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Comptes Rendus. Physique
Modeling the mechanical properties of nanoparticles: a review
Comptes Rendus. Physique, Volume 22 (2021) no. S3, pp. 35-66.

Part of the special issue: Plasticity and Solid State Physics

Nanoparticles are commonly used in various fields of applications such as electronics, catalysis or engineering where they can be subjected to a certain amount of stress leading to structural instabilities or irreversible damages. In contrast with bulk materials, nanoparticles can sustain extremely high stresses (in the GPa range) and ductility, even in the case of originally brittle materials. This review article focuses on the modeling of the mechanical properties of nanoparticles, with an emphasis on elementary deformation processes. Various simulation methods are described, from classical molecular dynamics calculations, the best suited method when applied to the modeling the mechanics of nanoparticles, to dislocation dynamics based hybrid methodologies. We detail the mechanical behaviour of nanoparticles for a large array of material classes (metals, semi-conductors, ceramics, etc.), as well as their deformation processes. Regular crystalline nanoparticles are addressed, as well as more complex systems such as nanoporous or core-shell particles. In addition to the exhaustive review on the recent works published on the topic, challenges and future trends are proposed, providing solid foundations for forthcoming investigations.

Online First:
Published online:
DOI: 10.5802/crphys.70
Keywords: Nanoparticles, Mechanical properties, Plastic deformation, Dislocations, Numerical simulations
Jonathan Amodeo 1, 2; Laurent Pizzagalli 3

1 Aix Marseille Univ., Université de Toulon, CNRS, IM2NP, Marseille, France
2 Université de Lyon, INSA-Lyon, MATEIS, UMR 5510 CNRS, 69621 Villeurbanne, France
3 Departement of Physics and Mechanics of Materials, Institut P ′ , CNRS UPR 3346, Université de Poitiers, SP2MI, Boulevard Marie et Pierre Curie, TSA 41123, 86073 Poitiers Cedex 9, France
     author = {Jonathan Amodeo and Laurent Pizzagalli},
     title = {Modeling the mechanical properties of nanoparticles: a review},
     journal = {Comptes Rendus. Physique},
     pages = {35--66},
     publisher = {Acad\'emie des sciences, Paris},
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     year = {2021},
     doi = {10.5802/crphys.70},
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Jonathan Amodeo; Laurent Pizzagalli. Modeling the mechanical properties of nanoparticles: a review. Comptes Rendus. Physique, Volume 22 (2021) no. S3, pp. 35-66. doi : 10.5802/crphys.70. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.70/

[1] G. Schmidt Nanoparticles: From Theory to Application, Wiley, Weinheim, 2010 | Article

[2] J. C. Nièpce; L. Pizzagalli Structure and phase transitions in nanocrystals, Nanomaterials and Nanochemistry, Springer, Berlin, Heidelberg, 2007, pp. 35-54 | Article

[3] Z. Kang; Y. Liu; S.-T. Lee Small-sized silicon nanoparticles: new nanolights and nanocatalysts, Nanoscale, Volume 3 (2011) no. 3, pp. 777-791 | Article

[4] R. G. Chaudhuri; S. Paria Core/shell nanoparticles: classes, properties, synthesis mechanisms, characterization, and applications, Chem. Rev., Volume 112 (2011) no. 4, pp. 2373-2433 | Article

[5] S. Fernández; L. Gao; J. P. Hofmann; J. Carnis; S. Labat; G. A. Chahine; A. J. F. van Hoof; M. W. G. M. T. Verhoeven; T. U. Schülli; E. J. M. Hensen; O. Thomas; M.-I. Richard In situ structural evolution of single particle model catalysts under ambient pressure reaction conditions, Nanoscale, Volume 43 (2019) no. 1, pp. 331-338 | Article

[6] D. Guo; G. Xie; J. Luo Mechanical properties of nanoparticles: basics and applications, J. Phys. D: Appl. Phys., Volume 47 (2014) no. 11, 013001

[7] C. E. Carlton; P. J. Ferreira In situ TEM nanoindentation of nanoparticles, Micron, Volume 43 (2012) no. 11, pp. 1134-1139 | Article

[8] J. Deneen; W. M. Mook; A. Minor; W. W. Gerberich; C. B. Carter In situ deformation of silicon nanospheres, J. Mater. Sci., Volume 41 (2006) no. 14, pp. 4477-4483 | Article

[9] W. W. Gerberich; W. M. Mook; C. R. Perrey; C. B. Carter; M. I. Baskes; R. Mukherjee; A. Gidwani; J. Heberlein; P. H. McMurry; S. L. Girshick Superhard silicon nanospheres, J. Mech. Phys. Solids, Volume 51 (2003) no. 6, pp. 979-992 | Article

[10] D. Mordehai; S.-W. Lee; B. Backes; D. J. Srolovitz; W. D. Nix; E. Rabkin Size effect in compression of single-crystal gold microparticles, Acta Mater., Volume 59 (2011) no. 13, pp. 5202-5215 | Article

[11] D. D. Stauffer; A. Beaber; A. Wagner; O. Ugurlu; J. Nowak; K. A. Mkhoyan; S. Girshick; W. Gerberich Strain-hardening in submicron silicon pillars and spheres, Acta Mater., Volume 60 (2012) no. 6-7, pp. 2471-2478 | Article

[12] R. Maaß; L. Meza; B. Gan; S. Tin; J. R. Greer Ultrahigh strength of dislocation-free Ni 3 Al nanocubes, Small, Volume 8 (2012) no. 12, pp. 1869-1875 | Article

[13] M. Ramos; L. Ortiz-Jordan; A. Hurtado-Macias; S. Flores; J. Elizalde-Galindo; C. Rocha; B. Torres; M. Zarei-Chaleshtori; R. Chianelli Hardness and elastic modulus on six-fold symmetry gold nanoparticles, Materials, Volume 6 (2013) no. 1, pp. 198-205 | Article

[14] D. R. Saha; A. Mandal; S. Mitra; M. R. Mada; P. Boughton; S. Bandyopadhyay; D. Chakravorty Nanoindentation studies on silver nanoparticles, AIP Conf. Proc., Volume 1536 (2013) no. 1, pp. 257-258 | Article

