As
pointed out on the previous page, there are 14 different types
of crystal unit cell structures or lattices are found in nature.
However most metals and many other solids have unit cell structures
described as body center cubic (bcc), face centered cubic (fcc)
or Hexagonal Close Packed (hcp). Since these structures are most
common, they will be discussed in more detail.
Body-Centered Cubic (BCC) Structure
The body-centered cubic unit cell has atoms at each of the eight corners of a cube (like the cubic unit cell) plus one atom in the center of the cube (left image below). Each of the corner atoms is the corner of another cube so the corner atoms are shared among eight unit cells. It is said to have a coordination number of 8. The bcc unit cell consists of a net total of two atoms; one in the center and eight eighths from corners atoms as shown in the middle image below (middle image below). The image below highlights a unit cell in a larger section of the lattice.
The bcc arrangement does not allow the atoms to pack together
as closely as the fcc or hcp arrangements. The bcc structure is
often the high temperature form of metals that are close-packed
at lower temperatures. The volume of atoms in a cell per the total
volume of a cell is called the packing factor.
The bcc unit cell has a packing factor of 0.68.
Some of the materials that have a bcc structure include lithium, sodium, potassium, chromium, barium, vanadium, alpha-iron and tungsten. Metals which have a bcc structure are usually harder and less malleable than close-packed metals such as gold. When the metal is deformed, the planes of atoms must slip over each other, and this is more difficult in the bcc structure. It should be noted that there are other important mechanisms for hardening materials, such as introducing impurities or defects which make slipping more difficult. These hardening mechanisms will be discussed latter.
Face Centered Cubic (FCC) Structure
The face centered cubic structure has atoms located at each of the corners and the centers of all the cubic faces (left image below). Each of the corner atoms is the corner of another cube so the corner atoms are shared among eight unit cells. Additionally, each of its six face centered atoms is shared with an adjacent atom. Since 12 of its atoms are shared, it is said to have a coordination number of 12. The fcc unit cell consists of a net total of four atoms; eight eighths from corners atoms and six halves of the face atoms as shown in the middle image above. The image below highlights a unit cell in a larger section of the lattice.
In the fcc structure (and the hcp structure) the atoms can pack
closer together than they can in the bcc structure. The atoms
from one layer nest themselves in the empty space between the
atoms of the adjacent layer. To picture packing arrangement, imagine
a box filled with a layer of balls that are aligned in columns
and rows. When a few additional balls are tossed in the box, they
will not balance directly on top of the balls in the first layer
but instead will come to rest in the pocket created between four
balls of the bottom layer. As more balls are added they will pack
together to fill up all the pockets. The packing factor (the volume
of atoms in a cell per the total volume of a cell) is 0.74 for
fcc crystals. Some of the metals that have the fcc structure include
aluminum, copper, gold, iridium, lead, nickel, platinum and silver.
Hexagonal Close Packed (HPC) Structure
Another common close packed structure is the hexagonal close pack. The hexagonal structure of alternating layers is shifted so its atoms are aligned to the gaps of the preceding layer. The atoms from one layer nest themselves in the empty space between the atoms of the adjacent layer just like in the fcc structure. However, instead of being a cubic structure, the pattern is hexagonal. (See image below.) The difference between the HPC and FCC structure is discussed later in this section.
The hcp structure has three layers of atoms. In each the top
and bottom layer, there are six atoms that arrange themselves
in the shape of a hexagon and a seventh atom that sits in the
middle of the hexagon. The middle layer has three atoms nestle
in the triangular "grooves" of the top and bottom plane.
Note that there are six of these "grooves" surrounding
each atom in the hexagonal plane, but only three of them can be
filled by atoms.
As shown in the middle image above, there are six atoms in the hcp unit cell. Each of the 12 atoms in the corners of the top and bottom layers contribute 1/6 atom to the unit cell, the two atoms in the center of the hexagon of both the top and bottom layers each contribute ½ atom and each of the three atom in the middle layer contribute 1 atom. The image on the right above attempts to show several hcp unit cells in a larger lattice.
The coordination number of the atoms in this structure is 12. There are six nearest neighbors in the same close packed layer, three in the layer above and three in the layer below. The packing factor is 0.74, which is the same as the fcc unit cell. The hcp structure is very common for elemental metals and some examples include beryllium, cadmium, magnesium, titanium, zinc and zirconium.
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Body-Centered Cubic (BCC) Structure
The body-centered cubic unit cell has atoms at each of the eight corners of a cube (like the cubic unit cell) plus one atom in the center of the cube (left image below). Each of the corner atoms is the corner of another cube so the corner atoms are shared among eight unit cells. It is said to have a coordination number of 8. The bcc unit cell consists of a net total of two atoms; one in the center and eight eighths from corners atoms as shown in the middle image below (middle image below). The image below highlights a unit cell in a larger section of the lattice.
Some of the materials that have a bcc structure include lithium, sodium, potassium, chromium, barium, vanadium, alpha-iron and tungsten. Metals which have a bcc structure are usually harder and less malleable than close-packed metals such as gold. When the metal is deformed, the planes of atoms must slip over each other, and this is more difficult in the bcc structure. It should be noted that there are other important mechanisms for hardening materials, such as introducing impurities or defects which make slipping more difficult. These hardening mechanisms will be discussed latter.
Face Centered Cubic (FCC) Structure
The face centered cubic structure has atoms located at each of the corners and the centers of all the cubic faces (left image below). Each of the corner atoms is the corner of another cube so the corner atoms are shared among eight unit cells. Additionally, each of its six face centered atoms is shared with an adjacent atom. Since 12 of its atoms are shared, it is said to have a coordination number of 12. The fcc unit cell consists of a net total of four atoms; eight eighths from corners atoms and six halves of the face atoms as shown in the middle image above. The image below highlights a unit cell in a larger section of the lattice.
Hexagonal Close Packed (HPC) Structure
Another common close packed structure is the hexagonal close pack. The hexagonal structure of alternating layers is shifted so its atoms are aligned to the gaps of the preceding layer. The atoms from one layer nest themselves in the empty space between the atoms of the adjacent layer just like in the fcc structure. However, instead of being a cubic structure, the pattern is hexagonal. (See image below.) The difference between the HPC and FCC structure is discussed later in this section.
As shown in the middle image above, there are six atoms in the hcp unit cell. Each of the 12 atoms in the corners of the top and bottom layers contribute 1/6 atom to the unit cell, the two atoms in the center of the hexagon of both the top and bottom layers each contribute ½ atom and each of the three atom in the middle layer contribute 1 atom. The image on the right above attempts to show several hcp unit cells in a larger lattice.
The coordination number of the atoms in this structure is 12. There are six nearest neighbors in the same close packed layer, three in the layer above and three in the layer below. The packing factor is 0.74, which is the same as the fcc unit cell. The hcp structure is very common for elemental metals and some examples include beryllium, cadmium, magnesium, titanium, zinc and zirconium.
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