Random packing of monoatomic structures

The dependence of the first coordination number k _n on the packing factor k _y is obtained for four cubic structures: fcc, bcc, simple cubic, and diamond. The k _n (k _y ) dependence is described by a third-degree polynomial k _n = ?71.76782 + 467.78914 k _y ? 925.48451 k _y ² + 603.01146 k _y ³ with the confidence factor R _d = 1. The k _n (k _y ) function has an N loop with a maximum at k _n = 6.32; k _y = 0.454 and a minimum at k _n = 5.84; k _y = 0.573. The tangents intersect the k _n (k _y ) curve at extrema at k _y = 0.4 and k _y = 0.625. Around the N loop, i.e., at 5.84 ≤ k _n ≤ 6.32 and 0.4 ≤ k _y ≤ 0.625, two or three packing factors correspond to a certain value of the coordination number. Therefore, this range of the k _n and k _y values can be defined as a “random packing” region. Estimations presented here agree well with the results of calculations, both geometric and numerical. For monoatomic solids with the random packing parameters, the difference between the specific volumes of the solid and liquid phases is insignificant. The dilatancy effect is possible in the region where ?k _n / ?k _y ≤ 0.