Nanostructures in silicon (Si) induced by phase transformations have been investigated during the past 50 years. Performances of nanostructures are improved compared to that of bulk counterparts. Nevertheless, the confinement and loading conditions are insufficient to machine and fabricate high-performance devices. As a consequence, nanostructures fabricated by nanoscale deformation at loading speeds of m/s have not been demonstrated yet. In this study, grinding or scratching at a speed of 40.2 m/s was performed on a custom-made setup by an especially designed diamond tip (calculated stress under the diamond tip in the order of 5.11 GPa). This leads to a novel approach for the fabrication of nanostructures by nanoscale deformation at loading speeds of m/s. A new deformation-induced nanostructure was observed by transmission electron microscopy (TEM), consisting of an amorphous phase, a new tetragonal phase, slip bands, twinning superlattices, and a single crystal. The formation mechanism of the new phase was elucidated by ab initio simulations at shear stress of about 2.16 GPa. This approach opens a new route for the fabrication of nanostructures by nanoscale deformation at speeds of m/s. Our findings provide new insights for potential applications in transistors, integrated circuits, diodes, solar cells, and energy storage systems.

New Deformation-Induced Nanostructure in Silicon.

Effect of lattice distortion on solid solution strengthening of BCC high-entropy alloys

The deformation behavior of Ti–22Al–25Nb alloy at elevated temperatures and different stain rates was investigated using uniaxial tensile test. It was found that the tension was accompanied with the effect of hardening and softening, under which the stress–strain curve was characterized by a rise to a peak followed by a nearly linear drop in flow stress. The peak stress was strongly dependent on the temperature and strain rate. The underlying mechanism was clarified in terms of dislocation dynamics. Work hardening and strain rate hardening both contributed to the hardening mechanism, and the softening mode was dominated by dynamic recovery. The effect of work hardening was completely neutralized by dynamic recovery. Owing to the strain rate hardening, the alloy exhibited certain degree of superplasticity. The further drop in flow stress after the peak was due to the rise in temperature, which originated from the heat generated during deformation. The deformation mechanism was dominated by dislocation slip and climb. The misorientation distribution between β/B2 and α2 phase scarcely changed, implying a harmonious deformation of the two phases.

Tensile deformation behavior of Ti–22Al–25Nb alloy at elevated temperatures

Nanocrystalline (NC) body-centered cubic (bcc) metals behave very differently from how NC metals with other crystal structures behave. Their strain rate sensitivity decreases with decreasing grain size, which is an observation that has not been well understood. Here, we report a significant effect of grain size on the deformation mechanism of NC bcc Mo. With decreasing grain size, the density of mixed and edge dislocations increases, while the density of screw dislocations decreases. When the grains become very small, the overall dislocation density decreases with decreasing grain size. These observations provide a logical explanation for the observed effect of grain size on strain rate sensitivity.

https://www.tandfonline.com/doi/pdf/10.1080/21663831.2012.739580

Grain Size Effect on Deformation Mechanisms of Nanocrystalline bcc Metals

By using the first-principles calculations based on the density-functional theory (DFT), we study the stability and the nonlinear elasticity of two-dimensional (2D) hexagonal structures of Si and Ge. The reproduced structure optimization and phonon–dispersion curves demonstrate that Si and Ge can form stable 2D hexagonal lattices with low-buckled structures, and provide a good agreement with the previous DFT calculations. The second- and third-order elastic constants are calculated by using the method of homogeneous deformation. The present results of the linear elastic moduli agree well with the previous results. In comparison with the linear approach, the nonlinear effects really matter while strain is larger than approximately 3.5%. The force–displacement behaviors and the breaking strength of 2D hexagonal Si and Ge are discussed using the nonlinear stress–strain relationship. By using the available results of graphene, we reasonably demonstrate that the radius of the atom increases and breaking strength of this element decreases for 2D hexagonal structures of group IV-elements.

