PART 1-The Simple Cubic Lattice 1. Construct a single unit cell of the simple cu

Question

PART 1-The Simple Cubic Lattice 1. Construct a single unit cell of the simple cubic latice (see figure) using the balls and toothpicks. The dots in the figure represent centers of atoms; in your model, spheres should be in contact. By using only four more balls, extend your model in the c direction so that you end up with two unit cells in contact. Note that four of the balls are shared by the two unit cells. In similar fashion, extend the model in the a and b directions. Continue building unti you have used a total of 27 balls and have formed a large cube containing eight unit cells. Focus your attention on one unit cell. Note that the spheres are in contact along the cube's edge. A) What is the length of the edge of the unit cell, in terms of r? Now, focus your attention on the sphere hidden in the center of the 27-ball model. B) What fraction of this sphere lies in each unit cell? C) Determine the # of spheres in one unit cell.

Explanation / Answer

A) If edge of unit cell is "a" and "r" is radius of each sphere

So, Edge length a = 2r

B) Each sphere is shared by 8 adjacent unit cells.

So, 1/8 fraction of each sphere lies in the unit cell.

C) In the simple cubic unit cell, each sphere is shared by 8 adjacent unit cells.

1/8 fraction in each unit cell.

Total 8 atoms in each unit cell. 8*1/8 = 1

1 sphere in one unit cell.

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