Percolated Strain Networks and Universal Scaling Properties of Strain Glasses

Hongxiang Zong, Haijun Wu, Xuefei Tao, Deqing Xue, Jun Sun, Stephen J. Pennycook, Tai Min, Zhenyu Zhang, and Xiangdong Ding

Phys. Rev. Lett. 123, 015701 – Published 3 July 2019

Abstract

Strain glass is being established as a conceptually new state of matter in highly doped alloys, yet the understanding of its microscopic formation mechanism remains elusive. Here, we use a combined numerical and experimental approach to establish, for the first time, that the formation of strain glasses actually proceeds via the gradual percolation of strain clusters, namely, localized strain clusters that expand to reach the percolating state. Furthermore, our simulation studies of a wide variety of specific materials systems unambiguously reveal the existence of distinct scaling properties and universal behavior in the physical observables characterizing the glass transition, as obeyed by many existing experimental findings. The present work effectively enriches our understanding of the underlying physical principles governing glassy disordered materials.

Received 11 October 2018

DOI:https://doi.org/10.1103/PhysRevLett.123.015701

Physics Subject Headings (PhySH)

Ferroelasticity Glass transition Martensitic phase transition

Alloys Shape-memory materials

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Hongxiang Zong¹, Haijun Wu³, Xuefei Tao¹, Deqing Xue¹, Jun Sun¹, Stephen J. Pennycook³, Tai Min¹, Zhenyu Zhang^2,*, and Xiangdong Ding ^1,†

¹State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, China
²International Center for Quantum Design of Functional Materials (ICQD), Hefei National Laboratory for Physical Sciences at Microscale, and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
³Department of Materials Science and Engineering, National University of Singapore, 117574 Singapore

^*To whom all correspondence should be addressed. zhangzy@ustc.edu.cn
^†To whom all correspondence should be addressed. dingxd@mail.xjtu.edu.cn

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Vol. 123, Iss. 1 — 3 July 2019

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Images

Figure 1
Strain percolation and strain glass transition. (a)–(d) Schematic of the formation of strain network: randomly distributed point defect(s) induce strain cluster(s) (a),(c). The growth and connecitvity of strain clusters upon cooling [(a) to (b); (c) to (d)] gives rise to the formation of a percolated strain network. The central effective dopant and other cluster atoms inside the dashed circles of 1(c) and 1(d) are colored by red and blue, respectively. (e)–(h) Results of molecular dynamics simulations, displaying typical atomic structures of strain glass with the martensitic regions colored yellow, parent phase regions colored blue and dopant atoms colored red (e),(f), and related strain clusters above and below the glass transition temperature (g),(h).
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Figure 2
Temperature dependence of the dynamic pair distribution function (DPDF). (a) The DPDF of Ni-Zr pairs showing peak splitting for the fourth neighbor in the course of the transition, indicating a local symmetry broken within the strain clusters. The inset show radial distribution function $g (r)$ for the prototypical, martensitic, and strain cluster structures. (b) Instantaneous $G (r, t = 0)$ and time-averaged $G (r, ω = 0)$ Ni-Zr DPDFs for the fourth peak, showing changes of lattice distortion with temperature. (c) The magnitude of the instantaneous peak shift $D_{inst}$ and its static $D_{static}$ and dynamic $D_{dyn}$ components vs temperature.
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Figure 3
Simulated properties during the glass transition of ${Zr}_{96} {Ni}_{4}$ . (a) Spanning length $L_{S N}$ of the largest network divided by the edge length $L_{0}$ of the simulation supercell, and temperature dependence of the mole fraction of atoms $f$ belonging to the strain networks. (b) Kinetic slowing down measured by the average relaxation time as a function of temperature, obtained by fitting the curves in the self-intermediate scattering function [19]. The inset shows the temperature dependence of the viscosity. The line above the glass transition temperature is fitted by the Vogel-Fulcher law $η = η_{0} e^{E / k_{B} (T - T_{V F})}$ with the reference viscosity $η_{0} = 1.72 \times 10^{6}$ , Boltzmann constant $k_{B}$ , Vogel-Fulcher temperature $T_{V F} = 108 K$ and activation energy $E / k_{B} = 102 K$ .
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Figure 4
Experimentally observed structural and strain networks. (a)–(d) Structural identification: (a) Low-magnification STEM ABF image of ${Ti}_{50} ({Pd}_{42} {Cr}_{8})$ at the martensite phase showing large-scale domains, with a high-magnification STEM HAADF image showing a twin boundary (inset). (b) TEM image of ${Ti}_{50} ({Pd}_{41} {Cr}_{9})$ at the crossover transition showing hierarchical nanodomain architecture, with an electron diffraction pattern showing sharp superlattices of the martensite phase (inset). (c) TEM image of ${Ti}_{50} ({Pd}_{40} {Cr}_{10})$ at the strain glass transition, with an electron diffraction pattern showing diffusive superlattices of the martensite phase (inset). (d) Atomically resolved HRTEM image of ${Ti}_{50} ({Pd}_{40} {Cr}_{10})$ , with FFT image inset. (e) GPA results of (d), namely the component $ϵ_{y y}$ of the strain, displaying the onset of percolated strain clusters in the strain glass state.
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Figure 5
Universal scaling behavior and generic phase diagram. (a) Power-law scaling of $N_{r} / n_{r}$ vs the doping level $x$ for a wide variety of doped ferroelastic alloys from both MD simulations and experimental measurements. The exponents are fitted via the maximum likelihood method. (b) Phase diagram spanned by $Δ H_{doping}^{mix}$ and $x_{e}$ for doped ferroelastic alloys. In (b), the solid line is the result of a classification fit of the atomistic simulation data. The fitted line effectively separates the ferroelastic transition (FT) and strain glass transition (SGT) of the experimental data.
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