Skip to main content
SpringerLink
Log in

Temperature-dependent elastic stiffness constants of fcc-based metal nitrides from first-principles calculations

  • Published:
Journal of Materials Science Aims and scope Submit manuscript

Abstract

Temperature-dependent single-crystal elastic stiffness constants and the associated polycrystalline aggregate properties of fcc-based metal nitrides (MNs; M = Ti, Al, Zr, and Hf) have been investigated using a quasistatic approach via first-principles calculations. It is confirmed that the four studied nitrides are brittle materials and mechanically stable, agreeing with experimental results. Among these compounds, TiN and AlN possess the highest strength and the highest hardness, respectively. The cross-slip and the resistance to microcracks are analyzed based on the elastic anisotropy ratio. Additionally, it is found that the decreasing trend of C 11 with respect to temperature is larger than that of C 12 or C 44. With increasing temperature, the resistance of shear deformation, stiffness, hardness, and strength of these four nitrides decrease. The computed properties of MNs agree well with the experimental data available in the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Mihailescu IN, Gyorgy E, Chitica N, Teodorescu VS, Mavin G, Luches A, Perrone A, Martino M, Neamtu J (1996) J Mater Sci 31:2909. doi:10.1007/BF00356001

    Article  CAS  ADS  Google Scholar 

  2. Ashley NJ, Grimes RW, McClellan KJ (2007) J Mater Sci 42:1884. doi:10.1007/s10853-006-1321-z

    Article  CAS  ADS  Google Scholar 

  3. Sarioglu C (2006) Surf Coat Technol 201:707

    Article  CAS  Google Scholar 

  4. Wuchina E, Opeka M, Causey S, Buesking K, Spain J, Cull A, Routbort J, Guitierrez-Mora F (2004) J Mater Sci 39:5939. doi:10.1023/B:JMSC.0000041690.06117.34

    Article  CAS  ADS  Google Scholar 

  5. Wadsworth I, Lewis DB, Williams G (1996) J Mater Sci 31:5907. doi:10.1007/BF01152140

    Article  CAS  ADS  Google Scholar 

  6. Li JG, Gao L, Guo JK, Yan DS (2002) J Am Ceram Soc 85:724

    Article  CAS  Google Scholar 

  7. Zhou QG, Bai XD, Ling YH, Peng DQ (2005) J Mater Sci 40:2733. doi:10.1007/s10853-005-2118-1

    Article  CAS  ADS  Google Scholar 

  8. Yao HZ, Ouyang LZ, Ching W-Y (2007) J Am Ceram Soc 90:3194

    Article  CAS  Google Scholar 

  9. Bendavid A, Martin PJ, Netterfield RP, Kinder TJ (1994) Surf Coat Technol 70:97

    Article  CAS  Google Scholar 

  10. Karlsson L, Hultman L, Sundgren J-E (2000) Thin Solid Films 371:167

    Article  CAS  ADS  Google Scholar 

  11. Zhao J-H, Qi W-J, Ho PS (2002) Microelectron Reliab 42:27

    Article  Google Scholar 

  12. Hebbache M (2000) Solid State Commun 113:427

    Article  CAS  ADS  Google Scholar 

  13. Ding Z, Zhou S, Zhao Y (2004) Phys Rev B 70:184117

    Article  ADS  Google Scholar 

  14. Ganeshan S, Shang SL, Wang Y, Liu Z-K (2010) J Alloys Compd 498:191

    Article  CAS  Google Scholar 

  15. Kanoun MB, Goumri-Said S, Reshak AH (2009) Comput Mater Sci 47:491

    Article  CAS  Google Scholar 

  16. Gülseren O, Cohen RE (2002) Phys Rev B 65:064103

    Article  ADS  Google Scholar 

  17. Chen XJ, Struzhkin VV, Wu ZG, Somayazulu M, Qian J, Kung S, Christensen AN, Zhao YS, Cohen RE, Mao HK, Hemley RJ (2005) Proc Natl Acad Sci USA 102:3198

