The metal iron is cubic with a=2,86 A and with two iron atoms in the unit cube at 0,0,0 and 1/2,1/2,1/2.How many nearest neighbours does each iron atom have and how far away are they ?

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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To figure out where are located the atoms, we'll draw a cubic unit hat has the edge of 2,86 A.

We'll reproduce same cube parallel to the original one and one another and we'll obtain a typical body centered arrangement. 

In this arrangement, the atom located at 1/2,1/2,1/2 has to be surrounded by 8 atoms. An atom is the one located in the origin of the cube (0,0,0) and other 7 atoms at the corners of the cube.

Conclusion: each atom that has a body centered arrangement has coordination number 8.

We'll calculate the interatomic distance d:

d = sqrt [(a/2 - 0)^2 + (a/2 - 0)^2 + (a/2 - 0)^2]

d = sqrt (3a^2/4)

d = a(sqrt3)/2, where a = 2.86

d = 2.86*sqrt3/2

d = 2.48 A

The distance between 2 neighbor iron atoms is d = 2.48 A.