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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

(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.

(a) What is the driving force for recrystallization? (b) For grain growth?

Two previously undeformed specimens of the same metal are to be plastically deformed by reducing their cross-sectional areas. One has a circular cross section, and the other is rectangular; during deformation the circular cross section is to remain circular, and the rectangular is to remain as such. Their original and deformed dimensions are as follows: $$ \begin{array}{lcr} \hline & \begin{array}{c} \text { Circular } \\ \text { (diameter, } \mathbf{m m}) \end{array} & \begin{array}{c} \text { Rectangular } \\ (\mathbf{m m}) \end{array} \\ \hline \text { Original dimensions } & 15.2 & 125 \times 175 \\ \text { Deformed dimensions } & 11.4 & 75 \times 200 \\ \hline \end{array} $$ Which of these specimens will be the hardest after plastic deformation, and why?

Explain the differences in grain structure for a metal that has been cold worked and one that has been cold worked and then recrystallized.

Experimentally, it has been observed for single crystals of a number of metals that the critical resolved shear stress \(\tau_{\text {crsss }}\) is a function of the dislocation density \(\rho_{D}\) as $$ \tau_{\text {crss }}=\tau_{0}+A \sqrt{\rho_{D}} $$ where \(\tau_{0}\) and \(A\) are constants. For copper, the critical resolved shear stress is \(2.10 \mathrm{MPa}\) (305 psi) at a dislocation density of \(10^{5} \mathrm{~mm}^{-2}\). If it is known that the value of \(A\) for copper is \(6.35\) \(\times 10^{-3} \mathrm{MPa} \cdot \mathrm{mm}(0.92 \mathrm{psi} \cdot \mathrm{mm})\), compute \(\tau_{\text {crss }}\) at a dislocation density of \(10^{7} \mathrm{~mm}^{-2}\).
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