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Chapter 7: Problem 3

Is it possible for two screw dislocations of opposite sign to annihilate each other? Explain your answer.

Short Answer

Expert verified
Explain your answer. Answer: Yes, two screw dislocations of opposite signs can annihilate each other. This occurs when their opposite Burgers vectors cancel out, resulting in a configuration with no net dislocation. This annihilation process leads to a reduction in the total energy of the crystal lattice, which supports the theoretical possibility of dislocations with opposite signs annihilating each other.

Step by step solution

01

Understanding Screw Dislocations

Screw dislocations are a type of defect in the crystal lattice of a solid material. They occur when crystal planes are displaced along a line known as the dislocation line. The sign of a screw dislocation is determined by the direction of the Burgers vector (b) with respect to the dislocation line. A positive screw dislocation has the Burgers vector parallel to the dislocation line, while a negative screw dislocation has the Burgers vector antiparallel to the dislocation line.
02

Annihilation of Dislocations

Annihilation of dislocations occurs when a pair of dislocations with opposite signs comes close to each other, and the resulting interaction causes the dislocations to cancel out, leading to a configuration with no net dislocation. The annihilation process reduces the total energy of the crystal lattice, as the presence of dislocations increases the system's energy.
03

Screw Dislocations of Opposite Signs

Now we need to examine whether two screw dislocations of opposite signs can annihilate each other. When two screw dislocations with opposite signs approach each other, their Burgers vectors (b) will have opposite directions. During the annihilation process, their Burgers vectors will cancel out, and the resulting crystal lattice will be free of dislocations. So, theoretically speaking, it is possible for two screw dislocations of opposite sign to annihilate each other.
04

Conclusion

In conclusion, it is possible for two screw dislocations of opposite signs to annihilate each other, as their opposite Burgers vectors will cancel out, leading to a configuration with no net dislocation. This is consistent with the fact that annihilation of dislocations reduces the total energy of the crystal lattice.

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Most popular questions from this chapter

An undeformed specimen of some alloy has an average grain diameter of \(0.040 \mathrm{~mm}\). You are asked to reduce its average grain diameter to \(0.010 \mathrm{~mm}\). Is this possible? If so, explain the procedures you would use and name the processes involved. If it is not possible, explain why.

(a) From the plot of yield strength versus (grain diameter) \(^{-1 / 2}\) for a \(70 \mathrm{Cu}-30 \mathrm{Zn}\) cartridge brass, Figure \(7.15\), determine values for the constants \(\sigma_{0}\) and \(k_{y}\) in Equation \(7.7\). (b) Now predict the yield strength of this alloy when the average grain diameter is \(1.0 \times 10^{-3} \mathrm{~mm}\)

(a) Show, for a tensile test, that $$ \% \mathrm{CW}=\left(\frac{\epsilon}{\epsilon+1}\right) \times 100 $$ if there is no change in specimen volume during the deformation process (i.e., \(A_{0} l_{0}=A_{d} l_{d}\) ). (b) Using the result of part (a), compute the percent cold work experienced by naval brass (the stress-strain behavior of which is shown in Figure 6.12) when a stress of 400 MPa \((58,000\) psi) is applied.

Consider a metal single crystal oriented such that the normal to the slip plane and the slip direction are at angles of \(43.1^{\circ}\) and \(47.9^{\circ}\), respectively, with the tensile axis. If the critical resolved shear stress is \(20.7\) MPa (3000 psi), will an applied stress of 45 MPa (6500 psi) cause the single crystal to yield? If not, what stress will be necessary?

(a) Compare planar densities (Section \(3.11\) and Problem 3.54) for the (100), (110), and (111) planes for FCC. (b) Compare planar densities (Problem 3.55) for the (100), (110), and (111) planes for BCC.
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