Invariance of the relation between α relaxation and β relaxation in metallic glasses to variations of pressure and temperature

Dielectric relaxation experiments performed at ambient and elevated pressures P in molecular, ionic, and polymeric glass formers have established that the relation of the Johari-Goldstein (JG) \ensuremath{\beta}-relaxation time ${\ensuremath{\tau}}_{\ensuremath{\beta}}(T,P)$ to the \ensuremath{\alpha}-relaxation time ${\ensuremath{\tau}}_{\ensuremath{\alpha}}(T,P)$ is invariant to changes of T and P while the latter is kept constant. This property of the JG \ensuremath{\beta} relaxation is remarkable despite the fact that the invariance of the ratio ${\ensuremath{\tau}}_{\ensuremath{\beta}}(T,P)/{\ensuremath{\tau}}_{\ensuremath{\alpha}}(T,P)$ from experiment is sometimes approximate because the \ensuremath{\beta} relaxation is composed of a distribution of processes, and the ${\ensuremath{\tau}}_{\ensuremath{\beta}}(T,P)$ determined can be arbitrary. The property indicates the fundamental importance of the JG \ensuremath{\beta} relaxation and it cannot be neglected whenever the \ensuremath{\alpha} relaxation is considered. Notwithstanding, the property has not been checked on whether it applies to metallic glasses. Conventional experiment techniques cannot fulfill the task, and the alternative is molecular dynamics simulations. In this paper we report the results of molecular dynamics simulations of dynamical mechanical spectroscopy performed on two very different metallic glasses, $\mathrm{Z}{\mathrm{r}}_{50}\mathrm{C}{\mathrm{u}}_{50}$ and $\mathrm{N}{\mathrm{i}}_{80}{\mathrm{P}}_{20}$, at different pressures P. The JG \ensuremath{\beta} relaxation appears as an excess wing on the low-temperature side of the \ensuremath{\alpha} loss peak at ${T}_{\ensuremath{\alpha},P}$ in the isochronal loss modulus spectra ${{E}_{P}}^{\ensuremath{''}}(T)$. On the other hand, the isochronal non-Gaussian parameter $\ensuremath{\alpha}{2}_{P}(T)$ peaks at the temperature ${T}_{\ensuremath{\alpha}2,P}$ different from ${T}_{\ensuremath{\alpha},P}$ of ${{E}^{\ensuremath{''}}}_{P}(T)$. From the fact that ${T}_{\ensuremath{\alpha}2,P}$ is significantly lower than ${T}_{\ensuremath{\alpha},P}$, we identified the peak temperature ${T}_{\ensuremath{\alpha}2,P}$ of $\ensuremath{\alpha}{2}_{P}(T)$ with the JG \ensuremath{\beta} relaxation, and hence the JG \ensuremath{\beta} relaxation is fully resolved by studying the isochronal non-Gaussian parameter $\ensuremath{\alpha}{2}_{P}(T)$. After scaling temperature by ${T}_{\ensuremath{\alpha},P}$, the normalized ${{E}_{P}}^{\ensuremath{''}}(T/{T}_{\ensuremath{\alpha},P})$ and $\ensuremath{\alpha}{2}_{P}(T/{T}_{\ensuremath{\alpha},P})$ both show superposition of data taken at various pressures for all $T/{T}_{\ensuremath{\alpha},P}$ covering the JG \ensuremath{\beta} relaxation and the \ensuremath{\alpha} relaxation. Moreover the ratio ${T}_{\ensuremath{\alpha}2,P}/{T}_{\ensuremath{\alpha},P}$ is invariant to changes of T and P while ${\ensuremath{\tau}}_{\ensuremath{\alpha}}(T,P)$ is maintained constant. Thus we have verified for two different metallic glasses, $\mathrm{Z}{\mathrm{r}}_{50}\mathrm{C}{\mathrm{u}}_{50}$ and $\mathrm{N}{\mathrm{i}}_{80}{\mathrm{P}}_{20}$, that ${\ensuremath{\tau}}_{\ensuremath{\alpha}}(T,P)/{\ensuremath{\tau}}_{\ensuremath{\beta}}(T,P)$ is invariant to changes of T and P at constant ${\ensuremath{\tau}}_{\ensuremath{\alpha}}(T,P)$, as found in soft matter.