Mechanical instabilities

In actual practice, a weight W is obtained, which is less than the ideal value W. The reason for this becomes evident when the process of drop formation is observed closely. What actually happens is illustrated in Fig. 11-10. The small drops arise from the mechanical instability of the thin cylindrical neck that develops (see Section II-3) in any event, it is clear that only a portion of the drop that has reached the point of instability actually falls—as much as 40% of the liquid may remain attached to the tip. 

Figure C2.4.3. Pressure-area isotlienn for a fatty acid. The molecules are in a gaseous, liquid or solid state, depending on tire area per molecule available. If tire pressure is furtlier increased, a mechanical instability occurs and tire film breaks down.

In a force-displacement curve, the tip and sample surfaces are brought close to one another, and interact via an attractive potential. This potential is governed by intermolecular and surface forces [18] and contains both attractive and repulsive terms. How well the shape of the measured force-displacement curve reproduces the true potential depends largely on the cantilever spring constant and tip radius. If the spring constant is very low (typical), the tip will experience a mechanical instability when the interaction force gradient (dF/dD) exceeds the... 

Fig. 1. Schematic diagram illustrating the mechanical instability for (a) a weak spring (spring constant k) a distance D from the surface, experiencing an arbitrary surface force (after [19]) and (b) the experimentally observed force-distance curve relative to the AFM sample position (piezo displacement) for the same interaction.

The belt suffers from mechanical instability, thus often causing it to break, usually at the most inconvenient time ( Murphy s Law - the most important scientific principle in any experimental discipline ). The tunnel seals, used to isolate the differential vacuum regions of the interface, are the most likely places for the belt to snag. Inefficient cleaning of the belt of residual sample and/or inorganic buffers (see below) tends to exacerbate this problem. 

The studies on adhesion are mostly concerned on predictions and measurements of adhesion forces, but this section is written from a different standpoint. The author intends to present a dynamic analysis of adhesion which has been recently published [7], with the emphasis on the mechanism of energy dissipation. When two solids are brought into contact, or inversely separated apart by applied forces, the process will never go smoothly enough—the surfaces will always jump into and out of contact, no matter how slowly the forces are applied. We will show later that this is originated from the inherent mechanical instability of the system in which two solid bodies of certain stiffness interact through a distance dependent on potential energy. 

The mechanical instability, jump-in and pull-off phenomenon, can also be observed in a macroscopic system, and both the trajectory and force curves exhibit similar patterns to those in Fig. 6. As a comparison, Fig. 9 shows a force curve obtained from SFA experiments of mica surface separation in diy air [8]. The pattern of the force variation, the... 

This paper is, thus, a double tribute to Professor Berthier. On one side, G. Berthier has provided excellent analysis of quantum mechanical instabilities [4], while additionally being at the origin of the interest of the Namur group for studies of (hyper)polarizabilities in organic molecules and chains. 

Four solid oxide electrolyte systems have been studied in detail and used as oxygen sensors. These are based on the oxides zirconia, thoria, ceria and bismuth oxide. In all of these oxides a high oxide ion conductivity could be obtained by the dissolution of aliovalent cations, accompanied by the introduction of oxide ion vacancies. The addition of CaO or Y2O3 to zirconia not only increases the electrical conductivity, but also stabilizes the fluorite structure, which is unstable with respect to the tetragonal structure at temperatures below 1660 K. The tetragonal structure transforms to the low temperature monoclinic structure below about 1400 K and it is because of this transformation that the pure oxide is mechanically unstable, and usually shatters on cooling. The addition of CaO stabilizes the fluorite structure at all temperatures, and because this removes the mechanical instability the material is described as stabilized zirconia (Figure 7.2). 

The conditions for mechanical instability can be derived from a set of criteria for the stability of equilibrium systems put forward by Gibbs [8], Considering instability with regard to temperature and pressure, the criteria for stability are... 

Earlier we used a relatively simple model composed of a slider and substrate to demonstrate how mechanical instabilities lead to energy dissipation and friction. However, realistic contacts are much more complex. For instance, real contacts can rarely be described as one-dimensional and almost always contain some molecules that act as impurities. Understanding the frictional aspects of these systems will require a consideration of the role instabilities play in systems that are more complex than the PT model. In this section, we discuss studies that investigate instabilities in more realistic systems. 

Platinum corrosion and Use of a titanium reference liner with mechanical instability extended change-out frequency for a given full-scale reactor every 500 hr or longer... 

