Other Types of Dislocations

While edge dislocation theory can be used to explain many of the important features of plastic deformation in crystals, it is necessary to invoke the presence of other types of dislocations to explain other aspects of deformation. The generalized dislocation theory can explain essentially every known feature of plastic deformation in crystals.

5.2.3 Other Types of Dislocations

Figure 5.2–8 shows an edge dislocation along with several other types of dislocations, including a screw dislocation, a mixed dislocation, and a dislocation loop. In the case of thescrew dislocation(Figure 5.2–8b) the Burgers vector is parallel to the dislocation line 共b 储 t兲. A screw dislocation can also be envisioned as forming the axis of a helical ramp that runs through the crystal.¹Recall that for any dislocation the plane that contains both b and t is a potential slip plane. Since b is parallel to t for a screw dislocation, any plane that contains the line defined by b (or, equivalently, t) is a potential slip plane. Therefore, the screw dislocation can glide (move) from one valid slip plane onto another valid slip plane. This is in contrast to the edge dislocation, which has a unique slip plane and which can glide on only that plane. For this reason, screw dislocations are generally more mobile than edge dislocations.

Figure 5.2–8c shows a curved dislocation. At position A the dislocation has an edge character共b ⊥ t兲, and at position B it has a screw character 共b 储 t兲. At intermediate points between A and B, the dislocation has a mixed character (i.e., neither edge nor screw). It is therefore known as a mixed dislocation. Note that Burgers circuits at points A and B each yield the same Burgers vector. In fact, the Burgers vector is an invariant for a dislocation, meaning that the Burgers vector is constant for any given dislocation.

Figure 5.2–8d shows a dislocation loop within a crystal. The loop has the same Burgers vector at all positions, but its character (i.e., edge, screw, or mixed) continuously changes.

It is also possible to form dislocation loops that have the same orientation at all points.

1A reasonable mental image for a screw dislocation is the type of helical ramp that is often found in parking garages. Movement (displacement) along the ramp (dislocation) allows a car to move from one

(a) Edge

dislocation line

(b) b

Burgers vector b Dislocation

line

(c) Disclocation

line b

t

t

B A

b t

b

(d) b Burgers vector

Unit tangent vector, t

In the example shown in Figure 5.2–9, a portion of a (1 1 1) plane is removed from an FCC crystal. This might happen, for example, by the formation of a disk-shaped cluster of vacancies. Here the Burgers vector is perpendicular to the plane of the loop so that the dislocation has pure edge characteristics over its entire length.

The preceding examples illustrate several key features of dislocations:

1. The character of a dislocation is defined by the relationship between its Burgers vector and unit tangent vector. For edges b⊥ t, for screws b 储 t, and for mixed dislocations, b and t may form angle between 0⬚ and 90⬚.

2. The plane on which a dislocation may slip contains both b and t. The disloca-tion can glide (move) on this plane provided it is an admissible slip plane for the crystal type (i.e., a plane of high atomic density).

3. The Burgers vector is invariant. Thus, while the character of a dislocation may change from position to position, the Burgers vector is always the same.

4. A dislocation cannot end in the middle of a defect-free region of a crystal. It can end at the surface of the crystal, on itself, or on another dislocation.

FIGURE 5.2–8 Illustrations of four types of dislocations: (a) an edge dislocation, (b) a screw dislocation, (c) a mixed dislocation, and (d) a dislocation loop. (Source: (b) William D. Callister, Jr., Materials Science and Engineering, 2nd ed., Copyright䊚 1991 by John Wiley & Sons. Used with permission of John Wiley & Sons, Inc. (c) James F.

Shackelford, Introduction to Materials Science for Engineering, 3rd ed. Copyright䊚 Macmillan Publishing Company, Inc.

Used with permission of Macmillan College Publishing Company.)

(a) Dislocation

loop

C B A C B A

C B A C B A

(b) (c)

Remove atoms here (e.g., clustering of vacancies)

C B C B

A (a /3 ) [1 1 1]

b

V

We need to further explain the significance of the second sentence in the second observation above. We have stated two restrictions on the slip plane of a dislocation:

(1) from a geometric point of view the slip plane is defined by the relationship b⫻ t; and (2) from a crystallographic point of view the slip plane must be the highest–atomic density plane. A dislocation is free to move by the glide mechanism (i.e., the mechanism shown in Figure 5.2–4兲 only if its geometric slip plane coincides with an allowable crystallo-graphic slip plane. The valid slip planes and directions for the three common metal crystal structures are discussed in the next subsection.

FIGURE 5.2–10 Climb of edge dislocation. The dislocation moves up one atomic spacing when it absorbs a vacancy.

FIGURE 5.2–9 Formation of a dislocation loop by removal of a circular portion of a plane of atoms: (a) a 3-D view of the dislocation loop, (b) a 2-D view showing the section of the plane to be removed, and (c) the atomic displace-ment that occurs when the atoms are removed.

Region of distortion

Region of compression Region of expansion

Even if a dislocation cannot glide, it is possible for it to move by a different mechanism.

This mechanism involves the diffusion of atoms, vacancies, or both toward the dislocation (see Figure 5.2–10). When a dislocation moves in this way, the process is called disloca-tion climb. When the atoms along the dislocation line exchange places with a nearby linear array of vacancies, the dislocation “moves up” one atomic plane. This motion occurs in a direction perpendicular to the plane defined by b⫻ t and is therefore funda-mentally different from dislocation glide. We will see in the chapter on mechanical behavior that dislocation climb is important at high temperatures, where the vacancy concentration is high and linear arrangements of vacancies are more likely.