Tables for
Volume E
Subperiodic groups
Edited by V. Kopský and D. B. Litvin

International Tables for Crystallography (2010). Vol. E, ch. 5.2, pp. 400-401   | 1 | 2 |

Section Orthogonal, inclined and triclinic scanning

V. Kopskýa* and D. B. Litvinb

aFreelance research scientist, Bajkalská 1170/28, 100 00 Prague 10, Czech Republic, and bDepartment of Physics, The Eberly College of Science, Penn State – Berks Campus, The Pennsylvania State University, PO Box 7009, Reading, PA 19610–6009, USA
Correspondence e-mail: Orthogonal, inclined and triclinic scanning

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It is convenient for future reference to refine the basic categories of orthogonal and inclined scanning as follows:

  • (1) Orthogonal scanning. We call the scanning orthogonal if the scanning group is orthorhombic, tetragonal, trigonal or hexagonal.

  • (2a) Monoclinic/orthogonal scanning. This term is used if the scanning group is monoclinic and the vector d defines its unique axis.

    In both cases the vector d is orthogonal to the vectors [{\bf a}'] and [{\bf b}'] and they occur whenever the orientation orbit is a special orbit with fixed parameters.

    The absolute value [d = |{\bf d}|] of the scanning vector is, in cases of orthogonal scanning, equal to the interplanar distance defined by the Miller indices of the orientation.

  • (2b) Monoclinic/inclined scanning. The scanning is called monoclinic/inclined if the scanning group is monoclinic and its unique axis is one of the vectors [{\bf a}'], [{\bf b}']. The vector d is actually not necessarily inclined to the orientation [V({\bf a}'], [{\bf b}')]. It may be orthogonal owing to special metric conditions of the lattice which are determined by the scanned group [\cal G]. It is, however, a vector of a monoclinic basis which lies in the plane orthogonal to the unique axis. This case occurs when the orientation orbit is a special orbit with one variable parameter.

    The interplanar distance d in the case of inclined scanning is [d = |{\bf d}|\cos \varphi] where [\varphi] is the angle of the vector d with the normal to the plane.

  • (3) Triclinic scanning. The scanning is called triclinic or trivial if the scanning group is triclinic. This case occurs when the orientation orbit is a general orbit.

The difference between monoclinic/orthogonal and monoclinic/inclined scanning is illustrated in Fig.[link]. The orientation in the first case is fixed, while the second case applies to various orientations containing the monoclinic unique axis. The orientation can be defined by one free parameter, the angle [\varphi]; we use instead Miller indices [(mn0)].


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Monoclinic/orthogonal (left) and monoclinic/inclined (right) scanning.

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