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source: Tutorials/TOF Calibration/Calibration of a TOF powder diffractometer.htm @ 1726

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fix mimetype on a new tutorial
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1128
1129	<div class=WordSection1>
1130
1131	<p class=MsoNormal><span class=Heading1Char><span style='font-size:24.0pt'>Calibration
1132	of a TOF powder diffractometer</span></span><b><span style='font-size:14.0pt;
1133	color:#365F91;mso-themecolor:accent1;mso-themeshade:191'><o:p></o:p></span></b></p>
1134
1135	<p class=MsoNormal>In this tutorial, data collected on the SNS instrument
1136	POWGEN, are used. The calibration process will use the fitted positions of all
1137	visible peaks in a pattern of NIST SRM 660b La<sup>10</sup>B<sub>6</sub> (a=4.15689Å)
1138	obtained in a multiple single peak fit. The positions will be compared to those
1139	expected from the known lattice parameters to establish the diffractometer
1140	constants (<span class=SpellE>difC</span>, <span class=SpellE>difA</span>, <span
1141	class=SpellE>difB</span> and Zero) used for calculating TOF peak positions from
1142	d-<span class=SpellE>spacings</span>. For the second part of this tutorial, the
1143	suite of peaks will be extended to include every visible peak in the pattern
1144	and the peak fitting will include the various profile coefficients thus fully
1145	describing the instrument contribution to the peak profiles. Note that menu
1146	entries and user input are shown in bold face below as <b style='mso-bidi-font-weight:
1147	normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1148	minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;
1149	mso-bidi-theme-font:minor-latin'>Help/About GSAS-II</span></b>, which lists
1150	first the name of the menu (here <b style='mso-bidi-font-weight:normal'><span
1151	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1152	mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
1153	minor-latin'>Help</span></b>) and second the name of the entry in the menu
1154	(here <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1155	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:
1156	Calibri;mso-bidi-theme-font:minor-latin'>About GSAS-II</span></b>).</p>
1157
1158	<p class=MsoNormal>If you have not done so already, <u><span style='color:#0070C0'><a
1159	href="Starting%20GSAS.htm"><span style='color:windowtext;text-decoration:none;
1160	text-underline:none'>start GSAS-II</span></a></span></u>.</p>
1161
1162	<h1>Part I. Determine the diffractometer constants</h1>
1163
1164	<h2>Step 1: Read in the data file</h2>
1165
1166	<p class=MsoNormal><span style='mso-spacerun:yes'> </span>Use the <b
1167	style='mso-bidi-font-weight:normal'>Import/Powder data/from GSAS powder data
1168	file</b> menu item to read the data file into the current GSAS-II project. </p>
1169
1170	<p class=MsoNormal><span style='mso-spacerun:yes'> </span></p>
1171
1172	<p class=MsoNormal>A file selection dialog will be shown; its appearance will
1173	depend on your OS. Change the search directory to <b style='mso-bidi-font-weight:
1174	normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1175	minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;
1176	mso-bidi-theme-font:minor-latin'>/Exercises/TOF Powder Calibration</span></b>
1177	and then select the file </p>
1178
1179	<p class=MsoNormal><b style='mso-bidi-font-weight:normal'><span
1180	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1181	mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
1182	minor-latin'>PG3_17541.gsa</span></b> and press <b style='mso-bidi-font-weight:
1183	normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1184	minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;
1185	mso-bidi-theme-font:minor-latin'>Open</span></b>.<span style='mso-no-proof:
1186	yes'> A window will appear </span><b style='mso-bidi-font-weight:normal'><span
1187	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1188	mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>Is this the file you want?</span></b><span
1189	style='mso-no-proof:yes'>. Press Yes.<o:p></o:p></span></p>
1190
1191	<p class=MsoNormal><span style='mso-no-proof:yes'>The file selection dialog
1192	will reappear; select the </span><b style='mso-bidi-font-weight:normal'><span
1193	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1194	mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>PGHR_60-2015A.prm</span></b><span
1195	style='mso-no-proof:yes'> file. It contains the POWGEN instrument parameters
1196	provided along with the data; this file is in the old GSAS iparm file format
1197	and does not include all the instrument parameters used by GSAS-II. This is
1198	what we will be improving in this tutorial.<o:p></o:p></span></p>
1199
1200	<p class=MsoNormal><span style='mso-no-proof:yes'><o:p> </o:p></span></p>
1201
1202	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype
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1229
1230	<p class=MsoNormal>At this point the data tree window will have several entries
1231	and the powder pattern will appear. Although it is not necessary in this case,
1232	you may wish to change the limits (green & red vertical dashed lines). If
1233	so select the <b style='mso-bidi-font-weight:normal'><span style='font-family:
1234	"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1235	minor-latin'>Limits</span></b> item in the GSASII Data tree under <b
1236	style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1237	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>PWDR
1238	PG3_17541.gsa Bank 1</span></b> and set them as appropriate (usually due to
1239	unusable data at the ends of the pattern).</p>
1240
1241	<p class=MsoNormal><b style='mso-bidi-font-weight:normal'><span
1242	style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_16"
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1244	visibility:visible;mso-wrap-style:square'>
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1246	o:title=""/>
1247	</v:shape><![endif]--><![if !vml]><img border=0 width=625 height=536
1248	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image003.png"
1249	v:shapes="Picture_x0020_16"><![endif]></span></b><span
1250	style='mso-spacerun:yes'> </span><b style='mso-bidi-font-weight:normal'><o:p></o:p></b></p>
1251
1252	<h2><span style='mso-spacerun:yes'> </span>Step 2: Select peaks</h2>
1253
1254	<p class=MsoNormal>Under the <b style='mso-bidi-font-weight:normal'><span
1255	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1256	mso-hansi-theme-font:minor-latin'>PWDR PG3_17541.gsa Bank 1 </span></b>GSASII
1257	Data tree item find the <b style='mso-bidi-font-weight:normal'><span
1258	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1259	mso-hansi-theme-font:minor-latin'>Peak List</span></b> entry; it will be empty.
1260	Select the menu item <b style='mso-bidi-font-weight:normal'><span
1261	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1262	mso-hansi-theme-font:minor-latin'>Peak Fitting/Auto search</span></b> to
1263	populate the <b style='mso-bidi-font-weight:normal'><span style='font-family:
1264	"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1265	minor-latin'>Peak List</span></b>. This will select almost every peak in the
1266	pattern (I got 66 peaks).</p>
1267
1268	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1269	id="Picture_x0020_17" o:spid="_x0000_i1055" type="#_x0000_t75" style='width:466.5pt;
1270	height:399.75pt;visibility:visible;mso-wrap-style:square'>
1271	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image004.png"
1272	o:title=""/>
1273	</v:shape><![endif]--><![if !vml]><img border=0 width=622 height=533
1274	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image005.png"
1275	v:shapes="Picture_x0020_17"><![endif]></span></p>
1276
1277	<p class=MsoNormal>However, it can fail by selecting a peak multiple times if
1278	the data is too noisy. You should check through the list and eliminate any
1279	close duplicates (in this instance there didnt appear to be any). A peak can
1280	be eliminated by placing the cursor on the vertical blue line and pressing the
1281	right mouse button; the line should vanish and the entry in the table deleted.
