Deconfinement leads to changes in the nanoscale plasticity of silicon

Journal name:
Nature Nanotechnology
Year published:
Published online


Silicon crystals have an important role in the electronics industry, and silicon nanoparticles have applications in areas such as nanoelectromechanical systems, photonics and biotechnology1, 2. However, the elastic–plastic transition observed in silicon is not fully understood; in particular, it is not known if the plasticity of silicon is determined by dislocations or by transformations between phases. Here, based on compression experiments and molecular dynamics simulations, we show that the mechanical properties of bulk silicon3, 4, 5, 6 and silicon nanoparticles are significantly different. We find that bulk silicon exists in a state of relative constraint, with its plasticity dominated by phase transformations, whereas silicon nanoparticles are less constrained and display dislocation-driven plasticity. This transition, which we call deconfinement, can also explain the absence of phase transformations in deformed silicon nanowedges7, 8. Furthermore, the phenomenon is in agreement with effects observed in shape-memory alloy nanopillars9, and provides insight into the origin of incipient plasticity10, 11, 12, 13, 14, 15, 16, 17, 18, 19.

At a glance


  1. Mechanical response of nanodeformed silicon from bulk to nanoparticles.
    Figure 1: Mechanical response of nanodeformed silicon from bulk to nanoparticles.

    a, P–δ response of silicon deduced from nanoindentation in bulk3, 4, 5, 6 and our nanocompression experiments on silicon nanospheres (Supplementary Fig. S1). A combination of PI during loading and PO during unloading is denoted the PI–PO effect. The sequence PO right arrow PI–PO right arrow PI indicates a transition from bulk to nanoparticle behaviour. b, Results of nanocompression tests on silicon nanospheres with radii of 19–169 nm and bulk silicon nanoindentation data3, 4, 5. The PI-only (green) response is relevant to the smaller nanospheres (R ≤ 57 nm), and the PO-only (black) record is characteristic of bulk silicon (R right arrow ∞). Larger nanoparticles (R ≥ 67 nm) demonstrate the PI–PO effect (red), covering the transition area between bulk and pure PI response. As PO marks the Si-II right arrow Si-XII/III + α-Si phase transition, its gradual disappearance (PO right arrow PI–PO right arrow PI) with decreasing radius is in accordance with suppression of the reverse martensitic transformation reported for shape-memory alloy nanopillars9.

  2. Mechanical response of a compressed silicon nanoparticle.
    Figure 2: Mechanical response of a compressed silicon nanoparticle.

    a, MD simulations of silicon nanospheres compressed between two rigid plates. Displacement δ under applied load P is quantified in terms of ε = δ/R strain. b, Contact pressure (pc = P/A, where A is contact area) versus strain relationship (pcε) demonstrates that the maximum value of pc reached in the nanoparticles (21.3–23.5 GPa) is nearly double that (~12 GPa) of bulk silicon18. Elastic deformation follows Hertzian theory25 (solid line). After the PI (onset of plasticity), multiple singularities reflect the nature of plasticity. c, Slip vector (SV) analysis of the unstable dislocation structure of the silicon nanoparticle (R2 = 10 nm). Perfect dislocation loops (|SV| = 3.8 Å, b = |1/2[101]| = 3.84 Å, atoms marked in yellow) nucleate immediately after the PI (ε = 0.108), and terminate inside the nanosphere. After unloading, a majority of the dislocation loops vanish, whereas those at the nanoparticle surface stabilize, hence the nearly complete silicon particle shape recovery following a PI, referred to as ‘reversible plasticity’15.

