Changeset 5039


Ignore:
Timestamp:
Sep 28, 2021 10:55:35 AM (8 months ago)
Author:
toby
Message:

missed tutorial update

File:
1 edited

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  • Tutorials/SeqRefine/SequentialTutorial.htm

    r4457 r5039  
    13941394</BL></P><P></P>
    13951395 
    1396 <p class=MsoNormal>Sequential refinement is a way to fit a series of datasets
    1397 with a set of closely related models that evolve over the course of the
    1398 measurements.<span style='mso-spacerun:yes'>  </span>Sequential refinements can
     1396<p class=MsoNormal>Sequential refinement is a way to fit a series of
     1397  datasets collected under similar conditions with a set of closely
     1398  related models. Each dataset receives an independent
     1399  fit. Thus it is possible to track how the models
     1400  evolve over the course of the measurements. One or more phases may
     1401  be used to fit all all the datasets or some phases may appear in
     1402  just some of the measurements, should there be phase transitions.
     1403<P></P>
     1404  Sequential refinements can
    13991405be performed in three different ways: </p>
    1400 
    1401 <p class=MsoListParagraphCxSpFirst style='margin-left:.75in;mso-add-space:auto;
    1402 text-indent:-.25in;mso-list:l4 level1 lfo2'><![if !supportLists]><span
    1403 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1.<span
    1404 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>with
    1405 differing starting parameters for each histogram</p>
    1406 
    1407 <p class=MsoListParagraphCxSpMiddle style='margin-left:.75in;mso-add-space:
    1408 auto;text-indent:-.25in;mso-list:l4 level1 lfo2'><![if !supportLists]><span
    1409 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span
    1410 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>with
    1411 the same starting parameters for each histogram</p>
    1412 
    1413 <p class=MsoListParagraphCxSpLast style='margin-left:.75in;mso-add-space:auto;
    1414 text-indent:-.25in;mso-list:l4 level1 lfo2'><![if !supportLists]><span
    1415 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3.<span
    1416 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>where
    1417 the resulting parameters after refinement with a histogram are used as the
    1418 starting point for the next histogram.</p>
     1406  <OL>
     1407    <LI>where the resulting parameters after a fit for a
     1408    histogram are used as the starting point for the next histogram.</LI>
     1409    <LI>with differing starting parameters for each histogram</LI>
     1410    <LI>with the same starting parameters for each histogram</LI>
     1411</OL><P></P>
     1412Most commonly the first mode is used initially, where the parameters
     1413for each fir are copied as the starting point for the fit of next
     1414dataset. After this initial refinement of all datasets is complete,
     1415the refinement is continued where each dataset has its own
     1416parameters.
    14191417
    14201418<p class=MsoNormal><o:p>&nbsp;</o:p></p>
    14211419
    1422   <p class=MsoNormal>
     1420<p class=MsoNormal>
     1421In this example, we will fit a temperature series where both the unit
     1422cell and atomic parameters evolve with temperature. Note that
     1423it is also possible to fit a temperature series as a combined refinement and,
     1424as will be seen, one can still deal with thermal expansion (using the
     1425Hydrostatic/Elastic strain terms), but a combined refinement would
     1426allow only a single set of (averaged) atomic parameters for
     1427all temperatures. A sequential refinement allows each
     1428data set to determine the atomic parameters and allows their variation
     1429with temperature to be determined.
     1430<P></P>
    14231431Data for this example will be downloaded with the tutorial, if you used
    14241432that option to see this page. Otherwise, download file
    14251433<A href="https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/SeqRefine/data/">
    14261434SeqTut.zip from here</A>.
    1427 In this example, we will fit a temperature series. Note that
    1428 it is also possible to fit a temperature series as a combined refinement and,
    1429 as will be seen, one can still deal with thermal expansion (using the
    1430 Hydrostatic/Elastic strain terms), but a combined refinement would average the
    1431 atomic parameters across all temperatures. A sequential refinement allows each
    1432 data set to determine the atomic parameters; their variation with temperature
    1433 might be of interest.</p>
    1434 
    1435 <p class=MsoNormal>This example assumes that one is already familiar with use
     1435This example assumes that one is already familiar with use
    14361436of GSAS-II for simple refinements. <span style='mso-bidi-font-size:12.0pt;
    14371437mso-fareast-font-family:"Times New Roman";mso-fareast-language:EN-US'>Note that
    1438 menu entries are listed in bold face below as </span><b style='mso-bidi-font-weight:
     1438menu entries are listed in bold face below, such as </span><b style='mso-bidi-font-weight:
    14391439normal'><span style='mso-bidi-font-size:12.0pt;font-family:"Calibri",sans-serif;
    14401440mso-fareast-font-family:"Times New Roman";mso-fareast-language:EN-US'>Help/About
     
    1449144912.0pt;font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";
    14501450mso-fareast-language:EN-US'>About GSAS-II</span></b><span style='mso-bidi-font-size:
    1451 12.0pt;mso-fareast-font-family:"Times New Roman";mso-fareast-language:EN-US'>).</span>If
    1452 you have not done so already, start GSAS-II. </p>
     145112.0pt;mso-fareast-font-family:"Times New
     1452Roman";mso-fareast-language:EN-US'>).</span>
     1453</p>
     1454
     1455<h1>Step I: Fit a single temperature. </h1>
     1456<p></p>
     1457
     1458If you have not done so already, start GSAS-II. While it is possible
     1459to start a sequential refinement reading in all phases and datasets
     1460from the beginning, usually it is best to know something about how the
     1461fit will be performed and this usually means performing one or more
     1462fits to representative individual datasets as the conditions or phases
     1463present change. One way to do this could be to read in all datasets but select
     1464only a single individual dataset for that fit until we are ready to
     1465fit the entire sequence. Here we will start by reading in only the
     1466first dataset and fit that. Then we will add more datasets and perform
     1467a sequential fit.
    14531468
    14541469<p class=MsoNormal><o:p>&nbsp;</o:p></p>
    14551470
    1456 <h1>Step 1: Fit a single temperature. </h1>
    1457 
    1458 <p class=MsoNormal><o:p>&nbsp;</o:p></p>
    1459 
    1460 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l6 level1 lfo4'><![if !supportLists]><span
    1461 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1.<span
    1462 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Use
     1471<H3>1. Read phase files <B>CuCr2O4.cif</B> and <B>CuO.cif</B> from file <b>SeqTut.zip</B>.</H3>
     1472
     1473<OL style='PADDING-LEFT:0.75in' type="A"><LI>
     1474 Use
    14631475the <b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    1464 mso-hansi-theme-font:major-latin'>Import/Phase/from CIF file menu item</span></b>
    1465 to read the phase information </p>
    1466 
    1467 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    1468 
    1469 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l6 level1 lfo4'><![if !supportLists]><span
    1470 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span
    1471 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>In
     1476mso-hansi-theme-font:major-latin'>
     1477Import/Phase/from CIF file menu item</span></b> to read the phase information.</p>
     1478  <P></P>
     1479In
    14721480the file browser dialog window that is created, <span style='mso-bidi-font-weight:
    14731481bold'>change the file type from<b> “</b></span><b><span style='font-family:
     
    14961504bold'>input files. Press<b> </b></span><b><span style='font-family:"Calibri",sans-serif;
    14971505mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>OK</span></b>.
    1498 </p>
    1499 
    1500 <p class=MsoListParagraphCxSpMiddle>(Note that if files CuCr2O4.cif or the
    1501 CuO.cif already exist, you will be asked to OK overwriting them.)</p>
    1502 
    1503 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    1504 
    1505 <p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l6 level1 lfo4'><![if !supportLists]><span
    1506 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3.<span
    1507 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>You
     1506<P></p>
     1507(If this exercise is being repeated, files CuCr2O4.cif or the
     1508CuO.cif will already exist. If so, you will be asked to OK overwriting them.)
     1509
     1510<P></p>
     1511<LI>You
    15081512will be asked sequentially for the name for each phase. The defaults (<b
    15091513style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     
    15161520style='mso-spacerun:yes'>  </span></p>
    15171521
     1522<P></P>
     1523<LI>Note that for CuCr<sub>2</sub>O<sub>4</sub>, the space group (<I>Fddd</I>) can
     1524be set with two origin choices. Select <B>Keep current coordinates</B>
     1525since the coordinates are already set properly.
     1526<P></P>
     1527<I>Discussion:
     1528When there is a choice, GSAS-II requires the use of Origin 2, which
     1529places the origin at a center of symmetry, and this CIF has been set
     1530that way
     1531(the presence of a -x,-y,-z symmetry operation confirms that), but GSAS-II
     1532notes the possible choice and offers to apply the shift to the
     1533coordinates that would shift from Origin 1 to Origin 2.
     1534As shown in the window where this
     1535choice would be made, this shift were applied,
     1536the unit cell contents would be
     1537Cu<sub>16</sub>Cr<sub>8</sub>O<sub>32</sub> rather than the correct
     1538CuCr<sub>2</sub>O<sub>4</sub> stoichiometry, so this also confirms the
     1539origin setting is correct and no coordinate shift should be applied.
     1540<B>Choice of origin is a common problem in crystallographic
     1541computations and many CIFs do not define this setting clearly, so use care with this.</B>
     1542</I>
     1543
    15181544<p class=MsoNormal><o:p>&nbsp;</o:p></p>
    1519 
    1520 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l6 level1 lfo4'><![if !supportLists]><span
    1521 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>4.<span
    1522 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span
    1523 style='mso-spacerun:yes'> </span>Read in the ~7 K dataset (<b style='mso-bidi-font-weight:
     1545</OL>
     1546
     1547<H3>2.
     1548Read in file <B>OH_00.fxye</B> from file <b>SeqTut.zip</B> and <B>map
     1549both phases</B> to this dataset.  </H3>
     1550
     1551<OL style='PADDING-LEFT:0.75in' type="A"><LI>
     1552Read in the ~7 K dataset (<b style='mso-bidi-font-weight:
    15241553normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    15251554major-latin;mso-hansi-theme-font:major-latin'>OH_00.fxye</span></b>) using <b><span
     
    15661595src="SequentialTutorial_files/image001.png" v:shapes="Picture_x0020_54"><![endif]></span></p>
    15671596
    1568 <p class=MsoListParagraphCxSpMiddle>You will be shown the first few lines from
     1597<P></P>
     1598<LI>You will be shown the first few lines from
    15691599the file. Confirm that the selected file is correct by <span style='mso-bidi-font-weight:
    15701600bold'>pressing<b> </b></span><b><span style='font-family:"Calibri",sans-serif;
     
    15791609</v:shape><![endif]--><![if !vml]><img width=366 height=233
    15801610src="SequentialTutorial_files/image002.png" v:shapes="Picture_x0020_55"><![endif]></span></p>
    1581 
     1611<P></P>
    15821612<p class=MsoListParagraphCxSpMiddle>Note that the instrument parameter file
    15831613with the matching name (<b style='mso-bidi-font-weight:normal'><span
     
    15871617<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    15881618
    1589 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l6 level1 lfo4'><![if !supportLists]><span
    1590 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>5.<span
    1591 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Map
     1619<A name="I.2.C">
     1620<LI>Map
    15921621the phases to the data: After reading in the dataset, a window used to select
    15931622phases is shown.</p>
     
    16011630src="SequentialTutorial_files/image003.png" v:shapes="Picture_x0020_56"><![endif]></span></p>
    16021631
     1632<P></P>
    16031633<p class=MsoListParagraphCxSpMiddle><span style='mso-bidi-font-weight:bold'>Select
    16041634both phases and press<b> </b></span><b><span style='font-family:"Calibri",sans-serif;
    16051635mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>OK</span>.</b><span
    16061636style='mso-spacerun:yes'>  </span></p>
     1637</OL>
    16071638
    16081639<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    16091640
    1610 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    1611 
    1612 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l6 level1 lfo4'><![if !supportLists]><span
    1613 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>6.<span
    1614 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>We
     1641<A name="I.3"></A>
     1642<H3>3. Prepare for fit: define <B>phase fraction constraint</B></H3>
     1643<P></P>
     1644<p class=MsoListParagraphCxSpMiddle>
     1645We
    16151646want to fit the lattice parameters, background, and a phase fraction
    1616 initially.<span style='mso-spacerun:yes'>  </span>To illustrate how constraints
     1647initially. To illustrate how constraints
    16171648are used, we will refine both phase fractions, but constrain their sum to be
    1618 one. To set up the constraint, <span style='mso-bidi-font-weight:bold'>click on
     1649one. <I>Discussion: a single powder diffraction pattern provides
     1650enough information to determine an overall scale factor and the
     1651relative amounts of each phase (with two phases: two observables), but
     1652with the scale factor and two phase fractions being varied
     1653independently, we have three arbitrary
     1654parameters, which would result in a very unstable refinement where the
     1655GSAS-II minimizer would likely remove a degree of freedom. By defining
     1656a constraint that sets the sum of the two phase fractions, we reduce
     1657this to an appropriate two parameter problem. The error of refining the scale
     1658factor and all phase fractions is made often enough that GSAS-II will
     1659warn about this and will offer to define this constraint.</I>
     1660
     1661<OL style='PADDING-LEFT:0.75in' type="A"><LI>
     1662To set up the phase fraction constraint, <span style='mso-bidi-font-weight:bold'>click on
    16191663the<b> </b></span><b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    16201664major-latin;mso-hansi-theme-font:major-latin'>Constraints</span> </b><span
     
