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Calorimetric Glass Transition
Yuanzheng Yue
Wuhan University of Technology, China
Aalborg University, Denmark
Joint ICTP-IAEA Workshop, Trieste, Italy, Nov. 6-10, 2017
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Outline• Background and motivation• Case 1: Borosilicate and phosphate glasses
– Dulong Petit Law – The Cp m relation– Pressure effect on fictive temperature– Structural source of the Cp change– Prediction of Tg by topological model
• Case 2: Hyperquenched (HQ) glasses– Relaxation in multi-component oxide systems– Relaxation in metallic glasses– Tg of SiO2
– Relaxation in HQ strong glass formers (SiO2 and GeO2)
• Case 3: Mechanically vitrified glasses• Case 4: Metal-organic framework glasses
– Evidence for polyamorprphism in ZIF-4– Melting and glass transition of ZIFs– Ultrahigh glass-forming ability of ZIF-62
2
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Outline• Background and motivation• Case 1: Borosilicate and phosphate glasses
– Dulong Petit Law – The Cp m relation– Pressure effect on fictive temperature– Structural source of the Cp change– Prediction of Tg by topological model
• Case 2: Hyperquenched (HQ) glasses– Relaxation in multi-component oxide systems– Relaxation in metallic glasses– Tg of SiO2
– Relaxation in HQ strong glass formers (SiO2 and GeO2)
• Case 3: Mechanically vitrified glasses• Case 4: Metal-organic framework glasses
– Evidence for polyamorprphism in ZIF-4– Melting and glass transition of ZIFs– Ultrahigh glass-forming ability of ZIF-62
3
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One of the 125 big questions in science (till 2030):
What is the nature of the glass transition? Science, 2005
Numerous models about glass transition are emerging:Macroscopic models (entropy, energy, free volume), Mode-coupling theory, Frustration-based model, Elastic model (harmonic), Local expansion model, Shoving model, Liquid fragility theory, Topological model….
Angell, Science 1995
Debenedetti & Stillinger, Nature 2001
Ediger, Harrowell, J. Chem. Phys. 2012
…..
Here I focus on the calorimetric glass transition.
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Calorimetric glass transition is reflected by a sudden change in heat capacity
400 500 600 700 800 9000.8
1.0
1.2
1.4
1.6
1.8
qh=qc=10 K/min
upscan
downscan
Tg
Cp (
Jg
-1K
-1)
T (K)
Cp = (dH/dT)p Cv
• Glass transition temperature (Tg) is a dynamic temperature, measured as the onset temperature of glass-liquid transition.
• Melting temperature (Tm) is a thermodynamic temperature.
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Key values for glass transition:Heat capacity (Cpg) and its jump at Tg (Cp)
for a normally cooled glass
400 500 600 700 800 9000.8
1.0
1.2
1.4
1.6
1.8
Cpl
Cpg
qh=qc=10 K/min
Tg
Cp (
Jg
-1K
-1)
T (K)
Cp
Cp(PO3)2 glass
d
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Heat capacity for a hyperquenched glass
(rockwool glass at ~106 K/s)
400 600 800 1000
0.6
0.8
1.0
1.2
1.4
1.6
64 J/g
Tg
Tc
The hatched area:
energy released from 1g fiber
upscan 1
upscan 2
T (K)
Cp (
Jg
-1K
-1)
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Determination of the glass transition (Tg)
and the fictive temperatures (Tf)
Basic equation:
Y. Z. Yue, et al., Chem. Phys. Lett. 2002; J. Chem. Phys. 2004
f
g
eq
c
T
Tpgplp
T
Tp dTCCdTCC )()( 12
400 600 800 1000 1200
0.8
1.0
1.2
1.4
1.6
1.8
BA
B
A
Cpg
Cpl
Cp2
Cp1
=
Tg=941 K Tf=1141 K
T (K)
Cp (
Jg
-1K
-1)
Cpg = a + bT + c/T2 + d/T0.5
900 950 1000 1050 1100 1150
=Tg=941 K Tf=1141 K
T (K)
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Glass transition
Influenced by
• Chemical composition and liquid fragility
• Thermal and mechanical history
• Types and strength of chemical bonds
• Network connectivity
• Topological degree of atomic freedom
• Atomic packing
• Microscopic heterogeneity
• Cluster structure
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Outline• Background and motivation• Case 1: Borosilicate and phosphate glasses
– Dulong Petit Law – The Cp m relation– Pressure effect on fictive temperature– Structural source of the Cp change– Prediction of Tg by topological model
• Case 2: Hyperquenched (HQ) glasses– Relaxation in multi-component oxide systems– Relaxation in metallic glasses– Tg of SiO2
– Relaxation in HQ strong glass formers (SiO2 and GeO2)
• Case 3: Mechanically vitrified glasses• Case 4: Metal-organic framework glasses
– Evidence for polyamorprphism in ZIF-4– Melting and glass transition of ZIFs– Ultrahigh glass-forming ability of ZIF-62
10
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Dulong Petit Law applies when the unit of Cp is converted to J/mol of atoms?
