Presented by Dr. Mark Ediger Part of the 2019 MRSEC Summer Seminar Series The thermodynamics of glasses were reviewed and how the state of a glass is influenced by different methods of preparation was briefly described. A qualitative description of glasses within the framework of the potential energy landscape was presented, with an emphasis on the configurational entropy. Relaxation processes in glasses were also discussed, including physical aging, sub-Tg relaxations, and quantum tunneling two-level systems. Along the way, the audience was led to understand what is wrong with these statements: 1) All glasses with a given composition have the same properties. 2) Nothing can move in a glass. 3) There is nothing interesting about glasses.

1. Thermodynamics and Dynamics of Glasses
Mark Ediger (UW-Madison)
NSF MRSEC
1

2. Glasses are solids with greater variation of
local structure than crystals – and are better
materials for some applications
http://www.reddit.comhttp://cdn.c.photoshelter.com

3. Knowledge of our universe – brought to you by glass!
3Hubble image
Hubble space
telescope mirror
Macroscopic homogeneity,
compositional flexibility

4. Modern communication depends upon glass
4NASA image
CBS News image
techepics.com
Optical fibers Organic light emitting
diode (OLED) display
Processability

5. 5
Plazek and Magill, J. Chem. Phys. 49, 3678 (1968)
Molarvolume(ml/mol)
Temperature (°C)
crystal
super-
cooled
liquid
glasses
Plazek and Magill, JCP 1966
TNB
Observed transition from liquid to glass is continuous and
occurs because of slow kinetics (not thermodynamics)
Logh/P
1000 K/T

6. 6
Plazek and Magill, J. Chem. Phys. 49, 3678 (1968)
Observed transition from liquid to glass is continuous and
occurs because of slow kinetics (not thermodynamics)
Logh/P
1000 K/T
Zr41.2Ti13.8Cu12.5Ni10Be22.5 (Vitreloy 1)
Lu et al. / Acta Materialia 51 (2003) 3429–3443

7. 7
Gujral, et al. Chemistry of Materials
2015
Molarvolume(ml/mol)
Temperature (°C)
crystal
super-
cooled
liquid
glasses
Plazek and Magill, JCP 1966
TPDTNB
Glasses are non-equilibrium solids without long
range order

8. What constraints does thermodynamics place
upon glass formation?
8Plazek and Magill, JCP 1966
Molarvolume(ml/mol)
Temperature (°C)
crystal
super-
cooled
liquid
glasses
TNB
Is this extrapolated behavior
accurate down to T = 0 K, or
is there an end of the line for
the liquid state?
liquid
Tg

9. The entropy crisis and the ideal glass
9Ediger and Harrowell, JCP 2012; Data from Chang and Bestul, JCP 1972
Vanishing
configurational
entropy (by
extrapolation)
defines ideal glass
packing
Random first order
transition predicted
(Kirkpatrick,
Thirumalai and
Wolynes), but can’t
be reached by liquid
cooling.

10. Kauzmann entropy crisis
Ediger and Harrowell, JCP 137, 080901 (2012)
Yamamuro et al, J. Phys. Chem. B 1998, 102, 1605-1609
Tatsumi, et al. PRL 109, 045701 (2012);
toluene
OTP
10
T (K)

11. The potential energy landscape can be used to illustrate glass
formation and define fundamental questions
These states: Entropy crisis? Underlying phase transition?
Properties of the ideal glass? Useful material properties?
11
Figure from Ediger, JCP (2017), inspired by Debenedetti and Stillinger, Nature (2001)
Berthier
simulations
Ta Tg

12. Deep connections between thermodynamics and
dynamics of supercooled liquids
Richert in: Structural Glasses and Supercooled
Liquids: Theory, Experiment, and Applications, First
Edition. Edited by Peter G. Wolynes and Vassiliy
Lubchenko. 2012 John Wiley & Sons, Inc.
Wolynes and Lubchenko, Annu. Rev. Phys. Chem. (2007)
12
(thermodynamics)
(dynamics)

13. What would an
ideal glass look like?
13
Simulations of cavities with fixed
boundaries (Bouchaud, Biroli)
At low temperature, at
equilibrium, boundary imposes a
particular packing arrangement
even for large R
Berthier, Ozawa, Scalliet, JCP (2019)

14. PVD glasses can closely approach ideal glass packing
(Ramos, Oguni, Ishii, and Nakayama)
14Adapted from Ramos, Oguni, Ishii, Nakayama, J. Phys. Chem. B (2011)
PVD glasses of
ethylbenzene deposited
as low as 0.92 Tg (1.04 TK)
have enthalpy expected for the
equilibrated supercooled
liquid.
end of the line for the
liquid state – the ideal glass
Liquid-cooled
glass
TK
PVD glasses

15. Glasses are not “dead” in terms of dynamics and relaxation processes
Below Tg – Crystallization can occur in some systems. Transition to stable
thermodynamic state. 75 million years for obsidian at room temperature. More
than 3 billion years for silicate “moon glass"
Between 0.5 Tg and Tg – Physical aging on long time scales (hours to millions of
years). Relaxation of glass structure towards thermodynamically preferred
amorphous state.
Between 0.5 Tg and Tg – Sub-Tg relaxations on short times scales (milliseconds,
seconds). Constrained atomic and molecular rearrangements within an overall
fixed glass structure. b relaxation is an example.
Less than 10 K – Quantum tunneling two level systems (TLS). Small
rearrangements with a fixed glass structure. ”Noise” for quantum computing.

16. 16
Berthier and Ediger, Physics Today (2016)

17. Glasses age: Cooling from the liquid to just below Tg forms a barely stable
glass whose properties change with time
J.Q. Wang et al. / Acta Materialia 104 (2016); Au49Cu26.9Ag5.5Pd2.3Si16.3
crystal
supercooled
liquid
glasses
17

18. Beta relaxation process
Kudlik et al., Europhys. Lett., 40 (6),
pp. 649-654 (1997)
Beta relaxation time extrapolates
back to ~ 10-16 s
Stillinger, Science (1995)
18

19. Beta relaxation process
in metallic glasses has been linked with ductility
Yu, Wang, Samwer, Materials Today (2013) 19
La68.5Ni16Al14Co1.5
1 Hz

20. Low temperature properties of glasses: Interpretation
as quantum tunneling two-level systems
Data from: Lasjaunias et al.,
SolidState Commun. (1975)
Zeller and Pohl,
Phys. Rev. B (1971)
Anderson, Halperin,
and Varma, Philo.
Mag. (1972)
20

21. Residual motion suppressed in high density PVD glasses
21
Yu, Richert et al., PRL 115, 185501 (2015)
Possible physical
picture:
Orientation
exploration in a
cone of ~ 3°
(vapor deposited
glass) instead of
~ 7 °(liquid-
cooled glass)

22. Heat capacity below 2 K is strongly suppressed in
stable PVD glasses: Where are the two-level systems?
22
Perez-Castenada, PNAS 111, 11275 (2014)
silicon

23. Questions?
• For more information, 4 weeks of lectures on glasses
(including 4.5 hours of me) from a 2017 summer
school on disordered systems:
https://www.youtube.com/watch?v=iB0q5gFhzpY&ind
ex=23&list=PL8mMEmoXNBfaBEMiKdQnTvCLOVRni
OrPb
23