Link between volume, thermal expansion, and bulk metallic glass formability

The specific volumes and thermal expansion coefficients of 41 transition-metal based alloy liquids, which include both bulk and marginal glass-formers, are presented. Those parameters are compared with their values either in the corresponding crystal phases or in their constituent elemental liquids. The volume differences in both cases at the liquidus temperature, $T_l$, correlate well with the critical thicknesses, $d_{\mathrm{crit}}$ of the corresponding glass, taken either from literature or from estimates. The estimates are based on a recent study [Dai et al., J. Non-Cryst. Solids 525, 119673 (2019)], which requires knowledge of the liquid expansion coefficient and viscosity. The volume differences between the better glass-forming liquids and the crystal phases are smaller; they are larger when compared with the elemental liquids. The thermal expansion coefficients of the liquids correlate well with the cohesive energies and fragilities. Their differences with the crystal phases and estimates from elemental liquids correlate well with $d_{\mathrm{crit}}$. The differences are smaller for the former and larger for the latter for alloy liquids having larger values of $d_{\mathrm{crit}}$. This parameter then appears to be a prime indicator of glass formability. The results are explained in terms of changes in the anharmonicity and structural contributions to the expansion coefficients on alloying.

Figure 1

The volume changes on melting of the crystals of some BMGs are compared with the literature values for critical thickness ($d_{\mathrm{crit}}$). The alloy numbers are the same as in Tables 1 and 2. A linear fit excluding the alloy numbers 36 and 37 are also shown.

Figure 2

The measured volume of the liquid at $T_l$ in excess of the estimated volume from the elemental liquids at the $T_l$ of the alloys. The alloy numbers are the same as listed in Tables 1 and 2. The error bars include measured differences from multiple samples of the same composition as well as different thermal cycles. No error bars are shown for the data from a single sample since they are negligible in such measurements.

Figure 3

The liquid expansion coefficient as a function of cohesive energy (a) and fragility (b). The alloy numbers are the same as in Tables 1 and 2. The fit parameters are provided in the text.

Figure 4

The difference in the thermal expansion coefficients of the liquids and crystals as a function of critical thickness for 15 BMGs. The linear fit parameters are provided in the text.

Figure 5

Difference between the experimentally measured (${\alpha }_{\mathrm{liq}}$) and estimated (${\alpha }_{\mathrm{liq}\mathrm{estm}}$) liquid thermal expansion coefficients from the elemental liquids, as a function of estimated critical thicknesses. The parameters and alloy numbers are listed in Tables 1 and 2.