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1<html>
2<head>
3   <title>EXPGUI</title>
4   <meta name="keywords" content="crystallography, Rietveld, diffraction,
5   GSAS, EXPGUI">
6</HEAD>
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16<?
17   include("/var/www/include/navigation.inc");
18   include("/var/www/include/utility.inc");
19?>
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22<TABLE BORDER BGCOLOR="#FFFF40" ALIGN=RIGHT>
23<TR><TH><A  Href="expgui.html">EXPGUI top</A> 
24</TH><TH><A Href="expgui6A.html">Next page</A>
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28<center><h1>
29<HR noshade width="75%" size="2" align="center">
30EXPGUI, part 7
31<HR noshade width="75%" size="2" align="center">
32</h1></center>
33
34<h3>A.7 Restraints panel</h3>
35<DL><DL>
36GSAS offers two ways to limit changes to parameters that are based on
37  expectations
38  created by a crystallographer to create what is felt to be the most
39  reasonable model.
40  Restraints penalize the fit if
41aspects of a model (for example, bond lengths) differ from selected
42  values. They are sometimes called "soft constraints", but they are
43  not true constraints. They "push" the model towards the expectation(s)
44  specified by the scientist, but do not require that expectation be
45  maintained. Note that each expectation is weighted by the uncertainty
46  (sometimes s.u. or E.S.D.) for the expectation as well as the overall Restraint
47  Weighting factor. The smaller the uncertainty and the larger Restraint
48  Weighting factor, the stronger the model is "pushed" towards
49  following the expectation.
50<P> 
51  Restraints effectively add additional
52  "observations" to the data that are
53  fit in GSAS. Of course, these "observations" are
54  conjectures made by the scientist and are not actually real data.
55These are distingished from constraints (sometimes called "hard
56  constraints") which are listed on the
57<A Href="expgui6.html">Constraints panel</A>). Constraints actually
58  reduce the actual number of refined parameters in a model,
59by grouping parameters so that a single shift (possibly scaled) is
60applied to each parameter in the group.
61<P>
62  The Restraints panel can be used to set up restraints on
63  <a href="#DistanceRestraints"><B>Interatomic Distances</B></A> and
64  on <a href="#Chemical Restraints"><B>Atomic Composition</B></A>. Note
65  that the atomic composition constraints can be used to establish
66  quite complex constraints that account for charge balance or even
67  segregation of elements between phases. GSAS offers many other types
68  of restraints, but EXPEDT must be used to access them.
69</DL></DL>
70
71<a name="DistanceRestraints"></a>
72<H4>A.7.1 Distance Restraints</H4>
73<DL><DL>
74 When the distance restraints tab is first selected, the active
75  distance restraints for the selected phase are shown. The <B>Atom 1</B> and
76  <B>Atom 2</B> buttons can be used to sort this list.
77  <P>
78  The <B>Restraint Weight</B> parameter is very important. As this
79  determines how strongly the distance restraints will be used in the
80  refinement relative to the diffraction data. This value is sometimes
81  set as high as 500,000 in the initial stages of a fit, but should be
82  lowered as much as is possible in the final stages of the fit, as
83  needed to obtain chemically plausible interatomic distances. For
84  some refinements, a value of 0.0 is possible for the Restraint
85  Weight in the final stages. This removes any restraint effect.
86
87  To see how restraints are affecting the refinement, one can look at
88  the ratio of the "Sum(w*d**2)" (shown in the .LST file) for the
89  diffraction histograms vs. the restraint histogram.
90<P>
91  The <B>Active Restraints Editor</B> can be used to select distances
92  to be restrained or edit the restraints. If there are too many
93  distances shown, the options at the top of the window can be used to
94  select a distance range, or specific atoms to include. Likewise,
95  only restrained or unrestrained distances can be selected. The
96  changes are applied when the <B>Filter</B> button is pressed.
97<P>
98  The bottom section of the window shows individual interatomic
99  distances. A <B>Restraint</B> and <B>Tolerance</B> value is needed to restrain
100  that distance.
101</DL></DL>
102<img src="dist1.png" alt="Distance constraint example screen">.
