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Estimation of grain boundary segregation enthalpy and its role in stable nanocrystalline alloy design

  • Heather A. Murdoch (a1) and Christopher A. Schuh (a1)

Grain boundary segregation provides a method for stabilization of nanocrystalline metals—an alloying element that will segregate to the boundaries can lower the grain boundary energy, attenuating the driving force for grain growth. The segregation strength relative to the mixing enthalpy of a binary system determines the propensity for segregation stabilization. This relationship has been codified for the design space of positive enthalpy alloys; unfortunately, quantitative values for the grain boundary segregation enthalpy exist in only very few material systems, hampering the prospect of nanocrystalline alloy design. Here we present a Miedema-type model for estimation of grain boundary segregation enthalpy, with which potential nanocrystalline phase-forming alloys can be rapidly screened. Calculations of the necessary enthalpies are made for ∼2500 alloys and used to make predictions about nanocrystalline stability.

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1.Weissmüller J.: Alloy effects in nanostructures. Nanostruct. Mater. 3(1–6), 261 (1993).
2.Weissmüller J.: Some basic notions on nanostructured solids. Mater. Sci. Eng., A 179180(Part 1), 102 (1994).
3.Kirchheim R.: Grain coarsening inhibited by solute segregation. Acta Mater. 50(2), 413 (2002).
4.Liu F. and Kirchheim R.: Nano-scale grain growth inhibited by reducing grain boundary energy through solute segregation. J. Cryst. Growth 264(1–3), 385 (2004).
5.Kirchheim R.: Reducing grain boundary, dislocation line and vacancy formation energies by solute segregation. I. Theoretical background. Acta Mater. 55(15), 5129 (2007).
6.Foiles S.M.: Calculation of grain-boundary segregation in Ni-Cu alloys. Phys. Rev. B 40(17), 11502 (1989).
7.Purohit Y., Jang S., Irving D.L., Padgett C.W., Scattergood R.O., and Brenner D.W.: Atomistic modeling of the segregation of lead impurities to a grain boundary in an aluminum bicrystalline solid. Mater. Sci. Eng., A 493(1–2), 97 (2008).
8.Detor A.J. and Schuh C.A.: Grain boundary segregation, chemical ordering and stability of nanocrystalline alloys: Atomistic computer simulations in the Ni–W system. Acta Mater. 55(12), 4221 (2007).
9.Menyhard M., Yan M., and Vitek V.: Atomistic vs phenomenological approaches to grain boundary segregation: Computer modeling of Cu-Ag alloys. Acta Metall. et Mater. 42(8), 2783 (1994).
10.Kirchner A. and Kieback B.: Thermodynamic model of alloy grain boundaries. Scr. Mater. 64(5), 406 (2011).
11.Lejcek P.: Grain Boundary Segregation in Metals Vol. 136 (Springer, Berlin, Germany, 2010).
12.Alber U., Müllejans H., and Rühle M.: Bismuth segregation at copper grain boundaries. Acta Mater. 47(15–16), 4047 (1999).
13.Chang L.S. and Huang K.B.: Temperature dependence of the grain boundary segregation of Bi in Ni polycrystals. Scr. Mater. 51(6), 551 (2004).
14.Chen Z., Liu F., Yang X., Shen C., and Fan Y.: Analysis of controlled-mechanism of grain growth in undercooled Fe–Cu alloy. J. Alloys Compd. 509(25), 7109 (2011).
15.Liu F.: Grain growth in nanocrystalline Fe-Ag thin film. Mater. Lett. 59(11), 1458 (2005).
16.Weissmüller J., Krauss W., Haubold T., Birringer R., and Gleiter H.: Atomic structure and thermal stability of nanostructured Y-Fe alloys. Nanostruct. Mater. 1(6), 439 (1992).
17.Chen X. and Mao J.: Thermal stability and tensile properties of electrodeposited Cu-Bi alloy. J. Mater. Eng. Perform. 20(3), 481 (2011).
18.Darling K.A., VanLeeuwen B.K., Koch C.C., and Scattergood R.O.: Thermal stability of nanocrystalline Fe-Zr alloys. Mater. Sci. Eng., A 527(15), 3572 (2010).
19.Krill C.E., Ehrhardt H., and Birringer R.: Thermodynamic stabilization of nanocrystallinity. Z. Metallkd. 96(10), 1134 (2005).
20.Atwater M., Bahmanpour H., Scattergood R., and Koch C.: The thermal stability of nanocrystalline cartridge brass and the effect of zirconium additions. J. Mater. Sci. 148(1), 220226 (2012).
