Journal of Materials Science

, Volume 52, Issue 11, pp 6235–6248 | Cite as

Understanding dislocation slip in stoichiometric rocksalt transition metal carbides and nitrides

  • Hang Yu
  • Mohammadreza Bahadori
  • Gregory B. Thompson
  • Christopher R. Weinberger
Original Paper

Abstract

The slip systems for B1 MX compounds (M=Ti, Zr, Hf, V, Nb, Ta and X=C, N) have been studied extensively both experimentally and computationally as they influence the materials mechanical behavior at both high and low temperatures. Despite many investigations, the differences in observed slip systems, either \(\{111\}\) or \(\{110\}\), in these materials remain an open question. In this paper, the factors that may determine the slip preference of these compounds have been studied based on the results from first principle calculations. The generalized stacking fault surfaces for all of the materials were computed and used to provide a more comprehensive understanding of slip plane choices. Through analysis of this data, it is found that among different indicators of slip, the normalized splitting width and the intrinsic stacking fault energy are the most useful indicators of the choice of slip planes in these materials. In addition, these indicators of slip are controlled by the structural energy differences between the B1 and tungsten carbides structures, which are correlated well with the number of valence electrons.

References

  1. 1.
    Wuchina E, Opila E, Opeka M, Fahrenholtz W, Talmy I (2007) UHTCs: ultra-high temperature ceramic materials for extreme environment applications. Electrochem Soc Interface 16:30Google Scholar
  2. 2.
    Fahrenholtz WG, Wuchina EJ, Lee WE, Zhou Y (2014) Ultra-high temperature ceramics: materials for extreme environment applications. Wiley, New YorkCrossRefGoogle Scholar
  3. 3.
    Dieter GE, Bacon DJ (1986) Mechanical metallurgy, vol 3. McGraw-Hill, New YorkGoogle Scholar
  4. 4.
    Rv Mises (1928) Mechanik der plastischen formänderung von kristallen. Z Angew Math Mech 8:161–185CrossRefGoogle Scholar
  5. 5.
    Hollox G, Smallman R (1966) Plastic behavior of titanium carbide. J Appl Phys 37:818–823CrossRefGoogle Scholar
  6. 6.
    Hannink R, Kohlstedt D, Murray M (1972) Slip system determination in cubic carbides by hardness anisotropy. Proc R Soc Lond A Math Phys Eng Sci 326:409–420CrossRefGoogle Scholar
  7. 7.
    Kumashiro Y, Itoh A, Kinoshita T, Sobajima M (1977) The micro-vickers hardness of TiC single crystals up to 1500\(^{\circ }\)C. J Mater Sci 12:595–601. doi:10.1007/BF00540285 CrossRefGoogle Scholar
  8. 8.
    Kumashiro Y, Nagai Y, Katō H, Sakuma E, Watanabe K, Misawa S (1981) The preparation and characteristics of ZrC and TaC single crystals using an r.f. floating-zone process. J Mater Sci 16:2930–2933. doi:10.1007/BF00552985 CrossRefGoogle Scholar
  9. 9.
    Rowcliffe DJ, Hollox GE (1971) Plastic flow and fracture of tantalum carbide and hafnium carbide at low temperatures. J Mater Sci 6:1261–1269. doi:10.1007/BF00552039 CrossRefGoogle Scholar
  10. 10.
    Lee D, Haggerty J (1969) Plasticity and creep in single crystals of zirconium carbide. J Am Ceram Soc 52:641–647CrossRefGoogle Scholar
  11. 11.
    Chien F, Ning X, Heuer A (1996) Slip systems and dislocation emission from crack tips in single crystal TiC at low temperatures. Acta Mater 44:2265–2283CrossRefGoogle Scholar
  12. 12.
    Chatterjee D, Mendiratta M, Lipsitt H (1979) Deformation behaviour of single crystals of titanium carbide. J Mater Sci 14:2151–2156. doi:10.1007/BF00688420 CrossRefGoogle Scholar
  13. 13.
    Kumashiro Y, Sakuma E (1980) The vickers micro-hardness of non-stoichiometric niobium carbide and vanadium carbide single crystals up to 1500\(^{\circ }\)C. J Mater Sci 15:1321–1324. doi:10.1007/BF00551827 CrossRefGoogle Scholar
  14. 14.
    Morgan G, Lewis M (1974) Hardness anisotropy in niobium carbide. J Mater Sci 9:349–358. doi:10.1007/BF00737834 CrossRefGoogle Scholar
  15. 15.
    De Leon N, Yu Xx YuH, Weinberger CR, Thompson GB (2015) Bonding effects on the slip differences in the B1 monocarbides. Phys Rev Lett 114:165502CrossRefGoogle Scholar
  16. 16.
    Hultman L, Shinn M, Mirkarimi P, Barnett S (1994) Characterization of misfit dislocations in epitaxial (001)-oriented TiN, NbN, VN, and (Ti, Nb)N film heterostructures by transmission electron microscopy. J Cryst Growth 135:309–317CrossRefGoogle Scholar
  17. 17.
    Odén M, Ljungcrantz H, Hultman L (1997) Characterization of the induced plastic zone in a single crystal TiN (001) film by nanoindentation and transmission electron microscopy. J Mater Res 12:2134–2142CrossRefGoogle Scholar
  18. 18.
    Li N, Yadav S, Liu XY, Wang J, Hoagland R, Mara N, Misra A (2015) Quantification of dislocation nucleation stress in TiN through high-resolution in situ indentation experiments and first principles calculations. Sci Rep 5:15813CrossRefGoogle Scholar
  19. 19.
    Vahldiek F, Mersol S (1977) Slip and microhardness of IVa to VIa refractory materials. J. Less Common Metals 55:265–278CrossRefGoogle Scholar
