question 5. Please explain the concept and show all the steps. Thank you! List t

Question

question 5. Please explain the concept and show all the steps. Thank you!

List the point coordinates of all atoms in a face-centred cubic (FCC) unit cell. Calculate the distance between point 1,0,0 and point 1/2, 1, 1/2 in the FCC lattice. Express the distance as a function of lattice constant (a) and atomic radius (R). Sketch the following directions and planes in a cubic unit cell, and then calculate the angle between them: [110] and [221]; ii) (111) and (121) Which lattice plane contains these two lattice directions [110] and [221]? Determine the intersection line direction between (111) and (121) planes. Prove that the three planes, (103), (111). and (230) share a zone axis.

Explanation / Answer

Hi, according to Chegg question policy, I will be answering the first question for you.

1. In an fcc lattice, fractions of atoms are present at each of the 8 corners of the cube, as well as at the center of each of the 6 faces. Thus, a total of 8+6= 14 coordinates are to be defined.

Considering the origin to be 0,0,0 and the unit cell length to be equal to 1 unit.

The coordinates of the atoms at the corners will be of the kind 0,1,0. The coordinates of the atoms at the centers of the faces will lie halfway between the length and will take the form 0,1/2, 0

The 14 coordinates are:

0,0,0

0,1,0

1,0,0

0,0,1

1,0,1

1,1,0

0,1,1

1,1,1

1/2, 0, 1/2

1, 1/2, 1/2

1/2, 1/2, 1

1/2, 1, 1/2

1/2, 1/2, 0

0, 1/2, 1/2

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