[15] I. Issa; J. Amodeo; J. Réthoré; L. Joly-Pottuz; C. Esnouf; J. Morthomas; M. Perez; J. Chevalier; K. Masenelli-Varlot In situ investigation of MgO nanocube deformation at room temperature, Acta Mater., Volume 86 (2015) no. C, pp. 295-304 | Article

[16] W.-Z. Han; L. Huang; S. Ogata; H. Kimizuka; Z.-C. Yang; C. Weinberger; Q.-J. Li; B.-Y. Liu; X.-X. Zhang; J. Li; E. Ma; Z.-W. Shan From “smaller is stronger” to “size-independent strength plateau”: towards measuring the ideal strength of iron, Adv. Mater., Volume 27 (2015) no. 22, pp. 3385-3390 | Article

[17] E. Hintsala; A. Wagner; W. Gerberich; K. Mkhoyan The role of back stress in sub-50 nm Si nanocubes, Scr. Mater., Volume 114 (2016), pp. 51-55 | Article

[18] A. Sharma; J. Hickman; N. Gazit; E. Rabkin; Y. Mishin Nickel nanoparticles set a new record of strength, Nat. Commun., Volume 9 (2018) no. 1, pp. 1-9 | Article

[19] I. Z. Jenei; F. Dassenoy; T. Epicier; A. Khajeh; A. Martini; D. Uy; H. Ghaednia; A. Gangopadhyay Mechanical response of gasoline soot nanoparticles under compression: an in situ TEM study, Tribol. Int., Volume 131 (2019), pp. 446-453 | Article

[20] M. D. Uchic; D. M. Dimiduk; J. N. Florando; W. D. Nix Sample dimensions influence strength and crystal plasticity, Science, Volume 305 (2004) no. 5686, pp. 986-989 | Article

[21] J. Greer; J. De Hosson Plasticity in small-sized metallic systems: intrinsic versus extrinsic size effect, Prog. Mater. Sci., Volume 56 (2011) no. 6, pp. 654-724 | Article

[22] D. Kiener; A. M. Minor Source truncation and exhaustion: insights from quantitative in situ TEM tensile testing, Nano Lett., Volume 11 (2011) no. 9, pp. 3816-3820 | Article

[23] F. Mompiou; M. Legros; A. Sedlmayr; D. S. Gianola; D. Caillard; O. Kraft Source-based strengthening of sub-micrometer Al fibers, Acta Mater., Volume 60 (2012) no. 3, pp. 977-983 | Article

[24] D. J. Dunstan; A. J. Bushby The scaling exponent in the size effect of small scale plastic deformation, Int. J. Plast., Volume 40 (2013) no. C, pp. 152-162 | Article

[25] P. S. Phani; K. E. Johanns; E. P. George; G. M. Pharr A simple stochastic model for yielding in specimens with limited number of dislocations, Acta Mater., Volume 61 (2013) no. 7, pp. 2489-2499 | Article

[26] A. Beaber; J. Nowak; O. Ugurlu; W. Mook; S. Girshick; R. Ballarini; W. Gerberich Smaller is tougher, Phil. Mag., Volume 91 (2011) no. 7-9, pp. 1179-1189 | Article

[27] W. Mook; J. Nowak; C. Perrey; C. Carter; R. Mukherjee; S. Girshick; P. McMurry; W. Gerberich Compressive stress effects on nanoparticle modulus and fracture, Phys. Rev. B, Volume 75 (2007) no. 21, 214112 | Article

[28] W. W. Gerberich; D. D. Stauffer; A. R. Beaber; N. I. Tymiak A brittleness transition in silicon due to scale, J. Mater. Res., Volume 27 (2012), pp. 552-561 | Article

[29] M. T. McDowell; S. W. Lee; J. T. Harris; B. A. Korgel; C. Wang; W. D. Nix; Y. Cui In situ TEM of two-phase lithiation of amorphous silicon nanospheres, Nano Lett., Volume 13 (2013) no. 2, pp. 758-764 | Article

[30] K. Kendall The impossibility of comminuting small particles by compression, Nature, Volume 272 (1978) no. 5655, pp. 710-711 | Article

[31] M. Chen; E. Ma; K. J. Hemker; H. Sheng; Y. Wang; X. Cheng Deformation twinning in nanocrystalline aluminum, Science, Volume 300 (2003) no. 5623, pp. 1275-1277 | Article

[32] A. J. Wagner; E. D. Hintsala; P. Kumar; W. W. Gerberich; K. A. Mkhoyan Mechanisms of plasticity in near-theoretical strength sub-100nm Si nanocubes, Acta Mater., Volume 100 (2015) no. C, pp. 256-265 | Article

[33] J. Rabier; L. Pizzagalli; J.-L. Demenet Dislocations in silicon at high stress, Dislocation in Solids (L. Kubin; J. P. Hirth, eds.), Volume 16, Elsevier, 2010, pp. 47-108 | Article

[34] A. Merabet; M. Texier; C. Tromas; S. Brochard; L. Pizzagalli; L. Thilly; J. Rabier; A. Talneau; Y. M. Le Vaillant; O. Thomas; J. Godet Low-temperature intrinsic plasticity in silicon at small scales, Acta Mater., Volume 161 (2018), pp. 54-60 | Article

[35] L. Pizzagalli; J. Godet; S. Brochard; H. J. Gotsis; T. Albaret Stacking fault formation created by plastic deformation at low temperature and small scales in silicon, Phys. Rev. Mater., Volume 4 (2020) no. 9, 093603

[36] R. Cherian; C. Gerard; P. Mahadevan; N. T. Cuong; R. Maezono Size dependence of the bulk modulus of semiconductor nanocrystals from first-principles calculations, Phys. Rev. B, Volume 82 (2010), 235321 | Article

[37] M. Cococcioni; F. Mauri; G. Ceder; N. Marzari Electronic-enthalpy functional for finite systems under pressure, Phys. Rev. Lett., Volume 94 (2005) no. 14, 093603 | Article

