Fundamentals of the glassy state and the
glass transition
Michael I. Ojovan
Department of Nuclear Energy, IAEA
Joint ICTP-IAEA Workshop on Fundamentals of Vitrification and Vitreous Materials for Nuclear Waste Immobilization.
6 - 10 November 2017, Leonardo Building, ICTP, Trieste, Italy
I. Background to solid melting and glass
transition
II. Bonds breaking on irradiation
III. Viscosity on irradiation
IV. Glass transition on irradiation
V. Nuclear waste vitrification
VI.Conclusions
Outline
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I. Background to solid melting and glass transition
We are interested in understanding fundamentals of
vitrification to ensure a safe utilisation of vitreous materials
for immobilisation of nuclear wastes.
Jerzy Zarzycki,
Professor of Materials Science at the
University of Montpellier:
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4
Finding Tg
log 𝑇𝑔 = 9 ÷ 13
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Configuron Percolation Theory (CPT)
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Depending on the kind of measurement performed,
the glass transition thus manifests itself either as a
continuous or as a discontinuous transformation. As
for first-order thermodynamic properties (volume,
enthalpy, entropy), there is no discontinuity of
transport properties (viscosity, electrical conductivity,
etc.), but a change in temperature
dependence.
In contrast, the variations of second-order
thermodynamic properties across the glass transition
range are rapid enough to be considered practically
as discontinuities.
If the glass is just a very viscous liquid then …
Kauzmann paradox: A configurational contribution causes the
heat capacity of a liquid to be generally higher than that of a
crystal of the same composition. As a consequence, the entropy
of the liquid decreases faster than that of a crystal when the
temperature is lowered.
Solid
Configuron Percolation Theory (CPT)
Crystalline structure (crystal) Solid-like material
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Crystalline structure (crystal) Solid-like material
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1D 2D 3D
Topological equivalence of objects
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0D
1D 2D
1D 2D 3D
Fragmentation (disintegration) of objects
Broken bonds
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1D 2D 3D
0D
1D 2D
An approach to melting of solids and glass transition:
based on analysing broken bonds
summary
Since 2004
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0D
1D 2D
1D 2D 3D
Thermal fluctuations break bonds causing solids melting
(i) Broken bonds are randomly generated within a solid; The higher the temperature the
higher broken bond concentration;
(ii) Broken bonds are mobile (Brownian motion) and can associate to form clusters.
Clusters are larger at higher temperatures.
1D 91/48 2D 2.4 … 2.5
We account that:
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1D 2D 3D
0D
The melting temperature corresponds approximately to the bond percolation threshold
1996
2003
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Configuron Percolation Theory (CPT)
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Vitrification has been considered as a
second order phase transition in which a
supercooled melt yields, on cooling, a
glassy structure and properties similar to
those of crystalline materials e.g. of an
isotropic solid material.
IUPAC. Compendium of Chemical Terminology. 66, 583, RSC, Cambridge 1997
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The physical picture of the glass transition in amorphous materials involves the representation of the
topology change of disordered bonds lattice (network) and of its Hausdorff dimension.
Increase of temperature
MI Ojovan, WE Lee. J. Physics: Condensed Matter 18, 11507 (2006)
Configuron Percolation Theory (CPT)
C.A. Angell, K.J. Rao. Configurational excitations in condensed matter, and “bond
lattice” model for the liquid-glass transition. J. Chem. Phys. 1972, 57, 470-481
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Material
Tg, K
Exper Tgth , K
err%
Log()
Reference for experiment
SiO2
1475
1480
1479
4
-1
0.3
0.08
11.7
G. Urbain, Y. Bottinga, and P. Richet, Geochim.
Cosmochim. Acta 46, 1061 (1982).
B.O. Mysen, P. Richer. Silicate glasses and melts.
Elsevier, Amsterdam, 2005.
GeO2
786
795
9
1
13
E.H. Fontana and W.A. Plummer, “A study of Viscosity-
Temperature relationships in the GeO2 and SiO2
Systems,” Phys. Chem. Glasses, 7, 139-46 (1966)
SLS
870
870
0
0
8.8
H. R. Lillie, “Viscosity-Time-Temperature Relations in
Glass at Annealing Temperatures,” J. Am. Ceram. Soc.,
16, 619-31 (1933).
Salol
220
250
30
14
9.8
Laughlin, W.T and Uhlmann D. R., J. Phys. Chem. 76,
2317 (1972)
Cresol
220
242
22
10
8.83
Laughlin, W.T and Uhlmann D. R., J. Phys. Chem. 76,
2317 (1972)
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Diopside 1005 1109 104 10 11.5 B.O. Mysen, P. Richer. Silicate glasses and melts.
Elsevier, Amsterdam, 2005.
Configuron Percolation Theory (CPT)
Bartenev (1951) – Ritland (1954)
equation
Theory
Cooling rate (q) dependence
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Configuron Percolation Theory (CPT)
Experiment
Theory
Sample size (L) dependence
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Glass transition interval
Theory
The percolation transition is not a sharp threshold, actually it is a region of non-zero
width for systems of finite size [A. Coniglio. Cluster structure near the percolation
threshold. J. Phys. A, 15, 3829–3844 (1982)].
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0D
1D 2D
1D 2D 3D
(i) Broken bonds are randomly generated within a solid; The higher
the temperature the higher broken bond concentration;
(ii)Broken bonds are mobile (Brownian motion) and can associate
to form clusters. Clusters are larger at higher temperatures.