    16291673style='mso-bidi-font-weight:bold'> menu item<b>.</b></span></p>
    16301674
    1631 <p class=MsoListParagraphCxSpMiddle><span style='mso-spacerun:yes'> </span></p>
    1632 
    1633 <p class=MsoListParagraphCxSpMiddle>In the next window use a <b
     1675
     1676  <LI>In the next window use a <b
    16341677style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    16351678mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Filter</span></b>
     
    16531696style='mso-spacerun:yes'> </span></p>
    16541697
    1655 <p class=MsoListParagraphCxSpMiddle>In the next window, either <span
     1698<P></P>
     1699
     1700<LI>After pressing "OK" a new window
     1701appears; in that next window either
     1702<span
    16561703style='mso-bidi-font-weight:bold'>select the other phase fraction<b> (</b></span><b><span
    16571704style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
     
    16621709style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    16631710mso-hansi-theme-font:major-latin'>all:0:Scale</span></b><span style='font-family:
    1664 "Cambria",serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>)<o:p></o:p></span></p>
    1665 
     1711"Cambria",serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>). The same result is obtained since there is only one additional
     1712phase.
     1713
     1714<P></P>
    16661715<p class=MsoListParagraphCxSpMiddle><span style='font-family:"Cambria",serif;
    16671716mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_58"
     
    16731722style='font-family:"Cambria",serif'><o:p></o:p></span></p>
    16741723
    1675 <p class=MsoListParagraphCxSpMiddle>This creates the desired constraint, which
    1676 forces the sum to be 1. (If the desired sum was different or different
    1677 multipliers were desired, press the <b style='mso-bidi-font-weight:normal'><span
     1724<P></P>
     1725<p class=MsoListParagraphCxSpMiddle>
     1726<LI>Press OK and this creates the desired constraint, which
     1727forces the sum of phase fractions to be 1. (This is not needed here,
     1728but to change the sum and/or multipliers, press the constraint's <b style='mso-bidi-font-weight:normal'><span
    16781729style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    1679 mso-hansi-theme-font:major-latin'>Edit</span></b> button for the constraint.) </p>
     1730mso-hansi-theme-font:major-latin'>Edit</span></b> button.) </p>
    16801731
    16811732<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
     
    16891740<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    16901741
    1691 <p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l6 level1 lfo4'><![if !supportLists]><span
    1692 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>7.<span
    1693 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Now
    1694 we select the variables to refine. </p>
    1695 
    1696 <p class=MsoNormal><o:p>&nbsp;</o:p></p>
    1697 
    1698 <p class=MsoListParagraphCxSpFirst><span style='mso-bidi-font-weight:bold'>Select
     1742</OL>
     1743
     1744<H3>4. Initial fit: optimize <B>lattice</B> parameters & <B>phase
     1745fractions</B>;
     1746<B>background</B> (with <B>6 terms</B>); <B>scale factor</B>.
     1747</H3>
     1748<P></P>
     1749<p class=MsoListParagraphCxSpMiddle>
     1750 Now we select the variables to refine for each phase and then the
     1751histogram parameters. </p>
     1752
     1753<OL style='PADDING-LEFT:0.75in' type="A"><LI>
     1754  Select
    16991755the first phase</span> (<b style='mso-bidi-font-weight:normal'><span
    17001756style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
     
    17051761style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    17061762mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>General</span></b>
    1707 tab). (On a Mac you will likely need to click on the triangle to the left of
     1763tab). (You might need to click on the triangle to the left of
    17081764the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    17091765mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Phase</span></b>
     
    17261782src="SequentialTutorial_files/image064.png" v:shapes="Picture_x0020_60"><![endif]></span></p>
    17271783
    1728 <p class=MsoListParagraphCxSpMiddle>Repeat this with the second phase (<b
     1784<p></P>
     1785<LI>Repeat this with the second phase (<b
    17291786style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    17301787mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>CuO</span></b>),
     
    17431800mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Phase
    17441801fraction</span> </b><span style='mso-bidi-font-weight:bold'>box</span> to cause
    1745 that to be refined.<span style='mso-spacerun:yes'>  </span>Also <span
    1746 style='mso-bidi-font-weight:bold'>click on the single<b> </b></span><b><span
    1747 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    1748 mso-hansi-theme-font:major-latin'>microstrain</span></b> (isotropic) term for
    1749 this second phase.</p>
    1750 
    1751 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    1752 
    1753 <p class=MsoListParagraphCxSpMiddle>Also <span style='mso-bidi-font-weight:
    1754 bold'>select<b> </b>the<b> </b></span><b><span style='font-family:"Calibri",sans-serif;
     1802that to be refined.
     1803
     1804<P></P>
     1805<LI>To refine the background,<span style='mso-bidi-font-weight:
     1806bold'>
     1807select the </span><b><span style='font-family:"Calibri",sans-serif;
    17551808mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Background</span>
    1756 </b><span style='mso-bidi-font-weight:bold'>entry</span> under <b
     1809</b><span style='mso-bidi-font-weight:bold' entry</span>
     1810entry under the <b
    17571811style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1758 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>PWDR
    1759 OH_00.fxye Bank 1</span></b> in the GSAS-II data tree (for a Mac, you will
    1760 likely need to click on the triangle to the left of the entry to “open” the
    1761 tree item.) Confirm that <b style='mso-bidi-font-weight:normal'><span
     1812mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>
     1813PWDR
     1814OH_00.fxye Bank 1</span></b> histogram sub-entries in the GSAS-II data tree. Confirm that <b style='mso-bidi-font-weight:normal'><span
    17621815style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    17631816mso-hansi-theme-font:major-latin'>Background function</span></b> should already
    17641817be set as <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1765 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>chebyshev</span></b>
     1818mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>chebyshev-1</span></b>
    17661819and the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    17671820mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Refine</span></b>
     
    17731826to introduce more background terms. </p>
    17741827
    1775 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    1776 
    1777 <p class=MsoListParagraphCxSpMiddle>The histogram scale factor, on the <b
     1828<P></P>
     1829<LI>The overall histogram scale factor should already be set to be
     1830refined by default, but you may want to confirm this by clicking on the <b
    17781831style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    17791832mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Sample
    1780 Parameters</span></b> entry should already be set as refined by default, but you
    1781 may want to confirm this.</p>
     1833Parameters</span></b> data tree entry.
     1834</OL>
    17821835
    17831836<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    17841837
    1785 <p class=MsoListParagraphCxSpMiddle>Finally, note that the first broad peak in
    1786 these data is spurious. It is known to arise from the kapton window in the
     1838<H3>5.<span
     1839style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
     1840</span></span></span><![endif]>
     1841Reduce <B>Data Range</B> to 4.5 degrees</H3>
     1842
     1843<P></P>
     1844
     1845<p class=MsoListParagraphCxSpMiddle>Finally, note that the first broad
     1846peak at ~1.5 degrees in these data is spurious.
     1847This artifact is known to arise from scattering from the kapton window in the
    17871848cryostat used for sample cooling; this was confirmed by collecting data without
    1788 a sample. We could model this peak, but it is easier to simply drop the data
     1849a sample. We could model this peak, but it is easier to simply cut off the data
    17891850below the first peak at ~5 degrees. To do this<b style='mso-bidi-font-weight:
    17901851normal'>, </b><span style='mso-bidi-font-weight:bold'>select the<b> </b></span><b><span
     
    18021863<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    18031864
    1804 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l6 level1 lfo4'><![if !supportLists]><span
    1805 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>8.<span
    1806 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span
    1807 style='mso-bidi-font-weight:bold'>Use the </span><b><span style='font-family:
     1865<H3>6. Perform initial fit</H3>
     1866
     1867<p class=MsoListParagraphCxSpMiddle>
     1868Use the<b><span style='font-family:
    18081869"Calibri",sans-serif;mso-ascii-theme-font:major-latin;mso-hansi-theme-font:
    1809 major-latin'>Calculate/Refine</span></b><span style='mso-bidi-font-weight:bold'>
     1870major-latin'>
     1871Calculate/Refine</span></b><span style='mso-bidi-font-weight:bold'>
    18101872main GSAS-II menu item</span> to initiate the refinement. Since the project has
    18111873not been saved, you will be asked to select a name (and optionally a directory)
     
    18151877is assumed here. The refinement progresses quickly to a Rw of ~17%. </p>
    18161878
    1817 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    1818 
    1819 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l6 level1 lfo4'><![if !supportLists]><span
    1820 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>9.<span
    1821 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>There
    1822 are several additional variables that should now be added. One should always
    1823 refine a sample displacement parameter (or rarely one refines a zero correction.) In this
    1824 case, the best choice is to <span style='mso-bidi-font-weight:bold'>add the<b> </b></span><b><span
    1825 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    1826 mso-hansi-theme-font:major-latin'>Sample X displ.</span> </b><span
    1827 style='mso-bidi-font-weight:bold'>parameter</span> on the <b style='mso-bidi-font-weight:
    1828 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    1829 major-latin;mso-hansi-theme-font:major-latin'>Sample Parameters</span></b> section
    1830 of histogram <b style='mso-bidi-font-weight:normal'><span style='font-family:
    1831 "Calibri",sans-serif;mso-ascii-theme-font:major-latin;mso-hansi-theme-font:
    1832 major-latin'>PWDR OH_00.fxye Bank 1</span></b>. (NB: a data range &gt;&gt;90
    1833 degrees is needed before the Sample Y displ. term can be included). Set the <b
    1834 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1835 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin;mso-bidi-theme-font:
    1836 major-latin'>Goniometer radius</span></b> to <b style='mso-bidi-font-weight:
    1837 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    1838 major-latin;mso-hansi-theme-font:major-latin;mso-bidi-theme-font:major-latin'>1000</span></b>.
    1839 Note that since this instrument is very well characterized, there is no need to
    1840 refine any of the instrumental terms. </p>
    1841 
    1842 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    1843 
    1844 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    1845 mso-no-proof:yes'>Selecting</span><b> </b><span style='mso-bidi-font-weight:
    1846 bold'>the<b> </b></span><b><span style='font-family:"Calibri",sans-serif;
    1847 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>PWDR
    1848 OH_00.fxye Bank 1</span> </b><span style='mso-bidi-font-weight:bold'>entry</span>
    1849 shows the “Rietveld plot” and zooming in on different regions of the pattern
    1850 provides insight on how the fit could be improved. You can alter the view to
    1851 show the square root of the intensity (use the ‘<b style='mso-bidi-font-weight:
    1852 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    1853 major-latin;mso-hansi-theme-font:major-latin'>S</span></b>’ key to toggle
    1854 this). The background is not well fit in the low angle range and examination
    1855 shows a “hump” of low-angle scattering from ~4.5 to 6 degrees. This is more
    1856 easily fit by adding a background peak than extra terms to the background
    1857 function. <span style='mso-bidi-font-weight:bold'>Select the<b> </b></span><b><span
    1858 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    1859 mso-hansi-theme-font:major-latin'>Background </span></b><span style='mso-bidi-font-weight:
    1860 bold'>item</span> in histogram <b style='mso-bidi-font-weight:normal'><span
    1861 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    1862 mso-hansi-theme-font:major-latin'>PWDR OH_00.fxye Bank 1</span></b> and <span
    1863 style='mso-bidi-font-weight:bold'>change </span><b><span style='font-family:
    1864 "Calibri",sans-serif;mso-ascii-theme-font:major-latin;mso-hansi-theme-font:
    1865 major-latin'>Peaks in Background</span> </b><span style='mso-bidi-font-weight:
    1866 bold'>to<b> </b></span><b><span style='font-family:"Calibri",sans-serif;
    1867 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>1</span>.</b><span
    1868 style='mso-spacerun:yes'>  </span><span style='mso-bidi-font-weight:bold'>Change
    1869 the<b> </b>peak position</span> (<b style='mso-bidi-font-weight:normal'><span
    1870 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    1871 mso-hansi-theme-font:major-latin'>pos</span></b>) to the approximate peak
    1872 center (<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1873 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>5.25</span></b>
    1874 degrees) and <span style='mso-bidi-font-weight:bold'>set the intensity (</span><b><span
    1875 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    1876 mso-hansi-theme-font:major-latin'>int</span></b><span style='mso-bidi-font-weight:
    1877 bold'>) and Gaussian width<b> </b>(</span><b><span style='font-family:"Calibri",sans-serif;
    1878 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>sig</span></b><span
    1879 style='mso-bidi-font-weight:bold'>) to be refined</span>.<span
    1880 style='mso-spacerun:yes'>  </span><b style='mso-bidi-font-weight:normal'><i
    1881 style='mso-bidi-font-style:normal'><u>Important</u></i></b>: note that one must
    1882 click on another box to ensure that input is recorded.</p>
    1883 
     1879<h1>Step II: Improve the single-temperature fit. </h1>
     1880
     1881<P></P>
     1882There are several additional variables that should now be added, now
     1883that we have reasonable starting unit cell parameters, etc. This
     1884includes a sample displacement parameter, a better background treatment
     1885and some sample broadening terms for the profile.
     1886
     1887<H3>1. Improve sample-dependent fitting.</H3>
     1888
     1889<OL style='PADDING-LEFT:0.75in' type="A">
     1890<LI>Refine the <B>Sample X displacement</B> term</LI>
     1891
     1892<P></P><p class=MsoNormal>
     1893Click on the <B>Sample
     1894Parameters</B> data tree subitem for <B>PWDR OH_00.fxye Bank 1</B>.
     1895Select the refine checkbox that is
     1896labeled <B>Sample X disp. perp. to peak</B>. The value for this is the
     1897displacement in microns (10<sup>-6</sup> m), provided the
     1898diffractometer radius is entered correctly. Set the Goniometer radius to 1000.
     1899</P>
     1900
     1901<P></P>
     1902<p class=MsoListParagraphCxSpMiddle><I>Discussion: Diffractometers are never 
     1903perfectly aligned, which means one should always an alignment
     1904parameter. While in older programs, the alignment parameter was a zero
     1905correction (except for Bragg-Brentano instruments), this does not
     1906properly correct for mispositioning of the sample from the center of
     1907the goniometer arc. GSAS-II offers a geometrical correction for that
     1908being offset perpendicular to the
     1909direction of the beam as the Sample X displacement (and for where data is
     1910collected to angles above 120 degrees 2theta, it is also possible to fit a
     1911second term, Sample Y displacement for displacement along the beam
     1912direction.)
     1913When using GSAS-II, refine the Sample X displacement parameter rather than
     1914the 2theta-zero correction. (Refinement of both is not normally
     1915possible).</I>
     1916
     1917
     1918<P></P><p class=MsoNormal>
     1919Note: With a well characterized
     1920instrument, as is the case here for 11-BM at the APS, none of the
     1921Instrument Parameters or other Sample Parameters (beyond
     1922"Histogram scale factor" and "Sample X displ.") need to be fit.
     1923
     1924<P></P>
     1925<LI>Add a background peak.</LI>
     1926
     1927<P></P><p class=MsoNormal>
     1928Add a background peak at <B>pos=5.25</B> degrees with <B>int=5.0</B>
     1929and a <B>sig=2000</B>.
     1930</P>
     1931
     1932<P></P><p class=MsoNormal>
     1933The background is not very well fit even with a six term polynomial
     1934due to a kapton scattering peak in the range of 4-6 degrees
     19352theta. This can be seen by selecting the
     1936<b>PWDR OH_00.fxye Bank 1</b> tree entry and viewing the “Rietveld
     1937plot.”
     1938Then to see more detail, either press "s" to see the plot in the
     1939square-root of intensities, or zoom in so the vertical intensity scale
     1940is 0-500 counts and the horizontal region covers the first ~5 degrees
     1941in the pattern.
     1942While the fit for this could be improved by adding many more
     1943background terms, a simpler way to improve this fit is to add a broad
     1944peak in the pattern via the background fitting. This only needs 2 or 3
     1945additional parameters.
     1946
     1947<P></P><p class=MsoNormal> 
     1948After selecting the <b>Background</b> sub-item in the
     1949<B>PWDR OH_00.fxye Bank 1</b> histogram, change the <b>Peaks in
     1950Background</b> setting from "0" to "1". Then change
     1951the peak position (<b>pos</b>) value to the approximate peak
     1952center (<b>5.25</b> degrees) but that value should not be varied until
     1953the background is fairly well fit. Since the background generated by the
     1954Chebyschev polynomial and the background peak are highly correlated,
     1955we need to get the width and intensity into the right vicinity. Note
     1956that as the values in the peaks list are changed, the background curve
     1957(in red) is recomputed. In that way the effect of the change in values
     1958can be seen. A <B>sig</B> value of 2000 gives a Gaussian FWHM for this peak of
     1959~2 degrees. Changing the <B>int</B> value from 1 to 5 makes the peak
     1960much easier to see and also helps start the initial fit. Set both
     1961<B>sig</B> and <B>int</B> to be <B>refined</B>.
     1962
     1963<P></P><p class=MsoNormal> 
     1964<i><u>Important</u></i></b>: note that after clicking on a checkbox, one must
     1965click elsewhere in the window so that the input is recorded.</p>
     1966
     1967<P></P>
    18841968<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    18851969mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_62" o:spid="_x0000_i1052"
     
