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  • Calculate the efficiency of packing in case of a metal crystal for (i) simple cubic

1.10   Calculate the efficiency of packing in case of a metal crystal for

               (i) simple cubic

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(i) Simple cubic :-  In a simple cubic lattice the atoms are located only on the corners of the cube.

                               Thus, the side of the cube ‘a’, and the radius of each particle, r are related as:

                                                     a = 2r

                               Volume of cubic unit cell = (2r)^3 = 8r^3                               

                           And Volume of 1 atom : 

                                                                =\frac{4}{3}\Pi r^3

                              Packing\ efficiency = \frac{Volume\ of\ one\ atom}{Volume\ of\ cubic\ unit\ cell}\times100 \%

                                                                          

                                                                          = \frac{\frac{4}{3}\Pi r^3}{8\Pi r^3}\times100 \% = \frac{\Pi }{6}\times100\%

                                                                          = 52.4\%

Thus packing efficiency of simple cubic is 52.4\%

Posted by

Devendra Khairwa

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