First-principles study of Mn, Al and C distribution and their effect on stacking fault energies in fcc Fe
Introduction
The deformation behavior of high manganese steels such as Hadfield steel has been a subject of intensive investigations for many years [1], [2], [3], [4], [5]. Recent developments in steels have resulted in a second generation of high strength steels with austenitic microstructures, which show enhanced plasticity and high strength along with excellent formability [6], [7], [8]. The extraordinary mechanical properties of austenitic steels with a high Mn content in the range from 15% up to 30 at.% are related to the twining-induced plasticity (TWIP) mechanism, which provides a continuous strengthening process.
The active deformation mechanism associated with enhanced plasticity and high strength in high manganese austenitic alloys is controlled by the intrinsic stacking fault energy (SFE) [7], [8], [9], [10], [11], [12], [13], [14]. This stacking fault can be produced by dissociation of perfect dislocations into the Shockley partials with a Burgers vector of 1/6〈1 1 2〉 that creates a hexagonal close packed region, which is equivalent to the crystal structure of ε-martensite. The stacking fault energy plays an important role in the formation of ε-martensite and deformation twins – the observation of either transformation induced plasticity or twinning induced plasticity depends on the SFE. When the SFE increases, the plasticity deformation mechanism changes from martensite transformation to mechanical twinning and then to dislocation glide. The deformation induced ε-martensite occurs for the SFE below 18 mJ/m2, whereas the deformation twinning may occur for the SFE between 15 and 35 mJ/m2. Twinning is delayed to a higher critical shear stress, or a greater strain, as the SFE is increased and the planar slip forming microbands dominates at a higher SFE (90 mJ/m2) as evident in austenitic Fe–28Mn–10Al–1C steel [14]. Because of the low SFE in these austenitic alloys, the twinning and the ε-martensite formation are competitive and multiple deformation mechanisms may be realized as well.
Substitutional and interstitial impurities may strongly affect the SFE and the plasticity mechanism [15], [16], [17], [18], [19]. The effect of the solute on the SFE is rather complex and depends on the solute concentration, temperature, grain size, magnetism and chemical interactions. The intrinsic stacking fault energy, γISF, is usually estimated from the thermodynamic model as γISF = 2ρΔGγ−ε + 2σγ/ε, where ΔGγ-ε is the difference in the Gibbs free energies of γ-austenite and ε-martensite phases, which are estimated from the regular solution model for multicomponent systems; ρ is the atomic density on the (1 1 1) plane, and σγ/ε is the interfacial energy between the γ and ε phases [16], [20]. Such estimations have demonstrated that carbon and aluminum strongly increase the SFE [16], [21], while the effect of manganese is more complex. A linear increase of the SFE with the manganese concentration up to 50 wt.% was obtained in [22], [23], while a parabolic dependence was predicted in [24], [25], [26] where the SFE minimum corresponded to 12 at.% [24], 15 at.% [25] and 22 at.% Mn [26]. Within the subregular solution model, the composition-dependent stacking fault energy maps were obtained for Fe–Mn–Al–C as dependent on the temperature and austenite grain size [27].
