Voids in Solid

As we have learn earlier the max packing faction is 74% (in HCP Or FCC) and the remaining space is void. Voids in solids is the vacant space between the constituent particles in a closed packed structure.
The size and distribution of voids in solid have a considerable effect on behaviour of materials property. eg, More is the void more will be diffusivity, and also affect the interstitial solubility.

Types of Voids :
    (1) Tetrahedral
    (2) Octahedral

Tetrahedral Void :
The tetrahedral Void form in crystal structure when the sphere of top layer lie just above the triangular voids formed be layer lying just below. A tetrahedron is formed by joining radius of all four spheres and the vacant space between them is tetrahedral void.

Octahedral Void :
The Octahedral Void form in crystal structure is between a triangular voids of first layer coincides ( having different orientation ) with the triangular voids of layer above or below it. A octahedron is formed by joining radius of all four spheres and the vacant space between them is octahedral void.

Voids in FCC

Tetrahedral Void in FCC :

➧ The FCC crystal structure have 8 tetrahedral voids which are located near the corners of cell. All Tetrahedral voids lie inside the cell
➧ The number of tetrahedral voids is 2 times the number of the atoms in cell.
➧ The size of largest interstitial atom that can fit into tetrahedral Void = $0.225\times \text{ Size of FCC atoms}$ $$\text{n atoms}\Rightarrow 2\times \text{n Tetrahedral Void}$$

Octahedral Void in FCC :

➧ The FCC crystal structure have 4 octahedral voids which are located at the :
      1) Center of cell = 1
      2) At every edge center contributing 1/4th => $\frac{1}{4}\times 12=3$ Voids
➧ The number of octahedral voids is equal to the number of the atoms in cell.
➧ The size of largest interstitial atom that can fit into octahedral Void = $0.414\times \text{ Size of FCC atoms}$ $$\text{n atoms}\Rightarrow \text{n Octahedral Void}$$

Voids in BCC

➧ The BCC materials have distorted Tetrahedral and Octahedral voids.
➧ Number of Tetrahedral voids : 12
➧ Number of Octahedral voids : 6

Voids in HCP

➧ Number of Total Tetrahedral voids : 12 or 4 Voids/cell
➧ Number of Total Octahedral voids : 6 or 2 Voids/cell

---

Crystal	Void	Position	$\frac{voids}{unit}$	$\frac{voids}{atoms}$	$\frac{r_{voids}}{r_{atoms}}$
FCC	Tetrahedral	8 $(\frac{1}{4},\frac{1}{4},\frac{1}{4})$	8	2	0.225
	Octahedral	Body Center : 1 $(\frac{1}{2},\frac{1}{2},\frac{1}{2})$ Edge Center : 3 $(\frac{1}{2},0,0)$	4	1	0.414
BCC	Distorted Tetrahedral	$\frac{4}{2}\times 6=12(0,\frac{1}{2},\frac{1}{4})$	12	6	0.155
	Distorted Octahedral	Face Center : $\frac{1}{2}\times 6=3(\frac{1}{2},\frac{1}{2},0)$ Edge Center : $\frac{1}{4}\times 12=3\text{(}(\frac{1}{2},0,0)$	6	3	0.291
HCP	Tetrahedral	$(0,0,\frac{3}{8}),(0,0,\frac{5}{8})$ $(\frac{2}{3},\frac{1}{3},\frac{1}{8}),(\frac{2}{3},\frac{1}{3},\frac{7}{8})$	4	2	-
	Octahedral	$(\frac{1}{3},\frac{2}{3},\frac{1}{4}),(\frac{1}{3},\frac{2}{3},\frac{3}{4})$	2	1	-