Explain with the help of diagram ABAB type of
arrangement in planal packing:
Answers
a. AAAA type of three dimensional packing is obtained by placing layers (of AAAA type of planar two dimensional crystal structure) one over the other. All the spheres of the successive layers are placed exactly above the spheres of the lower layers. b. This results in perfect horizontal and vertical alignment between spheres of various layers. The unit cell has simple cubic structure as shown in figure (a). c. This arrangement has more empty space. d. In this arrangement, the coordination number is six. Each sphere is in contact with four spheres in the layer, one above and one below the layer. ii. ABAB type of three dimensional packing: In this type (ABAB) of crystal structure, packing is more efficient than simple cubic structure. a. Three dimensional packing can be obtained by placing layers (of ABAB type of planar two dimensional crystal structure) one over the other. b. The spheres of second layer are placed into depressions between the spheres of the first layer. c. The first layer is designated as A type and second layer is designated as B type for convenience eventhough both the layers are of ABAB type. d. This arrangement of two layers is AB type shown in figure (a) and its top view is shown in figure (b). e. In this arrangement, 1. Tetrahedral voids are formed by three spheres in the first layer and one sphere in the second layer. This happens when the sphere of second layer covers the triangular open space of first layer. Due to this, only half the number of triangular open spaces of first layers are covered. 2. Tetrahedralvoids are also formed by three spheres in the second layer and one sphere in the first layer. 3. Octahedral voids are formed by three spheres in the first layer and three spheres in the second layer. This happens when the three spheres of second layer covers the triangular open space of first layer. Due to this, the remaining half the number of triangular open spaces of first layers are covered. f. Thus, formation of tetrahedral voids involves four spheres and formation of octahedral voids involves six spheres. g. A tetrahedron can be formed by connecting the centres of four spheres involved in the formation of tetrahedral voids. An octahedron can be formed by connecting the centres of six spheres involved in the formation of octahedral voids. h. For N close packed spheres, the number of octahedral voids is N and the number of tetrahedral voids is 2N. i. Third layer can be placed over the second layer in two ways: 1. The spheres of the third layer can be placed into tetrahedral voids to form ABAB type structure. 2. The spheres of the third layer can be placed into octahedral voids to form ABCABC type structure. j. Placing the spheres of the third layer into the tetrahedral voids: In ABAB type structure, there is horizontal and vertical alignment between the spheres of first layer and third layer. Similarly there is horizontal and vertical alignment between the spheres of second layer and fourth layer. This arrangement is called hexagonal close packed (hcp) structure. This is shown in the following figure: iii. ABCABC type of three dimensional packing: OR Placing the spheres of the third layer into octahedral voids: a. The spheres of the third layer can be placed into octahedral voids. The arrangement of third layer is different from that of first and second layers. Hence, third layer is designated as C layer and the structure is called ABCABC type. b. When fourth layer is placed, there is horizontal and vertical alignment between the spheres of first layer and fourth layer. This is shown in figure (a). c. This arrangement is called cubic close packed (ccp) structure. It is same as face-centred cubic structure. d. In both arrangements (hcp and ccp), the coordination number is 12. Each sphere is in contact with 6 neighbouring spheres in its own layer, 3 spheres in the layer above and 3 spheres in the layer below. It is not possible to increase coordination number beyond 12. Hence, hcp and ccp packing are equally efficient. Read more on Sarthaks.com - https://www.sarthaks.com/1196550/explain-with-the-help-neat-diagrams-aaaa-abab-and-abcabc-type-three-dimensional-packings