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how to derive the height of a hcp unit cell? please discuss in detail.

how to derive the height of a hcp unit cell? please discuss in detail.

Grade:11

1 Answers

Godfrey Classic Prince
633 Points
9 years ago

Dear tejaswini tummala,

A,B,C,E (red dots) will represents the centres of sphere of atoms in HCP closed packing,

now, AB=BC=CA=EB = 2R (edge lengths of HCP)

BD=\frac{2R}{\sqrt{3}}  ,as BD divides the median through B in 2:1 ratio from B...

now EDB is rt. triangle,

by pythagores theorem :

(\frac{2R}{\sqrt{3}})^2+h^2=(2R)^2

=> h=2R\sqrt{\frac{2}{3}}

now, their will be another atom which will be mirror image of E on plane ABC

so, the height (c) of HCP will be 2h

c=2h=4R\sqrt{\frac{2}{3}}

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