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[Imgcif-l] imgCIF Standard Axis definition

  • To: The Crystallographic Binary File and its imgCIF application to image data <imgcif-l@iucr.org>
  • Subject: [Imgcif-l] imgCIF Standard Axis definition
  • From: David Brown <idbrown@mcmaster.ca>
  • Date: Thu, 03 May 2007 15:08:51 -0400
A proposal for the definition of a reference axis system in imgCIF (and 
by inference other CIF dictionaries).

By I.David Brown

The imgCIF dictionary recognizes that authors will require to use a 
number of different axis systems to describe, e.g., the crystal 
orientation, the reciprocal space orientation and the detector.  There 
is clearly a need to be able to relate these axes to each other.

For this purpose imgCIF defines a standard laboratory coordinate system 
(SLCS) based on directions that can be derived from the diffraction 
equipment being used.  Two directions are needed to define the SLCS and 
in the first version of the imgCIF dictionary, these directions are the 
incident beam and the spatially fixed rotation axis of the goniometer 
that holds the specimen.  X is defined as lying along the goniometer 
axis, Z as perpendicular to this and lying in the plane of X and the 
incident beam, and Y is chosen to complete a right handed rectangular 
coordinate system.  The origin is placed at the sample.

Problems arise if there is no goniometer as may occur, e.g.,  in small 
angle scattering experiments.  The incident beam will always define one 
direction, but a second direction is needed to define the X axis.

A recent proposal made by Bernstein is to use the principal axis of the 
detector, defined as the direction in which the detector is most rapidly 
scanned (for 1- annd 2-dimensional detectors).  An alternative might be 
the direction of the fixed rotation axis of the detector if one exists.  
The possibility remains, however, that no unique detector direction can 
be defined.   In this case Bernstein suggests that the Y axis be chosen 
in the direction of the gravitational field (down) or, in the case where 
the incident beam is vertical, the Y axis be chosen to point to the north.

While the original definition in the current imgCIF dictionary is simple 
and covers the majority of cases, if there is no goniometer the choices 
for the second axis start to multiply and some seem quite bizarre.  
Taking directions from the diffraction equipment makes sense because the 
relationship between the goniometer and the detector is relevant to 
interpreting the results.  But directions such as 'down' and 'north' are 
not related to the operation of the equipment or the interpretation of 
the measurements.  Rotating the apparatus while maintaining the 
relationship between its individual components would change the SLCS but 
make no difference to the relationship between the different practical 
axis systems.

The sole purpose in defining the SLCS is to allow the relationships 
between other axis systems to be expressed in a straightforward manner 
against some common coordinate system.  The way in which the SLCS is 
defined is irrelevant so long as it is used consistently within a 
related set of CIFs.  It is easier to interpret the transformation 
matrices used to define other axis systems if everyone chooses the same 
SLCS and it is convenient to base this SLCS on the obvious directions 
defined by the apparatus, but in those cases where the incident beam  is 
the only natural direction then the choice of the SLCS X axis is 
arbitrary and there is no reason why everyone need use the same SLCS.  
Since Bernstein's proposed choice of X axis depends on whether there the 
sample is mounted on a goniometer, and what kind of detector is in use, 
whether the incident beam is vertical etc.,  there will no longer be a 
universal definition applicable to all experiments.

PROPOSAL
My proposal is to keep the current definition using the fixed axis of 
the sample goniometer where such a direction exists and otherwise to 
allow the X axis direction to be chosen arbitrarily by the user with the 
understanding that it must be used consistently within any set of 
related CIFs (though it is not obvious that even this restriction is 
needed since it is only the relationship between the practical units 
that is ultimately needed).  It is likely that a standard SLCS would be 
adopted for instruments mounted at a major installation, even for that 
small subset of experiments that do not involve an identifiable fixed 
rotation axis for the specimen.   An item should be defined in the 
dictionary where the user can explain how the X axis has been chosen.  
This proposal would have the advantage of simplicity without defeating 
the purpose of the SLCS in those rare cases where the specimen is not 
mounted on a goniometer.


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