Ultrahigh Poisson's ratio glasses

The manner in which metallic glasses fail under external loading is known to correlate well with those glasses' Poisson's ratio $\nu$: Low-$\nu$ (compressible) glasses typically feature brittle failure patterns with scarce plastic deformation, while high-$\nu$ (incompressible) glasses typically fail in a ductile manner, accompanied by a high degree of plastic deformation and extensive liquidlike flow. Since the technological utility of metallic glasses depends on their ductility, materials scientists have been concerned with fabricating high-$\nu$ glassy alloys. To shed light on the underlying micromechanical origin of high-$\nu$ metallic glasses, we employ computer simulations of a simple glass-forming model with a single tunable parameter that controls the interparticle potential's stiffness. We show that the presented model gives rise to ultrahigh-$\nu$ glasses, reaching $\nu =0.45$ and thus exceeding the most incompressible laboratory metallic glass. We discuss the possible role of the so-called unjamming transition in controlling the elasticity of ultrahigh-$\nu$ glasses. To this aim, we show that our higher-$\nu$ computer glasses host relatively softer quasilocalized glassy excitations, and establish relations between their associated characteristic frequency, macroscopic elasticity, and mechanical disorder.

Figure 1

Pairwise potential $\phi \left(r\right)$, expressed in terms of the microscopic units of energy $\varepsilon$, plotted for the studied values of the parameter $Q$ that controls the interparticle stiffness.

Figure 2

(a) The average shear ($G$) and bulk ($K$) moduli of our glass ensembles, plotted vs the parameter $Q$ that controls the stiffness of the repulsive part of the employed pairwise potential. (b) The densities of each of the $Q$ ensembles (see text for precise values) were set such that the pressure-to-bulk-modulus ratio of all glass ensembles generated in this paper is on the order of ${10}^{-3}$.

Figure 3

Poisson's ratio (PR) $\nu$ is plotted vs the parameter $Q$ that controls the interparticle stiffness (see Fig. 1) of the computer glass model put forward in this paper. The dashed line corresponds to the PR of the platinum-rich glass studied in Ref. [21], which is the highest reported for a laboratory metallic glass to date.

Figure 4

The ratio $G/K$ is plotted vs the parameter $Q$; the “unjamming”-based prediction $G/K\sim 1/\sqrt{Q}$ (see Ref. [27]) is not followed by our data (yellow symbols), but might be the correct asymptotic form of $G/K$ at large $Q$.

Figure 5

Radial distribution functions $g\left(r\right)$ of “large-large” particles in our model glasses for various $Q$ ensembles as specified in the legend, plotted vs the dimensionless distance $r/a_0$, where $a_0\equiv {(V/N)}^{1/3}$ is an interparticle distance. These distributions behave similarly to those measured in soft-sphere packings near unjamming [23]. Inset: the maximum of $g\left(r\right)$ increases slightly more quickly with decreasing $G/K$ than the $\sim {(G/K)}^{-2}$ scaling seen in soft-sphere unjamming.

Figure 6

Low-frequency vibrational spectra of our glassy ensembles measured for the same $Q$ parameters as described in the main text and plotted against the rescaled frequency $\omega /{\omega }_0$, where ${\omega }_0\equiv c_{\mathrm{s}}/a_0$ and $c_s$ is the shear-wave speed. The solid lines represent fits to the universal $\sim {\omega }^4$ nonphononic spectra seen quite generally in structural glasses [29].

Figure 7

(a) The dimensionless prefactors $A_{\mathrm{g}}{\omega }_0^5$ of the universal nonphononic spectra of our glasses scale as $\sim {(G/K)}^{-5/2}$ for small $G/K$, as predicted from the physics of the unjamming transition. (b) The sample-to-sample mean minimal vibrational frequency of quasilocalized excitations—made dimensionless by rescaling by ${\omega }_0$—scales as $\sim \sqrt{G/K}$ as predicted from the physics of the unjamming transition; see text for further discussion.

Figure 8

(a) The mechanical disorder quantifier $\chi$ is plotted against the ratio $G/K$. The agreement with prediction $\chi \sim {(G/K)}^{-3/4}$ spelled out in the text is reasonable; larger statistical ensembles and larger glassy samples might reduce the noise in $\chi$ and result in better agreement. (b) The dimensionless prefactors $A_{\mathrm{g}}{\omega }_0^5$—extracted from the spectral analysis presented in Fig. 6—are plotted against the quantifier $\chi$ of mesoscopic mechanical disorder. The solid line represents the prediction $A_{\mathrm{g}}{\omega }_0^5\sim {\chi }^{10/3}$ spelled out and tested in Ref. [15], and also explained in the text.

Figure 9

The ratio between the destabilizing stiffness and force terms, $k_{-}/f_{-}$, measured for low-energy quasilocalized excitations and plotted against the parameter $Q$. These data highlight a qualitative difference in the micromechanics of our glasses compared with repulsive sphere packings for which $k_{-}/f_{-}$ vanishes identically.