The Liebau Method for Crystal Chemical Classification of Silicates

We suppose the reader is familiar with the classification method of Friedrich Liebau as presented in his book
Structural Chemistry of Silicates - Structure, Bonding, and Classification. Springer-Verlag, 1985.
What we describe here are
The Method
In agreement with Friedrich Liebau we have exchanged steps 2 and 3 for selecting fundamental chains.
Thus we have implemented the following

Rules to Select Fundamental Chains

  1. The fundamental chains are chosen as chains of lowest periodicity which run parallel to the shortest identity period within the anion, regardless of their branchedness, and from which the anion can be generated by successive linkage.
  2. If more than one chain is derived in agreement with rule (1) the fundamental chains are chosen in the order of preference:
    unbranched (uB) > loop-branched (lB) > open-branched (oB) > mixed-branched (olB) > hybrid (hB).
  3. If more than one chain is derived in agreement with rules (1) and (2) the fundamental chains are chosen such that their number is lowest.

The order of the rules has been changed since with the original order preference is given for fundamental chains with branches over unbranched chains. As an example consider Naujakasite. It has been classified in the book of Liebau as unbranched vierer double layer. This result you only get with the new order of the rules. According to the original order the structure would have to be classified as loop-branched vierer double layer.

Multiplicity of Layer Silicates

Currently we use a method to compute the multiplicity of layers being not in accordance with the intuitive understanding of layers in some rare cases. The reason for this problem is that we need a formal definition of multi layers for our algorithms. Such a definition could not be derived from the informal description of multiplicity. As a consequence, the classification computed for layered structures should be checked with respect to the multiplicity parameter. The interactive graphical interface is well suited for this purpose.
The current method for computing multiplicity in case of layers (D = 2) is restricted to the distinction of single and double layers and works as follows:
The set of fundamental chains computed as described above is searched for two disjunct subsets (i.e. a partition) containing the same number of fundamental chains and having the following property: For every fundamental chain in one of the subsets there is a chain in the other set such that both chains are directly connected.
This proceeding is well-suited for most of the double layers we analyzed but it may result in the classification of a silicate as a single layer when there are fundamental chains in the two "layers" not being connected to the other "layer".


Input
The following structure data have to be supplied to the program system:
  • trivial name of the structure
  • spacegroup number (as given in the International Tables)
  • change of axes
  • setting (0: normal setting, 1: monoclinic first setting, 2: rhombohedral setting)
  • lattice centering
  • axes and angles of the unit cell
  • maximal bond distance (Si,Al,... - O)
  • kind and coordinates of all atoms in the asymmetric unit
  • two lists of atoms: one with atoms to be regarded as cations (T-atoms), the other with atoms to be regarded as anions
    A description of the format of these data is added to the input mask. The system needs your email address in order to send you the result of the analysis by email if the analysis cannot be finished within a few seconds. We intend to build up a database with classified structures. Your data will be added to the database only if you give the permission by selecting the appropriate button ("no" is the default choice).
    Depending on the version of your browser some of the input data are generated automatically if they can be derived from other data (e.g. angles after specification of the spacegroup number). If your browser may run JavaScript, it is possible to check the consistency of the format of input data.

    Output
    Output data are available in textual as well as in graphical form (VRML and Java applet).
    Textual output data are given in the following order:

  • input data
  • parameters and content of the primitive cell
  • distances between T-atoms and adjacent O-atoms

    For each T-atom of the asymmetric unit:

  • coordination number (CNT)

    For each T-atom of the primitive cell:

  • neighbours (other T-atoms sharing O-atoms with the atom)

    For each connected unit (single ring, layer, framework):

  • connectedness s and linkedness L of each T-atom
  • T-atoms of the connected unit
  • type of anion
  • dimensionality D
  • coordination number
  • linkedness
  • chain periodicity P
  • multiplicity M
  • branchedness B
  • information on chains (shortest repetition direction and distance, branchedness, atoms, symmetry relation to other chains)

    Start the system