symbol
The basic structures have a three-letter code e.g. srs for the
SrSi2 net and dia for the diamond net.
Some derived structures are designated thus (see below for definitions)
| -a | augmented net |
| -b | binary net |
| -c | catenated pair |
| -d | dual |
| -e | edge net |
| -f, -g etc. | decorated nets |
| -x | extended coordination |
| -z | alternative configuration |
- augmented net
-
is one in which the vertices of the original net are replaced by a
polygon or polyhedron corresponding to the original coordination
figure. The net (cab) named for CaB6 is the
augmented primitive cubic (pcu) net and can also be found using
the symbol pcu-a.
- binary net
-
is one derived from a uninodal net with even rings by alternating
vertices AB such that A is bonded only to B and
vice versa. The sphalerite structure of ZnS is the binary version of
diamond (dia-b). A binary net can have one kind of vertex
colored as in tbo-b or even one kind of node three-colored as
in tbo-b3. Yet another possibility is that a uninodal net may
have the nodes split into unequal parts as in srs‑b* in which ¼
of the nodes are one color and ¾ another color (the net is no longer
bipartite now).
- catenated net
-
refers to a pair of self-dual nets (such as diamond)
intergrown. Notice that the symmetry of the pair is different from
that of just one. Multiple (n-fold) catenations are indicated
by extension ‑cn. There may be two different catenations
of the same multiplicity as in dia-c3 and dia-c3*.
- dual net
-
is the net of the tiling dual the natural tiling of the first
net. This is the same net in the case of self-dual
nets. E.g. dia-d = dia.
- edge net
-
(also expanded net) is obtained from the original net by placing
vertices in the middle of the edges, discarding the original vertices
and edges, and joining the new vertices to enclose the coordination
figure of the original vertices.
- decorated nets
-
are obtained by replacing the vertices of the original net by groups
of vertices. Augmented nets are special cases of decorated nets. (To
see examples enter bcu.)
- extended coordination
-
Occasionally one wants to consider other than nearest neighbors in the
coordination shell. An example is provided by the body-centered cubic
lattice. Each vertex has eight first neighbors and 6 second
neighbors. The structure bcu is eight-coordinated and is the
dual of nbo. bcu-x is 14-coordinated and is the dual
of sod. [bcu-x is the structure corresponding to a
vertex- and tile-transitive tiling of space by tetrahedra].
- alternative configuration
-
Sometimes a configuration other than the maximum volume is of
interest. See for example the configuration (ths-z) of the
3-coordinated ths net with the three edges meeting at a vertex
forming a T shape. In nets such as sld-z and rld-z in
the maximum symmetry configuration two or more vertices occupy the
same site. For such nets the embed type is given as 5 followed by the
symbol for the maximum-symmetry space group.
Reference:
O'Keeffe, M.; Peskov, M/ A.; Ramsden, S. J.; Yaghi,
O. M. Accts. Chem. Res. 2008, 41, 1782-1789.