[38] P. Maioli; T. Stoll; H. E. Sauceda; I. Valencia; A. Demessence; F. Bertorelle; A. Crut; F. Vallée; I. L. Garzón; G. Cerullo; N. D. Fatti Mechanical vibrations of atomically defined metal clusters: from nano- to molecular-size oscillators, Nano Lett., Volume 18 (2018) no. 11, pp. 6842-6849 | Article

[39] L. Pizzagalli Finite-temperature mechanical properties of nanostructures with first-principles accuracy, Phys. Rev. B, Volume 102 (2020) no. 9, 094102 | Article

[40] H. Jonsson; G. Mills; K. W. Jacobsen Nudged elastic band method for finding minimum energy paths of transitions, Classical and Quantum Dynamics in Condensed Phase Simulations, World Scientific, Singapore, 1998, pp. 385-404 | Article

[41] E. Bitzek; P. Koskinen; F. Gähler; M. Moseler Structural relaxation made simple, Phys. Rev. Lett., Volume 97 (2006), 170201 | Article

[42] J. Guénolé; W. G. Nöhring; A. Vaid; F. Houllé; Z. Xie; A. Prakash; E. Bitzek Assessment and optimization of the fast inertial relaxation engine (FIRE) for energy minimization in atomistic simulations and its implementation in lammps, Comput. Mater. Sci., Volume 175 (2020), 109584 | Article

[43] N. Mousseau; G. T. Barkema Traveling through potential energy landscapes of disordered materials: the activation-relaxation technique, Phys. Rev. E, Volume 57 (1998) no. 2, pp. 2419-2424 | Article

[44] T. Zhu; J. Li; A. Samanta; A. Leach; K. Gall Temperature and strain-rate dependence of surface dislocation nucleation, Phys. Rev. Lett., Volume 100 (2008) no. 2, 025502

[45] C. R. Weinberger; A. T. Jennings; K. Kang; J. R. Greer Atomistic simulations and continuum modeling of dislocation nucleation and strength in gold nanowires, J. Mech. Phys. Solids, Volume 60 (2012) no. 1, pp. 84-103 | Article

[46] Q.-J. Li; B. Xu; S. Hara; J. Li; E. Ma Sample-size-dependent surface dislocation nucleation in nanoscale crystals, Acta Mater., Volume 145 (2018), pp. 19-29

[47] J. Amodeo; E. Maras; D. Rodney Site dependence of surface dislocation nucleation in ceramic nanoparticles (2021) (in press), to be published in npj Computational Materials

[48] O. Kovalenko; C. Brandl; L. Klinger; E. Rabkin Self-healing and shape memory effects in gold microparticles through the defects-mediated diffusion, Adv. Sci., Volume 4 (2017) no. 8, 1700159

[49] S. Plimpton Fast parallel algorithms for short-range molecular-dynamics, J. Comput. Phys., Volume 117 (1995) no. 1, pp. 1-19 | Article | Zbl: 0830.65120

[50] S. A. S. Asif; K. J. Wahl; R. J. Colton Nanoindentation and contact stiffness measurement using force modulation with a capacitive load-displacement transducer, Rev. Sci. Instrum., Volume 70 (1999) no. 5, pp. 2408-2413 | Article

[51] O. L. Warren; S. A. Downs; T. J. Wyrobek Challenges and interesting observations associated with feedback-controlled nanoindentation, Zeitschrift für Metallkunde, Volume 95 (2004) no. 5, pp. 287-296 | Article

[52] J.-J. Bian; G.-F. Wang Atomistic deformation mechanisms in copper nanoparticles, J. Comput. Theor. Nanosci., Volume 10 (2013) no. 9, pp. 2299-2303 | Article

[53] J. Bian; X. Niu; H. Zhang; G. Wang Atomistic deformation mechanisms in twinned copper nanospheres, Nanoscale Res. Lett., Volume 9 (2014) no. 1, pp. 335-337 | Article

[54] J. Amodeo; K. Lizoul Mechanical properties and dislocation nucleation in nanocrystals with blunt edges, Mater. Des., Volume 135 (2017), pp. 223-231 | Article

[55] A. M. Goryaeva; C. Fusco; M. Bugnet; J. Amodeo Influence of an amorphous surface layer on the mechanical properties of metallic nanoparticles under compression, Phys. Rev. Mater., Volume 3 (2019) no. 3, 033606

[56] D. Kilymis; C. Gerard; J. Amodeo; U. V. Waghmare; L. Pizzagalli Uniaxial compression of silicon nanoparticles: an atomistic study on the shape and size effects, Acta Mater., Volume 158 (2018), pp. 155-166 | Article

[57] T. X. T. Sayle; B. J. Inkson; A. Karakoti; A. Kumar; M. Molinari; G. Möbus; S. C. Parker; S. Seal; D. C. Sayle Mechanical properties of ceria nanorods and nanochains; the effect of dislocations, grain-boundaries and oriented attachment, Nanoscale, Volume 3 (2011) no. 4, pp. 1823-1837 | Article

[58] F. Caddeo; A. Corrias; D. C. Sayle Tuning the properties of nanoceria by applying force: stress-induced ostwald ripening, J. Phys. Chem. C, Volume 120 (2016) no. 26, pp. 14337-14344 | Article

[59] T. F. Kelly; M. K. Miller Invited review article: Atom probe tomography, Rev. Sci. Instrum., Volume 78 (2007) no. 3, 031101

[60] A. Prakash; J. Guenole; J. Wang; J. Müller; E. Spiecker; M. J. Mills; I. Povstugar; P. Choi; D. Raabe; E. Bitzek Atom probe informed simulations of dislocation-precipitate interactions reveal the importance of local interface curvature, Acta Mater., Volume 92 (2015), pp. 33-45 | Article

[61] T. Persenot; G. Martin; R. Dendievel; J.-Y. Buffière; E. Maire Enhancing the tensile properties of EBM as-built thin parts: effect of HIP and chemical etching, Mater. Charact., Volume 143 (2018), pp. 82-93 | Article

