Free energies of generalized stacking faults in Si and implications for the brittle-ductile transition

Kaxiras, Efthimios; Duesbery, M. S.

doi:10.1103/physrevlett.70.3752

Cited by 166 publications

(90 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Recently, Kaxiras and Duesbery [36] have reported similar calculations done by DFT-LDA, for shearing of Si along (111) planes. They studied both unrelaxed and relaxed configurations, in the sense of block-like lattice motions as in Fig.…”

Section: Results For Si From Density Functional Theorymentioning

confidence: 79%

Estimates from atomic models of tension-shear coupling in dislocation nucleation from a crack tip

Sun

Beltz

Rice

1993

Materials Science and Engineering: A

140

108

View full text Add to dashboard Cite

The normal stress distribution across a slip plane has the effect of reducing the critical loading required for dislocation emission from a crack tip. The reduction by normal stresses was found to be very significant for Si, based on properties estimated for it using density functional theory, to be large for Fe as modeled by the embedded atom method (EAM), and to be smaller in AI, Ni and ordered Ni3A1, estimated using the EAM. The general dependence over a wide range on parameters characterizing the tension-shear coupling was also determined. In the context of a Peierls model for dislocation nucleation at a crack tip (J. R. Rice, J. Mech. Phys. Solids, 40 (1992) 239), our approach was to search for onset of the dislocation nucleation instability based on the numerical solution of the system of non-linear integral equations describing an incipient dislocation. The incipient dislocation consists of a distribution of sliding and opening displacements along a slip plane emanating from the crack tip; these displacements are related to the shear and tensile stresses across the slip plane by constitutive relations based on the atomic models mentioned. Results from the atomic models are used to parametrize constitutive relations involving a Frenkel sinusoidal dependence of shear stress on sliding displacement at any fixed opening displacement, and a Rose-Ferrante-Smith universal binding form of dependence of tensile stress on opening displacement at any fixed shear displacement. These relations then enter the system of integral equations, solved numerically, which describe the elasticity solution for a non-uniform distribution of sliding and opening along the slip plane. The results show that tension-shear coupling will often significantly reduce the loading for dislocation emission from the value estimated on the basis of an unstable stacking energy Yu~ determined with neglect of such coupling, in a shear-only type analysis. For the EAM models of the metals considered, a simple and approximate method to account for the tension effects is to use a modified quantity yo iu*~, which is an unstable stacking energy for lattice planes which are constrained to a fixed opening A0*, corresponding to that for vanishing normal stress at the unstable shear equilibrium position. Moreover, it is found that the normal stress effect can be described well in these cases by replacing the unstable stacking energy 7u~ in the shear-only model by a tension softened ~' u~(q~), which depends on the phase angle ~p of the combined tension-shear loading along the slip plane according to the stress intensity factors of the elastic singular solution. The same simple procedures for accounting for tension effects on nucleation are less suitable for lattices with strong coupling such as Si.

show abstract

Section: Results For Si From Density Functional Theorymentioning

confidence: 79%

Estimates from atomic models of tension-shear coupling in dislocation nucleation from a crack tip

Sun

Beltz

Rice

1993

Materials Science and Engineering: A

140

108

View full text Add to dashboard Cite

show abstract

“…However, the likelihood of their occurrence varies rather differently with the change of the sample or conditions. It resembles the brittle-ductile mode change in 3D solids, with silicon crystal as an example well explained from first principles (24). The goal of this article is to determine which of these mechanisms apply to the experimental conditions of tensile tests at ambient temperatures, a duration of seconds (instead of picoseconds as in generic MD run) and a CNT length Ͼ1 m. Although some trends could be revealed in our early work (25) and especially in the detailed analysis of classical potential-based MD simulations (26), the force field used there tends to underestimate the activation barriers (15), while it is shown (27) to overestimate the forces at large strain, which essentially excludes possibility of brittle mode.…”

Section: Resultsmentioning

confidence: 99%

Symmetry-, time-, and temperature-dependent strength of carbon nanotubes

Dumitrică

Hua

Yakobson

2006

Proc. Natl. Acad. Sci. U.S.A.