    18901974src="SequentialTutorial_files/image065.png" v:shapes="Picture_x0020_62"><![endif]></span></p>
    18911975
    1892 <p class=MsoListParagraphCxSpMiddle>Once the fit has been improved we can then
    1893 add the position of this peak to the fit. </p>
    1894 
    1895 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    1896 
    1897 <p class=MsoListParagraphCxSpMiddle>While in other projects I might postpone
    1898 this until later, we can also start on improving the peak fit. We will do this
    1899 by varying the sample broadening for the major phase (since the instrumental
    1900 terms are very good.) <span style='mso-bidi-font-weight:bold'>Select the first
    1901 phase (</span><b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    1902 major-latin;mso-hansi-theme-font:major-latin'>CuCr2O4</span></b><span
    1903 style='mso-bidi-font-weight:bold'>)</span> and its <b><span style='font-family:
    1904 "Calibri",sans-serif;mso-ascii-theme-font:major-latin;mso-hansi-theme-font:
    1905 major-latin'>Data</span> </b><span style='mso-bidi-font-weight:bold'>tab</span>,
    1906 <span style='mso-bidi-font-weight:bold'>click on the </span><b><span
    1907 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    1908 mso-hansi-theme-font:major-latin'>Cryst. Size</span></b><span style='mso-bidi-font-weight:
    1909 bold'> and </span><b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    1910 major-latin;mso-hansi-theme-font:major-latin'>microstrain</span></b><span
    1911 style='mso-bidi-font-weight:bold'> parameters</span> to add them to the
    1912 fit.<span style='mso-spacerun:yes'>  </span></p>
    1913 
    1914 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    1915 
    1916 <p class=MsoListParagraphCxSpMiddle>There are now 20 refined parameters and a
    1917 repeat of the fitting (Use the Calculate/Refine menu item) causes the fit to
    1918 improve to a wR of &lt;16%.</p>
    1919 
    1920 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    1921 
    1922 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l6 level1 lfo4'><![if !supportLists]><span
    1923 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>10.<span
    1924 style='font:7.0pt "Times New Roman"'>&nbsp; </span></span></span><![endif]>We
    1925 can now <span style='mso-bidi-font-weight:bold'>include the position flag (</span><b><span
    1926 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    1927 mso-hansi-theme-font:major-latin'>pos/refine</span></b><span style='mso-bidi-font-weight:
    1928 bold'>) for the background peak</span> in the refinement. Do this at the <b
    1929 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1930 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Background</span></b>
    1931 item, as before. Be sure to click on some other box after clicking on the
    1932 refine flag, so that the setting is recorded. </p>
    1933 
    1934 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    1935 
    1936 <p class=MsoListParagraphCxSpMiddle>Close examination of the pattern shows that
     1976<P></P><p class=MsoNormal> 
     1977Once the background fit has been
     1978improved we can then add the position of this peak to the fit.</p>
     1979<P></P>
     1980
     1981<LI>Treat sample broadening.</LI>
     1982
     1983<P></P><p class=MsoNormal> 
     1984Refine <B>Cryst. Size</B> and isotropic <B>microstrain</B> parameters for the
     1985CuCr2O4 phase and the isotropic <B>microstrain</B> parameter for the
     1986CuO impurity.
     1987
     1988<P></P><p class=MsoNormal> 
     1989It will be easier to start the sequential refinement with a good fit
     1990for the sample broadening. For the majority phase, we should consider
     1991both crystallite and microstrain broadening. For the CuO impurity,
     1992which only has a few visible peaks, refinement of more than one
     1993broadening parameter is not likely to succeed and use of either
     1994parameter should be fine.
     1995Select the <B>CuCr2O4 phase</B> and the <B>Data</B> tab on the top of
     1996the window and then select to refine the <B>Cryst. Size</B> and
     1997<B>microstrain</B> parameters.
     1998Then select the <B>CuO phase</B> (note that the <B>Data</B> tab is
     1999still displayed) and select to refine the <B>microstrain</B> parameter.
     2000
     2001</OL>
     2002 
     2003<H3>2. Perform additional fit</H3>
     2004
     2005<P></P><p class=MsoListParagraphCxSpMiddle>
     2006Starting an additional refinement (using the Calculate/Refine menu item)
     2007with the addition of the six new variables to the refinement improves
     2008the fit significantly visually, though the Rw value drops only to ~15.5%.
     2009
     2010<H3>3. Still more sample parameters.</H3>
     2011
     2012<OL style='PADDING-LEFT:0.75in' type="A"><LI>
     2013  Vary background peak position</LI>
     2014 
     2015<P></P><p class=MsoNormal> 
     2016Selecting the <b>Background</b> sub-item in the
     2017<B>PWDR OH_00.fxye Bank 1</b> histogram and click on the checkbox to
     2018  refine the position (<B>pos</B>) value for the single background
     2019  peak.
     2020
     2021  <P></P>
     2022<LI>Use Uniaxial (010 axis) microstrain broadening for CuCr2O4</LI>
     2023
     2024<P></P><p class=MsoNormal>Close examination of the pattern shows that
    19372025the peak widths are still not as well fit as desired. Since strain broadening
    19382026seems more significant that sample broadening, we could use an anisotropic
     
