Changeset 1428


Ignore:
Timestamp:
Jul 22, 2014 3:45:19 PM (7 years ago)
Author:
vondreele
Message:

fixes to element stuff
cleanout old parametric fitting files

Location:
trunk
Files:
2 deleted
6 edited

Legend:

Unmodified
Added
Removed
  • trunk/GSASIIElem.py

    r1413 r1428  
    2121import atmdata
    2222
    23 getElSym = lambda sym: sym.split('+')[0].split('-')[0]
     23getElSym = lambda sym: sym.split('+')[0].split('-')[0].capitalize()
    2424def GetFormFactorCoeff(El):
    2525    """Read X-ray form factor coefficients from `atomdata.py` file
  • trunk/GSASIIpwdGUI.py

    r1418 r1428  
    24762476        ElList = subst['Elements'].keys()
    24772477        for El in ElList:
    2478             Info = G2elem.GetAtomInfo(El.strip().upper())
     2478            Info = G2elem.GetAtomInfo(El.strip().capitalize())
    24792479            Info.update(subst['Elements'][El])
    24802480            data['Substances'][name]['Elements'][El] = Info
     
    25732573        if dlg.ShowModal() == wx.ID_OK:
    25742574            for El in dlg.Elem:
    2575                 El = El.strip().upper()
     2575                El = El.strip().capitalize()
    25762576                Info = G2elem.GetAtomInfo(El)
    25772577                Info.update({'Num':1})
     
    37633763            El = PE.Elem
    37643764            if El not in ElList and El != 'None':
    3765                 ElemSym = El.strip().upper()               
     3765                ElemSym = El.strip().capitalize()               
    37663766                FpMu = G2elem.FPcalc(G2elem.GetXsectionCoeff(ElemSym), keV)
    37673767                ElData = G2elem.GetFormFactorCoeff(ElemSym)[0]
  • trunk/help/Fitting Small Angle Scattering Data.htm

    r1351 r1428  
    2525  <o:Author>Von Dreele</o:Author>
    2626  <o:LastAuthor>Von Dreele</o:LastAuthor>
    27   <o:Revision>5</o:Revision>
    28   <o:TotalTime>2074</o:TotalTime>
     27  <o:Revision>6</o:Revision>
     28  <o:TotalTime>2076</o:TotalTime>
    2929  <o:Created>2014-05-01T13:58:00Z</o:Created>
    30   <o:LastSaved>2014-05-03T16:24:00Z</o:LastSaved>
    31   <o:Pages>10</o:Pages>
     30  <o:LastSaved>2014-07-22T15:10:00Z</o:LastSaved>
     31  <o:Pages>9</o:Pages>
    3232  <o:Words>1444</o:Words>
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    883883<div class=WordSection1>
    884884
    885 <h1><strong><span style='mso-bidi-font-weight:normal'>Fitting Small Angle X-Ray
    886 Data – Alumina Powder</span><o:p></o:p></strong></h1>
     885<h1><strong>Fitting</strong><strong><span style='mso-bidi-font-weight:normal'>
     886Small Angle X-Ray Data – Alumina Powder</span><o:p></o:p></strong></h1>
    887887
    888888<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'>In
    889889this tutorial you will fit small angle scattering data for an alumina polishing
    890 powder using data from a constant wavelength synchrotron X-ray USAXS instrument.
    891 You will use both a lognormal distribution of spherical particles model and a
    892 unified <span class=SpellE>Guinier-Porod</span> model. The data were collected
    893 from <span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;
    894 mso-bidi-font-weight:bold;mso-bidi-font-style:italic'>powders spread onto
    895 sticky tape and covered with another layer of the same tape. The data were
    896 corrected for background using data collected from two layers of sticky tape.
    897 However, the sample thickness is not</span> accurately known <span
     890powder using data from a constant wavelength synchrotron X-ray USAXS
     891instrument. You will use both a lognormal distribution of spherical particles
     892model and a unified <span class=SpellE>Guinier-Porod</span> model. The data
     893were collected from <span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
     894minor-latin;mso-bidi-font-weight:bold;mso-bidi-font-style:italic'>powders
     895spread onto sticky tape and covered with another layer of the same tape. The
     896data were corrected for background using data collected from two layers of
     897sticky tape. However, the sample thickness is not</span> accurately known <span
    898898style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;
    899899mso-bidi-font-weight:bold;mso-bidi-font-style:italic'>so the data are not
     
    944944minor-latin'> to find the file</span>; you will have to select the <b
    945945style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
    946 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>any file (*.*)</span></b>
    947 filter to see it.</p>
     946mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>any file
     947(*.*)</span></b> filter to see it.</p>
    948948
    949949<p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
     
    10361036mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-no-proof:
    10371037yes'><span style='mso-element:field-begin'></span><span
    1038 style='mso-spacerun:yes'> </span>REF _Ref386699439 \h <span
    1039 style='mso-spacerun:yes'> </span>\* MERGEFORMAT <span style='mso-element:field-separator'></span></span></b><![endif]--><b
     1038style='mso-spacerun:yes'> </span>REF _Ref386699439 \h<span
     1039style='mso-spacerun:yes'>  </span>\* MERGEFORMAT <span style='mso-element:field-separator'></span></span></b><![endif]--><b
    10401040style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
    10411041mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Step 4
     
    11491149mso-hansi-theme-font:minor-latin'>Size Distribution</span></b> tutorial, you
    11501150would know that there were two populations of particles in the sample. One had
    1151 a mean diameter of ~1300A and the other had a mean diameter of ~150A. You will also
    1152 need something to describe the very lowest Q portion of the data. Do <b
     1151a mean diameter of ~1300A and the other had a mean diameter of ~150A. You will
     1152also need something to describe the very lowest Q portion of the data. Do <b
    11531153style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
    11541154mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Models/Add</span></b>
     
    13731373<p class=MsoNormal><o:p>&nbsp;</o:p></p>
    13741374
    1375 <p class=MsoNormal>Finally, you can refine these coefficients to find the best
    1376 fit to the data. As a beginner, I’d start by refining just the two <span
     1375<p class=MsoNormal>Finally, you can refine these coefficients to find the best fit
     1376to the data. As a beginner, I’d start by refining just the two <span
    13771377class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
    13781378"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     
    16491649style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
    16501650mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'> Mean</span></b>
    1651 values obtained earlier. Also note that this model makes no reference to the
    1652 substance contrast used earlier (the <b style='mso-bidi-font-weight:normal'><span
     1651values obtained earlier. Also note that this model makes no reference to the substance
     1652contrast used earlier (the <b style='mso-bidi-font-weight:normal'><span
    16531653style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;
    16541654mso-hansi-theme-font:minor-latin'>Size Distribution</span></b> plot will not
  • trunk/help/ParametricFitting.htm

    r1352 r1428  
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     24  <o:LastAuthor>Von Dreele</o:LastAuthor>
     25  <o:Revision>28</o:Revision>
     26  <o:TotalTime>953</o:TotalTime>
    2927  <o:Created>2014-05-09T19:20:00Z</o:Created>
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    1035947the fit parameters from the fit and <i style='mso-bidi-font-style:normal'>their
    1036948estimated uncertainty</i> (<span class=SpellE>s.u</span>.) can be computed by
    1037 defining one or more "pseudo-variables" (Pseudo <span class=SpellE>Vars</span>)
     949defining one or more &quot;pseudo-variables&quot; (Pseudo <span class=SpellE>Vars</span>)
    1038950Note that the covariance matrix from the fit is used to provide appropriate
    1039 treatment the correlation in parameters with respect to uncertainty
    1040 estimation.<span style="mso-spacerun:yes">&nbsp; </span>In addition, parametric
    1041 equations in terms of sample parameters such as temperature and pressure, etc. can
    1042 be fit to either the parameters from the fit or the Pseudo Vars. </p>
     951treatment of the correlation in parameters with respect to uncertainty
     952estimation.<span style='mso-spacerun:yes'>  </span>In addition, parametric
     953equations in terms of sample parameters such as temperature and pressure, etc.
     954can be fit to either the parameters from the fit or the Pseudo Vars. </p>
    1043955
    1044956<p class=MsoNormal><o:p>&nbsp;</o:p></p>
     
    1046958<p class=MsoNormal>This tutorial assumes that the steps in the <span
    1047959style='mso-bidi-font-family:"Times New Roman"'><a href="SequentialTutorial.htm">Sequential
    1048 refinement of multiple datasets</a> tutorial have already been performed. <o:p></o:p></span></p>
    1049 
    1050 <p class=MsoNormal><span style='mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
    1051 
    1052 <h2>Step 1. Open the previous Sequential Fit</h2>
     960refinement of multiple datasets</a> tutorial have already been performed. </span>If
     961you have not done so already, <a href="Starting%20GSAS.htm">start GSAS-II</a>.
     962Some of the pictures in this tutorial are from a Mac OSX machine; these
     963illustrate the differences in menu location from Windows/Linux machines.<o:p></o:p></p>
     964
     965<h1><span class=GramE>Step 1.</span> Open the previous Sequential Fit</h1>
    1053966
    1054967<p class=MsoNormal><o:p>&nbsp;</o:p></p>
    1055968
    1056 <p class=MsoListParagraph style='margin-bottom:6.0pt;text-indent:-.25in;
    1057 mso-list:l6 level1 lfo1'><![if !supportLists]><span style='mso-fareast-font-family:
    1058 Cambria;mso-fareast-theme-font:minor-latin;mso-bidi-font-family:Cambria;
    1059 mso-bidi-theme-font:minor-latin'><span style='mso-list:Ignore'>1.<span
    1060 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Start
    1061 GSAS-II</p>
    1062 
    1063 <p class=MsoListParagraph style='margin-bottom:6.0pt;text-indent:-.25in;
    1064 mso-list:l6 level1 lfo1'><![if !supportLists]><span style='mso-fareast-font-family:
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    1066 mso-bidi-theme-font:minor-latin'><span style='mso-list:Ignore'>2.<span
    1067 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
    1068 style='mso-bidi-font-weight:normal'>Click on the File/Open Project</b> menu
    1069 item to load file named <span class=SpellE><span style='font-family:Courier'>SeqTut.gpx</span></span>.
     969<p class=MsoListParagraphCxSpFirst style='margin-bottom:6.0pt;mso-add-space:
     970auto;text-indent:-.25in;mso-list:l4 level1 lfo2'><![if !supportLists]><span
     971style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
     972style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
     973</span></span></span><![endif]>Select the<b style='mso-bidi-font-weight:normal'>
     974</b><b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
     975mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>File/Open
     976Project</span></b> menu item to load file named <span class=SpellE><b
     977style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
     978mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>SeqTut.gpx</span></b></span>.
    1070979</p>
    1071980
    1072 <p class=MsoListParagraph style='margin-bottom:6.0pt;text-indent:-.25in;
    1073 mso-list:l6 level1 lfo1'><![if !supportLists]><span style='mso-fareast-font-family:
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    1075 mso-bidi-theme-font:minor-latin'><span style='mso-list:Ignore'>3.<span
    1076 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
    1077 style='mso-bidi-font-weight:normal'>Click on the Sequential results </b>item in
    1078 the data tree. The sequential refinement results data table is displayed, as
    1079 below. </p>
    1080 
    1081 <p class=MsoListParagraph style='margin-bottom:6.0pt'><span style='mso-fareast-language:
    1082 EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype id="_x0000_t75"
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     981<p class=MsoListParagraphCxSpMiddle style='margin-bottom:6.0pt;mso-add-space:
     982auto;text-indent:-.25in;mso-list:l4 level1 lfo2'><![if !supportLists]><span
     983style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
     984style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
     985</span></span></span><![endif]>Select the <b style='mso-bidi-font-weight:normal'><span
     986style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin;
     987mso-hansi-theme-font:major-latin'>Sequential results</span></b> item in the
     988data tree. The sequential refinement results data table is displayed, as below.
     989</p>
     990
     991<p class=MsoListParagraphCxSpLast style='margin-bottom:6.0pt;mso-add-space:
     992auto'><span style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype
     993 id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
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    1085995 <v:stroke joinstyle="miter"/>
    1086996 <v:formulas>
     