[62] M. Dupraz; G. Beutier; T. W. Cornelius; G. Parry; Z. Ren; S. Labat; M. I. Richard; G. A. Chahine; O. Kovalenko; M. De Boissieu; E. Rabkin; M. Verdier; O. Thomas 3D imaging of a dislocation loop at the onset of plasticity in an indented nanocrystal, Nano Lett., Volume 17 (2017) no. 11, pp. 6696-6701 | Article

[63] S. Roy; R. Gatti; B. Devincre; D. Mordehai A multiscale study of the size-effect in nanoindentation of Au nanoparticles, Comput. Mater. Sci., Volume 162 (2019), pp. 47-59 | Article

[64] B. Devincre; L. P. Kubin Mesoscopic simulations of dislocations and plasticity, Mater. Sci. Eng. A, Volume 234 (1997), pp. 8-14 | Article

[65] M. Tang; M. Fivel; L. P. Kubin From forest hardening to strain hardening in body centered cubic single crystals: simulation and modeling, Mater. Sci. Eng. A, Volume 309–310 (2001), pp. 256-260 | Article

[66] V. Bulatov; L. Hsiung; M. Tang; A. Arsenlis; M. Bartelt; W. Cai; J. Florando; M. Hiratani; M. Rhee; G. Hommes Dislocation multi-junctions and strain hardening, Nature, Volume 440 (2006) no. 7088, pp. 1174-1178 | Article

[67] L. P. Kubin Dislocations, Mesoscale Simulations and Plastic Flow, Oxford University Press, Oxford, 2013 | Article

[68] E. Van der Giessen; A. Needleman Discrete dislocation plasticity: a simple planar model, Model. Simul. Mater. Sci. Eng., Volume 3 (1995) no. 5, pp. 689-735

[69] M. Fivel; M. Verdier; G. Canova 3D simulation of a nanoindentation test at a mesoscopic scale, Mater. Sci. Eng. A, Volume 234 (1997), pp. 923-926 | Article

[70] C. Lemarchand; J. L. Chaboche; B. Devincre; L. P. Kubin Multiscale modelling of plastic deformation, J. Phys. IV, Volume 09 (1999) no. PR9, p. Pr9-271–Pr9-277

[71] A. Vattré; B. Devincre; F. Feyel; R. Gatti; S. Groh; O. Jamond; A. Roos Modelling crystal plasticity by 3D dislocation dynamics and the finite element method: the discrete-continuous model revisited, J. Mech. Phys. Solids, Volume 63 (2014), pp. 491-505 | Article | MR: 3147303

[72] Y. Cui; Z. Liu; Z. Zhuang Quantitative investigations on dislocation based discrete-continuous model of crystal plasticity at submicron scale, Int. J. Plast., Volume 69 (2015), pp. 54-72 | Article

[73] O. Jamond; R. Gatti; A. Roos; B. Devincre Consistent formulation for the discrete-continuous model: improving complex dislocation dynamics simulations, Int. J. Plast., Volume 80 (2016), pp. 19-37 | Article

[74] T. Mura Micromechanics of Defects in Solids, Springer Science & Business Media, 1987 | Article

[75] H.-J. Chang; M. Fivel; D. Rodney; M. Verdier Multiscale modelling of indentation in FCC metals: from atomic to continuum, C. R. Phys., Volume 11 (2010) no. 3-4, pp. 285-292 | Article

[76] H. H. M. Cleveringa; E. Van der Giessen; A. Needleman Comparison of discrete dislocation and continuum plasticity predictions for a composite material, Acta Mater., Volume 45 (1997) no. 8, pp. 3163-3179 | Article

[77] A. Vattré; B. Devincre Orientation dependence of plastic deformation in nickel-based single crystal superalloys: discrete-continuous model simulations, Acta Mater., Volume 58 (2010), pp. 1938-1951 | Article

[78] V. S. Deshpande; A. Needleman; E. Van der Giessen Discrete dislocation modeling of fatigue crack propagation, Acta Mater., Volume 50 (2002) no. 4, pp. 831-846 | Article

[79] M. D. Sangid; H. J. Maier; H. Sehitoglu The role of grain boundaries on fatigue crack initiation – An energy approach, Int. J. Plast., Volume 27 (2011) no. 5, pp. 801-821 | Article | Zbl: 1395.74082

[80] S. Groh; B. Devincre; L. P. Kubin; A. Roos; F. Feyel; J. L. Chaboche Dislocations and elastic anisotropy in heteroepitaxial metallic thin films, Phil. Mag. Lett., Volume 83 (2003) no. 5, pp. 303-313 | Article

[81] C. R. Weinberger; S. Aubry; S.-W. Lee; W. D. Nix; W. Cai Modelling dislocations in a free-standing thin film, Model. Simul. Mater. Sci. Eng., Volume 17 (2009) no. 7, 075007-27

[82] J. A. El-Awady; S. I. Rao; C. Woodward; D. M. Dimiduk; M. D. Uchic Trapping and escape of dislocations in micro-crystals with external and internal barriers, Int. J. Plast., Volume 27 (2011) no. 3, pp. 372-387 | Article | Zbl: 1426.74099

[83] Y. Cui; G. Po; N. Ghoniem Size-tuned plastic flow localization in irradiated materials at the submicron scale, Phys. Rev. Lett., Volume 120 (2018) no. 21, 215501

[84] S. Bel Haj Salah Plasticité des nanoparticules métalliques Cubiques à Faces Centrées (2018) (Ph. D. Thesis)

[85] P. Armstrong; W. Peukert Size effects in the elastic deformation behavior of metallic nanoparticles, J. Nanopart. Res., Volume 14 (2012) no. 12, 1288 | Article

[86] A. Hazarika; E. Peretz; V. Dikovsky; P. Santra; R. Shneck; D. Sarma; Y. Manassen STM verification of the reduction of the Young’s modulus of CdS nanoparticles at smaller sizes, Surf. Sci., Volume 630 (2014), pp. 89-95 | Article

[87] K. L. Johnson Contact Mechanics, Cambridge University Press, Cambridge, 1987 | Zbl: 0599.73108

[88] B. Luan; M. O. Robbins The breakdown of continuum models for mechanical contacts, Nature, Volume 435 (2005) no. 7044, pp. 929-932 | Article

