Triangle as AB6 (3D or 2D)
or A-only framework (3D or 2D
and PDB) A world not as big as the zeolites and SiO2 polymorphs world (4-connected 3D nets), but fascinating too. Remove B in AB3 compounds built from AB6 octahedra sharing exclusively corners. Then connect A atoms with their six A atoms next nearest neighbours : you have drawn a 6-connected 3D net.
Armel Le Bail - created 12 Februrary 1996 - updated 19 June 1996.
Presented as a poster (in french) at the Journées de la Division Chimie du Solide (SFC), Paris, 4-6 Septembre 1996.
This VRML site is best viewed (3D files) by Netscape 3 + Live3D (choose preferably flat shading). PDB files may be viewed by RASMOL. The links noted 2D are .gif files.
The 6-connected 3D nets family currently shows rings built from 3, 4, 5 or 6 octahedra, exclusively. Represented either by AB6 octahedra or by the A-only framework in capped-sticks mode.
Triangle as AB6 (3D or 2D)
or A-only framework (3D or 2D
and PDB)
Square as AB6 (3D or 2D)
or A-only framework (3D or 2D
and PDB)
Pentagon as AB6 (3D or 2D)
or A-only framework (3D or 2D
and PDB)
Hexagon as AB6 (3D or 2D)
or A-only framework (3D or 2D
and PDB)
Combinations of the above rings lead to few possibilities for assembling 3D building units or cages.
Tetrahedra of octahedra (3:4 meaning 4 faces with 3 edges, in fact the
second number should be as exponent) as AB6 (3D
or 2D) or A-only framework (3D
or 2D and PDB)
Trigonal prism of octahedra (3:2-4:3 meaning 2 faces with 3 edges and 3
faces with 4 edges as AB6 (3D or 2D)
or A-only framework (3D or 2D
and PDB)
Cube of octahedra (4:6) as AB6 (3D or 2D)
or A-only framework (3D or 2D
and PDB)
Pentagonal prism (4:5-5:2) as AB6 (3D or
2D) or A-only framework (3D
or 2D and PDB)
Hexagonal prism (4:6-6:2) as AB6 (3D or 2D)
or A-only framework (3D or 2D
and PDB)
Friauf polyhedra (truncated tetrahedra : the pyrochlore cage) (3:4-6:4)
as AB6 (3D or 2D)
or A-only framework (3D or 2D
and PDB)
4:3 as AB6 (3D or 2D)
or A-only framework (3D or 2D
and PDB). These units build clusters of 10
AlF6 octahedra in t-AlF3 (3D or 2D)
and 15 octahedra in Na4Ca4Al7F33 (3D or 2D).
The clusters in both cases are chained, connected by one vertex of an octahedra.
5:4 as AB6 (3D or 2D)
or A-only framework (3D or 2D
and PDB). These 8-octahedra cavities are unoccupied
in t-AlF3 and occupied by the Na atoms in Na4Ca4Al7F33 (3D
or 2D).
3:1-5:3 as AB6 (3D or 2D)
or A-only framework (3D or 2D
and PDB)
5:2-6:1 as AB6 (3D or 2D)
or A-only framework (3D or 2D
and PDB). These units may be considered as forming
larger 4:2-5:4 ones by sharing 4 octahedra of the hexagonal ring with another
5:2-6:1 unit (3D or 2D).
Examples are taken mainly among inorganic fluorides because most of the recently discovered nets have not yet oxide counterparts, although they should have some day. Do not search for a complete review paper about this subject. There is none but this electronic publication. One of the most recent reviews on AB3 nets (Z. Kristallogr. 205, 85-97, 1993) lists only three of the nine geometries gathered below. In part, this is because stuffed AB3 nets are also considered here.
If you want to rebuild AB3 from the 6-connected nets, consider A at the net points and add B approximately at the middle of each line. Relaxation might be necessary for recovering regular AB6 octahedra.
Before 1989, 6 types were known. Then, 3 new types were disclosed.
alpha-AlF3 perovskite. AB6 (3D or 2D)
or A-only framework (3D or 2D
and PDB). The simplest of all these 6-connected
3D nets : cubes in the high temperature cubic form, or distorted ones at
room temperature (3D or 2D).
