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. 2015 Nov 10;112(45):13762-7.
doi: 10.1073/pnas.1503741112. Epub 2015 Oct 26.

Interatomic repulsion softness directly controls the fragility of supercooled metallic melts

Johannes Krausser  1 , Konrad H Samwer  2 , Alessio Zaccone  3
Affiliations

Interatomic repulsion softness directly controls the fragility of supercooled metallic melts

Johannes Krausser et al. Proc Natl Acad Sci U S A. .

Abstract

We present an analytic scheme to connect the fragility and viscoelasticity of metallic glasses to the effective ion-ion interaction in the metal. This is achieved by an approximation of the short-range repulsive part of the interaction, combined with nonaffine lattice dynamics to obtain analytical expressions for the shear modulus, viscosity, and fragility in terms of the ion-ion interaction. By fitting the theoretical model to experimental data, we are able to link the steepness of the interionic repulsion to the Thomas-Fermi screened Coulomb repulsion and to the Born-Mayer valence electron overlap repulsion for various alloys. The result is a simple closed-form expression for the fragility of the supercooled liquid metal in terms of few crucial atomic-scale interaction and anharmonicity parameters. In particular, a linear relationship is found between the fragility and the energy scales of both the screened Coulomb and the electron overlap repulsions. This relationship opens up opportunities to fabricate alloys with tailored thermoelasticity and fragility by rationally tuning the chemical composition of the alloy according to general principles. The analysis presented here brings a new way of looking at the link between the outer shell electronic structure of metals and metalloids and the viscoelasticity and fragility thereof.

Keywords: fragility of liquids; glass transition; liquid metals; metallic glasses; supercooled liquids.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
(A) Approximation of the repulsive part of the first peak of g(r) using two different values for the steepness λ. An increase in λ is linked to a steeper slope of g(r). (B) In the high-frequency regime the affine shear modulus represents a good approximation to the actual behavior of the shear modulus G=GA−GNA.
Fig. 2.
Fig. 2.
The experimental data points for various glass-forming alloys from ref. and the respective fitting curves for the shear modulus in A and the viscosity in B. The solid lines are the one-parameter fitting curves obtained using the expressions in Eqs. 5 and 6, for the shear modulus and viscosity, respectively. The values used for the fittings are reported in Table 1.
Fig. 3.
Fig. 3.
(A) The Ashcroft–Born–Mayer pseudopotential is depicted for four different glass-forming alloys. The fragility m increases with the pseudopotential steepness. (B) The value of the Born–Mayer energy scale increases linearly with the fragility. Also, it is observed that the average ionic diameter decreases linearly with the fragility.
Fig. 4.
Fig. 4.
(Left) The distance between the atoms decreases as the temperature is increased, leading to a smaller overlap of the effective interaction potentials. (Right) The growth of the cage by ΔR when increasing the temperature by ΔT and the corresponding loss of stabilizing energy ΔE. The potentials are shifted for the sake of clarity.
Fig. S1.
Fig. S1.
Comparison of the Ashcroft–Born–Mayer pseudopotential with the logarithmic potential of mean force (including the two separate contributions to the pseudopotential). The plot was generated for a repulsive steepness λ=99.7.
Fig. S2.
Fig. S2.
Illustration of a cut through an idealized spherical STZ. The diameter of the STZ is roughly six times larger than the diameter of the characteristic atomic volume Vc. The colored spheres represent the average ionic cores of the atoms in the alloy. The objects are approximately drawn to scale.
See this image and copyright information in PMC

References

    1. Na JH, et al. Compositional landscape for glass formation in metal alloys. Proc Natl Acad Sci USA. 2014;111(25):9031–9036. - PMC - PubMed
    1. Bennett C, Polk D, Turnbull D. Role of composition in metallic glass formation. Acta Metall. 1971;19(12):1295–1298.
    1. Hafner J. 1987. From Hamiltonians to Phase Diagrams, Springer Series in Solid-State Sciences (Springer, Berlin), Vol 70.
    1. Götze W. Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory. Oxford Univ Press; Oxford: 2009.
    1. Mattsson J, et al. Soft colloids make strong glasses. Nature. 2009;462(7269):83–86. - PubMed

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