journal article·2016-02

Atomistic modelling of zirconium and silicon segregation at twist and tilt grain boundaries in molybdenum

Olena Lenchuk, Jochen Rohrer, Karsten Albe

Journal of Materials Science· Volume 51· Issue 4
Publisher page

Abstract

We investigate the influence of Zr and Si segregation on the cohesive strength of grain boundaries (GBs) in molybdenum using density functional theory calculations. A tilt $$\Sigma $$ 5(310)[001] and twist $$\Sigma $$ 5[001] GB in bicrystal geometry are chosen as structural models. We determine the site preference of Zr and Si for segregation in these GBs and define the segregation energy. We quantify the effect of solutes on the stability of the GBs against brittle fracture by means of the Griffith criterion (work of separation). Additionally, the intrinsic bond strength of the GB containing a solute is quantified by means of the theoretical strength. The results show that Zr and Si tend to segregate at the GBs if the low-energy insertion sites are available. However, the work of separation is decreased by the presence of Zr and Si and even in the presence of oxygen, there is no increase of the Griffith energy. Contributions of strain and chemical energy are analysed in order to explain our findings.
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OpenAlex topics: Microstructure and mechanical properties · Fusion materials and technologies · Nuclear Materials and Properties

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References (54)

Show source-provided references
1. Miller MK, Bryhan AJ (2002) Effect of Zr, B and C additions on the ductility of molybdenum. Mater Sci Eng A 327(1):80–83. doi: 10.1016/S0921-5093(01)01880-910.1016/S0921-5093(01)01880-9 ↗
2. Chakraborty SP, Banerjee S, Sharma IG, Paul B, Suri AK (2009) Studies on the synthesis and characterization of a molybdenum-based alloy. J Alloy Compd 477:256–261. doi: 10.1016/j.jallcom.2008.10.09310.1016/j.jallcom.2008.10.093 ↗
3. Saage H, Krüger M, Sturm D, Heilmaier M, Schneibel JH, George E, Heatherly L, Somsen C, Eggeler G, Yang Y (2009) Ductilization of Mo–Si solid solutions manufactured by powder metallurgy. Acta Mater 57(13):3895–3901. doi: 10.1016/j.actamat.2009.04.04010.1016/j.actamat.2009.04.040 ↗
4. Jung J, Zhou N, Jian L (2012) Effects of sintering aids on the densification of Mo–Si–B alloys. J Mater Sci 47(24):8308–8319. doi: 10.1007/s10853-012-6815-210.1007/s10853-012-6815-2 ↗
5. Schneibel JH, Tortorelli PF, Ritchie RO, Kruzic JJ (2005) Optimization of Mo–Si–B intermetallic alloys. Metall Mater Trans A 36:525–531. doi: 10.1007/s11661-005-0166-410.1007/s11661-005-0166-4 ↗
6. Fan J, Lu M, Cheng H, Tian J, Huang B (2009) Effect of alloying elements Ti, Zr on the property and microstructure of molybdenum. Int J Refract Met H 27:78–82. doi: 10.1016/j.ijrmhm.2008.03.00610.1016/j.ijrmhm.2008.03.006 ↗
7. Geller CB, Smith RW, Hack JE, Saxe P, Wimmer E (2005) A computational search for ductilizing additives to Mo. Scripta Mater 52:205–210. doi: 10.1016/j.scriptamat.2004.09.03410.1016/j.scriptamat.2004.09.034 ↗
