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## Constraining Peak Widths

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[The reference to use for XFIT or FOURYA in any resulting publications is: Cheary, R. W. & Coelho, A. A. (1996). Programs XFIT and FOURYA, deposited in CCP14 Powder Diffraction Library, Engineering and Physical Sciences Research Council, Daresbury Laboratory, Warrington, England. (http://www.ccp14.ac.uk/tutorial/xfit-95/xfit.htm)]

### The Problem

Following is an example using simulated data showing how with unconstrained peak widths, you can get a variety of results. But with peak-widths constrained to be the same values, results more consistent with the true values.

In this case the datasets consists of the following, but we will only dot his on widths\3010.xdd:

```The two PV peaks has the following values:

pk1:
area = 100
th2 = 30
FWHM = 0.2
PV-lortz = 0.5

pk2:
area = 100
th2 = 30.1 for 3010.xdd, 30.15 for 3015.xdd
and 30.20 for 3002.xdd
FWHM = 0.2
PV-lortz = 0.5
```
• Run XFIT, (maximise the screen if you wish) and do File, Load Data and open the widths\3010.xdd dataset. You can maximize the data to fit the entire XFIT screen. It should look something like the following. (if you can't see the active mouse output on the bottom right of the XFIT screen - maximise your XFIT window)

• If you fit these without any constraints, the values you obtain depend on the starting peak positions. E.g.,
```
Peak1    Peak2    Area1    Area2   FWHM1    FWHM2
True Results:          30.0     30.1     100      100     0.2      0.2

Starting   Starting  Refined  Refined  Refined  Refined  Refined  Refined
Peak 1     Peak 2     Peak1    Peak2    Area1    Area2    FWHM1    FWHM2
29.9907    30.0818   29.9873   30.0787   67       133     0.202    0.215
29.9907    30.0818   29.9868   30.0784   66       134     0.202    0.215

29.8450    30.2639   29.9864   30.0483    0       200     0.396    0.242
30.0211    30.0514   29.9875   30.0788   67       133     0.202    0.215
29.8936    30.0454   29.9523   30.0503    5       193     0.170    0.241
```
• As you can see from the following, this example fit from one of the above looks superficially quite excellent - if you are ignorant of the true value.

• To link the widths of the peaks together. You can either:
1. delete the old peaks, add two new peaks and constrain the widths.
2. Or you can keep these peaks; fix the widths to the identical numeric value;

• Taking the second option, first go into File Details, Peaks, Pseudo Voight, Values and set the two peak FWHMs to be the same. To do this, click and drag to select the peaks, then in the Change Selections To change to a suitable value (in this case a FWHM of 0.1).

• Then go into the Codes section and link the FWHMs together by using a suitable/arbitrary code-word (in this case link).

• Refining on this .

```
Peak1    Peak2    Area1    Area2   FWHM1    FWHM2
True Results:          30.0     30.1     100      100     0.2      0.2

Starting   Starting  Refined  Refined  Refined  Refined  Refined  Refined
Peak 1     Peak 2     Peak1    Peak2    Area1    Area2    FWHM1    FWHM2
29.9907    30.0818   30.0003   30.0878   90       110     0.210    0.210
29.8450    30.2639   30.0003   30.0878   90       110     0.211    0.211
30.0211    30.0514   30.0003   30.0878   90       110     0.211    0.211
```

Though it is still possible to get into false minima even with this FWHM constraint. Using appropriate constraints such as this makes it more likely that with repeated tries, you will get closer to a truer value more consistently than false values

```
Peak1    Peak2    Area1    Area2   FWHM1    FWHM2
True Results:          30.0     30.1     100      100     0.2      0.2

Starting   Starting  Refined  Refined  Refined  Refined  Refined  Refined
Peak 1     Peak 2     Peak1    Peak2    Area1    Area2    FWHM1    FWHM2
29.8936    30.0454   29.9726   30.0522   15       184     0.238    0.238
```

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