1282	Notice that the position for the highest TOF peak is misplaced. You can shift
1283	it by placing the cursor on the blue line and with the left mouse button down,
1284	drag the line to match the peak top (zooming in before can help). If you want
1285	you can add more of the unpicked lines to the list (I didnt). To do this
1286	(zooming in helps) place the cursor on a data point at the top of a peak and
1287	press the left mouse button. It is easiest to proceed from right to left so the
1288	tool tip stays out of the way as you work. For any of these operations the zoom
1289	buttons at the bottom left of the plot window must be turned off (NB: one is
1290	turned on in the above plot).</p>
1291
1292	<h2>Step 3: Fit peaks</h2>
1293
1294	<p class=MsoNormal>To do the initial fit to the peaks, select the <b
1295	style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1296	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Peak Fitting/<span
1297	class=SpellE>Peakfit</span></span></b> menu item in the <b style='mso-bidi-font-weight:
1298	normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1299	minor-latin;mso-hansi-theme-font:minor-latin'>Peak List</span></b> data window.
1300	GSAS-II will ask for a project name before continuing, enter a name (I chose <b
1301	style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1302	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>calibrate</span></b>).
1303	The project file (<span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1304	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1305	mso-hansi-theme-font:minor-latin'>calibrate.gpx</span></b></span>) will be
1306	written into your local directory selected in the File Dialog; then the refinement
1307	will proceed. The resulting plot will look like (I keyed <b style='mso-bidi-font-weight:
1308	normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1309	minor-latin;mso-hansi-theme-font:minor-latin'>s</span></b> and <b
1310	style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1311	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>q</span></b>
1312	on the plot to get a <span class=SpellE>sqrt</span>(I) vs q plot which spread
1313	out the peaks a bit better than a I vs TOF plot).</p>
1314
1315	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1316	id="_x0000_i1054" type="#_x0000_t75" style='width:525pt;height:450pt;
1317	visibility:visible;mso-wrap-style:square'>
1318	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image006.png"
1319	o:title=""/>
1320	</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
1321	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image006.png"
1322	v:shapes="_x0000_i1054"><![endif]></span></p>
1323
1324	<p class=MsoNormal>The fit to the background can be improved by adding more
1325	terms; I set the number of <span class=SpellE>chebyschev</span> terms to <b
1326	style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1327	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>6</span></b>.
1328	The peak positions should also be refined; to set them go back to the <b
1329	style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1330	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Peak List</span></b>
1331	data window, select one of the items under the 1<sup>st</sup> <b
1332	style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1333	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>refine</span></b>
1334	column, select the <b style='mso-bidi-font-weight:normal'><span
1335	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1336	mso-hansi-theme-font:minor-latin'>refine</span></b> box (the column will turn
1337	blue), then press <b style='mso-bidi-font-weight:normal'><span
1338	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1339	mso-hansi-theme-font:minor-latin'>y</span></b>. All the position refine boxes
1340	will be checked. Then repeat the <b style='mso-bidi-font-weight:normal'><span
1341	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1342	mso-hansi-theme-font:minor-latin'>Peak Fitting/<span class=SpellE>Peakfit</span></span></b>
1343	menu item; a new plot will appear with a better fit.</p>
1344
1345	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1346	id="_x0000_i1053" type="#_x0000_t75" style='width:525pt;height:450pt;
1347	visibility:visible;mso-wrap-style:square'>
1348	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image007.png"
1349	o:title=""/>
1350	</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
1351	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image007.png"
1352	v:shapes="_x0000_i1053"><![endif]></span></p>
1353
1354	<h2>Step 4: Setup for calibration</h2>
1355
1356	<p class=MsoNormal>Now that we have a reasonably well fit set of peak
1357	positions, we next need to index them with respect to the lattice parameters of
1358	the standard. Select the <b style='mso-bidi-font-weight:normal'><span
1359	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1360	mso-hansi-theme-font:minor-latin'>Index Peak List</span></b> entry in the
1361	GSAS-II Data tree, an empty data window will appear. Populate it by selecting <b
1362	style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1363	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Operations/Load/Reload</span></b>
1364	menu item. The data table will show the positions & intensities along with
1365	000 for <span class=SpellE>hkl</span> for each one.</p>
1366
1367	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1368	id="_x0000_i1052" type="#_x0000_t75" style='width:367.5pt;height:225pt;
1369	visibility:visible;mso-wrap-style:square'>
1370	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image008.png"
1371	o:title=""/>
1372	</v:shape><![endif]--><![if !vml]><img border=0 width=490 height=300
1373	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image008.png"
1374	v:shapes="_x0000_i1052"><![endif]></span></p>
1375
1376	<p class=MsoNormal>Next, select the <b style='mso-bidi-font-weight:normal'><span
1377	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1378	mso-hansi-theme-font:minor-latin'>Unit Cells List</span></b> from the GSAS-II
1379	Data tree. A new window will appear. Change <span class=SpellE>Bravais</span>
1380	lattice to <b style='mso-bidi-font-weight:normal'><span style='font-family:
1381	"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1382	minor-latin'>Pm3m</span></b>, select <b style='mso-bidi-font-weight:normal'><span
1383	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1384	mso-hansi-theme-font:minor-latin'>P m 3 m</span></b> for the Space group and
1385	enter the lattice parameter (<b style='mso-bidi-font-weight:normal'><span
1386	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1387	mso-hansi-theme-font:minor-latin'>4.15689</span></b>) in the <b
1388	style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1389	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Unit cell: a
1390	=</span></b> box (Press <b style='mso-bidi-font-weight:normal'><span
1391	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1392	mso-hansi-theme-font:minor-latin'>Enter</span></b> to set the value). The
1393	window should look like</p>
1394
1395	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1396	id="_x0000_i1051" type="#_x0000_t75" style='width:546pt;height:184.5pt;
1397	visibility:visible;mso-wrap-style:square'>