241

203

View full text Add to dashboard Cite

Although the strength of carbon nanotubes has been of great interest, their ideal value has remained elusive both experimentally and theoretically. Here, we present a comprehensive analysis of underlying atomic mechanisms and evaluate the yield strain for arbitrary nanotubes at realistic conditions. For this purpose, we combine detailed quantum mechanical computations of failure nucleation and transition-state barriers with the probabilistic approach of the rate theory. The numerical results are then summarized in a concise set of equations for the breaking strain. We reveal a competition between two alternative routes of brittle bond breaking and plastic relaxation, determine the domains of their dominance, and map the nanotube strength as a function of chiral symmetry, tensile test time, and temperature.mechanics ͉ plasticity ͉ isomerization ͉ rate theory T he highest strengths of solids are obtained from specimens of utmost uniformity and perfection. Even a single defect can cause drastic loss of strength. Thin solid filaments (whiskers) have long been viewed as material structures that can sustain the greatest mechanical tension (1, 2). Small cross sections permit little room for defects in their bulk, and the only heterogeneity is caused by inevitable presence of the surface and the interfacet edges. Discovery (3) of carbon nanotubes (CNTs) offered, at least in principle, the next level of perfection, when in a cylindrical network all atoms are equivalently tied to the neighbors, and no ''weak spot'' is apparent. This intrinsic uniformity, together with the known strength of carbon bonds, must lead to extreme resistance to mechanical tension, as has been anticipated all along (4, 5). On the other hand, establishing the quantitative level of breaking strain and identifying the details of atomic-scale rearrangements responsible for initial yield turned out to be elusive both experimentally and theoretically.In recent years, much progress has been made in elucidating the atomic mechanisms of CNT failure. In experiment, refined loading techniques often based on atomic force microscopy and combined with electron microscopic imaging allowed one to measure the breaking-strain level and observe the overall failure patterns (6-10). The reported experimental values of breaking strain ranged within 2-19% because of variability of the samples and measurement conditions (6-8). In theory, bond rotation [that is a concerted movement of two atoms, known in chemistry as Stone-Wales isomerization (SW) (11)] has been recognized as a key step in mechanical relaxation (12)(13)(14). It leads to the lowest energy defect, a cluster of two pentagons and heptagons, 5͞7͞ 7͞5. In the lattice of hexagons (the nanotube body) it represents a dislocation dipole, which explains its formation under high tension. This particular relaxation step is most favorable thermodynamically, but because of the high barrier of SW (15-17) it requires thermal activation. In contrast, another mechanism recently analyzed (18) needs no thermal activation but...

show abstract

“…33 The energy elevation is quite small, only~6.4 meV/atom, in line with previous theoretical calculations. 33,34 The small energy difference can be understood from the bonding configuration, that is, the number of tetrahedral bonds per atom remains unchanged. By performing quantum chemistry bonding analysis using the crystal orbital overlap population (COOP) 29,35 method, we have quantified the bonding contributions (blue curves in Figure 4).…”

Section: Hrtem Characterization Of the Cat Processmentioning

confidence: 99%

In situ TEM study of deformation-induced crystalline-to-amorphous transition in silicon

et al. 2016

View full text Add to dashboard Cite

The mechanism responsible for deformation-induced crystalline-to-amorphous transition (CAT) in silicon is still under considerable debate, owing to the absence of direct experimental evidence. Here we have devised a novel core/shell configuration to impose confinement on the sample to circumvent early cracking during uniaxial compression of submicron-sized Si pillars. This has enabled large plastic deformation and in situ monitoring of the CAT process inside a transmission electron microscope. We demonstrate that diamond cubic Si transforms into amorphous silicon through slip-mediated generation and storage of stacking faults (SFs), without involving any intermediate crystalline phases. By employing density functional theory simulations, we find that energetically unfavorable single-layer SFs create very strong antibonding interactions, which trigger the subsequent structural rearrangements. Our findings thus resolve the interrelationship between plastic deformation and amorphization in silicon, and shed light on the mechanism underlying deformation-induced CAT in general.

show abstract

Free energies of generalized stacking faults in Si and implications for the brittle-ductile transition

Cited by 166 publications

References 17 publications

Estimates from atomic models of tension-shear coupling in dislocation nucleation from a crack tip

Estimates from atomic models of tension-shear coupling in dislocation nucleation from a crack tip

Symmetry-, time-, and temperature-dependent strength of carbon nanotubes

In situ TEM study of deformation-induced crystalline-to-amorphous transition in silicon

Contact Info

Product

Resources

About