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Chapter 4: Problem 26

Cite the relative Burgers vector-dislocation line orientations for edge, screw, and mixed dislocations.

Short Answer

Expert verified
Answer: For edge dislocations, the Burgers vector is perpendicular to the dislocation line, resulting in an extra half-plane of atoms within the crystal structure. For screw dislocations, the Burgers vector is parallel to the dislocation line, causing a helical path along the dislocation line in the crystal structure. In mixed dislocations, the Burgers vector is at an angle to the dislocation line, exhibiting characteristics of both edge and screw dislocations with a combination of an extra half-plane of atoms and a helical path along the dislocation line.

Step by step solution

01

Edge Dislocation

In an edge dislocation, the Burgers vector is perpendicular to the dislocation line. The defect appears as an extra half-plane of atoms within the crystal structure, leading to a distortion in the atomic arrangement.
02

Screw Dislocation

In a screw dislocation, the Burgers vector is parallel to the dislocation line. This type of dislocation occurs when the crystal structure forms a helical path along the dislocation line, causing distortion in the atomic arrangement.
03

Mixed Dislocation

In a mixed dislocation, the Burgers vector is neither parallel nor perpendicular to the dislocation line, which means it is at an angle to the dislocation line. This type of dislocation has characteristics of both edge and screw dislocations, with the defect appearing as a combination of an extra half-plane of atoms and a helical path along the dislocation line.

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Most popular questions from this chapter

For both \(\mathrm{FCC}\) and \(\mathrm{BCC}\) crystal structures there are two different types of interstitial sites. In each case, one site is larger than the other, and is normally occupied by impurity atoms. For FCC, this larger one is located at the center of each edge of the unit cell; it is termed an octahedral interstitial site. On the other hand, with BCC the larger site type is found at \(0 \frac{1}{2} \frac{1}{4}\) positions - that is, lying on \\{100\\} faces, and situated midway between two unit cell edges on this face and one-quarter of the distance between the other two unit cell edges; it is termed a tetrahedral interstitial site. For both \(\mathrm{FCC}\) and \(\mathrm{BCC}\) crystal structures, compute the radius \(r\) of an impurity atom that will just fit into one of these sites in terms of the atomic radius \(R\) of the host atom.

For a BCC single crystal, would you expect the surface energy for a (100) plane to be greater or less than that for a (110) plane? Why? (Note: You may want to consult the solution to Problem 3.54 at the end of Chapter \(3 .\)

Germanium forms a substitutional solid solution with silicon. Compute the weight percent of germanium that must be added to silicon to yield an alloy that contains \(2.43 \times 10^{21} \mathrm{Ge}\) atoms per cubic centimeter. The densities of pure Ge and \(\mathrm{Si}\) are 5.32 and \(2.33 \mathrm{g} / \mathrm{cm}^{3}\) respectively .

For an ASTM grain size of \(6,\) approximately how many grains would there be per square inch at (a) a magnification of \(100,\) and (b) without any magnification?

Determine the ASTM grain size number if 30 grains per square inch are measured at a magnification of 250
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