Strong temperature – Dependence of Ni -alloying influence on the stacking fault energy in austenitic stainless steel

Strong temperature – Dependence of Ni -alloying influence on the stacking fault energy in austenitic stainless steel

Scripta Materialia 178 (2020) 438–441 Contents lists available at ScienceDirect Scripta Materialia journal homepage: www.elsevier.com/locate/scripta...

626KB Sizes 0 Downloads 29 Views

Scripta Materialia 178 (2020) 438–441

Contents lists available at ScienceDirect

Scripta Materialia journal homepage: www.elsevier.com/locate/scriptamat

Strong temperature – Dependence of Ni -alloying influence on the stacking fault energy in austenitic stainless steel Zhihua Dong a,∗, Wei Li a, Guocai Chai b,c, Levente Vitos a,d,e a

Applied Materials Physics, Department of Materials Science and Engineering, KTH-Royal Institute of Technology, Stockholm SE-10044, Sweden AB Sandvik Materials Technology R&D Center, Sandviken SE-81181, Sweden c Division of Engineering Materials, Department of Management and Engineering, Linköping University, Linköping SE-58183, Sweden d Department of Physics and Astronomy, Division of Materials Theory, Uppsala University, Box 516, Uppsala SE-75121, Sweden e Research Institute for Solid State Physics and Optics, Wigner Research Center for Physics, P.O. Box 49, Budapest H-1525, Hungary b

a r t i c l e

i n f o

Article history: Received 23 August 2019 Revised 6 November 2019 Accepted 9 December 2019

Keywords: Alloying Stacking fault energy Temperature Austenitic stainless steel Ab initio calculation

a b s t r a c t Using ab initio alloy theory, we calculate the impact of Ni on the stacking fault energy in austenitic stainless steel as a function of temperature. We show that the influence of Ni strongly couples with temperature. While a positive effect on the stacking fault energy is obtained at ambient temperature, the opposite negative effect is disclosed at elevated temperatures. An important rationale behind is demonstrated to be the variation of magneto-volume coupling induced by Ni alloying. The alloy influence on the finite temperature evolution of Ni impact is evaluated for elements Cr, Mo and N.

Austenitic stainless steels, for instance the 300 series, possess excellent resistance to oxidation and corrosion, and retain a good combination of strength and ductility over a wide temperature range [1,2]. Owing to the favorable properties, some of the austenitic stainless steels have been successfully applied in energy, chemical, and construction industries, where the operating temperature varies from cryogenic to elevated temperatures for particular applications. With the demand for high efficiency and consequently low pollutant emissions in energy production as well as for high temperature applications such as fire resistant structures, steel components are proposed to operate/expose at very high temperatures (࣡10 0 0 K) out of reach of many currently available austenitic stainless steels [3–5]. Designing advanced austenitic stainless steel offering remarkable high temperature properties is thus highly desirable. The stacking fault energy (γ ) is an essential parameter closely correlating with the dislocation-mediated plasticity mechanisms of face-centered cubic (fcc) metals and alloys, which are responsible for the deformation properties such as strength, toughness and creep resistance [6–10]. At high γ values (࣡45 mJ m−2 ), dissociation of dislocations is difficult, the deformation and strain-harding process are thus mainly controlled by dislocation glide. At intermediate or low γ values, forming wide partial dislocations is ener∗

Corresponding author. E-mail address: [email protected] (Z. Dong).

https://doi.org/10.1016/j.scriptamat.2019.12.013 1359-6462/© 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