[89] G. Wang; J. Bian; J. Feng; X. Feng Compressive behavior of crystalline nanoparticles with atomic-scale surface steps, Mater. Res. Express, Volume 2 (2015) no. 1, 015006

[90] D. Kilymis; C. Gerard; L. Pizzagalli Ductile deformation of core-shell Si-SiC nanoparticles controlled by shell thickness, Acta Mater., Volume 164 (2019), pp. 560-567 | Article

[91] Y. Hong; N. Zhang; M. A. Zaeem Metastable phase transformation and deformation twinning induced hardening-stiffening mechanism in compression of silicon nanoparticles, Acta Mater., Volume 145 (2018), pp. 8-18 | Article

[92] L. M. Hale; X. Zhou; J. A. Zimmerman; N. R. Moody; R. Ballarini; W. W. Gerberich Phase transformations, dislocations and hardening behavior in uniaxially compressed silicon nanospheres, Comput. Mater. Sci., Volume 50 (2011) no. 5, pp. 1651-1660 | Article

[93] D. Chrobak; N. Tymiak; A. Beaber; O. Ugurlu; W. Gerberich; R. Nowak Deconfinement leads to changes in the nanoscale plasticity of silicon, Nat. Nanotechnol., Volume 6 (2011), pp. 480-484 | Article

[94] P. Valentini; W. W. Gerberich; T. Dumitrica Phase-transition plasticity response in uniaxially compressed silicon nanospheres, Phys. Rev. Lett., Volume 99 (2007) no. 17, 175701-4 | Article

[95] Y. Feruz; D. Mordehai Towards a universal size-dependent strength of face-centered cubic nanoparticles, Acta Mater., Volume 103 (2016), pp. 433-441 | Article

[96] J. Bian; H. Zhang; X. Niu; G. Wang Anisotropic deformation in the compressions of single crystalline copper nanoparticles, Crystals, Volume 8 (2018) no. 3, 116 | Article

[97] L. Yang; J.-J. Bian; G.-F. Wang Impact of atomic-scale surface morphology on the size-dependent yield stress of gold nanoparticles, J. Phys. D: Appl. Phys., Volume 50 (2017) no. 24, 245302-6 | Article

[98] K. Shreiber; D. Mordehai Dislocation-nucleation-controlled deformation of Ni 3 Al nanocubes in molecular dynamics simulations, Model. Simul. Mater. Sci. Eng., Volume 23 (2015), 085004 | Article

[99] J. Amodeo; E. Bitzek; C. Begau Atomistic simulations of compression tests on Ni 3 Al nanocubes, Mater. Res. Lett., Volume 2 (2014) no. 3, pp. 140-145 | Article

[100] D. Chachamovitz; D. Mordehai The stress-dependent activation parameters for dislocation nucleation in molybdenum nanoparticles, Sci. Rep., Volume 8 (2018) no. 1, 3915 | Article

[101] A. Sharma; R. Kositski; O. Kovalenko; D. Mordehai; E. Rabkin Giant shape- and size-dependent compressive strength of molybdenum nano- and microparticles, Acta Mater., Volume 198 (2020), pp. 72-84 | Article

[102] J. J. Bian; L. Yang; X. R. Niu; G. F. Wang Orientation-dependent deformation mechanisms of bcc niobium nanoparticles, Philos. Mag. A, Volume 98 (2018), pp. 1-17

[103] Q. Yu; L. Qi; R. K. Mishra; X. Zeng; A. M. Minor Size-dependent mechanical properties of Mg nanoparticles used for hydrogen storage, Appl. Phys. Lett., Volume 106 (2015) no. 26, 261903-6

[104] W. W. Gerberich; W. M. Mook; M. J. Cordill; C. B. Carter; C. R. Perrey; J. V. Heberlein; S. L. Girshick Reverse plasticity in single crystal silicon nanospheres, Int. J. Plast., Volume 21 (2005) no. 12, pp. 2391-2405 | Article | Zbl: 1101.74319

[105] S. Bel Haj Salah; C. Gerard; L. Pizzagalli Influence of surface atomic structure on the mechanical response of aluminum nanospheres under compression, Comput. Mater. Sci., Volume 129 (2017), pp. 273-278 | Article

[106] S. Brochard; P. Hirel; L. Pizzagalli; J. Godet Elastic limit for surface step dislocation nucleation in face-centered cubic metals: temperature and step height dependence, Acta Mater., Volume 58 (2010) no. 12, pp. 4182-4190 | Article

[107] J. Schloesser; J. Roesler; D. Mukherji Deformation behaviour of freestanding single-crystalline Ni 3 Al-based nanoparticles, Int. J. Mater. Res., Volume 102 (2011) no. 5, pp. 532-537 | Article

[108] A. Sharma; N. Gazit; L. Klinger; E. Rabkin Pseudoelasticity of metal nanoparticles is caused by their ultrahigh strength, Adv. Funct. Mater., Volume 30 (2019) no. 18, 1807554 | Article

[109] J. D. Nowak; A. R. Beaber; O. Ugurlu; S. L. Girshick; W. W. Gerberich Small size strength dependence on dislocation nucleation, Scr. Mater., Volume 62 (2010) no. 11, pp. 819-822 | Article

[110] D. Mordehai; O. David; R. Kositski Nucleation-controlled plasticity of metallic nanowires and nanoparticles, Adv. Mater., Volume 305 (2018), 1706710-17

[111] J. Glucklich; L. J. Cohen Size as a factor in the brittle-ductile transition and the strength of some materials, Int. J. Fract. Mech., Volume 3 (1967) no. 4, pp. 278-289 | Article

[112] B. L. Karihaloo A note on complexities of compression failure, Proc. R. Soc. A, Volume 368 (1979) no. 1735, pp. 483-493

[113] J. T. Hagan Impossibility of fragmenting small particles: brittle–ductile transition, J. Mater. Sci., Volume 16 (1981) no. 10, pp. 2909-2911 | Article

