Molecular Dynamics of QED Stiffening in Nanowires

Oct. 25, 2012 - PRLog -- Background

Over the past decade, the observation of significant stiffening of nanowires (NW’s) has been a subject of great interest. Numerous mechanisms [1] have been proposed including: high surface-to-volume ratio, surface stresses, bulk nonlinear elasticity, surface stiffness, surface tension, surface reconstruction, surface strain and stress, and skin depth energy pinning. However, the stiffening of NW’s is not based on direct measurements of material properties, but rather inferred from indirect measurements of increased resistance to buckling, enhanced resonant frequencies, and the like. In contrast, the traditional uniaxial tensile test of a nanowire gives mechanical properties directly, but is difficult to perform because of the nanoscopic size of the tensile specimen.

Nevertheless, Young’s modulus and yield stress of fivefold twinned silver NW’s was recently measured [2] in tensile tests and found to show stiffening consistent with indirect measurements, the stiffening mechanism thought to be the high surface-to-volume ratio in combination with the annihilation of dislocations at free surfaces and enhanced strain hardening from fivefold twinning. However, like other stiffening mechanisms proposed to date, the quantitative basis in linking dislocations and strain hardening to mechanical properties, say enhanced Young’s modulus, is lacking.  Moreover, dislocations and strain hardening find basis in classical physics contrary to the fact stiffening is not observed at the macroscale, but rather only observed in < 100 nm diameter NW’s.

What this means is only the size effect of QM may explain the stiffening of NW’s.  To wit, QED radiation is induced in NW’s from absorbed EM energy that under the TIR confinement creates photons within the wire instead of increasing the NW temperature. QM stands for quantum mechanics, QED for quantum electrodynamics, EM for electromagnetic, and TIR for total internal reflection. QED radiation relies on Planck’s QM given by the Einstein-Hopf relation for the harmonic oscillator that requires the heat capacity of the atoms in nanostructures to vanish. See http://www.prlog.org/11966118-stiffening-of-nanowires-by-...  

Problem

Molecular dynamics (MD) simulations are required to quantify the link between the size effect of QM and the stiffening of NW’s. However, MD relies on classical physics that allows the atoms in NW’s to have heat capacity contrary to QM. Standard MD programs are therefore not applicable and modifications are required to be consistent with QM.  

Simulations

MD modified for QM was performed for a simple square cross-section having sides w and length L as illustrated by the VMD graphics in the thumbnail.  The silver NW was modeled in the FCC configuration with an atomic spacing of 4.09 A comprising 550 silver atoms having sides w = 8.18 A and length L = 87.9 A interacting with each other through the Lennard-Jones potentials. The NW model was equilibrated in the stress free condition by holding one end fixed and the other end free for 5000 iterations with 1-5 fs time steps.  The NW was displacement loaded by 0.15 to 0.5 A at the free end with convergence found within 5000 iterations. During equilibration and loading, the QM requirement of vanishing heat capacity was simulated by holding the temperature of the atoms < 0.01 K with the Nose-Hoover thermostat.

In the MD simulation, the energy of the QED induced electrostatic repulsion of atoms was taken to be equal to their thermal kT energy.  It was found that only about 30% of the full kT energy produced the enhancement in the Young’s modulus of the NW, the remainder lost to the surroundings. However, NW stiffening need not be limited to thermal loading and may include hysteresis heating during the loading and unloading that accompanies strain hardening.

A complete description of the MD simulation is given in  http://www.nanoqed.org, at “Molecular Dynamics of Stiffening in Nanowires,” 2012.
   
Conclusions

1.  In tensile tests of silver NW’s, QED induced radiation is created by EM energy from the temperature of the grips that hold the NW in combination with the mechanical heat associated with strain hardening under repeated loading and unloading cycles. The QED photons charge the silver atoms by the photoelectric effect to induce electrostatic repulsion placing the NW under high hydrostatic tension.

2.  The shape of the fracture surface supports the notion that once failure starts at a surface defect, the increasing hydrostatic tension is sufficiently high to cause the emission of silver atoms by Coulomb explosion.

3. The Young’s modulus of NW’s is enhanced above bulk because the hydrostatic tension pressure reduces the longitudinal strain by the Poisson effect consistent with classical elasticity.  

4.  MD solutions of 8 A square NW show the QED induced charge repulsion of silver atoms give Young’s moduli of about 45x10⁶ psi; whereas, the data [2] shows  26x10⁶ for the 34 nm NW.  MD solutions of the larger 34 nm NW’s are far more computationally intensive and require computing power and could not be performed with the PC used in this study.

5.  The QED induced stiffening of NW’s in tensile tests occurs anytime EM energy is absorbed including thermal energy from grips and mechanical heat from repeated loading and unloading. Indeed, electron beam irradiation [3] giving a 40% enhancement in Young’s modulus of zinc tin oxide NW’s is consistent with QED induced stiffening.    

6. QM stiffening of nanowires may be verified if raising the temperature of cantilever or simple supports enhances Young’s moduli. Alternatively, by applying a voltage across the tensile specimen, the Young’s moduli should be significantly enhanced by the accompanying Joule heating.

References

[1] X. J. Lu, et al., “Size-induced elastic stiffening of ZnO nanostructures: Skin-depth energy pinning,” App. Phys. Lett., 94, 131902, 2009.
[2] Y. Zhu, et al., “Size effects on elasticity, yielding, and fracture of silver nanowires: In situ experiments,” Phys. Rev. B, 85, 045443, 2012.
[3] J. Zang, et al., “Electron Beam Irradiation Stiffens Zinc Tin Oxide Nanowires,” Nano Lett., 11, pp. 4885–4889, 2011.