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Recent trends and open questions in grain boundary segregation

Published online by Cambridge University Press:  26 July 2018

Pavel Lejček ,
Monika Všianská  and
Mojmír Šob
Pavel Lejček*
Affiliation:
Institute of Physics, Academy of Sciences of the Czech Republic, 182 21 Praha 8, Czech Republic
Monika Všianská
Affiliation:
Central European Institute of Technology, Masaryk University, CEITEC MU, 625 00 Brno, Czech Republic; Institute of Physics of Materials, Academy of Sciences of the Czech Republic, 616 62 Brno, Czech Republic; and Department of Chemistry, Faculty of Science, Masaryk University, 611 37 Brno, Czech Republic
Mojmír Šob
Affiliation:
Central European Institute of Technology, Masaryk University, CEITEC MU, 625 00 Brno, Czech Republic; Institute of Physics of Materials, Academy of Sciences of the Czech Republic, 616 62 Brno, Czech Republic; and Department of Chemistry, Faculty of Science, Masaryk University, 611 37 Brno, Czech Republic
*
a)Address all correspondence to this author. e-mail: lejcekp@fzu.cz
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Abstract

Recently, significant progress in the field of grain boundary segregation was achieved, for example, in better understanding and modeling the stabilization of nanocrystalline structures by grain boundary segregation, searching for more advanced approaches to theoretical calculation of segregation energies and development of the complexion approach. Nevertheless, with each progress, new important questions appear which need to be solved. Here, we focus on two basic questions appearing recently: How can be the experimental results on the grain boundary segregation compared reliably to their theoretical counterparts? Is the preferred segregation site of a solute in the grain boundary core substitutional or interstitial? We also show that the entropy of grain boundary segregation is a very important quantity which cannot be neglected in thermodynamic considerations as it plays a crucial role, for example, in prediction of thermodynamic characteristics of grain boundary segregation and in the preference of the segregation site at the boundary.

Keywords

grain boundarieschemical compositionFegrain boundary segregationgrain boundary magnetismthermodynamics

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Type
Invited Feature Paper
Information
Journal of Materials Research , Volume 33 , Issue 18 , 28 September 2018 , pp. 2647 - 2660
Copyright
Copyright © Materials Research Society 2018 

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This paper has been selected as an Invited Feature Paper.

References

REFERENCES

Hampe, W.: Beiträge zu der Metallurgie des Kupfers. Z. Berg-, Hütten- und Salinenwesen 23, 93 (1874).Google Scholar
Stewart, M.T., Thomas, R., Wauchope, K., Winegard, W.C., and Chalmers, B.: New segregation phenomena in metals. Phys. Rev. 83, 657 (1951).CrossRefGoogle Scholar
Hondros, E.D., Seah, M.P., Hofmann, S., and Lejček, P.: Surface and interfacial microchemistry. In Physical Metallurgy, 4th ed., Cahn, R.W. and Haasen, P., eds. (North-Holland, Amsterdam, 1996); pp. 1201–1289.CrossRefGoogle Scholar
Kalderon, D.: Steam turbine failure at Hinkley point ‘A’. Proc. Inst. Mech. Eng. 186, 341 (1972).CrossRefGoogle Scholar
Hashimoto, M., Ishida, Y., Yamamoto, R., and Doyama, M.: Atomistic studies of grain boundary segregation in Fe–P and Fe–B alloys. I. Atomistic structure and stress distribution. Acta Metall. 32, 1 (1984).CrossRefGoogle Scholar
Masuda-Jindo, K.: On the grain boundary segregation of sp-valence impurities in b.c.c. transition metal. Phys. Status Solidi B 134, 545 (1986).CrossRefGoogle Scholar
Lejček, P., Šob, M., and Paidar, V.: Interfacial segregation and grain boundary embrittlement: An overview and critical assessment of experimental data and calculated results. Prog. Mater. Sci. 87, 83 (2017).CrossRefGoogle Scholar