J. Phys.: Conden. Matter 2, 5663-5677 (1990).
beta-AlF3 : HTB (Hexagonal Tungsten Bronze) AB6 (3D
or 2D) or A-only framework (3D
or 2D and PDB)
J. Solid State Chem. 77, 96-101 (1988).
Ca2TlTa5O15 : perovskite-HTB intergrowth shown as AB6 (3D
or 2D) or A-only framework (3D
or 2D and PDB)
J. Solid State Chem. 29, 9-13 (1979).
TTB (Tetragonal Tungsten Bronze). Tunnels with trigonal, square and pentagonal
sections. AB6 (3D or 2D)
or A-only framework (3D or 2D
and PDB)
Acta Cryst. B29, 1654-1658 (1973).
NaNb(Nb5O15)F. Another way to combine tunnels with trigonal, square and
pentagonal sections, different from TTB. Shown as AB6 (3D
or 2D) or A-only framework (3D
or 2D and PDB)
Acta Chem. Scand. 19, 2285-2290 (1965).
AlF3 pyrochlore. The 6-connected 3D net of Al atoms is now simply the beta-cristoballite
structure. Large cages with hexagonal section. Tetrahedra of AlF6 octahedra
reproducing the O subnetwork in SiO2. In fact not really AlF3 but Al[(OH),F]3.
AB6 (3D or 2D)
or A-only framework (3D or 2D
and PDB)
Eur. J. Solid State Inorg. Chem. 25, 535-540 (1988).
t-AlF3, a recently discovered AB3 polymorph. AB6 (3D
or 2D) or A-only framework (3D1
or 2D1 and PDB
and also 3D2 or 2D2
and PDB). This compound contains the 4 new
building units to which must be added the old 3:4 one. More
on t-AlF3 is available as the MOTM (Molecule Of The Month) at Bristol,
March 1997.
J. Solid State Chem. 100, 151-159 (1992).
Na4Ca4Al7F33. The AB3 framework is [Ca4Al7F33]. A complex stuffed polytype
of t-AlF3 ; tetrahedra of octahedra (3:4) have disappeared. Shown as AB6
(3D or 2D)
or A-only framework (3D or 2D
and PDB). The compound contains only 2 of
the new building units 4:3 and 5:4, exclusively. The structure may be seen
also with the 5:4 cavities occupied by the Na atoms (3D
or 2D). The network built with the Na polyhedra
is shown too (3D or 2D).
J. Solid State Chem. 84, 153 (1990).
Rb2NaAl6F21. The AB3 framework is now [NaAl6F21]. An Hybrid of HTB (2 layers)
and pyrochlore types. AB6 (3D or 2D)
or A-only framework (3D or 2D
and PDB). This compound does not contain any
of the new building units, it is made only from old ones.
Eur. J. Solid State Inorg. Chem. 26, 281-288 (1989).
If you know other 6-connected 3D nets based on at least one existing triperiodical structure, E-mail me please. Hypothetical structures or guessed intergrowths are out of the subject. Electronic microscopically observed non-periodical intergrowths are out too. Only well defined crystal structures will be listed. Thanks are due to Yvon Laligant for having pointed to the absence of the Ca2TlTa5O15 and NaNb6O15F structure-types in the first version.
For the 6-connected 3D nets, if you have not a VRML viewer for .wrl files, you may consider copying the .pdb files and view them with RASMOL, this is really fine too (do not take seriously the word PROTEIN in the latter files). How files were they created ? A first drawing was made with STRUPLO or ORTEP starting from SHELX .ins files. Then atoms forming polyhedra (exclusively octahedra for the 6-connected 3D nets) were selected from the numbered list created by STRUPLO or ORTEP and inserted in a new .ins file. This SHELX .ins file was converted into a .pdb file by the BABEL program (using the -renum option and sometimes replacing atom names by fictitious ones selected for fitting requested bond distances). Then the .pdb files were converted into .wrl files by the PDB2VRML program.
Almost all programs cited here may be found by browsing into the Crystallography Virtual Library.
Have a look at the ILL's gallery of interactive 3D crystal structures in which originated the present page idea.
