Atomistic modeling of the coupling between electric field and bulk plastic deformation in fcc metals

A notable impediment in maintaining high electric fields in accelerating structures is the onset of breakdown events. While bulk mechanical properties of the materials are known to significantly affect the breakdown propensity, the underlying mechanisms coupling electric fields to bulk plastic deformation in experimentally relevant thermal and electrical loading conditions remain to be identified at the atomic scale. We present the results of large-scale molecular dynamics simulations (MD) to investigate a possible mode of coupling. Specifically, we consider the activation of Frank-Read sources, which leads to dislocation multiplication, under the combined action of biaxial thermal stresses caused by rf losses and surface tractions induced by electric fields. With the help of a charge-equilibration formalism incorporated in a classical MD model, we show that the creation of surface slipped steps can couple to electric fields in a way that enhances local stresses and facilitates further activation of existing dislocation sources. We quantify the possible enhancement of surface slip under typical microstructural parameters of annealed copper. We show that such a mechanism could potentially promote breakdown precursor formation at very high electric fields, but that its impact is limited at fields typical of the operation of accelerator structures. In this regime, thermal stresses caused by rf losses are expected to be the main drivers of plastic deformation.

Figure 1

Activation of Frank-Read sources in fcc Cu where an initially undeformed edge dislocation (a) starts to bow out (b) under sufficient external stress. The emitted dislocation loop then approaches the free surface (c) eventually exiting (d) to leave behind a surface step (e). Resolved shear stress required to maintain the activation (f) should be above the critical threshold (black dashed line) which might not be the case always (e.g., see the stresses for constant volume simulations depicted by the blue curve).

Figure 2

Surface traction components under an electric field of $10\mathrm{GV}/\mathrm{m}$ acting normal to the surface for a structure with slip step height of 18 b. The shaded region highlights the sharp change in traction magnitude due to the presence of slip step (magnified atomistic configuration inset).

Figure 3

Effect of surface slip height growth on the field-enhanced peak traction values normalized by $E^2$. Circles refer to QEq-MD simulation results, whereas the dotted lines indicate fitting to Eq. (1). Continuum large-step limits are depicted by solid lines.

Figure 4

Comparison of RSS in bulk material due to step height growth (4b, 8b and 18b from left to right) as obtained from molecular dynamics (a–c) and linear elasticity solution (d–f) under an E-field of $10\mathrm{GV}/\mathrm{m}$. The black solid line indicates a length of 10 nm.

Figure 5

Schematic depicting plastic strain relaxation after a dislocation loop emitted by a FR source located at a distance $h$ from the surface exits free surface creating a surface step.

Figure 6

Stress (RSS) enhancement and relaxation for steps A (a) and B (b) for FR sources located at a depth of 20 nm from the surface as computed for typical OFHC Cu microstructural parameters listed in Table 2. Solid lines correspond to constant volume cases when thermal stresses can relax, while dashed lines represent growth of RSS when at a fixed thermal stress for heating at $80°\mathrm{C}$.

Figure 7

Surface slip height enhancement due to emissions from FR sources located inside the bulk material under an E field of $10\mathrm{GV}/\mathrm{m}$ and heating of $80°\mathrm{C}$.

Figure 8

Resolved shear stress evolution at typical breakdown fields reported in experiments [8]. Thermal stresses are considered for $20.6°\mathrm{C}$ heating under similar material parameters used in Fig 6. Solid lines correspond to relaxation in thermal stresses whereas dashed lines indicate fixed thermal stresses. As the step-induced enhancement is almost negligible in this regime of E fields, RSS in both types of steps evolves identically.