Changeset 5027


Ignore:
Timestamp:
Sep 17, 2021 1:46:47 PM (2 months ago)
Author:
vondreele
Message:

revise LeBail? tutorial

Location:
Tutorials/LeBail
Files:
17 added
11 edited

Legend:

Unmodified
Added
Removed

  • Tutorials/LeBail/LeBailSucrose.fld/filelist.xml

    r4946 r5027  
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    6  <o:File HRef="image002.png"/>
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    78 <o:File HRef="image006.png"/>
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     20 <o:File HRef="image035.png"/>
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     22 <o:File HRef="image037.png"/>
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    14  <o:File HRef="image013.png"/>
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     26 <o:File HRef="image018.png"/>
     27 <o:File HRef="image019.png"/>
     28 <o:File HRef="image020.png"/>
     29 <o:File HRef="image021.png"/>
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  • Tutorials/LeBail/LeBailSucrose.htm

    r4902 r5027  
    2222 <o:DocumentProperties>
    2323  <o:Author>Von Dreele</o:Author>
    24   <o:LastAuthor>Toby, Brian H.</o:LastAuthor>
    25   <o:Revision>6</o:Revision>
    26   <o:TotalTime>2444</o:TotalTime>
     24  <o:LastAuthor>Von Dreele, Robert B.</o:LastAuthor>
     25  <o:Revision>9</o:Revision>
     26  <o:TotalTime>3113</o:TotalTime>
    2727  <o:Created>2020-11-16T01:37:00Z</o:Created>
    28   <o:LastSaved>2021-03-08T03:53:00Z</o:LastSaved>
     28  <o:LastSaved>2021-09-17T18:29:00Z</o:LastSaved>
    2929  <o:Pages>1</o:Pages>
    30   <o:Words>1557</o:Words>
    31   <o:Characters>8877</o:Characters>
     30  <o:Words>2011</o:Words>
     31  <o:Characters>11468</o:Characters>
    3232  <o:Company>Argonne National Laboratory</o:Company>
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    13951082ol
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    … …  
    14331120Extraction in GSAS-II - Sucrose<o:p></o:p></span></h1>
    14341121
    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
     1124style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin'><span
     1125style='mso-spacerun:yes'>  </span>Exercise files are found <a href="data/"
     1126target="_blank">here</a>. The data files are also used in the 3rd section of
     1127the <a href="../FitPeaks/Fit%20Peaks.htm#sucrose_peak_fit" target="_blank">Fit
     1128Peaks/Autoindexing tutorial</a>. <o:p></o:p></span></p>
     1129
     1130</BL>
    14441131
    14451132<h1><span style='mso-fareast-font-family:"Times New Roman"'>Background <o:p></o:p></span></h1>
    14461133
    14471134<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>
     1135minor-latin'>In a Rietveld fit, a number of different items are fit,
     1136potentially at the same time. These include the lattice parameters, atomic positions
     1137and displacement (aka “temperature”, <span class=SpellE>U<sub>iso</sub></span>
     1138and <span class=SpellE>U<sub>ij</sub></span>) parameters for one or more
     1139phases, as well as peak shapes parameters either for broadening from either the
     1140sample or the instrument (avoid doing both together), background fitting terms
     1141and one or two correction terms needed to describe peak shifts due to apparent
     1142sample placement. In addition, there could be other terms needed to describe
     1143additional experimental conditions such as for absorption, preferred
     1144orientation or extinction. These parameters can be divided into four
     1145categories: experimental (peak shapes, peak shifts and background), lattice
     1146parameters, structural parameters (atom positions and U values) and intensity
     1147correction terms (absorption, preferred orientation and extinction).<o:p></o:p></span></p>
    14601148
    14611149<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
    … …  
    14631151
    14641152<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). &quot;Unit-Cell Refinement from Powder Diffraction
    1470 Scans.&quot; 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). &quot;Whole powder pattern decomposition methods
    1473 and applications: A retrospection.&quot; 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 intensities: the idea behind this is that for every point in a pattern where one
    1477 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 multiplicity
    1480 (<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 estimate
    1483 improves as the crystal structure model approaches reality. Le Bail’s method
    1484 cleverly appropriates Rietveld’s 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<sub>obs</sub>
    1498 values equal for complete reflection overlap; neither is likely to be accurate.)