Lejček, P.: Grain Boundary Segregation in Metals (Springer, Berlin, 2010).CrossRefGoogle Scholar
Murdoch, H.A. and Schuh, C.A.: Stability of binary nanocrystalline alloys against grain growth and phase separation. Acta Mater. 61, 2121 (2013).CrossRefGoogle Scholar
Murdoch, H.A. and Schuh, C.A.: Estimation of grain boundary segregation enthalpy and its role in stable nanocrystalline alloy design. J. Mater. Res. 28, 2154 (2013).CrossRefGoogle Scholar
Chookajorn, T. and Schuh, C.A.: Thermodynamics of stable nanocrystalline alloys: A Monte Carlo analysis. Phys. Rev. B 89, 064102 (2014).CrossRefGoogle Scholar
Saber, M., Koch, C.C., and Scattergood, R.O.: Thermodynamic grain size stabilization models: An overview. Mater. Res. Lett. 3, 65 (2015).CrossRefGoogle Scholar
Abdeljawad, F. and Foiles, S.M.: Stabilization of nanocrystalline alloys via grain boundary segregation: A diffuse interface model. Acta Mater. 101, 159 (2015).CrossRefGoogle Scholar
Liang, T., Chen, Z., Yang, X., Zhang, J., and Zhang, P.: The thermodynamic stability induced by solute co-segregation in nanocrystalline ternary alloys. Int. J. Mater. Res. 108, 435 (2017).CrossRefGoogle Scholar
Zhou, N., Hu, T., Huang, J., and Luo, J.: Stabilization of nanocrystalline alloys at high-temperatures via utilizing high-entropy grain boundary complexions. Scr. Mater. 124, 160 (2016).CrossRefGoogle Scholar
Svoboda, J. and Fischer, F.D.: Abnormal grain growth: A non-equilibrium thermodynamic model for multigrain binary systems. Modell. Simul. Mater. Sci. Eng. 22, 015013 (2014).CrossRefGoogle Scholar
Waseda, O., Goldenstein, H., Lenz Silva, G.F.B., Neiva, A., Chantrenne, P., Morthomas, J., Perez, M., Becquart, C.S., and Veiga, R.G.A.: Stability of nanocrystalline Ni-based alloys: Coupling Monte Carlo and molecular dynamics simulations. Modell. Simul. Mater. Sci. Eng. 25, 075005 (2017).CrossRefGoogle Scholar
Chookajorn, T. and Schuh, C.A.: Nanoscale segregation behavior and high-temperature stability of nanocrystalline W–20 at.% Ti. Acta Mater. 73, 128 (2014).CrossRefGoogle Scholar
Abdeljawad, F., Lu, P., Argibay, N., Clarke, B.G., Boyce, B.L., and Foiles, S.M.: Grain boundary segregation in immiscible nanocrystalline alloys. Acta Mater. 126, 528 (2017).CrossRefGoogle Scholar
Chen, Z., Liu, F., Yang, X.Q., Shen, C.J., and Zhao, Y.M.: A thermokinetic description of nano-scale grain growth under dynamic grain boundary segregation conditions. J. Alloys Compd. 608, 338 (2014).CrossRefGoogle Scholar
Luo, J.: A short review of high-temperature wetting and complexion transitions with a critical assessment of their influence on liquid metal embrittlement and corrosion. Corrosion 72, 897 (2016).CrossRefGoogle Scholar
Kobayashi, S., Maruyama, T., Saito, S., Tsurekawa, S., and Watanabe, T.: In situ observations of crack propagation and role of grain boundary microstructure in nickel embrittled by sulfur. J. Mater. Sci. 49, 4007 (2014).CrossRefGoogle Scholar
Djamal, B., Gall, R.L., and Lefkaier, I.K.: Effect of small content and annealing temperature on the intergranular fracturing susceptibility of metallic nickel. Surf. Rev. Lett. 23, 1650050 (2016).CrossRefGoogle Scholar
Li, Z.W., Kong, X.S., Wei, L., Liu, C.S., and Fang, Q.F.: Segregation of alloying atoms at a tilt symmetric grain boundary in tungsten and their strengthening and embrittling effects. Chin. Phys. B 23, 106107 (2014).CrossRefGoogle Scholar
Scheiber, D., Razumovskiy, V.I., Pusching, P., Pippan, R., and Romaner, L.: Ab initio description of segregation and cohesion of grain boundaries in W–25 at.% Re alloys. Acta Mater. 88, 180 (2015).CrossRefGoogle Scholar
Lejček, P., Šandera, P., Horníková, J., Řehák, P., and Pokluda, J.: Grain boundary segregation of elements of groups 14 and 15 and its consequences for intergranular cohesion of ferritic iron. J. Mater. Sci. 52, 5822 (2017).CrossRefGoogle Scholar
