Commensurability effects

Figure 4.29. Back-calculated results for files VALIDX.dat. The data are presented sequentially from left to right. The ordinate is in % of the nominal concentration. Numbers X = 1,2, and 3 indicate the data file. Each bracket indicates a day s worth of results (sorted by concentration). The log/log format tends to produce positive deviations at low concentrations, while the lin/lin format does the opposite, to the point of suggesting negative concentrations The reason is that the low concentration values are tightly clustered at the left end of the lin/lin depiction whereas the values are evenly spread in the log/log depiction, with commensurate effects on the position of Xmean, the sum Sxx< and the influence each coordinate has on the slope. The calibration design was optimized for the log/log format.

It is important to remark here that the periodicity of the cation sublattice in the chain direction z just coincides with 2kF periodicity in the case of TEA(TCNQ)2, and with 4kF periodicity in the case of MEM(TCNQ)2. This fact would suffice by itself to account, in terms of electron-cation interaction and commensurability effect, for the intrinsic chain tetramerization of TEA(TCNQ)2 and for the intrinsic chain dimerization of MEM(TCNQ)2, in particular for the residual dimerization still above 335 K. However, the cation subsystem certainly has a more direct, steric influence than through only the electron-ion interaction discussed above on the overall structural properties of the organic salts. 

Nb thin films have been deposited on porous silicon (PS) substrates. The PS templates consists of a short-range order matrix of pores with mean diameter of 10 nm and mean interpore distance of 40 nm, which act as an array of artificial pinning centers. Commensurability effects between the Abrikosov vortex lattice and the artificial one were investigated by transport measurements. 

The structure is of the fluorite type with extra sheets of atoms inserted into the parent YX2 structure. When these are ordered, a homologous series of phases results. When they are disordered, there is a non-commensurate, non-stoichiometric phase, while partial ordering will give a Vernier or semi-commensurate effect. Other layer structures can be treated in the same way. 

We have already discussed confinement effects in the channel flow of colloidal glasses. Such effects are also seen in hard-sphere colloidal crystals sheared between parallel plates. Cohen et al. [103] found that when the plate separation was smaller than 11 particle diameters, commensurability effects became dominant, with the emergence of new crystalline orderings. In particular, the colloids organise into z-buckled" layers which show up in xy slices as one, two or three particle strips separated by fluid bands see Fig. 15. By comparing osmotic pressure and viscous stresses in the different particle configurations, tlie cross-over from buckled to non-buckled states could be accurately predicted. 

Abstract Data are presented to show that the surfaces of a common clay mineral, montmorillonite, modify the properties of the nearhy water to a depth of at least 3.S nm and that the value of every water property depends exponentially on t, the thickness of the films of adsorbed water, but is independent of the character of the surfaces. The viscosity and yield point are among the properties of the water that are modified. A modification of either of these properties has a commensurate effect on the flow of water between adjacent surfaces. Data are also presented to show that the surface-induced... 

Huang, E., Mansky, P. et al. (2000) Mixed lamellar films evolution, commensurability effects, and preferential defect formation. Macromolecules, 33(1), 80-88. 

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