Characterization of the free volume in a Zr45.0Cu39.3Al7.0Ag8.7 bulk metallic glass by reverse Monte Carlo simulation and density measurements

The absolute contents of free volume in the as-cast and annealed Zr45.0Cu39.3Al7.0Ag8.7 bulk metallic glass (BMG) samples were quantified by density measurements and reverse Monte Carlo (RMC) simulation using the total structural factors F(Q) determined by X-ray diffraction (XRD) experiments as fitting constraints. The densities of the as-cast, annealed and crystallized samples measured by Archimedes method are 7.319, 7.327 and 7.342 g/cm3 (precision ± 0.003 g/cm3), respectively. A new approach was used in the RMC simulation to define the free volume as the difference between the volume of the Voronoi polyhedron and the volume of the Wigner–Seitz cell of the constituent atoms. Two types of initial configurations were constructed: (1) in configuration A, all types of potential atomic pairs are allowed; (2) in configuration B, Al-Al and Ag-Ag atomic pairs are excluded. The contents of free volume in the as-cast and annealed samples were found to be 0.59% and 0.39% (configuration A), 0.55% and 0.34% (configuration B), respectively (precision ± 0.03%). The probability distribution of the as-calculated free volume can be well-fitted by the equation proposed by Turnbull and Cohen. Finally, it is shown that the contents of free volume determined by density measurements and RMC are comparable, while the discrepancy of the results is discussed.