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    1107 src="ParametricFitting_files/image002.png" v:shapes="Picture_x0020_1"><![endif]></span></p>
    1108 
    1109 <h2>Step 2. Create a Pseudo <span class=SpellE>Var</span></h2>
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     1016src="ParametricFitting_files/image069.png" v:shapes="Picture_x0020_36"><![endif]></span></p>
     1017
     1018<h1>Step 2. Create a Pseudo <span class=SpellE>Var</span></h1>
    11101019
    11111020<p class=MsoNormal><o:p>&nbsp;</o:p></p>
     
    11161025expression can be used to define this. While one can plot <i style='mso-bidi-font-style:
    11171026normal'>a</i>, <i style='mso-bidi-font-style:normal'>b</i> and <i
    1118 style='mso-bidi-font-style:normal'>c</i> axis lengths by clicking on the appropriate
    1119 column of the table, to compare them one might want to scale them. Alternately,
    1120 as will be done here, we will plot the ratio of <i style='mso-bidi-font-style:
    1121 normal'>b</i> and <i style='mso-bidi-font-style:normal'>c</i>.</p>
     1027style='mso-bidi-font-style:normal'>c</i> axis lengths by clicking on the
     1028appropriate column of the table, to compare them one might want to scale them.
     1029Alternately, as will be done here, we will plot the ratio of <i
     1030style='mso-bidi-font-style:normal'>b</i> and <i style='mso-bidi-font-style:
     1031normal'>c</i>.</p>
    11221032
    11231033<p class=MsoNormal><o:p>&nbsp;</o:p></p>
    11241034
    1125 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l2 level1 lfo2'><![if !supportLists]><span
    1126 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin;
    1127 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span
    1128 style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
     1035<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l2 level1 lfo4'><![if !supportLists]><span
     1036style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
     1037style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    11291038</span></span></span><![endif]><b style='mso-bidi-font-weight:normal'>Click on
    11301039the Pseudo <span class=SpellE>Vars</span>/Add</b> menu item to create a new
     
    11351044<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    11361045mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_2" o:spid="_x0000_i1052"
    1137  type="#_x0000_t75" style='width:159pt;height:46pt;visibility:visible;
     1046 type="#_x0000_t75" style='width:159pt;height:45.75pt;visibility:visible;
    11381047 mso-wrap-style:square'>
    11391048 <v:imagedata src="ParametricFitting_files/image003.png" o:title=""/>
    1140 </v:shape><![endif]--><![if !vml]><img border=0 width=161 height=48
    1141 src="ParametricFitting_files/image004.png" v:shapes="Picture_x0020_2"><![endif]></span></p>
    1142 
    1143 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    1144 
    1145 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l2 level1 lfo2'><![if !supportLists]><span
    1146 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin;
    1147 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span
    1148 style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
     1049</v:shape><![endif]--><![if !vml]><img border=0 width=212 height=61
     1050src="ParametricFitting_files/image072.jpg" v:shapes="Picture_x0020_2"><![endif]></span></p>
     1051
     1052<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     1053
     1054<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l2 level1 lfo4'><![if !supportLists]><span
     1055style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
     1056style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    11491057</span></span></span><![endif]>A window opens to define a formula</p>
    11501058
     
