D I D O 9 5 , V O I D 9 5 & D I D O D E M O (PC versions 9/1997)

by Elke Koch & Werner Fischer, Marburg

For any crystal structure or for any 3-periodic set of points DIDO95 and VOID95 together enable the calculation of the Dirichlet domains (Wirkungsbereiche, Voronoi polyhedra) of all different atoms (points) and the calculation of all the corresponding different kinds of coordination polyhedra (cf. Koch & Fischer, Z. Kristallogr. 211, 251-253, 1996). The programs have been written in FORTRAN and designed as DOS applications for use on any PC, but will also run under WINDOWS.

Installation:

DIDO95 and VOID95 are distributed in packed form. In order to instal them, copy the file DIDOPK02.EXE into any directory. This programm unpacks itself when started. It also makes up the following 5 subdirectories that are needed to run DIDO95/VOID95:

All files in the different subdirectories connected with the same problem are stored under the same name (cf. examples included).

Input:

DIDO95 and VOID95 run interactively and ask for all input data in a self-explaining dialogue. Thereby the information on the crystal structure (or on the original point set) may either be given via keyboard or read from a file in DIDODATA. In the first case a DIDODATA file is produced by the program. A file in RGGEN containing the space-group generators has to be prepared in advance. Each space group may be described in any conventional or non-conventional setting. For all standard settings of space groups respective files are included. For non-standard descriptions such files may be prepared by the user in addition. Each file has to contain the following information:

At the beginning of each run some general control parameters may be changed:

  -   For the drawings of Dirichlet domains and coordination polyhedra in inclined projection the projection angle and the reduction factor for the direction perpendicular to the projection plane may be redefined by the user. Default values are 30 degrees and 0.5.
  -   For the calculation of a coordination polyhedron both programs display a list of those neighbours that give rise to faces of the Dirichlet domain (cf. below). The limiting value for neighbours with very small faces to be shown in this table may be changed. The default value is 0.5% of 4*π.

These changes only hold for the current run.

Output

The complete output data are directed to a file either in subdirectory DIDOPRNT or in subdirectory VOIDPRNT. The drawings of the polyhedra can only be sent to the printer by means of the PRINT SCREEN button (press ENTER for continuation).

Hardware requirements :

IBM-compatible PC with arithmetic coprocessor

Software limitations

D I D O 9 5

DIDO95 calculates and plots the Dirichlet domains for all atoms (points) with atomic label 1. Thereby only atoms with label 1 are used as neighbours that may give rise to faces of the Dirichlet domain.

Normally calculations are performed using bisecting planes between neighbour atoms, but different atomic radii may also be taken into account in different ways: by means of radical planes (Potenzebenen), or as proposed by Hoppe (Angew. Chemie 82, 7-16, 1970), or according to Carter (Acta Cryst. B34, 2962-2966, 1978). Only the use of bisecting planes or of radical planes results in a space partition without gaps between the polyhedra (Fischer, Koch & Hellner, N.Jahrb. Min.Mh. 1971, 227-237).

A distant neighbour may generate a face of the Dirichlet domain with the following property: The straight line connecting the center of the domain and the neighbour does not intersect the corresponding face. Such faces and neighbours are marked by an asterisk.

Optionally DIDO95 calculates and plots also the coordination polyhedra for the atoms with label 1 coordinated by other such atoms. At most those atoms may be included into the coordination shell that give rise to a face of the Dirichlet domain, but very small faces (i.e. faces corresponding to a spatial angle less than 0.5% of 4*π) are neglected automatically. The user may further reduce the coordination number. For the faces of the coordination polyhedra a slight puckering is allowed. The default limit of 0.2 Angstrom may be changed by the user.

DIDO95 prepares an input file for VOID95 in subdirectory DIDOVOID. It contains the coordinates of all atoms (points) with atomic label 0 and, in addition, for each kind of symmetrically equivalent vertices of the Dirichlet domains the coordinates of one point. (The vertices in a Dirichlet partition correspond uniquely to the centers of all polyhedral voids in the original set of atoms or points.)

V O I D 9 5

VOID95 uses a similar procedure to calculate and plot the coordination polyhedra for all coordinate triplets contained in the corresponding file in DIDOVOID. It only considers the coordination by atoms (points) with label 1. Dirichlet domains are used only in the course of the construction of the coordination polyhedra and are neither shown nor documented.

If a user is interested only in the coordination polyhedra of atoms with label 0, these coordination polyhedra may exclusively be calculated by VOID95. In this case, VOID95 requires input via keyboard (or manipulation of a DIDOVOID file produced within DIDO95 by any editor) and then generates a DIDOVOID file containing only the coordinates of atoms with label 0.

D E M O D I D O

DEMODIDO is a version of DIDO95 which shows, how the Dirichlet domain of one point from a set of symmetrically equivalent points changes, if the (metrical and coordinate) parameters of the central point vary along a one-dimensional path. To this end, the only output is a plot of each Dirichlet domain on the screen. The input is reduced to the following items expected on a file in the subdirectory DEMODATA (cf. sample files):

Such a file may be prepared with the aid of a program DEMOPREn, if the path is defined by a formula (e.g. for a sphere-packing type, cf. sample programs). It may be generated by any editor if experimental values shall be used (cf. file Q_I_). Then additional interpolation nodes may be supplied by a program like DEMOINTP. All the auxiliary programs distributed together with DEMODIDO prepare such files for the way forth and back along the one-dimensional path with halts at both ends.

All other input items are asked for by the program in analogy with DIDO95. The sequence of Dirichlet domains may either be shown step by step or automatically in a movielike procedure. In the latter case the performance may be stopped at arbitrarily chosen points by making the first lattice constant negative in the input file. Then DEMODIDO expects a comment of up to 50 characters on the next line (of course a blank line will also do).

The calculation of Dirichlet domains normally is fast enough to produce an appropriate effect on a PC 486DX/2 66. In case of a still faster computer slowing down is made available.

Authors' address:

Institut für Mineralogie, Petrologie und Kristallographie
Philipps-Universität Marburg
Hans-Meerwein-Straße
D-35032 Marburg
Fax 06421/282 8919