Triple 
What Triple does
Triple is used for processing diffraction intensities, obtained from
either electron diffraction or X-ray diffraction or from amplitudes and phases obtained
from high resolution electron microscopy images. Triple includes the following functions:
- Merge data from diffraction patterns with different exposure times and/or from different
zone axes.
- Merge symmetry-related reflections according to the space group.
- Calculate E-values (= normalised crystallographic structure factors).
- Phase extension.
- Calculate d-values.
- Sort reflections into different categories.
- Triple runs under Win9x, WinNT and Win2000.
Running
The basic operation of Triple is to open a file containing reflection
data, click to specify the space group using
the Space Group Explorer, and to perform various operations on the reflection data.
Triple menus:

File Open opens a
file.
A data sets loaded into Triple may look like this:

SpGroup 
Browse opens the Space Group Explorer and enables the user to specify a space group for
this data set. The space group can be specified by either the space group number or the
space group symbol.

Space Group Explorer gives you information about equivalent positions,
which reflections that are systematically absent (forbidden), phase restrictions,
seminvariant vectors and modulus, and other information about the current space group.
You can find out which reflections that are symmetry-related to a
certain reflection, for example 3 2 0, by the option . Both indices and phase values are given. The e = 2 stands for reflections
which are systematically enhanced.

If you click you will
find a Help-file with several useful scientific references explaining the topics in Space
Group Explorer, such as rotation matrices, phase restrictions, seminvariants etc.
Tools |

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Compact HKL will
merge symmetry-related reflections according to the current space group. For P1,
only the Friedel pair h k l and -h -k -l will be merged.
Expand HKL will
expand the current list to a complete list (half of reciprocal space) according to the
current space group.
KASH will start a
procedure for determining the phases of some very low angle reflections using a rigid
least squares refinement of a sphere. This operation is only useful for 3D diffraction
data on large unit cells whose contents can be modelled as a sphere of uniform density,
for example proteins.
Sayre starts the
calculation of phases using the Sayre equation. This is a preliminary implementation which
tries to calculate the phases of reflections using the phases of known reflections. In
optimal cases the phasing can start from no known reflections, but in normal use a few low
resolution phases will be known.
The Sayre phasing operates on E-values, which are the observed
diffraction amplitudes scaled in bins of resolution. Normally the user will divide
reciprocal space into bins of , although the
option is given to use another power. The program gives you the choice of how many bins of
resolution to use.
Merge data sets
opens a new dialogue box for merging several data sets into one.

All of the opened data sets which are currently opened are presented as
candidates for merging, and the user picks which ones to use. An option is provided for attempting to merge a data set
into the merged data set without actually modifying the merged data set. The actual
merging takes place only when you click .
The merged data will be placed in the highlighted (dark blue) file to the left of the button. The original data is now overwritten in
the memory by this new merged data, but your original file will be changed only if you save
the file.
The original data file |
A summary of the results of merging |
A summary of the results of compacting |
The resulting data file |
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After clicking Try or Merge, Triple will present two
Tables with detailed statistics about the reflections (see the two windows to the right).
In the upper Table, the reflections are sorted according to their amplitudes A. In the
lower Table, the reflections are sorted according to their d-values. nrefl = number
of reflections in the bin, Scale = the merging scale factor, Aaver = average
amplitude/intensity in the respective bins, A = amplitude interval, Multipl
= multiplicity, d-val = d-value.
The quality of the data can be judged both from the Scale factor
and the Rmerge value. For example, if two diffraction patterns from the same area
of a crystal are merged, the scale factor should be equal to the relative exposure times.
The Rmerge should ideally be 0%, but a value below 5% or 10% is usually quite good. Rmerge
gives the average difference between the data in the two films, after they have been
scaled together.
Change Lattice parameters
allows you to modify the lattice parameters. In the input file there is an initial set of
lattice parameters, provided by the creating program. These are read from the file, and
written to the new file, and here you have the chance to modify them. |

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Shift HKL allows you to apply a phase shift to the reflections,
according to the formula Pmod = Pinit + h * sh + k * sk + l * sl, where Pmod is the
modified phase, Pinit is the initial phase, h, k and l are the indices, and sh, sk and sl
are the phase shifts along these directions. This function is used for shifting the origin
within the unit cell.

Recalculate d-values does just that. This operation may
be necessary if the operations you perform (for example modifying the unit cell) result in
a change of d-values.
Calculate E-values
allows you to calculate E-values. If this step has not been performed before doing a Sayre
equation, then this dialogue box opens automatically on starting Sayre.
Perform bin smoothing should always be activated. |

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List |

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Clear clears the
current list shown on the screen. The latest data is still stored in the memory.
List HKL list
lists the latest reflection data sets (may be already modified). The old data sets in the
dialogue box will be deleted only if you click on Clear . You can scroll in the data using the (vertical) scroll bar.
Format opens a new window, called HKL List Options which
shows the current formats of the files to be saved and the formats of the files to
be listed on the screen. These formats can be modified if required. In this way
you can determine exactly what you will get in the output file. See the description of
file formats in order to select which fields you require. The amplitude format box allows
you to change the size of the amplitude field in the file, and to specify the number of
decimals. Similarly for d-values. |

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Sorting
The reflection data can be sorted in six different ways; by
d-value, intensity, index and so on. The sorting options are available in the List menu.
Note that there are several ways to sort the data according to index.
Window
Here are conventional Windows functions for organising windows.
Help
Use this manual when you need help.
Solving structures by Direct Methods using SIR97
Due to a collaboration with Professor
Carmelo Giacovazzo and Dr. Gianluca Cascarano in Italy, electron diffraction data obtained
for example by ELD and Triple can be used as input to their program SIR97.
Note the line electrons which specifies that the data is from electron
diffraction, rather than the usual X-ray diffraction. The line Format (3I4,2F8.2) tells
that SIR97 expects a data set with H K L Amplitude and SigmaAmpl in the fixed format 3
times Integer*4 and 2 times floating point data with 2 decimals.
A detailed explanation of the file formats and how to run SIR97 can be
found on the www-site quoted below. |
%Window
%Structure 3931cuni
%Initialize
%Job 3931cuni
%Data
electrons
Cell 11.351 14.052 3.322 90. 90. 90.
SpaceGroup P n n m
Content ti 24 s 12
Reflexions 3931cuni.hkl
Format (3I4,2F8.2)
%normal
%invar
emin 1.0
%phase
random
nneg
nngq
minfo 2. 50
%four
set 1
peaks 60
%cont |
SIR97 can be downloaded from http://www.ba.cnr.it/IRMEC/SirWare_main.html
on the Internet. SIR97 is available free for academic users.
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