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Shear-induced anisotropic plastic flow from body-centred-cubic tantalum before melting

Abstract

There are many structural and optical similarities between a liquid and a plastic flow. Thus, it is non-trivial to distinguish between them at high pressures and temperatures, and a detailed description of the transformation between these phenomena is crucial to our understanding of the melting of metals at high pressures. Here we report a shear-induced, partially disordered viscous plastic flow from body-centred-cubic tantalum under heating before it melts into a liquid. This thermally activated structural transformation produces a unique, one-dimensional structure analogous to a liquid crystal with the rheological characteristics of Bingham plastics. This mechanism is not specific to Ta and is expected to hold more generally for other metals. Remarkably, this transition is fully consistent with the previously reported anomalously low-temperature melting curve and thus offers a plausible resolution to a long-standing controversy about melting of metals under high pressures.

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Figure 1: Predicted MD boundary between b.c.c. and plastic flow, as well as previously reported melting curves of Ta.
Figure 2: Structural properties compared between b.c.c., one-dimensional plastic flow and glass.
Figure 3: Time history of thermal shear relaxation and transition temperature as a function of external stress.
Figure 4: Significant anisotropy observed in the ab initio energy landscape along the b.c.c.-to-h.c.p. Burgers transformation.

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References

  1. Errandonea, D. et al. Systematics of transition-metal melting. Phys. Rev. B. 63, 132104 (2001).

    Article  Google Scholar 

  2. Errandonea, D., Somayazulu, M., Hausermann, D. & Mao, H. K. Melting of tantalum at high pressure determined by angle dispersive x-ray diffraction in a double-sided laser-heated diamond-anvil cell. J. Phys. Condens. Matter 15, 7635–7649 (2003).

    Article  CAS  Google Scholar 

  3. Errandonea, D. Improving the understanding of the melting behaviour of Mo, Ta and W at extreme pressures. Physica B 357, 356–364 (2005).

    Article  CAS  Google Scholar 

  4. Errandonea, D. Phase behavior of metals at very high PT conditions: A review of recent experimental studies. J. Phys. Chem. Solids 67, 2017–2027 (2006).

    Article  CAS  Google Scholar 

  5. Errandonea, D., Boehler, R. & Ross, M. Melting of the alkaline-earth metals to 80 GPa. Phys. Rev. B 65, 012108 (2001).

    Article  Google Scholar 

  6. Boehler, R., Santamaría-Pérez, D., Errandonea, D. & Mezouar, M. Melting, density, and anisotropy of iron at core conditions: New X-ray measurements to 150 GPa. J. Phys. Conf. Ser. 121, 022018 (2008).

    Article  Google Scholar 

  7. Boehler, R. & Ross, M. Melting curve of aluminum in a diamond cell to 0.8 Mbar: Implications for iron. Earth Planet. Sci. Lett. 153, 223–227 (1997).

    Article  CAS  Google Scholar 

  8. Japel, S., Schwager, B., Boehler, R. & Ross, M. Melting of copper and nickel at high pressure: The role of d electrons. Phys. Rev. Lett. 95, 167801 (2005).

    Article  Google Scholar 

  9. Dewaele, A., Mezouar, M., Guignot, N. & Loubeyre, P. Melting of lead under high pressure studied using second-scale time-resolved x-ray diffraction. Phys. Rev. B. 76, 144106 (2007).

    Article  Google Scholar 

  10. Brown, J. M. & Shaner, J. W. in Shock Waves in Condensed Matter—1983 (eds Asay, J. A., Graham, R. A. & Straub, G. K.) (North-Holland, 1984).

    Google Scholar 

  11. Fateeva, N. S. & Vereshchagin, L. F. Melting curve of tantalum up to 60 kbar. Sov. Phys. 16, 322–323 (1971).

    Google Scholar 

  12. Wang, Y., Ahuja, R. & Johnsson, B. Melting of iron and other metals at earth’s core conditions: A simplified computational approach. Phys. Rev. B 65, 014104 (2001).

