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Separating the configurational and vibrational entropy contributions in metallic glasses


Glassy materials exist in nature and play a critical role in technology, but key differences between the glass, liquid and crystalline phases are not well understood. Over several decades there has been controversy about the specific heat absorbed as a glass transforms to a liquid—does this originate from vibrational entropy or configurational entropy? Here we report direct in situ measurements of the vibrational spectra of strong and fragile metallic glasses in the glass, liquid and crystalline phases. For both types of material, the measured vibrational entropies of the glass and liquid show a tiny excess over the crystal, representing less than 5% of the total excess entropy measured with step calorimetry. These results reveal that the excess entropy of metallic glasses is almost entirely configurational in origin, consistent with the early theories of Gibbs and co-workers describing the glass transition as a purely configurational transition.

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Figure 1: Schematic representation of the excess entropy of the liquid over the crystal.
Figure 2: Differential scanning calorimetry of amorphous Cu50Zr50 and Cu46Zr46Al8.
Figure 4: Vibrational entropy of Cu50Zr50 and Cu46Zr46Al8.
Figure 3: Phonon DOS curves of Cu50Zr50.
Figure 5: Measured heat capacity of Cu50Zr50.
Figure 6: Total excess entropy of the liquid over the crystal phase of Cu50Zr50.

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  1. Gibbs, J. H. & DiMarzio, E. A. Nature of the glass transition and the glassy state. J. Chem. Phys. 28, 373–383 (1958).

    Article  ADS  Google Scholar 

  2. Adam, G. & Gibbs, J. H. On the temperature dependence of cooperative relaxation properties in glass-forming liquids. J. Chem. Phys. 43, 139–146 (1965).

    Article  ADS  Google Scholar 

  3. Goldstein, M. Viscous liquids and the glass transition: a potential energy barrier picture. J. Chem. Phys. 51, 3728–3739 (1969).

    Article  ADS  Google Scholar 

  4. Debenedetti, P. G. & Stillinger, F. H. Supercooled liquids and the glass transition. Nature 410, 259–267 (2001).

    Article  ADS  Google Scholar 

  5. Goldstein, M. Viscous liquids and the glass transition. V. Sources of the excess specific heat of the liquid. J. Chem. Phys. 64, 4767–4774 (1976).

    Article  ADS  Google Scholar 

  6. Martinez, L.-M. & Angell, C. A. A thermodynamic connection to the fragility of glass-forming liquids. Nature 410, 663–667 (2001).

    Article  ADS  Google Scholar 

  7. Gujrati, P. D. & Goldstein, M. Viscous liquids and the glass transition. 9. Nonconfigurational contributions to the excess entropy of disordered phases. J. Phys. Chem. 84, 869–873 (1980).

    Article  Google Scholar 

  8. Johari, G. P. Contributions to the entropy of a glass and liquid, and the dielectric relaxation time. J. Chem. Phys. 112, 7518–7523 (2000).

    Article  ADS  Google Scholar 

  9. Russew, K., Stojanova, L., Yankova, S., Fazakas, E. & Varga, L. K. Thermal behavior and melt fragility number of Cu100−xZrx glassy alloys in terms of crystallization and viscous flow. J. Phys. Conf. Ser. 144, 012094 (2009).

    Article  Google Scholar 

  10. Yu, P., Bai, H. Y. & Wang, W. H. Superior glass-forming ability of CuZr alloys from minor additions. J. Mater. Res. 21, 1674–1679 (2006).

    Article  ADS  Google Scholar 

  11. Angell, C. A. Spectroscopy simulation and scattering, and the medium range order problem in glass. J. Non-Cryst. Solids 73, 1–17 (1985).

    Article  ADS  Google Scholar 

  12. Jiang, Q. K. et al. Zr–(Cu, Ag)–Al bulk metallic glasses. Acta Mater. 56, 1785–1796 (2008).

    Article  Google Scholar 

  13. Syrykh, G., Zemlyanov, M. & Ishmaev, S. Experimental study of partial vibrational spectra in amorphous alloys. Physica B 234, 450–451 (1997).

    Article  ADS  Google Scholar 

  14. Syrykh, G., Ishmaev, S., Zemlyanov, M. & Sashin, I. Concentration dependence of partial vibrational spectra in Ni-Nb and Cu-Zr metallic glasses. J. Non-Cryst. Solids 250, 642–644 (1999).

    Article  ADS  Google Scholar 

  15. Suck, J. et al. Dynamical structure factor and frequency distribution of the metallic glass Cu46Zr54 at room-temperature. J. Phys. C 13, L167–L172 (1980).

