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How will you distinguish between the following? (i) Hexagonal close packing and cubic close packing. (ii) Crystal lattice and unit cell. (iii) Tetrahedral void and octahedral void.

How will you distinguish between the following? (i) Hexagonal close packing and cubic close packing. (ii) Crystal lattice and unit cell. (iii) Tetrahedral void and octahedral void.

Grade:upto college level

1 Answers

Gaurav
askIITians Faculty 164 Points
6 years ago
Hello Student
If the spheres in the second layer are just placed over the spheres in the first layer so that the spheres in the two layers are vertically aligned, its voids will come above the voids in the first layer. This is an inefficient way of filling the space and results in the formation of simple cubic lattice .

When a third layer is placed over the second layer in such a way that the spheres cover the tetrahedral or ‘a’ voids; a three dimensional closest packing is obtained where the spheres in every third or alternate layers are vertically aligned (i.e. the third layer is directly above the first, the fourth above the second layer and so on) calling the first layer A and second layer as layer B, the arrangement is called ABAB …………. pattern orhexagonal close packing (hcp) as it has hexagonal symmetry.

In hcp as well as ccp only 74% of the available space is occupied by spheres.
The remaining space is vacant and constitutes interstitial voids or interstices or holes.
These are of two types:(a)Tetrahedral voids and (b) Octahedral voids

Tetrahedral voids
In close packing arrangement, each sphere in the second layer rests on the hollow (triangular void) in three touching spheres in the first layer.The centres of theses four spheres are at the corners of a regular tetrahedral.
The vacant space between these four touching spheres is called tetrahedral void.In a close packing, the number of tetrahedral void is double the number of spheres, so there are two tetrahedral voids for each sphere.However, one half of the triangular voids in the first layer are occupied by spheres in the second layer while the other half remains unoccupied.
The triangular voids in the first layer is overlapped by the triangular voids in the second layer.The interstitial void, formed by 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 octahedron255-1177_2014910-14144333-5750-CP_interstitial-2-(1).png

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