    11531061<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    11541062mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_3" o:spid="_x0000_i1051"
    1155  type="#_x0000_t75" style='width:310pt;height:152pt;visibility:visible;
     1063 type="#_x0000_t75" style='width:309.75pt;height:152.25pt;visibility:visible;
    11561064 mso-wrap-style:square'>
    11571065 <v:imagedata src="ParametricFitting_files/image005.png" o:title="" croptop="4214f"
    11581066  cropbottom="8982f" cropleft="3852f" cropright="3654f"/>
    1159 </v:shape><![endif]--><![if !vml]><img border=0 width=312 height=154
    1160 src="ParametricFitting_files/image006.png" v:shapes="Picture_x0020_3"><![endif]></span></p>
     1067</v:shape><![endif]--><![if !vml]><img border=0 width=413 height=203
     1068src="ParametricFitting_files/image073.png" v:shapes="Picture_x0020_3"><![endif]></span></p>
    11611069
    11621070<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    11631071
    11641072<p class=MsoListParagraphCxSpMiddle><!--[if gte vml 1]><v:shape id="Picture_x0020_4"
    1165  o:spid="_x0000_s1032" type="#_x0000_t75" style='position:absolute;left:0;
     1073 o:spid="_x0000_s1031" type="#_x0000_t75" style='position:absolute;left:0;
    11661074 text-align:left;margin-left:178.3pt;margin-top:846.2pt;width:229.5pt;height:86.5pt;
    11671075 z-index:251658240;visibility:visible;mso-wrap-style:square;
    1168  mso-wrap-distance-left:9pt;mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
     1076 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;
     1077 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
    11691078 mso-wrap-distance-bottom:0;mso-position-horizontal:right;
    11701079 mso-position-horizontal-relative:margin;mso-position-vertical:absolute;
    1171  mso-position-vertical-relative:margin'>
     1080 mso-position-vertical-relative:margin;mso-width-percent:0;
     1081 mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'>
    11721082 <v:imagedata src="ParametricFitting_files/image007.png" o:title=""/>
    11731083 <w:wrap type="square" anchorx="margin" anchory="margin"/>
    1174 </v:shape><![endif]--><![if !vml]><img width=232 height=89
    1175 src="ParametricFitting_files/image008.png" align=right hspace=9 v:shapes="Picture_x0020_4"><![endif]>In
    1176 this window, <b style='mso-bidi-font-weight:normal'>type a Python expression, "b/c",</b>
    1177 but note that the variables <b style='mso-bidi-font-weight:normal'>c</b> and <b
    1178 style='mso-bidi-font-weight:normal'>b</b> here are arbitrary labels. After
    1179 entering the formula, <b style='mso-bidi-font-weight:normal'>press the Validate
    1180 button</b> or wait a few seconds and the validation will be tested
    1181 automatically. Note that if you pause too long, while typing, an error message
    1182 may be displayed as the incomplete formula is found to be invalid. If so, make
    1183 corrections or keep typing until the entire expression is entered. <span
    1184 style="mso-spacerun:yes">&nbsp;</span>The error message will sometimes show
    1185 where error is encountered, though not in this case. </p>
     1084</v:shape><![endif]--><![if !vml]><img width=306 height=115
     1085src="ParametricFitting_files/image074.jpg" align=right hspace=12 v:shapes="Picture_x0020_4"><![endif]>In
     1086this window, <b style='mso-bidi-font-weight:normal'>type a Python expression,
     1087&quot;b/c&quot;,</b> but note that the variables <b style='mso-bidi-font-weight:
     1088normal'>c</b> and <b style='mso-bidi-font-weight:normal'>b</b> here are
     1089arbitrary labels. After entering the formula, <b style='mso-bidi-font-weight:
     1090normal'>press the Validate button</b> or wait a few seconds and the validation
     1091will be tested automatically. Note that if you pause too long, while typing, an
     1092error message may be displayed as the incomplete formula is found to be
     1093invalid. If so, make corrections or keep typing until the entire expression is
     1094entered.<span style='mso-spacerun:yes'>  </span>The error message will
     1095sometimes show where error is encountered, though not in this case. </p>
    11861096
    11871097<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     
    11951105<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    11961106mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_5" o:spid="_x0000_i1050"
    1197  type="#_x0000_t75" style='width:310pt;height:152pt;visibility:visible;
     1107 type="#_x0000_t75" style='width:309.75pt;height:152.25pt;visibility:visible;
    11981108 mso-wrap-style:square'>
    11991109 <v:imagedata src="ParametricFitting_files/image009.png" o:title="" croptop="4435f"
    12001110  cropbottom="8537f" cropleft="3852f" cropright="3650f"/>
    1201 </v:shape><![endif]--><![if !vml]><img border=0 width=312 height=154
    1202 src="ParametricFitting_files/image010.png" v:shapes="Picture_x0020_5"><![endif]></span></p>
    1203 
    1204 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    1205 
    1206 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l2 level1 lfo2'><![if !supportLists]><span
    1207 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin;
    1208 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span
    1209 style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
     1111</v:shape><![endif]--><![if !vml]><img border=0 width=413 height=203
     1112src="ParametricFitting_files/image075.png" v:shapes="Picture_x0020_5"><![endif]></span></p>
     1113
     1114<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     1115
     1116<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l2 level1 lfo4'><![if !supportLists]><span
     1117style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
     1118style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    12101119</span></span></span><![endif]><!--[if gte vml 1]><v:shape id="Picture_x0020_6"
    1211  o:spid="_x0000_s1031" type="#_x0000_t75" style='position:absolute;left:0;
     1120 o:spid="_x0000_s1030" type="#_x0000_t75" style='position:absolute;left:0;
    12121121 text-align:left;margin-left:37.3pt;margin-top:1143.2pt;width:88.5pt;height:65.5pt;
    12131122 z-index:251659264;visibility:visible;mso-wrap-style:square;
    1214  mso-wrap-distance-left:9pt;mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
     1123 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;
     1124 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
    12151125 mso-wrap-distance-bottom:0;mso-position-horizontal:right;
    12161126 mso-position-horizontal-relative:margin;mso-position-vertical:absolute;
    1217  mso-position-vertical-relative:margin'>
     1127 mso-position-vertical-relative:margin;mso-width-percent:0;
     1128 mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'>
    12181129 <v:imagedata src="ParametricFitting_files/image011.png" o:title=""/>
    12191130 <w:wrap type="square" anchorx="margin" anchory="margin"/>
    1220 </v:shape><![endif]--><![if !vml]><img width=91 height=68
    1221 src="ParametricFitting_files/image012.png" align=right hspace=9 v:shapes="Picture_x0020_6"><![endif]>Assign
     1131</v:shape><![endif]--><![if !vml]><img width=118 height=87
     1132src="ParametricFitting_files/image076.jpg" align=right hspace=12 v:shapes="Picture_x0020_6"><![endif]>Assign
    12221133the label for the numerator by <b style='mso-bidi-font-weight:normal'>clicking
    12231134on the menu button next to label b</b>; this will bring up a list of variable
    1224 types, from this <b style='mso-bidi-font-weight:normal'>select Phase</b> to
    1225 bring up a list of phase variables, from that list <b style='mso-bidi-font-weight:
     1135types, from this <b style='mso-bidi-font-weight:normal'>select Phase</b> to bring
     1136up a list of phase variables, from that list <b style='mso-bidi-font-weight:
    12261137normal'>select variable </b><b style='mso-bidi-font-weight:normal'><span
    1227 style='font-family:Courier'>0<span class=GramE>::</span>b</span>,</b> which is
    1228 the <i style='mso-bidi-font-style:normal'>b</i> lattice parameter for phase 0
    1229 (CuCr<sub>2</sub>O<sub>4</sub>). Repeat this process to select <b
    1230 style='mso-bidi-font-weight:normal'>assign to label c variable </b><b
    1231 style='mso-bidi-font-weight:normal'><span style='font-family:Courier'>0<span
    1232 class=GramE>::</span>b</span></b>.</p>
     1138style='font-family:Courier'>0::b</span>,</b> which is the <i style='mso-bidi-font-style:
     1139normal'>b</i> lattice parameter for phase 0 (CuCr<sub>2</sub>O<sub>4</sub>).
     1140Repeat this process to select <b style='mso-bidi-font-weight:normal'>assign to
     1141label c variable </b><b style='mso-bidi-font-weight:normal'><span
     1142style='font-family:Courier'>0::b</span></b>.</p>
    12331143
    12341144<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     
    12361146<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    12371147mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_8" o:spid="_x0000_i1049"
    1238  type="#_x0000_t75" style='width:316pt;height:129pt;visibility:visible;
     1148 type="#_x0000_t75" style='width:315.75pt;height:129pt;visibility:visible;
    12391149 mso-wrap-style:square'>
    12401150 <v:imagedata src="ParametricFitting_files/image013.png" o:title="" croptop="4597f"
    12411151  cropbottom="9873f" cropleft="3348f" cropright="3506f"/>
    1242 </v:shape><![endif]--><![if !vml]><img border=0 width=318 height=131
    1243 src="ParametricFitting_files/image014.png" v:shapes="Picture_x0020_8"><![endif]></span></p>
     1152</v:shape><![endif]--><![if !vml]><img border=0 width=421 height=172
     1153src="ParametricFitting_files/image077.png" v:shapes="Picture_x0020_8"><![endif]></span></p>
    12441154
    12451155<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     
    12551165<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    12561166mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_9" o:spid="_x0000_i1048"
    1257  type="#_x0000_t75" style='width:314pt;height:154pt;visibility:visible;
     1167 type="#_x0000_t75" style='width:314.25pt;height:153.75pt;visibility:visible;
    12581168 mso-wrap-style:square'>
    12591169 <v:imagedata src="ParametricFitting_files/image015.png" o:title="" croptop="3770f"
    12601170  cropbottom="8549f" cropleft="3371f" cropright="3424f"/>
    1261 </v:shape><![endif]--><![if !vml]><img border=0 width=316 height=156
    1262 src="ParametricFitting_files/image016.png" v:shapes="Picture_x0020_9"><![endif]></span></p>
     1171</v:shape><![endif]--><![if !vml]><img border=0 width=419 height=205
     1172src="ParametricFitting_files/image078.png" v:shapes="Picture_x0020_9"><![endif]></span></p>
    12631173
    12641174<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     
    12721182<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    12731183mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_10" o:spid="_x0000_i1047"
    1274  type="#_x0000_t75" style='width:354pt;height:181pt;visibility:visible;
     1184 type="#_x0000_t75" style='width:354pt;height:180.75pt;visibility:visible;
    12751185 mso-wrap-style:square'>
    12761186 <v:imagedata src="ParametricFitting_files/image017.png" o:title="" croptop="2743f"
    12771187  cropbottom="7533f" cropleft="2917f" cropright="3097f"/>
    1278 </v:shape><![endif]--><![if !vml]><img border=0 width=356 height=183
    1279 src="ParametricFitting_files/image018.png" v:shapes="Picture_x0020_10"><![endif]></span></p>
     1188</v:shape><![endif]--><![if !vml]><img border=0 width=472 height=241
     1189src="ParametricFitting_files/image079.png" v:shapes="Picture_x0020_10"><![endif]></span></p>
    12801190
    12811191<p class=MsoListParagraphCxSpMiddle><!--[if gte vml 1]><v:shape id="Picture_x0020_11"
    1282  o:spid="_x0000_s1030" type="#_x0000_t75" style='position:absolute;left:0;
     1192 o:spid="_x0000_s1029" type="#_x0000_t75" style='position:absolute;left:0;
    12831193 text-align:left;margin-left:42.3pt;margin-top:666.2pt;width:93.5pt;height:39pt;
    12841194 z-index:251660288;visibility:visible;mso-wrap-style:square;
    1285  mso-wrap-distance-left:9pt;mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
     1195 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;
     1196 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
    12861197 mso-wrap-distance-bottom:0;mso-position-horizontal:right;
    12871198 mso-position-horizontal-relative:margin;mso-position-vertical:absolute;
    1288  mso-position-vertical-relative:margin'>
     1199 mso-position-vertical-relative:margin;mso-width-percent:0;
     1200 mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'>
    12891201 <v:imagedata src="ParametricFitting_files/image019.png" o:title=""/>
    12901202 <w:wrap type="square" anchorx="margin" anchory="margin"/>
    1291 </v:shape><![endif]--><![if !vml]><img width=96 height=41
    1292 src="ParametricFitting_files/image020.png" align=right hspace=9 v:shapes="Picture_x0020_11"><![endif]>Also
     1203</v:shape><![endif]--><![if !vml]><img width=125 height=52
     1204src="ParametricFitting_files/image080.jpg" align=right hspace=12 v:shapes="Picture_x0020_11"><![endif]>Also
    12931205note that positioning the mouse above any cell in the table and waiting for a
    1294 few <span class=GramE>seconds</span> causes the <span class=SpellE>s.u</span>. <span
    1295 class=GramE>to</span> be shown as a tooltip. </p>
     1206few seconds causes the <span class=SpellE>s.u</span>. to be shown as a tooltip.
     1207</p>
    12961208
    12971209<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    12981210
    12991211<p class=MsoListParagraphCxSpMiddle><b style='mso-bidi-font-weight:normal'>Double
    1300 clicking on the column</b> will cause the pseudo <span class=SpellE>var</span> to
    1301 be plotted:</p>
     1212clicking on the column</b> will cause the pseudo <span class=SpellE>var</span>
     1213to be plotted:</p>
    13021214
    13031215<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     
    13051217<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    13061218mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_12" o:spid="_x0000_i1046"
    1307  type="#_x0000_t75" style='width:352pt;height:303pt;visibility:visible;
     1219 type="#_x0000_t75" style='width:351.75pt;height:303pt;visibility:visible;
    13081220 mso-wrap-style:square'>
    13091221 <v:imagedata src="ParametricFitting_files/image021.png" o:title="" croptop="2107f"
    13101222  cropbottom="4939f" cropleft="3133f" cropright="3309f"/>
    1311 </v:shape><![endif]--><![if !vml]><img border=0 width=354 height=305
    1312 src="ParametricFitting_files/image022.png" v:shapes="Picture_x0020_12"><![endif]></span></p>
     1223</v:shape><![endif]--><![if !vml]><img border=0 width=469 height=404
     1224src="ParametricFitting_files/image081.png" v:shapes="Picture_x0020_12"><![endif]></span></p>
    13131225
    13141226<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    13151227
    13161228<p class=MsoListParagraphCxSpMiddle><b style='mso-bidi-font-weight:normal'>Press
    1317 the "s" key</b> inside the plot to <b style='mso-bidi-font-weight:normal'>select
    1318 Temperature</b> as the x-axis. </p>
     1229the &quot;s&quot; key</b> inside the plot to <b style='mso-bidi-font-weight:
     1230normal'>select Temperature</b> as the x-axis. </p>
    13191231
    13201232<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     
    13221234<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    13231235mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_13" o:spid="_x0000_i1045"
    1324  type="#_x0000_t75" style='width:163pt;height:156pt;visibility:visible;
     1236 type="#_x0000_t75" style='width:162.75pt;height:156pt;visibility:visible;
    13251237 mso-wrap-style:square'>
    13261238 <v:imagedata src="ParametricFitting_files/image023.png" o:title="" croptop="4105f"
    13271239  cropbottom="8920f" cropleft="6109f" cropright="5911f"/>
    1328 </v:shape><![endif]--><![if !vml]><img border=0 width=165 height=158
    1329 src="ParametricFitting_files/image024.png" v:shapes="Picture_x0020_13"><![endif]></span></p>
     1240</v:shape><![endif]--><![if !vml]><img border=0 width=217 height=208
     1241src="ParametricFitting_files/image082.png" v:shapes="Picture_x0020_13"><![endif]></span></p>
    13301242
    13311243<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     
    13371249<p class=MsoListParagraphCxSpLast><span style='mso-fareast-language:EN-US;
    13381250mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_14" o:spid="_x0000_i1044"
    1339  type="#_x0000_t75" style='width:353pt;height:304pt;visibility:visible;
     1251 type="#_x0000_t75" style='width:353.25pt;height:303.75pt;visibility:visible;
    13401252 mso-wrap-style:square'>
    13411253 <v:imagedata src="ParametricFitting_files/image025.png" o:title="" croptop="1859f"
    13421254  cropbottom="5066f" cropleft="3024f" cropright="3203f"/>
    1343 </v:shape><![endif]--><![if !vml]><img border=0 width=355 height=306
    1344 src="ParametricFitting_files/image026.png" v:shapes="Picture_x0020_14"><![endif]></span></p>
     1255</v:shape><![endif]--><![if !vml]><img border=0 width=471 height=405
     1256src="ParametricFitting_files/image083.png" v:shapes="Picture_x0020_14"><![endif]></span></p>
    13451257
    13461258<h2>Step 3: Fitting a simple parametric equation to the unit cell volume</h2>
     
