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## Monday, April 22, 2019

### SIMPLE CUBIC CELL(SCC):

(1) 2D square close packing sheets are involved to generate simple cubic cell as well as body centred cell. In which each corner atom is touching potion with its adjacent corner atom.
(2) Take two 2D square close packing sheet and Placing a second square packing layer (sheet) directly over a first square packing layer forms a "simple cubic" structure.
(3) The simple “cube” appearance of the resulting unit cell is the basis for the name of this three dimensional structure.
(4) This packing arrangement is often symbolized as "AA...", the letters refer to the repeating order of the layers, starting with the bottom layer.
(5) The coordination number of each lattice point is six. This becomes apparent when inspecting part of an adjacent unit cell.
(6) The unit cell contain eight corner spheres, however, the total number of spheres within the unit cell is 1 (only 1/8th of each sphere is actually inside the unit cell). The remaining 7/8ths of each corner sphere resides in 7 adjacent unit cells.
(7) PACKING EFFICIENCY):
In simple cubic unit cell:
(1) Let ‘a’ be the edge length of the unit cell and r be the radius of sphere.
(2) As sphere are touching each other therefore a = 2r
(3) No. of spheres per unit cell = 8*1/8=1
(4) Volume of the sphere = 4/3(pi) r3
(5) Volume of the cube = a3= (2r)3 = 8r3
(6)  Packing efficiency (space occupied):
(7) Density of simple unit cell:
(8) Coordination Number:
(1) The nearest neighbour distance is just the lattice parameter (a) therefore coordination number for a given atom in SCC unit cell is 6 (six).
(2) The next nearest neighbour are 12 at distance a/root 2 (each face diagonal in x ,y and Z plane).
(3) 3rd neighbour (Next to Next nearest neighbour) are (8) at distance a root 3 (each corner along body diagonal.