DOES STRUCTURE DETERMINE PROPERTY IN AMORPHOUS SOLIDS? 1)

doi:10.6052/0459-1879-19-368

Abstract

Abstract:

The mechanical properties and plastic deformation mechanisms of crystalline solids are mainly determined by their structural defects, e.g., the motion of the versatile dislocations. However, how structures determine properties in non-crystalline solids remains as a major unsolved issue in both solid mechanics, materials sciences, as well as condensed matter physics. Structure determines property is the traditional paradigm of materials science. Following this rule, there are vast experimental characterizations, theoretical studies, and computer simulations appeared in the literature, trying to establish a one-to-one correspondence between a specific structural feature with a unique dynamic property in the general amorphous solids. However, up to date, people gain very little understanding of the structure-property relationships in amorphous solids, not to mention whether there exists any hidden rule behind the structure-property relationships. For this purpose, we focus on the unique features of deformations mechanisms in amorphous solids as well as their microstructure characteristics. Thorough proper samplings of the activation energies of the excitation of these structural parameters by an advanced molecular dynamics technique, we are trying to quantitatively assess the validity of simple short-range structures and medium- to long-range structures in determination of their properties. This is done by examination of the possible correlation between parameters of structures with their activation energies, which implies the level of difficulty in activation of the events. By this we find that the hidden governing rule of structure-property relationship in amorphous solids involves a critical role of spatial autocorrelation length of the specific structural parameter. Constraint is more relevant than geometry itself. If only one structural descriptor presents spatial autocorrelation length up to sub nanometer level, it might effectively predict the mechanical property of amorphous solids; otherwise, the short-range local structures lacking such correlation length fails to predict property. Furthermore, we present a general metric to assess the utilities of structures in determining functions of the amorphous solids, which can be served as a screening rule to seeking for effective structures in amorphous solids.

Key words: amorphous solids, structure-property relationship, activation energy, glassy structure

CLC Number:

O344.4

Wang Yunjiang, Wei Dan, Han Dong, Yang Jie, Jiang Mingqiang, Dai Lanhong. DOES STRUCTURE DETERMINE PROPERTY IN AMORPHOUS SOLIDS? ¹⁾[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(2): 303-317.

Figures/Tables 8

Fig. 1 Contour plot of viscosity in a typical binary metalllic gass Cu$_{50}$Zr$_{50}$. There is remarkable spatial flucturation in dynamic property due to the structural heterogeneity. Both solid-like region and liquid-like region coexist in a glass sample

Table 1 Summary of the thermodynamic and dynamic features of deformation mechanisms in amorphous solids, in comparison with conventional coarse-grained polycrystals, and nanocrystals

Fig. 2 In constrast with crystal, there are abundant short-range structures in amorphous solid, as demonstrated by the plenty Voronoi polyhedra that is found in the glass model. The upper and bottom panel denote those clusters which are centered at a Cu, or Zr atom, respectively

Fig. 3 Schematic illustration of the ART technique, which is capable of sampling activation energies for local structural exitations from potential energy landscape

Fig. 4 A specfic short-range Voronoi structure corresponds to wide range of activation energies, i.e. there does not exist a straightforward, one-to-one structure-property correlation in amorphous solids. The upper and bottom panel denote those clusters which are centered at a Cu, or Zr atom,respectively. Only the spectra of activation energies for the most four frequent Voronoi polyhedra are shown

Fig. 5 Scattered plots of the activation energies as a function of short-range structural indexs. The structural indexs include ①Voronoi Volume, ②coordination number, ③bond-oreintational order $Q_6 $, ④local five-fold symmetery L5FS, and ⑤local six-fold symmetry L6FS,respectively. (a)$\sim$(e) and (f)$\sim$(j) are corresponding to the cases of Cu and Zr atoms, respectively

Fig. 6 Correlation between activation energy and vibrational MSD. Every data point stands for the average value of 100 neighbouring data. (a) and (b) are corresponding to the cases of Cu and Zr atoms, respectively

Fig.7 The spatial autocorrelation function of total vibrational MSD ($\Delta r^2)$ and directional resolved vibrational MSDs ($\Delta x^2,\Delta y^2,\Delta z^2)$ at different temperatures. The squares denote the correlation function $C_{\Delta r^2} \left( r \right)$ of total vibration MSD in any direction, i.e. $\Delta r^2=\Delta x^2+$\\ $\Delta y^2+\Delta z^2$. And circle stand for the correlation functions $C_{\Delta x^2,\Delta y^2,\Delta z^2} \left( r \right)$ for the directional MSDs $\Delta x^2$, $\Delta y^2$, and $\Delta z^2$, respectively