    Article  PubMed  CAS  PubMed Central  ADS  Google Scholar 

  18. Kim JO, Achenbach JD, Mirkarimi PB, Shinn M, Barnett SA (1992) J Appl Phys 72:1805

    Article  CAS  ADS  Google Scholar 

  19. Lazar P, Redinger J, Podloucky R (2007) Phys Rev B 76:174112

    Article  ADS  Google Scholar 

  20. Zaoui A, Bouhafs B, Ruterana P (2005) Mater Chem Phys 91:108

    Article  CAS  Google Scholar 

  21. Zhao E, Wang JP, Meng J, Wu ZJ (2010) Comput Mater Sci 47:1064

    Article  CAS  Google Scholar 

  22. Zhao E, Wu Z (2008) J Solid State Chem 181:2814

    Article  CAS  ADS  Google Scholar 

  23. Verma UP, Bisht PS (2010) Solid State Sci 12:665

    Article  CAS  ADS  Google Scholar 

  24. Tasnádi F, Abrikosov IA, Rogström L, Almer J, Johansson MP, Odén M (2010) Appl Phys Lett 97:231902

    Article  ADS  Google Scholar 

  25. Steneteg P, Hellman O, Vekilova YO, Shulumba N, Tasnadi F, Abrikosov A (2013) Phys Rev B 87:094114

    Article  ADS  Google Scholar 

  26. Chen L, Du Y, Mayrhofer PH, Wang SQ, Li J (2008) Surf Coat Technol 202:5158

    Article  CAS  Google Scholar 

  27. Dinsdale AT (1991) CALPHAD 15:317

    Article  CAS  Google Scholar 

  28. Liu ZK et al (2010) Scr Mater 63:686

    Article  CAS  ADS  Google Scholar 

  29. Wang Y, Wang JJ, Zhang H, Manga VR, Shang SL, Chen L-Q, Liu Z-K (2010) J Phys Condens Matter 22:225404

    Article  PubMed  CAS  ADS  Google Scholar 

  30. Shang SL, Zhang H, Wang Y, Liu Z-K (2010) J Phys Condens Matter 22:375403

    Article  PubMed  Google Scholar 

  31. Shang SL, Wang Y, Kim D, Liu Z-K (2010) Comput Mater Sci 47:1040

    Article  CAS  Google Scholar 

  32. Ledbetter H (2006) Mater Sci Eng A 442:31

    Article  Google Scholar 

  33. Wang Y, Liu Z-K, Chen L-Q (2004) Acta Mater 52:2665

    Article  MathSciNet  CAS  Google Scholar 

  34. Shang SL, Wang Y, Liu Z-K (2007) Phys Rev B 75:024302

    Article  ADS  Google Scholar 

  35. Alling B, Ruban AV, Karimi A, Peil OE, Simak SI, Hultman L, Abrikosov IA (2007) Phys Rev B 75:045123

    Article  ADS  Google Scholar 

  36. Wang AJ, Shang SL, Zhao DD, Wang J, Chen L, Du Y, Liu ZK, Xu T, Wang SQ (2012) CALPHAD 37:126

    Article  CAS  Google Scholar 

  37. Shang SL, Wang Y, Liu ZK (2007) Appl Phys Lett 90:101909

    Article  ADS  Google Scholar 

  38. Wang AJ, Shang SL, Du Y, Kong Y, Zhang LJ, Chen L, Zhao DD, Liu ZK (2010) Comput Mater Sci 48:705

    Article  CAS  Google Scholar 

  39. Hill R (1952) Proc Phys Soc Lond A 65:349

    Article  ADS  Google Scholar 

  40. Davies GF (1974) J Phys Chem Solids 35:1513

    Article  CAS  ADS  Google Scholar 

  41. Wolverton C, Hass KC (2001) Phys Rev B 63:024102

    Article  ADS  Google Scholar 

  42. Orlikowski D, Soderlind P, Moriarty JA (2006) Phys Rev B 74:054109

    Article  ADS  Google Scholar 

  43. Wang Y, Li L (2000) Phys Rev B 62:196

    Article  CAS  ADS  Google Scholar 

  44. Blöchl PE (1994) Phys Rev B 50:17953

    Article  ADS  Google Scholar 

  45. Kresse G, Furthmüller J (1996) Phys Rev B 54:11169

    Article  CAS  ADS  Google Scholar 

  46. Kresse G, Furthmüller J (1996) Comput Mater Sci 6:15