Mehta, Y., Dabhade, V.V., and Chaudhari, G.P.: Effect of silicon and nitrogen on the microstructure and mechanical behavior of high-phosphorus steels. Metallogr., Microstruct., Anal. 5, 384 (2016).CrossRefGoogle Scholar
He, X., Wu, S., Jia, L., Wang, D., Dou, Y., and Yang, W.: Grain boundary segregation of substitutional solutes/impurities and grain boundary decohesion in bcc Fe. Energy Procedia 127, 377 (2017).CrossRefGoogle Scholar
Babicheva, R.I., Dmitriev, S.V., Bai, L., Ying, Z., Kang, G., and Zhou, K.: Effect of grain boundary segregation on the deformation mechanism and mechanical properties of nanocrystalline binary aluminum alloys. Comput. Mater. Sci. 117, 445 (2016).CrossRefGoogle Scholar
Zinovev, A.V., Bapanina, M.G., Babicheva, R.I., Enikeev, N.A., Dmitriev, S.V., and Zhou, K.: Deformation of nanocrystalline binary aluminum alloys with segregation of Mg, Co and Ti at grain boundaries. Phys. Met. Metallogr. 118, 65 (2017).CrossRefGoogle Scholar
Sauvage, X., Lee, S., Matsuda, K., and Horita, Z.: Origin of the influence of Cu and Ag micro-additions on the age hardening behavior of ultrafine-grained Al–Mg–Si alloys. J. Alloys Compd. 710, 199 (2017).CrossRefGoogle Scholar
Basu, I., Pradeep, K.G., Mießen, C., Barrales-Mora, L.A., and Salman, T.: The role of atomic scale segregation in designing highly ductile magnesium alloy. Acta Mater. 116, 77 (2016).CrossRefGoogle Scholar
Jo, M.G., Madakashira, P.P., Suh, J.Y., and Han, H.N.: Effect of nitrogen on microstructure and mechanical properties of vanadium. Mater. Sci. Eng., A 675, 92 (2016).CrossRefGoogle Scholar
Shi, S., Zhu, L., Zhang, H., and Sun, Z.: Segregation effects of Y, Ti, Cr, and Si on the intergranular fracture of niobium. J. Alloys Compd. 711, 637 (2017).CrossRefGoogle Scholar
Kovalev, A.I., Wainstein, D.L., and Rashkovskiy, A.Y.: Al grain boundary segregations in doped intermetallic NiAl and their effect on brittleness at room temperature. Bull. Russ. Acad. Sci. Phys. 80, 1253 (2016).CrossRefGoogle Scholar
Gibson, M.A. and A Schuh, C.: Segregation-induced changes in grain boundary cohesion and embrittlement in binary alloys. Acta Mater. 95, 145 (2015).CrossRefGoogle Scholar
Gibson, M.A. and Schuh, C.A.: A survey of ab initio calculations shows that segregation induced grain boundary embrittlement is predicted by bond breaking arguments. Scr. Mater. 113, 55 (2016).CrossRefGoogle Scholar
Esin, V.A. and Souhar, Y.: Solvent grain boundary diffusion in binary solid solutions: A new approach to evaluate solute grain boundary segregation. Philos. Mag. 94, 4066 (2014).CrossRefGoogle Scholar
Kaptay, G.: Modelling equilibrium grain boundary segregation, grain boundary energy and grain boundary segregation transition by the extended Butler equation. J. Mater. Sci. 51, 1738 (2016).CrossRefGoogle Scholar
L’vov, P.E. and Svetukhin, V.V.: Influence of grain boundaries on the distribution of components in binary alloys. Phys. Solid State 59, 2453 (2017).CrossRefGoogle Scholar
Lejček, P. and Hofmann, S.: Interstitial and substitutional solute segregation at individual grain boundaries of α-iron: Data revisited. J. Phys.: Condens. Matter 28, 064001 (2016).Google ScholarPubMed
Lejček, P., Zheng, L., Hofmann, S., and Šob, M.: Applied thermodynamics: Grain boundary segregation. Entropy 16, 1462 (2014).CrossRefGoogle Scholar
Lejček, P., Jäger, A., and Gärtnerová, V.: Reversed anisotropy of grain boundary properties and its effect on grain boundary engineering. Acta Mater. 58, 1930 (2010).CrossRefGoogle Scholar
Raabe, D., Sandlöbes, S., Millán, J., Ponge, D., Assadi, H., Herbig, M., and Choi, P.P.: Segregation engineering enables nanoscale martensite to austenite phase transformation at grain boundaries: A pathway to ductile martensite. Acta Mater. 61, 6152 (2013).CrossRefGoogle Scholar
