SIMPLE CUBIC . FCC BCC
UNIT CELL side A 2r 4r/sqrt2 4r/sqrt3
FACE DIAGONAL SQRT 2 (2r) 4r sqrt (2/3)4r
body diagonal sqrt3 (2r) sqrt (3/2)4r 4r
NO OF ATOMS 1 4 2
cell VOLUME 8r ^3 (32r^3)/sqrt 2 64r^3/3sq3
here r = atomic radius.
no of atoms in hcp = 6
co ordination number of HCP , FCC = 12
co ordination number of bcc = 8
atomic radius of hcp r = a/2
atomic radius of simple cubic r = a/2
BCC atomic radius = asqrt(3/4)
fcc atomic radius = a sqrt2/4
IN FCC , HCP LATTICES EMPTY SPACE = 26%
IN BCC LATTICES EMPTY SPACE = 32 %
TOTAL NO OF ATOMS PER UNIT CELL IS GIVEN BY
N = Nt + Nf / 2 +Nc/8
where Nt = np of interior atoms , Nf = no of atoms on faces , Nc = no of atoms on corners .
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