References 106

[1]	Wei D, Yang J, Jiang MQ , et al. Assessing the utility of structure in amorphous materials. J Chem Phys, 2019,150:114502
[2]	Cai W, Nix WD. Imperfections in Crystalline Solids. Cambridge University Press, 2016
[3]	Kocks UF, Argon AS, Ashby MF . Thermodynamics and kinetics of slip. Prog Mater Sci, 1975,19:1-278
[4]	Argon A. Strengthening Mechanisms in Crystal Plasticity. vol. 4. Oxford : Oxford University Press on Demand, 2008
[5]	Caillard D, Martin JL . Thermally Activated Mechanisms in Crystal Plasticity. vol. 8. New York: Elsevier Ltd, 2003
[6]	Frenkel J . Zur Theorie der Elastizitätsgrenze und der Festigkeit kristallinischer Körper. Zeitschrift Für Phys, 1926,37:572-609
[7]	Qiao JC, Wang Q, Pelletier JM , et al. Structural heterogeneities and mechanical behavior of amorphous alloys. Prog Mater Sci, 2019,104:250-329
[8]	Schuh CA, Hufnagel TC, Ramamurty U . Mechanical behavior of amorphous alloys. Acta Mater, 2007,55:4067-4109
[9]	Hufnagel TC, Schuh CA, Falk ML . Deformation of metallic glasses: Recent developments in theory, simulations, and experiments. Acta Mater, 2016,109:375-393
[10]	Nicolas A, Ferrero EE, Martens K , et al. Deformation and flow of amorphous solids: a review of mesoscale elastoplastic models. Rev Mod Phys, 2018,90:045006
[11]	Cheng YQ, Ma E . Atomic-level structure and structure-property relationship in metallic glasses. Prog Mater Sci, 2010,56:379-473
[12]	Cheng YQ, Ma E, Sheng HW . Atomic level structure in multicomponent bulk metallic glass. Phys Rev Lett, 2009,102:245501
[13]	Cheng YQ, Cao AJ, Sheng HW , et al. Local order influences initiation of plastic flow in metallic glass: Effects of alloy composition and sample cooling history. Acta Mater, 2008,56:5263-5275
[14]	Cheng YQ, Sheng HW, Ma E . Relationship between structure, dynamics, and mechanical properties in metallic glass-forming alloys. Phys Rev B, 2008,78:14207
[15]	Sheng HW, Luo WK, Alamgir FM , et al. Atomic packing and short-to-medium-range order in metallic glasses. Nature, 2006,439:419-425
[16]	Zhu F, Hirata A, Liu P , et al. Correlation between local structure order and spatial heterogeneity in a metallic glass. Phys Rev Lett, 2017,119:215501
[17]	Hirata A, Guan P, Fujita T , et al. Direct observation of local atomic order in a metallic glass. Nat Mater, 2011,10:28-33
[18]	Liu XJ, Xu Y, Hui X , et al. Metallic liquids and glasses: Atomic order and global packing. Phys Rev Lett, 2010,105:155501
[19]	Liu XJ, Wang SD, Wang H , et al. Local structural mechanism for frozen-in dynamics in metallic glasses. Phys Rev B, 2018,97:134107
[20]	Han D, Wei D, Yang J , et al. Atomistic structural mechanism for the glass transition: Entropic contribution. Phys Rev B, 2020,101:014113
[21]	Tanaka H, Tong H, Shi R , et al. Revealing key structural features hidden in liquids and glasses. Nat Rev Phys, 2019,1:333-348
[22]	Royall CP, Williams SR . The role of local structure in dynamical arrest. Phys Rep, 2015,560:1-75
[23]	Hu YC, Li YW, Yang Y , et al. Configuration correlation governs slow dynamics of supercooled metallic liquids. Proc Natl Acad Sci U S A, 2018,115:6375-6380
[24]	Tong H, Tanaka H . Revealing hidden structural order controlling both fast and slow glassy dynamics in supercooled liquids. Phys Rev X, 2018,8:011041
[25]	Sastry S, Debenedetti PG, Stillinger FH . Signatures of distinct dynamical regimes in the energy landscape of a glass-forming liquid. Nature, 1998,393:554-557
[26]	Debenedetti PG, Stillinger FH . Supercooled liquids and the glass transition. Nature, 2001,410:259-267
[27]	Stillinger FH . Energy Landscapes, Inherent Structures, and Condensed-Matter Phenomena. Princeton: Princeton University Press, 2016
[28]	Wales D. Energy Landscapes: Applications to Clusters, Biomolecules and Glasses. Cambridge: Cambridge University Press, 2004