1398	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image009.png"
1399	o:title=""/>
1400	</v:shape><![endif]--><![if !vml]><img border=0 width=728 height=246
1401	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image009.png"
1402	v:shapes="_x0000_i1051"><![endif]></span></p>
1403
1404	<p class=MsoNormal>Press the <b style='mso-bidi-font-weight:normal'><span
1405	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1406	mso-hansi-theme-font:minor-latin'>Show <span class=SpellE>hkl</span> positions</span></b>
1407	button, the plot should show a suite of red dashed vertical lines giving all
1408	the allowed reflection positions which should closely match the blue peak position
1409	lines.</p>
1410
1411	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1412	id="Picture_x0020_23" o:spid="_x0000_i1050" type="#_x0000_t75" style='width:560.25pt;
1413	height:450pt;visibility:visible;mso-wrap-style:square'>
1414	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image010.png"
1415	o:title=""/>
1416	</v:shape><![endif]--><![if !vml]><img border=0 width=747 height=600
1417	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image010.png"
1418	v:shapes="Picture_x0020_23"><![endif]></span></p>
1419
1420	<p class=MsoNormal>The Index Peak List window now shows <span class=SpellE>hkl</span>
1421	values for each entry</p>
1422
1423	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1424	id="Picture_x0020_24" o:spid="_x0000_i1049" type="#_x0000_t75" style='width:367.5pt;
1425	height:225pt;visibility:visible;mso-wrap-style:square'>
1426	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image011.png"
1427	o:title=""/>
1428	</v:shape><![endif]--><![if !vml]><img border=0 width=490 height=300
1429	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image011.png"
1430	v:shapes="Picture_x0020_24"><![endif]></span></p>
1431
1432	<p class=MsoNormal>The calibration set up is now complete.</p>
1433
1434	<h2>Step 5: Calibration of diffractometer constants</h2>
1435
1436	<p class=MsoNormal>As we now have a set of reflection positions each properly
1437	indexed so that the d-<span class=SpellE>spacings</span> are known, we can now
1438	determine the diffractometer coefficients (C, A, B and Z) that give TOF from
1439	d-spacing according to</p>
1440
1441	<p class=MsoNormal><o:p> </o:p></p>
1442
1443	<p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
1444	m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
1445	style='font-family:"Cambria Math",serif'><m:r>TOF</m:r><m:r>=</m:r><m:r>Cd</m:r><m:r>+</m:r><m:r>A</m:r></span></i><m:sSup><m:sSupPr><span
1446	style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1447	mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1448	normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
1449	normal'><span style='font-family:"Cambria Math",serif'><m:r>d</m:r></span></i></m:e><m:sup><i
1450	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup><i
1451	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>+</m:r></span></i><m:f><m:fPr><m:type
1452	m:val="skw"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1453	"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1454	mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
1455	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>B</m:r></span></i></m:num><m:den><i
1456	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>d</m:r></span></i></m:den></m:f><i
1457	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>+</m:r><m:r>Z</m:r></span></i></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span
1458	style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1459	"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
1460	mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
1461	id="_x0000_i1025" type="#_x0000_t75" style='width:2in;height:18.75pt'>
1462	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image022.png"
1463	o:title="" chromakey="white"/>
1464	</v:shape><![endif]--><![if !vml]><img width=192 height=25
1465	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image018.png"
1466	v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
1467
1468	<p class=MsoNormal><o:p> </o:p></p>
1469
1470	<p class=MsoNormal>Select <b style='mso-bidi-font-weight:normal'><span
1471	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1472	mso-hansi-theme-font:minor-latin'>Instrument Parameters</span></b> from the
1473	GSAS-II Data tree. The data window will show</p>
1474
1475	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1476	id="_x0000_i1048" type="#_x0000_t75" style='width:411pt;height:220.5pt;
1477	visibility:visible;mso-wrap-style:square'>
1478	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image014.png"
1479	o:title=""/>
1480	</v:shape><![endif]--><![if !vml]><img border=0 width=548 height=294
1481	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image014.png"
1482	v:shapes="_x0000_i1048"><![endif]></span></p>
1483
1484	<p class=MsoNormal>And the plot will show the corresponding function curves </p>
1485
1486	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1487	id="Picture_x0020_26" o:spid="_x0000_i1047" type="#_x0000_t75" style='width:560.25pt;
1488	height:450pt;visibility:visible;mso-wrap-style:square'>
1489	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image015.png"
1490	o:title=""/>
1491	</v:shape><![endif]--><![if !vml]><img border=0 width=747 height=600
1492	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image015.png"
1493	v:shapes="Picture_x0020_26"><![endif]></span></p>
1494
1495	<p class=MsoNormal>Although a previous calibration gave values for <span
1496	class=SpellE>difA</span> and Zero, we will start fresh; set them both to zero.
1497	Select the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1498	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1499	mso-hansi-theme-font:minor-latin'>difC</span></b></span><b style='mso-bidi-font-weight:
1500	normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1501	minor-latin;mso-hansi-theme-font:minor-latin'> <span class=GramE>Refine</span></span></b>?
1502	<span class=GramE>box</span> and do <b style='mso-bidi-font-weight:normal'><span
1503	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1504	mso-hansi-theme-font:minor-latin'>Operations/Calibrate</span></b>; the plot
1505	will show the result of the calibration</p>
1506
1507	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1508	id="_x0000_i1046" type="#_x0000_t75" style='width:560.25pt;height:450pt;
1509	visibility:visible;mso-wrap-style:square'>
1510	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image016.png"
1511	o:title=""/>
1512	</v:shape><![endif]--><![if !vml]><img border=0 width=747 height=600
1513	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image016.png"
1514	v:shapes="_x0000_i1046"><![endif]></span></p>
1515
1516	<p class=MsoNormal>It is obvious we have one very bad data point at a short
1517	d-spacing. Use the mouse cursor to determine its position (<b style='mso-bidi-font-weight:
1518	normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1519	minor-latin;mso-hansi-theme-font:minor-latin'>7205.47</span></b>) so we can
1520	find it in the <b style='mso-bidi-font-weight:normal'><span style='font-family:
1521	"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1522	minor-latin'>Index Peak List</span></b>. Select that data item from the tree.
