Triple Icon

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.


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:

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File Open opens a file.

A data sets loaded into Triple may look like this:



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.

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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.


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.

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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.


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.


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.


Here are conventional Windows functions for organising windows.


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.

%Structure 3931cuni
%Job 3931cuni
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)
emin 1.0
minfo 2. 50
set 1
peaks 60

SIR97 can be downloaded from on the Internet. SIR97 is available free for academic users.


Copyright 2013, Calidris