400 500 600 700 800 900
15
20
25
30
35
40
45
Cp (
J m
ol-1
K-1)*
T (K)
*Jouls per mole of atoms, not per mole of molecules
B2O3 increases
3R
0 20 40 60 80
23
24
25
Cp
g a
t T
g (
Jm
ol-1
K-1)*
B2O3 (mol%)
Dulong Petit Lawworks at Tg
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Cp≈3R law works for oxide glasses at Tg
400 600 800 1000 1200 1400 1600
15
20
25
30
35
40
45
50
Cp (
J m
ol-1
K-1)*
T (K)
*Jouls per mole of atoms
3R
NaPoLi
CMP
borosilicate
basaltic
Diopsite
SiO2
35Al2O365SiO2
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Cp as a function of composition
100 200 300 400 500 60050
80
110
140
170
Cp (
J m
ol-1
K-1)
T (oC)
75B
63B-12Si
51B-24Si
37B-37Si
24B-51Si
12B-63Si
6B-69Si
75Si400 450 500 550 600
75
100
125
150
175
Tg
Cpg
Cpl
0 20 40 60 8010
20
30
40
50
60
1.2
1.3
1.4
1.5
1.6
Experiment (Cp)
Model (Cp)
C
p (
J m
ol-1
K-1)
[B2O3] (mol%)
Experiment (Cp,l/Cp,g)
Cp
,l/C
p,g (
-)
Smedskjaer et al. J. Phys. Chem. B. 115 (2011) 12930
Configurational heat capacity (Cp) increases with increasing the B2O3/SiO2
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Relation between Cp and kinetic fragility
20 30 40 50 600
10
20
30
40
50
60
C
p (
J m
ol-1
K-1)
m (-)
Implication: There is a link between Cp to the kinetic fragility for the same series of glasses.
)1(0
mm
TA
pg
C
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The network connectivity increases with increasing B2O3, but the fragility increases.
0 20 40 60 80
0.0
0.2
0.4
0.6
0.8
NB
O/T
B2O3 (mol%)
Implication: The network connectivity is not the main controlling factor for liquid fragility.
0 20 40 60 8010
20
30
40
50
60
1.2
1.3
1.4
1.5
1.6
Experiment (Cp)
Model (Cp)
C
p (
J m
ol-1
K-1)
[B2O3] (mol%)
Experiment (Cp,l/Cp,g)
Cp
,l/C
p,g (
-)
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B2O3 mol% increase
IRO B3SiO4-O-
q=1.0
q=0.08400 600 800 1000 1200 1400 1600
Rela
tive I
nte
nsity (
A.U
.)
Wavenumber (cm-1)
The IRO band is greatly enhanced by increasing B2O3 content
Raman on 75q B2O3 - 75(1-q) SiO2 - 15Na2O - 10CaOq = [B2O3]/([B2O3]+[SiO2])
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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
40
44
48
52
56
fragili
ty m
Total Area of IRO bands0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
20
30
40
50
Cp
,co
nf (
J m
ol-1
K-1)
Total Area of IRO Bands
IRO units increase Cp,conf and m
Link between Cp,conf and IRO units
The content of IRO units has a dominant contribution to the evolution of Cp,conf with composition in borate-silicate glasses.
