High-entropy alloys (HEAs) are multi-component alloys with non-diluted solute concentrations that retain their single-phase structure. Various high-entropy alloys have impressive mechanical properties such as high yield strength at room temperature, high ultimate strength, high ductility and/or high fracture toughness. With the increasing interest in the metallurgy of such complex alloys, the study of intensification mechanisms has become a research topic. A general theoretical model has been proposed to predict the yield strength of FCC and BCC HEAs as a function of temperature and strain rate. This theory postulates that solute-dislocation interactions drive dislocations into wavy shapes in order to find locally favorable fluctuations in the local solute arrangement, fixing dislocation segments in these local environments. Then, a combination of analytical shear stress and temperature is required to generate thermally activated dislocation gliding and volumetric plastic flow. The theory of stochastic FCC and BCC alloys has shown good consistency across many different alloy systems and has been simplified to provide analytical formulas that can be easily applied to or designed for new alloys. Recently, a theory of strengthening of multi-component non-diluted alloys with short-range ordered (SRO) has been proposed. The theory predicts that, in addition to the well-known thermal strengthening, SRO also has a significant effect on solute-dislocation interactions, which can reduce or increase strength relative to random alloys.
Academics from the Swiss Federal Institute of Technology in Lausanne have conducted elaborate atomic simulations in a binary niobium-tungsten alloy model to demonstrate that the strength of the alloy due to solute-dislocation interactions can increase or decrease, depending on the SRO, and is consistent with theoretical predictions. Specifically, in an alloy system with very small true solute-solute interactions, a fictitious solute-solute interaction is used to introduce SRO, and then the energy barrier of dislocation motion at the lower edge of various SRO levels is calculated using the bare elastic band (NEB) method. When the Warren-Cowley SRO parameter is negative (the attraction of different solutes), both the energy barrier and the alloy strength decrease. The theoretical predictions of the same system are reasonably consistent with the simulation results in terms of quantity. These results suggest that SRO has the potential to reduce strength unexpectedly, and further validate the validity of analytical theory as a tool to guide alloy design. The work was published in Acta Materialia in a research article titled "Atomistic simulations reveal strength reductions due to short-range order in alloys".
Paper Links:
https://doi.org/10.1016/j.actamat.2023.119471
Figure 1. (a) Absolute mismatch volume of binary alloys with concentrations of 50%-50% in the niobium-tantalum-tungsten alloy family calculated by EAM potential. (b) The effective pair potential Veffpq of the BCC MoNbTaW series calculated with EAM potential as a function of the effective pair potential of the normalized rth neighbor pair separation dr and the normalized neighbor pair interval.
Figure 2. (a) and (b) show the solute-edge dislocation interaction energies of the Nb solute and the W solute in the average atomic NbW alloy Un sd,i. (c) and (d) show elastic estimates of the solute-edge dislocation interaction Unsd,i for Nb and W solutes. (e) and (f) show the residual chemical Unchem interaction.
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Figure 3. The SRO parameters (mean and standard deviation of the 4 samples) between two different elements (W and Nb in this case) calculated by Monte Carlo simulations with different x(1) values as a function of normalized r-nearest neighbor pair resolution
Figure 4. Average Stress τA Direct Atom Simulations and Theoretical Predictions Using SROs with 4 Nearest Neighbor Pairs. The corresponding SRO parameters are shown in Figure 3.
Figure 5. (a) The energy distribution of the dislocations generated by the Monte Carlo simulation as a function of position as they pass through a simulation element with SRO under the condition of x(1)=1.3. The minimum and maximum values are marked in red and blue, respectively. The designators correspond to the differential configuration shown in the figure above. (b) Schematic diagram of the atomic configuration between dislocation positions 1 and 2 and NEB calculations.
Figure 6. The cumulative probability distribution of the energy barrier of dislocations sliding in the +x and -x directions, in the case of an SRO system resulting from inert x(1)=0.8. Equalizing the reinforcement effect makes the barrier in the +x direction smaller, and can be eliminated by averaging the barrier in both directions.
Figure 7. The cumulative probability distribution of the energy barrier ΔEb and the degree of SRO, characterized by the tenacity and the first adjacent WC SRO parameters. x(1)=1.0 is equivalent to a random alloy.
In this study, a detailed atomic study of the barriers to edge dislocation slip in BCC alloys with SROs was performed. One of the strengthening effects of SRO is thermal strengthening due to dislocation slip that disrupts SRO. The second strengthening effect of SRO is the intensity of thermal activation due to changes in local solute fluctuations in the presence of SRO, which affects the collective interaction energy of solute-differential discharge. We evaluated these two main effects of SRO on yield stress and, using a suitable EAM potential, compared them to a new strengthening theory for alloys with SRO. In terms of the relationship between intensity change and the degree of SRO, good agreement between theoretical analysis and simulation suggests that this new theory of reinforcement accurately captures the impact of SRO. (Text: SSC)
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