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The 4-connected nets of interest in crystal chemistry can all be realized as 4-coordinated sphere packings, in which the sphere centres correspond to the vertices of the net and the sphere contacts correspond to edges. This ensures that each vertex has exactly four equidistant nearest neighbours. In practice, a further restriction is useful2; in the conformation of maximum volume subject to the constraint of equal edges, the structure should remain 4-coordinated.

The net of the new ice structure fits these criteria, and I give coordinates for maximum volume and equal (unit ) edge length. The symmetry is I&4macr;2d with a = 2.988, c = 1.424, c/a = 0.477. The vertices are of two kinds: A in 4 a, 0,0,0 ⃛. and B in 8 d, x,1/4,1/8 ⃛ with x = 0.3675. This is close to the conformation (c/a = 0.485, x = 0.3643) found in the real material1.

The vertex symbols3, which give the number and kind of smallest rings contained in each angle, are for A: 72·72·72·72·84·84and for B:7·73·73·73·84·84. It turns out that every angle containing 7-rings also contains two 8-rings, and the total ring count for the unit cell is sixteen 7-rings and twenty-four 8-rings.

Figure 1 (left) shows the net projected down c. It should be clear that there are no 5-rings. I find this structure remarkable because every other known 4-connected net of interest in crystal chemistry contains smallest rings that are 6-rings or smaller. This is true for all the 130 or so zeolite structures; indeed, it is true for all 400 or so individual vertices of these structures.4

Figure 1: Nets projected down c with numbers giving elevations in multiples of c/8.
figure 1

Left, the ice XII net. Links between vertices are shown as lines, pairs of links up and down as double lines, and links between vertices in adjoining cells as broken lines (for example, a line between vertex at elevation 6 and one at elevation 1 is really a link between vertices at elevations -2 and 1, or at 6 and 9). The dashed square outlines a unit cell. Right, a second net with the same symmetry as that of ice XII but of lower density.

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It is also true for all my collection of more than 200 uninodal and binodal nets, most of which occur in one or more contexts in crystal chemistry. From a study of such structures, it was concluded5 that “a tetrahedral framework whose smallest rings are 7-membered or more will probably not be possible”.

A net has been described3 with only 7-rings, but this is an exceptional structure that cannot be realized as a 4-coordinated sphere packing and with one angle that lacks rings. It is not likely to serve as a framework for structures such as ices and alumino-silicates.

The new structure (in the maximum-volume form given above) is one of the densest 4-connected nets in known crystal structures (I exclude intergrowths of two or more nets such as are found in some dense forms of ice). For unit edge length, the number of vertices per unit volume is r = 0.944. This might be compared with r = 0.845 for coesite (the densest 4-connected silica net) and r = 0.750 for quartz.

The most nearly comparable structure is that of ice IV (ref. 6), which also occurs metastably in the ice V stability field and for which I find r = 0.971 in the maximum-volume form. The vertex symbols for the two vertices (which occur in the ratio 1:3) in this structure are 62·82·62·82·62·82and 6·62·6·83·6·88(this structure also contains 10-membered rings).

Another net (Fig. 1, right) that has the same symmetry as that of ice XII but is of lower density (r = 0.669) does contain 5- and 7-rings and appears in simulated annealing experiments7 as a silicon net in SiO2. For this net (again with unit edges), a = 3.193, c = 1.760, and the vertices are 5·5·5·5·82·82at 0,0,0, and 5·5·5·7·7·7 at 0.1556,1/4,1/8.