H. Liu, et al., PCCP, 18 (2016) 10887
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Topological model and temperature dependent constraint theory
Phillips & Thorpe:
• Atomic structure of a glass- a network of bond constraints
• Each atom has 3 degrees of freedom, but they are removed by:
Two - body Linear constraints
Three – body angular constraints
Gupta & Mauro:
• Temperature dependent constraint theory
• network constraints vs. composition
Predicting glass properties, e.g.,Tg , m, Hv
Phillips & Thorpe, Sol .State Commun. (1985)
Gupta & Mauro, J. Chem. Phys. (2009) SeSe
SeSe
SeSe
(a)
(b)
(c)
GeGe
GeGe GeGe
SeSeSeSe
SeSe
SeSeSeSe
(a)
(b)
(c)
GeGe
GeGe GeGe
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Type and counting of Constraints
• type: B-O and MNB-O linear constraintsTwo constraints at each oxygen
• Β type: O-B-O angular constraints− Five β constraints at each Q4 unit.− Three at each Q3 unit.
• γ type: B-O-B and B-O-M(NB) angular constraints− One g constraint at each bridging oxygen
• μ type: modifier rigidity (due to clustering)− Two μ constraints per NBO-forming Na atom
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Ranking of Constraints
Each type of constraint has its onset temperatures, which is the temperature where constraints become rigid as temperature is lowered.
T T T Tg
0 10 20 30 40
0
1
2
3
O-
Na+ Na
+
Na+
O
T > T
T < T < T
T < T < T
Tg < T < T
Ato
mic
degre
es o
f fr
eedom
[Na2O] (mol%)
T < Tg
Co
olin
g
B-O
MNB
-O
O
B
B B
O
O- O
-
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Predicting Tg by using temperature dependent constraint theory
Good prediction, but challenge for complex systems
Smedskjaer, Mauro, Sen, Yue, Chem. Mater. 22 (2010) 5358Smedskjaer, Mauro, Youngman, Hogue, Potuzak, Yue, J. Phys. Chem. B 115 (2011) 12930.
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Pressure induced enhancement of the Cp overshoot for CaP2O6 glass
500 600 700 800 90080
100
120
140
160
180
200
2nd DSC upscan
Cp (
Jm
ol-1
K-1)
T (K)
1st DSC upscan after
500 MPa compression
780 790 800 810 820 830
120
140
160
180
200
220
Cp (
Jm
ol-1
K-1
)
T (K)
P (MPa)
a: 500
b: 300
c: 200
d: 100
e: 20
0.1
a
b
cd
e
Why? Pressure drives glass deep in the potential energy landscape. When being heated, glass absorb energy from the surrounding, and hence enhances Cp’.
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Thermodynamic consequences of compression and relaxation for CMP
300
400
500
600
700
800
0 100 200 300 400 500 600 700
0.5
0.6
0.7
0.8
0.9 b)
a)
780 800 820 840100
120
140
160
180
Cpl
Cp(T)
T2T1
Hover
Cp (
Jm
ol-1
K-1
)
T (K)
H
over (J
mol-1
)
S
over (J
mol-1
)
P (MPa)
dTCTCHT
T plpover 2
1
))((
dTST
T T
CTC
overplp
2
1
))((
Potential energy decreases during compression.
Entropy change decreases during compression.