8. Schneibel JH, Kramer MJ, Ünal O, Wright RN (2001) Processing and mechanical properties of a molybdenum silicide with the composition Mo–12Si–8.5B (at.%). Intermetallics 9(1):25–31. doi: 10.1016/S0966-9795(00)00093-510.1016/S0966-9795(00)00093-5 ↗
9. Nieh TG, Wang JG, Liu CT (2001) Deformation of a multiphase Mo–9.4Si–13.8B alloy at elevated temperatures. Intermetallics 9(1):73–79. doi: 10.1016/S0966-9795(00)00098-410.1016/S0966-9795(00)00098-4 ↗
10. Schneibel JH, Kramer MJ, Easton DS (2002) A Mo–Si–B intermetallic alloy with a continuous $$\alpha $$ α -Mo matrix. Scripta Mater 46(3):217–221. doi: 10.1016/S1359-6462(01)01227-110.1016/S1359-6462(01)01227-1 ↗
11. Van der Ven A, Ceder G (2004) The thermodynamics of decohesion. Acta Mater 52:1223–1235. doi: 10.1016/j.actamat.2003.11.00710.1016/j.actamat.2003.11.007 ↗
12. Watanabe T (2011) Grain boundary engineering: historical perspective and future prospects. J Mater Sci 46(12):4095–4115. doi: 10.1007/s10853-011-5393-z10.1007/s10853-011-5393-z ↗
13. Hiraoka Y, Irie H, Okada M (1984) Tensile properties of electron-beam-welded Mo–Nb, Mo–Zr and Mo–Re alloys. J Jpn Weld Soc 2(1):154–15910.2207/qjjws.2.154 ↗
14. Mousa M, Wanderka N, Timpel M, Singh S, Krüger M, Heilmaier M, Banhart J (2011) Modification of Mo–Si alloy microstructure by small additions of Zr. Ultramicroscopy 111:706–710. doi: 10.1016/j.ultramic.2010.12.00210.1016/j.ultramic.2010.12.002 ↗
15. Krüger M, Franz S, Saage H, Heilmaier M, Schneibel JH, Jéhanno P, Böning M, Kestler H (2008) Mechanically alloyed Mo–Si–B alloys with a continuous $$\alpha $$ α -Mo matrix and improved mechanical properties. Intermetallics 16:933–941. doi: 10.1016/j.intermet.2008.04.01510.1016/j.intermet.2008.04.015 ↗
16. Schneibel JH, Brady MP, Meyer HM, Horton JA, Kruzic JJ, Ritchie RO (2005) Mo–Si–B alloy development. In: 19th annual conference on fossil energy materials, Knoxville, TN
17. Lemberg JA, Middlemas MR, Weingärtner T, Gludovatz B, Cochran JK, Ritchie RO (2012) On the fracture toughness of fine-grained Mo–3Si–1B (wt.%) alloys at ambient to elevated (1300 $$^\circ $$ ∘ C) temperatures. Intermetallics 20(1):141–154. doi: 10.1016/j.intermet.2011.09.00310.1016/j.intermet.2011.09.003 ↗
18. Burk S, Gorr B, Trindade VB, Christ H-J (2010) Effect of Zr addition on the high-temperature oxidation behaviour of Mo–3Si–1B alloys. Oxid Met 73:163–181. doi: 10.1007/s11085-009-9175-910.1007/s11085-009-9175-9 ↗
19. Cook B, Bonino C, Trainham J (2014) Solid-state processing of oxidation-resistant molybdenum borosilicide composites for ultra-high-temperature applications. J Mater Sci 49(22):7750–7759. doi: 10.1007/s10853-014-8485-810.1007/s10853-014-8485-8 ↗
20. Sturm D, Heilmaier M, Schneibel JH, Jéhanno P, Skrotzki B, Saage H (2007) The influence of silicon on the strength and fracture toughness of molybdenum. Mater Sci Eng A 463:107–114. doi: 10.1016/j.msea.2006.07.15310.1016/j.msea.2006.07.153 ↗
21. Northcott L (1956) Molybdenum. Butterworths Scientific Publications, London