© 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

getically preferable, which hinders dislocation glide and promotes various secondary plasticity mechanisms such as mechanical twinning (18 ࣠ γ ࣠ 45 mJ m−2 ) [8,9] and martensite transformation from austenite ( ࣠ 18 mJ m−2 ) [10], leading to the so-called TWIP and TRIP plasticity, respectively. Therefore, tuning γ value to achieve desirable mechanical properties is becoming an important and flexible strategy for intelligent design of high performance alloys based on fundamental plasticity mechanisms. Chemical composition is one of crucial factors in determining γ value. At ambient temperature, γ in austenitic stainless steels has been extensively studied both from experiment and theory [11–18] (and references therein). Using the existing databases, the alloy effect on γ has been evaluated for some commonly adopted elements such as Ni, Cr, Mn, Co, and Nb, which indicates strong sensitivity to the chemical composition of the host where the alloy effect is exacted from. For instance, Ni was reported to increase γ in Fe-Cr-Ni system at ambient temperature, but it turns to decrease when Nb is added more than ~ 3 at % [14]. Despite the complexity in the rationale behind, magnetism was recognized to be one of the most important [14,19]. Nevertheless, at elevated temperatures, attempts to understand the alloy effect on γ in austenitic steel remain very scarce to date. Although a few data of γ have been reported at finite temperature in recent experimental and theoretical works [10,19–24], they limit to the few given compositions within certain temperature intervals and are insufficient to properly reveal the alloy impact at elevated temperatures. Thus, learning the al-

Z. Dong, W. Li and G. Chai et al. / Scripta Materialia 178 (2020) 438–441

loy influence on γ at finite temperature and thereby clarifying the potential differences from that well established at ambient temperature are important for tailoring high temperature properties of advanced austenitic steels. Here we use first principles alloy theory to investigate the impact of Ni on the stacking fault energy as a function of temperature in 316L-type austenitic steel. We show that the influence of Ni on γ strongly couples with temperature, which ultimately leads to an opposite impact of Ni alloying at elevated temperatures. The rationale behind is elucidated by correlating with chemical, magnetic and volumetric interactions, from which alloy contributions from Cr, Mo and N to the finite temperature evolution of Ni impact are analyzed. The stacking fault energy is computed using the supercell approach as detailed in our earlier works [22,23]. The exact muffintin orbitals (EMTO) method [25–28] was applied to solve the one-electron Kohn–Sham equations on basis of the generalized gradient approximation [29]. The soft-core scheme and the scalarrelativistic approximation were adopted. Considering the main alloy contributions, the 316L-type austenitic stainless steel is modeled as multicomponent Fe80−c Cr18 Mo2 Nic (c is the concentration of Ni in at %). The chemical disorder in the steel was accounted for using the coherent-potential approximation [30,31]. Owing to the low magnetic transition temperatures of austenitic steels [32], all the calculations were carried out in the paramagnetic state, the magnetic disorder of which was described via the disordered local moment theory [33–35]. Longitudinal spin fluctuations (LSFs) are not considered here, which actually induce finite local moment on Ni and Cr at thermal state. Nevertheless, it was demonstrated that in the present alloys LSFs result in minor effect on γ [36]. The thermal effect was included by accounting for thermal lattice expansion and the associated magnetic contribution. At ambient temperature, the concentration dependent lattice parameter was derived from the empirical formula established using a great variety of experimental data of austeinitic steels [37]. The lattice parameter was then rescaled to elevated temperatures using the experimentally determined thermal expansion coefficients [38], where alloy effects were accounted for. For discussion, we split γ in the internal energy (γ int ) and magnetic entropy (γ mag ) contribution, which is defined as γ int = E int /A and γ mag = −T Smag /A, respectively.  represents the change in internal energy/magnetic entropy induced by the fault, and A is the interface area per atom. The magnetic entropy is estimated using the mean filed expres sion S = kB i ci ln(1 + μi ) (kB , ci and μi is the Boltzmann constant, concentration and local moment of component i, respectively). We elaborate on the results below. Fig. 1(a) shows the computed γ as a function of Ni concentration at different temperatures. For reference, available experimental data at ambient temperature are included for the similar steels, the main alloy components of which are listed in the parentheses. Compared to the experimental measurements at ambient temperature, the amplitude of γ calculated at 300 K shows a close agreement with the values reported in Refs. [39,40], which are somewhat lower than those in Ref. [17]. Nevertheless, the positive concentration dependence of γ observed in the paper is well reproduced in our calculations, which is also in line with the previous theoretical predictions [10,12,19]. By fitting a quadratic polynomial to the results, we quantified the evolution of γ upon Ni concentration and list the fitting coefficients in Table 1. Despite the weak second order term, the dominated linear coefficient is determined to be 1.637 mJ m−2 per at. % at 300 K, which perfectly falls in the interval 1.4-2.4 mJ m−2 per wt. % determined by the multilinear regression analysis of γ reported in experiments for a series of austenitic steels [11,40]. In addition, the overall increase of γ with temperature (explicitly that of γ int ) is in line with the exper-

