Two main types of interstitial voids (between the bigger atoms) occupied by interstitial (small) solute atoms are: 1. Tetrahedral Voids 2. Octahedral Voids.

When same sized spheres (hard balls) are packed in three dimensions, void spaces are present between the spheres. These voids are called interstitial voids.

The size of the interstitial sites is always smaller than the common five atoms which sit there (Table 2.1). The solvent atoms move apart a little without altering the structure i.e., expansion occurs by such a solution. Solid solubility cannot thus be very large.

Type # 1. Tetrahedral Void:

A tetrahedral void forms when an atom is put in the valley formed by three spheres of a close-packed plane. If the atom is put on the top of the three atoms, it is an upright tetrahedral void, but if this atom is put from the bottom, it is an inverted tetrahedral void. Fig. 2.8 (a) illustrates three atoms of close packed plane, and an atom still not put on the top of the valley of these three atoms, Fig. 2.8 (b) illustrates after putting this atom on top.


Fig. 2.8 (d) illustrates the plan of this arrangement of atoms. Fig. 2.8 (e) illustrates when the atom is put from the bottom side and Fig. 2.8 (f) depicts its plan. This is inverted tetrahedral void. The name, tetrahedral has been derived because a regular tetrahedron is formed when the centres of the four atoms are joined. There are thus two tetrahedral voids for every atom in three dimensional arrangements of atoms in close-packed structures.

A FCC unit cell is illustrated in Fig. 2.9 (a). One such tetrahedral hole, centred at Y is shown here by stacking atoms numbered 1, 2, 3 and 4 (on top of other three). The centre lies on body diagonal at (3/4, 1/4, 3/4). The Fig. also illustrates that tetrahedral voids are eight in number inside this unit cell (drawn as small spheres). These are located at other equivalent positions of, (1/4, 1/4, 1/4), (3/4, 3/4, 3/4) and are on the body diagonals.


There are four effective atoms per unit FCC cell. Thus, the ratio of tetrahedral voids to atoms per unit cell of FCC comes out to be 2:1. The size of the atom which can fit tight in the tetrahedral void is 0.225 r; where r is the radius of the solvent atom in the close packed arrangement.

A BCC unit cell is illustrated in Fig. 2.9 (b) with one tetrahedral void clearly being shown, though all such voids have been shown by small spheres. These tetrahedral voids are located on the faces of the cube at (1/2, 1/4, 0) and other equivalent positions. There are 12 tetrahedral voids per unit cell (six faces have in total 24 voids, but each face of the cube is shared between two unit cells).

A HCP unit cell is illustrated in Fig. 2.9 (c), with one tetrahedral void clearly shown. Various such voids have been shown by small spheres. There are 12 voids per unit cell (8 inside + 12 edges x 1/3). As there are 6 atoms per unit cell of HCP, thus, the ratio of tetrahedral voids to atoms is 2 : 1. The size is 0.225 r.

Type # 2. Octahedral Void:

It is surrounded by six solvent atoms situated at the six corners of a regular octahedron (called octahedral because of eight equal faces of equilateral triangles). This arrangement of atoms has four atoms, square-based and one sphere on the top and one at the bottom as illustrated in 2.10 (b) with 2.10 (a) as a bit exploded view.


It can also be visualised to have formed when three spheres on a close-packed plane and three other spheres on the adjacent plane are placed in such a way that the centres of the three spheres are directly over the three triangular valleys surrounding the central valley of the first plane when no sphere sits on the central valley as illustrated in 2.10 (c). There is one octahedral void per sphere in the three dimensional arrangement of the spheres.

A FCC unit cell is illustrated in Fig. 2.11 (a). One octahedral void at the body centre has been demarcated, though other octahedral voids have been represented by small spheres. The centre of the octahedral void is at 1/2, 1/2, 1/2 (body centre) and at the mid points of unit cell edges, 0, 0, 1/2, etc. The effective number of octahedral voids per unit cell,


1 (body centre) + 12 (mid-point of edges but each edge is shared by four unit cells) × 1/4 = 4

As there are 4 atoms per unit cell in FCC crystal, the ratio of octahedral voids to effective atoms per unit cell is 1: 1. The largest sphere (solute atom) which touches its six solvent large spheres, and which can fit tight in an octahedral void is 0.414 rx where rx is the radius of solvent atom.

A BCC unit cell is illustrated in Fig. 2.11 (c). One of the octahedral holes has been clearly demarcated and rests all are being shown as small spheres. They are at the midpoint of edges (0, 0, 1/2, etc.) and at the centre of each face (1/2, 1/2, 0, etc.) Each void is surrounded by six solvent atoms at the corners of a slightly compressed octahedron (two atoms are nearer to the octahedral centre as compared to four others), and that makes the octahedral void smaller than the tetrahedral void in this unit cell. (The former has a size of 0.15 r, but latter has 0.29 r).


A HCP unit cell is illustrated in 2.11 (d) where one of the octahedral voids has been clearly demarcated. All the six are shown as small spheres and all lie inside the unit cell of the hexagon. As there are six atoms per unit cell and as there are six octahedral voids, the ratio between them is 1: 1.

In gamma-iron (FCC), the octahedral void can accommodate-fit a spherical atom of 0.52 A radius, whereas the tetrahedral void in the FCC gamma-iron can accommodate-fit an atom of 0.28 A radius.

Thus, the carbon atom (0.77 A radius) or the nitrogen atom (0.71 A radius) sits in the larger octahedral void with an expansion of the lattice. In alpha-iron (BCC), there is room for an interstitial atom of 0.36 A radius in tetrahedral void and room for an atom of only 0.19 A radius in the octahedral void.

There are evidences that the carbon atoms in α -iron are present in octahedral void, though it is smaller of the two. A carbon atom in the tetrahedral void, if present would displace all the four atoms of the iron at four corners of the tetrahedron causing more distortion, whereas if present in octahedral void displaces only two nearest atoms resulting in less distortion.

This makes the interstitial solubility of carbon in a-iron more difficult than its solubility in γ -iron because of severe distortion which takes place (due to smaller size of the octahedral void) in alpha iron. This explains why, at the same temperature of 727°C (A1), gamma-iron can dissolve carbon up to 0.77 wt %, whereas alpha-iron is able to dissolve up to 0.025 wt %.


Calculate to compare the number of octahedral and tetrahedral-holes per atom in BCC structure.