    Article  Google Scholar 

  16. Abernathy, D. L. et al. Design and operation of the wide angular-range chopper spectrometer ARCS at the Spallation Neutron Source. Rev. Sci. Instrum. 83, 015114 (2012).

    Article  ADS  Google Scholar 

  17. Wallace, D. C. Statistical Physics of Crystals and Liquids (World Scientific, 2002).

    MATH  Google Scholar 

  18. Allen, P. B. Anharmonic phonon quasiparticle theory of zero-point and thermal shifts in insulators: heat capacity, bulk modulus, and thermal expansion. Phys. Rev. B 92, 064106 (2015).

    Article  ADS  Google Scholar 

  19. Lind, M. L., Duan, G. & Johnson, W. L. Isoconfigurational elastic constants and liquid fragility of a bulk metallic glass forming alloy. Phys. Rev. Lett. 97, 015501 (2006).

    Article  ADS  Google Scholar 

  20. Busch, R. The thermophysical properties of bulk metallic glass-forming liquids. JOM 52, 39–42 (2000).

    Article  Google Scholar 

  21. Kubaschewski, O., Alcock, C. B. & Spencer, P. J. Materials Thermochemistry 6th edn (International Series on Materials Science and Technology, Pergamon, 1993).

    Google Scholar 

  22. Phillips, W. A., Buchenau, U., Nücker, N., Dianoux, A.-J. & Petry, W. Dynamics of glassy and liquid selenium. Phys. Rev. Lett. 63, 2381–2384 (1989).

    Article  ADS  Google Scholar 

  23. Johari, G. P. The entropy loss on supercooling a liquid and anharmonic contributions. J. Chem. Phys. 116, 2043–2046 (2002).

    Article  ADS  Google Scholar 

  24. Gjersing, E. L., Sen, S. & Aitken, B. G. Vibrational entropy near glass transition in a chalcogenide glass and supercooled liquid. J. Non-Cryst. Solids 355, 748–752 (2009).

    Article  ADS  Google Scholar 

  25. Ohsaka, K. et al. Specific volumes of the Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 alloy in the liquid, glass, and crystalline states. Appl. Phys. Lett. 70, 726–728 (1997).

    Article  ADS  Google Scholar 

  26. Stillinger, F. H. A topographic view of supercooled liquids and glass formation. Science 267, 1935–1939 (1995).

    Article  ADS  Google Scholar 

  27. Sciortino, F. Potential energy landscape description of supercooled liquids and glasses. J. Stat. Mech. 2005, P05015 (2005).

    Article  Google Scholar 

  28. Arnold, O. et al. Mantid—data analysis and visualization package for neutron scattering and μ sr experiments. Nucl. Instrum. Methods Phys. Res. A 764, 156–166 (2014).

    Article  ADS  Google Scholar 

  29. Sears, V., Svensson, E. & Powell, B. Phonon density of states in vanadium. Can. J. Phys. 73, 726–734 (1995).

    Article  ADS  Google Scholar 

  30. de Wette, F. W. & Rahman, A. Inelastic scattering of neutrons by polycrystals. Phys. Rev. 176, 784–790 (1968).

    Article  ADS  Google Scholar 

  31. Kresch, M., Delaire, O., Stevens, R., Lin, J. Y. Y. & Fultz, B. Neutron scattering measurements of phonons in nickel at elevated temperatures. Phys. Rev. B 75, 104301–104307 (2007).

    Article  ADS  Google Scholar 

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The authors would like to acknowledge S. Randolph for her help with data collection. A portion of this research at Oak Ridge National Laboratory’s Spallation Neutron Source was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy. This work benefited from DANSE software developed under NSF Grant No. DMR-0520547. This work was supported by DOE BES under contract DE-FG02-03ER46055.

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Samples were prepared by H.L.S., A.H., G.R.G., D.S.K. and M.D.D. Neutron data collection was performed by H.L.S., D.L.A., M.B.S., C.W.L., A.H., G.R.G., F.C.Y., M.S.L., T.S.-W. and B.F. Heat capacity measurements were carried out by H.L.S., A.H., G.R.G. and M.D.D. Data analysis was performed by H.L.S., C.W.L., D.S.K., J.Y.Y.L., M.D.D. and B.F. The manuscript was written by H.L.S., C.W.L. M.D.D. and B.F. All authors discussed the results and provided input on the paper.

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Correspondence to Hillary L. Smith or B. Fultz.

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Smith, H., Li, C., Hoff, A. et al. Separating the configurational and vibrational entropy contributions in metallic glasses. Nature Phys 13, 900–905 (2017).

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