The phenomenon of entropy-dominated grain boundary segregation is introduced and discussed. Numerous examples of the grain boundaries and solutes exhibiting this phenomenon are compiled and predicted for example of α-iron-based alloys and other host materials. Consequences of entropy-dominated grain boundary segregation for grain size stabilization and intergranular embrittlement are shown.
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The data sets generated and/or analyzed in the present study are available from the corresponding author on reasonable request.
Stølen S, Grande T (2003) Chemical thermodynamics of materials. Wiley, Chichester
Ewing RH (1971) An analytical approach to interfacial entropy. Acta Metall 19:1359–1362. https://doi.org/10.1016/0001-6160(71)90073-3
Fultz B (2010) Vibrational thermodynamics of materials. Prog Mater Sci 55:247–352. https://doi.org/10.1016/j.pmatsci.2009.05.002
George EP, Raabe D, Ritchie RO (2019) High-entropy alloys. Nat Rev Mater 4:515–534. https://doi.org/10.1038/s41578-019-0121-4
Lejček P, Všianská M, Šob M (2018) Recent trends and open questions in grain boundary segregation. J Mater Res 33:2647–2660. https://doi.org/10.1557/jmr.2018.230
Lejček P, Hofmann S, Všianská M, Šob M (2021) Entropy matters in grain boundary segregation. Acta Mater 206:116597. https://doi.org/10.1016/j.actamat.2020.116597
duPlessis J, van Wyk GN (1988) A model for surface segregation in multicomponent alloys—part I: equilibrium segregation. J Phys Chem Solids 49:1441–1450. https://doi.org/10.1016/0022-3697(88)90118-7
duPlessis J, van Wyk GN (1988) A model for surface segregation in multicomponent alloys—part II: comment of other segregation analyses. J Phys Chem Solids 49:1451–1458. https://doi.org/10.1016/0022-3697(88)90119-9
Wagih M, Schuh CA (2019) Spectrum of grain boundary segregation energies in polycrystal. Acta Mater 181:228–237. https://doi.org/10.1016/j.actamat.2019.09.034
McLean D (1957) Grain boundaries in metals. Oxford University Press, Oxford
Yang X, Zhang Y (2012) Prediction of high-entropy stabilized solid-solution in multicomponent alloys. Mater Chem Phys 132:233–238. https://doi.org/10.1016/j.matchemphys.2011.11.021
Erhart H, Grabke HJ (1981) Equilibrium segregation of phosphorus at grain boundaries of Fe–P, Fe–C–P, Fe–Cr–P, and Fe–Cr–C–P alloys. Metal Sci 15:401–408. https://doi.org/10.1179/030634581790426877
Briant CL (1999) The effect of grain boundary segregation on intergranular failures. In: Briant CL (ed) Impurities in engineering materials. Marcel Dekker, New York, pp 193–224
Lejček P, Hofmann S (2016) Interstitial and substitutional solute segregation at individual boundaries of α-iron: data revisited. J Phys Condens Matter 28:064001. https://doi.org/10.1088/0953-8984/28/6/064001
Ishida Y, Yokoyama S, Nishizawa T (1985) Grain boundary segregation in ferromagnetic alloys. Acta Metall 33:255–264. https://doi.org/10.1016/0001-6160(85)90143-9
Hänsel H, Grabke HJ (1986) Grain boundary segregation of phosphorus and carbon in ferritic iron. Scr Metall 20:1641–1644. https://doi.org/10.1016/0036-9748(86)90411-4
Seah MP, Lea C (1975) Surface segregation and its relation to grain boundary segregation. Philos Mag A 31:627–645. https://doi.org/10.1080/14786437508226543
Mast R, Viefhaus H, Grabke HJ (1999) Grain boundary segregation of antimony in iron base alloys and its effect on toughness. Steel Res 70:239–246. https://doi.org/10.1002/srin.199905633
Lejček P (2004) Grain boundary segregation of antimony in α-iron: prediction and experiment. J Alloys Compd 378:85–88. https://doi.org/10.1016/j.jallcom.2003.10.076
Lejček P, Pokluda J, Šandera P, Horníková J, Jenko M (2012) Solute segregation at 46.8°(111) twist grain boundary of a phosphorus doped Fe–2.3%V alloy. Surf Sci 606:258–262. https://doi.org/10.1016/j.susc.2011.10.002