1523	The bad point is at the bottom of the table; uncheck the <span class=SpellE><b
1524	style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1525	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>use</span></b></span>
1526	box for it. Go back to <b style='mso-bidi-font-weight:normal'><span
1527	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1528	mso-hansi-theme-font:minor-latin'>Instrument Parameters</span></b> and repeat <b
1529	style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1530	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Operations/Calibrate</span></b>;
1531	the plot will look a lot better.</p>
1532
1533	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1534	id="_x0000_i1045" type="#_x0000_t75" style='width:560.25pt;height:450pt;
1535	visibility:visible;mso-wrap-style:square'>
1536	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image017.png"
1537	o:title=""/>
1538	</v:shape><![endif]--><![if !vml]><img border=0 width=747 height=600
1539	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image017.png"
1540	v:shapes="_x0000_i1045"><![endif]></span></p>
1541
1542	<p class=MsoNormal>What is shown is the discrepancy between observed and
1543	calculated position divided by the position (ΔT/T) vs d-spacing. The error
1544	bars reflect the uncertainty in the fitted peak positions. The red dashed line
1545	is obviously zero discrepancy and the blue dashed lines represent the width of
1546	a data bin above and below zero (e.g. 2 bins from one blue line to the other)
1547	to give you a sense of how significant the discrepancies are. One can improve
1548	the fit by including the <span class=SpellE><b style='mso-bidi-font-weight:
1549	normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1550	minor-latin;mso-hansi-theme-font:minor-latin'>difA</span></b></span> parameter;
1551	select it and repeat <b style='mso-bidi-font-weight:normal'><span
1552	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1553	mso-hansi-theme-font:minor-latin'>Operations/Calibrate</span></b>. The fit is
1554	much improved.</p>
1555
1556	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1557	id="Picture_x0020_35" o:spid="_x0000_i1044" type="#_x0000_t75" style='width:525pt;
1558	height:450pt;visibility:visible;mso-wrap-style:square'>
1559	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image024.png"
1560	o:title=""/>
1561	</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
1562	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image024.png"
1563	v:shapes="Picture_x0020_35"><![endif]></span></p>
1564
1565	<p class=MsoNormal>One might get some improvement by refining Zero. I got the f<span
1566	style='mso-no-proof:yes'>ollowing new parameters<o:p></o:p></span></p>
1567
1568	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1569	id="Picture_x0020_36" o:spid="_x0000_i1043" type="#_x0000_t75" style='width:411pt;
1570	height:203.25pt;visibility:visible;mso-wrap-style:square'>
1571	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image025.png"
1572	o:title=""/>
1573	</v:shape><![endif]--><![if !vml]><img border=0 width=548 height=271
1574	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image025.png"
1575	v:shapes="Picture_x0020_36"><![endif]></span></p>
1576
1577	<p class=MsoNormal>The fitted values are clearly within one half TOF bin of
1578	zero.</p>
1579
1580	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1581	id="Picture_x0020_33" o:spid="_x0000_i1042" type="#_x0000_t75" style='width:525pt;
1582	height:450pt;visibility:visible;mso-wrap-style:square'>
1583	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image026.png"
1584	o:title=""/>
1585	</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
1586	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image026.png"
1587	v:shapes="Picture_x0020_33"><![endif]></span></p>
1588
1589	<p class=MsoNormal>As these values have now been established, uncheck all their
1590	refinement boxes. These new instrument parameters can be saved for later use;
1591	select <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1592	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Operations/Save
1593	profile</span></b> from the menu. A file name is requested (no extension);
1594	this file can be used in place of the old GSAS instrument parameter file when
1595	reading new data for this instrument. This ends the first part of this tutorial
1596	exercise; you may save the project if you wish, select <b style='mso-bidi-font-weight:
1597	normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1598	minor-latin;mso-hansi-theme-font:minor-latin'>File/Save project</span></b> from
1599	the GSAS-II data tree window. Notice that we did not establish values for the
1600	instrument profile coefficients (alpha, beta & sig terms). These will be
1601	established in the second part of the tutorial.</p>
1602
1603	<h1>Part II. Determine the instrument profile coefficients</h1>
1604
1605	<p class=MsoNormal>To best establish the profile coefficients one must have the
1606	best model for the fitting. In this case we will change the background function
1607	to something more flexible than the 6 term <span class=SpellE>chebyschev</span>
1608	function used above and add all visible peaks beyond those found by the
1609	automatic procedure used above.</p>
1610
1611	<h2>Step 1. Change background</h2>
1612
1613	<p class=MsoNormal>Select the <b style='mso-bidi-font-weight:normal'><span
1614	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1615	mso-hansi-theme-font:minor-latin'>Background</span></b> tree item; you should
1616	see</p>
1617
1618	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1619	id="Picture_x0020_18" o:spid="_x0000_i1041" type="#_x0000_t75" style='width:402pt;
1620	height:160.5pt;visibility:visible;mso-wrap-style:square'>
1621	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image027.png"
1622	o:title=""/>
1623	</v:shape><![endif]--><![if !vml]><img border=0 width=536 height=214
1624	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image027.png"
1625	v:shapes="Picture_x0020_18"><![endif]></span></p>
1626
1627	<p class=MsoNormal>From the <b style='mso-bidi-font-weight:normal'><span
1628	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1629	mso-hansi-theme-font:minor-latin'>Background function</span></b> pulldown,
1630	select <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1631	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>log
1632	interpolate</span></b> and set the <b style='mso-bidi-font-weight:normal'><span
1633	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1634	mso-hansi-theme-font:minor-latin'>No. <span class=SpellE>coeff</span>.</span></b>
1635	<span class=GramE>to</span> <b style='mso-bidi-font-weight:normal'><span
1636	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1637	mso-hansi-theme-font:minor-latin'>10</span></b>. This will select 10 fixed
1638	position points across the pattern between the limits located in constant <span
1639	class=GramE>log(</span>TOF) steps; this puts more points at the short TOF end
1640	of the pattern where the background is changing most rapidly. Return to <b
1641	style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1642	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Peak List</span></b>
1643	and do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1644	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Peak
1645	Fitting/<span class=SpellE>Peakfit</span></span></b>; this should give a better
1646	fit to the background.</p>
1647
1648	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1649	id="Picture_x0020_19" o:spid="_x0000_i1040" type="#_x0000_t75" style='width:525pt;
1650	height:450pt;visibility:visible;mso-wrap-style:square'>
1651	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image028.png"
1652	o:title=""/>
1653	</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
1654	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image028.png"
1655	v:shapes="Picture_x0020_19"><![endif]></span></p>
1656
1657	<h2>Step 2. Add more peaks to be fitted</h2>
1658
1659	<p class=MsoNormal>Now zoom in on the right hand end of the pattern and select
1660	every unmarked peak you can see. Be sure the zoom button is off and you can use
1661	the < > buttons to shift the pattern left or right. It is essential to
1662	include as many peaks as possible because including them forces the background
1663	to its true level and thus giving each peak its true shape. The high Q end of
1664	my pattern looked like</p>
1665
1666	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1667	id="Picture_x0020_20" o:spid="_x0000_i1039" type="#_x0000_t75" style='width:525pt;
1668	height:450pt;visibility:visible;mso-wrap-style:square'>
1669	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image029.png"
1670	o:title=""/>
1671	</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
1672	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image029.png"
1673	v:shapes="Picture_x0020_20"><![endif]></span></p>
1674
1675	<p class=MsoNormal>When I was done; I had 128 peaks. Do <b style='mso-bidi-font-weight:
1676	normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1677	minor-latin;mso-hansi-theme-font:minor-latin'>Peak fitting/<span class=SpellE>Peakfit</span></span></b>;
1678	all peaks should fit in a few seconds and the background line should drop a bit.</p>
1679
1680	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1681	id="Picture_x0020_21" o:spid="_x0000_i1038" type="#_x0000_t75" style='width:525pt;
1682	height:450pt;visibility:visible;mso-wrap-style:square'>
1683	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image030.png"
1684	o:title=""/>
1685	</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
1686	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image030.png"
1687	v:shapes="Picture_x0020_21"><![endif]></span></p>
1688
1689	<p class=MsoNormal>Ive dragged the difference curve up so you can see it.
