Commensurate systems

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. 

The two surfaces that comprise a contact can be oriented in any number of specific ways however, for crystalline surfaces, interfacial symmetries correspond to either of two broad classifications. The first type of orientation is called the commensurate case and is found when two identical surfaces are perfectly aligned. The term incommensurate corresponds to the case in which two crystalline surfaces are misoriented or have different periodicities. An example of a commensurate systems is given as structure A in Figure 7, whereas structures B through D are incommensurate. Interestingly, the orientation of the surfaces within a contact has a tremendous influence on... 

Figure 18 Coverage dependence of the kinetic friction coefficient pk of a system containing 0.25-2.5 monolayers of a simple fluid. Commensurate systems (c) are denoted with open symbols, and incommensurate systems (ic) are designated with closed symbols. Reproduced with permission from Ref. 82.

Conventionally, the ratio cjc-a is used as a basis for dividing these systems into two categories—commensurate and incommensurate. The ciassical definition assigns the inclusion compound as commensurate if cjc is a rational number and as incommensurate if Cg/ci, is an irrational number. However, because experimental measurements of and c can never be made with absolute precision, it is more practical to define an inclusion compound as commensurate if (and only if) Cg/cj, is sufficiently close to a rational number with low denominator. This is equivalent to stating that, for a commensurate system, small integers p and q can be found that satisfy the relationship pcy, = qc,. If no sufficiently small integers p and q can be found, the inclusion compound is incommensurate. 

Although the focus in this article is on the conventional urea inclusion compounds, we note that the inclusion compounds formed between urea and certain specific guest molecules arc commensurate tunnel stme-tures. For such commensurate systems, the host stmeture is usually distorted from the hexagonal tunnel stmeture shown in Fig. I. Examples are the inclusion compounds formed between urea and the guest molecules 1,6-dibromohexane, - " sebaconitrile and (a + l),(to - 1)-... 

Guest molecules in solid host structures are often constrained to exhibit uncharacteristic conformational properties, which can be exploited as a means of carrying out spectroscopic characterization of such conformations. For example, guest molecules in the 1,6-dibromohexane/urea inclusion compound (a commensurate system) exist exclusively with both bromine end groups in the gauche conformation allowing a definitive characterization of the vibrational properties of this conformation. 

V is measured from the unperturbed Larmor frequency, and << Vj is assumed, as is valid for RbQ 3M0O3. K is a normalizing constant. On the other hand the spectrum of a commensurate system consists of a small number... 

Flame spraying is no longer the most widely used melt-spraying process. In the power-feed method, powders of relatively uniform size (<44 fim (325 mesh)) are fed at a controlled rate into the flame. The torch, which can be held by hand, is aimed a few cm from the surface. The particles remain in the flame envelope until impingement. Particle velocity is typically 46 m/s, and the particles become at least partially molten. Upon impingement, the particles cool rapidly and soHdify to form a relatively porous, but coherent, polycrystalline layer. In the rod-feed system, the flame impinges on the tip of a rod made of the material to be sprayed. As the rod becomes molten, droplets of material leave the rod with the flame. The rod is fed into the flame at a rate commensurate with melt removal. The torch is held at a distance of ca 8 cm from the object to be coated particle velocities are ca 185 m/s. 

Response time may not be commensurate with the system s fast-changing needs. 

This is an extremely important aspect of the whole exercise. The basic purpose of all checks and controls is to reduce reworking, reprocessing, failures or rejections during the work process with a view to produce a product of the required quality and hence minimize cost for better financial returns. A high-cost input not commensurate with the type of the product may defeat the basic puipose of adopting such a system. 

In the next paper [160], Villain discussed the model in which the local impurities are to some extent treated in the same fashion as in the random field Ising model, and concluded, in agreement with earlier predictions for RFIM [165], that the commensurate, ordered phase is always unstable, so that the C-IC transition is destroyed by impurities as well. The argument of Villain, though presented only for the special case of 7 = 0, suggests that at finite temperatures the effects of impurities should be even stronger, due to the presence of strong statistical fluctuations in two-dimensional systems which further destabilize the commensurate phase. 

In many cases, it is necessary to complement physical security by the installation of an intruder alarm system in order to achieve the standard of security commensurate to the risk exposure. The scope of protection to be afforded by the alarm system depends on the security risk, but it may embrace fences, windows, doors, roofs, walls, internal areas, yards and external open areas, and vehicles inside and outside buildings. There is a comprehensive range of detection devices, but the choice of detector is critical to ensure that it provides the desired level of protection and is stable in the particular environment. 

Refrigeration system pipes are sized to offer a lowresistance to flow, since this reflects directly on compression ratio, commensurate with economy of pipe cost and minimum flow velocities to ensure oil return with the halocarbons. 

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