Skip to main content
SpringerLink
Log in

Elastic properties, hardness, and anisotropy in baddeleyite IVTMO2 (M=Ti, Zr, Hf)

  • Articles
  • Published:
Science China Materials Aims and scope Submit manuscript

Abstract

In this article, we used plane-wave density functional theory to investigate the elasticity, anisotropy, and minimum thermal conductivities of baddeleyite type the IVTMO2 (m-TiO2, m-ZrO2, and m-HfO2). The elastic constants and modulus, Poisson’s ratio, hardness, sound speed, Debye temperature, and minimum thermal conductivities at high temperature were calculated. These calculations show that m-MO2 is not superhard, with a hardness range of about 8–13 GPa. Among these materials, m-TiO2 is the hardest, while m-HfO2 is the least hard. Their elastic and plastic anisotropy are given in detail. Moreover, the m-HfO2 thin film is the most likely to develop microcracks during preparation because it has the highest elastic anisotropy. Among the three dioxides, m-HfO2 is the best thermal barrier because it has the lowest thermal conductivity.

中文摘要

本文用平面波密度泛函理论研究了斜锆石型IVTMO2 (m-TiO2, m-ZrO2和m-HfO2)的弹性, 各向异性以及最小热导率. 通过 计算给出了弹性常数及其模量、泊松比、硬度、声速及德拜温度高温下的最小热导率. 结果表明, m-MO2不是超硬材料, 其硬度范围 为8−13 GPa. m-TiO2是其中最硬的, 而m-HfO2的硬度最小. 同时还对弹性及塑性的各向异性进行了详细的分析, 表明由于m-HfO2具有 最强的各向异性, 在制作薄膜时最容易产生微裂纹. 值得指出的是, 在三种氧化物中, m-HfO2由于具有最小的高温热导率而最有可能作 为热障材料应用.

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

Similar content being viewed by others

References

  1. Zydor A, Elliott SD. Thermal stability of precursors for atomic layer deposition of TiO2, ZrO2, and HfO2: an ab initio study of a-hydrogen abstraction in bis-cyclopentadienyl dimethyl complexes. J Phys Chem A, 2010, 114: 1879–1886

    Article  Google Scholar 

  2. Zhu HX, Zhou PX, Li X, et al. Electronic structures and optical properties of rutile TiO2 with different point defects from DFT+U calculations. Phys Lett A, 2014, 378: 2719–2724

    Article  Google Scholar 

  3. Fadda G, Zanzotto G, Colombo L. First-principles study of the effect of pressure on the five zirconia polymorphs. II. Static dielectric properties and Raman spectra. Phys Rev B, 2010, 82: 064106

    Article  Google Scholar 

  4. Franta D, Ohlídal I, Necas D, et al. Optical characterization of HfO2 thin films. Thin Solid Films, 2011, 519: 6085–6091

    Article  Google Scholar 

  5. Luo XH, Zhou W, Ushakov SV, et al. Monoclinic to tetragonal transformations in hafnia and zirconia: a combined calorimetric and density functional study. Phys Rev B, 2009, 80: 134119

    Article  Google Scholar 

  6. Wilk GD, Wallace RM, Anthony JM. High-k gate dielectrics: current status and materials properties considerations. J Appl Phys, 2001, 89: 5243–5275

    Article  Google Scholar 

  7. Wallace RM, Wilk G. Alternative gate dielectrics for microelectronics. MRS Bull, 2002, 27: 186–191

    Article  Google Scholar 

  8. Cava RF, Peck WF, Krajewski JJ. Enhancement of the dielectric constant of Ta2O5 through substitution with TiO2. Nature, 1995, 377: 215–217

    Article  Google Scholar 

  9. Debernardi A, Fanciulli M. Structural and vibrational properties of high-dielectric oxides, HfO2 and TiO2: a comparative study. Mat Sci Semicon Proc, 2006, 9: 1014–1019

    Article  Google Scholar 

  10. Zhao C, Roebben G, Heyns M, et al. Crystallisation and tetragonal-monoclinic transformation in ZrO2 and HfO2 dielectric thin films. Key Eng Mat, 2002, 206: 1285–1288

    Article  Google Scholar 

  11. Liu QJ, Zhang NC, Liu FS, et al. Structural, electronic, optical, elastic properties and Born effective charges of monoclinic HfO2 from first-principles calculations. Chinese Phys B, 2014, 23: 047101

    Article  Google Scholar 

  12. Al-Khatatbeh Y, Lee KKM, Kiefer B. Phase diagram up to 105 GPa and mechanical strength of HfO2. Phys Rev B, 2010, 82: 144106

    Article  Google Scholar 

  13. Olsen JS, Gerward L, Jiang JZ. On the rutile/a-PbO2-type phase boundary of TiO2. J Phys Chem Solids, 1999, 60: 229–233