103<DL><DL>
104
105  The quantity minimized is
106<blockquote>
107<blockquote>
108 "Restraint Weight" * SUM{  [ (Distance - Restraint) / Tolerance ]**2 }
109</blockquote>
110</blockquote>
111thus the "Tolerance" provides individual weighting for each
112  restraint.
113<P>
114  To set a large number of restraints at the same time, select the
115  check button next to the distance(s), or use the <B>Check
116  All</B>. Then use the section above to enter a global
117  <B>Restraint</B> and <B>Tolerance</B> value. These values are set
118  when the <B>Set Checked</B> button is used.  The <B>Delete
119  Checked</B> button removes restraints from all selected distances.
120<P>
121The entered restraint information will be used onlt when the <B>Save
122  Changes</B> button is pressed. The <B>Cancel</B> button will reverse
123  any changes made while the window is open. Closing the window has
124  the same effect as "Cancel."
125  <P>
126  Once distances are entered, they are shown on the main panel, as
127  shown below.
128</DL></DL>
129<img src="dist2.png" alt="Distance constraint example screen">.
130<DL><DL>
131  Note that the interatomic distances that are shown are determined by
132  the parameters to program DISAGL. These are controlled with the
133  <B>Edit Search Distance Parameters</B> button.
134</DL></DL>
135<a name="Chemical Restraints"></a>
136<H4>A.7.2 Chemical (or Compositional) Restraints</H4>
137<DL><DL>
138  Chemical constraints allow a model to be penalized if it moves away
139  from expectations defined on the chemical compositions.
140  Up to 9 constraints, of form
141  <center>
142  <I>Target</I> =
143  W<sub>1</sub> * O<sub>1</sub> * M<sub>1</sub> +
144  W<sub>2</sub> * O<sub>2</sub> * M<sub>2</sub> +
145  W<sub>3</sub> * O<sub>3</sub> * M<sub>3</sub> + ...
146  </center>
147can be defined,
148  where O<sub>i</sub> is the occupancy of atom <I>i</I> (often refined),
149  M<sub>i</sub> is the site multiplicity atom <I>i</I> (determined by
150  the site symmetry) and W<sub>i</sub> and <I>Target</I> are set by
151  the scientist who defines the constraint.
152This allows chemical constraints to be used in many different
153  ways. They can be used to "push" a model to have a particular
154  composition on a site, or "push" an overall unit cell compositon or
155  even encourage that the chemistry follow rules such a balanced
156  charges with fixed atomic valency.
157<P>
158  When the panel is first loaded, it will be mostly blank, as shown below:
159</DL></DL>
160<img src="chem0.png" alt="Chemical constraint example screen">.
161<DL><DL>
162The "Add Constraint" button is used to enter one or more constraints,
163  which are then defined by selecting the phase, and atom name for
164  each atom in the constraint, as well as the weighting factor for
165  each atom (W<sub>i</sub>, above) as well as the Target value for the
166  sum (W<sub>1</sub> * O<sub>1</sub> * M<sub>1</sub> +
167  W<sub>2</sub> * O<sub>2</sub> * M<sub>2</sub> +
168  W<sub>3</sub> * O<sub>3</sub> * M<sub>3</sub> + ...) and the
169  uncertainty (ESD) for the sum, as shown below:
170</DL></DL>
171<img src="chem1.png" alt="Chemical constraint example screen">.
172<DL><DL>
173A more complex example, which implements a charge balance constraint,
174  is shown below.
175</DL></DL>
176<img src="chem2.png" alt="Chemical constraint example screen">.
177<DL><DL>
178Constraints are saved as the values are typed in. Also, the sum of the
179  actual
180W<sub>i</sub> * O<sub>i</sub> * M<sub>i</sub> values is shown in the
181  upper right.
182Atom entries where
183  the weight is blank or set to zero are ignored. New rows (up to 297)
184  are added when the existing ones are all used. If an error is
185  encountered in a constraint, a question mark ("?") is displayed for
186  the Actual Sum and the constraint is not saved.
187
188</DL></DL>
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