    Article  CAS  Google Scholar 

  47. Methfessel M, Paxton AT (1989) Phys Rev B 40:3616

    Article  CAS  ADS  Google Scholar 

  48. Blöchl PE, Jepsen O, Andersen OK (1994) Phys Rev B 49:16223

    Article  ADS  Google Scholar 

  49. Van de Walle A, Asta M, Ceder G (2002) CALPHAD 26:539

    Article  Google Scholar 

  50. Van de Walle A (2009) CALPHAD 33:266

    Article  Google Scholar 

  51. Shang SL, Wang Y, Zhang H, Liu ZK (2007) Phys Rev B 76:052301

    Article  ADS  Google Scholar 

  52. Shang SL, Wang Y, Du Y, Liu ZK (2010) Intermetallics 18:961

    Article  CAS  Google Scholar 

  53. Aigner K, Lengauer W, Rafaja D, Ettmayer P (1994) J Alloys Compd 215:121

    Article  CAS  Google Scholar 

  54. Lengauer W, Ettmayer P (1991) J Less Common Met 168:L7

    Article  CAS  Google Scholar 

  55. Bogdanov VS, Neshpor VS, Kondrashev YD, Goncharuk AB, Pityulin AN (1982) Sov Powder Metall Met Ceram 21:412

    Article  Google Scholar 

  56. Touloukian YS, Kirky RK, Taylor RE, Lee TYR (eds) (1975) Thermal properties of matter, TPRC data books, vol 13. Plenum Press, New York

    Google Scholar 

  57. Yang Q, Lengauer W, Koch T, Scheerer M, Smid I (2000) J Alloys Compd 309:L5

    Article  CAS  Google Scholar 

  58. Zhang RF, Veprek S (2008) Thin Solid Films 516:2264

    Article  CAS  ADS  Google Scholar 

  59. Ojha P, Aynyas M, Sanyal SP (2007) J Phys Chem Solids 68:148

    Article  CAS  ADS  Google Scholar 

  60. Nagao S, Nordlund K, Nowak R (2006) Phys Rev B 73:144113

    Article  ADS  Google Scholar 

  61. Kral C, Lengauer W, Rafaja D, Ettmayer P (1998) J Alloys Compd 265:215

    Article  CAS  Google Scholar 

  62. Chen K, Bielawski M (2008) Surf Coat Technol 203:598

    Article  CAS  Google Scholar 

  63. Wu Z, Chen X-J, Struzhkin VV, Cohen RE (2005) Phys Rev B 71:214103

    Article  ADS  Google Scholar 

  64. Nye JF (1985) Physical properties of crystals: their representation by tensors and matrices. Oxford University Press, Oxford

    Google Scholar 

  65. Beckstein O, Klepeis LE, Hart GLW, Pankratov O (2001) Phys Rev B 63:134112

    Article  ADS  Google Scholar 

  66. Frantsevich IN, Voronov FF, Bokuta SA (1983) Elastic moduli of metals and insulators handbook. Naukova Dumka, Kiev

    Google Scholar 

  67. Ledbetter H, Miglioria A (2006) J Appl Phys 100:063516

    Article  ADS  Google Scholar 

  68. Tvergaard V, Hutchinson JW (1988) J Am Ceram Soc 71:157

    Article  CAS  Google Scholar 

  69. Luo X, Wang B (2008) J Appl Phys 104:073518

    Article  ADS  Google Scholar 

  70. Yoo MH (1986) Scr Metall 20:915

    Article  CAS  Google Scholar 

  71. Brazhkin VV, Lyapin AG, Hemley RJ (2002) Philos Mag A 82:231

    Article  CAS  ADS  Google Scholar 

  72. Chen X-Q, Niu H, Li D, Li Y (2011) Intermetallics 19:1275

    Article  CAS  Google Scholar 

  73. Gou H, Hou L, Zhang J, Gaoa F (2008) Appl Phys Lett 92:241901

    Article  ADS  Google Scholar 

  74. Pierson HO (1996) Handbook of refractory carbides and nitrides: properties, characteristics and applications. Noyes, Westwood