1690	Notice that it is mostly from position errors; so set the refine boxes for
1691	position (<span class=SpellE>i.e</span> pick a box, pick the <b
1692	style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1693	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>refine</span></b>
1694	column heading & press <b style='mso-bidi-font-weight:normal'><span
1695	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1696	mso-hansi-theme-font:minor-latin'>y</span></b>). Repeat <b style='mso-bidi-font-weight:
1697	normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1698	minor-latin;mso-hansi-theme-font:minor-latin'>Peak Fitting/<span class=SpellE>Peakfit</span></span></b>;
1699	the fit will improve. On the console listing before the peak listing the
1700	residuals are shown; <span class=SpellE>Rwp</span> ~10.0%</p>
1701
1702	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1703	id="Picture_x0020_22" o:spid="_x0000_i1037" type="#_x0000_t75" style='width:525pt;
1704	height:450pt;visibility:visible;mso-wrap-style:square'>
1705	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image031.png"
1706	o:title=""/>
1707	</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
1708	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image031.png"
1709	v:shapes="Picture_x0020_22"><![endif]></span></p>
1710
1711	<p class=MsoNormal>You might want to save the project at this point; do <b
1712	style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1713	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>File/Save
1714	project</span></b> from the main GSAS-II data tree window.</p>
1715
1716	<h2>Step 3. Refine profile coefficients</h2>
1717
1718	<p class=MsoNormal>In this step you will be selecting some profile coefficients
1719	(alpha to sig-q) for refinement, doing peak fits and hopefully improving the
1720	fit to the profile. Occasionally the refinement will diverge or fail; use the <b
1721	style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1722	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Peak
1723	fitting/Undo</span></b> command immediately to recover. The Background,
1724	Instrument Parameters and Peak List values will all be restored. Select <b
1725	style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1726	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Instrument
1727	Parameters</span></b> from the GSAS-II data tree; the data window will show</p>
1728
1729	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1730	id="Picture_x0020_37" o:spid="_x0000_i1036" type="#_x0000_t75" style='width:411pt;
1731	height:203.25pt;visibility:visible;mso-wrap-style:square'>
1732	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image032.png"
1733	o:title=""/>
1734	</v:shape><![endif]--><![if !vml]><img border=0 width=548 height=271
1735	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image032.png"
1736	v:shapes="Picture_x0020_37"><![endif]></span></p>
1737
1738	<p class=MsoNormal>You should realize that alpha largely affects the sharpness
1739	of the leading TOF edge of each peak; larger values mean sharper front edges.
1740	Beta terms affect the trailing TOF edge in the same way. Sig terms affect the
1741	Gaussian shape component of the peak profiles; larger values result in broader
1742	peaks. The coefficients describe the alpha, beta and sig values as follows:</p>
1743
1744	<p class=MsoNormal><!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:
1745	normal'><span style='font-family:"Cambria Math",serif'><m:r>α</m:r><m:r>=</m:r></span></i><m:f><m:fPr><m:type
1746	m:val="skw"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1747	"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1748	mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSub><m:sSubPr><span
1749	style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1750	mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1751	normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i style='mso-bidi-font-style:
1752	normal'><span style='font-family:"Cambria Math",serif'><m:r>α</m:r></span></i></m:e><m:sub><i
1753	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:sub></m:sSub></m:num><m:den><i
1754	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>d</m:r></span></i></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span
1755	style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1756	"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1757	top:6.0pt;mso-text-raise:-6.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1758	EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1759	type="#_x0000_t75" style='width:48pt;height:19.5pt'>
1760	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image033.png"
1761	o:title="" chromakey="white"/>
1762	</v:shape><![endif]--><![if !vml]><img width=64 height=26
1763	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image019.png"
1764	v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
1765	style='mso-spacerun:yes'> </span><span style='mso-spacerun:yes'> </span><!--[if gte msEquation 12]><m:oMath><i
1766	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>β</m:r><m:r>=</m:r></span></i><m:sSub><m:sSubPr><span
1767	style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1768	mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1769	normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i style='mso-bidi-font-style:
1770	normal'><span style='font-family:"Cambria Math",serif'><m:r>β</m:r></span></i></m:e><m:sub><i
1771	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:sub></m:sSub><i
1772	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>+</m:r></span></i><m:f><m:fPr><m:type
1773	m:val="skw"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1774	"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1775	mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSub><m:sSubPr><span
1776	style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1777	mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1778	normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i style='mso-bidi-font-style:
1779	normal'><span style='font-family:"Cambria Math",serif'><m:r>β</m:r></span></i></m:e><m:sub><i
1780	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:sub></m:sSub></m:num><m:den><m:sSup><m:sSupPr><span
1781	style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1782	mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1783	normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
1784	normal'><span style='font-family:"Cambria Math",serif'><m:r>d</m:r></span></i></m:e><m:sup><i
1785	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>4</m:r></span></i></m:sup></m:sSup></m:den></m:f><i
1786	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>+</m:r></span></i><m:f><m:fPr><m:type
1787	m:val="skw"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1788	"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1789	mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSub><m:sSubPr><span
1790	style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1791	mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1792	normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i style='mso-bidi-font-style:
1793	normal'><span style='font-family:"Cambria Math",serif'><m:r>β</m:r></span></i></m:e><m:sub><i
1794	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>q</m:r></span></i></m:sub></m:sSub></m:num><m:den><m:sSup><m:sSupPr><span
1795	style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1796	mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1797	normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
1798	normal'><span style='font-family:"Cambria Math",serif'><m:r>d</m:r></span></i></m:e><m:sup><i
1799	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span
1800	style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1801	"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1802	top:7.0pt;mso-text-raise:-7.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1803	EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1804	type="#_x0000_t75" style='width:123pt;height:24pt'>
1805	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image035.png"
1806	o:title="" chromakey="white"/>
1807	</v:shape><![endif]--><![if !vml]><img width=164 height=32
1808	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image020.png"
1809	v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
1810	style='mso-spacerun:yes'> </span><!--[if gte msEquation 12]><m:oMath><m:sSup><m:sSupPr><span
1811	style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1812	mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1813	normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
1814	normal'><span style='font-family:"Cambria Math",serif'><m:r><span
1815	style='mso-spacerun:yes'> </span></m:r><m:r>σ</m:r></span></i></m:e><m:sup><i
1816	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup><i
1817	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:sSubSup><m:sSubSupPr><span
1818	style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1819	mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1820	normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1821	normal'><span style='font-family:"Cambria Math",serif'><m:r>σ</m:r></span></i></m:e><m:sub><i
1822	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:sub><m:sup><i
1823	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSubSup><i
1824	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>+</m:r></span></i><m:sSubSup><m:sSubSupPr><span
1825	style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1826	mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1827	normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1828	normal'><span style='font-family:"Cambria Math",serif'><m:r>σ</m:r></span></i></m:e><m:sub><i
1829	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:sub><m:sup><i
1830	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSubSup><m:sSup><m:sSupPr><span
1831	style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1832	mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1833	normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
1834	normal'><span style='font-family:"Cambria Math",serif'><m:r>d</m:r></span></i></m:e><m:sup><i
1835	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup><i
1836	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>+</m:r></span></i><m:sSubSup><m:sSubSupPr><span
1837	style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1838	mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1839	normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1840	normal'><span style='font-family:"Cambria Math",serif'><m:r>σ</m:r></span></i></m:e><m:sub><i