    13511263equations of state to different parameters. As a simple example, we can <b
    13521264style='mso-bidi-font-weight:normal'>double-click on </b><b style='mso-bidi-font-weight:
    1353 normal'><span style='font-family:Courier'>0<span class=GramE>::</span><span
    1354 class=SpellE>Vol</span></span></b>, to plot the unit volume for the first phase
    1355 vs. T, and fit this to a straight line. <span
    1356 style="mso-spacerun:yes">&nbsp;</span></p>
     1265normal'><span style='font-family:Courier'>0::<span class=SpellE>Vol</span></span></b>,
     1266to plot the unit volume for the first phase vs. T, and fit this to a straight
     1267line.<span style='mso-spacerun:yes'>  </span></p>
    13571268
    13581269<p class=MsoNormal><o:p>&nbsp;</o:p></p>
     
    13601271<p class=MsoListParagraphCxSpFirst><span style='mso-fareast-language:EN-US;
    13611272mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_15" o:spid="_x0000_i1043"
    1362  type="#_x0000_t75" style='width:356pt;height:305pt;visibility:visible;
     1273 type="#_x0000_t75" style='width:356.25pt;height:305.25pt;visibility:visible;
    13631274 mso-wrap-style:square'>
    13641275 <v:imagedata src="ParametricFitting_files/image027.png" o:title="" croptop="2107f"
    13651276  cropbottom="4567f" cropleft="3024f" cropright="2769f"/>
    1366 </v:shape><![endif]--><![if !vml]><img border=0 width=358 height=307
    1367 src="ParametricFitting_files/image028.png" v:shapes="Picture_x0020_15"><![endif]></span></p>
    1368 
    1369 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo4'><![if !supportLists]><span
    1370 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin;
    1371 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span
    1372 style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
     1277</v:shape><![endif]--><![if !vml]><img border=0 width=475 height=407
     1278src="ParametricFitting_files/image084.png" v:shapes="Picture_x0020_15"><![endif]></span></p>
     1279
     1280<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
     1281style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
     1282style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    13731283</span></span></span><![endif]><!--[if gte vml 1]><v:shape id="Picture_x0020_16"
    1374  o:spid="_x0000_s1029" type="#_x0000_t75" style='position:absolute;left:0;
     1284 o:spid="_x0000_s1028" type="#_x0000_t75" style='position:absolute;left:0;
    13751285 text-align:left;margin-left:21.8pt;margin-top:891.2pt;width:73pt;height:53pt;
    13761286 z-index:251661312;visibility:visible;mso-wrap-style:square;
     
    13831293 <v:imagedata src="ParametricFitting_files/image029.png" o:title=""/>
    13841294 <w:wrap type="square" anchorx="margin" anchory="margin"/>
    1385 </v:shape><![endif]--><![if !vml]><img width=75 height=55
    1386 src="ParametricFitting_files/image030.png" align=right hspace=9 v:shapes="Picture_x0020_16"><![endif]><b
     1295</v:shape><![endif]--><![if !vml]><img width=97 height=71
     1296src="ParametricFitting_files/image085.jpg" align=right hspace=12 v:shapes="Picture_x0020_16"><![endif]><b
    13871297style='mso-bidi-font-weight:normal'>Click on the Parametric Fit/Add</b> <b
    13881298style='mso-bidi-font-weight:normal'>equation</b> menu item, which opens a
    13891299window similar to what was used before to create a Pseudo <span class=SpellE>var</span>,
    1390 except that here an equation is defined. <span
    1391 style="mso-spacerun:yes">&nbsp;</span></p>
     1300except that here an equation is defined.<span style='mso-spacerun:yes'> 
     1301</span></p>
    13921302
    13931303<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     
    13951305<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    13961306mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_17" o:spid="_x0000_i1042"
    1397  type="#_x0000_t75" style='width:311pt;height:152pt;visibility:visible;
     1307 type="#_x0000_t75" style='width:311.25pt;height:152.25pt;visibility:visible;
    13981308 mso-wrap-style:square'>
    13991309 <v:imagedata src="ParametricFitting_files/image031.png" o:title="" croptop="4213f"
    14001310  cropbottom="8982f" cropleft="3490f" cropright="3653f"/>
    1401 </v:shape><![endif]--><![if !vml]><img border=0 width=313 height=154
    1402 src="ParametricFitting_files/image032.png" v:shapes="Picture_x0020_17"><![endif]></span></p>
     1311</v:shape><![endif]--><![if !vml]><img border=0 width=415 height=203
     1312src="ParametricFitting_files/image086.png" v:shapes="Picture_x0020_17"><![endif]></span></p>
    14031313
    14041314<p class=MsoListParagraphCxSpLast><o:p>&nbsp;</o:p></p>
     
    14101320<p class=MsoNormal><b style='mso-bidi-font-weight:normal'><o:p>&nbsp;</o:p></b></p>
    14111321
    1412 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo4'><![if !supportLists]><b
    1413 style='mso-bidi-font-weight:normal'><span style='mso-fareast-font-family:Cambria;
    1414 mso-fareast-theme-font:minor-latin;mso-bidi-font-family:Cambria;mso-bidi-theme-font:
    1415 minor-latin'><span style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;
    1416 </span></span></span></b><![endif]><b style='mso-bidi-font-weight:normal'>Click
    1417 the menu button</b> to select a dependent variable for "y". From the phase list,
    1418 select the unit cell volume for the CuCr<sub>2</sub>O<sub>4</sub> phase, <b
    1419 style='mso-bidi-font-weight:normal'>click on </b><b style='mso-bidi-font-weight:
    1420 normal'><span style='font-family:Courier'>0<span class=GramE>::</span><span
    1421 class=SpellE>Vol</span></span></b> and then <b style='mso-bidi-font-weight:
    1422 normal'>press OK.<o:p></o:p></b></p>
     1322<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><b
     1323style='mso-bidi-font-weight:normal'><span style='mso-fareast-font-family:"Times New Roman";
     1324mso-bidi-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span
     1325style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span></b><![endif]><b
     1326style='mso-bidi-font-weight:normal'>Click the menu button</b> to select a
     1327dependent variable for &quot;y&quot;. From the phase list, select the unit cell
     1328volume for the CuCr<sub>2</sub>O<sub>4</sub> phase, <b style='mso-bidi-font-weight:
     1329normal'>click on </b><b style='mso-bidi-font-weight:normal'><span
     1330style='font-family:Courier'>0::<span class=SpellE>Vol</span></span></b> and
     1331then <b style='mso-bidi-font-weight:normal'>press OK.<o:p></o:p></b></p>
    14231332
    14241333<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     
    14261335<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    14271336mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_19" o:spid="_x0000_i1041"
    1428  type="#_x0000_t75" style='width:314pt;height:132pt;visibility:visible;
     1337 type="#_x0000_t75" style='width:314.25pt;height:132pt;visibility:visible;
    14291338 mso-wrap-style:square'>
    14301339 <v:imagedata src="ParametricFitting_files/image033.png" o:title="" croptop="3830f"
    14311340  cropbottom="9359f" cropleft="3705f" cropright="3502f"/>
    1432 </v:shape><![endif]--><![if !vml]><img border=0 width=316 height=134
    1433 src="ParametricFitting_files/image034.png" v:shapes="Picture_x0020_19"><![endif]></span></p>
     1341</v:shape><![endif]--><![if !vml]><img border=0 width=419 height=176
     1342src="ParametricFitting_files/image087.png" v:shapes="Picture_x0020_19"><![endif]></span></p>
    14341343
    14351344<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    14361345mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_20" o:spid="_x0000_i1040"
    1437  type="#_x0000_t75" style='width:311pt;height:155pt;visibility:visible;
     1346 type="#_x0000_t75" style='width:311.25pt;height:155.25pt;visibility:visible;
    14381347 mso-wrap-style:square'>
    14391348 <v:imagedata src="ParametricFitting_files/image035.png" o:title="" croptop="3548f"
    14401349  cropbottom="8549f" cropleft="3611f" cropright="3665f"/>
    1441 </v:shape><![endif]--><![if !vml]><img border=0 width=313 height=157
    1442 src="ParametricFitting_files/image036.png" v:shapes="Picture_x0020_20"><![endif]></span></p>
    1443 
    1444 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    1445 
    1446 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo4'><![if !supportLists]><span
    1447 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin;
    1448 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span
    1449 style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
     1350</v:shape><![endif]--><![if !vml]><img border=0 width=415 height=207
     1351src="ParametricFitting_files/image088.png" v:shapes="Picture_x0020_20"><![endif]></span></p>
     1352
     1353<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     1354
     1355<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
     1356style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
     1357style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    14501358</span></span></span><![endif]>Now we <b style='mso-bidi-font-weight:normal'>enter
    1451 the equation</b> using Python syntax, which is simply "<b style='mso-bidi-font-weight:
    1452 normal'><span style='font-family:Courier'>m*x + b</span></b>", note that the
    1453 use of spaces and the choice of labels is arbitrary. If one were to accidentally
    1454 leave out the "<span style='font-family:Courier'>*</span>" and typed "<span
    1455 style='font-family:Courier'>mx</span>" then that would be considered a label,
    1456 if "<span style='font-family:Courier'>m x</span>" were typed, an error message
    1457 would be displayed. </p>
     1359the equation</b> using Python syntax, which is simply &quot;<b
     1360style='mso-bidi-font-weight:normal'><span style='font-family:Courier'>m*x + b</span></b>&quot;,
     1361note that the use of spaces and the choice of labels is arbitrary. If one were
     1362to accidentally leave out the &quot;<span style='font-family:Courier'>*</span>&quot;
     1363and typed &quot;<span style='font-family:Courier'>mx</span>&quot; then that
     1364would be considered a label, if &quot;<span style='font-family:Courier'>m x</span>&quot;
     1365were typed, an error message would be displayed. </p>
    14581366
    14591367<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     
    14611369<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    14621370mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_21" o:spid="_x0000_i1039"
    1463  type="#_x0000_t75" style='width:316pt;height:155pt;visibility:visible;
     1371 type="#_x0000_t75" style='width:315.75pt;height:155.25pt;visibility:visible;
    14641372 mso-wrap-style:square'>
    14651373 <v:imagedata src="ParametricFitting_files/image037.png" o:title="" croptop="3326f"
    14661374  cropbottom="8766f" cropleft="3010f" cropright="3419f"/>
    1467 </v:shape><![endif]--><![if !vml]><img border=0 width=318 height=157
    1468 src="ParametricFitting_files/image038.png" v:shapes="Picture_x0020_21"><![endif]></span></p>
     1375</v:shape><![endif]--><![if !vml]><img border=0 width=421 height=207
     1376src="ParametricFitting_files/image089.png" v:shapes="Picture_x0020_21"><![endif]></span></p>
    14691377
    14701378<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     
    14761384<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    14771385
    1478 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo4'><![if !supportLists]><span
    1479 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin;
    1480 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span
    1481 style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
     1386<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
     1387style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
     1388style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    14821389</span></span></span><![endif]><!--[if gte vml 1]><v:shape id="Picture_x0020_22"
    1483  o:spid="_x0000_s1028" type="#_x0000_t75" style='position:absolute;left:0;
     1390 o:spid="_x0000_s1027" type="#_x0000_t75" style='position:absolute;left:0;
    14841391 text-align:left;margin-left:43.8pt;margin-top:603.2pt;width:95pt;height:35pt;
    14851392 z-index:251662336;visibility:visible;mso-wrap-style:square;
    1486  mso-wrap-distance-left:9pt;mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
     1393 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;
     1394 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
    14871395 mso-wrap-distance-bottom:0;mso-position-horizontal:right;
    14881396 mso-position-horizontal-relative:margin;mso-position-vertical:absolute;
    1489  mso-position-vertical-relative:margin'>
     1397 mso-position-vertical-relative:margin;mso-width-percent:0;
     1398 mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'>
    14901399 <v:imagedata src="ParametricFitting_files/image039.png" o:title=""/>
    14911400 <w:wrap type="square" anchorx="margin" anchory="margin"/>
    1492 </v:shape><![endif]--><![if !vml]><img width=97 height=37
    1493 src="ParametricFitting_files/image040.png" align=right hspace=9 v:shapes="Picture_x0020_22"><![endif]>Assign
     1401</v:shape><![endif]--><![if !vml]><img width=127 height=47
     1402src="ParametricFitting_files/image090.jpg" align=right hspace=12 v:shapes="Picture_x0020_22"><![endif]>Assign
    14941403b and m as refinable parameters: <b style='mso-bidi-font-weight:normal'>Click
    14951404on the menu button</b> next to b and <b style='mso-bidi-font-weight:normal'>select
     