Lejček P, Hofmann S (2019) Modeling grain boundary segregation by prediction of all the necessary parameters. Acta Mater 170:253–567. https://doi.org/10.1016/j.actamat.2019.03.037
Lejček P, Hofmann S (2008) Thermodynamics of grain boundary segregation and applications to anisotropy, compensation effect and prediction. Crit Rev Sol State Mater Sci 33:133–163. https://doi.org/10.1080/10408430801907649
Ko WS, Kim NJ, Lee BJ (2012) Atomistic modeling of an impurity element and metal-impurity system: pure P and Fe–P system. J Phys Condens Matter 24:225002. https://doi.org/10.1088/0953-8984/24/22/225002
Sutton AP, Balluffi RW (1995) Interfaces in crystalline materials. Clarendon, Oxford
Massalski TB (1986) Binary alloy phase diagrams. ASM, Metals Park
Di Stefano D, Mrovec M, Elsässer Ch (2015) First-principles investigation of hydrogen trapping and diffusion at grain boundaries in nickel. Acta Mater 98:306–312. https://doi.org/10.1016/j.actamat.2015.07.031
Muzyk M, Kurzydlovski KJ (2011) Density functional theory calculations of properties of the grain boundaries in aluminum. MRS Symp Proc 1297:155–159. https://doi.org/10.1557/opl.2011.531
Rajagopalan M, Bhatia MA, Tschopp MA, Srolovitz DJ, Solanki KN (2014) Atomic-scale analysis of liquid-gallium embrittlement of aluminum grain boundaries. Acta Mater 73:312–325. https://doi.org/10.1016/j.actamat.2014.04.011
Razumovskii VI, Lozovoi AY, Razumovskiy IM (2015) First principles-aided design of a new Ni-base superalloy: influence of transition metal alloying elements on grain boundary and bulk cohesion. Acta Mater 82:369–377. https://doi.org/10.1016/j.actamat.2014.08.047
Scheiber D, Pippan R, Puschnig P, Ruban A, Romaner L (2016) Ab-initio search for cohesion-enhancing solute elements at grain boundaries in molybdenum and tungsten. Int J Refract Metals Hard Mater 60:75–81. https://doi.org/10.1016/j.ijrmhm.2016.07.003
Kirchheim R (2002) Grain coarsening inhibited by solute segregation. Acta Mater 50:413–419. https://doi.org/10.1016/S1359-6454(01)00338-X
Darling A, Chan RN, Wong PZ, Semones JE, Scattergood RO, Koch CC (2008) Grain-size stabilization in nanocrystalline FeZr alloys. Scr Mater 59:530–533. https://doi.org/10.1016/j.scriptamat.2008.04.045
Rice JR, Wang JS (1989) Embrittlement of interfaces by solute segregation. Mater Sci Eng A 107:23–40. https://doi.org/10.1016/0921-5093(89)90372-9
Všianská M, Šob M (2011) The effect of segregated sp-impurities on grain-boundary structure, magnetism and embrittlement. Prog Mater Sci 56:817–840. https://doi.org/10.1016/j.pmatsci.2011.01.008
Ma Y, Sun B, Schökel A, Song W, Ponge D, Raabe D, Bleck W (2020) Phase boundary segregation-induced strengthening and discontinuous yielding in ultrafine-grained duplex medium-Mn steels. Acta Mater 200:389–403. https://doi.org/10.1016/j.actamat.2020.09.007
Furuhara T, Zhang Y, Miyamoto G (2019) Roles of transformation interfaces in the design of advanced high strength steels. IOP Conf Ser Mater Sci Eng 580:012005. https://doi.org/10.1088/1757-899X/580/1/012005
Wicaksono AT, Militzer M (2017) Interaction of C and Mn in a Σ3 grain boundary of bcc iron. IOP Conf Ser Mater Sci Eng 219:012044. https://doi.org/10.1088/1757-899X/219/1/012044
Financial support was provided by the Czech Science Foundation (Project No. GA-20-08130S), by the Ministry of Education, Youth and Sports of the Czech Republic (CEITEC 2020-Project No. LQ1601), and by the Academy of Sciences of the Czech Republic (RVO:68378271).
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Lejček, P., Hofmann, S. Entropy-dominated grain boundary segregation. J Mater Sci 56, 7464–7473 (2021). https://doi.org/10.1007/s10853-021-05800-w