439

Fig. 1. Stacking fault energy of 316L-type austenitic stainless steel as a function of Ni concentration and temperature. The calculated γ are shown in panel (a), where available experimental data at 300 K are included for comparison. To make the comparison between theory and experiment possible, the strain contribution involved in the experimental values is excluded. Namely, the ideal γ values in a Ref. [17] and the values obtained by reducing 4 mJ m−2 (the strain contribution in austenitic steel [16,42,43]) from those in b Ref. [39] and c Ref. [40] are presented. The partial contributions of γ from the internal energy (γ int ) and the magnetic entropy (γ mag ) are shown in panels (b) and (c) for 300 and 1200 K, respectively. Namely, γ = γ int + γ mag . Table 1 Concentration dependence of γ at different temperatures. The alloy coefficients are quantified by fitting a quadratic polynomial, namely γ = C + B ∗ c + A ∗ c2 , to our calculations shown in Fig. 1. Ni concentration c is in at. %, T in K and γ is in mJ m−2 . The coefficient of determination R2 is listed. T

A

B

C

R2

300 600 900 1200

−0.0207 0.0018 0.0132 0.0324

1.637 0.055 −0.880 −1.955

−6.56 29.51 54.15 74.97

0.999 0.894 0.984 0.986

imental and theoretical findings for γ -Fe and austenitic stainless steels [20–22,41]. It is of interest that Ni impact on the stacking fault energy (dγ /dc) strongly depends on temperature. As shown in Fig. 1(a), increasing temperature from 300 K gradually weakens the influence of Ni, yielding reduced dγ /dc (less positive). At around 600 K, γ becomes insensitive to Ni content. With further increasing temperature, Ni addition, in contrast, tends to decrease γ and shows an enhanced effect towards high temperatures (more negative dγ /dc). Accordingly, the linear coefficient presented in Table 1 gradually decreases from 1.637 to -1.955 mJ m−2 per at. % with increasing temperature from 300 to 1200 K, changing both in sign and amplitude. Namely, tuning γ and thus plasticity mechanisms via Ni alloying is very sensitive to temperature, which can lead to the alloy effect completely opposite to the one observed at ambient temperature and should be accounted for in designing advanced austenitic steels towards high temperature applications. To look into the rationale behind the temperature dependence of dγ /dc, we show γ int and γ mag in Fig. 1(b) and (c) for 300 and 1200 K, respectively. At 300 K, the positive dγ /dc is primarily determined by the concentration dependence of γ int and partially counterbalanced by the negative one of γ mag . The similar contribution from γ mag is obtained at 1200 K. Nevertheless, the slightly increased dγ mag /dc (more negative) at 1200 K contributes to the transition of dγ /dc with temperature. More importantly, γ int at 1200 K gradually decreases with Ni content, which is opposite to the strong increasing trend at 300 K. That is, the evolution of

440

Z. Dong, W. Li and G. Chai et al. / Scripta Materialia 178 (2020) 438–441

Fig. 3. Alloy influence on Ni contribution to the stacking fault energy at finite temperature. Two sets of data show the results at 300 and 1200 K. In addition to 316Ltype steel, Ni effect on γ was evaluated under different alloy additions: including 4.0 at. %N ( ~ 1.0 wt%) by expanding the volumes [37] of austenitic steels without altering their chemical compositions ([N]4), increasing Cr to 22 at. % (Cr22) or reducing Mo to zero (Mo0) whilst keeping the content of Mo or Cr, respectively, as the original.