    19402028can introduce only two terms with the uniaxial model.<span
    19412029style='mso-spacerun:yes'>  </span>Trial and error will show that the 010
    1942 direction works best. Click on the first phase (<b style='mso-bidi-font-weight:
    1943 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    1944 major-latin;mso-hansi-theme-font:major-latin'>CuCr2O4</span></b>) and <b
    1945 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1946 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Data</span></b>
    1947 tab and <span style='mso-bidi-font-weight:bold'>select<b> </b></span><b><span
    1948 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    1949 mso-hansi-theme-font:major-latin'>uniaxial</span></b> for the <b
    1950 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1951 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Mustrain
    1952 model</span></b> and <span style='mso-bidi-font-weight:bold'>use<b> </b></span><b><span
    1953 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    1954 mso-hansi-theme-font:major-latin'>0 1 0</span> </b><span style='mso-bidi-font-weight:
    1955 bold'>for the<b> </b></span><b><span style='font-family:"Calibri",sans-serif;
    1956 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Unique axis</span></b><b
    1957 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1958 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>, HKL</span></b>
    1959 . <span style='mso-bidi-font-weight:bold'>Select refinement for both </span><b><span
    1960 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    1961 mso-hansi-theme-font:major-latin'>Equatorial</span></b><span style='mso-bidi-font-weight:
    1962 bold'> and </span><b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    1963 major-latin;mso-hansi-theme-font:major-latin'>Axial mustrain</span>.</b> </p>
    1964 
    1965 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    1966 
    1967 <p class=MsoListParagraphCxSpMiddle>Repeating the refinement causes the wR to
    1968 drop to ~14%. Clicking on the <b style='mso-bidi-font-weight:normal'><span
    1969 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    1970 mso-hansi-theme-font:major-latin'>Covariance</span></b> data tree item shows
    1971 that the goodness of fit (GOF) is 1.08 (corresponding to a reduced <b
    1972 style='mso-bidi-font-weight:normal'><span style='font-family:"Lucida Grande";
    1973 color:black'>&#967;</span></b><sup>2</sup> of 1.2) with 23 refined parameters.
    1974 While atomic parameters could now be refined, as shown in the plot, this is
     2030direction works best. Click on the first phase (<b>CuCr2O4</b>) and
     2031the <b>Data</b> tab and select <b>uniaxial</b> for the <b>Mustrain
     2032model</b> and change the <B>Unique axis, HKL</B> from "0 0 1" to <b>0
     20331 0</b>.
     2034Select refinement for both <b>Equatorial</b> and <b>Axial
     2035mustrain</b>.
     2036</OL>
     2037
     2038<H3>4. Perform additional fit</H3>
     2039
     2040<P></P><p class=MsoListParagraphCxSpMiddle>
     2041Starting an additional refinement (using the Calculate/Refine menu item)
     2042with the addition of two more optimized variables to the refinement improves
     2043the fit significantly visually and the Rw value drops to <14%, but the
     2044additon of the new background parameter causes issues with correlation
     2045between the background terms. Considering that we have not refined any
     2046atomic parameters, this is an very good fit despite the seemingly high
     2047Rw value, as shown in the plot below.  Clicking on the
     2048<b>Covariance</b> data tree item shows the
     2049GOF=1.08 and the Reduced &#967;<sup>2</sup>=1.16. This is close to
     2050ideal.
     2051While atomic parameters could now be refined, this is
    19752052clearly a good enough place to start refinement with all the datasets. </p>
    19762053
    1977 <p class=MsoListParagraphCxSpLast><span style='mso-fareast-language:EN-US;
    1978 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_63" o:spid="_x0000_i1051"
    1979  type="#_x0000_t75" style='width:6in;height:370.5pt;visibility:visible;
    1980  mso-wrap-style:square'>
    1981  <v:imagedata src="SequentialTutorial_files/image015.png" o:title=""/>
    1982 </v:shape><![endif]--><![if !vml]><img width=576 height=494
    1983 src="SequentialTutorial_files/image066.png" v:shapes="Picture_x0020_63"><![endif]></span></p>
    1984 
    1985 <h1>Step 2: Prepare for sequential fit. </h1>
    1986 
    1987 <p class=MsoListParagraph><o:p>&nbsp;</o:p></p>
    1988 
    1989 <p class=MsoNormal>There is one significant difference between fitting a
    1990 sequence of datasets versus fitting a single data set. Rather than fitting
     2054<h1>Step III: Prepare for sequential fit. </h1>
     2055
     2056<P></P>
     2057<p class=MsoNormal>
     2058For the initial fitting of datasets over a range of conditions, we
     2059will want to start from the fitted values we have fit, but only refine
     2060a minimal number of parameters until the scale factor, background and
     2061lattice parameters have been optimized for each dataset and more
     2062variables can be added back.
     2063<P></P>
     2064<p class=MsoNormal>There is one significant way that sequential
     2065fitting differs from the usual refinement process. Rather than fitting
    19912066lattice constants (for which there will be only one set for each phase in the
    19922067entire refinement), we will use the Hydrostatic/Elastic strain terms
    1993 (parameters &lt;p&gt;:&lt;h&gt;:Dxx) to treat the change in lattice parameters.
    1994 These items describe the change in lattice parameters and appear in the Phase
    1995 Data tab, where there is a set for each histogram assigned to the phase. We
    1996 will make a switch to use this for the current dataset, in preparation for the
    1997 sequential refinement with all datasets. </p>
    1998 
    1999 <p class=MsoNormal><o:p>&nbsp;</o:p></p>
    2000 
    2001 <p class=MsoNormal>Also at this point we will temporarily remove variables that
    2002 could make the fit diverge as the lattice constants shift. As an example, when
    2003 initially fitting a model with peaks that overlap with the observed peaks, but
    2004 not very well, the fit might be improved by a change in the phase fractions
    2005 (that might eliminate our impurity CuO phase) or make peaks quite a bit broader
    2006 than appropriate, these changes are improbable and could result in a model that
    2007 is less correct than the starting point but still be a local LS minimum. In
    2008 such cases the best-fit model may never be found. Accordingly, we will turn off
    2009 refinement of all parameters except those that determine peak positions (the
    2010 Dxx terms) and the overall scale factor. We might include the background terms
    2011 since they are unlikely to affect convergence. </p>
    2012 
    2013 <p class=MsoNormal><span style='mso-spacerun:yes'> </span></p>
    2014 
    2015 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l7 level1 lfo6'><![if !supportLists]><span
    2016 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1.<span
    2017 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span
    2018 style='mso-bidi-font-weight:bold'>Select the first phase<b> (</b></span><b><span
    2019 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2020 mso-hansi-theme-font:major-latin'>CuCr2O4</span>) </b><span style='mso-bidi-font-weight:
    2021 bold'>and on the<b> </b></span><b><span style='font-family:"Calibri",sans-serif;
    2022 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>General</span>
    2023 </b><span style='mso-bidi-font-weight:bold'>tab</span>, click on the <b
    2024 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2025 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Refine unit
    2026 cell</span></b> option to <span style='mso-bidi-font-weight:bold'>turn off
    2027 refinement</span>. </p>
     2068(parameters <tt>&lt;p&gt;:&lt;h&gt;:D<I>ij</i></tt>) to treat the change in
     2069lattice parameters from histgram to histogram.
     2070
     2071<P></P>
     2072<p class=MsoNormal><I>
     2073Note that GSAS-II shows the user unit cell parameters in the
     2074traditional a, b, c, &#945;, &#946; & &#947; (distances in &#8491, angles in
     2075degrees), but computations are performed internally only
     2076after converting this cell to
     2077a version of the reciprocal lattice tensor we call the "A tensor" or
     2078the <tt>A<i>j</i></tt> terms (<a
     2079href="https://gsas-ii.readthedocs.io/en/latest/GSASIIutil.html#gsasiilattice-unit-cells">see
     2080the GSASIIlattice documentation<a/>).
     2081The actual values refined in GSAS-II are the <tt>A<i>j</i></tt> terms, as
     2082allowed by unit cell symmetry. There is one set of <tt>A<i>j</i></tt> values
     2083for each phase, but to treat the situation where the use of a phase in
     2084each histogram may have somewhat different lattice parameters (<a
     2085href="https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/CWCombined/Combined%20refinement.htm">see
     2086the PbSO<sub>4</sub> combined fitting tutorial</a>, where the x-ray and
     2087neutron data were collected at different temperatures), GSAS-II
     2088defines <tt>D<I>ij</i></tt> terms, labeled as "Hydrostatic/elastic
     2089strain coefficients",  for each phase in each histogram and only the unique
     2090terms are shown on the Phase "Data" tab. These values
     2091are simply added to the <tt>A<i>j</i></tt> terms. When any <tt>D<I>ij</i></tt>
     2092terms are non-zero, the changed unit cell parameters are also shown on
     2093the "Data" tab and will differ from the unit cell values shown on the
     2094"General" tab.
     2095</I>
     2096
     2097
     2098<H3>1. Remove refinement of sensitive parameters (lattice, phase
     2099fractions, size/&#956;strain, background peak and sample displacement)
     2100and add refinement of the <tt>D<I>ij</i></tt> terms.</H3>
     2101
     2102<OL style='PADDING-LEFT:0.75in' type="A">
     2103<LI>
     2104Select the first phase (<B>CuCr2O4</B>) and on the <B>General</B> tab,
     2105click on the <B>Refine unit cell</B> option to turn off refinement. </P>
    20282106
    20292107<p class=MsoListParagraphCxSpMiddle><span style='mso-spacerun:yes'> </span><span
     
    20352113src="SequentialTutorial_files/image067.png" v:shapes="Picture_x0020_64"><![endif]></span></p>
    20362114
    2037 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    2038 
    2039 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l7 level1 lfo6'><![if !supportLists]><span
    2040 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span
    2041 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>On
    2042 the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2043 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Data</span></b>
    2044 tab, select <span style='mso-bidi-font-weight:bold'>the<b> </b></span><b><span
    2045 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2046 mso-hansi-theme-font:major-latin'>D11</span></b><span style='mso-bidi-font-weight:
    2047 bold'>, </span><b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2048 major-latin;mso-hansi-theme-font:major-latin'>D22</span></b><span
    2049 style='mso-bidi-font-weight:bold'> and </span><b><span style='font-family:"Calibri",sans-serif;
    2050 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>D33</span></b><span
    2051 style='mso-bidi-font-weight:bold'> terms</span> to refine the lattice strain
    2052 terms. While here, to simplify convergence for the sequential refinement, where
    2053 lattice constants change significantly, <B>turn
    2054 off</B> the refinement of the <b>three size and mustrain terms and the phase fraction</b>.
    2055 The <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2056 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Data</span></b>
    2057 window should look something like</p>
     2115  <P></P>
     2116  <LI>On the Data tab (for <B>CuCr2O4</B>), turn <U>off</U> refinement of the <B>Phase
     2117  fraction</B>, the <b>size</b> and both the <b>mustrain</b>
     2118  parameters. Turn <U>on</U> refinement of the <B>D11, D22</B> and
     2119  <B>D33</B> terms to allow the combined lattice parameters to vary.
     2120  The Data window should look something like
     2121  </p>
    20582122
    20592123<p class=MsoListParagraphCxSpMiddle><span style='mso-spacerun:yes'> </span><span
     
    20652129src="SequentialTutorial_files/image068.png" v:shapes="Picture_x0020_65"><![endif]></span></p>
    20662130
    2067 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    2068 
    2069 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l7 level1 lfo6'><![if !supportLists]><span
    2070 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3.<span
    2071 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span
    2072 style='mso-bidi-font-weight:bold'>Click on the second phase</span> (<b
    2073 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2074 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>CuO</span></b>)
    2075 and on the <b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2076 major-latin;mso-hansi-theme-font:major-latin'>General</span></b><span
    2077 style='mso-bidi-font-weight:bold'> tab</span>, click on the <b><span
    2078 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2079 mso-hansi-theme-font:major-latin'>Refine unit cell</span></b><span
    2080 style='mso-bidi-font-weight:bold'> option</span> to turn off refinement. </p>
    2081 
    2082 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    2083 
    2084 <p class=MsoListParagraphCxSpMiddle>On the <b><span style='font-family:"Calibri",sans-serif;
    2085 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Data</span></b><span
    2086 style='mso-bidi-font-weight:bold'> tab</span> for CuO, <span style='mso-bidi-font-weight:
    2087 bold'>click on the </span><b><span style='font-family:"Calibri",sans-serif;
    2088 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>D11</span></b><span
    2089 style='mso-bidi-font-weight:bold'>, </span><b><span style='font-family:"Calibri",sans-serif;
    2090 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>D22</span></b><span
    2091 style='mso-bidi-font-weight:bold'>, and </span><b><span style='font-family:
    2092 "Calibri",sans-serif;mso-ascii-theme-font:major-latin;mso-hansi-theme-font:
    2093 major-latin'>D33</span></b><span style='mso-bidi-font-weight:bold'> terms</span>
    2094 to refine the lattice strain terms and <span style='mso-bidi-font-weight:bold'>turn
    2095 off refinement of the phase fraction</span>.<span style='mso-spacerun:yes'> 
    2096 </span>We could refine the <b style='mso-bidi-font-weight:normal'><span
    2097 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2098 mso-hansi-theme-font:major-latin'>D13</span></b> term (which corresponds to the
    2099 CuO &#946;* angle), but we do not expect this to change much and expect the
    2100 refinement to be relatively insensitive to this, due to the small number of CuO
    2101 peaks that are in the pattern.)</p>
    2102 
    2103 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     2131  <P></P>
     2132  <LI>
     2133  Select the second phase (<B>CuO</B>) and on the
     2134Data tab (since that is shown first), turn <U>off</U> refinement of the <B>Phase
     2135  fraction</B> and the <b>microstrain</b>
     2136  parameters. Turn <U>on</U> refinement of the <B>D11, D22</B> and
     2137  <B>D33</B> terms to allow the combined lattice parameters to
     2138  vary. We could refine the <B>D13</B> term [which is related to
     2139  cos(&#946*) angle for CuO] but the changes to this are small and
     2140  since this is a minor phase and few CuO peaks are seen, it is best
     2141  to not vary this, at least initially.  The Data window should look
     2142  something like </P>
    21042143
    21052144<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
     
    21112150src="SequentialTutorial_files/image069.png" v:shapes="Picture_x0020_66"><![endif]></span></p>
    21122151
    2113 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    2114 
    2115 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l7 level1 lfo6'><![if !supportLists]><span
    2116 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>4.<span
    2117 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Also
    2118 at this stage, <span style='mso-bidi-font-weight:bold'>turn off the all the
    2119 background refinement terms</span> by clicking on <b style='mso-bidi-font-weight:
    2120 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2121 major-latin;mso-hansi-theme-font:major-latin'>Background</span></b> on the
    2122 histogram tree item and removing checks from all items (be sure to click
    2123 elsewhere in the window before going on to the next step.) </p>
    2124 
    2125 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     2152  <P></P>
     2153<LI> On the <B>General</B> tab for CuO,
     2154click on the <B>Refine unit cell</B> option to turn off refinement of
     2155that.
     2156
     2157  <P></P>
     2158<LI> Also
     2159at this stage, turn off
     2160refinement of the background peak refinement position and width (sig)
     2161terms by clicking on the <b>Background</b> histogram tree item and removing
     2162checks from the first and third items in the background peaks table
     2163(which has only one row). Be sure to click
     2164elsewhere in the window before going on to the next step. </p>
    21262165
    21272166<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
     
    21332172src="SequentialTutorial_files/image070.png" v:shapes="Picture_x0020_67"><![endif]></span></p>
    21342173
    2135 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    2136 
    2137 <p class=MsoListParagraphCxSpMiddle>Likewise, for the histogram Sample
    2138 Parameters, <span style='mso-bidi-font-weight:bold'>turn off the<b> </b></span><b><span
    2139 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2140 mso-hansi-theme-font:major-latin'>Sample X displ.</span> </b><span
    2141 style='mso-bidi-font-weight:bold'>parameter</span> by clicking on the <b
    2142 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2143 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Sample
    2144 Parameters</span></b> item in the histogram entries.</p>
     2174  <P></P>
     2175<LI>Likewise, select the histogram <B>Sample Parameters</B> tree entry
     2176and on that window, turn off the refinement flag for <b>Sample X displ.</b>
     2177</p>
    21452178
    21462179<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
     
