Electric current as a stabilizing thermodynamic field in metallic crystals.

Abstract

Electric current is typically associated with electromigration damage, but under steady current-carrying conditions it can also bias lattice stability. Here, in situ synchrotron X-ray diffraction and nanodiffraction show that a current density of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.5</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>3</mn></mrow></msup></math>A cm^-2 retains hexagonal η-Cu₆Sn₅ under conditions where temperature-matched thermal treatment drives the η → η' transformation. The retained η phase accommodates the current through anisotropic elastic distortion, with c-axis expansion of ~1.3% and basal-plane contraction of ~0.8%, accompanied by plane-selective dislocation rearrangement and partial lattice recovery after current removal. Grain-resolved stress/strain mapping yields a spatially averaged post-ECS principal-stress scale of ~30-40 MPa, consistent with an order-of-magnitude electron-wind estimate, while the associated elastic-energy density of 9-12 MJ m^-3 remains well below the reconstructive barrier of ~150 MJ m^-3. These results identify a phenomenological electron-wind-driven elastic accommodation regime in η-Cu₆Sn₅ under the present current density and experimental geometry, accompanied by plane-selective defect rearrangement, and are experimentally consistent with a Gibbs-like <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>-</mo><mi>σ</mi><mo>-</mo><mi>J</mi></math> description of the current-carrying steady state.