    14981407<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    14991408mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_23" o:spid="_x0000_i1038"
    1500  type="#_x0000_t75" style='width:314pt;height:153pt;visibility:visible;
     1409 type="#_x0000_t75" style='width:314.25pt;height:153pt;visibility:visible;
    15011410 mso-wrap-style:square'>
    15021411 <v:imagedata src="ParametricFitting_files/image041.png" o:title="" croptop="3992f"
    15031412  cropbottom="8541f" cropleft="3250f" cropright="3415f"/>
    1504 </v:shape><![endif]--><![if !vml]><img border=0 width=316 height=155
    1505 src="ParametricFitting_files/image042.png" v:shapes="Picture_x0020_23"><![endif]></span></p>
     1413</v:shape><![endif]--><![if !vml]><img border=0 width=419 height=204
     1414src="ParametricFitting_files/image091.png" v:shapes="Picture_x0020_23"><![endif]></span></p>
    15061415
    15071416<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     
    15121421<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    15131422
    1514 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo4'><![if !supportLists]><span
    1515 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin;
    1516 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span
    1517 style='mso-list:Ignore'>5.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
     1423<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
     1424style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
     1425style='mso-list:Ignore'>5.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    15181426</span></span></span><![endif]><!--[if gte vml 1]><v:shape id="Picture_x0020_24"
    1519  o:spid="_x0000_s1027" type="#_x0000_t75" style='position:absolute;left:0;
     1427 o:spid="_x0000_s1026" type="#_x0000_t75" style='position:absolute;left:0;
    15201428 text-align:left;margin-left:24.3pt;margin-top:837.2pt;width:75.5pt;height:26pt;
    15211429 z-index:251663360;visibility:visible;mso-wrap-style:square;
    1522  mso-wrap-distance-left:9pt;mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
     1430 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;
     1431 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
    15231432 mso-wrap-distance-bottom:0;mso-position-horizontal:right;
    15241433 mso-position-horizontal-relative:margin;mso-position-vertical:absolute;
    1525  mso-position-vertical-relative:margin'>
     1434 mso-position-vertical-relative:margin;mso-width-percent:0;
     1435 mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'>
    15261436 <v:imagedata src="ParametricFitting_files/image043.png" o:title=""/>
    15271437 <w:wrap type="square" anchorx="margin" anchory="margin"/>
    1528 </v:shape><![endif]--><![if !vml]><img width=78 height=28
    1529 src="ParametricFitting_files/image044.png" align=right hspace=9 v:shapes="Picture_x0020_24"><![endif]>To
     1438</v:shape><![endif]--><![if !vml]><img width=101 height=35
     1439src="ParametricFitting_files/image092.jpg" align=right hspace=12 v:shapes="Picture_x0020_24"><![endif]>To
    15301440set x as the temperature, <b style='mso-bidi-font-weight:normal'>click on the
    15311441menu button</b> next to x, <b style='mso-bidi-font-weight:normal'>select
     
    15351445<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    15361446
    1537 <p class=MsoListParagraphCxSpMiddle><span
    1538 style="mso-spacerun:yes">&nbsp;</span><span style='mso-fareast-language:EN-US;
    1539 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_25" o:spid="_x0000_i1037"
    1540  type="#_x0000_t75" style='width:245pt;height:109pt;visibility:visible;
    1541  mso-wrap-style:square'>
     1447<p class=MsoListParagraphCxSpMiddle><span style='mso-spacerun:yes'> </span><span
     1448style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     1449 id="Picture_x0020_25" o:spid="_x0000_i1037" type="#_x0000_t75" style='width:245.25pt;
     1450 height:108.75pt;visibility:visible;mso-wrap-style:square'>
    15421451 <v:imagedata src="ParametricFitting_files/image045.png" o:title="" croptop="5483f"
    15431452  cropbottom="10984f" cropleft="4191f" cropright="4159f"/>
    1544 </v:shape><![endif]--><![if !vml]><img border=0 width=247 height=111
    1545 src="ParametricFitting_files/image046.png" v:shapes="Picture_x0020_25"><![endif]></span></p>
     1453</v:shape><![endif]--><![if !vml]><img border=0 width=327 height=145
     1454src="ParametricFitting_files/image093.png" v:shapes="Picture_x0020_25"><![endif]></span></p>
    15461455
    15471456<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    15481457
    15491458<p class=MsoListParagraphCxSpMiddle>The window then changes, showing the values
    1550 of the dependent variable and the expression for the first refinement, as below.<span
    1551 style="mso-spacerun:yes">&nbsp; </span>Optionally, the values for m and b could
    1552 be changed manually and the displayed value will be updated when Validate is
    1553 pressed or after a short delay.</p>
     1459of the dependent variable and the expression for the first refinement, as
     1460below.<span style='mso-spacerun:yes'>  </span>Optionally, the values for m and
     1461b could be changed manually and the displayed value will be updated when
     1462Validate is pressed or after a short delay.</p>
    15541463
    15551464<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     
    15571466<p class=MsoListParagraphCxSpLast><span style='mso-fareast-language:EN-US;
    15581467mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_26" o:spid="_x0000_i1036"
    1559  type="#_x0000_t75" style='width:314pt;height:153pt;visibility:visible;
     1468 type="#_x0000_t75" style='width:314.25pt;height:153pt;visibility:visible;
    15601469 mso-wrap-style:square'>
    15611470 <v:imagedata src="ParametricFitting_files/image047.png" o:title="" croptop="3992f"
    15621471  cropbottom="8541f" cropleft="3490f" cropright="3294f"/>
    1563 </v:shape><![endif]--><![if !vml]><img border=0 width=316 height=155
    1564 src="ParametricFitting_files/image048.png" v:shapes="Picture_x0020_26"><![endif]></span></p>
     1472</v:shape><![endif]--><![if !vml]><img border=0 width=419 height=204
     1473src="ParametricFitting_files/image094.png" v:shapes="Picture_x0020_26"><![endif]></span></p>
    15651474
    15661475<p class=MsoNormal><o:p>&nbsp;</o:p></p>
    15671476
    1568 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo4'><![if !supportLists]><span
    1569 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin;
    1570 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span
    1571 style='mso-list:Ignore'>6.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
     1477<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
     1478style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
     1479style='mso-list:Ignore'>6.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    15721480</span></span></span><![endif]><b style='mso-bidi-font-weight:normal'>Press the
    15731481OK button</b> to save this parametric fit. The b and m values are then refined
     
    15781486
    15791487<p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space:
    1580 auto'><span style='font-family:Courier'><span
    1581 style="mso-spacerun:yes">&nbsp;&nbsp; </span><span class=GramE>::</span>m<span
    1582 style="mso-spacerun:yes">&nbsp; </span>= -0.4476(5)<o:p></o:p></span></p>
     1488auto'><span style='font-family:Courier'><span style='mso-spacerun:yes'>  
     1489</span>:<span class=GramE>:m</span><span style='mso-spacerun:yes'>  </span>=
     1490-0.4476(5)<o:p></o:p></span></p>
    15831491
    15841492<p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space:
    1585 auto'><span style='font-family:Courier'><span
    1586 style="mso-spacerun:yes">&nbsp;&nbsp; </span><span class=GramE>::</span>b<span
    1587 style="mso-spacerun:yes">&nbsp; </span>= 577.73(8)<o:p></o:p></span></p>
     1493auto'><span style='font-family:Courier'><span style='mso-spacerun:yes'>  
     1494</span>:<span class=GramE>:b</span><span style='mso-spacerun:yes'>  </span>=
     1495577.73(8)<o:p></o:p></span></p>
    15881496
    15891497<p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space:
     
