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
- a difference between our implementation and the algorithm given
in the book
- a method to compute the multiplicity parameter which may result in a classification
of layer silicates different from intuition
- the structure of the data you have to supply
- the information you get by our system
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
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.
- 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.
- 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).
- 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.
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".
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)
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
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:
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
chain periodicity P
information on chains (shortest repetition direction and distance,
branchedness, atoms, symmetry relation to other chains)
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