Question

Calculate the linear density for bcc (111) direction with a radius of 0.923 nm

Answer 1

Answer:

.5417

Explanation:

LD = 2 atoms / 4 R

LD = 2/4*.923

LD= .5417 nm

Answer 2

The linear density for the bcc (111) direction with a radius of 0.923 nm as 1.81 atoms/nm.

As per the question given,

The linear density for a crystal structure is defined as the number of atoms per unit length along a specific direction. In a body-centered cubic (bcc) crystal, the (111) direction passes through the centre of the cube and intersects each of the cubes faces. To calculate the linear density for this direction, we need to determine the distance between two adjacent atoms along the direction.

Using geometry, we can calculate the length of the edge of the bcc cube in terms of the atomic radius, which is given as 2r√3. Since the (111) direction passes through the centre of the cube, the length of the direction can be expressed as the diagonal of a square face of the cube. Using Pythagoras' theorem, we can find that the length of the (111) direction is 4r√3/√2.

Therefore, the linear density along the (111) direction can be calculated as the number of atoms per unit length, which is 1 divided by the distance between two adjacent atoms along the direction.

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