Raabe, D., Herbig, M., Sandlöbes, S., Li, Y., Tytko, D., Kuzmina, M., Ponge, D., and Choi, P.P.: Grain boundary segregation engineering in metallic alloys: A pathway to the design of interfaces. Curr. Opin. Solid State Mater. Sci. 18, 253 (2014).CrossRefGoogle Scholar
Kuzmina, M., Ponge, D., and Raabe, D.: Grain boundary segregation engineering and austenite reversion turn embrittlement into toughness: Example of a 9 wt% medium Mn steel. Acta Mater. 86, 182 (2015).CrossRefGoogle Scholar
Cantwell, P.R., Ming, S.T., Dillon, J., Luo, J., Rohrer, G.S., and Harmer, M.P.: Grain boundary complexions. Acta Mater. 62, 1 (2014).CrossRefGoogle Scholar
Dillon, S.J., Tai, K., and Chen, S.: The importance of grain boundary complexions in affecting physical properties of polycrystals. Curr. Opin. Solid State Mater. Sci. 20, 324 (2016).CrossRefGoogle Scholar
Kundu, A., Asl, K.M., Luo, J., and Harmer, M.P.: Identification a bilayer grain boundary complexion in Bi-doped Cu. Scr. Mater. 68, 146 (2013).CrossRefGoogle Scholar
Tewari, A. and Bowen, P.: Grain boundary complexion and transparent polycrystalline alumina from an atomistic simulation perspective. Curr. Opin. Solid State Mater. Sci. 20, 278 (2016).CrossRefGoogle Scholar
Xu, T., Zheng, L., Wang, K., and Misra, R.D.K.: Unified mechanism of intergranular embrittlement based on non-equilibrium grain boundary segregation. Int. Mater. Rev. 58, 263 (2013).CrossRefGoogle Scholar
Zheng, L., Chellali, R., Schlessinger, R., Meng, Y., Baither, D., and Schmitz, G.: Identical mechanism of isochronal embrittlement in Ni(Bi) alloy: Thermo-induced non-equilibrium grain boundary segregation of Bi. Appl. Surf. Sci. 337, 90 (2015).CrossRefGoogle Scholar
Liu, Z., Yu, H., Wang, K., and Xu, T.: Non-equilibrium grain-boundary segregation mechanism of hot ductility loss for austenitic and ferritic stainless steels. J. Mater. Res. 30, 2117 (2015).CrossRefGoogle Scholar
Song, S.H., Zhao, Y., and Si, H.: Non-equilibrium phosphorus grain-boundary segregation and its effect on embrittlement in a niobium-stabilized interstitial-free steel. Mater. Lett. 140, 20 (2015).CrossRefGoogle Scholar
Lee, H.B., Prinz, F.B., and Cai, W.: Atomistic simulations of grain boundary segregatiom in nanocrystalline yttria-stabilized zirconia and gadolinia-doped ceria solid oxide electrolytes. Acta Mater. 61, 3872 (2013).CrossRefGoogle Scholar
Yokoi, T., Yoshiya, M., and Yasuda, H.: Nonrandom point defect configurations and driving force transitions for grain boundary segregation in trivalent cation doped ZrO2. Langmuir 30, 14179 (2014).CrossRefGoogle Scholar
Zhang, F., Vanmeensel, K., Batuk, M., Hadermann, J., Inokoshi, M., Van Meerbeek, B., Naeret, I., and Vleugels, J.: Highly-translucent, strong and aging resistant 3Y-TZP ceramics for dental restoration by grain boundary segregation. Acta Biomater. 16, 215 (2015).CrossRefGoogle ScholarPubMed
Yokoi, T., Yoshiya, M., and Yasuda, H.: On modeling of grain boundary segregation in aliovalent cation-doped ZrO2: Critical factors in site-selective point defect occupancy. Scr. Mater. 102, 91 (2015).CrossRefGoogle Scholar
Zhang, F., Batuk, M., Hadermann, J., Manfredi, G., Mariën, A., Vanmeensel, K., Inokoshi, M., Van Meerbeek, B., Naert, I., and Vleugels, J.: Effect of cation-dopant radius on the hydrothermal stability of tetragonal zirconia: Grain boundary segregation and oxygen vacancy annihilation. Acta Mater. 106, 48 (2016).CrossRefGoogle Scholar
Feng, B., Yokoi, T., Kumamoto, A., Ikuhara, M., and Shibata, N.: Atomically ordered solute segregation behavior in an oxide grain boundary. Nat. Commun. 7, 11079 (2016).CrossRefGoogle Scholar
Ma, S., Cantwell, P.R., Pennycock, T.J., Zhou, N., Oxley, M.P., Leonard, D.N., Pennycook, S.J., Luo, J., and Harmer, M.P.: Grain boundary complexion transitions in WO3- and CuO-doped TiO2 bicrystals. Acta Mater. 61, 1691 (2013).CrossRefGoogle Scholar
Yan, J.K., Kang, K.Y., and Gan, G.Y.: Grain boundary segregation and the formation mechanism of secondary-phase in (Ce,Nb)-codoped TiO2 ceramics. Mater. Des. 99, 155 (2016).CrossRefGoogle Scholar
