-theme-font:major-bidi;mso-fareast-font-family:"Times New Roman";1783 mso-hansi-font-family:"Times New Roman";mso-hansi-theme-font:major-bidi;1784 mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi'><o:p> </o:p></span></p>1785 1786 <p class=MsoNormal><span style='mso-ascii-font-family:"Times New Roman";1787 mso-ascii-theme-font:major-bidi;mso-fareast-font-family:"Times New Roman";1788 mso-hansi-font-family:"Times New Roman";mso-hansi-theme-font:major-bidi;1789 mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi'>All that1790 is needed </span><span style='mso-ascii-font-family:"Times New Roman";1791 mso-ascii-theme-font:major-bidi;mso-hansi-font-family:"Times New Roman";1792 mso-hansi-theme-font:major-bidi;mso-bidi-font-family:"Times New Roman";1793 mso-bidi-theme-font:major-bidi'>at this stage</span><span style='mso-ascii-font-family:1794 "Times New Roman";mso-ascii-theme-font:major-bidi;mso-fareast-font-family:"Times New Roman";1795 mso-hansi-font-family:"Times New Roman";mso-hansi-theme-font:major-bidi;1796 mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi'> to perform1797 a combined Le Bail/Least Squares fit is to use the </span><span1798 style='mso-ascii-font-family:"Times New Roman";mso-ascii-theme-font:major-bidi;1799 mso-hansi-font-family:"Times New Roman";mso-hansi-theme-font:major-bidi;1800 mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi'>Calculate/Refine1801 menu command.</span><span style='mso-ascii-font-family:"Times New Roman";1802 mso-ascii-theme-font:major-bidi;mso-fareast-font-family:"Times New Roman";1803 mso-hansi-font-family:"Times New Roman";mso-hansi-theme-font:major-bidi;1804 mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi'><o:p></o:p></span></p>1805 1806 <p class=MsoNormal><span style='mso-ascii-font-family:"Times New Roman";1807 mso-ascii-theme-font:major-bidi;mso-fareast-font-family:"Times New Roman";1808 mso-hansi-font-family:"Times New Roman";mso-hansi-theme-font:major-bidi;1809 mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi'><o:p> </o:p></span></p>1810 1811 <p class=MsoNormal><span style='mso-ascii-font-family:"Times New Roman";1812 mso-ascii-theme-font:major-bidi;mso-hansi-font-family:"Times New Roman";1813 mso-hansi-theme-font:major-bidi;mso-bidi-font-family:"Times New Roman";1814 mso-bidi-theme-font:major-bidi;mso-no-proof:yes'><!--[if gte vml 1]><v:shape1815 id="Picture_x0020_54" o:spid="_x0000_i1030" type="#_x0000_t75" alt="Graphical user interface, application, Word Description automatically generated"1816 style='width:472pt;height:235pt;visibility:visible;mso-wrap-style:square'>1817 <v:imagedata src="LeBailSucrose.fld/image008.png" o:title="Graphical user interface, application, Word Description automatically generated"/>1818 </v:shape><![endif]--><![if !vml]><img border=0 width=472 height=2351819 src="LeBailSucrose.fld/image008.png"1820 alt="Graphical user interface, application, Word Description automatically generated"1821 v:shapes="Picture_x0020_54"><![endif]></span><span style='mso-ascii-font-family:1822 "Times New Roman";mso-ascii-theme-font:major-bidi;mso-hansi-font-family:"Times New Roman";1823 mso-hansi-theme-font:major-bidi;mso-bidi-font-family:"Times New Roman";1824 mso-bidi-theme-font:major-bidi'><o:p></o:p></span></p>1825 1826 <p class=MsoNormal><span style='mso-ascii-font-family:"Times New Roman";1827 mso-ascii-theme-font:major-bidi;mso-hansi-font-family:"Times New Roman";1828 mso-hansi-theme-font:major-bidi;mso-bidi-font-family:"Times New Roman";1829 mso-bidi-theme-font:major-bidi'><o:p> </o:p></span></p>1830 1831 <p class=MsoNormal><span style='mso-ascii-font-family:"Times New Roman";1832 mso-ascii-theme-font:major-bidi;mso-hansi-font-family:"Times New Roman";1833 mso-hansi-theme-font:major-bidi;mso-bidi-font-family:"Times New Roman";1834 mso-bidi-theme-font:major-bidi'>The refinement progresses well and a much1835 better, though far from perfect, fit is obtained. <o:p></o:p></span></p>1836 1837 <p class=MsoNormal><o:p> </o:p></p>1838 1839 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape1840 id="Picture_x0020_55" o:spid="_x0000_i1029" type="#_x0000_t75" alt="Graphical user interface, timeline Description automatically generated"1841 style='width:577pt;height:376pt;visibility:visible;mso-wrap-style:square'>1842 <v:imagedata src="LeBailSucrose.fld/image009.png" o:title="Graphical user interface, timeline Description automatically generated"/>1843 </v:shape><![endif]--><![if !vml]><img border=0 width=577 height=3761844 src="LeBailSucrose.fld/image009.png"1845 alt="Graphical user interface, timeline Description automatically generated"1846 v:shapes="Picture_x0020_55"><![endif]></span></p>1847 1848 <h2>Step 6: Add more parameters</h2>1849 1850 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape1851 id="Picture_x0020_56" o:spid="_x0000_i1028" type="#_x0000_t75" alt="Chart Description automatically generated"1852 style='width:634pt;height:220pt;visibility:visible;mso-wrap-style:square'>1853 <v:imagedata src="LeBailSucrose.fld/image010.png" o:title="Chart Description automatically generated"/>1854 </v:shape><![endif]--><![if !vml]><img border=0 width=634 height=2201855 src="LeBailSucrose.fld/image010.png"1856 alt="Chart Description automatically generated" v:shapes="Picture_x0020_56"><![endif]></span><span1857 style='mso-spacerun:yes'> </span></p>1858 1859 <p class=MsoNormal>Plotting the (<span1860 class=SpellE>obs-cal</span>)/sigma curve (press the w key)1861 