    1499 <o:p></o:p></span></p>
     1153minor-latin'>In Rietveld, the reflection intensities are generated from the
     1154structural and intensity correction parameters, but there are two approaches to
     1155full-pattern fitting that treat reflection intensities as arbitrary: (1) Pawley
     1156fitting, developed by Stuart Pawley [Pawley, G. S. (1981). &quot;Unit-Cell
     1157Refinement from Powder Diffraction Scans.&quot; Journal of Applied
     1158Crystallography 14: 357-361.], where peak intensities are treated as
     1159least-squares variables. (2) Le Bail fitting, from Armel Le Bail [Le Bail, A.
     1160(2005). &quot;Whole powder pattern decomposition methods and applications: A
     1161retrospection.&quot; Powder Diffraction 20(4): 316-326.] The Le Bail approach,
     1162demonstrated by this tutorial, takes advantage of the fact that Hugo Rietveld
     1163developed a rather ingenious approach to estimating reflection intensities: the
     1164idea behind this is that for every point in a pattern where one or more
     1165reflections contribute, one can estimate the relative contribution from each
     1166reflection from the structure factor magnitude, F<sup>2</sup><sub>calc</sub>,
     1167from the approximate crystal structure model, adjusted for reflection
     1168multiplicity (<i>m</i>), preferred orientation and various other geometric
     1169corrections. Simply apportioning the observed powder pattern intensities point
     1170by point to each reflection provides an estimate for the observed structure
     1171factors, F<sup>2</sup><sub>obs</sub>. The quality of this estimate improves as
     1172the crystal structure model approaches reality. Le Bail’s method cleverly
     1173appropriates Rietveld’s intensity extraction, but assuming the crystal
     1174structure model is unknown, sets all F<sup>2</sup><sub>calc</sub> values to an
     1175initial value (e.g. 1.0). After the intensity extraction is performed, a set of
     1176F<sup>2</sup><sub>obs</sub> values is obtained. These initially treat every F<sup>2</sup><sub>obs</sub>/<i>m</i>
     1177ratio as equivalent and will not be very accurate, but they are much better
     1178reflection estimates than the initial F<sup>2</sup><sub>calc</sub> values (all
     1179unity). The F<sup>2</sup><sub>calc</sub> values are set to the extracted F<sup>2</sup><sub>obs</sub>
     1180and the Le Bail fit can be repeated, giving even better intensity estimates.
     1181This process is equivalent to a steepest descents minimization and it will converge
     1182to a self-consistent set of intensities that will give best possible agreement
     1183to the observed pattern. Note that the apportionment of intensity for
     1184reflections that are very closely overlapped will tend to make their F<sup>2</sup><sub>calc</sub>
     1185values approximately equal. (Note that the Pawley approach will tend make <i>m</i>*F<sup>2</sup><sub>obs</sub>
     1186values equal for complete reflection overlap; neither is likely to be
     1187accurate.) <o:p></o:p></span></p>
    15001188
    15011189<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
    … …  
    15041192<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
    15051193minor-latin'>Note that when either Pawley or Le Bail intensity extraction are
    1506 used, all structural and intensity correction parameters no longer affect the intensity
    1507 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>
     1194used, the structural and intensity correction parameters no longer affect the
     1195intensity computations. Such parameters should not be included in the fit as
     1196they will produce singularities in the refinement. If included inadvertently,
     1197GSAS-II will usually remove them from the fit along with providing annoying warning
     1198messages, but it is possible that this parameter removal process could fail and
     1199the refinement may not run properly.</span></p>
    15121200
    15131201<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
    … …  
    15151203
    15161204<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>
     1205minor-latin'>After the LeBail option has been invoked, the Calculate/Refine
     1206menu command will execute a preliminary LeBail only “zero cycles” refinement in
     1207which only F<sup>2</sup><sub>obs</sub> is adjusted via the LeBail method. It is
     1208cycled 10 times or until a minimum is reached. After that completes, the
     1209Rietveld/LeBail refinement proceeds allowing least-squares minimization of
     1210non-intensity dependent parameters toward a more global fit to the data.