Yan, J.K., Kang, K.Y., Du, J.H., Gan, G.Y., and Yi, J.H.: Grain boundary segregation and secondary-phase transition of (La,Nb) codoped TiO2 ceramic. Ceram. Int. 42, 11584 (2016).CrossRefGoogle Scholar
Meng, B., Lin, Z.L., Zhou, Y.J., Yang, Q.Q., Kong, M., and Meng, B.F.: Effects of Fe-dopings through solid solution and grain-boundary segregation on the electrical properties of CeO2-based solid electrolytes. Ionics 21, 2575 (2015).CrossRefGoogle Scholar
Andersson, D.A., Tonks, M.R., Casillas, L., Vyas, S., Nerikar, P., Ubruaga, B.P., and Stanek, C.R.: Multiscale simulation of xenon diffusion and grain boundary segregation in UO2. J. Nucl. Mater. 462, 15 (2015).CrossRefGoogle Scholar
Straumal, B.B., Protasova, S.G., Mazilkin, A.A., Goering, E., Schütz, G., Straumal, P.B., and Baretzky, B.: Ferromagnetic behavior of ZnO: The role of grain boundaries. Beilstein J. Nanotechnol. 7, 1936 (2016).CrossRefGoogle ScholarPubMed
Stoffers, A., Cojocaru-Mirédin, O., Seifert, W., Zaefferer, S., Riepe, S., and Raabe, D.: Grain boundary segregation in multicrystalline silicon: Correlative characterization by EBSD, EBIC, and atom probe tomography. Prog. Photovoltaics Res. Appl. 23, 1742 (2015).CrossRefGoogle Scholar
Mondal, R.A., Murty, B.S., and Murthy, V.R.K.: Maxwell-Wagner polarization in grain boundary segregated NiCuZn ferrite. Curr. Appl. Phys. 14, 1727 (2014).CrossRefGoogle Scholar
Mondal, R.A., Murty, B.S., and Murthy, V.R.K.: Temperature and frequency dependent electrical properties of NiCuZn ferrite with CuO-rich grain boundary segregation. J. Alloy. Comp. 595, 206 (2014).CrossRefGoogle Scholar
Mondal, R.A., Murty, B.S., and Murthy, V.R.K.: Origin of magnetocapacitance in chemically homogeneous and inhomogeneous ferrites. Phys. Chem. Chem. Phys. 17, 2432 (2015).CrossRefGoogle ScholarPubMed
Yoon, H.I., Lee, D.K., Bae, H.B., Jo, G.Y., Chung, H.S., Kim, J.G., Kang, S.J., and Chung, S.Y.: Probing dopant segregation in distinct cation sites at perovskite oxide polycrystal interfaces. Nat. Commun. 8, 1417 (2017).CrossRefGoogle ScholarPubMed
Cao, W., Kundu, A., Yu, Z., Harmer, M.P., and Vinci, R.P.: Direct correlations between fracture toughness and grain boundary segregation behavior in ytterbium-doped magnesium aluminate spinel. Scr. Mater. 69, 81 (2013).CrossRefGoogle Scholar
Zachariasz, P., Kulawik, J., and Gudzek, P.: Preparation and characterization of the microstructure, dielectric and magnetoelectric properties of multiferroic Sr3CuNb2O9–CoFe2O4 ceramics. Mater. Des. 86, 627 (2015).CrossRefGoogle Scholar
Boyle, C., Carvillo, P., Chen, Y., Barbero, E.J., Mcintyre, D., and Song, X.: Grain boundary segregation and thermoelectric performance enhancement of bismuth doped calcium cobaltite. J. Eur. Ceram. Soc. 36, 601 (2016).CrossRefGoogle Scholar
Nagano, T., Tamahashi, K., Sasajima, Y., and Onuki, J.: Cs corrected STEM observation and atomic modeling of grain boundary impurities of very narrow Cu interconnect. ECS Electrochem. Lett. 2, H23 (2013).CrossRefGoogle Scholar
Yu, Z., Wu, Q., Rickman, J.M., Chan, H.M., and Harmer, M.P.: Atomic resolution observation of Hf doped alumina grain boundaries. Scr. Mater. 68, 703 (2013).CrossRefGoogle Scholar
Walther, T., Hopkinson, M., Daneau, N., Recnik, A., Ohno, Y., Inoue, K., and Yonenaga, I.: How to best measure atomic segregation to grain boundaries by analytical transmission electron microscopy. J. Mater. Sci. 49, 3898 (2014).CrossRefGoogle Scholar
Babinsky, K., Weidow, J., Knabl, W., Lorich, A., Leitner, H., and Primig, S.: Atom probe study of grain boundary segregation in technically pure molybdenum. Mater. Charact. 87, 95 (2014).CrossRefGoogle Scholar
Sandim, M.J.R., Tytko, D., Kostka, A., Choi, P., Awaji, S., Watanabe, K., and Raabe, D.: Grain boundary segregation in a bronze-route Nb3Sn superconducting wire studied by atom probe tomography. Supercond. Sci. Technol. 26, 05508 (2013).CrossRefGoogle Scholar
