Question

The two types of holes which occur in any close packed structures are
A) Tetrahedral, octahedral
B) Trigonal, octahedral
C) Trigonal, tetrahedral
D) Only octahedral

Answer 1

In hexagonal close packing(hcp) or in cubic close packing (ccp) only 74 percent of the available space is occupied by the spheres. The remaining space is vacant and constitutes interstitial voids or spaces.

Complete step by step answer:
In the formation of crystals, the constituent particles try to pack as closely as possible so as to attain a state of maximum possible density and stability. Since in different crystals, the units of pattern have different shapes and sizes, the actual mode of closest packing is different for different crystals.
In close packing arrangement, each sphere in the second layer rests on the hollow (triangular void) in the three touching spheres in the first layer. The centres of these four spheres are at the corners of a regular tetrahedron. The vacant space between these four touching spheres is called a tetrahedral void.
In a close packing, the number of tetrahedral voids is double the number of spheres. So, there are two tetrahedral voids associated with each sphere, one above the sphere and one below the sphere.
As mentioned above, the spheres in the second layer rest on the triangular voids in the first layer. However, one half of the triangular voids in the first layer are occupied by the spheres in the second layer while the other half remain unoccupied. The triangular voids in the first layer are overlapped by the triangular voids in the second layer. The interstitial void formed by the combination of two triangular voids of the first and second layer is called octahedral void because this is enclosed between six spheres, centres of which occupy corners of a regular octahedron.
In a close packing, the number of octahedral voids is equal to the number of spheres. Thus, there is only one octahedral void associated with each sphere.
Therefore, from the above discussed reasons we can conclude that the two types of holes that occur in any close packed structures are tetrahedral and octahedral voids.
Option A is the correct answer.

Additional information: Radius ratio of tetrahedral void, $\dfrac{{{{\text{r}}_{{\text{void}}}}}}{{{{\text{r}}_{{\text{sphere}}}}}}{\text{ = 0}}{\text{.225}}$
Radius ratio of octahedral void, $\dfrac{{{{\text{r}}_{{\text{void}}}}}}{{{{\text{r}}_{{\text{sphere}}}}}}{\text{ = 0}}{\text{.414}}$

Note:
Octahedral void is larger than a tetrahedral void. Both hexagonal close packing and cubic close packing arrangements are three dimensional ones.