21.Choi P., da Silva M., Klement U., Al-Kassab T., and Kirchheim R.: Thermal stability of electrodeposited nanocrystalline Co-1.1at.%P. Acta Mater. 53(16), 4473 (2005).
22.Atwater M.A., Roy D., Darling K.A., Butler B.G., Scattergood R.O., and Koch C.C.: The thermal stability of nanocrystalline copper cryogenically milled with tungsten. Mater. Sci. Eng., A 558, 226 (2012).
23.Atwater M.A., Scattergood R.O., and Koch C.C.: The stabilization of nanocrystalline copper by zirconium. Mater. Sci. Eng., A 559, 250 (2013).
24.Osmola D., Nolan P., Erb U., Palumbo G., and Aust K.T.: Microstructural evolution at large driving forces during grain growth of ultrafine-grained Ni–1.2wt%P. Phys. Status Solidi A 131(2), 569 (1992).
25.Talin A.A., Marquis E.A., Goods S.H., Kelly J.J., and Miller M.K.: Thermal stability of Ni-Mn electrodeposits. Acta Mater. 54(7), 1935 (2006)
26.Pellicer E., Varea A., Sivaraman K.M., Pane S., Surinach S., Dolors Baro M., Nogues J., Nelson B.J., and Sort J.: Grain boundary segregation and interdiffusion effects in nickel-copper alloys: An effective means to improve the thermal stability of nanocrystalline nickel. ACS Appl. Mater. Interfaces 3(7) 2265 (2011).
27.Abe Y.R., Holzer J.C., and Johnson W.L.: Formation and stability of nanocrystalline Nb-Cu alloys In Structure and Properties of Interfaces in Materials, edited by Briant C.L., Clark W.A.T., and Dahmen U. (Mater. Res. Soc. Symp. Proc. 238, Warrendale, PA 1991), p. 721.
28.Detor A.J. and Schuh C.A.: Microstructural evolution during the heat treatment of nanocrystalline alloys. J. Mater. Res. 22(11), 3233 (2007).
29.VanLeeuwen B.K., Darling K.A., Koch C.C., Scattergood R.O., and Butler B.G.: Thermal stability of nanocrystalline Pd81Zr19. Acta Mater. 58(12), 4292 (2010).
30.da Silva M., Wille C., Klement U., Choi P., and Al-Kassab T.: Electrodeposited nanocrystalline Co-P alloys: Microstructural characterization and thermal stability. Mater. Sci. Eng., A 445446, 31 (2007).
31.Färber B., Cadel E., Menand A., Schmitz G., and Kirchheim R.: Phosphorus segregation in nanocrystalline Ni-3.6 at.% P alloy investigated with the tomographic atom probe (TAP). Acta Mater. 48(3), 789 (2000).
32.Hentschel T., Isheim D., Kirchheim R., Muller F., and Kreye H.: Nanocrystalline Ni-3.6 at.% P and its transformation sequence studied by atom-probe field-ion microscopy. Acta Mater. 48(4), 933 (2000).
33.Mehta S.C., Smith D.A., and Erb U.: Study of grain growth in electrodeposited nanocrystalline nickel-1.2 wt% phosphorus alloy. Mater. Sci. Eng., A 204(1–2), 227 (1995).
34.Eckert J., Holzer J.C., and Johnson W.L.: Thermal-stability and grain-growth behavior of mechanically alloyed nanocrystalline Fe-Cu alloys. J. Appl. Phys. 73(1), 131 (1993).
35.Rouya E., Stafford G.R., Bertocci U., Mallett J.J., Schad R., Begley M.R., Kelly R.G., Reed M.L., and Zangari G.: Electrodeposition of metastable Au-Ni alloys. J. Electrochem. Soc. 157(7), D396 (2010).
36.Bryden K.J. and Ying J.Y.: Thermal stability and hydrogen absorption characteristics of palladium-yttrium nanoalloys. Acta Mater. 44(9), 3847 (1996).
37.Trelewicz J.R. and Schuh C.A.: Grain boundary segregation and thermodynamically stable binary nanocrystalline alloys. Phys. Rev. B 79(9), 094112 (2009).
38.Chookajorn T., Murdoch H.A., and Schuh C.A.: Design of stable nanocrystalline alloys. Science 337(6097), 951 (2012).
39.Murdoch H.A. and Schuh C.A.: Stability of binary nanocrystalline alloys against grain growth and phase separation. Acta Mater. 61(6), 2121 (2013).
40.Lejcek P. and Hofmann S.: Thermodynamic state functions of interfacial segregation and their role in the compensation effect. Rev. Adv. Mater. Sci. 21(1), 27 (2009).