Li, Y.J., Choi, P., Goto, S., Borchers, C., Raabe, D., and Kirchheim, R.: Atomic scale investigation of redistribution of alloying elements in pearlitic steel wires upon cold-drawing and annealing. Ultramicroscopy 132, 233 (2013).CrossRefGoogle ScholarPubMed
Li, Y.J., Ponge, D., Choi, P., and Raabe, D.: Segregation of boron at prior austenite grain boundaries in a quenched martensitic steel studied by atom probe tomography. Scr. Mater. 96, 13 (2015).CrossRefGoogle Scholar
Herbig, M., Raabe, D., Li, Y.J., Choi, P., Zaeferer, S., and Goto, S.: Atomic scale quantification of grain boundary segregation in nanocrystalline material. Phys. Rev. Lett. 112, 126103 (2013).CrossRefGoogle Scholar
Mandal, S., Pradeep, K.G., Zaefferer, S., and Raabe, D.: A novel approach to measure grain boundary segregation in bulk polycrystalline materials in dependence of the boundaries’ five rotational degrees of freedom. Scr. Mater. 81, 16 (2014).CrossRefGoogle Scholar
Solanki, K.N., Tschopp, M.A., Bhatia, M.A., and Rhodes, N.R.: Atomistic investigation of the role of grain boundary structure on hydrogen segregation and embrittlement in α-iron. Metall. Mater. Trans. A 44, 1365 (2013).CrossRefGoogle Scholar
Rhodes, N.R., Tschopp, M.A., and Solanki, K.N.: Quantifying the energetics and length scales of carbon segregation to α-Fe symmetric tilt grain boundaries using atomistic simulations. Modell. Simul. Mater. Sci. Eng. 21, 035009 (2013).CrossRefGoogle Scholar
Li, C.X., Dang, S.H., Wang, L.P., Zhang, C.L., and Han, P.D.: First principles investigation into effects of Cr on segregation of S and Cl at α-Fe Σ5(210) grain boundary. Mater. Res. Innovations 18, S41012 (2014).CrossRefGoogle Scholar
Jin, H., Elfimov, I., and Militzer, M.: Study of the interaction of solutes with Σ5(013) tilt grain boundary in iron using density-functional theory. J. Appl. Phys. 115, 093506 (2014).CrossRefGoogle Scholar
Tahir, A.M., Janisch, R., and Hartmaier, A.: Hydrogen embrittlement of a carbon segregated Σ5 (310) [001] symmetrical tilt grain boundary in α-Fe. Mater. Sci. Eng., A 612, 462 (2014).CrossRefGoogle Scholar
Bhattacharya, S.K., Kohyama, M., Tanaka, S., and Shiihara, Y.: Si segregation at Fe grain boundaries analyzed by ab initio local energy and local stress. J. Phys.: Condens. Matter 26, 355005 (2014).Google ScholarPubMed
Suzudo, T. and Yamaguchi, M.: Simulation of He embrittlement at grain boundaries in bcc transition metals. J. Nucl. Mater. 465, 695 (2015).CrossRefGoogle Scholar
Zemła, M.R., Wróbel, J.S., Wejrzanowski, T., Nguyen-Manh, D., and Kurzydłowski, K.J.: The helium effect at grain boundaries in Fe–Cr alloys? A first-principles study. Nucl. Instrum. Methods Phys. Res., Sect. B 393, 118 (2017).CrossRefGoogle Scholar
Bentria, E.L.T., Lefkaier, I.K., and Bentria, B.: The effect of vanadium impurity on nickel Σ5(210) grain boundary. Mater. Sci. Eng., A 577, 197 (2013).CrossRefGoogle Scholar
Razumovskiy, V.I., Lozovoi, A.Y., and Razumovskii, I.M.: 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 (2015).CrossRefGoogle Scholar
Subashiev, A.V. and Nee, H.H.: Hydrogen trapping at divacancies and impurity-vacancy complexes in nickel: First principles study. J. Nucl. Mater. 487, 135 (2017).CrossRefGoogle Scholar
Das, N.K., Shoji, T., Nishizumi, T., Fukuoka, T., Sugawara, T., Sasaki, R., Tatsuki, T., Yuya, H., Ito, K., Tatsumi, K., Ooki, S., Sueishi, Y., and Takada, K.: First-principles calculations of hydrogen interactions with nickel containing a monovacancy and divacancies. Mater. Res. Express 4, 076505 (2017).CrossRefGoogle Scholar
Divi, S., Agrahari, G., Kadulkar, S.R., Kumar, S., and Chatterjee, A.: Improved prediction of heat of mixing and segregation in metallic alloys using tunable mixing rule for embedded atom method. Modell. Simul. Mater. Sci. Eng. 25, 085011 (2017).CrossRefGoogle Scholar
