Structural Fragility

When a liquid is cooled quickly below its melting temperature, it rapidly loses kinetic energy, resulting in a sharply increasing viscosity and an accompanying ordering of the liquid structure. When crystallization can be avoided, the liquid can persist in a metastable amorphous state, known as a glass.  The nature of the glass transition and why some liquids are better glass formers than others rank among the most important and interesting questions in condensed matter and materials science. First discovered more than 50 years ago [1], metallic glasses are now finding increasing utility as useful materials for technological applications [2]. Ultimately, glass formation hinges on bypassing crystallization.  Since the viscosity varies by some 15 orders of magnitude from its value at the melting temperature to that at the glass transition temperature, it is a particularly sensitive property for characterizing different liquids.

Angell proposed that the temperature dependencies of the viscosities of different liquids can be described within the concept of fragility.  


As shown in the figure, the “Strong Liquids” are those whose viscosity changes gradually over a wide temperature range while “Fragile Liquids” display rapid change in the viscosity as the glass transition temperature is approached.  Although generally defined in terms of dynamical properties, such as the viscosity or the relaxation rate, theoretical and experimental evidence [3-5] indicates that fragility is related fundamentally to thermodynamic properties, including the excess entropy and specific heat, suggesting that it should also have a structural signature. This presumed link to structural ordering is often used to qualitatively describe fragility.

We’re working on an idea that the structural evolution of a liquid also can be characterized by fragility.  There seems to be some evidence from this from previous studies of metallic glasses, however, quantitative studies of the structural evolution of liquids and glasses together remain elusive, largely because the liquid is so difficult to probe and because structural studies of liquids are notoriously susceptible to scattering artifacts.  Recently, with the development of the Washington University Beamline Electrostatic Levitator (WU-BESL) we been able to make tremendous strides in searching for this “Structural Fragility.”

In a few cases, for example Cu50Zr50, the structural evolution of the liquid and glass was determined from in situ high-energy X-ray diffraction measurements. The temperature dependence of the static X-ray structure factor for the glass was measured from room temperature to above the glass transition temperature. Data were obtained for equilibrium and supercooled liquids in a containerless environment using electrostatic levitation.   In this case, the structure factors and the total pair correlation functions display an anomalous evolution, indicating a rapid acceleration of short-range order in the liquid above, but near, the glass transition temperature.  The behavior is sketched out below.  Note that at the glass transition temperature, the viscosity reached a value for which flow doesn’t occur on laboratory timescales.  Above the temperature, the system is a viscous fluid.



The rapid acceleration in Cu50Zr50 (and other fragile liquids) contrasts sharply with that observed in high glass forming ability metallic liquids.  This suggests that there is a structural signature associated with a good glass-forming liquid, and that this signature may be universal, at least in metallic liquids.

For some more papers on this topic from the Mauro research group please see:

Anomalous structural evolution in Cu50Zr50 glass-forming liquids.” N. A. Mauro, A. J. Vogt, M. L. Johnson, J. C. Bendert, and K. F. Kelton. Applied Physics Letters. 103 (2013) 021904.

Anomalous structural evolution and liquid fragility signatures in Cu–Zr and Cu–Hf liquids and glasses.” N.A. Mauro, Adam J. Vogt, Mark L. Johnson, James C. Bendert, Ryan Soklaski, Li Yang, K.F. Kelton. Acta Materialia. 61(2013)7411.

Anomalous Structural Evolution in Ni-Nb and Ni-Nb-Ta Liquids and Glasses.”N. A. Mauro, M. L. Johnson, J. C. Bendert and K. F. Kelton. Journal of Non-Crystalline Solids. 362 (2013) 237.


[1] Klement, W., Willens, R. H. & Duwez, P. O. L. Non-crystalline Structure in Solidified Gold-Silicon Alloys. Nature 187, 869-870 (1960)
[2] Schroers, J. Bulk Metallic Glasses. Physics Today 66, 32-37 (2013).
[3] Ito, K., Moynihan, C. T. & Angell, C. A. Thermodynamic determination of fragility in liquids and a fragile-to-strong liquid transition in water. Nature 398, 492-495 (1999).
[4] Martinez, L. -. & Angell, C. A. A thermodynamic connection to the fragility of glass-forming liquids. Nature 410, 663-667 (2001).
[5] Sastry, S., Debenedetti, P. G. & Stillinger, F. H. Signatures of distinct dynamical regimes in the energy landscape of a glass-forming liquid. Nature 393, 554-557 (1998).