1841	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sub><m:sup><i
1842	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSubSup><m:sSup><m:sSupPr><span
1843	style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1844	mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1845	normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
1846	normal'><span style='font-family:"Cambria Math",serif'><m:r>d</m:r></span></i></m:e><m:sup><i
1847	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>4</m:r></span></i></m:sup></m:sSup><i
1848	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>+</m:r></span></i><m:f><m:fPr><m:type
1849	m:val="skw"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1850	"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1851	mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSubSup><m:sSubSupPr><span
1852	style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1853	mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1854	normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
1855	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>σ</m:r></span></i></m:e><m:sub><i
1856	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>q</m:r></span></i></m:sub><m:sup><i
1857	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSubSup></m:num><m:den><m:sSup><m:sSupPr><span
1858	style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1859	mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1860	normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
1861	normal'><span style='font-family:"Cambria Math",serif'><m:r>d</m:r></span></i></m:e><m:sup><i
1862	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span
1863	style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1864	"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1865	top:7.0pt;mso-text-raise:-7.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1866	EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1867	type="#_x0000_t75" style='width:183pt;height:25.5pt'>
1868	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image037.png"
1869	o:title="" chromakey="white"/>
1870	</v:shape><![endif]--><![if !vml]><img width=244 height=34
1871	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image021.png"
1872	v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
1873
1874	<p class=MsoNormal><o:p> </o:p></p>
1875
1876	<p class=MsoNormal>The refinable coefficients are: alpha (α<sub>0</sub>), beta-0
1877	(<!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span style='font-family:
1878	"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:
1879	"Cambria Math";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i
1880	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>β</m:r></span></i></m:e><m:sub><i
1881	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:sub></m:sSub></m:oMath><![endif]--><![if !msEquation]><span
1882	style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1883	"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1884	top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1885	EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1886	type="#_x0000_t75" style='width:12pt;height:14.25pt'>
1887	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image039.png"
1888	o:title="" chromakey="white"/>
1889	</v:shape><![endif]--><![if !vml]><img width=16 height=19
1890	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image064.png"
1891	v:shapes="_x0000_i1025"><![endif]></span><![endif]>), beta-1 (<!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span
1892	style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1893	mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1894	normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i style='mso-bidi-font-style:
1895	normal'><span style='font-family:"Cambria Math",serif'><m:r>β</m:r></span></i></m:e><m:sub><i
1896	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:sub></m:sSub></m:oMath><![endif]--><![if !msEquation]><span
1897	style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1898	"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1899	top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1900	EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1901	type="#_x0000_t75" style='width:12pt;height:14.25pt'>
1902	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image041.png"
1903	o:title="" chromakey="white"/>
1904	</v:shape><![endif]--><![if !vml]><img width=16 height=19
1905	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image065.png"
1906	v:shapes="_x0000_i1025"><![endif]></span><![endif]>), beta-q (<!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span
1907	style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1908	mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1909	normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i style='mso-bidi-font-style:
1910	normal'><span style='font-family:"Cambria Math",serif'><m:r>β</m:r></span></i></m:e><m:sub><i
1911	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>q</m:r></span></i></m:sub></m:sSub></m:oMath><![endif]--><![if !msEquation]><span
1912	style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1913	"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1914	top:4.5pt;mso-text-raise:-4.5pt;mso-ansi-language:EN-US;mso-fareast-language:
1915	EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1916	type="#_x0000_t75" style='width:12pt;height:15.75pt'>
1917	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image043.png"
1918	o:title="" chromakey="white"/>
1919	</v:shape><![endif]--><![if !vml]><img width=16 height=21
1920	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image066.png"
1921	v:shapes="_x0000_i1025"><![endif]></span><![endif]>), sig-0 (<!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1922	style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1923	mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1924	normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1925	normal'><span style='font-family:"Cambria Math",serif'><m:r>σ</m:r></span></i></m:e><m:sub><i
1926	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:sub><m:sup><i
1927	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span
1928	style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1929	"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1930	top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1931	EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1932	type="#_x0000_t75" style='width:13.5pt;height:14.25pt'>
1933	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image045.png"
1934	o:title="" chromakey="white"/>
1935	</v:shape><![endif]--><![if !vml]><img width=18 height=19
1936	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image067.png"
1937	v:shapes="_x0000_i1025"><![endif]></span><![endif]>), sig-1 (<!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1938	style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1939	mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1940	normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1941	normal'><span style='font-family:"Cambria Math",serif'><m:r>σ</m:r></span></i></m:e><m:sub><i
1942	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:sub><m:sup><i
1943	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span
1944	style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1945	"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1946	top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1947	EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1948	type="#_x0000_t75" style='width:13.5pt;height:14.25pt'>
1949	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image047.png"
1950	o:title="" chromakey="white"/>
1951	</v:shape><![endif]--><![if !vml]><img width=18 height=19
1952	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image068.png"
1953	v:shapes="_x0000_i1025"><![endif]></span><![endif]>), sig-2 (<!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1954	style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1955	mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1956	normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1957	normal'><span style='font-family:"Cambria Math",serif'><m:r>σ</m:r></span></i></m:e><m:sub><i
1958	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sub><m:sup><i
1959	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span
1960	style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1961	"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1962	top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1963	EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1964	type="#_x0000_t75" style='width:13.5pt;height:14.25pt'>
1965	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image049.png"
1966	o:title="" chromakey="white"/>
1967	</v:shape><![endif]--><![if !vml]><img width=18 height=19
1968	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image069.png"
1969	v:shapes="_x0000_i1025"><![endif]></span><![endif]>) and sig-q (<!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1970	style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1971	mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1972	normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1973	normal'><span style='font-family:"Cambria Math",serif'><m:r>σ</m:r></span></i></m:e><m:sub><i
1974	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>q</m:r></span></i></m:sub><m:sup><i
1975	style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span
1976	style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1977	"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1978	top:4.5pt;mso-text-raise:-4.5pt;mso-ansi-language:EN-US;mso-fareast-language:
1979	EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1980	type="#_x0000_t75" style='width:13.5pt;height:15.75pt'>
1981	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image051.png"
1982	o:title="" chromakey="white"/>
1983	</v:shape><![endif]--><![if !vml]><img width=18 height=21
1984	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image070.png"
1985	v:shapes="_x0000_i1025"><![endif]></span><![endif]>). Some of the values given
1986	above are probably not appropriate; looking at the difference curve it appears
1987	that the peak width is most in error. Refine <b style='mso-bidi-font-weight:
1988	normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1989	minor-latin;mso-hansi-theme-font:minor-latin'>sig-1</span></b> and <b
1990	style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1991	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>sig-2</span></b>.