The above solution model, which is used to predict the impurity effect on ΔGγ−ε, does not adequately take into account the changes in the structure and chemical bonding caused by alloying and, therefore, does not provide correctly the atomistic origin of the SFE dependence on the impurity. For this, first-principles methods, which have been successfully used to study the structural and magnetic phase stability of Fe [28], [29], [30], Fe–Mn [31], [32], Fe–C [33], [34], and Fe–Mn–C [36], [37], were recently employed to calculate the SFE in γ–Fe [38], [39], Fe–N [40], Fe–Mn [39], [40], [41], Fe–C [42], and in Fe–Cr–Ni, Fe–Cr–Ni–Mn, Fe–Cr–Ni–Nb alloys [43], [44]. Although the first-principles approaches give the results at zero temperature, they provide an important atomistic information on the changes in the SFE with alloying. The ab initio calculations [38], [39], [40], [41] predict the SFE in fcc Fe to be negative, in agreement with the thermodynamic instability of austenite against ε-martensite. Nitrogen and carbon were found to increase the SFE by 65–80 mJ/m2 per 1 at.% [40], [42], while manganese decreases the SFE at a rate of 3 mJ/m2 per 1 at.% Mn up to the concentration of 8 at.% Mn [40]. Modeling of the manganese effect in austenitic Fe1−xMnx alloys using the ordered structures of Fe75Mn25, Fe50Mn50 and Fe25Mn75, predicts a monotonic increase in the SFE and a thermodynamic instability of the austenite phase up to 100 at.% Mn [39]. This result contradicts the experimental and theoretical findings on the austenite to ε-martensite transformation in Fe1−xMnx. The recent calculations for chemically disordered Fe–Mn alloy [41] demonstrated that the non-linear dependence of the SFE with a minimum at 20 at.% Mn and 40 at.% Mn may be reproduced for nonmagnetic and paramagnetic states, respectively. However, these calculations (for ordered and nonmagnetic, for disordered and nonmagnetic, as well as for disordered and paramagnetic alloys) predict the SFE to be lower than −150 mJ/m2 for all Mn concentrations. As was noted earlier [41], this discrepancy may appear due to the thermal effects, crystal defects, local deformations as well as due to interstitial impurities (e.g. C and N), which are always present in steel.
It should be noted that manganese and carbon may form Mn–C clusters in Fe–Mn–C alloys and significantly retard the dislocation motion [45], [46]. Aluminum is an effective alloying element to raise the SFE and to suppress the formation of deformation twins, but these alloys still maintain high work hardening rates [6], [7], [8], [9] that was associated with the planar slip and the formation of high dislocation density sheets [8]. There is strong evidence [5] that short range order (SRO) is important in the work hardening behavior prior to the formation of twins. The influence of short range order and formation of Mn–C clusters on the SFE in Fe–Mn–Al–C alloys has not been studied using either thermodynamic models or ab initio methods. Since the interaction between the solute and the interstitial atoms plays an important role in mechanical properties, the knowledge of impurity distribution is critical for understanding the microscopic origin of the impurity effect.
In this paper, we used the ab initio approach to study the distribution of carbon with respect to the substitutional manganese and aluminum, as well as the location of these impurities with respect to each other in nonmagnetic fcc Fe. The local crystal distortions and variation in lattice parameters were accurately determined via the atomic force and total energy minimization. We calculated the generalized stacking fault energies (GSFE) which represent the energies for sliding of atomic planes, and studied the influence of manganese, carbon and aluminum on the GSFE by considering their different positions and concentrations at stacking faults.
Section snippets
Computational method
We employed the Vienna ab initio simulation package (VASP) with the projector augmented waves (PAW) for pseudopotentials [47], [48] and the generalized gradient approximation (GGA) [49] for the exchange–correlation functional. Simulation of impurity distribution in fcc Fe was performed for 32-atom supercells, where one substituted impurity corresponds to the 3 at.% concentration. As has been shown previously [35], [36], [37], [50], a 32-atom supercell is large enough to predict correctly the
Distribution of interstitial carbon and substitutional Mn and Al impurities in austenitic Fe–Mn–Al–C alloys
For nonmagnetic (NM) fcc Fe, we obtained the optimized lattice parameter of 3.456 Å, which is in accord with the previous ab initio calculations [28], [36], [50]. Interstitial octa-site carbon at 3 at.% concentration (Fe32C) slightly increases the lattice parameter up to 3.472 Å that is in good agreement with the experimental measurement of the fcc lattice parameter with varying carbon content [57]. The nearest Fe atoms move outward from carbon and the Fe–C distance increases from 1.73 Å to 1.87 Å
Conclusions
The ab initio calculations were performed to find the preferable distribution of C, Mn and Al impurities in a fcc Fe matrix. We predict that carbon atoms repel each other and avoid the occupation of the nearest interstitial sites. Carbon demonstrates attractive interaction with manganese and may form Mn–C pairs. Aluminum prefers to substitute for the second nearest iron atoms with respect to carbon and the predicted distribution of Al and C in fcc Fe corresponds to the ordered structure of κ
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