Incommensurate Superlattices

A superlattice is temied commensurate when all matrix elements uij j are integers. If at least one matrix element uij j is an irrational number (not a ratio of integers), then the superlattice is temied incommensurate. A superlattice can be inconnnensiirate in one surface dimension, while commensurate in the other surface dimension, or it could be mconmiensurate in both surface dimensions. 

The comparison of PTCDA with its parent perylene molecule is extremely interesting. For perylene MLs on Ag(l 11), electron diffraction suggests an orientational liquid, in which the molecules are positionally ordered in an incommensurate close-packed superlattice but orientationally disordered and mobile. The same activated Raman peaks as for PTCDA are observed but they are, however, orders of magnitude weaker, indicating that, while a molecular reaction centre may still exist in the perylene backbone, its residual activity would be too small for the molecule to recognize a preferred site. 

Iodine oxidation of Ni(OEP) and Cu(OEP) yields polycrystalline materials with a range of stoichiometries.108 Resonance Raman studies indicate the presence of I5- in contrast to the I3 observed for larger ring macrocycles. Single crystal studies of Ni(TMP)I indicate a metal-over-metal stack arrangement but with the Ni(TMP) unit puckered. The iodine superlattice is incommensurate with the Bragg lattice.107 The room temperature conductivity is 10 Q-1 cm-1 and increases on lowering the temperature to reach a rounded maximum at 115 K. The spin susceptibility is temperature independent down to a transition temperature of 28 K, well below the conductivity maximum. Below 28 K the susceptibility decreases in an activated fashion with Ajk 60 K.108... 

Adsorption processes on crystallographically well-defined substrate surfaces lead to the formation of 2D Meads phases with well-ordered structures denoted as overlayers". Generally, three different types of overlayers, depending on the degree of registry between overlayer and substrate, can be distinguished commensurate, higher-order commensurate or incommensurate overlayers, as illustrated schematically in Fig. 3.14. TTie term superlattice stmcture" is frequently used for commensurate overlayers which can be characterized by either the Wood or the matrix notation [3.271-3.274]. 

Figure 8.20 Superlattice reflections on diffraction patterns (a) strong reflections are indexed in terms of the parent structure (b) normal superlattice reflections can be indexed in terms of a larger supercell (c) co-linear incommensurate superlattice reflections, (associated with the 000, filled circles, and 210 reflections, open circles), (d) non-co-linear incommensurate superlattice reflections, (associated with the 000, filled circles, and 210 reflections, open circles)...

Figure 37. X-ray intensities as a function of temperature for incommensurate N2 (filled circles and solid line) and CO (unfilled circles and dashed line) on graphite (Papyex) at a coverage of about 1.17 + 10% monolayers. The intensity plotted on a linear scale is the superlattice peak intensity of the orientationally ordered structure divided by the peak intensity of the (V3 X s/3)Ri0 center-of-mass stmcture present in both the orientationally ordered and disordered phases. (Adapted from Fig. 6 of Ref. 242.)...

---