1992	Remember to go back to <b style='mso-bidi-font-weight:normal'><span
1993	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1994	mso-hansi-theme-font:minor-latin'>Peak List</span></b> to do the fitting. My <span
1995	class=SpellE>Rwp</span> improved to 7.32% and the new coefficients looked like</p>
1996
1997	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1998	id="Picture_x0020_38" o:spid="_x0000_i1035" type="#_x0000_t75" style='width:411pt;
1999	height:220.5pt;visibility:visible;mso-wrap-style:square'>
2000	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image053.png"
2001	o:title=""/>
2002	</v:shape><![endif]--><![if !vml]><img border=0 width=548 height=294
2003	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image053.png"
2004	v:shapes="Picture_x0020_38"><![endif]></span></p>
2005
2006	<p class=MsoNormal>After adding <b style='mso-bidi-font-weight:normal'><span
2007	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2008	mso-hansi-theme-font:minor-latin'>sig-0</span></b> and <b style='mso-bidi-font-weight:
2009	normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2010	minor-latin;mso-hansi-theme-font:minor-latin'>sig-q</span></b> to the refinement,
2011	my residual improved slightly to <span class=SpellE>Rwp</span>=6.9%. A zoom
2012	view of some peaks around TOF~20000µs</p>
2013
2014	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2015	id="Picture_x0020_25" o:spid="_x0000_i1034" type="#_x0000_t75" style='width:525pt;
2016	height:450pt;visibility:visible;mso-wrap-style:square'>
2017	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image054.png"
2018	o:title=""/>
2019	</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2020	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image054.png"
2021	v:shapes="Picture_x0020_25"><![endif]></span></p>
2022
2023	<p class=MsoNormal>Suggests that the beta terms are too large, i.e. the
2024	trailing edges are calculating too sharp compared to the data. In two steps
2025	first add <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2026	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>beta-0</span></b>
2027	to the refinement and then second add <b style='mso-bidi-font-weight:normal'><span
2028	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2029	mso-hansi-theme-font:minor-latin'>beta-1</span></b>. The two refinements improve
2030	the fit (<span class=SpellE>Rwp</span>=6.23% after the 1<sup>st</sup> step and <span
2031	class=SpellE>Rwp</span>=5.50% after the 2<sup>nd</sup>). The resulting coefficients
2032	are</p>
2033
2034	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2035	id="Picture_x0020_39" o:spid="_x0000_i1033" type="#_x0000_t75" style='width:411pt;
2036	height:220.5pt;visibility:visible;mso-wrap-style:square'>
2037	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image055.png"
2038	o:title=""/>
2039	</v:shape><![endif]--><![if !vml]><img border=0 width=548 height=294
2040	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image055.png"
2041	v:shapes="Picture_x0020_39"><![endif]></span></p>
2042
2043	<p class=MsoNormal>And the fit in the above region is now much better.</p>
2044
2045	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2046	id="Picture_x0020_27" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:525pt;
2047	height:450pt;visibility:visible;mso-wrap-style:square'>
2048	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image056.png"
2049	o:title=""/>
2050	</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2051	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image056.png"
2052	v:shapes="Picture_x0020_27"><![endif]></span></p>
2053
2054	<p class=MsoNormal>The principal errors now seem to be on the front edge of the
2055	peaks. After adding <b style='mso-bidi-font-weight:normal'><span
2056	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2057	mso-hansi-theme-font:minor-latin'>alpha</span></b> to the refinement, I got <span
2058	class=SpellE>Rwp</span>=4.35% and the difference curve is almost flat.</p>
2059
2060	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2061	id="Picture_x0020_28" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:525pt;
2062	height:450pt;visibility:visible;mso-wrap-style:square'>
2063	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image057.png"
2064	o:title=""/>
2065	</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2066	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image057.png"
2067	v:shapes="Picture_x0020_28"><![endif]></span></p>
2068
2069	<p class=MsoNormal>The coefficients are</p>
2070
2071	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2072	id="Picture_x0020_40" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:411pt;
2073	height:220.5pt;visibility:visible;mso-wrap-style:square'>
2074	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image058.png"
2075	o:title=""/>
2076	</v:shape><![endif]--><![if !vml]><img border=0 width=548 height=294
2077	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image058.png"
2078	v:shapes="Picture_x0020_40"><![endif]></span></p>
2079
2080	<p class=MsoNormal>As this represents a very good fit to the profile, it would
2081	be useful to save the project (do <b style='mso-bidi-font-weight:normal'><span
2082	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2083	mso-hansi-theme-font:minor-latin'>File/Save project</span></b> from the main
2084	GSAS-II data tree menu) and make a new instrument file (do <b style='mso-bidi-font-weight:
2085	normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2086	minor-latin;mso-hansi-theme-font:minor-latin'>Operations/Save profile</span></b>
2087	from the Instrument Parameters menu; you can overwrite the existing one). I did
2088	try to refine beta-q; that gave a failed refinement. However, the material used
2089	for the calibration (SRM 660b La10B6) does have some sample broadening. As this
2090	almost always shows up as a Lorentzian contribution to the peak profiles one
2091	can accommodate it by refining <b style='mso-bidi-font-weight:normal'><span
2092	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2093	mso-hansi-theme-font:minor-latin'>X</span></b> and <b style='mso-bidi-font-weight:
2094	normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2095	minor-latin;mso-hansi-theme-font:minor-latin'>Y</span></b>. After refining them
2096	I get a substantial improvement <span class=SpellE>Rwp</span>=3.24% and there
2097	are considerable changes in the other coefficients because they no longer have
2098	to compensate for the missing Lorentzian component. Their values then represent
2099	the instrument contribution to the profile.</p>
2100
2101	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2102	id="Picture_x0020_41" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:411pt;
2103	height:220.5pt;visibility:visible;mso-wrap-style:square'>
2104	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image059.png"
2105	o:title=""/>
2106	</v:shape><![endif]--><![if !vml]><img border=0 width=548 height=294
2107	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image059.png"
2108	v:shapes="Picture_x0020_41"><![endif]></span></p>