    21522185src="SequentialTutorial_files/image025.png" v:shapes="Picture_x0020_68"><![endif]></span></p>
    21532186
    2154 <p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l7 level1 lfo6'><![if !supportLists]><span
    2155 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>5.<span
    2156 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>One
    2157 can confirm that the number of parameters is now 7 (3 Dxx terms for phase 1, 3
    2158 Dxx terms for phase 2 and a scale factor.) If the refinement is repeated, the
    2159 fit quality does not change, since these parameters are completely equivalent
    2160 to the previous. There may result in very small non-zero values for the Dxx
    2161 parameters, but these are much smaller than their uncertainties and are thus
    2162 within noise of zero. </p>
    2163 
    2164 <h1>Step 3: Import the remaining datasets.</h1>
     2187  <P></P>
     2188<LI>At this point the refinement could be repeated to show that the
     2189fit does not change significantly. If this is done, one will see
     2190small non-zero values for the <tt>D<I>ij</i></tt> terms, but the unit
     2191cell parameters displayed on the "Data" tab are not significantly
     2192different from those computed without the <tt>D<I>ij</i></tt> values
     2193shown on the "General" tab, but due to the larger uncertainties on the
     2194CuO unit cell parameters, the <tt>D<I>ij</i></tt> terms are much
     2195larger than for CuCr2O4.
     2196
     2197</OL>
     2198
     2199<h1>Step IV: Import the remaining datasets.</h1>
    21652200
    21662201<p class=MsoNormal><o:p>&nbsp;</o:p></p>
    21672202
    2168 <p class=MsoNormal>In this step we bring in the remaining data, duplicate the
    2169 histogram parameters as well as the phase/histogram parameters and set up to
    2170 perform a sequential fit. </p>
    2171 
    2172 <p class=MsoNormal><o:p>&nbsp;</o:p></p>
    2173 
    2174 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l2 level1 lfo8'><![if !supportLists]><span
    2175 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1.<span
    2176 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>The
    2177 remaining datasets are read <span style='mso-bidi-font-weight:bold'>using<b> </b></span><b><span
    2178 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2179 mso-hansi-theme-font:major-latin'>Import/Powder Data/from GSAS powder data file</span></b>
    2180 to open a file browser. Again <span style='mso-bidi-font-weight:bold'>select<b>
    2181 </b></span><b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2182 major-latin;mso-hansi-theme-font:major-latin'>zip archive</span> </b><span
    2183 style='mso-bidi-font-weight:bold'>and the downloaded<b> </b></span><b><span
    2184 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2185 mso-hansi-theme-font:major-latin'>SeqTut.zip</span></b> file. <span
    2186 style='mso-bidi-font-weight:bold'>Select all the .</span><b><span
    2187 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2188 mso-hansi-theme-font:major-latin'>fxye</span></b><span style='mso-bidi-font-weight:
    2189 bold'> files</span> except <b style='mso-bidi-font-weight:normal'><span
    2190 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2191 mso-hansi-theme-font:major-latin'>OH_00.fxye</span></b> (use of the filter can
    2192 again be helpful to show just the data file; press <b style='mso-bidi-font-weight:
    2193 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2194 major-latin;mso-hansi-theme-font:major-latin'>Set All</span></b> and then
    2195 unselect the one unneeded file). </p>
     2203<p class=MsoNormal>In this step we bring in the remaining data.
     2204Note that the values for the parameters for the newly-read histograms
     2205(on the Sample Parameters data item) and the phase/histogram
     2206parameters on each phase's Data tab are set to default values, so we
     2207copy the values from the first histogram to the new sets.
     2208We can then perform an initial sequential fit. </p>
     2209
     2210<H3>1. Read the remaining datasets.</H3>
     2211
     2212<P></P>
     2213<OL style='PADDING-LEFT:0.75in' type="A"><LI>
     2214  Read the
     2215remaining datasets using the <B>Import/Powder Data/from GSAS powder data file</span></b>
     2216to open a file browser. Again select <b>zip archive</b>
     2217and the downloaded <b>SeqTut.zip</b> file. Select all the <b>.fxye</b>
     2218files except <b>OH_00.fxye</b> (use of the filter can
     2219again be helpful to show just the data files; press <b>Set All</b> and then
     2220unselect the one unneeded file or equivalently one can select only the
     2221<b>OH_00.fxye</b> file and press <b>Toggle All</b>). The press OK to
     2222start reading the datasets.</p>
    21962223
    21972224<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
     
    22032230src="SequentialTutorial_files/image026.png" v:shapes="Picture_x0020_69"><![endif]></span></p>
    22042231
    2205 <p class=MsoListParagraphCxSpMiddle>This time one must <span style='mso-bidi-font-weight:
    2206 bold'>select the instrument parameter file</span>. </p>
     2232<P></P>
     2233  <LI>This time one must select the
     2234instrument parameter file (because the name does not match the dataset
     2235file name). </p>
    22072236
    22082237<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
     
    22142243src="SequentialTutorial_files/image071.png" v:shapes="Picture_x0020_70"><![endif]></span></p>
    22152244
    2216 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    2217 
    2218 <p class=MsoListParagraphCxSpMiddle><span style='mso-bidi-font-weight:bold'>Set
    2219 all data sets to use the two phases</span>, as before in step 1 #6. </p>
    2220 
    2221 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     2245<P></P>
     2246  <LI>Set
     2247all data sets to use the two phases</span>, as before in <A href="#I.2.C">
     2248 step I.2.C</A> (above).</LI>
    22222249
    22232250<p class=MsoListParagraphCxSpMiddle>Note that the files will be
     
    22292256correct order in the file browser. If files are not read in the
    22302257intended order, it will be necessary to
    2231 manually change the positions of the tree items (by dragging them with
     2258manually change the positions of the tree items (by dragging them in
     2259 the tree with
    22322260the right mouse button pressed).
    2233 This is not an issue in this example, since the files are listing in a
     2261This is not an issue in this example, since the files are listed in a
    22342262zip file in the order they need to be read, but may be of concern
    22352263for other cases.
    22362264</p>
    22372265
    2238 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    2239 
    2240 <p class=MsoListParagraphCxSpMiddle>Optional: Note that the default graphics
     2266<P></P><LI>Optional: Note that the default graphics
    22412267mode is to display the last dataset read in.<span style='mso-spacerun:yes'> 
    22422268</span>If you want to see the entire ensemble of data sets, click on the main
     
    22722298src="SequentialTutorial_files/image072.png" v:shapes="Picture_x0020_71"><![endif]></span></p>
    22732299
    2274 <p class=MsoListParagraphCxSpMiddle>You can then select the ‘<b
     2300<P></P><LI>You can then select the ‘<b
    22752301style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    22762302mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>C</span></b>’
     
    22902316src="SequentialTutorial_files/image073.png" v:shapes="Picture_x0020_72"><![endif]></span></p>
    22912317
    2292 <p class=MsoListParagraphCxSpLast>I’ve use ‘<b style='mso-bidi-font-weight:
     2318<p class=MsoListParagraphCxSpLast>Above, I’ve used ‘<b style='mso-bidi-font-weight:
    22932319normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    22942320major-latin;mso-hansi-theme-font:major-latin'>D</span></b>’ to increase the
    22952321contrast &amp; zoomed in to a location that shows the effect of temperature on
    22962322the peak positions.</p>
    2297 
    2298 <h1>Step 4: Duplicate information across histograms.</h1>
    2299 
    2300 <p class=MsoNormal><o:p>&nbsp;</o:p></p>
    2301 
    2302 <p class=MsoNormal>In this step we bring in the remaining data, duplicate the histogram
    2303 parameters as well as the phase/histogram parameters and set up to perform a
    2304 sequential fit. </p>
    2305 
    2306 <p class=MsoListParagraphCxSpFirst><o:p>&nbsp;</o:p></p>
    2307 
    2308 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l5 level1 lfo10'><![if !supportLists]><span
    2309 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1.<span
    2310 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Copy
    2311 the histogram parameters from the first histogram to the new ones: <span
    2312 style='mso-bidi-font-weight:bold'>Select the original </span><b><span
    2313 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2314 mso-hansi-theme-font:major-latin'>PWDR OH_00.fxye Bank 1</span></b><span
    2315 style='mso-bidi-font-weight:bold'> entry</span>. Use menu command <b><span
    2316 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2317 mso-hansi-theme-font:major-latin'>Commands/Copy params</span></b>. </p>
     2323</OL>
     2324<h3>2. Duplicate information across histograms.</h3>
     2325
     2326<P></P>
     2327<OL style='PADDING-LEFT:0.75in' type="A"><LI>
     2328To copy
     2329the histogram parameters from the first histogram to the new ones:
     2330  select the original <B>PWDR OH_00.fxye Bank 1</b> tree entry and then
     2331  use menu command <b>Commands/Copy params</b>.
     2332  We need to duplicate the values in the <b>Limits</b>,
     2333  <b>Background</b> and <b>Sample Parameters</b> sections between all
     2334  histograms. The <b>Instrument Parameters</b> have been read from the
     2335  instrument parameter file, and have not been changed in this
     2336  exercise, so they are already identical.
    23182337
    23192338<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    23202339
    2321 <p class=MsoListParagraphCxSpMiddle>This causes a dialog box where the sections
    2322 to be copied are selected. </p>
     2340<p class=MsoNormal>This opens a dialog box where the sections
     2341to be copied are selected. Limits, Background and Sample Parameters
     2342  must be selected; there will be no difference if Instrument
     2343  Parameters is selected, since the parameters start as identical, so
     2344  there also is no harm in copying them. This, the default entries,
     2345  selecting all sections, need not be changed. </p>
    23232346
    23242347<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
     
    23302353src="SequentialTutorial_files/image033.png" v:shapes="Picture_x0020_73"><![endif]></span></p>
    23312354
    2332 <p class=MsoListParagraphCxSpMiddle>We need to duplicate the <b
    2333 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2334 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Limits</span></b>,
    2335 <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2336 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Background</span></b>
    2337 and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2338 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Sample
    2339 Parameters</span></b> between all histograms. The <b style='mso-bidi-font-weight:
    2340 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2341 major-latin;mso-hansi-theme-font:major-latin'>Instrument Parameters</span></b>
    2342 have not been changed in this exercise and are all read from the same
    2343 instrument parameter file, but there is no harm in copying them, so the default
    2344 entries do not need to be changed. <span style='mso-bidi-font-weight:bold'>Press<b>
    2345 </b></span><b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2346 major-latin;mso-hansi-theme-font:major-latin'>OK</span></b>. Note that all
    2347 parameters are copied except measurement information such as setting angles,
    2348 temperature, etc. </p>
    2349 
    2350 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    2351 
    2352 <p class=MsoListParagraphCxSpMiddle>An additional dialog window is shown which
     2355
     2356<P></P><LI>
     2357  Press <b>OK</B>.
     2358  Note that all Sample Parameters are copied, except measurement
     2359  information such as setting angles, temperature, etc. </LI>
     2360
     2361
     2362<P></P><LI>
     2363  An additional dialog window is shown which
    23532364asks which histograms should receive the parameters. <span style='mso-bidi-font-weight:
    2354 bold'>Press<b> </b></span><b><span style='font-family:"Calibri",sans-serif;
    2355 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Set All</span></b><span
    2356 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2357 mso-hansi-theme-font:major-latin'> </span>to select all remaining histograms
    2358 and then <span style='mso-bidi-font-weight:bold'>press<b> </b></span><b><span
    2359 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2360 mso-hansi-theme-font:major-latin'>OK</span>.</b> </p>
     2365bold'>Press <b>Set All</b> to select all remaining histograms
     2366and then press<b>OK</b>. </LI>
    23612367
    23622368<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     
    23702376src="SequentialTutorial_files/image034.png" v:shapes="Picture_x0020_74"><![endif]></span></p>
    23712377
    2372 <p class=MsoListParagraphCxSpLast>That the copy has been performed can be
    2373 demonstrated by examining any of the other histogram plots (e.g. to see the
    2374 changed lower limit), etc. Next we need to copy the Phase/Histogram parameters
    2375 within each phase. </p>
    2376 
    2377 <p class=MsoNormal><o:p>&nbsp;</o:p></p>
    2378 
    2379 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l5 level1 lfo10'><![if !supportLists]><span
    2380 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span
    2381 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span
    2382 style='mso-bidi-font-weight:bold'>Select the first phase</span> (<b
    2383 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2384 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>CuCr2O4</span></b>)
    2385 and its <b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2386 major-latin;mso-hansi-theme-font:major-latin'>Data</span></b><span
    2387 style='mso-bidi-font-weight:bold'> tab</span>. Then do <b style='mso-bidi-font-weight:
    2388 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2389 major-latin;mso-hansi-theme-font:major-latin;mso-bidi-theme-font:major-latin'>Edit
    2390 Phase/</span></b><b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2391 major-latin;mso-hansi-theme-font:major-latin'>Copy data</span></b></p>
     2378<P></P><p class=MsoListParagraphCxSpLast>To verify that the copy has
     2379been performed, examining any of the other histogram plots (e.g. to see the
     2380changed lower limit), etc. or view the contents of the various updated sections.
     2381
     2382
     2383<P></P><LI>
     2384Next we need to copy the Phase/Histogram parameters
     2385within each phase. To do this, select the first phase (<b>CuCr2O4</b>)
     2386in the data tree
     2387and then the <b>Data</b> tab in the window. Then use the <b>Edit Phase/Copy data</b> menu
     2388command, which raises the selction window below.
     2389</LI>
    23922390
    23932391<p class=MsoListParagraphCxSpMiddle><span style='mso-spacerun:yes'> </span><span
     
