Climb motion

R.W. Balluffi and D.N. Seidman. Diffusion-limited climb rate of a dislocation Effect of climb motion on climb rate. J. Appl. Phys., 36(7) 2708—2711, 1965. 

Neglect any effects due to the climb motion of the dislocations and assume quasi-steady-state diffusion. The vacancy isoconcentration contours around the dislocations in the boundary will then appear approximately as illustrated in Fig. 13.20. 

The behavior of PAA solutions in response to agitation and aeration was different from the behavior in CMC and XTN solutions. In PAA solutions, small spherical, as well as inverted tear drop bubbles, were observed. This latter shape is the result of the interaction of elastic and surface tension forces, and has been reported to occur in stagnant [26,27] as well as in mildly stirred solutions [28]. It is known that in free climb motion, PAA bubbles have lower terminal rise velocities than... 

So far, no direct observation of metadislocation motion, for instance by in situ tensile tests in a transmission electron microscope, has been reported. Therefore, there is as yet no direct experimental confirmation of whether metadislocations motion takes place by glide or climb. However, besides the strong evidence in favor of climb motion given above, there is also a potent argument against glide. 

Fig. 30(c) shows a climb step (movement along [100] to the left) of a metadislocation by one a-lattice constant. Again, the initial and final tiles are drawn in black and gray lines, respectively. For a climb step, a much smaller number of vertex jumps is necessary. The number of necessary vertex jumps is now limited to the core region and it is now finite, no matter how far the associated phason planes are extended. Since each vertex jump physically represents a number of local atomic movements (Section 3.1.2), climb motion obviously is connected with much less atomic rearrangement than glide motion. 

It can be seen from Fig. 15(a) that the atom moves in a stick-slip way. In forward motion, for example, it is a stick phase from A to B during which the atom stays in a metastable state with little change in position as the support travels forward. Meanwhile, the lateral force gradually climbs up in the same period, leading to an accumulation of elastic energy, as illustrated in Fig. 15(fo). When reaching the point B where a saddle-node bifurcation appears, the metastable... 

Fence-disturbance sensors detect the motion or vibration of a fence, such as that caused by an intruder attempting to climb or cut through the fence. In general, fence-disturbance sensors are used on chain-link fences or on other fence types where a movable fence fabric is hung between fence posts. 

At the same time that the motor neurons send signals to the muscles, branches travel into other parts of the brain including the olivary nuclei, which send neurons into the cerebellum. The cerebellum acts as a kind of computer needed for fine tuning of the impulses to the muscles. Injury to the cerebellum leads to difficulty in finely coordinated motions. Input to the Purkinje cells arises from the climbing fibers, which originate in the inferior olive of the brain stem. Each climbing fiber activates a single Purkinje cell, but the dendrites of each Purkinje cell also form as many as 200,000 different synapses with parallel fibers that run across the cortex of the cerebellum (Fig. 30-15). 

Of particular interest in kinetics is the non-conservative dislocation motion (climb). The net force on a dislocation line in the climb direction (per unit length) consists of two parts Kei is the force due to elastic interactions (Peach-Koehler force), Kcbcm is the force due to the deviation from SE equilibrium in the dislocation-free bulk relative to the established equilibrium at the dislocation line. Sites of repeatable growth (kinks, jogs) allow fast equilibration at the dislocation. For example, if cv is the supersaturated concentration and c is the equilibrium concentration of vacancies, (in the sense of an osmotic pressure) is... 

The main difficulty with the first mode of oxidation mentioned above is explaining how the cation vacancies that arrive at the metal/oxide interface are accommodated. This problem has already been addressed in Section 7.2. Distinct patterns of dislocations in the metal near the metal/oxide interface and dislocation climb have been invoked to support the continuous motion of the adherent metal/oxide interface in this case [B. Pieraggi, R. A. Rapp (1988)]. If experimental rate constants are moderately larger than those predicted by the Wagner theory, one may assume that internal surfaces such as dislocations (and possibly grain boundaries) in the oxide layer contribute to the cation transport. This can formally be taken into account by defining an effective diffusion coefficient Del( = (1 -/)-DL+/-DNL, where DL is the lattice diffusion coefficient, DNL is the diffusion coefficient of the internal surfaces, and / is the site fraction of cations located on these internal surfaces. 

The influence of plastic deformation on the reaction kinetics is twofold. 1) Plastic deformation occurs mainly through the formation and motion of dislocations. Since dislocations provide one dimensional paths (pipes) of enhanced mobility, they may alter the transport coefficients of the structure elements, with respect to both magnitude and direction. 2) They may thereby decisively affect the nucleation rate of supersaturated components and thus determine the sites of precipitation. However, there is a further influence which plastic deformations have on the kinetics of reactions. If moving dislocations intersect each other, they release point defects into the bulk crystal. The resulting increase in point defect concentration changes the atomic mobility of the components. Let us remember that supersaturated point defects may be annihilated by the climb of edge dislocations (see Section 3.4). By and large, one expects that plasticity will noticeably affect the reactivity of solids. 

In the Kirkendall effect, the difference in the fluxes of the two substitutional species requires a net flux of vacancies. The net vacancy flux requires continuous net vacancy generation on one side of the markers and vacancy destruction on the other side (mechanisms of vacancy generation are discussed in Section 11.4). Vacancy creation and destruction can occur by means of dislocation climb and is illustrated in Fig. 3.36 for edge dislocations. Vacancy destruction occurs when atoms from the extra planes associated with these dislocations fill the incoming vacancies and the extra planes shrink (i.e., the dislocations climb as on the left side in Fig. 3.36 toward which the marker is moving). Creation occurs by the reverse process, where the extra planes expand as atoms are added to them in order to form vacancies, as on the right side of Fig. 3.36. This contraction and expansion causes a mass flow that is revealed by the motion of embedded inert markers, as indicated in Fig. 3.3 [4]. 

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. 

Thermally Activated Motion of Sharp Interfaces by Glide and Climb of Interfacial Dislocations... 

The motion of many interfaces requires the combined glide and climb of interfacial dislocations. However, this can take place only at elevated temperatures where sufficient thermal activation for climb is available. 

An approximate model for the rate of boundary motion can be developed if it is assumed that the rate of dislocation climb is diffusion limited [2], Neglecting any effects of the dislocation motion and the local stress fields of the dislocations on... 

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