    Article  Google Scholar 

  14. Levine JB, Tolbert SH, Kaner RB. Advancements in the search for superhard ultra-incompressible metal borides. Adv Funct Mater, 2009, 19: 3519–3533

    Article  Google Scholar 

  15. Swamy V, Muddle BC. Ultrastiff cubic TiO2 identified via first-principles calculations. Phys Rev Lett, 2007, 98: 035502

    Article  Google Scholar 

  16. Hohenberg P, Kohn W. Inhomogeneous electron gas. Phys Rev, 1964, 136: 864–871

    Article  Google Scholar 

  17. Segall MD, Lindan PJD, Probert MJ, et al. First-principles simulation: ideas, illustrations and the CASTEP code. J Phys-Condens Mat, 2002, 14: 2717–2744

    Article  Google Scholar 

  18. Ceperley DM, Alder BJ. Ground state of the electron gas by a stochastic method. Phys Rev Lett, 1980, 45: 566–569

    Article  Google Scholar 

  19. Perdew JP, Burke K, Ernzerhof M. Generalized gradient approximation made simple. Phys Rev Lett, 1996, 77: 3865–3868

    Article  Google Scholar 

  20. Vanderbilt D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys Rev B, 1990, 41: 7892–7895

    Article  Google Scholar 

  21. Hamann DR, Schlüter M, Chiang C. Norm-conserving pseudopotentials. Phys Rev Lett, 1979, 43: 1494–1497

    Article  Google Scholar 

  22. Monkhorst HJ, Pack JD. Special points for Brillouin-zone integrations. Phys Rev B, 1976, 13: 5188

    Article  Google Scholar 

  23. Broyden CG. The convergence of a class of double-rank minimization algorithms 2. The new algorithm. IMA J Appl Math, 1970, 6: 222–231

    Article  Google Scholar 

  24. Fletcher R. A new approach to variable metric algorithms. Comput J, 1970, 13: 317–322

    Article  Google Scholar 

  25. Goldfarb D. A family of variable-metric methods derived by variational means. Math Comput, 1970, 24: 23–26

    Article  Google Scholar 

  26. Shanno DF. Conditioning of quasi-Newton methods for function minimization. Math Comput, 1970, 24: 647–656

    Article  Google Scholar 

  27. Gu JB, Wang CJ, Cheng Y, et al. Structural, elastic, thermodynamic, electronic properties and phase transition in half-Heusler alloy NiVSb at high pressures. Comp Mater Sci, 2015, 96: 72–80

    Article  Google Scholar 

  28. Watt JP. Hashin-Shtrikman bounds on the effective elastic moduli of polycrystals with monoclinic symmetry. J Appl Phys, 1980, 51: 1520–1524

    Article  Google Scholar 

  29. Hill R. The elastic behaviour of a crystalline aggregate. P Phys Soc Lond A, 1952, 65: 349–355

    Article  Google Scholar 

  30. Ranganathan SI, Martin OS. Universal elastic anisotropy index. Phys Rev Lett, 2008, 101: 055504

    Article  Google Scholar 

  31. Chung DH, Buessem WR. The elastic anisotropy of crystals. J Appl Phys, 1967, 38: 2010–2012

    Article  Google Scholar 

  32. Swamy V, Dubrovinsky LS, Dubrovinskaia NA, et al. Size effects on the structure and phase transition behavior of baddeleyite TiO2. Solid State Commun, 2005, 134: 541–546

    Article  Google Scholar 

  33. Hill RJ, Cranswick LMD. International union of crystallography. Commission on powder diffraction. Rietveld refinement round robin. II. Analysis of monoclinic ZrO2. J Appl Crystallogr, 1994, 27: 802–844

    Article  Google Scholar 

  34. Näray-Szabo S. Zur Struktur des Baddeleyits ZrO2. Zeitschrift für Kristallographie Crystalline Mater, 1936, 94: 414–416

    Google Scholar 

  35. Adams DM, Leonard S, Russell DR, et al. X-ray diffraction study of hafnia under high pressure using synchrotron radiation. J Phys Chem Solids, 1991, 52: 1181–1186

    Article  Google Scholar 

  36. Ruh R, Corfield PWR. Crystal structure of monoclinic hafnia and comparison with monoclinic zirconia. J Am Ceram Soc, 1970, 53: 126–129

    Article  Google Scholar 

  37. Wu R, Zhou B, Li Q, et al. Elastic and vibrational properties of monoclinic HfO2 from first-principles study. J Phys D-Appl Phys, 2012, 45: 125304

    Article  Google Scholar 

  38. Mirgorodsky AP, Quintard PE. Lattice-dynamic treatment of vibrational and elastic properties of cotunnite-type ZrO2 and HfO2: comparison with ambient pressure polymorphs. J Am Ceram Soc, 1999, 82: 3121–3124

    Article  Google Scholar 

  39. Chan SK, Fang Y, Grimsditch M, et al. Temperature dependence of the elastic moduli of monoclinic zirconia. J Am Ceram Soc, 1991, 74: 1742–1744

