DFT-Based Elasticity and Dislocation Resistance in Crystalline Iron A Variational Framework Linking Strain Energy, Peierls Barriers, and Screw-Dislocation Mobility

This study formulates a density-functional-theory (DFT)-based framework forcalculating the elastic response and lattice resistance to dislocation motion inbody-centered-cubic (BCC) iron. The framework connects the second derivativesof the ground-state energy of a strained perfect crystal to its elastic tensor, andconnects the atomistically resolved energy landscape of a dislocation core to thePeierls barrier and the idealized stress required to initiate glide. For cubic α-Fe,the independent second-order elastic constants are C11, C12, and C44. They maybe determined from energy–strain or stress–strain derivatives after structural andnumerical convergence. For a 1/2⟨111⟩ screw dislocation, the resistance to glideis obtained from the minimum-energy path between equivalent core positions; itcannot be uniquely inferred from bulk elastic constants alone.A dimensionless Elastic–Peierls Resistance Index is proposed as a comparisondescriptor combining the Peierls barrier, a declared shear modulus scale, the Burgersvector magnitude, and the periodicity of the migration path. This index is a proposednormalization rather than a universal material constant. Its usefulness must betested against explicit DFT calculations and independent validation data. The study also emphasizes the need to specify the magnetic state, exchange- correlation approximation, strain convention, supercell geometry, and finite-size treatment. No new numerical DFT results are claimed here.