Nonconservative Motion

4 NONCONSERVATIVE MOTION INTERFACES AS SOURCES AND SINKS FOR ATOMIC FLUXES 

The basic mechanisms by which various types of interfaces are able to move non-conservatively are now considered, followed by discussion of whether an interface that is moving nonconservatively is able to operate rapidly enough as a source to maintain all species essentially in local equilibrium at the interface. When local equilibrium is achieved, the kinetics of the interface motion is determined by the rate at which the atoms diffuse to or from the interface and not by the rate at which the flux is accommodated at the interface. The kinetics is then diffusion-limited. When the rate is limited by the rate of interface accommodation, it is source-limited. Note that the same concepts were applied in Section 11.4.1 to the ability of dislocations to act as sources during climb. 

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We start with dislocations and describe both glissile (conservative) and climb (nonconservative) motion in Chapter 11. The motion of vapor/crystal interfaces and liquid/crystal interfaces is taken up in Chapter 12. Finally, the complex subject of the motion of crystal/crystal interfaces is treated in Chapter 13, including both glissile and nonconservative motion. 

Further aspects of the conservative and nonconservative motion of sharp interfaces are presented below. The mechanism for the motion of a diffuse interface is discussed in Section 13.3.4. 

Dislocations glide by the movement of kinks and climb by the movement of jogs. Since climb requires changing the number of point defects (reacting or absorbing them), we call it nonconservative motion. 

Climb is nonconservative motion because vacancies and/or interstitials must be absorbed or emitted (their number is not conserved). When a jog moves, it can either glide or climb. The special point to remember is that the glide plane of a jog is not the same as the glide plane of the dislocation on which is sits. If we force a dislocation jog to move on a plane, which is not its glide plane, it must adsorb or emit point defects, but it can glide. Since it is charged, it carries a current when it glides. 

The perpendicular motion of the two adjoining grains creates a stress concentration at the grain boundaries which must be relaxed in order for the deformation to proceed. This is equivalent to a nonconservative motion, and it is associated with the diffusional fluxes of the components to/from or along the interfaces, or to the dislocation motion, these being the main accommodation processes and the ratecontrolling process associated with GBS. 

The question then is, to what degree can the microscopic motions influence the macroscopic ones is there a flow of infonnation between them [66] Biological systems appear to be nonconservative par excellence and present at least the possibility that random thermal motions are continuously injecting new infonnation into the macroscales. There is certainly no shortage of biological molecular machines for turning heat into correlated motion (e.g. [67] and section C2.14.5 note also [16]). 

A second major difficulty with the Peierls model is that it is elastic and therefore conservative (of energy). However, dislocation motion is nonconservative. As dislocations move they dissipate energy. It has been known for centuries that plastic deformation dissipates plastic work, and more recently observations of individual dislocations has shown that they move in a viscous (dissipative) fashion. 

The mathematical models used to infer rates of water motion from the conservative properties and biogeochemical rates from nonconservative ones were flrst developed in the 1960s. Although they require acceptance of several assumptions, these models represent an elegant approach to obtaining rate information from easily measured constituents in seawater, such as salinity and the concentrations of the nonconservative chemical of interest. These models use an Eulerian approach. That is, they look at how a conservative property, such as the concentration of a conservative solute C, varies over time in an infinitesimally small volume of the ocean. Since C is conservative, its concentrations can only be altered by water transport, either via advection and/or turbulent mixing. Both processes can move water through any or all of the three dimensions... 

In Chapter 4, we saw how conservative chemicals are used to trace the pathway and rates of water motion in the ocean. True conservative behavior is exhibited by a relatively small number of chemicals, such as the major ions and, hence, salinity. In contrast, most of the minor and trace elements display nonconservative behavior because they readily undergo chemical reactions under the environmental conditions found in seawater. The rates of these reactions are enhanced by the involvement of marine organisms, particularly microorganisms, as their enzymes serve as catalysts. Rates are also enhanced at particle interfaces for several reasons. First, microbes tend to have higher growth rates on particle surfaces. Second, the solution in direct contact with the particles tends to be highly enriched in reactants, thereby increasing reaction probabilities. Third, adsorption of solutes onto particle surfaces can create fevorable spatial orientations between reactants that also increases reaction probabilities. 

The motion of a crystal/crystal interface is either conservative or nonconservative. As in the case of conservative dislocation glide, conservative interface motion occurs in the absence of a diffusion flux of any component of the system to or from the... 

We adopt Eq. (A.18) since it is the simplest choice for X(t), which accounts for the nonconservative nature of the motion and for its timescale dependence, and which is also consistent with the results of Machlup and Onsager. 

Even systems as seemingly simple as diatomic molecules often act as complex, many-body systems. Mechanistic understanding and insight, as opposed to mere empirical description, are based on the existence and discovery of patterns that owe their existence to approximate constants of motion. An approximate constant of motion is the eigenvalue of an operator that commutes with most, but not all, terms in the exact molecular Hamiltonian. Nonconservation of this quantity results in subtle rather than catastrophic corruption of the simple patterns on which spectroscopic assignments and mechanistic interpretations are based. 

Substituting Eq. (7.81) into Eq. (7.2) with k = B, results in the equation of motion for the upper arm (assuming that the torso is fixed), as shown in Eq. (7.82). would include all nonconservative or externally applied torques. 

In summaiy, the EP flux is a vector in the meridional plane whose components, in quasi-geostrophic theory, measure the zonally averaged northward eddy fluxes of momentum and temperature. Maps of the EP flux and its divergence may be prepared from observations or the results of model calculations. Such maps may be used to infer where and to what extent the eddy motions are acting to change the mean flow and where transient, nonconservative eddy motions are present. 

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