Edge climb

Inclined hearth furnaces tend to create more natural draft, pulling in cold air at the low end of the incline. Excessive hearth inclination interferes with pressure conditions in the furnace. (See chap. 7.) An inclination of more than 8 degrees is rare. The safe length of hearth also depends upon the shape of the contacting surfaces of the billets. If the billets or slabs have round edges, climbing occurs easily. Crooked billets also tend to climb. 

A special form of crevice attack can occur at a waterline or at the edges of water droplets. At the water surface, a meniscus region is present where surface tension causes water to climb up the metal surface it contacts. In effect, a crevice is formed between the air-liquid and liquid-metal interface at the meniscus. Oxygen concentration is high at the meniscus due to the greater accessibility of this region to the air. The meniscus region becomes cathodic to the adjacent metal surface. Corrosion occurs just below the meniscus, and chloride, if present, is... 

The other major defects in solids occupy much more volume in the lattice of a crystal and are refeiTed to as line defects. There are two types of line defects, the edge and screw defects which are also known as dislocations. These play an important part, primarily, in the plastic non-Hookeian extension of metals under a tensile stress. This process causes the translation of dislocations in the direction of the plastic extension. Dislocations become mobile in solids at elevated temperamres due to the diffusive place exchange of atoms with vacancies at the core, a process described as dislocation climb. The direction of climb is such that the vacancies move along any stress gradient, such as that around an inclusion of oxide in a metal, or when a metal is placed under compression. 

Figure 3.16 Edge dislocation climb (a) an edge dislocation before climb, (b) the start of climb by vacancy aggregation on the dislocation, and (c) the start of climb by interstitial aggregation on the dislocation.

Too early I sat there also and opened the edge of my cloak invitingly. With fastidious paws the cat climbed up on my lap and lay down. Its fur was cold to the touch, which made me shiver, so I refrained from trying to stroke it. I made a covering for it, leaving its head free. It purred. 

The liquid skin described above is anchored to the solid walls of the container around the edges of the surface. The angle the liquid surface makes with the solid support is called the contact angle. The tendency of most liquids to climb walls —think of a meniscus in a capillary—is a manifestation of the existence of these angles. 

One may conclude from Eqn. (3.6) that an (arbitrary) stress a exerts both a glide force and a climb force on edge dislocations, but no climb force on screw dislocations (s 6 F=0). Equation (3.6) can also be used to calculate the interaction between two dislocations, that is, the force which the stress field of one dislocation exerts on the unit length of another dislocation at a given coordinate. For parallel dislocations, this force can be written as [J. P. Hirth, J. Lothe (1982)]... 

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. 

To solve the vacancy flux equation between dislocations of opposite sign we have to know the dislocation geometry (distance and orientation) in the lattice as the boundary condition. If we consider as a zeroth order approach only the average distance, a, between the dislocations, even this quantity depends on the applied stress and the functioning of dislocation multiplication. Nevertheless, since about l/b2 vacancies are needed for a climb shift of unit length, we may conclude from Eqn. (14.28) and the vacancy flux that the steady-state climb velocity, >d, of a dislocation with edge character is... 

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]. 

Figure 11.1 Glide and climb of edge dislocation in primitive cubic crystal (b = [600],...

A dislocation is generally subjected to another type of force if nonequilibrium point defects are present (see Fig. 11.2). If the point defects are supersaturated vacancies, they can diffuse to the dislocation and be destroyed there by dislocation climb. A diffusion flux of excess vacancies to the dislocation is equivalent to an opposite flux of atoms taken from the extra plane associated with the edge dislocation. This causes the extra plane to shrink, the dislocation to climb in the +y direction, and the dislocation to act as a vacancy sink. In this situation, an effective osmotic force is exerted on the dislocation in the +y direction, since the destruction of the excess vacancies which occurs when the dislocation climbs a distance Sy causes the free energy of the system to decrease by 8Q. The osmotic force is then given by... 

By evaluating 8Q and Sy when SNy vacancies are destroyed, an expression for can be obtained. The quantity SQ is just —/lySNy, where the chemical potential of the vacancies, fiy, is given by Eq. 3.66. If a climbing edge dislocation destroys SNy vacancies per unit length, the climb distance will be Sy = (12/6) SNy. The osmotic force is therefore... 

Figure 11.2 Oblique view of edge dislocation climb due to destruction of excess...

The climb of mixed dislocations possessing some screw character can proceed by basically the same jog-diffusion mechanism as that for the pure edge dislocation.10 On the other hand, a pure screw dislocation can climb if the excess vacancies convert it into a helix, as in Fig. 11.10. Here the turns of the helical dislocation possess... 

R.M. Thomson and R.W. Balluffi. Kinetic theory of dislocation climb I. General models for edge and screw dislocations. J. Appl Phys., 33(3) 803—817, 1962. 

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