  20. 20.
    Li P, Howe J (2002) Dislocation reactions in ZrN. Acta Mater 50:4231–4239CrossRefGoogle Scholar
  21. 21.
    Vinson K, Yu XX, De Leon N, Weinberger CR, Thompson GB (2016) Plasticity mechanisms in HfN at elevated and room temperature. Sci Rep 6:34571CrossRefGoogle Scholar
  22. 22.
    Zhang R, Sheng S, Veprek S (2013) Origin of different plastic resistance of transition metal nitrides and carbides: Stiffer yet softer. Scripta Mater 68:913–916CrossRefGoogle Scholar
  23. 23.
    Sangiovanni DG, Hultman L, Chirita V (2011) Supertoughening in B1 transition metal nitride alloys by increased valence electron concentration. Acta Mater 59:2121–2134CrossRefGoogle Scholar
  24. 24.
    Li T, Morris J Jr, Nagasako N, Kuramoto S, Chrzan D (2007) Ideal engineering alloys. Phys Rev Lett 98:105503CrossRefGoogle Scholar
  25. 25.
    Holleck H (1986) Material selection for hard coatings. J Vac Sci Technol A 4:2661–2669CrossRefGoogle Scholar
  26. 26.
    Kresse G, Hafner J (1993) Ab initio molecular dynamics for liquid metals. Phys Rev B 47:558–561CrossRefGoogle Scholar
  27. 27.
    Kresse G, Hafner J (1994) Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium. Phys Rev B 49:14251–14269CrossRefGoogle Scholar
  28. 28.
    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 6:15–50CrossRefGoogle Scholar
  29. 29.
    Kresse G, Furthmüller J (1996) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 54:11169–11186CrossRefGoogle Scholar
  30. 30.
    Blöchl PE (1994) Projector augmented-wave method. Phys Rev B 50:17953–17979CrossRefGoogle Scholar
  31. 31.
    Kresse G, Joubert D (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59:1758–1775CrossRefGoogle Scholar
  32. 32.
    Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865CrossRefGoogle Scholar
  33. 33.
    Abbena E, Salamon S, Gray A (2006) Modern differential geometry of curves and surfaces with mathematica. CRC Press, CambridgeGoogle Scholar
  34. 34.
    Tsukimoto S, Moriyama M, Murakami M (2004) Microstructure of amorphous tantalum nitride thin films. Thin Solid Films 460:222–226CrossRefGoogle Scholar
  35. 35.
    Van Der Walt CM, Sole M (1967) On the plastic behaviour of crystals with the nacl-structure. Acta Metall 15:459–462CrossRefGoogle Scholar
  36. 36.
    Tang W, Sanville E, Henkelman G (2009) A grid-based bader analysis algorithm without lattice bias. J Phys Condens Matter 21:084204CrossRefGoogle Scholar
  37. 37.
    Jhi SH, Louie SG, Cohen ML, Ihm J (2001) Vacancy hardening and softening in transition metal carbides and nitrides. Phys Rev Lett 86:3348CrossRefGoogle Scholar
  38. 38.
    Wu Z, Chen XJ, Struzhkin VV, Cohen RE (2005) Trends in elasticity and electronic structure of transition-metal nitrides and carbides from first principles. Phys Rev B 71:214103CrossRefGoogle Scholar
  39. 39.
    Yu XX, Thompson GB, Weinberger CR (2015) Influence of carbon vacancy formation on the elastic constants and hardening mechanisms in transition metal carbides. J Eur Ceram Soc 35:95–103CrossRefGoogle Scholar
  40. 40.
    Vinitskii I (1972) Relation between the properties of monocarbides of groups IV-V transition metals and their carbon content. Powder Metall Metal Ceram 11:488–493CrossRefGoogle Scholar
  41. 41.
    Yu H, Guziewski M, Thompson GB, Weinberger CR (2016) A model for understanding the formation energies of nanolamellar phases in transition metal carbides and nitrides. Model Simul Mat Sci Eng 24:55004CrossRefGoogle Scholar
  42. 42.
    Hirth JP, Lothe J (1982) Theory of dislocations. Wiley, New YorkGoogle Scholar
  43. 43.
    Carlson O, Smith J, Nafziger R (1986) The vanadium-nitrogen system: a review. Metall Mater Trans A 17:1647–1656CrossRefGoogle Scholar
  44. 44.
    Brauer G (1960) Nitrides, carbonitrides and oxynitrides of niobium. J Less Common Metals 2:131–137CrossRefGoogle Scholar
  45. 45.
    Pierson HO (1996) Handbook of refractory carbides and nitrides; properties characteristics, processing and applications. Noyes Publications, WestwoodGoogle Scholar
  46. 46.
    Ryu S, Kang K, Cai W (2011) Predicting the dislocation nucleation rate as a function of temperature and stress. J Mater Res 26:2335–2354CrossRefGoogle Scholar
  47. 47.
    Warner DH, Curtin W (2009) Origins and implications of temperature-dependent activation energy barriers for dislocation nucleation in face-centered cubic metals. Acta Mater 57:4267–4277CrossRefGoogle Scholar
  48. 48.
    Kim C, Gottstein G, Grummon D (1994) Plastic flow and dislocation structures in tantalum carbide: deformation at low and intermediate homologous temperatures. Acta Metall Mater 42:2291–2301CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Mechanical Engineering and Mechanics DepartmentDrexel UniversityPhiladelphiaUSA
  2. 2.Metallurgical and Materials EngineeringThe University of AlabamaTuscaloosaUSA
  3. 3.Department of Mechanical EngineeringColorado State UniversityFort CollinsUSA

Personalised recommendations