Fig. 2. Total energy (left axis) and local magnetic moment on Fe (right axis) as a function of atomic volume in fcc and hcp lattices. Panel (a) and (b) show the results for the austenitic stainless steel containing 10 and 30 at. % Ni, respectively. Volumes at 300 and 1200 K are indicated for the two steels by the solid boundaries of the shaded areas, which illustrate the volume intervals corresponding to 10 ~ 30% Ni at the given temperatures.

dγ int /dc upon temperature predominately determines the strong temperature dependence of dγ /dc. The internal energy contribution to γ (γ int ), in fact, accounts for the contribution of magneto-volume coupling. To clarify, Fig. 2 shows the total energy and local moment on Fe (μFe ) as a function of volume for two austenitic steels containing 10 and 30 at. % Ni and with hexagonal close-packed (hcp) and fcc lattices. In the first order approximation, γ can be evaluated from the energy difference between hcp and fcc latices, namely E = E hcp − E fcc . We notice that vanishing local moments on Ni and Mo are obtained within the volume interval considered here, while spontaneous local moment on Cr arises only at large volumes above ~ 12.22 A˚ (not shown). As shown in Fig. 2(a) for 10 at. % Ni, μFe in hcp exhibits a non-magnetic to magnetic transition with volume expansion and is always smaller than that in fcc. The hcp lattice is energetically preferable in the nonmagnetic regime. It, however, rapidly destabilizes along with the magnetic transition, which ultimately leads to an hcp → fcc phase transition at the volume slightly larger than the one associated with 300 K. In comparison with panel (a), the results shown in Fig. 2(b) indicate that Ni addition stimulates μFe in both fcc and hcp lattices, and this chemical-magnetic effect gradually weakens towards large volumes. It is important to note that Ni impact on μFe in hcp is stronger than that in fcc, es˚ which significantly repecially at small volumes below ~ 11.5 A, duces the difference in the magnetic states and total energies between the two lattices. In consequence, the hcp → fcc phase tran-

sition occurs at smaller volume with Ni addition. Considering the volume associated with 300 K (green shaded), E = E hcp − E fcc increases from small negative to positive with Ni alloying, representing a strong positive effect on γ . On the other hand, at the volume corresponding to 1200 K (purple shaded), E remains positive but gets smaller with Ni addition, resulting in a negative effect on γ . This is also indicative from the substantial reduction in the difference of equilibrium bulk modulus between the two lattices, hcp namely B = |B0 − Bfcc |. While B is as high as ~ 95 GPa in 0 the austenitic steel containing 10 at. % Ni, it drops to ~ 20 GPa at 30 at. % Ni. Furthermore, Ni tends to reduce the thermal expansion coefficient of austenitic steel [38], which enlarges the volume difference between the steels at high temperatures (the solid boundaries of the shaded areas) and thereby partially contributes to the transition of dγ /dc with temperature. With the importance of magneto-volume coupling for the Ni impact on γ , it is interesting to look into the influence of alloying on the finite temperature evolution of Ni impact because many elements yield noticeable volumetric effect besides the chemical one. Here, we consider several alloy elements widely applied in austenitic steels, namely Cr, Mo, and N. To this end, we calculated γ as a function of Ni concentration at a varied content of Cr or Mo while keeping Mo or Cr, respectively, as the original (balance Fe). For computational feasibility, N is included by accounting for its volumetric effect, which was shown to constitute the primary impact of interstitial N and C on the stacking fault energy of steels [44]. The results calculated at 300 and 1200 K are shown in Fig. 3, where those of 316L-type austenitic steel are included for comparison. It is evident from Fig. 3 that adding 4 at. % N ( ~ 1 wt. %, denoted by [N]4) to 316L-type austenitic steel (solid lines) significantly weakens the positive impact of Ni at 300 K while enhances the negative influence at 1200 K, ultimately moving the sign transition of dγ /dc to low temperature. This can be associated with the strong positive effect of N on the lattice parameter of austenitic stainless steel (0.0056 A˚ per at. % [37]), which situates the steels at high lever of volume and thus more homogeneous magnetic