[114] Y. Yang; C.-C. Chen; M. C. Scott; C. Ophus; R. Xu; A. Pryor; L. Wu; F. Sun; W. Theis; J. Zhou; M. Eisenbach; P. R. C. Kent; R. F. Sabirianov; H. Zeng; P. Ercius; J. Miao Deciphering chemical order/disorder and material properties at the single-atom level, Nature, Volume 542 (2017) no. 7639, pp. 75-79 | Article

[115] H. Van Swygenhoven; P. M. Derlet; A. G. Frøseth Stacking fault energies and slip in nanocrystalline metals, Nat. Mater., Volume 3 (2004) no. 6, pp. 399-403 | Article

[116] R. Kositski; O. Kovalenko; S.-W. Lee; J. R. Greer; E. Rabkin; D. Mordehai Cross-split of dislocations: an athermal and rapid plasticity mechanism, Sci. Rep., Volume 6 (2016) no. 1, 25966-8 | Article

[117] D. Mordehai (Personnal Communication)

[118] J. Wang; Z. Zeng; C. R. Weinberger; Z. Zhang; T. Zhu; S. X. Mao In situ atomic-scale observation of twinning-dominated deformation in nanoscale body-centred cubic tungsten, Nat. Mater., Volume 14 (2015) no. 6, pp. 594-600 | Article

[119] L. Proville; D. Rodney; M.-C. Marinica Quantum effect on thermally activated glide of dislocations, Nat. Mater., Volume 11 (2012) no. 10, pp. 845-849 | Article

[120] K. Srivastava; R. Gröger; D. Weygand; P. Gumbsch Dislocation motion in tungsten: atomistic input to discrete dislocation simulations, Int. J. Plast., Volume 47 (2013), pp. 126-142 | Article

[121] C. Marichal; K. Srivastava; D. Weygand; S. Van Petegem; D. Grolimund; P. Gumbsch; H. Van Swygenhoven Origin of anomalous slip in tungsten, Phys. Rev. Lett., Volume 113 (2014) no. 2, 025501 | Article

[122] L. Dezerald; D. Rodney; E. Clouet; L. Ventelon; F. Willaime Plastic anisotropy and dislocation trajectory in BCC metals, Nat. Commun., Volume 7 (2016) no. 1, 11695 | Article

[123] A. Kraych; E. Clouet; L. Dezerald; L. Ventelon; F. Willaime; D. Rodney Non-glide effects and dislocation core fields in BCC metals, NPJ Comput. Mater., Volume 5 (2019) no. 1, pp. 1237-1238 | Article

[124] J. Amodeo; F. Pietrucci; J. Lam Out-of-equilibrium polymorph selection in nanoparticle freezing, J. Phys. Chem. Lett., Volume 11 (2020) no. 19, pp. 8060-8066 | Article

[125] D. Pope; S. Ezz Mechanical properties of Ni 3 AI and nickel-base alloys with high volume fraction of γ , Int. Met. Rev., Volume 29 (1984) no. 1, pp. 136-167 | Article

[126] R. C. Reed The Superalloys: Fundamentals and Applications, Cambridge University Press, New York, 2008

[127] L. Kovarik; R. R. Unocic; J. Li; P. Sarosi; C. Shen; Y. Wang; M. J. Mills Microtwinning and other shearing mechanisms at intermediate temperatures in Ni-based superalloys, Prog. Mater. Sci., Volume 54 (2009) no. 6, pp. 839-873 | Article

[128] R. R. Unocic; N. Zhou; L. Kovarik; C. Shen; Y. Wang; M. J. Mills Dislocation decorrelation and relationship to deformation microtwins during creep of a γ precipitate strengthened Ni-based superalloy, Acta Mater., Volume 59 (2011) no. 19, pp. 7325-7339 | Article

[129] L. Pizzagalli; J. Godet; J. Guénolé; S. Brochard Dislocation cores in silicon: new aspects from numerical simulations, J. Phys. Conf. Ser., Volume 281 (2011) no. 1, 012002

[130] D. Rodney; L. Ventelon; E. Clouet; L. Pizzagalli; F. Willaime Ab initio modeling of dislocation core properties in metals and semiconductors, Acta Mater., Volume 124 (2017), pp. 633-659 | Article

[131] N. Zhang; Q. Deng; Y. Hong; L. Xiong; S. Li; M. Strasberg; W. Yin; Y. Zou; C. R. Taylor; G. Sawyer; Y. Chen Deformation mechanisms in silicon nanoparticles, J. Appl. Phys., Volume 109 (2011) no. 6, 063534 | Article

[132] L. M. Hale; D. B. Zhang; X. Zhou; J. A. Zimmerman; N. R. Moody; T. Dumitrica; R. Ballarini; W. W. Gerberich Dislocation morphology and nucleation within compressed Si nanospheres: a molecular dynamics study, Comput. Mater. Sci., Volume 54 (2012), pp. 280-286 | Article

[133] K.-C. Fang; C.-I. Weng; S.-P. Ju An investigation into the mechanical properties of silicon nanoparticles using molecular dynamics simulations with parallel computing, J. Nanopart. Res., Volume 11 (2009) no. 3, pp. 581-588 | Article

[134] E. Maras; L. Pizzagalli; T. Ala-Nissila; H. Jonsson Atomic scale formation mechanism of edge dislocation relieving lattice strain in a GeSi overlayer on Si(001), Sci. Rep., Volume 7 (2017) no. 1, 11966 | Article

[135] J. Guenole; S. Brochard; J. Godet Unexpected slip mechanism induced by the reduced dimensions in silicon nanostructures: atomistic study, Acta Mater., Volume 59 (2011) no. 20, pp. 7464-7472 | Article

[136] J. Amodeo; S. Merkel; C. Tromas; P. Carrez; S. Korte-Kerzel; P. Cordier; J. Chevalier Dislocations and plastic deformation in MgO crystals: a review, Crystals, Volume 8 (2018) no. 6, pp. 240-253 | Article

[137] C. Hulse; J. Pask Mechanical properties of magnesia single crystals compression, J. Am. Ceram. Soc., Volume 43 (1960) no. 7, pp. 373-378 | Article

[138] C. Hulse; S. Copley; J. Pask Effect of crystal orientation on plastic deformation of magnesium oxide, J. Am. Ceram. Soc., Volume 46 (1963) no. 7, pp. 317-323 | Article

