To grasp the structure of metals and ionic compounds, you must account for the solid voids. As atoms occupy lattice points, they create a pattern of empty spaces between atoms.
Empty space resides within an extended array of atoms or ions. The character of solid voids produces the properties of alloys, the stoichiometry of ionic compounds, and the distribution of defects.
Two Dimensional Voids
As a start, consider voids created by a two dimensional array of spheres.
Figure 1: simple square packing in 2D with simple square void between atoms.
Square Packed Voids
For solids which feature simple square packing, a square void space is created in Figure 1. The empty space occupies the gap created where spheres touch each other, shown in yellow. This is the type of void found in simple cubic packed solids and body centered cubic lattices.
Figure 2: Trigonal void created by the junction of cubic close packed atoms
Close Packed Voids
The most common type of voids occur among close packed structures. Instead of the atoms touching where spheres meet, the placement improves when an atom rests in the groove between two adjoining atoms. This kind of structure creates a trigonal void between atoms, Figure 2.
Void Sites
To create three-dimensional voids, the atoms stack in layers. The way in which atoms add additional layers determines the inside geometry of the empty space.
Voids adopt either a tetrahedral or octahedral shape. Which shape a void takes comes from whether the next layer is placed in a center vacant site or an edge vacant site.
Square Packed Sites
Figure 3: center and edge atom placement in relation to square packed void.
A second layer added to a square packed void has two sites where an atom in a second can sit, Figure 3.
A second row atom occupies a space between all four atoms, an orange arrow. The second site takes a position at the edge of a square, a green arrow.
Close Packed Sites
Figure 4: Edge placement and center placement of second layer atom in respect to close packed trigonal void
There are two possible sites for a second row atom: an edge site or a center site, Figure 4. A second atom can occupy and edge site in relation to a trigonal void, shown with purple arrows. Or an atom can reside directly above a trigonal void in a center site, an orange arrow.
Three Dimensional Voids
The kind and number of voids comes from the placement of lattice atoms. Each crystal structure has a characteristic set of voids.
Voids take one of two possible geometries: tetrahedral or octahedral, Figure 5.
Cubic Packed Void Geometry
Figure 6: Top layer atoms (in blue) determine whether an octahedral or tetrahedral void site forms in cubic packed structures
Further, the next layer of atoms in a cubic packed structure has an atom which sits below the plane of square packed atoms in a center site, Figure 6.
The next atom can sit in an edge interstitial site or a in a center interstitial site.
When the new atom takes and edge site, it forms a tetrahedral void.
Occupation of a center site directly above an atom results in an octahedral void.
Close Packed Void Geometry
Figure 7: Octahedral and tetrahedral voids formed when a two-dimensional lattice adopts extra layers above and below its plane to adopt a three-dimensional array.
Close packed voids occur as face-centered cubic and hexagonal geometries.
Specifically, octahedral voids form when the space between four atoms has the empty space above and below the empty space filled, Figure 7.
Correspondingly, tetrahedral voids form when an atom takes the crook created by three adjacent atoms placed above their mutual plane.
Void Positions
It follows that void sites occupy specific positions within structure. This influences what kind of ionic compounds and alloys become possible.
Body-Centered Cubic
Figure 8: BCC voids, octahedral in yellow and tetrahedral in orange
Body-centered packing structures have the unique property of having all their interstitial spaces being shared with an adjacent unit cell, Figure 8.
Octahedral Voids
Octahedral voids occupy one of two positions. Voids appear at the center of each face, with the empty position 1/2 shared with another neighbor unit cell. The other type of site occurs at the center of each edge, where 1/4 of each octahedral space belongs to a unit cell.
Octahedral voids are shown in yellow.
Tetrahedral Voids
Tetrahedral voids share 1/2 of each space with an adjacent unit cell. Each face hosts 4 tetrahedral voids, in orange.
Face-Centered Cubic
Figure 9: Positions and kinds of tetrahedral and octahedral interstitial voids. Orange represents tetrahedral voids. Yellow spheres show the position of octahedral voids
Tetrahedral Voids
Tetrahedral voids in face-centered cubic cells reside in a single unit cell, Figure 9.
Each unit cell contains a total of eight tetrahedral spaces. The edges of a tetrahedral space is shown with orange lines. The orange spheres show the site of each tetrahedral void.
Octahedral Voids
Octahedral voids have one void completely centered at the center of the unit cell. Additional octahedral voids appear at the center of each edge. Each edge shared void contributes 1/4 of a void. This results in FCC unit cells having a total of three octahedral voids.
Hexagonal
Tetrahedral Voids
Figure 10: HCP tetrahedral and octahedral voids. Tetrahedral voids in orange, octahedral voids in yellow
Tetrahedral voids occur as both internal voids and voids which share an edge, Figure 10.
Orange circles represent voids.
There are six internal tetrahedral voids. Each edge contributes two voids, each of which gives 1/3. That means (12 x 1/3) = 4 additional tetrahedral voids.
Octahedral Voids
Octahedral voids reside within the hexagonal unit cell. One vertex of each octahedron extends through the face. The voids occupy a position between atoms that sit at the central triangle. This accounts for two layers of voids, which make a total of six octahedral voids in hexagonal unit cells.