The stability and the nonlinear elasticity of 2D hexagonal structures of Si and Ge from first-principles calculations☆

The dislocation width and Peierls barrier and stress have been calculated by the improved Peierls–Nabarro (PN) theory for silicon. In order to investigate the discreteness correction of a complex lattice quantitatively, a simple dynamics model has been used in which interaction attributed to a variation of bond length and angle has been considered. The results show that the dislocation core and mobility will be corrected significantly by the discrete effect. Another improvement is considering the contribution of strain energy in evaluating the dislocation energy. When a dislocation moves, both strain and misfit energies change periodically. Their amplitudes are of the same order, but phases are opposite. Because of the opposite phases, the misfit and strain energies cancel each other and the resulting Peierls barrier is much smaller than that given by the misfit energy conventionally. Due to competition between the misfit and strain energies, a metastable state appears separately for glide 90° and shuffle screw dislocations. In addition, from the total energy calculation it is found that besides the width of dislocation, the core of a free stable dislocation may be different according to where the core center is located. The exact position of the core center can be directly verified by numerical simulation, and provides a new prediction that can be used to verify the validity of PN theory. It is interesting that after considering discrete correction the Peierls stress for glide dislocation coincides with the critical stress at low temperature, and the Peierls stress for shuffle dislocation coincides with the critical stress at high temperature. The physical implication of the results is discussed.

https://iopscience.iop.org/article/10.1088/0953-8984/22/5/055801/pdf

Theoretical calculation of the dislocation width and Peierls barrier and stress for semiconductor silicon

The Peierls stress of the moving screw dislocation with a planar and non-dissociated core structure in Ta has been calculated. The elastic strain energy which is associated with the discrete effect of the lattice and ignored in classical Peierls–Nabarro (P–N) theory has been taken into account in calculating the Peierls stress, and it can make the Peierls stress become smaller. The Peierls stress we obtain is very close to the experimental data. As shown in the numerical calculations and atomistic simulations, the core structure of the screw dislocation undergoes significant changes under the explicit stress before the screw dislocation moves. Moreover, the mechanism of the screw dislocation is revealed by our results and the experimental data that the screw dislocation retracts its extension in three {110} planes and transforms its dissociated core structure into a planar configuration. Therefore, the core structure of the moving screw dislocation in Ta is proposed to be planar.

https://iopscience.iop.org/article/10.1088/0953-8984/21/34/345401/pdf

The Peierls stress of the moving \frac {1}{2}\langle 111\rangle \{110\} screw dislocation in Ta

By using the modified Peierls–Nabarro (P–N) model in which the lattice discrete effect is taken into account, the core structure and the Peierls stress of the ½〈1 1 1〉{1 1 0} edge dislocation in molybdenum (Mo) have been investigated in the anisotropic elasticity approximation. The coefficient of the lattice discrete correction and the energy coefficient are all calculated in the anisotropic elasticity approximation. By considering the lattice discrete effect, the core width obtained from the modified P–N model is much wider than the results obtained from the P–N model. Because the Peierls stress of the ½〈1 1 1〉{1 1 0} edge dislocation in Mo moving with the rigid mechanism is smaller than that with the kink mechanism, therefore, through investigating the Peierls stress of the edge dislocation we obtained with the atomistic simulations, it can be indicated that when the external stress is loaded on the ½〈1 1 1〉{1 1 0} edge dislocation in Mo, the dislocation may move with the rigid mechanism rather than the kink mechanism or other mechanisms.

The theoretical investigations of the core structure and the Peierls stress of the ½〈1 1 1〉{1 1 0} edge dislocation in Mo

The core structure of the edge dislocations in body-centered cubic (bcc) crystal Fe has been investigated by the modified Peierls–Nabarro (P–N) equation which includes the discrete correction. An analytical expression of the dislocation solution of the dislocation equation has been obtained by using the truncation approximation. It is found that the dislocation width is nearly doubled by the discrete effects and the agreement between the theoretical prediction and the numerical simulation is improved remarkably.

The discrete correction of the core structure for the \langle 100\rangle \{010\} edge dislocation in bcc Fe

Based on the tight-binding model of generalized honeycomb lattice on cylinder, the band structure changes induced by axial strain and twist are present for the signal-wall carbon nanotubes (SWCNTs). The deformation-modified hopping amplitudes are dominated by the metric tensor and the curvature tensor. The analytical relations of the energy bands and the band gaps to both armchair and zigzag tubes are obtained. For the chiral nanotubes, we have successfully investigated the deformation-induced changes in band structure of individual nanotubes of known chiral index. The results in our model, returning to the undeformed tubes, are in good agreement with the previous experiments and theories.

Ruiping Liu

Papers

Theoretical calculation of the dislocation width and Peierls barrier and stress for semiconductor silicon

The Peierls stress of the moving \frac {1}{2}\langle 111\rangle \{110\} screw dislocation in Ta

The theoretical investigations of the core structure and the Peierls stress of the ½〈1 1 1〉{1 1 0} edge dislocation in Mo

The discrete correction of the core structure for the \langle 100\rangle \{010\} edge dislocation in bcc Fe

Axial strain and twist-induced changes in the electronic structure of carbon nanotubes