Yue, et al. J. Chem. Phys. 2007
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Fictive temperature (Tf) decreases with pressure for CMP
0 100 200 300 400 500 600764
768
772
776
700 750 800 850100
120
140
160
180
A
B
BA =
Tf
Cp (
Jm
ol-1
K-1
)
T (K)
TfA
(K
)
P (MPa)
Moynihan, et al. J. Am. Ceram. Soc. 1976Yue, et al. Chem. Phys. Lett. 2002; J. Chem. Phys. 2007
To determine Tf correctly we should apply the correct method:Enthalpy-matching method
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Structural relaxation in compressed borate glasses
Smedskjaer et al, Sci. Rep. (2014)
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Outline• Background and motivation• Case 1: Borosilicate and phosphate glasses
– Dulong Petit Law – The Cp m relation– Pressure effect on fictive temperature– Structural source of the Cp change– Prediction of Tg by topological model
• Case 2: Hyperquenched (HQ) glasses– Relaxation in multi-component oxide systems– Relaxation in metallic glasses– Tg of SiO2
– Relaxation in HQ strong glass formers (SiO2 and GeO2)
• Case 3: Mechanically vitrified glasses• Case 4: Metal-organic framework glasses
– Evidence for polyamorprphism in ZIF-4– Melting and glass transition of ZIFs– Ultrahigh glass-forming ability of ZIF-62
26
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Approaches we used
NMRHRTEM
DSC
HyperquenchingBall milling
Sub-Tg annealing(at T<Tg)
Charaterizations
Stone Wool
Milled powder
Metallic glass
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DSC output reflects the change of potential energy during heating or annealing
400 600 800 1000
0.8
1.0
1.2
1.4
1.6 Stone wool
Cp1
Cp2
T (K)
Cp (
Jg
-1K
-1)
DSC is a sensitive tool for detecting the
energetic and structural evolution of glass
Tm Tf Tg
Supercooled liquid
standard
glass
HQG
Enth
alp
y
Temperature
H
annealing
Tf2
high Tf glass
(e.g. stone wool)
Tg
Tf1
Tm
Collective configuration coordinate
Crystal
low Tf glass
(e.g. ultrastable film)
Pote
ntial energ
y
Z*
Yue, et al. APL 2002Angell, et al. JPCM 2003Hu, et al. JPC-C 2009Qiao, et al. JACerS 2016
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Hyperquenching-Annealing-Calorimetry Hyperquenched (HQ) basalt glass
400 600 800 1000
0.6
0.8
1.0
1.2
1.4
1.6
Cp1
Teq
Cp2
T (K)
Cp (
Jg
-1K
-1)
Tc
Cp overshoot
400 600 800 10000.8
1.0
1.2
1.4
1.6
1.8ta=90 min
gf
Ta (K)
a: 573
b: 623
c: 673
d: 723
e: 773
f: 798
g: 823
edcba
T (K)
Cp (
Jg
-1K
-1)
An approach – for understanding the glass transition and relaxation
Excess enthalpy of fresh HQ fibers Excess enthalpy of annealed HQ fibers
eq
c
T
T ppexcess dTCCH )( 12
Yue and Angell, Nature 2004
Energy ‘bird’
Yue, et al., Appl. Phys. Lett. 2002;
Yue, et al. Chem. Phys. Lett. 2002
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Basalt (relatively fragile)
400 600 800 1000
0.55
0.60
0.65
0.70
0.75
0.80
T (K)
d
ta
a: 0 min
b: 30 min
c: 2 hrs
d: 11 hrs
e: 19 hrs
f : 27 hrs
g: standard
g
f
ec
b a
Cp (
Jg
-1K
-1)
Ta = 565 K (0.71Tg)
400 500 600 700 800 900 10000.8
1.0
1.2
1.4
1.6
1.8
IGFEDC
AB
Cp (
Jg
-1K
-1)
T (K)
H
ta
A: non-annealed
B: 1 min
C: 4 min
D: 15 min
E: 50 min
F: 3.5 h
G: 12 h
H: 2 days
I: 8 days
Onset of pre-endotherm
Ta=723 K (0.77Tg)
GeO2 (strong)
Differences in sub-Tg relaxation between a
fragile and a strong system
More heterogeneous
More non-exponential
Less cooperative
Pre-endotherm
Less heterogeneous
Less non-exponential
more cooperative
No pre-endotherm
Hu and Yue, JPC-B (2008)Yue and Angell, Nature (2004)
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Double “glass transition” upon 55 days aging
400 500 600 700 800 900 1000
1.0
1.2
1.4
1.6
1.8 upscan 1
upscan 2
cooled at 106 K/s
aged at 773 K for 55 days
Cp (
Jg
-1K
-1)
T (K)
400 500 600 700 800 900 1000 1100
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
Energy release exotherm
pre-endotherm
Cp
,exc (
Jg
-1K
-1)
T (K)
It shows that the relaxation is highly exponential, and hence, highly energetically heterogeneous
‘Shadow glass’ transition
Yue and Angell, Nature 2004
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0 20 40 60 80 100 120 140 1600.00
0.01
0.02
0.03
0.04
0.05
0.06
hyperquenched annealed super-annealed crystallized
Z(
)
(cm-1)
Vibrational density of state (VDOS) of HQ glasses
• VDOS peak at ~35 cm−1 in the HQ state
• The peak is suppressed by annealing.
• The peak disappears in crystallized state.
