Consider two hypothetical metallic crystal structures A and B. A has a simple cubic and B a fcc lattice structure. Both have the same unit cell volume. The Atomic Packing Factor for A is 0.520 and that for B is 0.740. What is the ratio of the fcc to simple cubic atomic radii?

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The Space Lattice and Unit Cells

Every matter consists of atoms, molecules, and ions. If these atoms, molecules, and ions (micro-particles) are represented in a three-dimensional space-occupying certain specific points in space, then these arrangements are termed as space lattices and the specific points which are being occupied by atoms, molecules and ions are termed as lattice points. The atoms, molecules, and ions at the lattice points are generally grouped in a regular fashion and repeat periodically at the three-dimensional space.