Fcc structure how many atoms

Closest Pack Crystal Structures Hexagonal Closest Packed HCP In a hexagonal closest packed structure, the third layer has the same arrangement of spheres as the first layer and covers all the tetrahedral holes.

The hexagonal closest packed hcp has a coordination number of 12 and contains 6 atoms per unit cell. The face-centered cubic fcc has a coordination number of 12 and contains 4 atoms per unit cell. The body-centered cubic bcc has a coordination number of 8 and contains 2 atoms per unit cell.

The simple cubic has a coordination number of 6 and contains 1 atom per unit cell. References Conway, J. Sphere Packings, Lattices, and Groups, 2nd ed. New York: Springer-Verlag, Krishna, P. Petrucci, Ralph H. Harwood, F. Geoffrey Herring, and Jeffry D. New Jersey: Pearson Education, Inc. Simple Unit Cell. Body-Centered Cubic. Face-centered Cubic. Notice that layer B spheres fit in the holes in the A layer.

Packing marbles in the third layer requires a decision. Again rows of atoms will nest in the hollows between atoms in the second layer but two possibilities exist. If the rows of marbles are packed so they are directly over the first layer A then the arrangement could be described as ABA. If the rows of atoms are packed in this third layer so that they do not lie over atoms in either the A or B layer, then the third layer is called C.

Both arrangements give the closest possible packing of spheres leaving only about a fourth of the available space empty. The smallest repeating array of atoms in a crystal is called a unit cell. A third common packing arrangement in metals, the body-centered cubic BCC unit cell has atoms at each of the eight corners of a cube plus one atom in the center of the cube.

Because each of the corner atoms is the corner of another cube, the corner atoms in each unit cell will be shared among eight unit cells. The BCC unit cell consists of a net total of two atoms, the one in the center and eight eighths from the corners. In the FCC arrangement, again there are eight atoms at corners of the unit cell and one atom centered in each of the faces. The atom in the face is shared with the adjacent cell.

FCC unit cells consist of four atoms, eight eighths at the corners and six halves in the faces. Table 1 shows the stable room temperature crystal structures for several elemental metals. As atoms of melted metal begin to pack together to form a crystal lattice at the freezing point, groups of these atoms form tiny crystals.

These tiny crystals increase in size by the progressive addition of atoms. The resulting solid is not one crystal but actually many smaller crystals, called grains. These grains grow until they impinge upon adjacent growing crystals. The interface formed between them is called a grain boundary. It is one of the most common structures for metals. Aluminum, calcium, nickel, copper, strontium, rhodium, palladium, silver, ytterbium, iridium, platinum, gold, lead, actinium, and thorium all have an FCC structure.

FCC metals are usually very ductile and have no ductile-to-brittle phase transformation. If you are interested in the differences between FCC and BCC another common structure , you may be interested in this article.

In a face-centered cubic crystal, each atom has 12 nearest neighbors NN. The face-centered cubic lattice is a cube with an atom on each corner and each face. Using the hard sphere model, which imagines each atom as a discrete sphere, the FCC crystal has each atom touch along the face diagonal of the cube. That means that the face diagonal has a length of , so with a bit of geometry we find that the lattice parameter , or side length of the cube, has a length of. If you wanted to describe the face-centered cubic crystal with math, you would describe the cell with the vectors.

Since we use the hard sphere model, each point inside the cell is either part of an atom, or part of the void. APF is basically the fraction of atoms to void.

For a full article explaining APF, check out this link. The total volume of the unit cell is just the volume of a cube. The cube side length is a, so the volume is. Now we need to count how many atoms are in each unit cell. It may look like there are 14 atoms because there are 8 corners and 6 faces, but actually the cell only intersects portions of those atoms.

The volume of a sphere is. We previously established that the volume of the whole cube is , and since , the volume of the cube is. Since FCC has the maximum type of packing, it is a close-packed structure. The other common close-packed structure is hexagonal close-packed HCP , although there are also lesser-known types like the close-packed rhombohedral structure found in Samarium.

The FCC cell that I have shown you is a conventional unit cell, not a primitive unit cell. This conventional cell has advantages because it is highly symmetric and easy for humans to understand. However, when dealing with mathematical descriptions of crystals, it may be easier to describe the unit cell in the smallest form possible.