Question

The pattern of successive layers of ccp arrangement can be designated as:
A.AB AB AB
B.AB ABC AB ABC
C.ABC ABC ABC
D.AB BA AB BA

Answer 1

Hint:‘ccp’ arrangement stands for cubic close packing arrangement. The arrangement in a cubic close packing is such that its packing efficiency is 74 percent. For such types of problems, you need high imagination skills in three dimensions. But the best approach can be to try to think of all layers individually and then try to figure out the pattern. For example – simple cubic lattice formed by AAA…. Arrangement.

Complete step by step answer:
-The ccp arrangement is obtained when the third layer of a structure is placed over the second layer.

-Now when the third layer is placed over the second, there are only two possibilities.
-First possibility by covering tetrahedral voids and the second by covering octahedral voids.
-First, we will understand tetrahedral voids and octahedral voids. So tetrahedral voids are formed when the sphere of the second layer is above the void of the first layer. Octahedral voids are present at the edge Centre and body Centre.
-When the third layer is placed over the second by covering tetrahedral voids then in this possibility the sphere of the third layer will be symmetric with the first layer and if we follow the pattern the spheres of the second layer will be aligned with the fourth layer and so on. So, now we can conclude that the pattern of spheres is repeated in alternate layers. The pattern can be written as ABAB…….. . This pattern is called hexagonal packed structure (hcp).
-Now when the third layer is placed over the second layer such that it covers the octahedral voids. In this manner, the third layer is not aligned with either of the first or second. So if we consider the first layer as A, the second layer as B and the third layer formed as C and so on. The pattern designated will be ABCABCABC……
-Final Result: The pattern of successive layers of ccp arrangement can be designated as ABC ABC ABC.
-Hence, the correct option is (C).

Note:
-There is a very important point to remember in ABC ABC ABC ….... pattern and that is if spheres of the third layer are placed into tetrahedral voids, the packing is hcp (hexagonal close packing).
ccp is cubic close packing, it is also called fcc (face-centered cubic).
-In fcc (face-centered cubic), spheres of the third layer are placed into octahedral voids.
-The number of these two types of voids depends upon the number of close-packed spheres.
-Let the number of closed packed spheres be N, then:
-The number of octahedral voids generated will be N.
-The number of tetrahedral voids generated will be 2N.