Z. Dong, W. Li and G. Chai et al. / Scripta Materialia 178 (2020) 438–441

state for given Ni contents and temperatures (see Fig. 2). The finding here is consistent with the decreasing trend of dγ /dc upon N experimentally observed in medium and high N austenitic steels at 300 K [11,40]. Similarly, owing to the noticeable influence of Mo on the lattice parameter (0.0053 A˚ per at. % [37]), reducing Mo from 2 at. % to zero (denoted by Mo0) enhances/weakens the positive/negative impact of Ni at 300 K/1200 K, and leads to the transition of dγ /dc arising at high temperature. Cr barely contributes to the slope of lattice parameter vs composition in austenitic steels (0.0 0 06 A˚ per at. % [37]). Consequently, increasing Cr from 18 to 22 at. % (denoted by Cr22) yields minor influence on dγ /dc at 300 K. Nevertheless, Cr shows a slightly enhanced impact at 1200 K and yields an increased dγ /dc (more negative). This varied behavior may be ascribed to the very small local moment arising on Cr when increasing its concentration at 1200 K. We notice that N significantly increases the γ value at ambient temperature, while Cr and Mo noticeably decrease. dγ /dc for N, Cr, and Mo are estimated to be 4.68, -1.01, and -0.57 mJ m2 per at. %, respectively, at fixed 10% Ni, which change slightly with Ni concentration and temperature. These values agree well with the alloying coefficients derived from the experimentally reported γ of austenitic steels. [11,40,44,45] Using first principles alloy theory, we have investigated the impact of Ni on the stacking fault energy in austenitic stainless steel as a function of temperature. The influence of Ni on γ has been demonstrated to strongly depend on temperature, and can become completely opposite to the one well established at ambient temperature. Variation of magneto-volume coupling emerging from Ni addition is shown to be an important rationale behind. The alloy contribution to the finite temperature evolution of Ni impact has been evaluated for Cr, Mo, and N. The findings here stress that owing to the complicated chemical, magnetic and volumetric/thermal interactions, alloy contribution to the stacking fault energy can significantly change with temperature, which is essential for tailoring high performance alloys towards finite temperature applications. Declaration of Competing Interest We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome. Acknowledgments This work was supported by the Swedish Research Council (2015-5335 and 2017-06474), the Swedish Foundation for Strategic Research (S14-0038 and SM16-0036), the Swedish Foundation for International Cooperation in Research and Higher Education (CH2015-6292), the Hungarian Scientific Research Fund (OTKA 128229), and the Carl Tryggers Foundation. The calculations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at the National Supercomputer Centre (NSC) in Linköping. References [1] R. Gupta, N. Birbilis, Corros. Sci. 92 (2015) 1–15, doi:10.1016/j.corsci.2014.11. 041. [2] K. Lo, C. Shek, J. Lai, Mater. Sci. Eng. R 65 (2009) 39–104, doi:10.1016/j.mser. 20 09.03.0 01. [3] L. Gardner, A. Insausti, K. Ng, M. Ashraf, J. Constr. Steel Res. 66 (2010) 634–647, doi:10.1016/j.jcsr.2009.12.016.