41.Hondros E.D. and Seah M.P.: The theory of grain boundary segregation in terms of surface adsorption analogues. Metall. Trans. A 8(9), 1363 (1977).
42.Seah M.P.: Grain boundary segregation. J. Phys. F: Metal Phys. 10(6), 1043 (1980).
43.McLean D.: Grain boundaries in metals (Oxford Clarendon Press, London, UK, 1957).
44.Wynblatt P. and Chatain D.: Anisotropy of segregation at grain boundaries and surfaces. Metall. Mater. Trans. A 37(9), 2595 (2006).
45.Darling K.A., VanLeeuwen B.K., Semones J.E., Koch C.C., Scattergood R.O., Kecskes L.J., and Mathaudhu S.N.: Stabilized nanocrystalline iron-based alloys: Guiding efforts in alloy selection. Mater. Sci. Eng., A 528(13–14), 4365 (2011).
46.Briant C.L.: Solid solubility and grain boundary segregation. Philos. Mag. Lett. 73(6), 345 (1996).
47.Friedel J.: Electronic structure of primary solid solutions in metals. Adv. Phys. 3(12), 446 (1954).
48.Wynblatt P. and Shi Z.: Relation between grain boundary segregation and grain boundary character in FCC alloys. J. Mater. Sci. 40(11), 2765 (2005).
49.Udler D. and Seidman D.N.: Solute segregation at [001] tilt boundaries in dilute f.c.c. alloys. Acta Mater. 46(4), 1221 (1998).
50.Udler D. and Seidman D.N.: Solute-atom segregation at (002) twist boundaries in dilute Ni–Pt alloys: Structural/chemical relations. Acta Metall. Mater. 42(6), 1959 (1994).
51.Udler D. and Seidman D.N.: Solute-atom segregation at high-angle (002) twist boundaries in dilute Au-Pt alloys. J. Mater. Res. 10(8), 1933 (1995).
52.Duparc O., Larere A., Lezzar B., Khalfallah O., and Paidar V.: Comparison of the intergranular segregation for eight dilute binary metallic systems in the Σ 11′ {332} tilt grain boundary. J. Mater. Sci. 40(12), 3169 (2005).
53.Purohit Y., Sun L., Irving D.L., Scattergood R.O., and Brenner D.W.: Computational study of the impurity induced reduction of grain boundary energies in nano- and bi-crystalline Al-Pb alloys. Mater. Sci. Eng., A 527(7–8), 1769 (2010).
54.Bakker H.: Enthalpies in Alloys: Miedema’s Semi-empirical Model (Trans Tech Publications, Enfield, New Hampshire, 1998). Boer F.R., Boom R., Mattens W.C.M., Miedema A.R., and Niessen A.K.: Cohesion in Metals: Transition Metal Alloys (North-Holland, Amsterdam, Netherlands, 1988).
56.Miedema A.R.: Surface segregation in alloys of transition-metals. Z. Metallkd. 69(7), 455 (1978).
57.Redlich O. and Kister A.T.: Algebraic representation of thermodynamic properties and the classification of solutions. Ind. Eng. Chem. 40(2), 345 (1948).
58.Moon I.H., Ryu S.S., Kim S.W., Won D.M., and Jang W.S.: Grain growth in the nanocrystalline W-Cu and Cu-Pb composite powders prepared by mechanical alloying. Z. Metallkd. 92(8), 986 (2001).
59.Mayr S.G. and Bedorf D.: Stabilization of Cu nanostructures by grain boundary doping with Bi: Experiment versus molecular dynamics simulation. Phys. Rev. B 76(2), 024111 (2007).
60.Zhu M., Wu Z., Zeng M., Ouyang L., and Gao Y.: Bimodal growth of the nanophases in the dual-phase composites produced by mechanical alloying in immiscible Cu–Ag system. J. Mater. Sci. 43(9), 3259 (2008).
61.Wu Z.F., Zeng M.Q., Ouyang L.Z., Zhang X.P., and Zhu M.: Ostwald ripening of Pb nanocrystalline phase in mechanically milled Al-Pb alloys and the influence of Cu additive. Scr. Mater. 53(5), 529 (2005).
62.Liu F.: Precipitation of a metastable Fe(Ag) solid solution upon annealing of supersaturated Fe(Ag) thin film prepared by pulsed laser deposition. Appl. Phys. A 81(5), 1095 (2005).
63.Pellicer E., Varea A., Pane S., Nelson B.J., Menendez E., Estrader M., Surinach S., Baro M.D., Nogues J., and Sort J.: Nanocrystalline electroplated Cu-Ni: Metallic thin films with enhanced mechanical properties and tunable magnetic behavior. Adv. Funct. Mater. 20(6), 983 (2010).
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