    23992397src="SequentialTutorial_files/image035.png" v:shapes="Picture_x0020_75"><![endif]></span></p>
    24002398
    2401 <p class=MsoListParagraphCxSpMiddle>a dialog window appears to select where to
    2402 copy the parameters. Press the <b><span style='font-family:"Calibri",sans-serif;
    2403 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Set All</span></b>
    2404 button and then <span style='mso-bidi-font-weight:bold'>press<b> </b></span><b><span
    2405 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2406 mso-hansi-theme-font:major-latin'>OK</span></b>.</p>
    2407 
    2408 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    2409 
    2410 <p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l5 level1 lfo10'><![if !supportLists]><span
    2411 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3.<span
    2412 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span
    2413 style='mso-bidi-font-weight:bold'>Copy the Phase/Histogram parameters within
    2414 the second phase</span> by clicking on it (<b style='mso-bidi-font-weight:normal'><span
    2415 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2416 mso-hansi-theme-font:major-latin'>CuO</span></b>) in the data tree (and
    2417 possibly on the <b style='mso-bidi-font-weight:normal'><span style='font-family:
    2418 "Calibri",sans-serif;mso-ascii-theme-font:major-latin;mso-hansi-theme-font:
    2419 major-latin'>Data</span></b> tab.) Then do <b style='mso-bidi-font-weight:normal'><span
    2420 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2421 mso-hansi-theme-font:major-latin;mso-bidi-theme-font:major-latin'>Edit
    2422 Phase/Copy data</span></b> from the menu<b> </b>and <span style='mso-bidi-font-weight:
    2423 bold'>select the histograms</span> as done in the previous step</p>
    2424 
    2425 <h1>Step 5: Setup and start the sequential refinement. </h1>
     2399<P></P>
     2400<p class=MsoListParagraphCxSpMiddle>
     2401Press the <b>Set All</b> button and then press the <b>OK</b> button.</p>
     2402
     2403<P></P><LI>
     2404Repeat the previous step for the CuO phase.
     2405Select <B>CuO</B> in the data tree and then copy the Phase/Histogram
     2406parameters in its <b>Data</b> tab by again using the <b>Edit
     2407Phase/Copy data</b> menu command. Again, select all histograms and
     2408then press the <b>OK</b> button.
     2409</LI>
     2410</OL>
     2411
     2412
     2413<h1>Step V: Setup and start the sequential refinement. </h1>
    24262414
    24272415<p class=MsoNormal><o:p>&nbsp;</o:p></p>
     
    24312419will be used for the subsequent refinements.</p>
    24322420
    2433 <p class=MsoNormal><o:p>&nbsp;</o:p></p>
    2434 
    2435 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo12'><![if !supportLists]><span
    2436 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1.<span
    2437 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>First,
    2438 <span style='mso-bidi-font-weight:bold'>select the<b> </b></span><b><span
    2439 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2440 mso-hansi-theme-font:major-latin'>Controls</span> </b><span style='mso-bidi-font-weight:
    2441 bold'>item</span> in the data tree and press the <b><span style='font-family:
    2442 "Calibri",sans-serif;mso-ascii-theme-font:major-latin;mso-hansi-theme-font:
    2443 major-latin'>Select data</span> </b><span style='mso-bidi-font-weight:bold'>button</span>.
    2444 </p>
     2421<H3>1. Set overall Controls for a sequential fit and launch it</H3>
     2422
     2423<P></P>
     2424<p class=MsoListParagraphCxSpMiddle>Here we enable sequential mode by
     2425setting the histograms to be included, set another control setting
     2426(max cycles) and launch the sequential fit.
     2427
     2428<OL style='PADDING-LEFT:0.75in' type="A"><LI>
     2429Select the <B>Controls</b> data tree item, in the window (as shown
     2430below) and press the "Sequential Refinement
     2431<b>Select data</b>" button.
     2432
    24452433
    24462434<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
     
    24522440src="SequentialTutorial_files/image074.png" v:shapes="Picture_x0020_76"><![endif]></span></p>
    24532441
    2454 <p class=MsoListParagraphCxSpMiddle>This opens a window where all histograms can
    2455 be selected (it would be equally valid to skip the first histogram, since that
    2456 has already been fully fit). <span style='mso-bidi-font-weight:bold'>Press<b> </b></span><b><span
    2457 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2458 mso-hansi-theme-font:major-latin;mso-bidi-theme-font:major-latin'>Set All</span>
    2459 </b><span style='mso-bidi-font-weight:bold'>and then<b> </b></span><b><span
    2460 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2461 mso-hansi-theme-font:major-latin'>OK</span></b> and note that the <b
    2462 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2463 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Controls</span></b>
    2464 window now lists the number of datasets in the sequential refinement and two
    2465 new controls. </p>
     2442<P></P>
     2443<p class=Msonormal>This opens the window where
     2444all histograms can be selected. Press <b>Set All</b> and then press
     2445<B>OK</B>. Note that the Controls window now lists the number of
     2446datasets in the sequential refinement and three new controls below
     2447  that. One is the new "Reverse order?" checkbox, which causes
     2448the sequential refinement to start with the last histogram, not the first.
     2449Sometimes this is useful, but not here. The "Clear previous
     2450  seq. results" will remove previous sequential results from a .gpx
     2451  file, reducing its size. The "Copy results to next histogram?" is
     2452  described in the next section. 
    24662453
    24672454<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
     
    24732460src="SequentialTutorial_files/image075.png" v:shapes="Picture_x0020_77"><![endif]></span></p>
    24742461
    2475 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    2476 
    2477 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo12'><![if !supportLists]><span
    2478 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span
    2479 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span
    2480 style='mso-bidi-font-weight:bold'>Check the<b> </b></span><b><span
    2481 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2482 mso-hansi-theme-font:major-latin'>Copy results to next histogram</span> </b><span
    2483 style='mso-bidi-font-weight:bold'>checkbox</span>. This is essential. If this
    2484 is not selected, then every refinement will start with the current parameters
    2485 (which are all identical, since they were set with the Copy operations.) The
    2486 first few refinements will go well, but after the temperature has changed
    2487 enough, the starting lattice parameters (determined from the cell and Dxx
    2488 values) will be too far off and the refinements will fail. </p>
    2489 
    2490 <p class=MsoListParagraphCxSpMiddle><span style='mso-spacerun:yes'> </span></p>
    2491 
    2492 <p class=MsoListParagraphCxSpMiddle>Note that the Reverse order checkbox causes
    2493 the sequential refinement to start with the last histogram, not the first.
    2494 Sometimes this is useful, but not here. </p>
    2495 
    2496 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    2497 
    2498 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo12'><![if !supportLists]><span
    2499 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3.<span
    2500 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span
    2501 style='mso-bidi-font-weight:bold'>Change </span><b><span style='font-family:
    2502 "Calibri",sans-serif;mso-ascii-theme-font:major-latin;mso-hansi-theme-font:
    2503 major-latin'>Max cycles</span></b><span style='mso-bidi-font-weight:bold'> to<b>
    2504 </b></span><b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2505 major-latin;mso-hansi-theme-font:major-latin'>10</span>.</b> This is important,
    2506 so that refinements have enough cycles to fully adjust to the changes in
    2507 lattice parameters before being used as the starting point for the next
    2508 refinement. </p>
    2509 
    2510 <p class=MsoListParagraphCxSpMiddle><span style='mso-spacerun:yes'> </span></p>
    2511 
    2512 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo12'><![if !supportLists]><span
    2513 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>4.<span
    2514 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Start
    2515 the sequential refinement with <b><span style='font-family:"Calibri",sans-serif;
    2516 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Calculate/Sequential
    2517 refine</span></b><span style='mso-bidi-font-weight:bold'>; this will take some
    2518 time as the refinement works its way through all the histograms.</span></p>
    2519 
    2520 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    2521 
    2522 <p class=MsoListParagraphCxSpMiddle>Note that if the copy operations in <b
    2523 style='mso-bidi-font-weight:normal'>Step 4</b> were not performed correctly,
    2524 the parameters in each refinement will not agree and the refinement will stop
    2525 with an error such as this: </p>
    2526 
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    2537   mso-wrap-distance-bottom:0;mso-position-horizontal:absolute;
    2538   mso-position-horizontal-relative:text;mso-position-vertical:absolute;
    2539   mso-position-vertical-relative:text;mso-width-percent:0;mso-height-percent:0;
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    2574 " filled="f" strokecolor="#4f81bd">
    2575   <v:path arrowok="t"/>
    2576   <v:textbox>
    2577    <![if !mso]>
    2578    <table cellpadding=0 cellspacing=0 width="100%">
    2579     <tr>
    2580      <td><![endif]>
    2581      <div>
    2582      <p class=MsoNormal><span style='font-size:10.0pt;font-family:Courier'>****
    2583      ERROR - variable list for this histogram does not match previous<o:p></o:p></span></p>
    2584      <p class=MsoNormal><span style='font-size:10.0pt;font-family:Courier'><o:p>&nbsp;</o:p></span></p>
    2585      <p class=MsoNormal><span style='font-size:10.0pt;font-family:Courier'>current
    2586      histogram PWDR OH_04.fxye Bank 1 has 6 variables<o:p></o:p></span></p>
    2587      <p class=MsoNormal><span style='font-size:10.0pt;font-family:Courier'>Variables
    2588      in previous but not in current: 1::D22, 1::D33, 1::D11, <o:p></o:p></span></p>
    2589      <p class=MsoNormal><span style='font-size:10.0pt;font-family:Courier'><o:p>&nbsp;</o:p></span></p>
    2590      <p class=MsoNormal><span style='font-size:10.0pt;font-family:Courier'>Previous
    2591      refinement has 7 variables<o:p></o:p></span></p>
    2592      <p class=MsoNormal><span style='font-size:10.0pt;font-family:Courier'>Variables
    2593      in current but not in previous: 1::Scale, 1::Mustrain;i, <o:p></o:p></span></p>
    2594      <p class=MsoNormal><span style='font-family:"Cambria",serif'><o:p>&nbsp;</o:p></span></p>
    2595      </div>
    2596      <![if !mso]></td>
    2597     </tr>
    2598    </table>
    2599    <![endif]></v:textbox>
    2600   <w:wrap type="topAndBottom"/>
    2601  </v:shape><![endif]--><![if !vml]><span style='mso-ignore:vglayout'>
    2602  <table cellpadding=0 cellspacing=0>
    2603   <tr>
    2604    <td width=48 height=0></td>
    2605   </tr>
    2606   <tr>
    2607    <td></td>
    2608    <td><img width=572 height=108 src="SequentialTutorial_files/image076.png"
    2609    alt="Text Box: **** ERROR - variable list for this histogram does not match previous&#13;&#10;&#13;&#10;current histogram PWDR OH_04.fxye Bank 1 has 6 variables&#13;&#10;Variables in previous but not in current: 1::D22, 1::D33, 1::D11, &#13;&#10;&#13;&#10;Previous refinement has 7 variables&#13;&#10;Variables in current but not in previous: 1::Scale, 1::Mustrain;i, &#13;&#10;&#13;&#10;"
    2610    v:shapes="Text_x0020_Box_x0020_3"></td>
    2611   </tr>
    2612  </table>
    2613  </span><![endif]><!--[if gte vml 1]></o:wrapblock><![endif]--><br
    2614 style='mso-ignore:vglayout' clear=ALL>
    2615 (This error results if the parameters for the second phase were not copied in
    2616 part 3 so that the phase fraction and strain broadening are retained for all
    2617 but the first histogram and the 1::D<i style='mso-bidi-font-style:normal'>ii</i>
    2618 terms are only included the first.)</p>
    2619 
    2620 <h1>Step 6: Examine the sequential refinement results.</h1>
    2621 
    2622 <p class=MsoListParagraphCxSpFirst><o:p>&nbsp;</o:p></p>
    2623 
    2624 <p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l3 level1 lfo14'><![if !supportLists]><span
    2625 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1.<span
    2626 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>When
    2627 the refinement completes, a window will be displayed where you are asked if you
    2628 want to load the results:</p>
     2462<P></P><LI>
     2463  Check the "<b>Copy results to next histogram</b>?" checkbox. When this
     2464  is selected, the parameters obtained after fitting each histogram
     2465  will be used as the starting point for the next fit, which is
     2466  essential here since the lattice parameters change considerably. If
     2467  this were not selected, then refinement of each histogram would
     2468  start with the current parameters -- that were obtained from fitting
     2469  the first (~7 K) dataset.
     2470  The first few refinements will go well, but when reaching datasets
     2471  where the temperature
     2472  was sufficiently different from 7 K, the starting lattice parameters may be
     2473  too far off and the refinements will fail. Even if that were not
     2474  true, since the temperatures increase in the series, the previous
     2475  histogram will have the closest set of lattice parameters and will
     2476  thus refine most quickly. </p>
     2477
     2478<P></P><LI>Also on the Controls window, change the <B>Max cycles</B>
     2479setting to <B>10</B>. This makes sure that the refinements have enough
     2480cycles to fully adjust to the changes in lattice parameters before
     2481being used as the starting point for the next refinement. Note that
     2482if the refinement converges, no additional cycles are used, so 10 is a
     2483maximum that is not likely to be reached.
     2484</LI>
     2485
     2486</OL>
     2487
     2488<H3>2. Start the sequential refinement</H3>
     2489
     2490
     2491<p class=MsoListParagraphCxSpMiddle>Start the sequential refinement
     2492with the <b>Calculate/Sequential refine</b> menu command (note that
     2493once the histograms were selected for a sequential fit in the previous
     2494step, the menu command was relabeled from Calculate/Sequential
     2495refine.) The refinement may take a few minutes as each of the 17
     2496datasets are fit in turn.</p>
     2497
     2498
     2499<h3>3. Accept the sequential refinement results.</h3>
     2500
     2501<p class=MsoListParagraphCxSpMiddle>When the refinement completes, a window will be displayed where you
     2502are asked if you want to load the results, as below.
    26292503
    26302504<p class=MsoNormal style='text-indent:.5in'><span style='mso-fareast-language:
     
