Shear melting of silicon and diamond and the disappearance of the polyamorphic transition under shear

Gianpietro Moras, Andreas Klemenz, Thomas Reichenbach, Adrien Gola, Hiroshi Uetsuka, Michael Moseler, and Lars Pastewka

Phys. Rev. Materials 2, 083601 – Published 3 August 2018

Abstract

Molecular dynamics simulations of diamond-cubic silicon and carbon under combined shear and compression show the formation of an amorphous solid with liquidlike structure at room temperature. Consistent with the opposite density changes of the two crystals upon melting, the amorphous material is denser than the crystal in silicon and less dense than the crystal in carbon. As a result, its rate of formation is enhanced by pressure in silicon but suppressed in carbon. These results are particularly unexpected for silicon, whose amorphous structure is supposed to be liquidlike only when hydrostatically compressed above the polyamorphic transition pressure ( $\sim 14 GPa$ ). Below this pressure, amorphous silicon is expected to have a low-density structure with density close to that of the diamond-cubic crystal. Our simulations show that this polyamorphic transition disappears under shear and high-density, liquidlike amorphous silicon with metallic ductility forms even at low pressure. These results are potentially transferable to other diamond-cubic crystals, like germanium and ice $I_{h}$ , and provide insights into nonequilibrium materials transformations that govern friction and wear in tribological systems.

Received 29 August 2017
Revised 9 March 2018

DOI:https://doi.org/10.1103/PhysRevMaterials.2.083601

Physics Subject Headings (PhySH)

Phase diagrams Phase transitions Plastic deformation Shear deformation Solid-solid transformations Tribology Wear

Amorphous materials Diamond Elemental semiconductors

Molecular dynamics

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Gianpietro Moras^1,*, Andreas Klemenz¹, Thomas Reichenbach¹, Adrien Gola², Hiroshi Uetsuka³, Michael Moseler^1,4, and Lars Pastewka^1,2

¹Fraunhofer IWM, MicroTribology Center μTC, Wöhlerstraße 11, 79108 Freiburg, Germany
²Department of Microsystems Engineering, University of Freiburg, Georges-Köhler-Allee 103, 79110 Freiburg, Germany and Institute for Applied Materials, Karlsruhe Institute of Technology, Straße am Forum 7, 76131 Karlsruhe, Germany
³Asahi Diamond Industrial Co. Ltd., 787 Tabi, Ichihara Chiba, 290-0515, Japan
⁴Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany

^*gianpietro.moras@iwm.fraunhofer.de

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Vol. 2, Iss. 8 — August 2018

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Images

Figure 1
(a), (b) $P − T$ phase diagrams for Si (a) and C (b) in the pressure range of interest for the simulations presented in this work. The red symbols show the melting temperature $T_{m} (P)$ calculated in this work by MD simulations (see discussion S1 in the Supplemental Material [34]). Squares refer to the diamond-cubic phase of Si and C, and circles to Si-II, while the black triangle shows the Si-I/Si-II transition pressure at 0 K. Open squares in panel (a) represent transitions involving a metastable Si-I phase. Lines connect calculated data and are guides to the eye. (c), (d) Pressure dependencies of the density for different Si (c) and C (d) phases, as obtained by MD simulations (see discussion S2 in the Supplemental Material [34]). Black solid lines refer to crystalline phases, red squares to the liquid phases of panels (a), (b). The purple solid line indicates the density of an amorphous phase obtained initially at $P = 0$ and hydrostatically compressed. Blue and green symbols refer to amorphous samples obtained by shear-induced amorphization and quenching from the melt, respectively. (e) Snapshots from MD simulations of two Si-I crystals sliding against each other at a velocity of $10 m s^{- 1}$ and 10 GPa normal load. The left snapshot is taken after pressure equilibration but before sliding, while the snapshot on the right is taken after 15 ns simulation time. Blue spheres are Si atoms in the Si-I phase, while gray spheres are Si atoms in an amorphous configuration. The red curve is an averaged velocity profile along $x$ and shows a Couette-like profile. Analogous snapshots for diamond are depicted in panel (f). Note that the Si and C model systems have the same number of atoms but their size is scaled so that they have the same size along $x$ in this figure. The volume variation upon amorphization is schematically shown as a variation of system height.
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Figure 2
(a) Time evolution of the a-Si region thickness $h$ (solid lines) and square root fitting functions [dashed lines, Eq. (1)] for the temperature/velocity combinations indicated in the legend and 10 GPa normal pressure. The inset shows the evolution of $h$ as a function of the sliding distance $v t$ for the simulations at 300 K. (b)–(e) Snapshots of the a/c interface during the shear-driven amorphization process. Blue spheres are Si atoms in the Si-I phase, while gray spheres are Si atoms in an amorphous configuration. The black and red circles indicate two atoms that are initially in a crystalline lattice position and are pushed into the crystal during the process, thus causing the advancement of the amorphous region. Their initial coordinate normal to the interface [in panel (b)] is indicated by the black and red solid lines.
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Figure 3
(a), (b) Evolution of the amorphous region thickness $h$ with sliding distance $v t$ for different values of the normal pressure $P$ for Si-I (a) and diamond (b) at 300 K. Solid lines are the $h$ values from the MD simulations, while dashed red lines are fits to the amorphization model, Eq. (1). (c), (d) Amorphization rate $λ$ (the increase in thickness per 100% of strain) for different values of normal pressure $P$ for Si-I (c) and diamond (d).
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Figure 4
Angular distribution function, $g (θ)$ , of amorphous and liquid C and Si for different pressure values. (a), (d) $g (θ)$ for amorphous structures obtained by quenching from the melt under constant pressure. (b), (e) $g (θ)$ for amorphous structures obtained during shear MD simulations. The inset to panel (b) shows $g (θ)$ obtained by hydrostatic compression of Si. (c), (f) $g (θ)$ for liquid structures at the melting point $T_{m}$ . The angular distributions functions are extracted from the spatial region that is in the liquid state in the phase coexistence calculations used to compute the melting lines in Figs. 1 and 1. The vertical gray lines show the angles of the reference crystalline structures: diamond-cubic (dc) and β-tin Si, dc C, and graphite.
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