Atomic sizes of Cu and Au in Cu-Au solid solution and the lattice relaxation effects on disorder-Cu3Au phase equilibria

[Display omitted] •First-principles CVM and Bader analysis revealed the atomic sizes in Cu-Au alloy.•Atomic sizes of Cu and Au in their pure metals remain almost unchanged in the alloy.•The atomic size effect well reproduces an order–disorder transition temperature. Based on the first-principles cluster variation method (CVM), the atomic sizes of Cu and Au in a Cu-Au solid solution were estimated as a function of concentration. The atomic volumes of both Cu and Au atoms in their pure metals remain almost unchanged over the entire concentration range. The Bader analysis based on the electronic structure of a random solid solution gave the information of the atomic size, confirming the results of the first-principles CVM. The Bader analysis further revealed that Cu atoms in the random phase are classified into two types: the first type increases in volume upon alloying while the other type loses volume despite both types losing charge. Computer simulation of the local lattice relaxation satisfactorily yielded the relaxation energy which resolved the discrepancy of the Cu3Au (L12)-disorder transition temperature between the first-principles CVM and experimental results.