441

[4] M. Calmunger, G. Chai, R. Eriksson, S. Johansson, J.J. Moverare, Metall. Mater. Trans. A 48 (2017) 4525–4538, doi:10.1007/s11661- 017- 4212- 9. [5] Z. Tao, X.-Q. Wang, M.K. Hassan, T.-Y. Song, L.A. Xie, J. Constr. Steel Res. 152 (2019) 296–311, doi:10.1016/j.jcsr.2018.02.020. [6] Z.H. Jin, S.T. Dunham, H. Gleiter, H. Hahn, P. Gumbsch, Scr. Mater. 64 (2011) 605–608, doi:10.1016/j.scriptamat.2010.11.033. [7] M. Jo, Y.M. Koo, B.-J. Lee, B. Johansson, L. Vitos, S.K. Kwon, Proc. Natl. Acad. Sci. 111 (2014) 6560–6565, doi:10.1073/pnas.1400786111. [8] B.C. De Cooman, Y. Estrin, S.K. Kim, Acta Mater. 142 (2018) 283–362, doi:10. 1016/j.actamat.2017.06.046. [9] B.C. De Cooman, O. Kwon, K.G. Chin, J. Mater. Sci. Technol. 28 (2012) 513–527, doi:10.1179/1743284711Y.0 0 0 0 0 0 0 095. [10] W. Li, S. Lu, D. Kim, K. Kokko, S. Hertzman, S.K. Kwon, L. Vitos, Appl. Phys. Lett. 108 (2016) 081903, doi:10.1063/1.4942809. [11] R.E. Schramm, R.P. Reed, Metall. Trans. A 6 (1975) 1345–1351, doi:10.1007/ BF02641927. [12] L. Vitos, J.O. Nilsson, B. Johansson, Acta Mater. 54 (2006) 3821–3826, doi:10. 1016/j.actamat.2006.04.013. [13] A. Saeed-Akbari, J. Imlau, U. Prahl, W. Bleck, Metall. Mater. Trans. A 40 (2009) 3076–3090, doi:10.10 07/s11661-0 09-0 050-8. [14] S. Lu, Q.-M. Hu, B. Johansson, L. Vitos, Acta Mater. 59 (2011) 5728–5734, doi:10. 1016/j.actamat.2011.05.049. [15] S. Curtze, V.-T. Kuokkala, A. Oikari, J. Talonen, H. Hänninen, Acta Mater. 59 (2011) 1068–1076, doi:10.1016/j.actamat.2010.10.037. [16] D. Pierce, J. Jiménez, J. Bentley, D. Raabe, C. Oskay, J. Wittig, Acta Mater. 68 (2014) 238–253, doi:10.1016/j.actamat.2014.01.001. [17] K.H. Antonsson, M. Grehk, J. Lu, L. Hultman, E. Holmstr, Acta Mater. 111 (2016) 39–46, doi:10.1016/j.actamat.2016.03.042. [18] D. Molnár, G. Engberg, W. Li, S. Lu, P. Hedström, S.K. Kwon, L. Vitos, Acta Mater. 173 (2019) 34–43, doi:10.1016/j.actamat.2019.04.057. [19] L. Vitos, P.A. Korzhavyi, B. Johansson, Phys. Rev. Lett. 96 (2006) 117210, doi:10. 1103/PhysRevLett.96.117210. [20] L. Rémy, Acta Metall. 25 (1977) 173–179, doi:10.1016/0 0 01- 6160(77)90120- 1. [21] L. Mosecker, D. Pierce, A. Schwedt, M. Beighmohamadi, J. Mayer, W. Bleck, J. Wittig, Mater. Sci. Eng. A 642 (2015) 71–83, doi:10.1016/j.msea.2015.06.047. [22] Z. Dong, S. Schönecker, D. Chen, W. Li, M. Long, L. Vitos, Int. J. Plast. 109 (2018) 43–53, doi:10.1016/j.ijplas.2018.05.007. [23] Z. Dong, S. Schönecker, D. Chen, W. Li, S. Lu, L. Vitos, Int. J. Plast. 