22. Bruckart WL, Craighead CM, Jaffee RI (1955) Investigation of molybdenum and molybdenum-base alloys made by powder-metallurgy technique, Fort Belvoir, OH, Belvoir Defense Technical Information Center, Columbus
23. Hofmann S, Lejček P (1996) Solute segregation at grain boundaries. Interfaces Sci 3(4):241–267. doi: 10.1007/BF0019470410.1007/BF00194704 ↗
24. Lejček P (2010) Grain boundary segregation in metals. Springer, Prague. doi: 10.1007/978-3-642-12505-810.1007/978-3-642-12505-8 ↗
25. Krüger M, Schliephake D, Jain P, Kumar KS, Schumacher G, Heilmaier M (2013) Effects of Zr additions on the microstructure and the mechanical behavior of PM Mo–Si–B alloys. JOM 65(2):301–306. doi: 10.1007/s11837-012-0475-110.1007/s11837-012-0475-1 ↗
26. Rice JR, Wang J-S (1989) Embrittlement of interfaces by solute segregation. Mater Sci Eng A 107:23–40. doi: 10.1016/0921-5093(89)90372-910.1016/0921-5093(89)90372-9 ↗
27. Lenchuk O, Rohrer J, Albe K (2015) Solubility of zirconium and silicon in molybdenum studied by first-principles calculations. Scripta Mater 97:1–4. doi: 10.1016/j.scriptamat.2014.10.00710.1016/j.scriptamat.2014.10.007 ↗
28. Tsurekawa A, Tanaka T, Yoshinaga H (1994) Grain boundary structure, energy and strength in molybdenum. Mater Sci Eng A 176(1—-2):341–348. doi: 10.1016/0921-5093(94)90997-010.1016/0921-5093(94)90997-0 ↗
29. Ikeda K, Morita K, Nakashima H, Abe H (1999) Misorientation dependence of grain boundary fracture strength and grain boundary energy for molybdenum $$\langle 001 \rangle $$ ⟨ 001 ⟩ symmetric tilt boundaries. J Jpn Inst Met 63(2):179–18610.2320/jinstmet1952.63.2_179 ↗
30. Sursaeva VG, Glebovsky VG, Schulga YM, Schvindlerman LS (1985) Strength of individual special tilt and twist boundaries in molybdenum bicrystals. Scripta Met 19(4):411–414. doi: 10.1016/0036-9748(85)90104-810.1016/0036-9748(85)90104-8 ↗
31. Kopetskii CV, Pashkovskii AI (1973) Mechanical properties of molybdenum bicrystals. Sov Phys Dokl 18:340–341
32. Kurishita H, Kuba S, Kubo H, Yoshinaga H (1985) Misorientation dependence of grain boundary fracture in molybdenum bicrystals with various $$\langle 110 \rangle $$ ⟨ 110 ⟩ twist boundaries. Trans Jpn Inst Met 26(5):332–34010.2320/matertrans1960.26.332 ↗
33. Howe JM (1997) Interfaces in materials: atomic structure, thermodynamics and kinetics of solid-vapor, solid-liquid and solid-solid interfaces. Wiley, New York
34. Blöchl PE (1994) Projector augmented-wave method. Phys Rev B 50:17953–17979. doi: 10.1103/PhysRevB.50.1795310.1103/PhysRevB.50.17953 ↗
35. Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev B 136:864–871. doi: 10.1103/PhysRev.136.B86410.1103/PhysRev.136.B864 ↗
36. Sham LJ, Kohn W (1966) One-particle properties of an inhomogeneous interacting electron gas. Phys Rev B 145:561–567. doi: 10.1103/PhysRev.145.56110.1103/PhysRev.145.561 ↗
37. Kresse G, Furthmüller J (1996) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 54:11169–11186. doi: 10.1103/PhysRevB.54.1116910.1103/PhysRevB.54.11169 ↗
38. Kresse G, Furthmüller J (1996) Efficiency of ab initio total-energy calculations for metals and semiconductors using a plane-wave basis set. Comput Mater Sci 6:15–50. doi: 10.1016/0927-0256(96)00008-010.1016/0927-0256(96)00008-0 ↗
39. Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865–3868. doi: 10.1103/PhysRevLett.77.386510.1103/PhysRevLett.77.3865 ↗
40. Monkhorst HJ, Pack JD (1976) Special points for brillouin-zone integrations. Phys Rev B 13:5188–5192. doi: 10.1103/PhysRevB.13.518810.1103/PhysRevB.13.5188 ↗
41. Okamoto H (2004) Mo–Zr (molybdenum–zirconium). J Phase Equilib Diff 25:485. doi: 10.1007/s11669-004-0146-110.1007/s11669-004-0146-1 ↗
42. Gokhale AB, Abbaschian GJ (1991) The Mo–Si (molybdenum-silicon) system. J Phase Equilib 12:493–498. doi: 10.1007/BF0264597910.1007/BF02645979 ↗
43. Rose JH, Smith JR, Ferrante J (1983) Universal features of bonding in metals. Phys Rev B 28:1835–1845. doi: 10.1103/PhysRevB.28.183510.1103/PhysRevB.28.1835 ↗
44. Friedel J (1958) Metalic alloys. Il Nuovo Cim 7:287–311. doi: 10.1007/BF0275148310.1007/BF02751483 ↗
45. Lang ND, Kohn W (1970) Theory of metal surfaces: charge density and surface energy. Phys Rev B 1:4555–4568. doi: 10.1103/PhysRevB.1.455510.1103/PhysRevB.1.4555 ↗
46. Cho J-H, Ismail, Zhang Z, Plummer EW (1999) Oscillatory lattice relaxation at metal surfaces. Phys Rev B 59:1677–1680. doi: 10.1103/PhysRevB.59.167710.1103/PhysRevB.59.1677 ↗
47. Sun YY, Huan AC, Feng YP, Wee ATS (2005) Reduction of amplitude and wavelength of Friedel oscillation on Na(111) surface. Phys Rev B 72:153404–153407. doi: 10.1103/PhysRevB.72.15340410.1103/PhysRevB.72.153404 ↗
48. Li JM, Wang J, Sun Q, Jia Y (2011) First-principles study of Friedel oscillations normal to the low index surfaces of Al. Phys B 406(14):2767–2771. doi: 10.1016/j.physb.2011.04.02410.1016/j.physb.2011.04.024 ↗
49. Lozovoi A, Paxton A, Finnis M (2006) Structural and chemical embrittlement of grain boundaries by impurities: a general theory and first-principles calculations for copper. Phys Rev B 74:155416–155428. doi: 10.1103/PhysRevB.74.15541610.1103/PhysRevB.74.155416 ↗
50. Kumar A, Eyre BL (1980) Grain boundary segregation and intergranular fracture in molybdenum. Proc R Soc Lond A 370:431–458. doi: 10.1098/rspa.1980.004310.1098/rspa.1980.0043 ↗
51. Janisch R, Elsässer C (2003) Segregated light elements at grain boundaries in niobium and molybdenum. Phys Rev B 67:224101–224111. doi: 10.1103/PhysRevB.67.22410110.1103/PhysRevB.67.224101 ↗
52. Yang R, Wang YM, Ye HQ, Wang CY (2001) First-principles study of the segregation effects on the cohesion of F.C.C. grain boundary. J Phys 13(20):4485–4493. doi: 10.1088/0953-8984/13/20/309
53. Hochmuth C, Schliephake D, Völkl R, Heilmaier M, Glatzel U (2014) Influence of zirconium content on microstructure and creep properties of Mo–9Si–8B alloys. Intermetallics 48:3–9. doi: 10.1016/j.intermet.2013.08.01710.1016/j.intermet.2013.08.017 ↗
54. Tahir AM, Janisch R, Hartmaier A (2013) Ab initio calculation of traction separation laws for a grain boundary in molybdenum with segregated C impurites. Model Simul Mater Sci 21(7):075005–075020. doi: 10.1088/0965-0393/21/7/07500510.1088/0965-0393/21/7/075005 ↗