# Bond defects in ring statistics

##### ABAB and BABA rings

The ring statistics of amorphous networks are often focused on finding rings made of a succession of atoms with an alternation of chemical species, called ABAB rings. The most common examples come from the alternation of Si and O atoms (in silica polymorphs) or Ge and S (in GeS\(_2\) polymorphs). These solids are usually built with tetrahedra (SiO\(_4\) or GeS\(_4\)) therefore we study the network distribution of tetrahedra.

The ideal technique to setup the analysis of such systems is to choose the atoms of highest coordination to initiate the search, respectively Si in SiO\(_2\) and Ge in GeS\(_2\). In most cases all rings can be found using this method. Nevertheless we can demonstrate that some solutions, so some rings, can be ignored by this analysis. This is highlighted in figure 5.24 which represents a cluster of atoms isolated from an AB\(_2\) amorphous network.

We can see that this piece of network is characterized by a bond defect. An atom of the B species appears to be over-coordinated by three atoms of the A species. When looking for rings, using the King's criterion [S. 5.5.2.1] and initiating the search using the A atoms, the central ring with 10 nodes is ignored. Nevertheless other rings with 10 nodes are found and stored as solutions of the analysis. In order to find the central ring the search has to be initiated from the overcoordinated B atom.

By analogy with the terminology ABAB this ring can be called a BABA ring. Indeed the alternation of chemical species is well respected. Therefore it is legitimate to question the relevance of the analysis without this result. In other words we have to check out if this BABA ring is, or not, an ABAB ring.

The properties of this ring meet the definition and can therefore improve the description of the connectivity of the network. This kind of coordination defect [Fig. 5.24] is uncommon in vitreous silica [1], [2], nevertheless it is frequent in chalcogenide glasses [3], [4].

##### Homopolar bonds

In amorphous materials the homopolar bond defects can have a significant influence on the ring statistics. This is true in particular for AB\(_2\) chalcogenide glasses. Figure 5.25 illustrates standard cases that may be encountered when looking for rings in an AB\(_2\) system which contains homopolar bonds.

The smallest rings found when initiating the search using the circled nodes (green color) are not ABAB rings. Therefore their size must be given using the total number of nodes. In figure 5.25 the smallest rings are a ring with 9 nodes and a ring with 11 nodes containing respectively an A-A and a B-B homopolar bond. These rings are significantly smaller than the shortest ABAB ring with 18 nodes that may be found when looking for rings using the same green-circled nodes to initiate the analysis [Fig. 5.25].

The * Atomes* program provides options to take into account or avoid A-B-A-B rings as well as homopolar bonds.

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