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Calculate the packing fraction for the Ca unit cell, given that Ca crystallizes in a face-centered cubic unit cell. |
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Answer» Solution :One-eighth of each CORNER ATOM and one-half of each face-centred atom are CONTAINED within the unit cell of Ca GIVING `Z=8 (1/8) + 6(1/2) = 4` Further, atomic RADIUS, `r=(sqrt(2)a)/4`…………….. (eqn 4) Volume of 4 atoms `4 xx 4/3 pi r^(3) = 4 xx 4/3 xx pi ((sqrt(2)a)/4)^(2) = (sqrt(2)pia^(3))/6` Packing fraction `=(sqrt(2)pia^(3))/6// a^(3) = (sqrt(2)pi)/6 = 0.74` |
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