• Source: topologically diverse defects
Implication: vibrational structure changes with the state of configurational excitation of the liquid.
Angell, Yue, et al. J. Phys: Cond. Mat. (2003)
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Relaxation in hyperquenched 20MgO-20CaO-60SiO2 glasses – detecting structural heterogeneity
400 600 800 1000 1200
0.9
1.2
1.5
Cp (
Jg
-1K
-1)
T (K)
Remarkable!
two sub-Tg energy
release peaks
Tg=999 K
400 600 800 1000
0.9
1.2
1.5
2nd upscan
Cp (
Jg
-1K
-1)
T (K)
1st upscan
2 sub-Tg relaxation peaks 2 kinds of structural domains?
400 600 800 1000
0.6
0.8
1.0
1.2
1.4
1.6T
g
Tc
upscan 1
upscan 2
T (K)
Cp (
Jg
-1K
-1)
Each has its own structural heterogeneity.
Two structural domains in the liquid state are frozen-in at high Tf.
Yue and Angell, Nature 2004, Yue, et al., Zhang, et al, JACerS 2013, 2017
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Effect of sub-Tg annealing time on the Cp pattern and hence on the
energetic elvolution of the two structural domains
Peak dimishes vertically
(like strong systems)
Peak diminshes horizontally
(like fragile systems)
Two structural domains (strong and fragile ones)?
400 600 800 1000
0.55
0.60
0.65
0.70
0.75
0.80
T (K)
d
a: 0 minb: 30 minc: 2 hrsd: 11 hrse: 19 hrsf : 27 hrsg: standard g
f
ec
b a
Cp (
Jg
-1K
-1)
400 600 800 10000.8
1.0
1.2
1.4
1.6
Cp (
Jg
-1K
-1)
T (K)
Ta=823 K
Fresh
Standard
1 h
6 h
24 h
4 d
(a)
400 500 600 700 800 900 10000.8
1.0
1.2
1.4
1.6
1.8
101 102 103 104 105 106
0.4
0.6
0.8
1.0
E
rem
/E
tot
ta (s)
IGFEDC
AB
Cp (
Jg
-1K
-1)
T (K)
H
ta
A: non-annealedB: 1 minC: 4 min D: 15 minE: 50 minF: 3.5 hG: 12 hH: 2 daysI: 8 days
Ta=723 K
Onset of pre-endotherm
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Tg of SiO2 drastically drops with increasing
water content
200 400 600 800 1000 1200 1400 1600 18000.7
0.8
0.9
1.0
1.1
1.2
1.3
1336 K
water content
~1 ppm
~1021 ppm
1434 K
Cp (
Jg
-1K
-1)
T (K)
Y. Z. Yue, Front. Mater. 2 (2015) 1
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Comparison between the measured Cp and the calculated Cp
400 800 1200 1600
40
50
60
70
80
data
Einstein Equation
SiO2 glass (<1 ppm water)
qh=10 K/min
Cp (
Jm
ol-1
K-1
)
T (K)
Cv = 3REi(Xi)
E(x) = x2ex/(ex-1)2
x = h/kT = /T
where = Einstein temperature
s = 1100 K (Si vibrations)
T = 370 K (transverse oxygen
vibrations)
L = 1220 K (longitudinal
oxygen oscillations)
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Tg of silica decreases with repeating the DSC scans
400 800 1200 16000.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
SiO2 glass (~1 ppm OH)
qh=10 K/min
upscan 11
upscan 1
Cp (
Jg
-1K
-1)
T (K)0 2 4 6 8 10 12
1300
1350
1400
1450
Tg (
K)
Number of DSC scans
Cristobalite formation and weakening of bonds by repeating reheating?
