Visualisation tools for medium energy ion scattering (MEIS):
stereographic projections and azimuthal sections

Introduction

1. Stereographic projections are well established tools for visualising the crystallography of differing faces of crystals of different space groups (reference 1). The technique of MEIS relies on aligning a crystal with a collimated ion beam along a known crystallographic axis; a technique known as channelling (reference 2). The use of a stereographic projection greatly assists the determination of the alignment of a crystal in a MEIS experiment. The projections shown here have been modified to make them more applicable to MEIS. In a MEIS experiment, the intensity of each individual direction or channel is determined by the interaction of the shadow cone (reference 2) and the distance between atoms in that specific direction. For instance, in an fcc system, the (110) type directions have the most intense channelling, i.e. the greatest shadowing of sub-surface atoms. Hence, the size of the spots marking the channels in these stereographic projections indicates the intensity of the channel. An empirical algorithm has been used to calculate the size of the markers. The algorithm has been designed to match the size of the markers to the size of the channel ( although the match is only approximate and will vary for different ion/ target combinations). Whilst the size of the channel can be calculated (reference 1), there remains the complication  of different ion/ target combinations.
   
   
2. The azimuthal sections are essential for designing MEIS experiments where geometries are required such that the ion beam illuminates only one, two or three or more layers. For example, on an fcc (100) surface the (110) direction illuminates just one layer, whilst the (120) illuminates two. Of course this simplistic view is complicated by thermal vibrations and possible surface reconstructions. The azimuthal sections are also useful for visualising the way different blocking directions (reference 2) carry structural information, e.g. for an fcc (100) surface the (130), (150) and (170) blocking directions carry information about the first layer spacing. The value given for the angle which each direction makes with the surface has been calculated from the standard expression for cubic crystals (reference 3);

Information:

Face centered cubic (fcc) crystal faces:

fcc(100)

fcc(110)

fcc(111)

Body centered cubic (bcc) crystal faces
Not yet available

Diamond structure crystal faces
Not yet available

Hexagonal close packed (hcp) crystal faces
Not yet available

References

1. Mayer and Rimini, Ion Beam Handbook for Materials Analysis, Pergamon Press, New York (1979)

2. J. F. van der Veen, Surf. Sci. Rep. 5 (1990) 199

3. B. D. Cullity, Elements of X-ray Diffraction, Pergamon Press

4. See also Medium Energy Ion Scattering, R. M. Tromp, Chapter 10: Practical Surface Analysis (2nd. Edition) Volume 2: Ion and Neutral Spectroscopy, Ed. D. Briggs and M. P. Seah, John Wiley and Sons, Chichester (1992)