    15921500<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    15931501mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_27" o:spid="_x0000_i1035"
    1594  type="#_x0000_t75" style='width:350pt;height:302pt;visibility:visible;
     1502 type="#_x0000_t75" style='width:350.25pt;height:302.25pt;visibility:visible;
    15951503 mso-wrap-style:square'>
    15961504 <v:imagedata src="ParametricFitting_files/image049.png" o:title="" croptop="2231f"
    15971505  cropbottom="5061f" cropleft="3133f" cropright="3524f"/>
    1598 </v:shape><![endif]--><![if !vml]><img border=0 width=352 height=304
    1599 src="ParametricFitting_files/image050.png" v:shapes="Picture_x0020_27"><![endif]></span></p>
     1506</v:shape><![endif]--><![if !vml]><img border=0 width=467 height=403
     1507src="ParametricFitting_files/image095.png" v:shapes="Picture_x0020_27"><![endif]></span><span
     1508style='font-family:"Cambria","serif";mso-ascii-theme-font:minor-latin;
     1509mso-hansi-theme-font:minor-latin'><o:p></o:p></span></p>
    16001510
    16011511<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    16021512
    16031513<p class=MsoListParagraphCxSpMiddle>Also, a plot shows the actual values and
    1604 the fit. Note that while the values are close to a straight line, the deviations
    1605 are huge compared to the estimated uncertainty values for the unit cell volume
    1606 (shown as very small error bars, unless the plot is magnified). <span
    1607 style="mso-spacerun:yes">&nbsp;</span>If a linear relationship had been defined
    1608 as a constraint (as can be done with other software packages) <I>the unit cell
    1609 parameters would have been forced onto this line with no obvious indication
    1610 that this was not a correct result.</I> </p>
    1611 
    1612 <p class=MsoListParagraphCxSpLast><span style="mso-spacerun:yes">&nbsp;</span></p>
     1514the fit. Note that while the values are close to a straight line, the
     1515deviations are huge compared to the estimated uncertainty values for the unit
     1516cell volume (shown as very small error bars, unless the plot is
     1517magnified).<span style='mso-spacerun:yes'>  </span>If a linear relationship had
     1518been defined as a constraint (as can be done with other software packages) <i>the
     1519unit cell parameters would have been forced onto this line with no obvious
     1520indication that this was not a correct result.</i> </p>
     1521
     1522<p class=MsoListParagraphCxSpLast><span style='mso-spacerun:yes'> </span></p>
    16131523
    16141524<h2>Step 4: Examples of more complex fitting equations</h2>
     
    16161526<p class=MsoNormal><o:p>&nbsp;</o:p></p>
    16171527
    1618 <p class=MsoNormal>Here we will look at how more sophisticated Python capabilities
    1619 can be used to fit more complex behavior. <span
    1620 style="mso-spacerun:yes">&nbsp;</span></p>
    1621 
    1622 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l1 level1 lfo6'><![if !supportLists]><span
    1623 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin;
    1624 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span
    1625 style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
     1528<p class=MsoNormal>Here we will look at how more sophisticated Python
     1529capabilities can be used to fit more complex behavior.<span
     1530style='mso-spacerun:yes'>  </span></p>
     1531
     1532<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span
     1533style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
     1534style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    16261535</span></span></span><![endif]>Optionally <b style='mso-bidi-font-weight:normal'>Double-click
    16271536on the </b><b style='mso-bidi-font-weight:normal'><span style='font-family:
    1628 Courier'>0<span class=GramE>::</span>c</span> column</b>. Note the changes in
    1629 the <i style='mso-bidi-font-style:normal'>c</i> unit cell parameter as a
    1630 function of temperature, as shown below. </p>
     1537Courier'>0::c</span> column</b>. Note the changes in the <i style='mso-bidi-font-style:
     1538normal'>c</i> unit cell parameter as a function of temperature, as shown below.
     1539</p>
    16311540
    16321541<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     
    16341543<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    16351544mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_28" o:spid="_x0000_i1034"
    1636  type="#_x0000_t75" style='width:350pt;height:303pt;visibility:visible;
     1545 type="#_x0000_t75" style='width:350.25pt;height:303pt;visibility:visible;
    16371546 mso-wrap-style:square'>
    16381547 <v:imagedata src="ParametricFitting_files/image051.png" o:title="" croptop="658f"
    16391548  cropbottom="2861f" cropleft="1709f" cropright="1878f"/>
    1640 </v:shape><![endif]--><![if !vml]><img border=0 width=352 height=305
    1641 src="ParametricFitting_files/image052.png" v:shapes="Picture_x0020_28"><![endif]></span></p>
    1642 
    1643 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    1644 
    1645 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo6'><![if !supportLists]><span
    1646 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin;
    1647 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span
    1648 style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
     1549</v:shape><![endif]--><![if !vml]><img border=0 width=467 height=404
     1550src="ParametricFitting_files/image096.png" v:shapes="Picture_x0020_28"><![endif]></span></p>
     1551
     1552<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     1553
     1554<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span
     1555style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
     1556style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    16491557</span></span></span><![endif]>We will now fit <i style='mso-bidi-font-style:
    1650 normal'>c</i> as a function of form 1/(1 + <span class=SpellE><span
    1651 class=GramE>exp</span></span><span class=GramE>[</span>k(t-t<sub>0</sub>)]). <b
    1652 style='mso-bidi-font-weight:normal'>Click on the Parametric Fit/Add</b> <b
    1653 style='mso-bidi-font-weight:normal'>equation</b> menu item (as before). For the
    1654 dependent variable, <b style='mso-bidi-font-weight:normal'>click on Phase</b>
    1655 and then <b style='mso-bidi-font-weight:normal'>select </b><b style='mso-bidi-font-weight:
    1656 normal'><span style='font-family:Courier'>0<span class=GramE>::</span>c</span></b>.
    1657 <span style="mso-spacerun:yes">&nbsp;</span></p>
    1658 
    1659 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    1660 
    1661 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo6'><![if !supportLists]><span
    1662 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin;
    1663 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span
    1664 style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
     1558normal'>c</i> as a function of form 1<span class=GramE>/(</span>1 + <span
     1559class=SpellE>exp</span>[k(t-t<sub>0</sub>)]). <b style='mso-bidi-font-weight:
     1560normal'>Click on the Parametric Fit/Add</b> <b style='mso-bidi-font-weight:
     1561normal'>equation</b> menu item (as before). For the dependent variable, <b
     1562style='mso-bidi-font-weight:normal'>click on Phase</b> and then <b
     1563style='mso-bidi-font-weight:normal'>select </b><b style='mso-bidi-font-weight:
     1564normal'><span style='font-family:Courier'>0::c</span></b>.<span
     1565style='mso-spacerun:yes'>  </span></p>
     1566
     1567<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     1568
     1569<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span
     1570style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
     1571style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    16651572</span></span></span><![endif]>We then <b style='mso-bidi-font-weight:normal'>enter
    16661573expression</b></p>
     
    16681575<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    16691576
    1670 <p class=MsoListParagraphCxSpMiddle style='text-indent:.5in'><span class=GramE><span
    1671 style='font-family:Courier'>b</span></span><span style='font-family:Courier'> +
    1672 c / (1+math.exp(k*(t-t0)))<o:p></o:p></span></p>
    1673 
    1674 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     1577<p class=MsoListParagraphCxSpMiddle style='text-indent:.5in'><span
     1578style='font-family:Courier'>b + c / (1+<span class=GramE>math.exp(</span>k*(t-t0)))<o:p></o:p></span></p>
     1579
     1580<p class=MsoListParagraphCxSpMiddle><span style='font-family:"Cambria","serif";
     1581mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'><o:p>&nbsp;</o:p></span></p>
    16751582
    16761583<p class=MsoListParagraphCxSpLast>Note that use of spaces here are arbitrary,
    16771584but all parentheses are required. Also note that the exponential function [<span
    1678 class=SpellE><span class=GramE>exp</span></span><span class=GramE>(</span>x) or
    1679 e<sup>x</sup>] is supplied in Python in the math and <span class=SpellE>numpy</span>
    1680 modules as <span class=SpellE>math.exp</span>(), <span class=SpellE>numpy.exp</span>().
    1681 Both of these can be used as well as the convenience abbreviation of <span
    1682 class=SpellE><span class=GramE>np.exp</span></span><span class=GramE>(</span>).
    1683 Further, there are also a small number of common functions that are defined
    1684 without the prefix for convenience [these include pi, <span class=SpellE><span
    1685 class=GramE>exp</span></span><span class=GramE>(</span>), <span class=SpellE>sqrt</span>(),
    1686 <span class=SpellE>sind</span>(), <span class=SpellE>cosd</span>(), <span
    1687 class=SpellE>tand</span>() where d indicates an argument in degrees.]<o:p></o:p></p>
     1585class=SpellE>exp</span>(x) or e<sup>x</sup>] is supplied in Python in the math
     1586and <span class=SpellE>numpy</span> modules as <span class=SpellE><span
     1587class=GramE>math.exp</span></span><span class=GramE>(</span>), <span
     1588class=SpellE>numpy.exp</span>(). Both of these can be used as well as the
     1589convenience abbreviation of <span class=SpellE><span class=GramE>np.exp</span></span><span
     1590class=GramE>(</span>). Further, there are also a small number of common
     1591functions that are defined without the prefix for convenience [these include
     1592pi, <span class=SpellE><span class=GramE>exp</span></span><span class=GramE>(</span>),
     1593<span class=SpellE>sqrt</span>(), <span class=SpellE>sind</span>(), <span
     1594class=SpellE>cosd</span>(), <span class=SpellE>tand</span>() where d indicates
     1595an argument in degrees.]</p>
    16881596
    16891597<p class=MsoNormal><o:p>&nbsp;</o:p></p>
    16901598
    1691 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l1 level1 lfo6'><![if !supportLists]><span
    1692 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin;
    1693 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span
    1694 style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
     1599<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span
     1600style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
     1601style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    16951602</span></span></span><![endif]><b style='mso-bidi-font-weight:normal'>Assign
    16961603free variables to b, c, k and t0</b>, similar as to what was done before. Note
     
