Strain Fields And Crystallographic Characteristics Of Interstitial Dislocation Loops of Various Geometry In BCC Iron

Abstract

The formation energy, the relaxation volume, the dipole-force tensor, the self strain tensor and strain fields of interstitial dislocation loops in bcc iron (clusters of self interstitial atoms) have been calculated by molecular statics. Hexagonal and square dislocation loops of different types with different Burgers vectors, directions of dislocation segments and habit planes containing up to ~2500 self-interstitials have been considered. Analytical expressions describing size dependence of the formation energy, the relaxation volume and the self strain tensor for the loops stated have been obtained. The most energetically favorable loops are hexagonal loops with Burgers vector a/2<111> and habit plane {11x}, where x takes values in the range from 0 to 1 depending on the loop size. The formation energy of a<100> loops with <100> and <110> dislocation segments is ~14% and 23% greater than that of hexagonal a/2<111> loops at N > 500, respectively. The analysis of the formation energies of a/2<111> and a<100> loops demonstrated that the nucleation of an a<100> loop by joining of two a/2<111> loops is possible when the total number of constituent self-interstitials in these loops is larger than 13.

Defect model for the dependence of breakdown rate on external electric fields

“…The formation entropy can be divided into a vibrational and configurational part, S f;tot ¼ S f;vib þ S f;con . Minimization of the configurational entropy [26] leads to an expression for the defect concentration [29][30][31][32] c ¼ ge…”

“…Such tips could, at least in principle, grow by emission of interstitial-type prismatic dislocation loops (platelets of extra atoms in the lattice) [37][38][39] or dislocation loops with the Burgers vector in the glide plane [24,37,40] in the similar size range. Large interstitial-like dislocation loops in metals are known to have a relaxation volume of % 1 per atom in the loop [31,40]. Assuming circular interstitial-like dislocation loops of one atom layer thickness, we can now roughly estimate the radius of one loop from r 2 d ¼ ÁV, where d is the thickness of one atomic layer.…”

Exchange interaction function for spin-lattice coupling in bcc iron

“…1 For example, the softening of tetragonal shear modulus CЈ = 1 2 ͑C 11 − C 12 ͒ at elevated temperature [2][3][4] and the resulting change in dominant orientation of dislocation loops from ͗110͘ to ͗100͘ at around 500°C, are believed to be results of the magnetic effect. [5][6][7] Using Monte Carlo simulation and magnetic cluster expansion model, Lavrentiev et al 8 also showed that magnetic fluctuations are responsible for the bcc-fcc phase transition of iron at 1184 K, which is slightly higher than the Curie temperature T C at 1043 K.…”