Calculations of the density of alloys based on Bernal-type models of the alloy's metal component agreed fairly well with the experimentally determined values from measurements on alloys consisting of a noble metal together with a metalloid, such as alloys of palladium and silicon, or alloys consisting of iron, phosphorus, and carbon, although small discrepancies remained. One difference between real alloys and the hard spheres used in Bernal models is that the components of an alloy have different sizes, so that models based on two sizes of spheres are more appropriate for a binary alloy, for example. The smaller metalloid atoms of the alloy might fit into holes in the dense, random-packed structure of the larger metal atoms.