     1211Successive runs allowing other parameters to be varied can then be used to
     1212progressively improve the fit and produce a best estimate of the F<sup>2</sup><sub>obs</sub>.<o:p></o:p></span></p>
    15391213
    15401214<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
    … …  
    15421216
    15431217<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'>&#967;</span><sup><span style='mso-fareast-font-family:
    1560 Calibri;mso-fareast-theme-font:minor-latin'>2</span></sup><span
     1218minor-latin'>There are many reasons to use Le Bail fitting. The technique was
     1219developed to obtain a set of reflection intensities for structure solution. It
     1220can also be used to treat an impurity, where lattice parameters are known but
     1221the structural details are not or for fitting lattice parameters where likewise
     1222the structure is not known. Le Bail fitting is also useful prior to a
     1223structural fit. It can allow determination of reasonable starting values for
     1224the background, peak shapes and unit cell parameters so they can be fixed until
     1225the late stages of the refinement, although the freedom in peak intensities may
     1226bias some parameters (e.g. background and profile coefficients) if there is a
     1227large number of overlapping reflections. Another use is to see when artifacts
     1228in the background or peak shapes limit how well the pattern can be fit. A Le Bail
     1229or Pawley fit provides an estimate for the best possible <span class=SpellE>R<sub>wp</sub></span>
     1230and reduced </span><span lang=EL style='mso-fareast-font-family:Calibri;
     1231mso-fareast-theme-font:minor-latin;mso-ansi-language:EL'>&#967;</span><sup><span
     1232style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin'>2</span></sup><span
    15611233style='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 difficult
    1563 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 space group with fewer extinctions should provide a better fit to warrant its
    1566 consideration.</span></p>
     1234values that can be expected for a dataset. For complex patterns, where it is
     1235difficult to discern where allowed reflections are present, comparison of Le
     1236Bail or Pawley fits can provide insight on extinction conditions. A lower
     1237symmetry space group with fewer extinctions should provide a better fit to
     1238warrant its consideration.</span></p>
    15671239
    15681240<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
    … …  
    15711243<h1><span style='mso-fareast-font-family:"Times New Roman"'>Prerequisite <o:p></o:p></span></h1>
    15721244
    1573 <p class=MsoNormal>In this exercise you we will use Le Bail fitting to extract approximate
    1574 reflection intensities. This is similar to what is done in the beginning of the
    1575 “Charge Flipping in GSAS-II - sucrose” tutorial, which uses Pawley fitting
    1576 instead. It follows logically from the third example in the “Fit
     1245<p class=MsoNormal>In this exercise you we will use Le Bail fitting to extract
     1246approximate reflection intensities. This is similar to what is done in the
     1247beginning of the “Charge Flipping in GSAS-II - sucrose” tutorial, which instead
     1248uses Pawley fitting. It follows logically from the third example in the “Fit
    15771249Peaks/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>&nbsp;</o:p></p>
     1250determined. Alternately, a project (<span class=SpellE><span style='font-family:
     1251Courier'>start.gpx</span></span>) file is provided in the <a href="data/"
     1252target="_blank">exercise files</a> to start without the previous tutorial.</p>
    15841253
    15851254<h2>Step 1: Setup for fit</h2>
    … …  
    15881257and creating the phase, make the the following changes:</p>
    15891258
    1590 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo15'><![if !supportLists]><span
     1259<p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
    15911260style='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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    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
     1261Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
     1262</span></span></span><![endif]><b>Controls</b>: Set the “<b><span
     1263style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     1264mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Max cycles</span></b>”
     1265value to 5 </p>
     1266
     1267<p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
    15971268style='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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    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
     1269Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
     1270</span></span></span><![endif]><b>Limits</b>: Raise the upper data limit from 8
     1271to <b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     1272mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>24</span></b>
     1273degrees</p>
     1274
     1275<p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
    16031276style='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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    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
     1277Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
     1278</span></span></span><![endif]><b>Background</b>: Add a background peak at <b><span
     1279style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     1280mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>5.5</span></b>
     1281deg with sigma=<b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     1282minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>10,000</span></b>,