[29]	Ashby MF . A first report on deformation-mechanism maps. Acta Metall, 1972,20:887-897
[30]	Zhu T, Li J . Ultra-strength materials. Prog Mater Sci, 2010,55:710-757
[31]	Yang XS, Wang YJ, Wang GY , et al. Time, stress, and temperature-dependent deformation in nanostructured copper: Stress relaxation tests and simulations. Acta Mater, 2016,108:252-263
[32]	Yang XS, Wang YJ, Zhai HR , et al. Time-, stress-, and temperature-dependent deformation in nanostructured copper: Creep tests and simulations. J Mech Phys Solids, 2016,94:191-206
[33]	Wang YJ, Gao GJ, Ogata S . Atomistic understanding of diffusion kinetics in nanocrystals from molecular dynamics simulations. Phys Rev B, 2013,88:115413
[34]	Wang YJ, Ishii A, Ogata S . Entropic effect on creep in nanocrystalline metals. Acta Mater, 2013,61:3866-3871
[35]	Wang YJ, Ishii A, Ogata S . Transition of creep mechanism in nanocrystalline metals. Phys Rev B, 2011,84:224102
[36]	Wang YJ, Ishii A, Ogata S . Grain size dependence of creep in nanocrystalline copper by molecular dynamics. Mater Trans, 2012,53:156-160
[37]	Hirata A, Kang LJ, Fujita T , et al. Geometric frustration of icosahedron in metallic glasses. Science, 2013,341:376-379
[38]	Ma J, Yang C, Liu X , et al. Fast surface dynamics enabled cold joining of metallic glasses. Sci Adv, 2019, 5: eaax7256
[39]	Spaepen F . A microscopic mechanism for steady state inhomogeneous flow in metallic glasses. Acta Metall, 1977,25:407-415
[40]	Argon AS . Plastic deformation in metallic glasses. Acta Metall, 1979,27:47-58
[41]	Johnson WL, Samwer K . A universal criterion for plastic yielding of metallic glasses with a ($T/T_{g})^{2/3}$ temperature dependence. Phys Rev Lett, 2005,95:195501
[42]	Falk ML, Langer JS . Dynamics of viscoplastic deformation in amorphous solids. Phys Rev E, 1998,57:7192
[43]	Wang Z, Wang WH . Flow units as dynamic defects in metallic glassy materials. Natl Sci Rev, 2018,6:304-323
[44]	Ding J, Patinet S, Falk ML , et al. Soft spots and their structural signature in a metallic glass. Proc Natl Acad Sci, 2014,111:14052-14056
[45]	Widmer-Cooper A, Perry H, Harrowell P, Reichman DR . Irreversible reorganization in a supercooled liquid originates from localized soft modes. Nat Phys, 2008,4:711-715
[46]	Shintani H, Tanaka H . Universal link between the boson peak and transverse phonons in glass. Nat Mater, 2008,7:870-877
[47]	Jiang MQ, Dai LH . The "ension transformation zone'' model of amorphous alloys. Chinese Sci Bull, 2017,62:2346-2357
[48]	Guan P, Chen MW, Egami T . Stress-temperature scaling for steady-State flow in metallic glasses. Phys Rev Lett, 2010,104:205701
[49]	Wang YJ, Zhang M, Liu L , et al. Universal enthalpy-entropy compensation rule for the deformation of metallic glasses. Phys Rev B, 2015,92:174118
[50]	Cui B, Yang J, Qiao J , et al. Atomic theory of viscoelastic response and memory effects in metallic glasses. Phys Rev B, 2017,96:094203
[51]	Qiao JC, Wang YJ, Zhao LZ , et al. Transition from stress-driven to thermally activated stress relaxation in metallic glasses. Phys Rev B, 2016,94:104203
[52]	Ju JD, Atzmon M . A comprehensive atomistic analysis of the experimental dynamic-mechanical response of a metallic glass. Acta Mater, 2014,74:183-188
[53]	Lei TJ, Dacosta LR, Liu M , et al. Microscopic characterization of structural relaxation and cryogenic rejuvenation in metallic glasses. Acta Mater, 2019,164:165-170
[54]	Lei TJ , Rangel DaCosta L, Liu M, et al. Shear transformation zone analysis of anelastic relaxation of a metallic glass reveals distinct properties of $\alpha $ and $\beta $ relaxations. Phys Rev E, 2019,100:033001
[55]	Miyazaki N, Wakeda M, Wang YJ , et al. Prediction of pressure-promoted thermal rejuvenation in metallic glasses. Npj Comput Mater, 2016,2:16013