    Google Scholar 

  75. Simunek A, Vackar J (2006) Phys Rev Lett 96:085501

    Article  PubMed  ADS  Google Scholar 

  76. Yang Y, Lu H, Yu C, Chen JM (2009) J Alloys Compd 485:542

    Article  CAS  Google Scholar 

  77. Yonenaga I, Shima T, Sluiter MHF (2002) Jpn J Appl Phys 1 41:4620

    Article  CAS  Google Scholar 

  78. Håkansson G, Sundgren JE, McIntyre D, Greene J, Münz W-D (1987) Thin Solid Films 153:55

    Article  Google Scholar 

  79. Quinto DT, Wolfe GJ, Jindal PC (1987) Thin Solid Films 153:19

    Article  CAS  ADS  Google Scholar 

  80. Chatterjee S, Chandrashekhar S, Sudarshan TS (1992) J Mater Sci 27:3409. doi:10.1007/BF01151815

    Article  CAS  ADS  Google Scholar 

  81. Jahnátek M, Hafner J, Krajčí M (2009) Phys Rev B 79:224103

    Article  ADS  Google Scholar 

  82. Zhang R, Sheng SH, Veprek S (2007) Appl Phys Lett 91:031906

    Article  ADS  Google Scholar 

  83. Pugh SF (1954) Philos Mag 45:823

    CAS  Google Scholar 

  84. Zhang RF, Sheng SH, Veprek S (2009) Appl Phys Lett 94:121903

    Article  ADS  Google Scholar 

  85. Lu X-G, Selleby M, Sundman B (2007) Acta Mater 55:1215

    Article  CAS  Google Scholar 

  86. Hugosson HW, Eriksson O, Jansson U, Johansson B (2001) Phys Rev B 63:134108

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by the Creative Research Group of the NSFC (Grant No. 51021063), the National Natural Science Foundation of China (NSFC) for Youth of China (Grant No. 51001120), the National Natural Science Foundation of China (Grant No. 51071179), the China Postdoctoral Science Foundation (Grant No. 2013M531682), and AQSIQ Science and Technology Plan Project (Grant No. 2012QK133). ZKL and SLS acknowledge the support from the NSFC with Grant No. 51028101 and the United States National Science Foundation under the Grant No. DMR-1006557.

Author information

Authors and Affiliations

  1. School of Materials Science and Engineering, Zhengzhou University, 100 Science Road, Zhengzhou, 450001, People’s Republic of China

    Aijun Wang, Rui Zhang, Deliang Chen & Bingbing Fan

  2. State Key Laboratory of Powder Metallurgy, Central South University, Changsha, 410083, Hunan, People’s Republic of China

    Aijun Wang, Yong Du & Li Chen

  3. Henan Institute of Product Quality Supervision and Inspection, 17 Dongming Road, Zhengzhou, 450004, People’s Republic of China

    Aijun Wang, Mingzhi He & Feiyan Meng

  4. Department of Materials Science and Engineering, Pennsylvania State University, University Park, PA, 16802, USA

    Shun-Li Shang & Zi-Kui Liu

  5. Aeronautical Industry Management, University Centre, Zhengdong New District, Zhengzhou, 450046, People’s Republic of China

    Rui Zhang

Authors
  1. Aijun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shun-Li Shang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mingzhi He
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yong Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Li Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Rui Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Deliang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Bingbing Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Feiyan Meng
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Zi-Kui Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yong Du.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, A., Shang, SL., He, M. et al. Temperature-dependent elastic stiffness constants of fcc-based metal nitrides from first-principles calculations. J Mater Sci 49, 424–432 (2014). https://doi.org/10.1007/s10853-013-7721-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10853-013-7721-y

Keywords

Search

Navigation