[139] S. Korte; W. Clegg Discussion of the dependence of the effect of size on the yield stress in hard materials studied by microcompression of MgO, Philos. Mag. A, Volume 91 (2011) no. 7-9, pp. 1150-1162 | Article

[140] J. Amodeo; P. Carrez; B. Devincre; P. Cordier Multiscale modelling of MgO plasticity, Acta Mater., Volume 59 (2011) no. 6, pp. 2291-2301 | Article

[141] D. C. Sayle; S. A. Maicaneanu; G. W. Watson Atomistic models for CeO 2 (111), (110), and (100) nanoparticles, supported on yttrium-stabilized zirconia, J. Am. Chem. Soc., Volume 124 (2002) no. 38, pp. 11429-11439 | Article

[142] G. Möbus; Z. Saghi; D. C. Sayle; U. M. Bhatta; A. Stringfellow; T. X. T. Sayle Dynamics of polar surfaces on ceria nanoparticles observed in situ with single-atom resolution, Adv. Funct. Mater., Volume 21 (2011) no. 11, pp. 1971-1976 | Article

[143] T. X. T. Sayle; M. Molinari; S. Das; U. M. Bhatta; G. Möbus; S. C. Parker; S. Seal; D. C. Sayle Environment-mediated structure, surface redox activity and reactivity of ceria nanoparticles, Nanoscale, Volume 5 (2013) no. 13, 6063-11

[144] K. Reed; A. Cormack; A. Kulkarni; M. Mayton; D. Sayle; F. Klaessig; B. Stadler Exploring the properties and applications of nanoceria: is there still plenty of room at the bottom?, Environ. Sci.: Nano, Volume 1 (2014) no. 5, pp. 390-405

[145] P. Sarobol; M. Chandross; J. D. Carroll; W. M. Mook; D. C. Bufford; B. L. Boyce; K. Hattar; P. G. Kotula; A. C. Hall Room temperature deformation mechanisms of alumina particles observed from in situ micro-compression and atomistic simulations, J. Therm. Spray Technol., Volume 25 (2015) no. 1, pp. 82-93

[146] A. H. De Aza; J. Chevalier; G. Fantozzi; M. Schehl; R. Torrecillas Crack growth resistance of alumina, zirconia and zirconia toughened alumina ceramics for joint prostheses, Biomaterials, Volume 23 (2002) no. 3, pp. 937-945 | Article

[147] D. Mordehai; E. Rabkin; D. J. Srolovitz Pseudoelastic deformation during nanoscale adhesive contact formation, Phys. Rev. Lett., Volume 107 (2011) no. 9, pp. 449-454 | Article

[148] A. T. Jennings; J. Li; J. R. Greer Emergence of strain-rate sensitivity in Cu nanopillars: transition from dislocation multiplication to dislocation nucleation, Acta Mater., Volume 59 (2011) no. 14, pp. 5627-5637 | Article

[149] R. Tenne; L. Rapoport; Y. Bilik; Y. Feldman; M. Homyonfer; S. R. Cohen Hollow nanoparticles of WS 2 as potential solid-state lubricants, Nature, Volume 387 (1997) no. 6635, pp. 791-793

[150] H. J. Fan; U. Gösele; M. Zacharias Formation of nanotubes and hollow nanoparticles based on kirkendall and diffusion processes: a review, Small, Volume 3 (2007) no. 10, pp. 1660-1671 | Article

[151] J. J. Teo; Y. Chang; H. C. Zeng Fabrications of hollow nanocubes of Cu 2 O and Cu via reductive self-assembly of CuO nanocrystals, Langmuir, Volume 22 (2006) no. 17, pp. 7369-7377 | Article

[152] N. Gazit; L. Klinger; G. Richter; E. Rabkin Formation of hollow gold-silver nanoparticles through the surface diffusion induced bulk intermixing, Acta Mater., Volume 117 (2016), pp. 188-196 | Article

[153] S. Ozden; C. S. Tiwary; J. Yao; G. Brunetto; S. Bhowmick; S. Asif; R. Vajtai; P. M. Ajayan Highly ordered carbon-based nanospheres with high stiffness, Carbon, Volume 105 (2016), pp. 144-150 | Article

[154] Z. W. Shan; G. Adesso; A. Cabot; M. P. Sherburne; S. A. S. Asif; O. L. Warren; D. C. Chrzan; A. M. Minor; A. P. Alivisatos Ultrahigh stress and strain in hierarchically structured hollow nanoparticles, Nat. Mater., Volume 7 (2008) no. 12, pp. 947-952 | Article

[155] R. P. Chaukulkar; K. de Peuter; P. Stradins; S. Pylypenko; J. P. Bell; Y. Yang; S. Agarwal Single-step plasma synthesis of carbon-coated silicon nanoparticles, ACS Appl. Mater. Inter., Volume 6 (2014) no. 21, pp. 19026-19034 | Article

[156] K. L. Firestein; D. G. Kvashnin; A. M. Kovalskii; Z. I. Popov; P. B. Sorokin; D. V. Golberg; D. V. Shtansky Compressive properties of hollow BN nanoparticles: theoretical modeling and testing using a high-resolution transmission electron microscope, Nanoscale, Volume 10 (2018) no. 17, pp. 8099-8105 | Article

[157] W. Yang; S. Mao; J. Yang; T. Shang; H. Song; J. Mabon; W. Swiech; J. R. Vance; Z. Yue; S. J. Dillon; H. Xu; B. Xu Large-deformation and high-strength amorphous porous carbon nanospheres, Sci. Rep., Volume 6 (2016) no. 1, 24187

[158] W. Gonçalves; J. Amodeo; J. Morthomas; P. Chantrenne; M. Perez; G. Foray; C. L. Martin Nanocompression of secondary particles of silica aerogel, Scr. Mater., Volume 157 (2018), pp. 157-161 | Article

[159] D. Kilymis; C. Gerard; L. Pizzagalli Mechanical properties of amorphous silicon nanoparticles, TMS 2019 148th Annual Meeting & Exhibition Supplemental Proceedings (The Minerals, Metals & Materials Series), Springer, Berlin, Heidelberg, 2019, pp. 1347-1354 | Article