Všianská, M., Vémolová, H., and Šob, M.: Segregation of sp-impurities at grain boundaries and surfaces: Comparison of fcc cobalt and nickel. Modell. Simul. Mater. Sci. Eng. 25, 085004 (2017).CrossRefGoogle Scholar
Rajagopalan, M., Bhatia, M.A., Solanki, K.N., and Tschopp, M.A.: Investigation of atomic-scale energetics on liquid metal embrittlement of aluminum due to gallium. TMS Ann. Meet. 2014, 1069 (2014).Google Scholar
Shen, X.J., Tanguy, D., and Connétable, D.: Atomistic modelling of hydrogen segregation to the Σ9 (221) [110] symmetric tilt grain boundary in Al. Philos. Mag. 94, 2247 (2014).CrossRefGoogle Scholar
Wang, H., Kohyama, M., Tanaka, S., and Shiihara, Y.: First-principles study of Si and Mg segregation in grain boundaries in Al and Cu: Application of local-energy decomposition. J. Mater. Sci. 50, 6864 (2015).CrossRefGoogle Scholar
Karkina, L.E., Karkin, I.N., Kuzetsov, A.R., Razumov, I.K., Korzhavyi, P.A., and Gornostyrev, Y.N.: Solute-grain boundary interaction and segregation formation in Al: First principles calculations and molecular dynamics modeling. Comput. Mater. Sci. 112, 18 (2016).CrossRefGoogle Scholar
Huber, L., Grabowski, B., Militzer, M., Neugebauer, J., and Rottler, J.: Ab initio modelling of solute segregation energies to a general grain boundary. Acta Mater. 132, 138 (2017).CrossRefGoogle Scholar
Scheiber, D., Pippan, R., Puschnig, P., Ruban, A., and Romaner, L.: Ab initio search for cohesion-enhancing solute elements at grain boundaries in molybdenum and tungsten. Int. J. Refract. Met. Hard Mater. 60, 75 (2016).CrossRefGoogle Scholar
Scheiber, D., Pippan, R., Puschnig, P., and Romaner, L.: Ab-initio search for cohesion-enhancing impurity elements at grain boundaries in molybdenum and tungsten. Modell. Simul. Mater. Sci. Eng. 24, 085009 (2016).CrossRefGoogle Scholar
Chen, N., Niu, L.L., Zhang, Y., Shu, X., Zhou, H.B., Jin, S., Ran, G., Lu, G.H., and Gao, F.: Energetics of vacancy segregation to [100] symmetric tilt grain boundaries in bcc tungsten. Sci. Rep. 6, 36955 (2014).CrossRefGoogle Scholar
Chai, J., Li, Y.H., Niu, L.L., Qin, S.Y., Zhou, H.B., Shuo, J., Zhang, Y., and Lu, G.H.: First-principles investigation of the energetics of point defects at a grain boundary of tungsten. Nucl. Instrum. Methods Phys. Res., Sect. B 393, 144 (2017).CrossRefGoogle Scholar
Wang, X.X., Niu, L.L., and Wang, S.: Strong trapping and slow diffusion of helium in a tungsten grain boundary. J. Nucl. Mater. 487, 158 (2017).CrossRefGoogle Scholar
Sun, L., Jin, S., Zhou, H.B., Zhang, Y., and Lu, G.Y.: Dissolution and diffusion of hydrogen in a molybdenum grain boundary: A first-principles investigation. Comput. Mater. Sci. 102, 243 (2015).CrossRefGoogle Scholar
Lenchuk, O., Rohrer, J., and Albe, K.: Atomistic modelling of zirconium and silicon segregation at twist and tilt grain boundaries in molybdenum. J. Mater. Sci. 51, 1873 (2016).CrossRefGoogle Scholar
Lindman, A., Helgee, E.E., Nyman, B.J., and Wahnström, G.: Oxygen vacancy segregation in grain boundaries of BaZrO3 using interatomic potentials. Solid State Ionics 230, 27 (2013).CrossRefGoogle Scholar
Helgee, E.E., Lindman, A., and Wahnström, G.: Origin space charge in grain boundaries of proton conducting BaZrO3. Fuel Cells 13, 19 (2013).CrossRefGoogle Scholar
Lindman, A., Helgee, E.E., and Wahnström, G.: Theoretical modeling of defect segregation and space charge formation in the BaZrO3 (210)[001] tilt grain boundary. Solid State Ionics 252, 121 (2013).CrossRefGoogle Scholar
Yang, J.H., Kim, B.K., and Kim, Y.C.: Calculations of proton conductivity at the Σ3(111)$\left[ {1\bar{1}0} \right]$ tilt grain boundary of barium zirconate using density functional theory. Solid State Ionics 279, 60 (2015).CrossRefGoogle Scholar
Kim, J.S. and Kim, Y.C.: Proton conduction in nonstoichiometric Σ3 BaZrO3 (210)[001] tilt grain boundary using density functional theory. J. Korean Ceram. Soc. 53, 301 (2017).CrossRefGoogle Scholar