[56]	Pan J, Wang YX, Guo Q , et al. Extreme rejuvenation and softening in a bulk metallic glass. Nat Commun, 2018,9:560
[57]	Ketov SV, Sun YH, Nachum S , et al. Rejuvenation of metallic glasses by non-affine thermal strain. Nature, 2015,524:200-203
[58]	Ding G, Li C, Zaccone A , et al. Ultrafast extreme rejuvenation of metallic glasses by shock compression. Sci Adv, 2019, 5: aaw6249
[59]	Wang YJ, Jiang MQ, Tian ZL , et al. Direct atomic-scale evidence for shear-dilatation correlation in metallic glasses. Scr Mater, 2016,112:37-41
[60]	Jiang MQ, Wilde G, Dai LH . Shear band dilatation in amorphous alloys. Scr Mater, 2017,127:54-57
[61]	Guan P, Lu S, Spector MJB , et al. Cavitation in amorphous solids. Phys Rev Lett, 2013,110:185502
[62]	Greer AL, Cheng YQ, Ma E . Shear bands in metallic glasses. Mater Sci Eng R Reports, 2013,74:71-132
[63]	Wu ZW, Li MZ, Wang WH , et al. Hidden topological order and its correlation with glass-forming ability in metallic glasses. Nat Commun, 2015,6:6035
[64]	Wu ZW, Kob W, Wang WH , et al. Stretched and compressed exponentials in the relaxation dynamics of a metallic glass-forming melt. Nat Commun, 2018,9:5334
[65]	Yang J, Wang YJ, Ma E , et al. Structural parameter of orientational order to predict the boson vibrational anomaly in glasses. Phys Rev Lett, 2019,122:015501
[66]	Han D, Wei D, Yang J , et al. Structural atomistic mechanism for the glass transition entropic scenario. ArXiv: 190703695 2019
[67]	Zhang Y, Zhang F, Wang CZ , et al. Cooling rates dependence of medium-range order development in Cu$_{64.5}$Zr$_{35.5}$ metallic glass. Phys Rev B, 2015,91:064105
[68]	Yang X, Liu R, Yang M , et al. Structures of local rearrangements in soft colloidal glasses. Phys Rev Lett, 2016,116:238003
[69]	Wei D, Yang J, Jiang MQ , et al. Revisiting the structure-property relationship of metallic glasses: Common spatial correlation revealed as a hidden rule. Phys Rev B, 2019,99:014115
[70]	Dyre JC . Colloquium: The glass transition and elastic models of glass-forming liquids. Rev Mod Phys, 2006,78:953
[71]	Pazmiño Betancourt BA, Hanakata PZ, Starr FW , et al. Quantitative relations between cooperative motion, emergent elasticity, and free volume in model glass-forming polymer materials. Proc Natl Acad Sci, 2015,112:2966-2971
[72]	Widmer-Cooper A, Harrowell P . Predicting the long-time dynamic heterogeneity in a supercooled liquid on the basis of short-time heterogeneities. Phys Rev Lett, 2006,96:185701
[73]	Ding J, Cheng YQ, Sheng H , et al. Universal structural parameter to quantitatively predict metallic glass properties. Nat Commun, 2016,7:13733
[74]	Fan Y, Iwashita T, Egami T . Evolution of elastic heterogeneity during aging in metallic glasses. Phys Rev E, 2014,89:062313
[75]	Dyre JC, Olsen NB, Christensen T . Local elastic expansion model for viscous-flow activation energies of glass-forming molecular liquids. Phys Rev B, 1996,53:2171
[76]	Sun BA, Hu YC, Wang DP , et al. Correlation between local elastic heterogeneities and overall elastic properties in metallic glasses. Acta Mater, 2016,121:266-276
[77]	Zylberg J, Lerner E , Bar-sinai Y, et al. Local thermal energy as a structural indicator in glasses. Proc Natl Acad Sci U S A, 2017,114:7289-7294
[78]	Fan Z, Ding J, Li QJ , et al. Correlating the properties of amorphous silicon with its flexibility volume. Phys Rev B, 2017,95:144211
[79]	Fan Y, Iwashita T, Egami T . Energy landscape-driven non-equilibrium evolution of inherent structure in disordered material. Nat Commun, 2017,8:15417
[80]	Fan Y, Iwashita T, Egami T . How thermally activated deformation starts in metallic glass. Nat Commun, 2014,5:5083
[81]	Fan Y, Iwashita T, Egami T . Crossover from localized to cascade relaxations in metallic glasses. Phys Rev Lett, 2015,115:045501
