A cubic metal (radius of hypothetical touching atomic spheres:r=0.77Å) showsplastic deformation by slip along...

A cubic metal (radius of hypothetical touching atomic spheres: r=0.77Å) shows
plastic deformation by slip along the<111>directions. Based on this
information, deduce the planar packing density (atoms/m2) for its densest family
of planes.

Expert Solution

Since there is a slip along <111> directtions, it should be a BCC system with a slip {110}, <111>

Therefore, in this case : a x cube root ( 3 ) = 4r

or, a = 4r / cube root (3 )

Substituting the given value of r = 0.77A^o = 0.77 x 10^-10 m we get,

a = 4 x 0.77 x 10^-10 / cube root (3) = 2.14 x 10^-10 m

Now densest planes are {110 } so packing density is -

2 atoms / { a² SQRT (2) } = 2 / [ 2.14 x 10^-10 ]² x 1.4142 = 3 .0883 x 10¹⁹ atoms / m²

or, = 3 x 10¹⁹ atoms / m²

queen_honey_blossom answered 2 years ago

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