A.C.Hannon Interfere and Merge in Excel
page 3
4. The contents of the Excel workbook
Once the data are in the workbook, it can be used to choose optimum values for the re-
normalising factors
α
i
and Q-limits for each detector group. The workbook also allows for the
possibility that it may be necessary to add a straight line to each
()
iQ
i
due to an imperfect result
having been obtained from the ATLAS suite;
() () ()
iQ IQ I Q AQ B
iiii
S
ii
=−++
α
, (2)
where
A
i
is the gradient of the linear correction and B
i
is its intercept. It is necessary to use non-zero
values for
A
i
and B
i
when the
()
iQ
i
calculated according to eqn (1) is not horizontal over a range in Q
in which it might be expected to be horizontal. Caution should be exercised in using this linear
correction because a necessity for non-zero values of
A
i
and B
i
may indicate that the absorption
correction (calculated by CORAL) has not been performed correctly due to the use of an incorrect
numerical value (such as effective number density, radius or absorption cross-section). Possible
reasons why the linear correction may be necessary include the presence of a small amount of
hydrogen in the sample (usually as -OH or H
2
O) or the effect of a low energy nuclear resonance for
one of the isotopes in the sample.
The first two worksheets of the workbook contain the data from the ATLAS suite. These
worksheets are named DCS and SLF, and they contain the data from the LAD12345.DCS and
LAD12345.SLF files respectively. The SLF worksheet shows a plot of the self scattering
()
IQ
i
S
for
each of the seven LAD detector angles (see Figure 1). In the example workbook INTMER.XLS the
maximum
y-value of all of the plots is set to be suitable for a sample for which the self scattering level
(σ
scatt
/4π) is about 0.33 barns atom
-1
steradian
-1
. For a sample with a significantly different value for
σ
scatt
it will be necessary to modify the y-limits of all of the plots in the workbook.
The next seven worksheets show data for each of the seven LAD detector angles (5°, 10°, 20°,
35°, 60°, 90° and 150°). Each of these worksheets has two plots of the data and also contains the
relevant values of
α
i
, A
i
and B
i
. The first plot shows
()
IQ
i
S
and the two
()
α
ii i i
IQ AQ B++ (for the
two sides of the instrument), whilst the second plot shows the two
()
iQ
i
together with current merged
()
iQ. Both of these plots can be used as a guide to set the value of
α
i
(and A
i
and B
i
if necessary).
The second plot is also useful for choosing the reliable
Q-range (Q
min
and Q
max
) for each detector
group. The relevant
Q-limits are shown on these worksheets for reference, but they may not be set at
this point. Figure 2 shows as an example the 150° worksheet for a tellurite glass [5].
The seven worksheets for the individual LAD detector angles are followed by a worksheet
named QLIM. This worksheet is used to set the values of
Q
min
and Q
max
for each detector group and
it shows plots of the current merged
()
iQ. The worksheet also repeats the values for
α
i
, A
i
and B
i
for
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