    Article  Google Scholar 

  13. Verma, A. K., Rao, R. & Godwal, B. K. Theoretical solid and liquid state shock hugoniots of Al, Ta, Mo and W. J. Phys. Condens. Matter 16, 4799–4809 (2002).

    Article  Google Scholar 

  14. Taioli, S., Cazorla, C., Gillan, M. J & Alfè, D. Melting curve of tantalum from first principles. Phys. Rev. B 75, 214103 (2007).

    Article  Google Scholar 

  15. Luo, S. & Swift, D. C. On high-pressure melting of tantalum. Physica B 388, 139–144 (2007).

    Article  CAS  Google Scholar 

  16. Liu, Z. L., Cai, L. C., Chen, X. R. & Jing, F. Q. Molecular dynamics simulations of the melting curve of tantalum under pressure. Phys. Rev. B 77, 024103 (2008).

    Article  Google Scholar 

  17. Xi, F. & Cai, L. Theoretical study of melting curves on Ta, Mo and W at high pressures. Physica B 403, 2065–2070 (2008).

    Article  CAS  Google Scholar 

  18. Belonoshko, A. B. et al. Molybdenum at high pressure and temperature: Melting from another solid phase. Phys. Rev. Lett. 100, 135701 (2008).

    Article  CAS  Google Scholar 

  19. Hixson, R.A., Boness, D.A., Shaner, J.W. & Moriarty, J. A. Acoustic velocities and phase transitions in molybdenum under strong shock compression. Phys. Rev. Lett. 62, 637–640 (1989).

    Article  CAS  Google Scholar 

  20. Belonoshko, A. B. & Dubrovinsky, L. S. A simulation study of induced failure and recrystallization of a perfect MgO crystal under non-hydrostatic compression: Application to melting in the diamond-anvil cell. Am. Mineral. 82, 441–451 (1997).

    Article  CAS  Google Scholar 

  21. Ross, M., Errandonea, D. & Boehler, R. Melting of transition metals at high pressure and the influence of liquid frustration: The early metals Ta and Mo. Phys. Rev. B 76, 184118 (2007).

    Article  Google Scholar 

  22. Jakse, N., Le Bacq, O. & Pasturel, A. Predication of the local structure of liquid and supercooled tantalum. Phys. Rev. B 70, 174203 (2004).

    Article  Google Scholar 

  23. Wolf, D., Okamoto, P. R., Yip, S., Lutsko, J. F. & Kluge, M. Thermodynamic parallels between solid-state amorphization and melting. J. Mater. Res. 5, 286–301 (1990).

    Article  CAS  Google Scholar 

  24. Belonoshko, A. B., Ahuja, R. & Johansson, B. Molecular dynamics of LiF melting. Phys. Rev. B 61, 11928–11935 (2000).

    Article  CAS  Google Scholar 

  25. Fiquet, G, Andrault, D., Itié, J. P., Gillet, P. & Richet, P. X-ray diffraction of periclase in a laser-heated diamond-anvil cell. Phys. Earth Planet. Inter. 95, 1–17 (1996).

    Article  CAS  Google Scholar 

  26. Vinod, K., Malik, V. S., Sharma, S. K. & Srivastava, S. K. Temperature dependence of thermal pressure of NaCl and KCl crystals. J. Phys. Chem. Solids 68, 32–35 (2007).

    Article  CAS  Google Scholar 

  27. Foata-Prestavoine, M., Robert, G., Nadal, M. H. & Bernard, S. First-principles study of the relations between the elastic constants, phonon dispersion curves, and melting temperatures of b.c.c. Ta at pressures up to 1000 GPa. Phys. Rev. B 76, 104104 (2007).

    Article  Google Scholar 

  28. Gulseren, O. & Cohen, R. E. High-pressure thermoelasticity of body-centred-cubic tantalum. Phys. Rev. B 65, 064103 (2002).

    Article  Google Scholar 

  29. Orlikowski, D., Soderlind, P. & Moriarty, J. A. First-principles thermoelasticity of transition metals at high pressure: Tantalum prototype in the quasiharmonic limit. Phys. Rev. B 74, 054109 (2006).

