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Chapter 12: Problem 43

What is the coordination number of each sphere in (a) a simple cubic lattice, (b) a body-centered cubic lattice, and (c) a face- centered cubic lattice? Assume the spheres to be of equal size.

Short Answer

Expert verified
The coordination numbers for a simple cubic lattice, a body-centered cubic lattice, and a face-centered cubic lattice are 6, 8, and 12 respectively.

Step by step solution

01

Coordination Number in Simple Cubic Lattice

In a simple cubic lattice, each sphere (or atom) is adjacent to six others: one each in left and right, up and down, and front and back. Thus, the coordination number for a simple cubic lattice is 6.
02

Coordination Number in Body-Centered Cubic Lattice

A body-centered cubic lattice has an additional sphere in the center of the cubic unit. This sphere is in touch with eight others which are at the corners of the cube, so the coordination number here is 8.
03

Coordination Number in Face-Centered Cubic Lattice

In a face-centered cubic lattice, each sphere is in contact with those in the center of all six faces, plus the twelve spheres that enclose the corners of the faces. This gives a coordination number of 12.

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