How many atoms are centered on the [100] direction in a FCC unit cell

In a face-centered cubic (FCC) unit crystal cell, the [100] direction is along the x-axis, assuming that the x, y, and z axes are aligned with the edges of the cubic unit cell. The [100] direction starts at one corner and ends at the corner on the opposite face of the cube, passing through the center of the face that is perpendicular to the x-axis.

An FCC unit cell consists of atoms at each of the eight corners of the cube and one atom centered on each of the six faces. However, each corner atom is shared by eight adjacent unit cells, and each face-centered atom is shared by two units cells. When considering just one unit cell, this means each corner atom contributes 1/8 of an atom to the cell, and each face-centered atom contributes 1/2 of an atom to the cell.

Now for the [100] direction: There is one corner atom at the start, one face-centered atom in the middle of the path, and another corner atom at the end of the [100] direction. Since we are considering a path starting and ending with corners that are within the same unit cell, the contribution of each of these corner atoms to the cell should be considered as whole atoms regarding this direction, as we are not considering the sharing of these atoms with adjacent cells along this path.

Therefore, along the [100] direction in a FCC unit cell, you will find a total of 3 atoms: one at the beginning corner, one in the center on the face, and one at the ending corner.

Extra: The crystal structure of materials is an important aspect of materials science which helps determine a variety of physical properties. The face-centered cubic structure is one of the closest-packed structures, with a high packing efficiency. The atoms are arranged in a way that maximizes the use of space, and this structure is found in many metals such as aluminum, copper, and gold. The notion of "directions" in a crystal lattice is described using Miller indices, which in the case of the [100] direction, indicate a vector that goes straight across the unit cell in one axis, with no components in the other two axes. Understanding the arrangement of atoms in a crystal lattice, including the directions and planes, is important for explaining properties such as slippage during deformation, the nature of grain boundaries, and how impurities and defects can influence the strength and other characteristics of materials.