The cube edge length a and the atomic radius R are related through Area of 100

The cube edge length a and the atomic radius r are

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The cube edge length a and the atomic radius R are related through Area of (100) plane = For this (100) plane there is one atom at each of the four cube corners, each of which is shared with four adjacent unit cells, while the center atom lies entirely within the unit cell. Thus, there is the equivalence of 2 atoms associated with this FCC (100) plane. Consider (111) plane of FCC
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Area of (111) plane: The planar section represented in the above figure is triangle, area of triangle is equal to one-half of the product of the base length (here it is equal to (4R ) and the height, h. i.e., From above figure Calculate the area of the plane.
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There are six atoms whose centers lie on this plane, which are labeled A through F . One-sixth of each of atoms A , D , and F are associated with this plane (yielding an equivalence of one-half atom), with one-half of each of atoms B , C , and E (or an equivalence of one and one-half atoms) for a total equivalence of two atoms. For a given material R is constant then, in case of FCC unit cell, .
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