    Article  Google Scholar 

  30. Butler, S. & Harrowell, P. The shear-induced disordering transition in a colloidal crystal: Nonequilibrium Brownian dynamic simulations. J. Chem. Phys. 103, 4653–4671 (1995).

    CAS  Google Scholar 

  31. King, R. P. Introduction to Practical Fluid Flow 117 (Butterworth-Heinemann, 2002).

    Book  Google Scholar 

  32. Bingham, E. C. An investigation of the laws of plastic flow. US Bureau of Standards Bulletin 13, 309–353 (1916).

    Article  Google Scholar 

  33. Moriarty, J. A. et al. Quantum-based atomistic simulation of materials properties in transition metals. J. Phys. Condens. Matter 14, 2825–2857 (2002).

    Article  CAS  Google Scholar 

  34. Moriarty, J. A. et al. Supplemental Proceedings: Volume 1: Minerals, Metals and Materials under Pressure for the 2008 TMS Annual Meeting, New Orleans, LA, 313.

  35. Hirth, J. P & Lothe, J. Theory of Dislocation 275 (Krieger, 1992).

    Google Scholar 

  36. Burgers, W. G. On the process of transition of the cubic-body-centered modification into the hexagonal-close-packed modification of zirconium. Physica 1, 561–586 (1934).

    Article  CAS  Google Scholar 

  37. Szczgielska, A., Burian, A., Duber, S., Dore, J. C. & Honkimaki, V. Radial distribution function analysis of the graphitization process in carbon materials. J. Alloys Compounds 328, 231–236 (2001).

    Article  Google Scholar 

  38. Jaime, M., Cai, W. & Bulatov, V. V. Dynamic transitions from smooth to rough to twinning in dislocation motion. Nature Mater. 3, 158–163 (2004).

    Article  Google Scholar 

  39. Wang, Y. et al. Amorphouslike diffraction pattern in solid metallic titanium. Phys. Rev. Lett. 95, 155501 (2005).

    Article  CAS  Google Scholar 

  40. Hattori, T. et al. Does bulk metallic glass of elemental Zr and Ti exist? Phys. Rev. Lett. 96, 255504 (2006).

    Article  Google Scholar 

  41. Streitz, F. H., Glosli, J. N. & Patel, M. V. Beyond finite-size scaling in solidification simulations. Phys. Rev. Lett. 96, 225701 (2006).

    Article  Google Scholar 

  42. Rodney, D. & Martin, G. Dislocation pinning by small interstitial loops: A molecular dynamics study. Phys. Rev. Lett. 82, 3272–3275 (1999).

    Article  CAS  Google Scholar 

  43. Allen, M. P. & Tildesley, D. J. Computer Simulations of Liquids (Clarendon, 1987.).

    Google Scholar 

  44. Gonze, X. et al. First-principles computation of material properties: The ABINIT software project. Comput. Mater. Sci. 25, 478–492 (2002).

    Article  Google Scholar 

  45. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    Article  CAS  Google Scholar 

  46. Troullier, N. & Martins, J. L. Efficient pseudopotentials for plane-wave calculations. Phys. Rev. B 43, 1993–2006 (1991).

    Article  CAS  Google Scholar 

  47. Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188–5192 (1976).

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank J. A. Moriarty for providing the MGPT Ta potential, M. Ross, N. C. Holmes, W. J. Evans, M. J. Lipp, M. Tang, R. Gee and D. A. Orlikowski for useful discussions and K. Kline and J. McInnis for their contributions in preparation of the manuscript and figures. This work was carried out under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

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Contributions

C.J.W. originated the central idea, performed and analysed the Ta MD simulations and the Ta ab initio electronic structure calculations, carried out code development (central symmetry) and wrote the paper; P.S. contributed in ab initio electronic structure calculations and manuscript editing; J.N.G. carried out MD code development; J.E.K. contributed in manuscript editing; all contributed to discussions.

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Correspondence to Christine J. Wu.

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Wu, C., Söderlind, P., Glosli, J. et al. Shear-induced anisotropic plastic flow from body-centred-cubic tantalum before melting. Nature Mater 8, 223–228 (2009). https://doi.org/10.1038/nmat2375

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