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revise LeBail? tutorial
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1113
1114	<body lang=EN-US link=blue vlink="#954F72" style='tab-interval:.5in;word-wrap:
1115	break-word'>
1116
1117	<div class=WordSection1>
1118
1119	<h1><span style='mso-fareast-font-family:"Times New Roman"'>Le Bail Intensity
1120	Extraction in GSAS-II - Sucrose<o:p></o:p></span></h1>
1121
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>
1131
1132	<h1><span style='mso-fareast-font-family:"Times New Roman"'>Background <o:p></o:p></span></h1>
1133
1134	<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
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>
1148
1149	<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
1150	minor-latin'><o:p> </o:p></span></p>
1151
1152	<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
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>
1188
1189	<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
1190	minor-latin'><o:p> </o:p></span></p>
1191
1192	<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
1193	minor-latin'>Note that when either Pawley or Le Bail intensity extraction are
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>
1200
1201	<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
1202	minor-latin'><o:p> </o:p></span></p>
1203
1204	<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
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>
1213
1214	<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
1215	minor-latin'><o:p> </o:p></span></p>
1216
1217	<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
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
1233	style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin'>
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>
1239
1240	<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
1241	minor-latin'><o:p> </o:p></span></p>
1242
1243	<h1><span style='mso-fareast-font-family:"Times New Roman"'>Prerequisite <o:p></o:p></span></h1>
1244
1245	<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
1249	Peaks/Autoindexing in GSAS-II tutorial, from where the sucrose unit cell was
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>
1253
1254	<h2>Step 1: Setup for fit</h2>
1255
1256	<p class=MsoNormal>From the final project file, after completing the indexing
1257	and creating the phase, make the the following changes:</p>
1258
1259	<p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1260	style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
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
1268	style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
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
1276	style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
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
1287	style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
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
1296	style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
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
1307	style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
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>
1318	term. </p>
1319
1320	<p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1321	style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
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>
1327
1328	<p class=MsoNormal><o:p> </o:p></p>
1329
1330	<p class=MsoNormal>These changes have been applied to a GSAS-II project file
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
1335	style='font-family:Courier'>start.gpx</span></span>.</p>
1336
1337	<h2>Step 2: Select Le Bail fitting</h2>
1338
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>
1343
1344	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype
1345	id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
1346	path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
1347	<v:stroke joinstyle="miter"/>
1348	<v:formulas>
1349	<v:f eqn="if lineDrawn pixelLineWidth 0"/>
1350	<v:f eqn="sum @0 1 0"/>
1351	<v:f eqn="sum 0 0 @1"/>
1352	<v:f eqn="prod @2 1 2"/>
1353	<v:f eqn="prod @3 21600 pixelWidth"/>
1354	<v:f eqn="prod @3 21600 pixelHeight"/>
1355	<v:f eqn="sum @0 0 1"/>
1356	<v:f eqn="prod @6 1 2"/>
1357	<v:f eqn="prod @7 21600 pixelWidth"/>
1358	<v:f eqn="sum @8 21600 0"/>
1359	<v:f eqn="prod @7 21600 pixelHeight"/>
1360	<v:f eqn="sum @10 21600 0"/>
1361	</v:formulas>
1362	<v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
1363	<o:lock v:ext="edit" aspectratio="t"/>
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>
1416
1417	<p class=MsoNormal><o:p> </o:p></p>
1418
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>
1514
1515	<p class=MsoNormal><o:p> </o:p></p>
1516
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>
1575
1576	<p class=MsoNormal><o:p> </o:p></p>
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
1588	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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>
1656
1657	<p class=MsoNormal><o:p> </o:p></p>
1658
1659	</div>
1660
1661	</body>
1662
1663	</html>

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