    16981605style='font-family:Courier'>b</span> label was set automatically to <span
    16991606style='font-family:Courier'>b_1</span>. If the same variable name (<span
    1700 style='font-family:Courier'>b</span>) <span class=GramE>was</span> used again
    1701 here, the same value would be used to fit both equations, which is certainly
    1702 not what we want here. <span style="mso-spacerun:yes">&nbsp;</span>Finally,
    1703 since this equation is too complex to fit without some reasonable starting
    1704 values, specify an approximate value for the vicinity of where <i
    1705 style='mso-bidi-font-style:normal'>c</i> starts to change, <b style='mso-bidi-font-weight:
    1706 normal'>enter 120 for </b><b style='mso-bidi-font-weight:normal'><span
    1707 style='font-family:Courier'>t0</span>.</b></p>
     1607style='font-family:Courier'>b</span>) was used again here, the same value would
     1608be used to fit both equations, which is certainly not what we want here.<span
     1609style='mso-spacerun:yes'>  </span>Finally, since this equation is too complex
     1610to fit without some reasonable starting values, specify an approximate value
     1611for the vicinity of where <i style='mso-bidi-font-style:normal'>c</i> starts to
     1612change, <b style='mso-bidi-font-weight:normal'>enter 120 for </b><b
     1613style='mso-bidi-font-weight:normal'><span style='font-family:Courier'>t0</span>.</b></p>
    17081614
    17091615<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     
    17111617<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    17121618mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_40" o:spid="_x0000_i1033"
    1713  type="#_x0000_t75" style='width:317pt;height:171pt;visibility:visible;
     1619 type="#_x0000_t75" style='width:317.25pt;height:171pt;visibility:visible;
    17141620 mso-wrap-style:square'>
    17151621 <v:imagedata src="ParametricFitting_files/image053.png" o:title="" croptop="3272f"
    17161622  cropbottom="7856f" cropleft="3218f" cropright="3436f"/>
    1717 </v:shape><![endif]--><![if !vml]><img border=0 width=319 height=173
    1718 src="ParametricFitting_files/image054.png" v:shapes="Picture_x0020_40"><![endif]></span></p>
    1719 
    1720 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    1721 
    1722 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo6'><![if !supportLists]><span
    1723 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin;
    1724 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span
    1725 style='mso-list:Ignore'>5.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
     1623</v:shape><![endif]--><![if !vml]><img border=0 width=423 height=228
     1624src="ParametricFitting_files/image097.png" v:shapes="Picture_x0020_40"><![endif]></span></p>
     1625
     1626<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     1627
     1628<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span
     1629style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
     1630style='mso-list:Ignore'>5.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    17261631</span></span></span><![endif]>Optionally, <b style='mso-bidi-font-weight:normal'>press
    17271632the Fit button</b> to see if the equation can be refined with starting values
    1728 of zero for the other three parameters.<span style="mso-spacerun:yes">&nbsp;
     1633of zero for the other three parameters.<span style='mso-spacerun:yes'> 
    17291634</span>A fit is obtained and is plotted. </p>
    17301635
    17311636<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    17321637
    1733 <p class=MsoListParagraphCxSpMiddle><span
    1734 style="mso-spacerun:yes">&nbsp;</span><span style='mso-fareast-language:EN-US;
    1735 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_41" o:spid="_x0000_i1032"
    1736  type="#_x0000_t75" style='width:317pt;height:169pt;visibility:visible;
    1737  mso-wrap-style:square'>
     1638<p class=MsoListParagraphCxSpMiddle><span style='mso-spacerun:yes'> </span><span
     1639style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     1640 id="Picture_x0020_41" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:317.25pt;
     1641 height:168.75pt;visibility:visible;mso-wrap-style:square'>
    17381642 <v:imagedata src="ParametricFitting_files/image055.png" o:title="" croptop="3477f"
    17391643  cropbottom="8265f" cropleft="3218f" cropright="3436f"/>
    1740 </v:shape><![endif]--><![if !vml]><img border=0 width=319 height=171
    1741 src="ParametricFitting_files/image056.png" v:shapes="Picture_x0020_41"><![endif]></span></p>
    1742 
    1743 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    1744 
    1745 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo6'><![if !supportLists]><span
    1746 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin;
    1747 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span
    1748 style='mso-list:Ignore'>6.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
     1644</v:shape><![endif]--><![if !vml]><img border=0 width=423 height=225
     1645src="ParametricFitting_files/image098.png" v:shapes="Picture_x0020_41"><![endif]></span></p>
     1646
     1647<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     1648
     1649<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span
     1650style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
     1651style='mso-list:Ignore'>6.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    17491652</span></span></span><![endif]><b style='mso-bidi-font-weight:normal'>Press OK</b>
    17501653to add this equation to the parametric fits and both equations are refit (and
     
    17561659<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    17571660mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_32" o:spid="_x0000_i1031"
    1758  type="#_x0000_t75" style='width:353pt;height:301pt;visibility:visible;
     1661 type="#_x0000_t75" style='width:353.25pt;height:300.75pt;visibility:visible;
    17591662 mso-wrap-style:square'>
    17601663 <v:imagedata src="ParametricFitting_files/image057.png" o:title="" croptop="2602f"
    17611664  cropbottom="4943f" cropleft="3024f" cropright="3097f"/>
    1762 </v:shape><![endif]--><![if !vml]><img border=0 width=355 height=303
    1763 src="ParametricFitting_files/image058.png" v:shapes="Picture_x0020_32"><![endif]></span></p>
    1764 
    1765 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    1766 
    1767 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo6'><![if !supportLists]><span
    1768 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin;
    1769 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span
    1770 style='mso-list:Ignore'>7.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
     1665</v:shape><![endif]--><![if !vml]><img border=0 width=471 height=401
     1666src="ParametricFitting_files/image099.png" v:shapes="Picture_x0020_32"><![endif]></span></p>
     1667
     1668<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     1669
     1670<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span
     1671style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
     1672style='mso-list:Ignore'>7.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    17711673</span></span></span><![endif]>We will now try a more complex equation for the
    17721674same data, where we set the value to <span style='font-family:Courier'>b</span>
    1773 for temperatures less than <span style='font-family:Courier'>t0</span> and a critical
    1774 phenomenon formulism [(t-t<sub>0</sub>)<sup>-a</sup>] for temperatures above <span
    1775 style='font-family:Courier'>t0</span>. To do this we use the Python syntax "<span
    1776 style='font-family:Courier'>x1 if <span class=SpellE>testexp</span> else x2</span>"
    1777 which is <span style='font-family:Courier'>x1</span> where the test expression (<span
    1778 class=SpellE><span style='font-family:Courier'>testexp</span></span> here) is <span
    1779 style='font-family:Courier'>True</span> and <span style='font-family:Courier'>x2</span>
    1780 elsewhere. Thus we can use an expression such as:</p>
    1781 
    1782 <p class=MsoListParagraphCxSpMiddle><span
    1783 style="mso-spacerun:yes">&nbsp;</span></p>
     1675for temperatures less than <span style='font-family:Courier'>t0</span> and a
     1676critical phenomenon formulism [(t-t<sub>0</sub>)<sup>-a</sup>] for temperatures
     1677above <span style='font-family:Courier'>t0</span>. To do this we use the Python
     1678syntax &quot;<span style='font-family:Courier'>x1 if <span class=SpellE>testexp</span>
     1679else x2</span>&quot; which is <span style='font-family:Courier'>x1</span> where
     1680the test expression (<span class=SpellE><span style='font-family:Courier'>testexp</span></span>
     1681here) is <span style='font-family:Courier'>True</span> and <span
     1682style='font-family:Courier'>x2</span> elsewhere. Thus we can use an expression
     1683such as:</p>
     1684
     1685<p class=MsoListParagraphCxSpMiddle><span style='mso-spacerun:yes'> </span></p>
    17841686
    17851687<p class=MsoListParagraphCxSpMiddle style='margin-left:1.0in;mso-add-space:
     
    17911693
    17921694<p class=MsoListParagraphCxSpMiddle>This may be easier to read with the
    1793 inclusion of extra parentheses (that have no effect on the execution):</p>
     1695inclusion of extra parentheses (that have no effect on the execution):<span
     1696style='font-family:"Cambria","serif";mso-ascii-theme-font:minor-latin;
     1697mso-hansi-theme-font:minor-latin'><o:p></o:p></span></p>
    17941698
    17951699<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     
    18041708<p class=MsoListParagraphCxSpMiddle>As before, <b style='mso-bidi-font-weight:
    18051709normal'>add an equation </b>(or edit an existing one), <b style='mso-bidi-font-weight:
    1806 normal'>set the dependent variable</b> to <span style='font-family:Courier'>0<span
    1807 class=GramE>::</span>c</span>, <b style='mso-bidi-font-weight:normal'>enter the
    1808 expression</b> and <b style='mso-bidi-font-weight:normal'>assign the free and
    1809 fixed variables</b>, as before. <b style='mso-bidi-font-weight:normal'>Set the
    1810 exponent and the t0</b> values to initial values of -0.025 and 120, respectively,
    1811 and turn off their refinement flags. Then <b style='mso-bidi-font-weight:normal'>press
    1812 Fit.</b></p>
     1710normal'>set the dependent variable</b> to <span style='font-family:Courier'>0::c</span>,
     1711<b style='mso-bidi-font-weight:normal'>enter the expression</b> and <b
     1712style='mso-bidi-font-weight:normal'>assign the free and fixed variables</b>, as
     1713before. <b style='mso-bidi-font-weight:normal'>Set the exponent and the t0</b>
     1714values to initial values of -0.025 and 120, respectively, and turn off their
     1715refinement flags. Then <b style='mso-bidi-font-weight:normal'>press Fit.</b><span
     1716style='font-family:"Cambria","serif";mso-ascii-theme-font:minor-latin;
     1717mso-hansi-theme-font:minor-latin'><o:p></o:p></span></p>
    18131718
    18141719<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
     
    18171722<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    18181723mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_42" o:spid="_x0000_i1030"
    1819  type="#_x0000_t75" style='width:316pt;height:169pt;visibility:visible;
     1724 type="#_x0000_t75" style='width:315.75pt;height:168.75pt;visibility:visible;
    18201725 mso-wrap-style:square'>
    18211726 <v:imagedata src="ParametricFitting_files/image059.png" o:title="" croptop="3691f"
    18221727  cropbottom="7919f" cropleft="2889f" cropright="3536f"/>
    1823 </v:shape><![endif]--><![if !vml]><img border=0 width=318 height=171
    1824 src="ParametricFitting_files/image060.png" v:shapes="Picture_x0020_42"><![endif]></span></p>
     1728</v:shape><![endif]--><![if !vml]><img border=0 width=421 height=225
     1729src="ParametricFitting_files/image100.png" v:shapes="Picture_x0020_42"><![endif]></span></p>
    18251730
    18261731<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     
    18341739<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    18351740mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_35" o:spid="_x0000_i1029"
    1836  type="#_x0000_t75" style='width:351pt;height:302pt;visibility:visible;
     1741 type="#_x0000_t75" style='width:351pt;height:302.25pt;visibility:visible;
    18371742 mso-wrap-style:square'>
    18381743 <v:imagedata src="ParametricFitting_files/image061.png" o:title="" croptop="2354f"
    18391744  cropbottom="4937f" cropleft="3349f" cropright="3198f"/>
    1840 </v:shape><![endif]--><![if !vml]><img border=0 width=353 height=304
    1841 src="ParametricFitting_files/image062.png" v:shapes="Picture_x0020_35"><![endif]></span></p>
     1745</v:shape><![endif]--><![if !vml]><img border=0 width=468 height=403
     1746src="ParametricFitting_files/image101.png" v:shapes="Picture_x0020_35"><![endif]></span></p>
    18421747
    18431748<p class=MsoListParagraphCxSpLast><o:p>&nbsp;</o:p></p>
     