  3. MD-simulated contrasting behaviour of confined (bulk) and deconfined (nanoparticle) silicon.
    Figure 3: MD-simulated contrasting behaviour of confined (bulk) and deconfined (nanoparticle) silicon.

    a, Initial plastic deformation of bulk silicon indented with a diamond sphere (R = 10 nm). As strain reaches ε = 0.101, the deformed volume under the indentation contact displays no evidence of dislocations. Coordination numbers ranging from 1 to 5 suggest an amorphous structure. b, Plasticity initiation in a compressed silicon nanosphere. Despite similar levels of strain, the mechanisms of plasticity in the silicon nanoparticle and bulk are essentially different. Plastic deformation in a nanoparticle begins with perfect dislocation loops (atoms marked in turquoise) joined by stacking fault regions (atoms marked in green). Perfect dislocations to the left and right of the yellow arrow lie on the ( 11) and (11 ) planes, respectively, whereas the stacking fault joining them is positioned on the (10 ) plane. c,d, Distribution of hydrostatic pressure (σh) in bulk silicon (c) and in the silicon nanosphere (R = 10 nm, d), both strained elastically up to ε = 0.0725. Atoms exposed to pressures higher than |σh| ≥ 1.5 GPa are marked in colours, indicating a higher stress concentration in confined silicon (c) than in the nanoparticle (d). Note that both distributions are presented on a common scale.

  4. Effect of deconfinement of silicon from bulk to nanosphere viewed in terms of stress analysis.
    Figure 4: Effect of deconfinement of silicon from bulk to nanosphere viewed in terms of stress analysis.

    Averaged ratio of hydrostatic (σh) and von Mises stresses (σm) determined using MD calculations during consecutive steps of elastic deformation. The left fenceσh/σmright fence values calculated for the nanoparticle (green) are systematically lower than those obtained for the bulk state (black), which suggests that the silicon particle is prone to undergo non-dilatational strain rather than the volumetric strain dominant in bulk.

  5. Schematic of silicon deconfinement process scaled with the pressure of the Si-II [rarr] Si-XII/III + [alpha]-Si phase transition.
    Figure 5: Schematic of silicon deconfinement process scaled with the pressure of the Si-II right arrow Si-XII/III + α-Si phase transition.

    General relationship determined by means of nanocompression experiments (green and red solid lines) for highly deconfined silicon (nanoparticles) appears to extrapolate for larger nanoparticles (red broken line) towards the data obtained for bulk silicon deformed by nanoindentation (black area). When the entire free surface of the bulk is under external high pressure, it is possible to imagine such a material as being ‘confined to a higher degree’ (with virtually no free surface). This is exactly what happens to silicon deformed in pressure cell experiments33, in which the characteristic pressure of the Si-II right arrow Si-XII/III transformation (magenta point) is certainly higher than for the nanoindented bulk crystal (black area). Note that in the deconfined state, silicon deforms with the contribution of phase transformation, but for higher degrees of deconfinement, there is no transformation at all (green solid line). The schematic thus constitutes a roadmap for a range of materials deconfined from their bulk state to nanoparticle, nanowire, nanowedge or nanopillar (cf. ref. 9).


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Author information

  1. These authors contributed equally to this work

    • Dariusz Chrobak &
    • Roman Nowak


  1. Nordic Hysitron Laboratory, School of Chemical Technology, Aalto University, Vuorimiehentie 2A, Espoo, 00076 Aalto, Finland

    • Dariusz Chrobak,
    • Natalia Tymiak &
    • Roman Nowak
  2. Institute of Materials Science, University of Silesia, Bankowa 12, 40-007 Katowice, Poland

    • Dariusz Chrobak
  3. Department of Chemical Engineering & Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA

    • Aaron Beaber,
    • Ozan Ugurlu &
    • William W. Gerberich
  4. Extreme Energy-Density Research Institute, Nagaoka University of Technology, Nagaoka, Niigata, 940-2188 Japan

    • Roman Nowak


D.C. carried out the calculations and analysed the compatibility of the theoretical and experimental data. R.N. conceived the concept of deconfinement-driven transition and designed the research project. N.T. analysed the data. W.W.G. designed and supervised the experimental part, and A.B. and O.U. performed nanocompression tests and analysed the output. R.N. and D.C. wrote the paper. All authors discussed the results.

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