Consider a screw dislocation with Burgers vector of b=a/2[011] in (111) plane of an FCC crystal. What is the direction of dislocation line? a. [011] b. [110] c.[101] d. [0111 Consider
The Correct Answer and Explanation is :
The correct answer is b. [110].
Explanation:
To understand the direction of the dislocation line in a screw dislocation in an FCC crystal, we need to consider the relationship between the Burgers vector, the dislocation line, and the crystal structure.
In FCC crystals, a screw dislocation involves a shear force that causes the lattice planes to shift relative to each other along a helical path around the dislocation line. The Burgers vector (b) and dislocation line (L) are related by the following condition:
- Screw dislocation: The dislocation line and Burgers vector are parallel. The displacement occurs in a direction parallel to the dislocation line.
Given the Burgers vector b = a/2[011] in the (111) plane, where “a” is the lattice constant, we can proceed as follows:
- Burgers vector direction: The Burgers vector describes the magnitude and direction of the atomic displacement in the crystal. The vector [011] means that the atoms in the crystal are displaced along the [011] direction.
- Dislocation line in screw dislocation: In a screw dislocation, the dislocation line is parallel to the Burgers vector. This means that the dislocation line is also aligned in the [011] direction.
- Finding the correct option: The options for the dislocation line are:
- a. [011]
- b. [110]
- c. [101]
- d. [0111]
However, the dislocation line’s direction is found through the crystal’s geometry and the relationships between the directions in the lattice. In FCC crystals, the typical screw dislocation line direction in the (111) plane is [110], which is the direction of the dislocation line when the Burgers vector is of the type [011].
Therefore, the correct answer is [110], because, in FCC crystals, a screw dislocation with a Burgers vector along [011] will have its dislocation line along the [110] direction.