    26362510src="SequentialTutorial_files/image041.png" v:shapes="Picture_x0020_78"><![endif]></span></p>
    26372511
    2638 <p class=MsoListParagraphCxSpFirst><span style='mso-bidi-font-weight:bold'>After
    2639 doing </span><b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2640 major-latin;mso-hansi-theme-font:major-latin'>OK</span></b>, the <b
    2641 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2642 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Sequential
    2643 Results</span></b> item in the data tree is automatically selected, which
    2644 displays a summary of the refinement results as a large table. </p>
    2645 
    2646 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     2512<P></P>
     2513<p class=MsoListParagraphCxSpFirst>After clicking on <B>OK</B>
     2514the Sequential Results item is created in the data tree and is is
     2515selected, which displays a summary of the refinement results as a
     2516large table, as below.</p>
     2517
    26472518
    26482519<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
     
    26622533been fit). The &#916;&#967;<sup>2</sup> value in the third column shows the
    26632534percent improvement in &#967;<sup>2</sup> seen in the last cycle of refinement.
    2664 (If this changes from 4.1 to 4.0, then the value will be 100*(4.1-4.0)/4.0, or
    2665 2.5). Since the convergence criterion in the controls is 0.0001 (or 0.01%) we
    2666 can see that only one refinement failed to converge. However, these shifts are
    2667 still quite small, so that there is no reason to provide further cycles of
    2668 refinement without adding new variable parameters. </p>
     2535(Meaning that if in that cycle the &#916;&#967;<sup>2</sup> value
     2536decreases from 4.1 to 4.0, then the value will be 100*(4.1-4.0)/4.0, or
     25372.5%; small numbers indicate that the fit converged.). Note that the
     2538fits had pretty well stopped improving, so there is no reason to
     2539provide further cycles of refinement without adding new variable
     2540parameters. </p>
    26692541
    26702542<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     
    26722544<p class=MsoListParagraphCxSpMiddle>Subsequent columns will show any of the
    26732545sample parameters that vary across the datasets, here only temperature and then
    2674 the direct cell lattice constants for each phase, generated from the A<i
    2675 style='mso-bidi-font-style:normal'>x</i> and D<i style='mso-bidi-font-style:
    2676 normal'>ij</i> terms. Scrolling further shows the values of each refined
    2677 parameter. </p>
    2678 
    2679 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     2546the direct cell lattice constants for each phase, generated from the A<i>x</i> and D<i>ij</i> terms. Scrolling further shows columns the values of most
     2547parameters that differ by histogram. Note that some parameters (such
     2548as the actual D<i>ij</i> terms) are not shown. The choices for which
     2549items that are included is determined by the "Hide columns..." command in
     2550the"Columns/Rows" menu.
     2551</p>
     2552
     2553<h3>4. Examine the sequential refinement results.</h3>
    26802554
    26812555<p class=MsoListParagraphCxSpMiddle>Before going further, it is useful to
     
    26872561this plot:</p>
    26882562
    2689 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    2690 
    26912563<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    26922564mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_80" o:spid="_x0000_i1034"
     
    26972569src="SequentialTutorial_files/image078.png" v:shapes="Picture_x0020_80"><![endif]></span></p>
    26982570
    2699 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    2700 
    2701 <p class=MsoListParagraphCxSpMiddle>Pressing the “<b style='mso-bidi-font-weight:
    2702 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2703 major-latin;mso-hansi-theme-font:major-latin'>K</span></b>” icon or <span
    2704 style='mso-bidi-font-weight:bold'>pressing the “</span><b><span
    2705 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2706 mso-hansi-theme-font:major-latin'>s</span></b><span style='mso-bidi-font-weight:
    2707 bold'>” key</span> brings up a menu where the x-axis can be selected as
     2571<P></P>
     2572<p class=MsoListParagraphCxSpMiddle>Pressing the “<b>K</b>” icon or pressing the “<b>s</b>” key brings up a menu where the x-axis can be selected as
    27082573Temperature. If the plot fails to update, click on another column and then
    27092574return to the original column. </p>
    2710 
    2711 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    27122575
    27132576<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
     
