Crystallography Online: the website of the International Union of Crystallography

Two comments on David's proposal:

1.  No matter how the direction of the X-axis is chosen,
it is important to place the origin of the X-axis in
the sample, not in the detector.  Otherwise calculations
of beam centers and detector distances become
quite difficult.

2.  If an X-axis is chosen that is different from
the pricipal axis of the goniometer, it is important
that it be clearly documented, so that, for example
the detector axes do not get miss-identified.

There is a draft of the current proposal prior to
David's suggestion at

http://www.bernstein-plus-sons.com/software/CBFlib_0.7.7/doc

Please do consider what is in the proposal and what
David has suggested as a modification, and please
send your comments and suggestions to this list.

  -- HJB

=====================================================
 Herbert J. Bernstein, Professor of Computer Science
   Dowling College, Kramer Science Center, KSC 121
        Idle Hour Blvd, Oakdale, NY, 11769

                 +1-631-244-3035
                 yaya at dowling.edu
=====================================================

On Thu, 3 May 2007, David Brown wrote:

> 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.
>
>