On the calculation of the density of multi-component solid solutions

In this paper, twelve methods that can be used to calculate the density of a multi-component solid solution are discussed. All the methods considered are mathematically simple and involve composition-weighted averages, sometimes with added corrections. Two of the density calculation methods discussed here are proposed for the first time and are innovative in using the polydispersity index of radii. The various methods have been tested by predicting the density of 60 multi-component solid solutions and comparing the value obtained with the density value reported (or calculated from their composition and lattice parameter) from papers found in the literature. The results may seem surprising, but they indicate that some (but not all) methods based on simple mixing laws can be very accurate. The more sophisticated methods also give good results (especially one of those proposed for the first time in this paper) and have the additional advantage of better explaining the underlying physics, which gives them additional value. Finally, expressions are proposed for calculating the various input parameters of the different methods so that there is consistency between them. • The paper addresses a basic, but underestimated, aspect of multi-component alloy: the accurate calculation of density. • The study tests 12 calculation methods, including 2 proposed by the authors for the first time. • Validation is carried out on a large set of 60 multicomponent solid solutions. • The results show that some simple methods based on mixing laws can be very effective. • More sophisticated methods also produce good results, allow for some fine-tuning and provide a better physical understanding.