and enlarging it (use the crossed-arrows button and drag the right mouse button1862 upwards inside the lower box), as shown above, shows that further background improvement might1863 be expected with more background terms. </p>1864 1865 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l7 level1 lfo16'><![if !supportLists]><span1866 style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:1867 Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> 1868 </span></span></span><![endif]><span dir=LTR></span>Change to use 6 chebyschev-11869 peaks. </p>1870 1871 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l7 level1 lfo16'><![if !supportLists]><span1872 style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:1873 Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> 1874 </span></span></span><![endif]><span dir=LTR></span>Also refine sig for the1875 single background peak. <o:p></o:p></p>1876 1877 <p class=MsoNormal><o:p> </o:p></p>1878 1879 <p class=MsoNormal>Repeating "Refine" improves the fit somewhat, as shown below. </p>1880 1881 <p class=MsoNormal><o:p> </o:p></p>1882 1883 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape1884 id="Picture_x0020_57" o:spid="_x0000_i1027" type="#_x0000_t75" alt="Graphical user interface Description automatically generated"1885 style='width:8in;height:375pt;visibility:visible;mso-wrap-style:square'>1886 <v:imagedata src="LeBailSucrose.fld/image011.png" o:title="Graphical user interface Description automatically generated"/>1887 </v:shape><![endif]--><![if !vml]><img border=0 width=576 height=3751888 src="LeBailSucrose.fld/image011.png"1889 alt="Graphical user interface Description automatically generated"1890 v:shapes="Picture_x0020_57"><![endif]></span></p>1891 1892 <p class=MsoNormal><o:p> </o:p></p>1893 1894 <h2>Step 7: Explore peak shape terms<o:p></o:p></h2>1895 1896 <p class=MsoNormal>At this point the fit is still far from what would be1897 expected based on counting statistics (which would yield a reduced <span1898 lang=EL style='mso-ansi-language:EL'>χ</span><sup>2</sup> value close to1899 1.) Looking closely at the data and computed pattern, as shown below for1900 example, leads one to believe that the profile is still not being well-fit.</p>1901 1902 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape1903 id="Picture_x0020_58" o:spid="_x0000_i1026" type="#_x0000_t75" alt="Graphical user interface Description automatically generated"1904 style='width:577pt;height:335pt;visibility:visible;mso-wrap-style:square'>1905 <v:imagedata src="LeBailSucrose.fld/image012.png" o:title="Graphical user interface Description automatically generated"1906 croptop="8315f" cropbottom="11209f" cropleft="7261f" cropright="3949f"/>1907 </v:shape><![endif]--><![if !vml]><img border=0 width=577 height=3351908 src="LeBailSucrose.fld/image013.png"1909 alt="Graphical user interface Description automatically generated"1910 v:shapes="Picture_x0020_58"><![endif]></span></p>1911 1912 <p class=MsoNormal>A Le Bail fit provides a good way to explore different1913 peak shape broadening options. Investigation of a number of models for1914 anisotropic peak broadening finds that the <span class=SpellE>R<sub>wp</sub></span> can be1915 reduced just a bit, to 11.9%, through use of the Stephens model for <span1916 class=SpellE>microstrain</span> (refining 9 terms in the Generalized <span1917 class=SpellE>Mustrain</span> model), with a plausible <span class=SpellE>microstrain</span>1918 directional plot, as below. Considering that 8 more terms have been added1919 to the refinement, this is a fairly minor improvement, which many would1920 say is not worthwhile. A fit that uses1921 fewer terms and is almost as good uses uniaxial crystallite1922 domain size broadening along1923 the 001 axis and uniaxial <span class=SpellE>microstrain</span> broadening1924 along the 010 axis. This adds 2 only parameters. <o:p></o:p></p>1925 1926 <p class=MsoNormal><o:p> </o:p></p>1927 1928 <p class=MsoNormal><b><i>The important result here is that <span class=GramE>this1929 sample exhibits</span> non-ideal broadening artifacts. This could be due to1930 milling of the sucrose during manufacture creating defects that cannot1931 be well-fit with a conventional peak shape. From this fit, it is now1932 clear that best possible fit to be expected from any structural1933 model will have a <span class=SpellE>R<sub>wp</sub></span> on the order of 12% and a reduced1934 </i></b><b><i><span lang=EL style='mso-ansi-language:EL'>χ</span><sup>2</sup>1935 value on the order of 11.8, since no crystal structure model could1936 give a better intensity fit than a Le Bail or Pawley fit. <o:p></o:p></i></b></p>1937 1938 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape1939 id="Picture_x0020_59" o:spid="_x0000_i1025" type="#_x0000_t75" alt="Chart, bubble chart Description automatically generated"1940 style='width:349pt;height:303pt;visibility:visible;mso-wrap-style:square'>1941 <v:imagedata src="LeBailSucrose.fld/image014.png" o:title="Chart, bubble chart Description automatically generated"/>1942 </v:shape><![endif]--><![if !vml]><img border=0 width=349 height=3031943 src="LeBailSucrose.fld/image014.png"1944 alt="Chart, bubble chart Description automatically generated" v:shapes="Picture_x0020_59"><![endif]></span></p>1945 1946 <p class=MsoNormal>This completes this exercise.</p>1947 1948 1659 </div> 1949 1660
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