Incommensurate conditions

Martin et al. obtained a very low friction coefficient under ultrahigh vacuum with M0S2 coatings containing less than 1 % of oxygen [6], In this case, weak friction can only be explained by the presence of layers in incommensurate conditions. These superimposed layers with a rotational disorder were observed by high-resolution transmission electron microscopy (TEM) on very thin wear particles where only two layers can be observed (Figure 2.3). 

Figure 2.3 Wear particles after friction between steel and M0S2 coatings, containing two superimposed stackings in incommensurate conditions (angle of 30° measured on optical diffractograms). Reprinted with perimssion from Martin et al. [6], Figure 4, (1993) by the American Physical Society...

The authors carried out new observations of wear particles and confirmed the formation of M0S2 sheets during the tests. Some of these sheets are in incommensurate conditions (Figure 2.98). The rotation angle between two sheets, determined from the optical diffrac-togram, is equal to 30°. 

The action mode of IF-M0S2 is based on an exfoliation of their external sheets to release single sheets inside the contact area. These sheets lead to a reduction of the friction coefficient. Some of these sheets are in incommensurate conditions. This explains the very low friction coefficients observed. The results show that the action mechanism of IF-WS2 is identical to... 

Figure 2.99 HRTEM image of WS2 sheets in incommensurate conditions. The diffractogram of the framed area shows an angle of 30° or 10° between the three superimposed sheets [53]...

The example demonstrates that the instability and consequent energy dissipation, similar to those in the Tomlinson model, do exist in a real molecule system. Keep in mind, however, that it is observed only in a commensurate system in which the lattice constants of two monolayers are in a ratio of rational value. For incommensurate sliding, the situation is totally different. Results shown in Fig. 21(b) were obtained under the same conditions as those in Fig. 21 (a), but from an incommensurate system. The lateral force and tilt angle in Fig. 21(b) fluctuate randomly and no stick-slip motion is observed. In addition, the average lateral force is found much smaller, about one-fifth of the commensurate one. 

At room temperature, no exchange is observed in the presence of 200 mTorr H2, 20 mTorr D2 and 5 mTorr CO. Under these conditions, a monolayer of ordered CO was observed by STM. It is a hexagonal ordered structure incommensurate with respect to the Pt(lll) surface and a coverage of about... 

These experiments were, however, not completely accepted by some chemists working in the area of prebiotic chemistry these critics were unhappy with some synthetic conditions used, such as the KCN concentrations (0.1-0.2 M at 373 K). They felt that cyanide in such concentrations would have been relatively rapidly hydrolysed at 373 K in addition, CO pressures of 75 atm were considered incommensurate with real conditions in hydrothermal systems. 

Unlike the bulk morphology, block copolymer thin films are often characterized by thickness-dependent highly oriented domains, as a result of surface and interfacial energy minimization [115,116]. For example, in the simplest composition-symmetric (ID lamellae) coil-coil thin films, the overall trend when t>Lo is for the lamellae to be oriented parallel to the plane of the film [115]. Under symmetric boundary conditions, frustration cannot be avoided if t is not commensurate with L0 in a confined film and the lamellar period deviates from the bulk value by compressing the chain conformation [117]. Under asymmetric boundary conditions, an incomplete top layer composed of islands and holes of height Lo forms as in the incommensurate case [118]. However, it has also been observed that microdomains can reorient such that they are perpendicular to the surface [ 119], or they can take mixed orientations to relieve the constraint [66]. 

Therefore, whenever we introduce symmetries into our systems, we risk observing behavior that is inconsistent with that observed when these symmetries are absent. Because opposing surfaces are almost always incommensurate unless they are prepared specifically, it will be important to avoid symmetries in simulations as much as possible. Unfortunately, it can be difficult to make two surfaces incommensurate in simulations, particularly when the interface is composed of two identical crystalline surfaces. These difficulties arise from the fact that only a limited number of geometries conform to the periodic boundary conditions in the lateral direction. Each geometry needs to be analyzed separately... 

Self-assembly of alkanethiols on Ag(l x l)-Au(lll) obtained under conditions of UPD has been studied applying STM, Auger electron spectroscopy, and electrochemical techniques [146]. Even for the adsorbed short-chain alkanethiolates, the surface structure exhibited an incommensurable hexagonal lattice with the nearest-neighbor distances of approximately 0.48 nm that is usually found for long-chain alkanethiolates adsorbed on Ag(lll). 

The highest induction effect should be expected in the case of inequality w3 vv2 fulfillment at nq > w2. In this regard, accumulation of final products by the overall reaction (2.15b), No. 2 under the condition of effective induction performance must proceed at an incommensurately higher rate than the primary one. As mentioned above, the induction effect at w2 w3 will be insignificant, approaching the limit I = 0. In this consideration, it is assumed that rate constants ku k2 and k2 characterize elementary reactions of the same kinetic order otherwise, concentration factors would also have to be taken into account which would necessarily complicate the analysis. 

Me-S interactions leading to higher order commensurate and under certain conditions to incommensurate Meads overlayer structures give superstructures" and moire pattern" which can also be described by the Wood or matrk notation (cf. Figs. 3.17, 3.19). 

Since our surroundings are three-dimensional, we tend to assume that crystals are formed by periodic arrangements of atoms or molecules in three dimensions. However, many crystals are periodic only in two, or even in one dimension, and some do not have periodic structure at all, e.g. solids with incommensurately modulated structures, certain polymers, and quasicrystals. Materials may assume states that are intermediate between those of a crystalline solid and a liquid, and they are called liquid crystals. Hence, in real crystals, periodicity and/or order extends over a shorter or longer range, which is a function of the nature of the material and conditions under which it was crystallized. Structures of real crystals, e.g. imperfections, distortions, defects and impurities, are subjects of separate disciplines, and symmetry concepts considered below assume an ideal crystal with perfect periodicity. ... 

Impuritiesand the a P-quartz tranition. The a- 3-quartz transition was the basis for one of the earliest systematic investigations of the variation of transition temperatures in response to impurities. Pure a-quartz undergoes a first-order transition to a microtwinned incommensurate structure at 573°C, and this modulated phase transforms to P-quartz at 574.3°C with second-order behavior (Van Tendeloo et al. 1976, Bachheimer 1980, Dolino 1990). Tuttle (1949) and Keith and Tuttle (1952) investigated 250 quartz crystals and observed that Tc for natural samples varied over a 38°C range. In their examination of synthetic specimens, substitution of Ge for Si raised the critical temperature by as much as 40°C, whereas the coupled exchange of Ar +Li o Si depressed Tc by 120°C. They concluded from their analyses that the departure of the a-P-quartz inversion temperature from 573°C could be used to assess the chemical environ-ment and the growth conditions for natural quartz. 

Measurements have been made on a wide variety of molecules adsorbed on Au, Ag, or Pb surfaces [3,4,131,132]. The phase of the adsorbed layer changes from fluid to crystal as the density is increased. As expected, motion of fluid layers produces viscous dissipation that is, the friction vanishes linearly with the sliding velocity. The only surprise is that the ratio between friction and velocity, called the drag coefficient, is orders of magnitude smaller than would be implied by the conventional no-slip boundary condition. When the layer enters an incommensurate phase, the friction retains the viscous form. Not only does the incommensurate crystal shde without measurable static friction, the drag coefficient is as much as an order of magnitude smaller than for the liquid phase ... 

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