Structure, energetics, and mechanical stability of Fe-Cu bcc alloys from first-principles calculations

Abstract

Atomic volumes, magnetic moments, mixing energies, and the elastic properties of bcc Fe 1−x Cu x solid solutions are studied by ab initio calculations based on the cluster expansion framework. For the calculation of concentration-dependent elastic moduli in disordered solid solutions, we introduce a generalization of the cluster expansion technique that is designed to handle tensorial quantities in high-symmetry phases. Calculated mixing energies, atomic volumes, and magnetic moments are found to be in good agreement with available measurements for metastable alloys prepared through nonequilibrium processing techniques. Additionally, the predicted variations of the bulk modulus and shear moduli C 44 and CЈ with respect to copper concentration are calculated for the disordered bcc phase. While the bulk modulus and C 44 are positive for all concentrations, CЈ is predicted to be positive only for Cu concentration less than 50 atomic %, and negative otherwise. Our results thus indicate that the mechanical instability of bcc Cu persists over a wide range of compositions. The implications of the present results are discussed in relation to the observed metastability of bcc Fe-Cu alloys, and the strengthening mechanism of nanoscale bcc precipitates in an ␣-Fe matrix.

Does aluminum play well with others? Intrinsic Al-A alloying behavior in 211/312 MAX phases

“…Once the cluster expansion is found-the convergence of the expansion is highly system-dependent-the energy of any configuration can be calculated by simply applying Equation (1). Once the ECIs have been determined, the energy of an equivalent random configuration can be obtained from [38]:…”

Strength Recovery in a High-Strength Steel During Multiple Weld Thermal Simulations

“…Many factors, such as misfit strengthening, chemical strengthening, modulus difference strengthening, and dislocation coreprecipitate interaction strengthening contribute to the overall Cu precipitate strengthening in steels. [29] The incorrect equation used to describe modulus difference strengthening by Fine and Isheim [29] has been pointed out by Liu et al [30] Since modulus strengthening based upon the model of Russell and Brown [31] plays the most important role among all the factors, the current focus is on evaluating the component of Cu precipitation strengthening provided by modulus strengthening. The Russell-Brown model assumes that the modulus strengthening effect is due to the relative difference in dislocation energy between the matrix and Cu precipitates as a result of the modulus difference, as a dislocation passes from the matrix through the Cu precipitate and back into the matrix.…”

High-Strength Low-Carbon Ferritic Steel Containing Cu-Fe-Ni-Al-Mn Precipitates

“…We note that SANS provides precipitate compositions based on questionable assumptions, [61] whereas the APT results are model independent. Additionally, the recent first-principles calculations by Liu et al [55] finds that the shear modulus relevant for dislocation glide varies at absolute 0 K from a negative value of 20 GPa for pure bcc Cu to a positive value of 78 GPa for bcc Fe, with a zero value for compositions near 50 at. pct Fe and 50 at.…”

“…[50] The source of this controversy is possibly a result of a combination of a number of precipitation strengthening mechanisms include lattice mismatch, modulus mismatch, and chemical hardening. [51][52][53][54][55][56][57] Also, when the dislocation enters the precipitate two partial dislocations are created that combine when the dislocation leaves the precipitate. Energy must be supplied to move the dislocation out of the precipitate.…”