119 (2019) 123–139, doi:10.1016/j.ijplas.2019.02.020. [24] D. Molnár, X. Sun, S. Lu, W. Li, G. Engberg, L. Vitos, Mater. Sci. Eng. A 759 (2019) 490–497, doi:10.1016/j.msea.2019.05.079. [25] L. Vitos, Computational Quantum Mechanics for Materials Engineers: The EMTO Method and Applications, Engineering Materials and Processes Series, Springer, London, 2007. [26] L. Vitos, Phys. Rev. B 64 (2001) 014107, doi:10.1103/PhysRevB.64.014107. [27] K. Kádas, L. Vitos, B. Johansson, J. Kollár, Phys. Rev. B 75 (2007) 035132, doi:10. 1103/PhysRevB.75.035132. [28] L. Vitos, H.L. Skriver, B. Johansson, J. Kollár, Comput. Mater. Sci. 18 (20 0 0) 24– 38, doi:10.1016/S0927-0256(99)0 0 098-1. [29] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865–3868, doi:10.1103/PhysRevLett.77.3865. [30] P. Soven, Phys. Rev. 156 (1967) 809–813, doi:10.1103/PhysRev.156.809. ˝ [31] B.L. Gyorffy, Phys. Rev. B 5 (1972) 2382–2384, doi:10.1103/PhysRevB.5.2382. [32] A.K. Majumdar, P.V. Blanckenhagen, Phys. Rev. B 29 (1984) 4079–4085, doi:10. 1103/PhysRevB.29.4079. [33] A.J. Pindor, J. Staunton, G.M. Stocks, H. Winter, J. Phys. F Met. Phys. 13 (1983) 979, doi:10.1088/0305-4608/13/5/012. ˝ [34] J. Staunton, B.L. Gyorffy, A.J. Pindor, G.M. Stocks, H. Winter, J. Magn. Magn. Mater. 45 (1984) 15–22, doi:10.1016/0304- 8853(84)90367- 6. ˝ [35] B.L. Gyorffy, A.J. Pindor, J. Staunton, G.M. Stocks, H. Winter, J. Phys. F Met. Phys. 15 (1985) 1337–1386, doi:10.1088/0305-4608/15/6/018. [36] Z. Dong, S. Schönecker, W. Li, D. Chen, L. Vitos, Sci. Rep. 8 (2018) 12211, doi:10. 1038/s41598- 018- 30732- y. [37] D.J. Dyson, B. Holmes, J. Iron and Steel Inst. 208 (1970) 469–474. [38] F.C. Hull, S.K. Hwang, J.M. Wells, R.I. Jaffee, J. Mater. Eng. 9 (1987) 81–92, doi:10.1007/BF02833790. [39] T.S. Byun, Acta Mater. 51 (2003) 3063–3071, doi:10.1016/S1359-6454(03) 00117-4. [40] M. Ojima, Y. Adachi, Y. Tomota, Y. Katada, Y. Kaneko, K. Kuroda, H. Saka, Steel Res. Int. 80 (2009) 477–481, doi:10.2374/SRI09SP038. [41] J. Talonen, H. Hänninen, Acta Mater. 55 (2007) 6108–6118, doi:10.1016/j. actamat.2007.07.015. [42] G.B. Olson, M. Cohen, Metall. Trans. A 7 (1976) 1897–1904, doi:10.1007/ BF02659822. [43] P. Ferreira, P. Müllner, Acta Mater. 46 (1998) 4479–4484, doi:10.1016/ S1359- 6454(98)00155- 4. [44] J.-Y. Lee, Y.M. Koo, S. Lu, L. Vitos, S.K. Kwon, Sci. Rep. 7 (2017) 11074, doi:10. 1038/s41598- 017- 11328- 4. [45] T.-H. Lee, E. Shin, C.-S. Oh, H.-Y. Ha, S.J. Kim, Acta Mater. 58 (2010) 3173–3186, doi:10.1016/j.actamat.2010.01.056.