Lindman, A., Bjørheim, T.S., and Wahnström, G.: Defect segregation to grain boundaries in BaZrO3 from first principles free energy calculations. J. Mater. Chem. A 5, 13421 (2017).CrossRefGoogle Scholar
Všianská, M. and Šob, M.: The effect of segregated sp-impurities on grain-boundary and surface structure, magnetism and embrittlement in nickel. Prog. Mater. Sci. 56, 817 (2011).CrossRefGoogle Scholar
Lejček, P. and Hofmann, S.: Thermodynamics of grain boundary segregation and applications to anisotropy, compensation effect and prediction. Crit. Rev. Solid State Mater. Sci. 33, 133 (2008).CrossRefGoogle Scholar
Lejček, P., Šob, M., Paidar, V., and Vitek, V.: Why calculated energies of grain boundary segregation are unreliable when segregant solubility is low. Scr. Mater. 68, 547 (2013).CrossRefGoogle Scholar
Rez, P. and Alvarez, J.R.: Calculation of cohesion and changes in electronic structure due to impurity segregation at boundaries in iron. Acta Mater. 47, 4069 (1999).CrossRefGoogle Scholar
Yuasa, M. and Mabuchi, M.: Bond mobility mechanism in grain boundary embrittlement: First-principles tensile tests of Fe with a P-segregated Σ3 grain boundary. Phys. Rev. B 82, 094108 (2010).CrossRefGoogle Scholar
Yuasa, M. and Mabuchi, M.: First-principles study on enhanced grain boundary embrittlement of iron by phosphorus segregation. Mater. Trans. 52, 1369 (2011).CrossRefGoogle Scholar
Wu, R., Freeman, A.J., and Olson, G.B.: First principles determination of phosphorus and boron on iron grain boundary cohesion. Science 265, 376 (1994).CrossRefGoogle ScholarPubMed
Fen, Y.Q. and Wang, C.Y.: Electronic effects of nitrogen and phosphorus on iron grain boundary cohesion. Comput. Mater. Sci. 20, 48 (2001).CrossRefGoogle Scholar
Yamaguchi, M.: First-principles study on the grain boundary embrittlement of metals by solute segregation: Part I. Iron (Fe)-solute (B, C, P, and S) systems. Metall. Mater. Trans. A 42, 319 (2011).CrossRefGoogle Scholar
Yamaguchi, M.: First-principles calculations of the grain-boundary cohesive energy—Embrittling or strengthening effect of solute segregation in a bcc FeΣ3(111) grain boundary. J. Japan Inst. Met. 72, 657 (2008).CrossRefGoogle Scholar
Rajagopalan, M., Tschopp, M.A., and Solanki, K.N.: Grain boundary segregation of interstitial and substitutional impurity atoms in alpha-iron. JOM 66, 129 (2014).CrossRefGoogle Scholar
Ko, W.S., Jeon, J.B., Lee, C.H., Lee, J.K., and Lee, B.J.: Intergranular embrittlement of iron by phosphorus segregation: An atomistic simulation. Modell. Simul. Mater. Sci. Eng. 21, 025012 (2013).CrossRefGoogle Scholar
Braithwaite, S. and Rez, P.: Grain boundary impurities in iron. Acta Mater. 53, 2715 (2005).CrossRefGoogle Scholar
Wachowicz, E. and Kiejna, A.: Effect of impurities on structural, cohesive and magnetic properties of grain boundaries in α-Fe. Modell. Simul. Mater. Sci. Eng. 19, 025001 (2011).CrossRefGoogle Scholar
Všianská, M. and Šob, M.: to be published.Google Scholar
Ko, W.S., Kim, N.J., and Lee, B.J.: Atomistic modeling of an impurity element and metal-impurity system: pure P and Fe–P system. J. Phys.: Condens. Matter 24, 225002 (2012).Google ScholarPubMed
Lejček, P., Hofmann, S., and Janovec, J.: Prediction of enthalpy and entropy of solute segregation at individual grain boundaries of α-iron and ferrite steels. Mater. Sci. Eng., A 462, 76 (2007).CrossRefGoogle Scholar
Erhart, H. and Grabke, H.J.: Equilibrium segregation of phosphorus at grain boundaries of Fe–P, Fe–C–P, Fe–Cr–P, and Fe–Cr–C–P alloys. Met. Sci. 15, 401 (1981).CrossRefGoogle Scholar
Zhang, Y., Feng, W.Q., Liu, Y.L., Lu, G.H., and Wang, T.: First-principles study of helium effect in a ferromagnetic iron grain boundary: Energetics, site preference and segregation. Nucl. Instrum. Methods Phys. Res., Sect. B 267, 3200 (2009).CrossRefGoogle Scholar