     1283set the flag to refine the peak intensity. This is to accommodate a broad peak
     1284in 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
    16101287style='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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    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
     1288Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
     1289</span></span></span><![endif]><b>Instrument parameters</b>: Use the <b><span
     1290style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     1291mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Operations/Reset
     1292profile</span></b> menu command to return to the beamline-supplied terms; turn
     1293off refinement of all terms</p>
     1294
     1295<p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
    16171296style='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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    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
     1297Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
     1298</span></span></span><![endif]><b>Sample parameters</b>: turn off refinement of
     1299the <b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     1300mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>histogram
     1301scale factor</span></b> and make sure the goniometer radius is <b><span
     1302style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     1303mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>1000</span></b>
     1304mm.</p>
     1305
     1306<p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
    16231307style='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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    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>
     1308Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
     1309</span></span></span><![endif]><b>Phase Sucrose/Data tab</b>: Use <b><span
     1310style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     1311mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Edit phase/Add
     1312powder histograms</span></b> to link this phase to the powder dataset; set the
     1313refine flag on for the <b><span style='font-family:"Calibri",sans-serif;
     1314mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     1315minor-latin'>size</span></b> term and the <span class=SpellE><b><span
     1316style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     1317mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>microstrain</span></b></span>
    16281318term. </p>
    16291319
    1630 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo15'><![if !supportLists]><span
     1320<p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
    16311321style='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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    1642 </span></span></span><![endif]><span dir=LTR></span><b>Phase Sucrose/General
    1643 tab</b>: Set the “Refine the unit cell” flag.</p>
     1322Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
     1323</span></span></span><![endif]><b>Phase Sucrose/General tab</b>: Set the <b><span
     1324style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     1325mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Refine unit
     1326cell</span></b> flag.</p>
    16441327
    16451328<p class=MsoNormal><o:p>&nbsp;</o:p></p>
    16461329
    16471330<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
     1331from 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:
     1333minor-latin;mso-bidi-theme-font:minor-latin'>Fit Peaks/Autoindexing in GSAS-II</span></b>”
     1334tutorial and is provided as for this tutorial as file <span class=SpellE><span
    16501335style='font-family:Courier'>start.gpx</span></span>.</p>
    16511336
    1652 <p class=MsoNormal><o:p>&nbsp;</o:p></p>
    1653 
    16541337<h2>Step 2: Select Le Bail fitting</h2>
    16551338
    1656 <p class=MsoNormal><o:p>&nbsp;</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:
     1341minor-latin;mso-bidi-theme-font:minor-latin'>Start Le Bail extraction?</span></b>
     1342button to put the refinement into Le Bail mode. </p>
    16601343
    16611344<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype
    … …  
    16791362 <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
    16801363 <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&#10;&#10;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&#10;&#10;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&#10;&#10;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
     1369src="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
     1372variables 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
     1379src="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
     1382extraction?”.</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;
     1387mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     1388minor-latin'>Calculate/Refine</span></b> menu command. A popup message will
     1389appear informing you that it will do the initial zero cycle LeBail fit of the
     1390intensities. </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
     1397src="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;
     1400mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     1401minor-latin'>Ok</span></b>. The refinement will proceed and yield <span
     1402class=SpellE>Rwp</span> ~34%. The popup has an Ok and Cancel buttons. The plot
     1403has 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
     1410src="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
     1413right places and that some calculated intensity is present under them.