    Article  Google Scholar 

  40. Pugh SF. XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals. The London, Edinburgh, and Dublin Philosophical Magazine and J Sci, 1954, 45: 823–843

    Article  Google Scholar 

  41. Gilman JJ. Electronic Basis of the Strength of Materials. Cambridge: Cambridge University Press, 2003

    Google Scholar 

  42. Gao FM, He JL, Wu ED, et al. Hardness of covalent crystals. Phys Rev Lett, 2003, 91: 015502

    Article  Google Scholar 

  43. Chen XQ, Niu HY, Li DZ, et al. Modeling hardness of polycrystalline materials and bulk metallic glasses. Intermetallics, 2011, 19: 1275–1281

    Article  Google Scholar 

  44. Chen XQ, Niu HY, Franchini C, et al. Hardness of T-carbon: density functional theory calculations. Phys Rev B, 2011, 84: 121405(R)

    Article  Google Scholar 

  45. Tian YJ, Xu B, Zhao ZS. Microscopic theory of hardness and design of novel superhard crystals. Int J Refract Met H, 2012, 33: 93–106

    Article  Google Scholar 

  46. Xu B, Tian YJ. Superhard materials: recent research progress and prospects. Sci China Mater, 2015, 58: 132–142

    Article  Google Scholar 

  47. Al-Khatatbeh Y, Lee KKM, Kiefer B. Phase relations and hardness trends of ZrO2 phases at high pressure. Phys Rev B, 2010, 81: 214102

    Article  Google Scholar 

  48. Haines J, Leger JM, Bocquillon G. Synthesis and design of superhard materials. Ann Rev Mater Res, 2001, 31: 1–23

    Article  Google Scholar 

  49. Clarke DR. Materials selection guidelines for low thermal conductivity thermal barrier coatings. Surf Coat Tech, 2003, 163: 67–74

    Article  Google Scholar 

  50. Cahill DG, Watson SK, Pohl RO. Lower limit to the thermal conductivity of disordered crystals. Phys Rev B, 1992, 46: 6131

    Article  Google Scholar 

  51. Duan YH, Sun Y, Lu L. Thermodynamic properties and thermal conductivities of TiAl3-type intermetallics in Al-Pt-Ti system. Comp Mater Sci, 2013, 68: 229–233

    Article  Google Scholar 

  52. Kittel C, Holcomb DF. Introduction to solid state physics. Am J Phys, 1967, 35: 547–548

    Article  Google Scholar 

  53. Cahill DG, Allen TH. Thermal conductivity of sputtered and evaporated SiO2 and TiO2 optical coatings. Appl Phys Lett, 1994, 65: 309–311

    Article  Google Scholar 

  54. Vassen R, Cao X, Tietz F, et al. Zirconates as new materials for thermal barrier coatings. J Am Ceram Soc, 2000, 83: 2023–2028

    Article  Google Scholar 

  55. Zhu D, Bansal NP, Miller RA. Thermal conductivity and stability of HfO2-Y2O3 and La2Zr2O7 evaluated for 1650°C thermal/environmental barrier coating applications. Proceedings of the 105th Annual Meeting and Exposition of the American Ceramic Society, the American Ceramic Society, Nashville, USA, 2003

    Google Scholar 

  56. Li CX, Duan YH, Hu WC. Electronic structure, elastic anisotropy, thermal conductivity and optical properties of calcium apatite Ca5(PO4)3X (X= F, Cl or Br). J Alloy Compd, 2015, 619: 66–77

    Article  Google Scholar 

  57. Nye JF. Physical Properties of Crystals: Their Representation by Tensors and Matrices. Oxford: Clarendon Press, 1985

    Google Scholar 

  58. Li F, Man YH, Li CM, et al. Mechanical properties, minimum thermal conductivity, and anisotropy in bc-structure superhard materials. Comp Mater Sci, 2015, 102: 327–337

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Materials and Energy, Southwest University, Chongqing, 400715, China

    Zhi-Qian Chen, Feng Li, Meng Hu & Chun-Mei Li

Authors
  1. Zhi-Qian Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Feng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Meng Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chun-Mei Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhi-Qian Chen.

Additional information

Zhi-Qian Chen is a professor of the Faculty of Materials and Energy, Southwest University. He received his PhD degree from Suzhou University in 2001. His research interests include physics and chemistry of materials.

Chun-Mei Li is an associate professor of the Faculty of Materials and Energy, Southwest University. She received her PhD degree from Central South University in 2015. Her research interests include computational materials science.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, ZQ., Li, F., Hu, M. et al. Elastic properties, hardness, and anisotropy in baddeleyite IVTMO2 (M=Ti, Zr, Hf). Sci. China Mater. 58, 893–905 (2015). https://doi.org/10.1007/s40843-015-0098-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40843-015-0098-2

Keywords

Search

Navigation