Oblate Spheroid Excitation Theory: A Unified, Lattice-Free Foundation for Plastic Deformation from Which Dislocations Emerge as Collective Excitations

Abstract

Dislocation theory has underpinned crystal plasticity for a century, yet its lattice-dependent definition cannot describe plastic flow in grain boundaries, glasses, ceramics, or nanocrystals near the glass transition, where no periodic lattice exists. We propose the Oblate Spheroid Excitation Theory (OSET): the elementary carrier of plastic deformation, in any solid, is a shear-eigenstrained oblate spheroid, the oblate-spheroidal transformation zone (OSTZ), treated within Eshelby's inclusion theory. The OSTZ requires no lattice and has a finite, non-singular, intrinsically thermally activated energy and stress fields. Three results are proved: a single OSTZ produces a non-singular elastic dipole, not a dislocation's singular field; a co-planar chain of N OSTZs is mathematically identical to a Peierls-Nabarro dislocation, core width and Burgers vector fixed by OSTZ geometry; and a genuine dislocation nucleates only once the chain reaches a host-lattice-set critical length. Dislocations emerge as a collective, large-$N$ limit of OSET rather than an assumed entity, and the theoretical shear strength, Peierls stress, core energy, Frank-Read critical stress, and stacking-fault energy follow as derived, parameter-free quantities. OSET is validated against grain-boundary-sliding data, independent literature spanning metals, ceramics, and bulk metallic glasses, and a recent 41-system compilation, reproducing the fitted dilatational and shear eigenstrains to within 2% and 15%, respectively. Because classical dislocation theory emerges from OSET but OSET does not require dislocations, it provides, in our view, a more fundamental, broadly applicable foundation for plastic deformation across material classes.