    18551760<p class=MsoNormal><o:p>&nbsp;</o:p></p>
    18561761
    1857 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l4 level1 lfo7'><![if !supportLists]><span
    1858 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin;
    1859 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span
    1860 style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
     1762<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l3 level1 lfo10'><![if !supportLists]><span
     1763style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
     1764style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    18611765</span></span></span><![endif]>As before, <b style='mso-bidi-font-weight:normal'>add
    18621766an equation </b>(or edit an existing one). For the dependent variable, <b
     
    18671771<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    18681772
    1869 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l4 level1 lfo7'><![if !supportLists]><span
    1870 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin;
    1871 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span
    1872 style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
     1773<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l3 level1 lfo10'><![if !supportLists]><span
     1774style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
     1775style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    18731776</span></span></span><![endif]>Then <b style='mso-bidi-font-weight:normal'>enter
    18741777the equation</b> as </p>
     
    18781781<p class=MsoListParagraphCxSpMiddle style='margin-left:1.0in;mso-add-space:
    18791782auto'><span style='font-family:Courier;mso-bidi-font-family:"Lucida Grande";
    1880 color:black'>(<span class=GramE>o1</span> + (a1*T)**k) if T &lt; 120 else (o2 +
     1783color:black'>(o1 + (a1*T<span class=GramE>)*</span>*k) if T &lt; 120 else (o2 +
    18811784a2*T</span><span style='font-family:Courier'>)<o:p></o:p></span></p>
    18821785
    1883 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    1884 
    1885 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l4 level1 lfo7'><![if !supportLists]><span
    1886 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin;
    1887 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span
    1888 style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
     1786<p class=MsoListParagraphCxSpMiddle><span style='font-family:"Cambria","serif";
     1787mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'><o:p>&nbsp;</o:p></span></p>
     1788
     1789<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l3 level1 lfo10'><![if !supportLists]><span
     1790style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
     1791style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    18891792</span></span></span><![endif]><b style='mso-bidi-font-weight:normal'>Assign
    1890 the free and fixed variables</b>, as shown below. Note that the exponent (k) and
    1891 scaling factor (a1<span class=GramE>),</span> cannot start as zero<b
     1793the free and fixed variables</b>, as shown below. Note that the exponent (k)
     1794and scaling factor (a1<span class=GramE>),</span> cannot start as zero<b
    18921795style='mso-bidi-font-weight:normal'>. </b></p>
    18931796
     
    18961799<p class=MsoListParagraphCxSpLast><span style='mso-fareast-language:EN-US;
    18971800mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_44" o:spid="_x0000_i1028"
    1898  type="#_x0000_t75" style='width:332pt;height:186pt;visibility:visible;
     1801 type="#_x0000_t75" style='width:332.25pt;height:186pt;visibility:visible;
    18991802 mso-wrap-style:square'>
    19001803 <v:imagedata src="ParametricFitting_files/image063.png" o:title="" croptop="3190f"
    19011804  cropbottom="8105f" cropleft="3416f" cropright="3246f"/>
    1902 </v:shape><![endif]--><![if !vml]><img border=0 width=334 height=188
    1903 src="ParametricFitting_files/image064.png" v:shapes="Picture_x0020_44"><![endif]></span></p>
     1805</v:shape><![endif]--><![if !vml]><img border=0 width=443 height=248
     1806src="ParametricFitting_files/image102.png" v:shapes="Picture_x0020_44"><![endif]></span></p>
    19041807
    19051808<p class=MsoNormal><o:p>&nbsp;</o:p></p>
    19061809
    1907 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l4 level1 lfo7'><![if !supportLists]><span
    1908 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin;
    1909 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span
    1910 style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
     1810<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l3 level1 lfo10'><![if !supportLists]><span
     1811style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
     1812style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    19111813</span></span></span><![endif]><b style='mso-bidi-font-weight:normal'>Press the
    19121814Fit button</b> and note that all the free variables are adjusted </p>
     
    19161818<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    19171819mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_45" o:spid="_x0000_i1027"
    1918  type="#_x0000_t75" style='width:334pt;height:189pt;visibility:visible;
     1820 type="#_x0000_t75" style='width:333.75pt;height:189pt;visibility:visible;
    19191821 mso-wrap-style:square'>
    19201822 <v:imagedata src="ParametricFitting_files/image065.png" o:title="" croptop="2815f"
    19211823  cropbottom="7542f" cropleft="3074f" cropright="3244f"/>
    1922 </v:shape><![endif]--><![if !vml]><img border=0 width=336 height=191
    1923 src="ParametricFitting_files/image066.png" v:shapes="Picture_x0020_45"><![endif]></span><span
    1924 style="mso-spacerun:yes">&nbsp;</span></p>
    1925 
    1926 <p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
    1927 
    1928 <p class=MsoListParagraphCxSpMiddle>Also, that the plotted result is close to the
    1929 values from the refinement.</p>
     1824</v:shape><![endif]--><![if !vml]><img border=0 width=445 height=252
     1825src="ParametricFitting_files/image103.png" v:shapes="Picture_x0020_45"><![endif]></span><span
     1826style='mso-spacerun:yes'> </span></p>
     1827
     1828<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     1829
     1830<p class=MsoListParagraphCxSpMiddle>Also, that the plotted result is close to
     1831the values from the refinement.</p>
    19301832
    19311833<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
     
    19331835<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
    19341836mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_48" o:spid="_x0000_i1026"
    1935  type="#_x0000_t75" style='width:349pt;height:302pt;visibility:visible;
     1837 type="#_x0000_t75" style='width:348.75pt;height:302.25pt;visibility:visible;
    19361838 mso-wrap-style:square'>
    19371839 <v:imagedata src="ParametricFitting_files/image067.png" o:title="" croptop="2231f"
    19381840  cropbottom="5061f" cropleft="3350f" cropright="3415f"/>
    1939 </v:shape><![endif]--><![if !vml]><img border=0 width=351 height=304
    1940 src="ParametricFitting_files/image068.png" v:shapes="Picture_x0020_48"><![endif]></span></p>
     1841</v:shape><![endif]--><![if !vml]><img border=0 width=465 height=403
     1842src="ParametricFitting_files/image104.png" v:shapes="Picture_x0020_48"><![endif]></span></p>
    19411843
    19421844<p class=MsoListParagraphCxSpLast><o:p>&nbsp;</o:p></p>
     
    19551857<p class=MsoNormal>The parametric refinement section of GSAS-II is intended to
    19561858be quite flexible, but for very complex fitting, a user may wish to define a
    1957 custom Python function. Such a function can be defined in a separate
    1958 module that will be accessed with a parametric equation (or pseudo
    1959 var).</p>
     1859custom Python function. Such a function can be defined in a separate module
     1860that will be accessed with a parametric equation (or pseudo var).</p>
    19601861
    19611862<p class=MsoNormal><o:p>&nbsp;</o:p></p>
    19621863
    1963 <p class=MsoNormal>As an example of that, if we create a file called
    1964 <span class=SpellE><span style='font-family:Courier'>fittest.py</span></span>
    1965 and locate that file in any directory in the Python path (most simply,
    1966 in the directory where the project file,
    1967 <span class=SpellE><span
    1968 style='font-family:Courier'>SeqTut.gpx</span></span>,
    1969 is located) and place a routine <span class=SpellE><span
    1970 style='font-family:Courier'>fitfxn</span></span> in that module:</p>
    1971 
    1972 <blockquote><blockquote><PRE>
    1973 # file fittest.py
    1974 def fitfxn(T,o1,o2,a1,a2,k):
    1975     if T < 120:
    1976         return o1 + (a1*T)**k
    1977     else:
    1978         return o2 + a2*T
    1979 </PRE></blockquote></blockquote>
     1864<p class=MsoNormal>As an example of that, if we create a file called <span
     1865style='font-family:Courier'>fittest.py</span> and locate that file in any
     1866directory in the Python path (most simply, in the directory where the project
     1867file, <span class=SpellE><span style='font-family:Courier'>SeqTut.gpx</span></span>,
     1868is located) and place a routine <span class=SpellE><span style='font-family:
     1869Courier'>fitfxn</span></span> in that module:</p>
     1870
     1871<blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'>
     1872
     1873<blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><pre><o:p>&nbsp;</o:p></pre><pre># file fittest.py</pre><pre>def fitfxn(T,o1,o2,a1,a2,k):</pre><pre><span style='mso-spacerun:yes'>    </span>if T &lt; 120:</pre><pre><span style='mso-spacerun:yes'>        </span>return o1 + (a1*T)**k</pre><pre><span style='mso-spacerun:yes'>    </span>else:</pre><pre><span style='mso-spacerun:yes'>        </span>return o2 + a2*T</pre></blockquote>
     1874
     1875</blockquote>
    19801876
    19811877<p class=MsoNormal>The function <span class=SpellE><span style='font-family:
     
    19871883<p class=MsoNormal><span style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    19881884 id="Picture_x0020_47" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:315pt;
    1989  height:185pt;visibility:visible;mso-wrap-style:square'>
     1885 height:185.25pt;visibility:visible;mso-wrap-style:square'>
    19901886 <v:imagedata src="ParametricFitting_files/image070.png" o:title="" croptop="3393f"
    19911887  cropbottom="7847f" cropleft="3471f" cropright="3290f"/>
    1992 </v:shape><![endif]--><![if !vml]><img border=0 width=317 height=187
    1993 src="ParametricFitting_files/image071.png" v:shapes="Picture_x0020_47"><![endif]></span></p>
     1888</v:shape><![endif]--><![if !vml]><img border=0 width=420 height=247
     1889src="ParametricFitting_files/image105.png" v:shapes="Picture_x0020_47"><![endif]></span></p>
    19941890
    19951891<p class=MsoNormal><o:p>&nbsp;</o:p></p>
    19961892
    1997 <p class=MsoNormal>Note that module <span class=SpellE><span style='font-family:
    1998 Courier'>fittest</span></span> is automatically located and loaded,
    1999 provided it is found in the path. No changes to the standard
    2000 distributed GSAS-II code are needed. Care to avoid use of a module name
    2001 already found in GSAS-II or Python is wise.</p>
     1893<p class=MsoNormal>Note that module <span style='font-family:Courier'>fittest</span>
     1894is automatically located and loaded, provided it is found in the path. No
     1895changes to the standard distributed GSAS-II code are needed. Care to avoid use
     1896of a module name already found in GSAS-II or Python is wise.</p>
    20021897
    20031898</div>
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