Journal of Materials Science

, Volume 51, Issue 4, pp 1873–1881 | Cite as

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

  • Olena LenchukEmail author
  • Jochen Rohrer
  • Karsten Albe
Original Paper


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.


Fracture Toughness Formation Energy Intergranular Fracture Cohesive Strength Coincidence Site Lattice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The research was supported by the German Research Foundation (DFG) through Project AL 578/9-1 within the Research Unit FOR 727 “Beyond Nickel-Base Superalloys”. The authors gratefully acknowledge the computing time granted by the John von Neumann Institute for Computing (NIC) and provided on the supercomputer JUROPA at Jülich Supercomputing Center (JSC). Computational time was also made available by the HRZ (Lichtenberg-Cluster) at TU Darmstadt. The authors would like to thank Prof. M. Heilmaier for scientific discussions.

Supplementary material

10853_2015_9494_MOESM1_ESM.pdf (10.5 mb)
Supplementary material 1 (PDF 10727 kb)


  1. 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)01880-9 CrossRefGoogle Scholar
  2. 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.2008.10.093 CrossRefGoogle Scholar
  3. 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.2009.04.040 CrossRefGoogle Scholar
  4. 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/s10853-012-6815-2 CrossRefGoogle Scholar
  5. 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/s11661-005-0166-4 CrossRefGoogle Scholar
  6. 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.2008.03.006 CrossRefGoogle Scholar
  7. 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.2004.09.034 CrossRefGoogle Scholar
  8. 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)00093-5 CrossRefGoogle Scholar
  9. 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)00098-4 CrossRefGoogle Scholar
  10. 10.
    Schneibel JH, Kramer MJ, Easton DS (2002) A Mo–Si–B intermetallic alloy with a continuous \(\alpha \)-Mo matrix. Scripta Mater 46(3):217–221. doi: 10.1016/S1359-6462(01)01227-1 CrossRefGoogle Scholar
  11. 11.
    Van der Ven A, Ceder G (2004) The thermodynamics of decohesion. Acta Mater 52:1223–1235. doi: 10.1016/j.actamat.2003.11.007 CrossRefGoogle Scholar
  12. 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-z CrossRefGoogle Scholar
  13. 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):154–159CrossRefGoogle Scholar
  14. 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.2010.12.002 CrossRefGoogle Scholar
  15. 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 \(\alpha \)-Mo matrix and improved mechanical properties. Intermetallics 16:933–941. doi: 10.1016/j.intermet.2008.04.015 CrossRefGoogle Scholar
  16. 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, TNGoogle Scholar
  17. 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.2011.09.003 CrossRefGoogle Scholar
  18. 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/s11085-009-9175-9 CrossRefGoogle Scholar
  19. 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/s10853-014-8485-8 CrossRefGoogle Scholar
  20. 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.2006.07.153 CrossRefGoogle Scholar
  21. 21.
    Northcott L (1956) Molybdenum. Butterworths Scientific Publications, LondonGoogle Scholar
  22. 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, ColumbusGoogle Scholar
  23. 23.
    Hofmann S, Lejček P (1996) Solute segregation at grain boundaries. Interfaces Sci 3(4):241–267. doi: 10.1007/BF00194704 CrossRefGoogle Scholar
  24. 24.
    Lejček P (2010) Grain boundary segregation in metals. Springer, Prague. doi: 10.1007/978-3-642-12505-8 Google Scholar
  25. 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/s11837-012-0475-1 CrossRefGoogle Scholar
  26. 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)90372-9 CrossRefGoogle Scholar
  27. 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.2014.10.007 CrossRefGoogle Scholar
  28. 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)90997-0 CrossRefGoogle Scholar
  29. 29.
    Ikeda K, Morita K, Nakashima H, Abe H (1999) Misorientation dependence of grain boundary fracture strength and grain boundary energy for molybdenum \(\langle 001 \rangle \) symmetric tilt boundaries. J Jpn Inst Met 63(2):179–186Google Scholar
  30. 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)90104-8 CrossRefGoogle Scholar
  31. 31.
    Kopetskii CV, Pashkovskii AI (1973) Mechanical properties of molybdenum bicrystals. Sov Phys Dokl 18:340–341Google Scholar
  32. 32.
    Kurishita H, Kuba S, Kubo H, Yoshinaga H (1985) Misorientation dependence of grain boundary fracture in molybdenum bicrystals with various \(\langle 110 \rangle \) twist boundaries. Trans Jpn Inst Met 26(5):332–340CrossRefGoogle Scholar
  33. 33.
    Howe JM (1997) Interfaces in materials: atomic structure, thermodynamics and kinetics of solid-vapor, solid-liquid and solid-solid interfaces. Wiley, New YorkGoogle Scholar
  34. 34.
    Blöchl PE (1994) Projector augmented-wave method. Phys Rev B 50:17953–17979. doi: 10.1103/PhysRevB.50.17953 CrossRefGoogle Scholar
  35. 35.
    Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev B 136:864–871. doi: 10.1103/PhysRev.136.B864 CrossRefGoogle Scholar
  36. 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.145.561 CrossRefGoogle Scholar
  37. 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.54.11169 CrossRefGoogle Scholar
  38. 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)00008-0 CrossRefGoogle Scholar
  39. 39.
    Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865–3868. doi: 10.1103/PhysRevLett.77.3865 CrossRefGoogle Scholar
  40. 40.
    Monkhorst HJ, Pack JD (1976) Special points for brillouin-zone integrations. Phys Rev B 13:5188–5192. doi: 10.1103/PhysRevB.13.5188 CrossRefGoogle Scholar
  41. 41.
    Okamoto H (2004) Mo–Zr (molybdenum–zirconium). J Phase Equilib Diff 25:485. doi: 10.1007/s11669-004-0146-1 CrossRefGoogle Scholar
  42. 42.
    Gokhale AB, Abbaschian GJ (1991) The Mo–Si (molybdenum-silicon) system. J Phase Equilib 12:493–498. doi: 10.1007/BF02645979 CrossRefGoogle Scholar
  43. 43.
    Rose JH, Smith JR, Ferrante J (1983) Universal features of bonding in metals. Phys Rev B 28:1835–1845. doi: 10.1103/PhysRevB.28.1835 CrossRefGoogle Scholar
  44. 44.
    Friedel J (1958) Metalic alloys. Il Nuovo Cim 7:287–311. doi: 10.1007/BF02751483 CrossRefGoogle Scholar
  45. 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.1.4555 CrossRefGoogle Scholar
  46. 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.59.1677 CrossRefGoogle Scholar
  47. 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.72.153404 CrossRefGoogle Scholar
  48. 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.2011.04.024 CrossRefGoogle Scholar
  49. 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.74.155416 CrossRefGoogle Scholar
  50. 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.1980.0043 CrossRefGoogle Scholar
  51. 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.67.224101 CrossRefGoogle Scholar
  52. 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 Google Scholar
  53. 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.2013.08.017 CrossRefGoogle Scholar
  54. 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: 10.1088/0965-0393/21/7/075005 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institut für MaterialwissenschaftTechnische Universität DarmstadtDarmstadtGermany

Personalised recommendations