     1414Otherwise you should press Cancel &amp; adjust things as appropriate (e.g.
     1415lattice parameters). </p>
    16891416
    16901417<p class=MsoNormal><o:p>&nbsp;</o:p></p>
    16911418
    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
     1424src="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;
     1427mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     1428minor-latin'>Ok</span></b> to save this &amp; proceed to the 1<sup>st</sup>
     1429full Rietveld/LeBail refinement. The next refinement will include those
     1430parameters you selected for a full Rietveld/LeBail refinement. The initial
     1431residual should be where the initial LeBail fit finished<span style='mso-no-proof:
     1432yes'>. </span>This will run through five cycles of Rietveld/Le Bail fitting and
     1433the 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
     1440src="LeBailSucrose.fld/image028.png" alt="Refinement results, Rw =12.560"
     1441v: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
     1450src="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;
     1453mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     1454minor-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
     1459examining the fit shows issues with background, profile shape and peak
     1460positions.</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
     1467src="LeBailSucrose.fld/image009.png" alt="GSAS-II plots: start.gpx" v:shapes="Picture_x0020_19"><![endif]></span><span
     1468style='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:
     1472minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>w</span></b>
     1473key) and enlarging it (use the crossed-arrows button and drag the right mouse
     1474button upwards inside the lower box), as shown above, shows that further
     1475background 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
     1478style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
     1479Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
     1480</span></span></span><![endif]>Change to use <b><span style='font-family:"Calibri",sans-serif;
     1481mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     1482minor-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
     1485style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
     1486Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
     1487</span></span></span><![endif]>Also refine <b><span style='font-family:"Calibri",sans-serif;
     1488mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     1489minor-latin'>sig</span></b> and <b><span style='font-family:"Calibri",sans-serif;
     1490mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     1491minor-latin'>pos</span></b> for the single background peak. </p>
     1492
     1493<p class=MsoNormal>The peak positions are probably offset from a sample
     1494position error (it is almost always present)</p>
     1495
     1496<p class=MsoListParagraph style='text-indent:-.25in;mso-list:l2 level1 lfo5'><![if !supportLists]><span
     1497style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
     1498Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
     1499</span></span></span><![endif]>Select <b><span style='font-family:"Calibri",sans-serif;
     1500mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     1501minor-latin'>Sample X <span class=SpellE>displ</span></span></b> in Sample
     1502Parameters </p>
     1503
     1504<p class=MsoNormal>The peak shape shows perhaps (in this case) inadequately
     1505determined instrumental U, V &amp; W parameters</p>
     1506
     1507<p class=MsoListParagraph style='text-indent:-.25in;mso-list:l2 level1 lfo5'><![if !supportLists]><span
     1508style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
     1509Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
     1510</span></span></span><![endif]>In Instrument Parameters select <b><span
     1511style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     1512mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>U, V &amp; W</span></b>
     1513for refinement. </p>
    16931514
    16941515<p class=MsoNormal><o:p>&nbsp;</o:p></p>
    16951516
    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"'>&#8984;B).</span></p>
     1517<p class=MsoNormal>Do <b><span style='font-family:"Calibri",sans-serif;
     1518mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     1519minor-latin'>Calculate/Refine</span></b>; there will be a high residual for the
     1520initial steps but will quickly settle down to <span class=SpellE>Rwp</span> ~
     15216.0%</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
     1528src="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
     1531profile that was better than what the provided instrument parameter file
     1532indicated</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
     1539src="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
     1542parameters, the crosses are from the single peak fits done in the peak fitting
     1543tutorial 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
     1548expected based on counting statistics (which would yield a reduced <span
     1549lang=EL style='mso-ansi-language:EL'>&#967;</span><sup>2</sup> value close to 1.)