    27212584<p class=MsoListParagraphCxSpLast><o:p>&nbsp;</o:p></p>
    27222585
    2723 <h1>Step 7: Continue the sequential refinement. </h1>
     2586<h1>Step VI: Continue the sequential refinement. </h1>
    27242587
    27252588<p class=MsoNormal><o:p>&nbsp;</o:p></p>
    27262589
    2727 <p class=MsoNormal>At this point we choose to continue the refinements from
    2728 their current values (note that the <b style='mso-bidi-font-weight:normal'><span
    2729 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2730 mso-hansi-theme-font:major-latin'>Copy results to next histogram</span></b>
    2731 checkbox is automatically unchecked after a successful sequential refinement)
    2732 including some additional parameters in the refinement. We will do this is a
    2733 few steps. </p>
    2734 
    2735 <p class=MsoListParagraph style='text-indent:-.25in;mso-list:l1 level1 lfo16'><![if !supportLists]><span
    2736 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1.<span
    2737 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span
    2738 style='mso-bidi-font-weight:bold'>Restore the refinement of background
    2739 parameters</span> as before for any one histogram and then <span
    2740 style='mso-bidi-font-weight:bold'>use the<b> </b></span><b><span
    2741 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2742 mso-hansi-theme-font:major-latin'>File/Copy flags</span></b> menu item to copy
    2743 these refinement flags (only) to all other histograms. NB: <b style='mso-bidi-font-weight:
    2744 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2745 major-latin;mso-hansi-theme-font:major-latin'>Copy</span></b> would copy the
    2746 parameter values as well; probably don’t want to do that here. </p>
    2747 
    2748 <p class=MsoNormal><o:p>&nbsp;</o:p></p>
    2749 
    2750 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l1 level1 lfo16'><![if !supportLists]><span
    2751 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span
    2752 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    2753 </span></span></span><![endif]>Likewise, in the Sample Parameters tree item
    2754 <span style='mso-bidi-font-weight:bold'>include the<b> </b></span><b><span
    2755 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2756 mso-hansi-theme-font:major-latin'>Sample X displ</span></b> parameter and again
    2757 use the <b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2758 major-latin;mso-hansi-theme-font:major-latin'>Command/Copy flags</span> </b><span
    2759 style='mso-bidi-font-weight:bold'>menu item<b>.</b></span> </p>
    2760 
    2761 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    2762 
    2763 <p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l1 level1 lfo16'><![if !supportLists]><span
    2764 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3.<span
    2765 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>For
    2766 Phase parameters <span style='mso-bidi-font-weight:bold'> in the Data
    2767 section, add the three
    2768 broadening terms</span> for the CuCr<sub>2</sub>O<sub>4</sub> phase and do <b
    2769 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2770 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin;mso-bidi-theme-font:
    2771 major-latin'>Edit Phase/Copy flags</span></b>. (Important: not Copy!) For the <span
    2772 style='mso-bidi-font-weight:bold'>CuO phase, add refinement of the single sample broadening
    2773 term and the remaining lattice parameter</span> via the <b style='mso-bidi-font-weight:
    2774 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2775 major-latin;mso-hansi-theme-font:major-latin'>D13</span></b> term.<span
    2776 style='mso-spacerun:yes'>  </span>Again, do <b style='mso-bidi-font-weight:
    2777 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2778 major-latin;mso-hansi-theme-font:major-latin;mso-bidi-theme-font:major-latin'>Edit
    2779 Phase/Copy flags</span></b>. Note that an additional step is needed in order to
    2780 vary Phase fractions, as will be discussed below. </p>
    2781 
    2782 <p class=MsoNormal><o:p>&nbsp;</o:p></p>
    2783 
    2784 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l1 level1 lfo16'><![if !supportLists]><span
    2785 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>4.<span
    2786 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Start
    2787 the sequential refinement again with the <b><span style='font-family:"Calibri",sans-serif;
    2788 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Calculate/Sequential
    2789 refine</span> </b><span style='mso-bidi-font-weight:bold'>menu item</span>. The
    2790 fits are significantly improved at higher temperatures, with R<sub>wp</sub>
    2791 values between 13.8 and 17.</p>
    2792 
    2793 <h1>Step 8: Further sequential refinements. </h1>
    2794 
    2795 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    2796 
    2797 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo16'><![if !supportLists]><span
    2798 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>5.<span
    2799 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>We
    2800 can now add the phase fractions into the refinement, by clicking on the <b
    2801 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2802 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Phase
    2803 fraction</span></b> checkbox in the Phase/Data tab. Do this for each
    2804 Phase followed by use of <b style='mso-bidi-font-weight:normal'><span
    2805 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2806 mso-hansi-theme-font:major-latin;mso-bidi-theme-font:major-latin'>Edit Phase/</span></b><b
    2807 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2808 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Copy
    2809 Flags</span></b>. However, a constraint is still needed as before, but
    2810 to be applied to each histogram. Constraints entered with a specific histogram
    2811 number, as was done before, will be ignored. For sequential
    2812 refinements, only constraints where the histogram number is specified
    2813 as "*" are used.
    2814 
    2815 <p class=MsoListParagraphCxSpFirst><o:p>&nbsp;</o:p></p>
    2816 
    2817 <p class=MsoListParagraphCxSpMiddle>To set up the new constraint, <span
    2818 style='mso-bidi-font-weight:bold'>click on the </span><b><span
    2819 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2820 mso-hansi-theme-font:major-latin'>Constraints</span></b><span style='mso-bidi-font-weight:
    2821 bold'> item</span> in the data tree and the <b><span style='font-family:"Calibri",sans-serif;
    2822 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Select tab/Histogram/Phase</span></b><span
    2823 style='mso-bidi-font-weight:bold'> menu item</span>, and then <span
    2824 style='mso-bidi-font-weight:bold'>click on the </span><b><span
    2825 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2826 mso-hansi-theme-font:major-latin'>Edit Constr./Add constraint equation</span></b>
    2827 menu item. From the menu, we either <b><span style='font-family:"Calibri",sans-serif;
    2828 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>0:*:Scale</span></b><span
    2829 style='mso-bidi-font-weight:bold'> or </span><b><span style='font-family:"Calibri",sans-serif;
    2830 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin;mso-bidi-theme-font:
    2831 major-latin'>1:*:Scale</span></b><span style='mso-bidi-font-weight:bold'> wild
    2832 card phase fraction</span>; they are at the bottom of each set </p>
    2833 
    2834 <p class=MsoListParagraphCxSpMiddle><span style='mso-spacerun:yes'> </span><span
    2835 style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2836  id="Picture_x0020_83" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:6in;
    2837  height:276pt;visibility:visible;mso-wrap-style:square'>
    2838  <v:imagedata src="SequentialTutorial_files/image050.png" o:title=""/>
    2839 </v:shape><![endif]--><![if !vml]><img width=576 height=368
    2840 src="SequentialTutorial_files/image081.png" v:shapes="Picture_x0020_83"><![endif]></span></p>
    2841 
    2842 <p class=MsoListParagraphCxSpMiddle>There will only be one possible matching variable
    2843 in the next window, so <span style='mso-bidi-font-weight:bold'>select that and
    2844 press </span><b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2845 major-latin;mso-hansi-theme-font:major-latin'>OK</span></b>.</p>
    2846 
    2847 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    2848 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_84" o:spid="_x0000_i1030"
    2849  type="#_x0000_t75" style='width:6in;height:161.25pt;visibility:visible;
    2850  mso-wrap-style:square'>
    2851  <v:imagedata src="SequentialTutorial_files/image052.png" o:title=""/>
    2852 </v:shape><![endif]--><![if !vml]><img width=576 height=215
    2853 src="SequentialTutorial_files/image052.png" v:shapes="Picture_x0020_84"><![endif]></span></p>
    2854 
    2855 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    2856 
    2857 <p class=MsoListParagraphCxSpMiddle>The initial and the most recently defined
    2858 constraints will then be shown. </p>
    2859 
    2860 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    2861 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_85" o:spid="_x0000_i1029"
    2862  type="#_x0000_t75" style='width:6in;height:137.25pt;visibility:visible;
    2863  mso-wrap-style:square'>
    2864  <v:imagedata src="SequentialTutorial_files/image053.png" o:title=""/>
    2865 </v:shape><![endif]--><![if !vml]><img width=576 height=183
    2866 src="SequentialTutorial_files/image082.png" v:shapes="Picture_x0020_85"><![endif]></span></p>
    2867 
    2868 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    2869 
    2870 <p class=MsoListParagraphCxSpMiddle>These two constraints do not
    2871 interfere, since the first will be used during a non-sequential
    2872 refinement and the second is used only for sequential fits, but if
    2873 desired the first constraint can be deleted by pressing the </span><b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2874 major-latin;mso-hansi-theme-font:major-latin'>Delete</span></b><span
    2875 style='mso-bidi-font-weight:bold'> button for the first</span> one to remove
    2876 it, but this is optional.</p>
    2877 
    2878 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    2879 
    2880 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo16'><![if !supportLists]><span
    2881 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>6.<span
    2882 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Start
    2883 the sequential refinement again with the <b><span style='font-family:"Calibri",sans-serif;
    2884 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Calculate/Sequential
    2885 refine</span> </b><span style='mso-bidi-font-weight:bold'>menu item<b>.</b></span>
    2886 Five new columns appear at the end of the table for <b style='mso-bidi-font-weight:
    2887 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2888 major-latin;mso-hansi-theme-font:major-latin'>::constr0</span></b> (generated
    2889 by the constraint) and the selected variables, <b style='mso-bidi-font-weight:
    2890 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2891 major-latin;mso-hansi-theme-font:major-latin'>0:*:Scale</span></b> and <b
    2892 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2893 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>1:*:Scale</span></b>. Also
    2894 included are the weight fractions for each phase. Note that the phase
    2895 fractions all add to one.
    2896 Changes to the R<sub>wp</sub> values are quite small, even though the value for
    2897 the minor phase changes significantly. This indicates that the refinement is
    2898 relatively insensitive to these values.
     2590<p class=MsoNormal>At this point we wish to continue the refinements
     2591using the the current as-refined parameter values as the starting
     2592point. This is the default action for the program as the <b>Copy
     2593results to next histogram</b> checkbox is automatically unchecked
     2594after a successful sequential refinement. Note that
     2595in subsequent actions we will use the "Copy flags" menu commands,
     2596which copy only refinement flags not parameter values (as opposed to
     2597the "Copy" commands used previously, which copy both values and flags.)
    28992598</p>
    29002599
    2901 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    2902 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_88" o:spid="_x0000_i1027"
    2903  type="#_x0000_t75" style='width:6in;height:198pt;visibility:visible;
    2904  mso-wrap-style:square'>
    2905  <v:imagedata src="SequentialTutorial_files/image057.png" o:title=""/>
    2906 </v:shape><![endif]--><![if !vml]><img width=576 height=264
    2907 src="SequentialTutorial_files/image084.png" v:shapes="Picture_x0020_88"><![endif]></span></p>
    2908 
    2909 <h1>Step 9: Complete the sequential refinement. </h1>
    2910 
    2911 <p class=MsoListParagraphCxSpFirst><o:p>&nbsp;</o:p></p>
    2912 
    2913 <p class=MsoListParagraphCxSpMiddle>The last thing we will add to the
     2600
     2601<h3>1. Restore the parameters that were previously fit.</h3>
     2602
     2603<OL style='PADDING-LEFT:0.75in' type="A"><LI>
     2604Restore the refinement of background parameters as
     2605  in the single-histogram fit. Select <B>Background</B> for any
     2606  histogram and add the "Peaks in Background" width (<B>sig</B>)
     2607  refine flag.
     2608  Note that the peak position could be refined as well, but this is
     2609  not well-determined by the data since very little of the low-angle
     2610  side of the peak is present, so inclusion of this adds to the
     2611  refinement instability without any significant improvement to the
     2612  fit.
     2613  </LI>
     2614  <P></P><LI>
     2615  After setting the refinement flag, use the
     2616  <B>Background/Copy flags</b> menu item to copy these refinement
     2617  flags to all other histograms.</LI>
     2618
     2619  <P></P><LI>
     2620  Likewise, in the <B>Sample Parameters</B> tree item, include the
     2621<B>Sample X displ</b> parameter and again
     2622use the <b>Copy flags</b> menu command (here in the <B>Command</B> menu).
     2623  </LI>
     2624 
     2625  <P></P><LI>
     2626  For the <B>CuCr<sub>2</sub>O<sub>4</sub></B> phase, return to the
     2627  <B>Data</B> tab and enable refinement for the <B>phase fraction</B>
     2628  and the three <B>broadening</B> terms (isotropic size and equatorial
     2629  and axial mustrain). Again use the <B>Edit Phase/Copy flags</b> menu
     2630  command to set these flags for all histograms. </LI>
     2631
     2632  <P></P><LI>
     2633  For the <B>CuO</B> phase, also on the <B>Data</B> tab,
     2634  enable refinement for the <B>phase fraction</B>
     2635  and the single isotropic <B>microstrain broadening</B> term. Also
     2636  add refinement of the <B>D13</B> term. Again use the <B>Edit
     2637  Phase/Copy flags</b> menu command to set this for all histograms.
     2638  </IL>
     2639
     2640  <P></P><LI>
     2641  Select the <B>Constraints</B> data tree item and note that the
     2642  second line of controls that appears for sequential fits.
     2643  Confirm that the <B>"Wildcard use"</B> setting is <B>"Set hist # to *"</B>.
     2644
     2645   <P></P>
     2646  <p class=MsoListParagraphCxSpMiddle>
     2647  <I>Note:
     2648  Refinement of phase
     2649  fractions requires a constraint as was added in <A href="#I.3">Step
     2650  I.3</A>, but for all histograms.
     2651  As of version 5038 of GSAS-II three modes were added for constraints
     2652  in sequential refinements.
     2653  <UL style='PADDING-LEFT:0.75in'>
     2654    <LI>In </I>"Ignore unless hist=*"<I> mode (which was
     2655  the only mode prior to this version), any constraints with a
     2656  specific histogram number specified (such as </I><tt>":0:0:Scale"</tt><I> and
     2657  </I><tt>":1:0:Scale"</tt><I> as used previously) would be ignored and a new
     2658  constraint defining </I><tt>":0:*:Scale + :1:*:Scale = 1"</tt><I> would be
     2659    required.
     2660    <LI>There is now a mode </I>"Set hist # to *"<I> where any
     2661  constraints are interpreted to apply to all histograms, despite the
     2662  supplied number. <LI>The third mode, </I>"Use as supplied", uses both types
     2663  of constraints, so differing constraints can be supplied for
     2664  different histograms, but if both </I><tt>":0:*:Scale + :1:*:Scale = 1"</tt><I> and
     2665  </I><tt>":0:0:Scale + :1:0:Scale = 1"</tt><I> were supplied, an error would occur
     2666    because both constraints would be used for histogram 0.
     2667    </UL>
     2668    </I>
     2669</OL>
     2670 
     2671<h3>2. Perform the refinement.</h3>
     2672
     2673  <p class=MsoListParagraphCxSpMiddle>
     2674Start an additional refinement (using the Calculate/Refine menu item).
     2675  Now that the full suite of variables is available for fitting
     2676  background, peak widths, etc., the fits improve significantly for
     2677  the higher temperature datasets. Before, for the highest temperature
     2678  datasets, the Rwp values were in the range of 25-30%. After this
     2679  fit, all the Rwp values range from 13-17%. Click on a row header to
     2680  see a plot of the fit and double-click on a row header to see the
     2681convariance matrix plotted.
     2682Note that additional columns appear now in the Sequential results
     2683table for the newly-added variables. Also
     2684included are the weight fractions. Note that the sum of the phase
     2685fractions for each histogram are indeed 1.0.
     2686</P>
     2687
     2688<h1>Step VII: Complete the sequential refinement. </h1>
     2689
     2690<P></P>
     2691<p class=MsoListParagraphCxSpFirst>
     2692The last thing we will add to the
    29142693refinement will be atomic parameters. Note that these are handled a bit
    29152694differently than the previous things we have refined. There is only one set of
    29162695coordinates for each phase and these will be refined for each histogram, but
    2917 are not saved individually, except in the summary table.<span
    2918 style='mso-spacerun:yes'>  </span>If we restart the refinement, the coordinates
    2919 from the last histogram will be used to fit the first. The Reverse order
    2920 checkbox on the Controls causes the sequential refinement to start with the
    2921 last histogram, which would avoid this problem. </p>
    2922 
    2923 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    2924 
    2925 <p class=MsoListParagraphCxSpMiddle><span style='mso-bidi-font-weight:bold'>Select
    2926 the </span><b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2927 major-latin;mso-hansi-theme-font:major-latin'>CuCr2O4</span></b><span
    2928 style='mso-bidi-font-weight:bold'> phase</span> to and then the <b
    2929 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2930 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Atoms</span></b>
    2931 tab. <span style='mso-bidi-font-weight:bold'>Double-click on the </span><b><span
    2932 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2933 mso-hansi-theme-font:major-latin'>refine</span></b><span style='mso-bidi-font-weight:
    2934 bold'> label</span> at the top of the atoms table, a refinement controls dialog
    2935 opens, <span style='mso-bidi-font-weight:bold'>select </span><b><span
    2936 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2937 mso-hansi-theme-font:major-latin'>X</span></b><span style='mso-bidi-font-weight:
    2938 bold'> to refine coordinates (only O has coordinates not fixed by symmetry) and
    2939 </span><b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2940 major-latin;mso-hansi-theme-font:major-latin'>U</span></b> to refine the atomic
    2941 displacement (Uiso) values.<span style='mso-spacerun:yes'>  </span><span
    2942 style='mso-bidi-font-weight:bold'>Press </span><b><span style='font-family:
    2943 "Calibri",sans-serif;mso-ascii-theme-font:major-latin;mso-hansi-theme-font:
    2944 major-latin'>OK</span></b><span style='mso-bidi-font-weight:bold'>.</span> </p>
    2945 
     2696are saved individually only in the Sequential results table. To update
     2697the coordinates shown in the Phase data tree entry, use the "Update
     2698Phase from selected" command in the"Columns/Rows" menu. If a row is
     2699selected in the table, that will be used. If no rows are selected, you
     2700will be prompted to select a histogram.
     2701
     2702</p>
     2703<h3>1. Vary CuCr<sub>2</sub>O<sub>4</sub> coordinates and
     2704U<sub>iso</sub> Parameters.</h3>
     2705
     2706<P></P>
     2707<OL style='PADDING-LEFT:0.75in' type="A"><LI>
     2708Select the <b>CuCr2O4</b> phase</span> and then the <b>Atoms</b>
     2709  tab. Double-click on the <b>refine</b>column label and a refinement
     2710  controls dialog opens as below, select <b>X</b> to refine
     2711  coordinates and <b>U</b> to refine the atomic displacement (Uiso)
     2712  values.
     2713  (<I>Note that only the O atom has coordinates that can be refined,
     2714  all coordinates for Cu and Cr are fixed by symmetry.
     2715  Use of the X flag for Cu and Cr will not cause those coordinates to
     2716  change.</I>)
     2717  </LI>
     2718 
    29462719<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    29472720mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_89" o:spid="_x0000_i1026"
     
    29522725src="SequentialTutorial_files/image059.png" v:shapes="Picture_x0020_89"><![endif]></span></p>
    29532726
    2954 <p class=MsoListParagraphCxSpMiddle>Note the change in the atom table.</p>
     2727<P></P>
     2728 
     2729  <LI>Note the change that appears in the refine column of the atoms
     2730  table, as below. Since these parameters are shared in all
     2731  histograms, no Copy or Copy flags menu item is needed or even is
     2732  available for atomic parameters.</LI>
    29552733
    29562734<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
     
    29622740src="SequentialTutorial_files/image085.png" v:shapes="Picture_x0020_90"><![endif]></span></p>
    29632741
    2964 <p class=MsoListParagraphCxSpMiddle>Note that since these parameters are shared
    2965 directly in all histograms, no Copy or Copy flags menu item is needed or even
    2966 available. </p>
    2967 
    2968 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    2969 
    2970 <p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l1 level1 lfo16'><![if !supportLists]><span
    2971 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>7.<span
    2972 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Start
    2973 the sequential refinement again with the <b><span style='font-family:"Calibri",sans-serif;
    2974 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Calculate/Sequential
    2975 refine</span> </b><span style='mso-bidi-font-weight:bold'>menu item</span>. The
    2976 fits are significantly improved at higher temperatures, with R<sub>wp</sub>
    2977 values between 13.8 and 16.4. Be sure to save the project file by <span
    2978 style='mso-bidi-font-weight:bold'>selecting the </span><b><span
    2979 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
    2980 mso-hansi-theme-font:major-latin'>File/Save project</span></b><span
    2981 style='mso-bidi-font-weight:bold'> menu item</span>, since this will used in a
    2982 later tutorial.</p>
    2983 
    2984 <p>This completes the sequential refinement tutorial, although many more things
    2985 could be attempted to further improve the refinement quality. In the <b
    2986 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2987 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Parametric Fitting
    2988 and Pseudo Variables for Sequential Fits</span></b> tutorial, functions of
    2989 fitted parameters are computed and plotted and results are fitted to equations
    2990 of state.</p>
     2742  </OL>
     2743  <P></P>
     2744<h3>2. Perform final sequential fit, including coordinates displacement parameters.</h3>
     2745  <P></P>
     2746<p class=MsoListParagraphCxSpMiddle> Start
     2747the sequential refinement again with the <b>Calculate/Sequential
     2748refine</b> menu item. Small but significant improvements are seen for
     2749  fits with the higher temperature datasets, with R<sub>wp</sub>
     2750values between 13.8 and 16.5. </P>
     2751
     2752 
     2753<p>This completes the sequential refinement tutorial, although a few more things
     2754could be attempted to try to further improve the refinement
     2755quality. Be sure to keep the final project file,
     2756  since this will used in the <b>Parametric Fitting and Pseudo Variables for
     2757Sequential Fits</b> tutorial, where functions of fitted parameters are
     2758computed and plotted and these results are fitted to equations of state.
     2759</p>
    29912760
    29922761</div>
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