[82]	Rodney D, Schuh C . Distribution of thermally activated plastic events in a flowing glass. Phys Rev Lett, 2009,102:235503
[83]	Rodney D, Schuh CA . Yield stress in metallic glasses: The jamming-unjamming transition studied through Monte Carlo simulations based on the activation-relaxation technique. Phys Rev B, 2009,80:184203
[84]	Wang YJ, Du JP, Shinzato S , et al. A free energy landscape perspective on the nature of collective diffusion in amorphous solids. Acta Mater, 2018,157:165-173
[85]	Patinet S, Vandembroucq D, Falk ML . Connecting local yield stresses with plastic activity in amorphous solids. Phys Rev Lett, 2016,117:045501
[86]	Xu B, Falk ML, Li JF , et al. Predicting Shear Transformation Events in Metallic Glasses. Phys Rev Lett, 2018,120:125503
[87]	Plimpton S . Fast parallel algorithms for short-range molecular dynamics. J Comput Phys, 1995,117:1-19
[88]	Mendelev MI, Kramer MJ, Ott RT , et al. Development of suitable interatomic potentials for simulation of liquid and amorphous Cu-Zr alloys. Philos Mag, 2009,89:967-987
[89]	Nosé Shūichi . A molecular dynamics method for simulations in the canonical ensemble. Mol Phys, 1984,52:255-268
[90]	Hoover WG . Canonical dynamics: Equilibrium phase-space distributions. Phys Rev A, 1985,31:1695-1697
[91]	Parrinello M, Rahman A . Polymorphic transitions in single crystals: A new molecular dynamics method. J Appl Phys, 1981,52:7182
[92]	Stukowski A . Visualization and analysis of atomistic simulation data with OVITO-the Open Visualization Tool. Model Simul Mater Sci Eng, 2010,18:015012
[93]	Wales DJ . Exploring Energy Landscapes. Annu Rev Phys Chem, 2018,69:401-425
[94]	Barkema GT, Mousseau N . Event-based relaxation of continuous disordered systems. Phys Rev Lett, 1996,77:4358
[95]	El-Mellouhi F, Mousseau N, Lewis LJ . Kinetic activation-relaxation technique: An off-lattice self-learning kinetic Monte Carlo algorithm. Phys Rev B, 2008,78:153202
[96]	Béland LK, Brommer P, El-Mellouhi F , et al. Kinetic activation-relaxation technique. Phys Rev E, 2011,84:46704
[97]	Mousseau N, Béland LK, Brommer P , et al. Following atomistic kinetics on experimental timescales with the kinetic Activation-Relaxation Technique. Comput Mater Sci, 2015,100:111-123
[98]	Wang N, Ding J, Yan F , et al. Spatial correlation of elastic heterogeneity tunes the deformation behavior of metallic glasses. Npj Comput Mater, 2018,4:19
[99]	Cubuk ED, Ivancic RJS, Schoenholz SS , et al. Structure-property relationships from universal signatures of plasticity in disordered solids. Science, 2017,358:1033-1037
[100]	Yu HB, Richert R, Samwer K . Structural Rearrangements Governing Johari-Goldstein Relaxations in Metallic Glass. Sci Adv, 2017,3:e1701577
[101]	Frank FC, Mott NF . Supercooling of liquids. Proc R Soc London Ser A Math Phys Sci, 1952,215:43-46
[102]	Cubuk ED, Schoenholz SS, Rieser JM , et al. Identifying structural flow defects in disordered solids using machine-learning methods. Phys Rev Lett, 2015,114:108001
[103]	Schoenholz SS, Cubuk ED, Sussman DM , et al. A structural approach to relaxation in glassy liquids. Nat Phys, 2016,12:469-471
[104]	Schoenholz SS, Cubuk ED, Kaxiras E , et al. The relationship between local structure and relaxation in out-of-equilibrium glassy systems. Proc Natl Acad Sci U S A, 2016,114:263-268
[105]	Ma X, Davidson ZS, Still T , et al. Heterogeneous Activation, Local Structure, and Softness in Supercooled Colloidal Liquids. Phys Rev Lett, 2019,122:028001
[106]	Wang Q, Jain A . A transferable machine-learning framework linking interstice distribution and plastic heterogeneity in metallic glasses. Nat Commun, 2019,10:5537

DOES STRUCTURE DETERMINE PROPERTY IN AMORPHOUS SOLIDS? ¹⁾

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