CNT conductive surface modification Both SWNTs and MWNTs can be deposited directly from a CNT dispersion as a random network or thin film on conventional electrodes. From the point of view of their construction such electrodes are very easy to prepare but they may suffer from mechanical instability, thus limiting their application. 

Interfacial turbulence [60] Due to a nonuniform distribution of surfactant molecules at the interface or to local convection currents close to the interface, interfacial tension gradients lead to a mechanical instability of the interface and therefore to production of small drops. 

The two aforementioned mechanisms involve a mechanical instability of the interface that breaks up and produces small droplets. 

In an optical micrograph of a commercially available nitinol stent s surface examined prior to implantation, surface craters can readily be discerned. These large surface defects are on the order of 1 to 10 p.m and are probably formed secondary to surface heating during laser cutting. As mentioned above, these defects link the macro and micro scales because crevices promote electrochemical corrosion as well as mechanical instability, each of which is linked to the other. Once implanted, as the nitinol is stressed and bent, the region around the pits experiences tremendous, disproportionate strain. It is here that the titanium oxide layer can fracture and expose the underlying surface to corrosion (9). 

The basic question is how to perform extrapolations so as to obtain a consistent set of values, taking into account various complications such as the potential presence of mechanical instability. Additional complications arise for elements which have a magnetic component in their Gibbs energy, as this gives rise to a markedly non-linear contribution with temperature. This chapter will concern itself with various aspects of these problems and also how to estimate the thermodynamic properties of metastable solid solutions and compound phases, where similar problems arise when it is impossible to obtain data by experimental methods. 

However, on the basis of calculations of lattice stabilities from spectroscopic data. Brewer (1967, 1979) has consistently maintained that interaction coefficients can change drastically with composition, and that extrapolated lattice stabilities obtained with simple models should therefore be considered as only effective values. While this may indeed be true when mechanical instability occurs, many of the assumptions which underlie Brewer s methodology are questionable. A core principle of the spectroscopic approach is the derivation of promotion energies which require the definition of both ground and excited levels. Assumptions concerning the relevant excited state have always been strongly coloured by adherence to the empirical views of Engel (1964) and Brewer (1967). By definition, the choice... 

This impasse was eventually resolved by taking into consideration the calculated elastic constants of metastable structiu-es in addition to their energy difference at 0 K. Craievich et al. (1994), Craievich and Sanchez (1995) and Guillermet et al. (1995), using independent calculations, have suggested that the difference between TC and ab initio predictions may be associated with mechanical instabilities in the metastable phase. This point had been raised earlier by Pettifor (1988) and has the following consequence as reported by Saunders et al. (1988) ... 

Furthermore, such instabilities will extend into the alloy system iq) to a critical composition and must therefore be taken into account by any effective solution-phase modelling. In the case of Ni-Cr, it is predicted that mechanical instability, as defined by a negative value of c = l/2(cn—C12), will occur between 60 and 70 at%Cr (Craievich and Sanchez 1995), so beyond this composition the f.c.c. phase cannot be considered as a competing phase. 

While this concept of mechanical instability offers a potential explanation for the large discrepancies between FP and TC lattice stabilities for some elements, the calculations of Craeivich et al. (1994) showed that such instabilities also occur in many other transition elements where, in fact, FP and TC values show relatively little disagreement. The key issue is therefore a need to distinguish between permissible and non-permissible mechanical instability. Using the value of the elastic constant C as a measure of mechanical instability, Craievich and Sanchez (1995) have found that the difference between the calculated elastic constant C for f.c.c. and b.c.c. structures of the transition elements is directly proportional to the FP value of(Fig. 6.9(a)). 

The position of Ti and Zr is again important in this context. While the b.c.c. phase in these elements has long been known to indicate mechanical instability at 0 K, detailed calculations for Ti (Petty 1991) and Zr (Ho and Harmon 1990) show tiiat it is stabilised at high temperatures by additional entropy contributions arising from low values of the elastic constants (soft modes) in specific crystal directions. This concept had already been raised in a qualitative way by Zener (1967), but the... 

Thermochemical methods generate lattice stabilities based on high-temperature equilibria that yield self-consistent multi-component phase-diagram calculations. However, as they are largely obtained by extrapolation, this means that in some cases they should only be treated as effective lattice stabilities. Particular difficulties may occur in relation to the liquid — glass transition and instances of mechanical instability. 

By contrast, electron energy calculations have the inherent capability of yielding accurate values for many metastable structures at 0 K but have little or no capability of predicting the temperature dependence of the Gibbs energy, especially in cases where mechanical instabilities are involved. 

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