The packing efficiency of the diamond cubic crystal structure is approximately 34 percent, which is a matter of basic crystallographic definition and geometric calculation.
The claim states a fundamental geometric property of the diamond cubic crystal structure (its atomic packing factor is pi * sqrt(3) / 16, which is approximately 0.34 or 34%). This is a mathematical fact inherent to the definition of the crystal lattice and requires no external citation or empirical verification, making it common knowledge in materials science and crystallography.