1D 91/48 2D 2.4 … 2.5
Thermal fluctuations break
bonds and this leads to
solids melting
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II. Bonds breaking on Irradiation
Unbinding (bond-breaking mobilising) reactions:
Network-breaking reaction:
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III. Viscosity without and with Irradiation
No irradiation
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Configuron formation enthalpy
Configuron motion enthalpy
Configuron motion entropy
Configuron formation entropy
The universal viscosity equation has been derived using Angell’s bond
lattice model. It relates the viscosity to thermodynamic parameters of
broken bonds (configurons) via CPT equation:
MI Ojovan, KP Travis, RJ Hand. J. Physics: Condensed Matter 19, 415107 (2007).
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At low temperatures the activation energy
of viscosity takes the full value QH=Hd+Hm
because the concentration of broken
bonds is low.
Ojovan MI, Travis KP and Hand RJ 2007 J. Physics: Condensed Matter 19, 415107.
At high temperatures the activation energy is completely
due to the energy needed to transfer a molecule or a
configuron from its original position to the adjacent
vacant site e.g. QL= Hm.
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No irradiation
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Irradiation
K. Zheng et.al., Nature Communications, 1:24,
1 (2011).
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Irradiation
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IV. Glass transition on irradiation
Irradiation
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Irradiation
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V. Vitrification of nuclear waste
Vitrification is the world-
wide accepted technology
for the immobilization of
high level radioactive
wastes.
• Glass can accommodate
the range of constituents
that are present in the
waste into the glassy
structure.
• The excellent durability
of vitrified radioactive
waste ensures a high
degree of environmental
protection.
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Facility Waste Melter Operational period Performance data
R7/T7, La Hague, France HLW IHC Since 1989/92 5573 tonnes in 14045 canisters to 2008, 6430 106 Ci
AVM, Marcoule, France HLW IHC 1978 – 2008 1138 tonnes in 3159 canisters, 45.67 106 Ci
R7, La Hague, France HLW CCM Since 2003 GCM: U-Mo glass
WVP, Sellafield, UK HLW IHC Since 1991 1800 tonnes in 4319 canisters to 2007, 513 106 Ci
DWPF, Savannah River, USA HLW JHCM 1996 – 2011 5850 tonnes in 3325 canisters, 40 106 Ci.
WVDP, West Valley, USA HLW JHCM 1996 – 2002 500 tonnes in 275 canisters, 24 106 Ci
EP-500, Mayak, Russia HLW JHCM Since 1987 6200 tonnes to 2013, 643 106 Ci
(P. Poluektov has earlier reported on 8000 tonnes
and 900 106 Ci to 2009 [1])
CCM, Mayak, Russia HLW CCM Pilot plant 18 kg/h by phosphate glass
Pamela, Mol, Belgium HLW JHCM 1985-1991 500 tonnes in 2200 canisters, 12.1 106 Ci
VEK, Karlsruhe, Germany HLW JHCM 2010 – 2011 60 m3 of HLW (24 106 Ci)
Tokai, Japan HLW JHCM Since 1995 > 100 tonnes in 241 canisters (110 L) to 2007, 0.4 106
Ci.
Radon, Russia LILW JHCM 1987-1998 10 tonnes
Radon, Russia LILW CCM Since 1999 > 30 tonnes
Radon, Russia ILW SSV4 2001-2002 10 kg/h, incinerator ash
VICHR, Bohunice, Slovakia HLW IHC 1997-2001, upgrading work to
restart operation
1.53 m3 in 211 canisters
WIP, Trombay, India HLW IHPT5 Since 2002
18 tonnes to 2010 (110 103 Ci) AVS, Tarapur, India HLW IHPT Since 1985
WIP, Kalpakkam, India HLW JHCM Under testing &
commissioning
WTP, Hanford, USA
LLW JHCM Pilot plant since 1998.
LLW/HLW vitrification plants
under construction.
1000 tonnes to 2000.
Capacities: LLW plant 2 x 15 tonnes/day; HLW plant
2 x 3 tonnes/day
Taejon, Korea LILW CCM Pilot plant, planned 2005 ?
Saluggia, Italy LILW CCM Planned ?
R.A. Robbins, M.I. Ojovan. Vitreous Materials for Nuclear Waste
Immobilisation and IAEA Support Activities.
http://www.dpaonthenet.net/article/52704/Glass-offers-improved-
means-of-storing-intermediate-level-nuclear-waste.aspx
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Waste vitrification is a mature technology demonstrated at
industrial scale.
• Continued advancements in glass waste forms and nuclear waste vitrification
technologies will be keys in enabling widespread deployment of nuclear energy.
• Additionally, the pressing issues regarding hazardous domestic disposal may
also be effectively solved using vitrification technologies.
• Stricter regulations regarding waste characterization and land disposal for
hazardous wastes will necessitate the need for effective waste treatment
methods.
Understanding the glass transition is important to successfully reveal the
rearrangements behind changes in the behaviour of amorphous materials on
vitrification. This is also important in respect to long term safety of nuclear waste
glasses.
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Vitrification is the world-wide accepted
technology for the immobilization of high
level radioactive wastes which provides a high
degree of environmental protection.
Interpretation of the glass transition in terms
of configuron percolation rather than
transitions from Deborah numbers < 1 to > 1
is preferable.
VI. Conclusions
