Question

How many atoms are centered on the (100) plane for the fcc crystal structure?

Answer 1

The (100) planar of the FCC crystal structure has a coordination number of 12, meaning that each atom is centered on 12 other atoms.

Step-by-step explanation:

The face-centered cubic (FCC) crystal structure has a coordination number of 12, meaning that each atom in the (100) plane is centered on 12 other atoms. This can be visualized as each atom being surrounded by a close-packed layer of six atoms in its own plane, three atoms in the layer above, and three atoms in the layer below. Because each atom touches 12 near neighbors, the coordination number is 12.

Answer 2

Here, we have to get the number of atoms present in the 100 plane of the FCC crystal lattice.

There will be 2 atoms in 100 plane of FCC crystal lattice.

In the face centered crystal (FCC) lattice there are atoms at each corner of the cube and each are shared by 4 another atoms. And an atom is present at the face of the crystal.

For the 100 plane of the Miller indices the intercepts are a, ∞, ∞ or 2a, ∞, ∞.

Thus, for the 4 atoms of the corner at the cube shared by 4 other atoms will contribute, 4 ×
`(1)/(4)` = 1 and the un-shared atoms at the face will contribute another 1, which make the total atom 1 + 1 = 2.