2109
2110	<p class=MsoNormal>The profile fit is almost perfect</p>
2111
2112	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2113	id="Picture_x0020_31" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:525pt;
2114	height:450pt;visibility:visible;mso-wrap-style:square'>
2115	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image060.png"
2116	o:title=""/>
2117	</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2118	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image060.png"
2119	v:shapes="Picture_x0020_31"><![endif]></span></p>
2120
2121	<p class=MsoNormal>Ive switched back to a q plot and positioned the difference
2122	curve to be about zero.</p>
2123
2124	<h2>Step 4. Check diffractometer constants </h2>
2125
2126	<p class=MsoNormal>Since these calibration fits for profile coefficients varied
2127	the peak positions, a final check on the diffractometer constants is needed. To
2128	do this, the new peak positions need to be loaded into the <b style='mso-bidi-font-weight:
2129	normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2130	minor-latin;mso-hansi-theme-font:minor-latin'>Index Peak List</span></b> (do <b
2131	style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2132	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Operations/Load/Reload</span></b>
2133	in that menu). Notice that the Index peaks are no longer indexed. In <b
2134	style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2135	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Unit Cells
2136	List</span></b>, press the <b style='mso-bidi-font-weight:normal'><span
2137	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2138	mso-hansi-theme-font:minor-latin'>Show <span class=SpellE>hkl</span> positions</span></b>
2139	button; this will index the lines. The go to <b style='mso-bidi-font-weight:
2140	normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2141	minor-latin;mso-hansi-theme-font:minor-latin'>Instrument Parameters</span></b>
2142	and uncheck all the profile coefficient <b style='mso-bidi-font-weight:normal'><span
2143	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2144	mso-hansi-theme-font:minor-latin'>Refine?</span></b> <span class=GramE>boxes</span>;
2145	then check those you varied at the beginning of the tutorial (<span
2146	class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
2147	"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2148	minor-latin'>difC</span></b></span>, <span class=SpellE><b style='mso-bidi-font-weight:
2149	normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2150	minor-latin;mso-hansi-theme-font:minor-latin'>difA</span></b></span> & <b
2151	style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2152	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Zero</span></b>).
2153	Do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2154	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Operations/Calibrate</span></b>.
2155	The agreement shows some deviations at very short d-spacing that werent
2156	evident in the initial calibration.</p>
2157
2158	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2159	id="Picture_x0020_42" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:525pt;
2160	height:450pt;visibility:visible;mso-wrap-style:square'>
2161	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image061.png"
2162	o:title=""/>
2163	</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2164	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image061.png"
2165	v:shapes="Picture_x0020_42"><![endif]></span></p>
2166
2167	<p class=MsoNormal>You will need to add the <span class=SpellE><b
2168	style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2169	mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>difB</span></b></span>
2170	parameter to the fit. Check the box and repeat <b style='mso-bidi-font-weight:
2171	normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2172	minor-latin;mso-hansi-theme-font:minor-latin'>Operations/Calibrate</span></b>.
2173	The fit now is better apart from a few stragglers at low d-<span class=SpellE>spacings</span></p>
2174
2175	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2176	id="Picture_x0020_43" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:525pt;
2177	height:450pt;visibility:visible;mso-wrap-style:square'>
2178	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image062.png"
2179	o:title=""/>
2180	</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2181	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image062.png"
2182	v:shapes="Picture_x0020_43"><![endif]></span></p>
2183
2184	<p class=MsoNormal>These are very weak peaks whose position was poorly
2185	determined. Almost all the rest are within a 1TOF bin width around zero. Save
2186	the project <b style='mso-bidi-font-weight:normal'><span style='font-family:
2187	"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2188	minor-latin'>(File/Save project</span></b> in the main GSAS-II data tree menu).</p>
2189
2190	<h2>Step 5. Make instrument parameter file</h2>
2191
2192	<p class=MsoNormal>We now have a fully calibrated instrument with
2193	diffractometer coefficients and profile coefficients. Uncheck all refinement
2194	boxes and set <b style='mso-bidi-font-weight:normal'><span style='font-family:
2195	"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2196	minor-latin'>X</span></b> and <b style='mso-bidi-font-weight:normal'><span
2197	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2198	mso-hansi-theme-font:minor-latin'>Y</span></b> back to zero. You should have</p>
2199
2200	<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2201	id="Picture_x0020_45" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:411pt;
2202	height:203.25pt;visibility:visible;mso-wrap-style:square'>
2203	<v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image063.png"
2204	o:title=""/>
2205	</v:shape><![endif]--><![if !vml]><img border=0 width=548 height=271
2206	src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image063.png"
2207	v:shapes="Picture_x0020_45"><![endif]></span></p>
2208
2209	<p class=MsoNormal>This removes from the instrument parameters any sample broadening
2210	effects and thus the remaining parameters are only dependent on the instrument.
2211	To make an instrument parameter file do <b style='mso-bidi-font-weight:normal'><span
2212	style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2213	mso-hansi-theme-font:minor-latin'>Operations/Save profile</span></b>; choose a
2214	suitable name expressing the particular instrument configuration used in
2215	collecting the calibration data. I named it <b style='mso-bidi-font-weight:
2216	normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2217	minor-latin;mso-hansi-theme-font:minor-latin'>POWGEN_1066.instprm</span></b> (with
2218	the default extension) to reflect the wavelength band used to collect it on
2219	POWGEN. This completes this tutorial.</p>
2220
2221	<p class=MsoNormal><o:p> </o:p></p>
2222
2223	</div>
2224
2225	</body>
2226
2227	</html>

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