Solid solution softening and hardening in binary BCC alloys

Abstract

Solute-dislocation interaction energies are calculated using Density Functional Theory and the 2-D lattice Greens function approach for Al, Ti, Cr, Fe, Zr, Nb, Mo, Ru, Hf, Ta, W, Re solutes in BCC Nb, Ta, Mo, and W. The predictions are then used in an extension of the Rao-Suzuki model to analyze the experimentally observed solid solution strengthening and softening in Nb-X, Fe-X, Ta-X, Mo-X and W-X crystals, X= Mo, W, Ta, Si or Re. DFT predictions for the solute dislocation interaction energies for Fe-Si, taken from the literature are also analyzed. The original Rao-Suzuki model considers kink migration controlled mobility of screw dislocations in body-centered cubic (BCC) structures and is valid for high solute concentrations (>5 at%) as well as above a critical temperature. Here, we extend the Rao-Suzuki model to include kink-pair nucleation statistics in the presence of solutes which is expected to be the rate limiting process at low temperatures (<0.2Tmelt). Such an extension should be valid up to low concentration of solutes as well as fairly low temperatures. The key parameters required for the model are solute – ½[111] screw dislocation interaction energies in pure Nb, Ta, Mo or W. These parameters were derived in this paper using first principles calculations. Using the calculated interaction energies, the model satisfactorily reproduces experimentally observed solution strengthening data in Nb-Mo, Nb-W, Nb-Re crystals at temperatures from 77 to 600K, for solute concentrations in the range 8.5 to 19 at% for Mo, 6 to 15 at.% for W and 5 to 9 at.% for Re. Similar agreement is found for strengthening/softening data for Ta-W, Ta-Re, Ta-Nb, Fe-Si, Mo-Re and W-Re crystals in the temperature range 77 – 600K. We also explore sensitivity of these predictions to the variation in the solute-dislocation energies. In Ta-W, a 10% variation (±0.015 eV) produces a modest change in solution hardening, which is within experimental error. The refined Rao-Suzuki model can be used in designing high strength, multi-component BCC alloys for high temperature applications.