height of hcp unit cell


 

2 years ago

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Dear Mukal,


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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