[160] H. K. Issa; A. Taherizadeh; A. Maleki Atomistic-level study of the mechanical behavior of amorphous and crystalline silica nanoparticles, Ceram. Int., Volume 46 (2020) no. 13, pp. 21647-21656 | Article

[161] J. Zhao; S. Nagao; G. M. Odegard; Z. Zhang; H. Kristiansen; J. He Size-dependent mechanical behavior of nanoscale polymer particles through coarse-grained molecular dynamics simulation, Nanoscale Res. Lett., Volume 8 (2013) no. 1, 541 | Article

[162] E. W. Bucholz; S. B. Sinnott Computational investigation of the mechanical and tribological responses of amorphous carbon nanoparticles, J. Appl. Phys., Volume 113 (2013) no. 7, 073509

[163] L. Pascazio; J. W. Martin; K. Bowal; J. Akroyd; M. Kraft Exploring the internal structure of soot particles using nanoindentation: a reactive molecular dynamics study, Combus. Flame, Volume 219 (2020), pp. 45-56 | Article

[164] I. Z. Jenei; F. Dassenoy; T. Epicier; A. Khajeh; A. Martini; D. Uy; H. Ghaednia; A. Gangopadhyay Mechanical characterization of diesel soot nanoparticles: in situ compression in a transmission electron microscope and simulations, Nanotechnology, Volume 29 (2018) no. 8, 085703

[165] M. J. Demkowicz; A. S. Argon Liquidlike atomic environments act as plasticity carriers in amorphous silicon, Phys. Rev. B, Volume 72 (2005) no. 24, 245205

[166] C. Fusco; T. Albaret; A. Tanguy The role of local order in the small-scale plasticity of model amorphous materials, Phys. Rev. E, Volume 82 (2010), 066116 | Article

[167] L. Yang; J. J. Bian; H. Zhang; X. R. Niu; G. F. Wang Size-dependent deformation mechanisms in hollow silicon nanoparticles, AIP Adv., Volume 5 (2015) no. 7, 077162 | Article

[168] J. Wu; S. Nagao; Z. Zhang; J. He Deformation and fracture of nano-sized metal-coated polymer particles: a molecular dynamics study, Eng. Fract. Mech., Volume 150 (2015), pp. 209-221 | Article

[169] R. A. Fleming; M. Zou The effects of confined core volume on the mechanical behavior of Al/a-Si core-shell nanostructures, Acta Mater., Volume 128 (2017), pp. 149-159 | Article

[170] F. J. Valencia; B. Pinto; M. Kiwi; C. J. Ruestes; E. M. Bringa; J. Rogan Nanoindentation of polycrystalline Pd hollow nanoparticles: grain size role, Comput. Mater. Sci., Volume 179 (2020), 109642

[171] F. Xu; T. Kobayashi; Z. Yang; T. Sekine; H. Chang; N. Wang; Y. Xia; Y. Zhu How the toughest inorganic fullerene cages absorb shockwave pressures in a protective nanocomposite: experimental evidence from two in situ investigations, ACS Nano, Volume 11 (2017) no. 8, pp. 8114-8121 | Article

[172] J. Pokluda; M. Černý; P. Šandera; M. Šob Calculations of theoretical strength: state of the art and history, J. Comput.-Aided Mater. Des., Volume 11 (2004) no. 1, pp. 1-28 | Article

[173] N. Bertin; R. B. Sills; W. Cai Frontiers in the simulation of dislocations, Annu. Rev. Mater. Res., Volume 50 (2020) no. 1, pp. 437-464 | Article

[174] A. F. Voter; F. Montalenti; T. C. Germann Extending the time scale in atomistic simulation of materials, Annu. Rev. Mater. Res., Volume 32 (2002), pp. 321-346 | Article

[175] D. Perez; B. P. Uberuaga; Y. Shim; J. G. Amar; A. F. Voter Chapter 4 accelerated molecular dynamics methods: introduction and recent developments (R. A. Wheeler, ed.) (Annual Reports in Computational Chemistry, no. Supplement C), Volume 5, Elsevier, 2009, pp. 79-98

[176] W. Gerberich; E. B. Tadmor; J. Kysar; J. A. Zimmerman; A. M. Minor; I. Szlufarska; J. Amodeo; B. Devincre; E. Hintsala; R. Ballarini Review article: case studies in future trends of computational and experimental nanomechanics, J. Vac. Sci. Technol. A, Volume 35 (2017) no. 6, 060801-0 | Article

[177] L. A. Zepeda-Ruiz; A. Stukowski; T. Oppelstrup; V. V. Bulatov Probing the limits of metal plasticity with molecular dynamics simulations, Nat. Mater., Volume 550 (2017), pp. 1-18

[178] J. Behler Perspective: machine learning potentials for atomistic simulations, J. Chem. Phys., Volume 145 (2016) no. 17, 170901 | Article

[179] F. Fan; S. Huang; H. Yang; M. Raju; D. Datta; V. B. Shenoy; A. C. T. van Duin; S. Zhang; T. Zhu Mechanical properties of amorphous Li x Si alloys: a reactive force field study, Model. Simul. Mater. Sci. Eng., Volume 21 (2013) no. 7, 074002

[180] T. Liang; T.-R. Shan; Y.-T. Cheng; B. D. Devine; M. Noordhoek; Y. Li; Z. Lu; S. R. Phillpot; S. B. Sinnott Classical atomistic simulations of surfaces and heterogeneous interfaces with the charge-optimized many body (COMB) potentials, Mater. Sci. Eng. R. Rep., Volume 74 (2013) no. 9, pp. 255-279 | Article

[181] P. Koskinen; V. Mäkinen Density-functional tight-binding for beginners, Comput. Mater. Sci., Volume 47 (2009) no. 1, pp. 237-253 | Article

[182] M. T. Kiani; Y. Wang; N. Bertin; W. Cai; X. W. Gu Strengthening mechanism of a single precipitate in a metallic nanocube, Nano Lett., Volume 19 (2019) no. 1, pp. 255-260 | Article

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