Abstract
When a spatially uniform temperature change is imposed on a solid with more than one phase, or on a polycrystal of a single, non-cubic phase (showing anisotropic expansion–contraction), the resulting thermal strain is inhomogeneous (non-affine). Thermal cycling induces internal stresses, leading to structural and property changes that are usually deleterious. Glasses are the solids that form on cooling a liquid if crystallization is avoided—they might be considered the ultimate, uniform solids, without the microstructural features and defects associated with polycrystals. Here we explore the effects of cryogenic thermal cycling on glasses, specifically metallic glasses. We show that, contrary to the null effect expected from uniformity, thermal cycling induces rejuvenation, reaching less relaxed states of higher energy. We interpret these findings in the context that the dynamics in liquids become heterogeneous on cooling towards the glass transition1, and that there may be consequent heterogeneities in the resulting glasses. For example, the vibrational dynamics of glassy silica at long wavelengths are those of an elastic continuum, but at wavelengths less than approximately three nanometres the vibrational dynamics are similar to those of a polycrystal with anisotropic grains2. Thermal cycling of metallic glasses is easily applied, and gives improvements in compressive plasticity. The fact that such effects can be achieved is attributed to intrinsic non-uniformity of the glass structure, giving a non-uniform coefficient of thermal expansion. While metallic glasses may be particularly suitable for thermal cycling, the non-affine nature of strains in glasses in general deserves further study, whether they are induced by applied stresses or by temperature change.
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Acknowledgements
This research was supported by the World Premier International Research Center Initiative (WPI), MEXT, Japan, by NSF China and MOST 973 China, and by the Engineering and the Engineering and Physical Sciences Research Council, UK (Materials World Network project). Y.H.S. acknowledges support from a China Scholarship Council (CSC) scholarship. M. L. Falk, T. C. Hufnagel, E. Ma, D. B. Miracle and J. Orava are thanked for discussions. All data accompanying this publication are directly available within the publication and the accompanying Extended Data figures and tables.
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Preparation of metallic glasses was by S.V.K. and Z.L. The thermal-cycling treatments were performed by Y.H.S., S.V.K., A.R.B. and A.C.; calorimetry by Y.H.S., S.V.K., Z.L., A.C. and A.R.B.; nano-indentation by S.N. and A.R.B.; compression and microhardness tests by S.V.K., Y.H.S., A.R.B. and A.C.; X-ray diffraction by S.V.K. and Y.H.S.; and resonant ultrasound spectroscopy by Y.H.S., M.A.C., A.R.B. and A.C. Direction of the work was by D.V.L.-L. (Sendai), H.Y.B. and W.H.W. (Beijing), and A.L.G (Cambridge). A.L.G. led the project and the writing of the paper. All authors contributed to interpretation and presentation of the results.
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Extended data figures and tables
Extended Data Figure 1 DSC traces for ribbons of La55Ni20Al25 glass (heated at 20 K min−1).
a, These example traces for as-cast samples show the exotherm, just below the glass-transition temperature, from which the heat of relaxation ΔHrel is determined. b, The effect of holding at 77 K: the traces show that the heat of relaxation ΔHrel, given by the exotherm just below the glass-transition temperature, is, within the experimental error of 4%, the same for an as-cast ribbon, and for a sample held for 4 h at 77 K.
Extended Data Figure 2 Differential scanning calorimetry (DSC) of La55Ni10Al35 bulk metallic glass.
The heat of relaxation ΔHrel is compared for discs (250–500 μm thick) pre-cut from the bulk rod and then treated with room temperature−77 K cycles, and for discs post-cut from treated rod samples. There is no difference between these cases within the error of ±30 J mol−1.
Extended Data Figure 3 Load-displacement curves for ribbons of La55Ni20Al25 metallic glass tested up to a maximum load Fmax of 40 mN.
The initial yield load Fy is indicated on the curves for the glass in three states: as-cast, after a 10-min hold at 77 K, and after a further ten room temperature−77 K cycles each with 1 min hold.
Extended Data Figure 4 Instrumented indentation of La55Ni20Al25 metallic glass ribbon.
a, Initial yielding, characterized by initial yield pressure Py and initial yield displacement Δh. Indentations are made for three states of the sample: as-cast, after a 10-min hold at 77 K, and after a further ten room temperature−77 K cycles each with 1-min hold. b, c, Distributions of the Young’s modulus, using data from the same indentations of the sample in three states as in Fig. 3 and in a. Values of the Young’s modulus in the glass E are determined (b) by the standard Oliver and Pharr36 method on unloading from Fmax and (c) from Hertzian fitting to the F–h curve up to the first pop-in.
Extended Data Figure 5 Elastic moduli derived from resonant ultrasound spectroscopy for Cu46Zr46Al7Gd1 BMG treated with room temperature−77 K thermal cycles.
Shear modulus (left axis); bulk modulus (right axis). Error bars, root mean square errors in the fitted frequencies.
Extended Data Figure 6 X-ray diffraction traces for Zr-based metallic glasses subjected to 338–77 K thermal cycles.
a, For melt-spun ribbons of Zr61.1Cu26.3Fe2.1Al10.5; b, for rods of Zr62.2Cu23.9Fe4.8Al9.1. No clear changes are induced by the cycling treatments.
Extended Data Figure 7 Compressive stress–strain curves for rod samples of Zr62Cu24Fe5Al9 BMG.
a, For rods of 2 mm diameter; b, for rods of 2.5 mm diameter. In each case, increasing numbers of 338 K to 77 K thermal cycles cause the plastic strain to increase.
Extended Data Figure 8 Dynamic mechanical analysis of ribbons of La55Ni20Al25 metallic glass.
The heating rate is 3 K min−1. The general form of the curve matches that shown in Fig. 1a, where an example was chosen of a metallic glass showing β relaxation at a particularly low value of T/Tg. For La55Ni20Al25 the β relaxation is centred at T/Tg ≈ 0.8.
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Ketov, S., Sun, Y., Nachum, S. et al. Rejuvenation of metallic glasses by non-affine thermal strain. Nature 524, 200–203 (2015). https://doi.org/10.1038/nature14674
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DOI: https://doi.org/10.1038/nature14674
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