     1550Looking closely at the data and computed pattern, as shown below for example,
     1551leads 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
     1558src="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
     1561shape broadening options. Moreover, if the intended use of the extracted
     1562structure factors is structure solution, then one wants the best LeBail fit
     1563possible. Investigation of a number of models for anisotropic peak broadening
     1564finds that the <span class=SpellE>R<sub>wp</sub></span> can be reduced to 5.23%,
     1565through 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
     1567class=SpellE>microstrain</span> directional plot, as below. A fit that uses
     1568fewer terms that is almost as good uses uniaxial crystallite domain size
     1569broadening along the 010 axis and uniaxial <span class=SpellE>microstrain</span>
     1570broadening 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
     1572and generalized mustrain models; my final <span class=SpellE>R<sub>wp</sub></span>
     1573after several sets of LeBail/Rietveld refinement was <span class=SpellE>R<sub>wp</sub></span>
     1574= 5.197%.</p>
    17021575
    17031576<p class=MsoNormal><o:p>&nbsp;</o:p></p>
    17041577
     1578<p class=MsoNormal><b><i>The important result here is that this sample exhibit
     1579non-ideal broadening artifacts. This could be due to milling of the sucrose
     1580during manufacture creating defects that cannot be well-fit with a conventional
     1581peak shape. From this fit, it is now clear that best possible fit to be
     1582expected from any structural model will have a <span class=SpellE>R<sub>wp</sub></span>
     1583on the order of 5% and a reduced </i></b><b><i><span lang=EL style='mso-ansi-language:
     1584EL'>&#967;</span><sup>2</sup> value on the order of 1.5, since no crystal
     1585structure model could give a better intensity fit than a Le Bail or Pawley fit.
     1586<o:p></o:p></i></b></p>
     1587
    17051588<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&#10;&#10;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&#10;&#10;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&#10;&#10;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
     1593src="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
     1598with the aim of using then in structure solution can be obtained by
     1599reinitializing the LeBail extraction using the now better parameter set. Go to
     1600the 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
     1607src="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
     1610the LeBail intensities, “cycle” the Le Bail button. Press <b><span
     1611style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     1612mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Stop Le Bail
     1613extraction</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
     1615to include the intensity dependent parameters. Now press it again (<b><span
     1616style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     1617mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Start Le bail
     1618extraction?</span></b>). The window will be redrawn again. The next refinement
     1619will start with new initial structure factor values (=1.0) and will do the
     1620preliminary “zero cycle” Le Bail refinement. You may leave the refinement
     1621parameters alone. The refinement will start out high (Rwp~67%) but will quickly
     1622drop 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
     1629src="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;
     1632mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     1633minor-latin'>OK</span></b> to continue with the Rietveld/LeBail part of the
     1634refinement; 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
     1641src="LeBailSucrose.fld/image021.png" alt="Refinement results, Rw =5.469"
     1642v:shapes="Picture_x0020_27"><![endif]></span></p>
     1643
     1644<p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif;
     1645mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     1646minor-latin'>OK</span></b>. Set the number of cycles to <b><span
     1647style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     1648mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>20</span></b>
     1649and repeat <b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     1650minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Calculate/Refine</span></b>
     1651until the fit has converged (it may take several repeats as this part of a Le
     1652Bail refinement does converge slowly). I got <span class=SpellE>Rwp</span> =
     16535.26% when I quit recycling the refinement. You can now use these extracted
     1654intensities 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>
