A Free-Volume Model for Thermal Expansion of Metallic Glass

Many mechanical, thermal and transport behaviors of polymers and metallic glasses are interpreted by the free-volume model, whereas their applications on thermal expansion behaviors of glasses is rarely seen. Metallic glass has a range of glassy states depending on cooling rate, making their coefficients of thermal expansion vary with the glassy states. Anharmonicity in the interatomic potential is often used to explain different coefficients of thermal expansion in crystalline metals or in different metallic-glass compositions. However, it is unclear how to quantify the change of anharmonicity in the various states of metallic glass of the same composition and to connect it with coefficient of thermal expansion. In the present work, isothermal annealing is applied, and the dimensional changes are measured for La_62Al_14Cu_11.7Ag_2.3Ni_5Co_5 and Zr_52.5Cu_17.9Ni_14.6Al_10Ti_5 metallic glasses, from which changes in density and the coefficients of thermal expansion of the specimens are both recorded. The coefficients of thermal expansion linearly decrease with densification reflecting the role of free volume in thermal expansion. Free volume is found to have not only volume but also entity with an effective coefficient of thermal expansion similar to that of gases. Therefore, the local regions containing free volume inside the metallic glass are gas-like instead of liquid-like in terms of thermal expansion behaviors.