Structural anisotropy: a ‘fingerprint’ of atomic-scale deformation mechanism of glasses

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Unique deformation features and properties of glasses

Glasses cover a variety of kinds in our everyday life, including window glasses in buildings or mobile vehicles, bottles for decoration or food containers, polymer glasses for plastic tools or toys, and metallic glasses—a new kind of coming materials for sports equipment like tennis racquets, golf clubs, and skis. From polymer glasses to metallic glasses, the modulus can change in a range from the order of 0.1 GPa to 100 GPa. One can always find an adaptable material according to the application requirement. Components comprising these materials also diversifies in atomic-level structure: some consist of large molecules with long molecular chains as that in polymer glasses; some consist of small molecules forming in a network-like structure as that in silicon glasses; and some consist of atoms of metallic elements as that in metallic glasses.

Surprisingly, despite of the diverse atomic-level structure, glassy materials display some common response feature when an external load imposes. Shear strain tends to be localized, rendering a brittle rupture of the material (due to the intercrossing of chains some polymer glasses could be an exception of this rule). This deformation feature connects with the disorder nature of the atomic/molecular structure. The disordered structure impedes a long-range transport of the plastic dissipation that is conventionally facilitated in a periodic lattice for crystals.

Nonaffine arrangement at the heart of glass deformation

The local response of amorphous solids to a load will not be uniform even under a homogeneous deform. The excess part to the linear response is the nonaffine arrangement that essentially dictates how the disordered structure dissipates the plastic deformation energy. Modern theories on modelling how the amorphous solids deform rely on the hypothesis of the localized nonaffine arrangement. Many structural ingredients have been proposed for such arrangement, typically involving the free volume which represents the extra space one atom can explore around and connects with the vibrational entropy, and the mirror symmetry that can result in a force imbalance even under uniform deformation. Generalization of these concepts to a broad range of glasses may not be straight forward, as much of these factors are proposed in atomic/particle systems. Covalent interaction is a more robust bonding between atoms relative to that of the metallic bonding. Covalent bonds in some glasses could overwhelm the effect of geometrical packing in local environment for the mechanical response. More generalized structural characterization is asked for to unveil the elusive mechanism for nonaffine arrangement.

Resolving the structural changes of a deformed glass on the atomic scale is challenging due to its disordered nature. This is especially hard in experiments. Too few structural indicators that are accessible to experimentalists have been proposed. Verification of the validity of these indicators for the nonaffine arrangement, hitherto, only stays on computational sciences. A direct experimental observation of one such fingerprint for nonaffine arrangement is challenging, but definitely significant.

Deciphering nonaffine arrangement through structural anisotropy

Now, we show that the nonaffine displacement correlates with the structural anisotropy, and it can resolve the detailed atom motion responsible for plastic deformation.

 

Figure 1: a Illustration of measuring the structural anisotropy with high-energy X-ray diffraction in experiments and the resulting anisotropic pair distribution function in metallic glasses. The local rearranging region can be determined by comparing the anisotropic term and the theoretical affine prediction. b Correlation of the structural anisotropy and nonaffine displacement field on atomic scale, and the associated bond-breaking events for the nonaffine arrangement in metallic glasses. c Similar correlation between the structural anisotropy and the nonaffinity, and the associated bond-reorientating events in polymer glasses.

We conducted high-energy X-ray diffraction measurement on the high-temperature crept samples, including the metallic glass, polymer glass, amorphous Se, and oxide glass, to detect the structural change for the plastic deformation. The structural anisotropy was measured by differentiating the diffraction patterns along two different orientations that are orthogonal to each other (Figure 1a). There are fingerprints left by the shear-induced structural transformation, and can be detected by this measurement. In the crept metallic glasses, the anisotropic term of the pair distribution functions does not vanish due to the creep. It, however, deviates from the one predicted from the affine transformation at short distance, revealing a localized transformation region with a radius around 11 Angstrom. In the crept polymer, amorphous Se, and oxide glasses, results of the anisotropic term show a quite different mechanism: there is no such localized transformation region by which the atomic motion could cooperate together. Instead, we found a preserved bond length after crept from the phase consistence of the anisotropic term with that of the isotropic term. The bonds reorientate during the nonaffine arrangement from the phase discrepancy of the anisotropic term with that of the affine prediction.

The correlation between the nonaffine displacement and structural anisotropy was verified on atomic level in classical molecular-dynamics (MD) simulations. The strength of the nonaffine arrangement increases with the structural anisotropy both in metallic glasses (Figure 1b) and polymer glasses (Figure 1c). Origin of the local nonaffine field, however, differs in these two kinds of glasses: it proceeds through the stretching or contraction of atomic bonds, accomplished by the breaking of some old bonds and forming of some new bonds in metallic glasses. In contrast, it operates through the reorientation of the covalent bonds dispersedly within the elastic matrix, while the length of the bonds are preserved.

This work provides the first experimental observation of atomic-scale nonaffine displacements responsible for plastic deformation. Atomic rearrangement modes that account for the nonaffine motion have been unveiled in atomic and molecular glasses. This is key to understand the elusive elastic and plastic response of disordered materials for a variety of kinds.

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