    17131656
    17141657<p class=MsoNormal><o:p>&nbsp;</o:p></p>
    17151658
    1716 <p class=MsoNormal>This will run through three cycles of Le Bail
    1717 fitting. <B><I>This will only optimize the intensities of reflections. No
    1718 other parameter values will be optimized until Step 5, when a least
    1719 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>&nbsp;</o:p></p>
    1723 
    1724 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1725  id="Picture_x0020_52" o:spid="_x0000_i1032" type="#_x0000_t75" alt="Graphical user interface&#10;&#10;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&#10;&#10;Description automatically generated"/>
    1728 </v:shape><![endif]--><![if !vml]><img border=0 width=576 height=378
    1729 src="LeBailSucrose.fld/image006.png"
    1730 alt="Graphical user interface&#10;&#10;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>&nbsp;</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<span
    1740 class=GramE>/“</span>Le Bail fit” menu command again. The fit improves very
    1741 slightly, as shown below. </p>
    1742 
    1743 <p class=MsoNormal><o:p>&nbsp;</o:p></p>
    1744 
    1745 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1746  id="Picture_x0020_53" o:spid="_x0000_i1031" type="#_x0000_t75" alt="Graphical user interface, timeline&#10;&#10;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&#10;&#10;Description automatically generated"/>
    1749 </v:shape><![endif]--><![if !vml]><img border=0 width=576 height=376
    1750 src="LeBailSucrose.fld/image007.png"
    1751 alt="Graphical user interface, timeline&#10;&#10;Description automatically generated"
    1752 v:shapes="Picture_x0020_53"><![endif]></span></p>
    1753 
    1754 <p class=MsoNormal><o:p>&nbsp;</o:p></p>
    1755 
    1756 <p class=MsoNormal>Since the improvement is so small, there is little value in running
    1757 this again (though there is also no harm in doing this). In other projects, it may
    1758 be necessary to perform this step more than twice before the fit no longer
    1759 improves significantly. Here, any improvement to the fit will require
    1760 refinement of the
    1761 the <span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin'>experimental
    1762 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, refinement
    1770 flags were set for three background terms, the intensity value for a single background
    1771 peak, a sample broadening term and a <span class=SpellE>microstrain</span>
    1772 broadening term plus four lattice parameters (10 parameters in total). This can
    1773 be verified using the Calculate<span class=GramE>/“</span>View LS parameters” menu
    1774 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"'>&#8984;</span><span
    1776 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>&nbsp;</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 that
    1790 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 perform
    1797 a combined Le Bail/Least Squares fit is to use the </span><span
    1798 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/Refine
    1801 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>&nbsp;</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:shape
    1815  id="Picture_x0020_54" o:spid="_x0000_i1030" type="#_x0000_t75" alt="Graphical user interface, application, Word&#10;&#10;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&#10;&#10;Description automatically generated"/>
    1818 </v:shape><![endif]--><![if !vml]><img border=0 width=472 height=235
    1819 src="LeBailSucrose.fld/image008.png"
    1820 alt="Graphical user interface, application, Word&#10;&#10;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>&nbsp;</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 much
    1835 better, though far from perfect, fit is obtained. <o:p></o:p></span></p>
    1836 
    1837 <p class=MsoNormal><o:p>&nbsp;</o:p></p>
    1838 
    1839 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1840  id="Picture_x0020_55" o:spid="_x0000_i1029" type="#_x0000_t75" alt="Graphical user interface, timeline&#10;&#10;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&#10;&#10;Description automatically generated"/>
    1843 </v:shape><![endif]--><![if !vml]><img border=0 width=577 height=376
    1844 src="LeBailSucrose.fld/image009.png"
    1845 alt="Graphical user interface, timeline&#10;&#10;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:shape
    1851  id="Picture_x0020_56" o:spid="_x0000_i1028" type="#_x0000_t75" alt="Chart&#10;&#10;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&#10;&#10;Description automatically generated"/>
    1854 </v:shape><![endif]--><![if !vml]><img border=0 width=634 height=220
    1855 src="LeBailSucrose.fld/image010.png"
    1856 alt="Chart&#10;&#10;Description automatically generated" v:shapes="Picture_x0020_56"><![endif]></span><span
