The REME phases - II. What's possible?

In the second contribution on the REM E phases, we enumerate the distinct networks resulting from the stacking in an eclipsed fashion of graphitic and puckered layers. Specifically, we derive all the distinct hypothetical lattices for up to N=7 layers per unit cell for planar (graphitic) sheets, and up to N= 10 for slightly puckered layers. For the networks with slightly puckered layers, there can be only an even number of layers/unit cell, N. Additionally, we formulate an empirical rule for network stability: the structure should have either a mirror plane or a twin operation (mirror plane, followed by a color change) bisecting it half-way up the stacking axis. Using these simple principles, from the original multitude of 2(N-1) structures for a given N, we are able to significantly narrow down the number of potential combinations. Thus, for N = 2, we find two nets, for N = 4, one, for N = 6, two, for N = 8, there are no such viable arrangements, and for N = 10, we exclude all but two distinct lattices. We sketch further guidelines to continue the enumeration for higher Ns. We also propose an 'overlapping' Aufbau, by which more-complex structures are derived from the smaller, basic ones. In the last part, we analyze the eclipsed stacking of diamond-type layers; the resulting networks are analogous (in sequencing) to those determined for slightly puckered sheets. The networks formed from staggered diamondtype layers are briefly discussed in the context of the related SiC polytypes.