    1857 style='mso-spacerun:yes'> </span></p>
    1858 
    1859 <p class=MsoNormal>Plotting the (<span
    1860 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 button
    1862 upwards inside the lower box), as shown above, shows that further background improvement might
    1863 be expected with more background terms. </p>
    1864 
    1865 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l7 level1 lfo16'><![if !supportLists]><span
    1866 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    1868 </span></span></span><![endif]><span dir=LTR></span>Change to use 6 chebyschev-1
    1869 peaks. </p>
    1870 
    1871 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l7 level1 lfo16'><![if !supportLists]><span
    1872 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    1874 </span></span></span><![endif]><span dir=LTR></span>Also refine sig for the
    1875 single background peak. <o:p></o:p></p>
    1876 
    1877 <p class=MsoNormal><o:p>&nbsp;</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>&nbsp;</o:p></p>
    1882 
    1883 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1884  id="Picture_x0020_57" o:spid="_x0000_i1027" type="#_x0000_t75" alt="Graphical user interface&#10;&#10;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&#10;&#10;Description automatically generated"/>
    1887 </v:shape><![endif]--><![if !vml]><img border=0 width=576 height=375
    1888 src="LeBailSucrose.fld/image011.png"
    1889 alt="Graphical user interface&#10;&#10;Description automatically generated"
    1890 v:shapes="Picture_x0020_57"><![endif]></span></p>
    1891 
    1892 <p class=MsoNormal><o:p>&nbsp;</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 be
    1897 expected based on counting statistics (which would yield a reduced <span
    1898 lang=EL style='mso-ansi-language:EL'>&#967;</span><sup>2</sup> value close to
    1899 1.) Looking closely at the data and computed pattern, as shown below for
    1900 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:shape
    1903  id="Picture_x0020_58" o:spid="_x0000_i1026" type="#_x0000_t75" alt="Graphical user interface&#10;&#10;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&#10;&#10;Description automatically generated"
    1906   croptop="8315f" cropbottom="11209f" cropleft="7261f" cropright="3949f"/>
    1907 </v:shape><![endif]--><![if !vml]><img border=0 width=577 height=335
    1908 src="LeBailSucrose.fld/image013.png"
    1909 alt="Graphical user interface&#10;&#10;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 different
    1913 peak shape broadening options. Investigation of a number of models for
    1914 anisotropic peak broadening finds that the <span class=SpellE>R<sub>wp</sub></span> can be
    1915 reduced just a bit, to 11.9%, through use of the Stephens model for <span
    1916 class=SpellE>microstrain</span> (refining 9 terms in the Generalized <span
    1917 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 added
    1919 to the refinement, this is a fairly minor improvement, which many would
    1920 say is not worthwhile. A fit that uses
    1921 fewer terms and is almost as good uses uniaxial crystallite
    1922 domain size broadening along
    1923 the 001 axis and uniaxial <span class=SpellE>microstrain</span> broadening
    1924 along the 010 axis. This adds 2 only parameters. <o:p></o:p></p>
    1925 
    1926 <p class=MsoNormal><o:p>&nbsp;</o:p></p>
    1927 
    1928 <p class=MsoNormal><b><i>The important result here is that <span class=GramE>this
    1929 sample exhibits</span> non-ideal broadening artifacts. This could be due to
    1930 milling of the sucrose during manufacture creating defects that cannot
    1931 be well-fit with a conventional peak shape. From this fit, it is now
    1932 clear that best possible fit to be expected from any structural
    1933 model will have a <span class=SpellE>R<sub>wp</sub></span> on the order of 12% and a reduced
    1934 </i></b><b><i><span lang=EL style='mso-ansi-language:EL'>&#967;</span><sup>2</sup>
    1935 value on the order of 11.8, since no crystal structure model could
    1936 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:shape
    1939  id="Picture_x0020_59" o:spid="_x0000_i1025" type="#_x0000_t75" alt="Chart, bubble chart&#10;&#10;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&#10;&#10;Description automatically generated"/>
    1942 </v:shape><![endif]--><![if !vml]><img border=0 width=349 height=303
    1943 src="LeBailSucrose.fld/image014.png"
    1944 alt="Chart, bubble chart&#10;&#10;Description automatically generated" v:shapes="Picture_x0020_59"><![endif]></span></p>
    1945 
    1946 <p class=MsoNormal>This completes this exercise.</p>
    1947 
    19481659</div>
    19491660
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