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Enthalpy relaxation of a hyperquenched (HQ) normal glass and a HQ Silica
400 600 800 1000 1200 1400 16000.7
0.8
0.9
1.0
1.1
1.2
Upscan 2
Upscan 1
Tg=1356 K (1083 ºC)
SiO2 fiber
T (K)C
p (
Jg
-1K
-1)
HQ vitreous silica
HQ normal glass
300 400 500 600 700 800 900
0.8
1.0
1.2
1.4
1.6
Upscan 1
Ca(PO3)2 fibers
qh=qc=20 K/min
T (K)
Cp (
Jg
-1K
-1)
Upscan 2
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Effect of the annealing temperature Ta on the Cp,exc
0.0
0.1
0.2
0.3
d)
c)
b)
ta=12 hrs Ta (K)
A not annealed
B 523
C 623
D 723
E 823
G
E
EF
D
D
C
CC
BB
B
A
A
A C ED
B
A
HQGeO2
HQBas HQSiO2
Cp,e
xc (
Jg
-1K
-1)
a)
ta=24 hrs Ta (K)
A not annealed
B 873
C 923
D 948
E 1073
0.5 0.6 0.7 0.8 0.9 1.0 1.1
0.0
0.1
0.2
0.3
T/Tg (K/K)
ta=3 hrs Ta (K)
A no-annealed
B 603
C 643
D 683
E 723
F 743
G 763
HQCmP
T/Tg (K/K)
0.5 0.6 0.7 0.8 0.9 1.0 1.1
ta=3 hrs Ta (K)
A not annealed
B 650
C 700
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Effect of annealing time (ta) on Cp,exc of HQ glasses
0.0
0.1
0.2
0.3
b)
A
ta (hrs)
A 0
B 0.017
C 0.25
D 3.5
E 12
F 192
Cp
,exc (
Jg
-1K
-1)
a)
d)
B
C
A
HQGeO2
HQSiO2
c)
0.5 0.6 0.7 0.8 0.9 1.0 1.1
0.0
0.1
0.2
0.3
T/Tg (K/K)
FEDC
B
B CD CA
ta (hrs)
A 0
B 0.25
C 3.5
ta (hrs)
A 0
B 3
C 24
HQCmP ta (hrs)
A 0
B 0.11
C 1
D 9
E 27
T/Tg (K/K)
0.5 0.6 0.7 0.8 0.9 1.0 1.1
BC
A
HQBas
Y. Z. Yue, Front. Mater. 2 (2015) 1
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(49m/s)
(35m/s) (25m/s) (17m/s)
Cu46Zr46Al8
monotonic
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Non-montonic structural response to sub-Tg
annealing measured by x-ray scattering
Annealing dependence of the structural unit size
Annealing dependence of the correlation length
Critical temperature for the dramatic decreases in Rc: Tc ~ around 1.3Tg
Total structural factors PDF
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Schematic scenario of the structural evolution during fragile-to-strong transition
Zhou, et al. J. Chem. Phys. (2015)
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Outline• Background and motivation• Case 1: Borosilicate and phosphate glasses
– Dulong Petit Law – The Cp m relation– Pressure effect on fictive temperature– Structural source of the Cp change– Prediction of Tg by topological model
• Case 2: Hyperquenched (HQ) glasses– Relaxation in multi-component oxide systems– Relaxation in metallic glasses– Tg of SiO2
– Relaxation in HQ strong glass formers (SiO2 and GeO2)
• Case 3: Mechanically vitrified glasses• Case 4: Metal-organic framework glasses
– Evidence for polyamorprphism in ZIF-4– Melting and glass transition of ZIFs– Ultrahigh glass-forming ability of ZIF-62
44
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Potential energy landscape
Two paths towards the glass state far from equilibirum:• Thermally hyperquench liquids• Mechanically hyper-mill crystals
Fiber spinner
Ball mill
hyperquenching
Tg
Tf
Crystal
Ultrastable glass
Tm
Pote
nti
al
En
ergy
Z collective configuration coordinate
mechanical milling
Sub-Tg relaxation
Higher Tf
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Contrasr in relaxation between hyperquenched and
milling-derived glasses
900700500300T (K)
Cp
(JK
-1g-1
)
0.5 0.6 0.7 0.8 0.9 1.0
0.0
0.1
0.2
0.3
Main peak
S2
B
HQBas
C
p (
JK
-1g
-1)
T/Tg (K/K)
As-milled Ag3PS
4A
S1Shoulder
Qiao, et al, J. Am. Ceram. 100 (2017) 968
360 400 440 480 520 560
-1.5
-1.0
-0.5
0.0
0.5
1.0T
g
S1
Cp2
C
p (
JK
-1g
-1)
T (K)
Cp1
S2
(a)
As-milled Ag3PS4
As-quenched basalt glass
As-milled Ag3PS4 glass is highly structurally heterogeneous.
The two peaks originate from - and –relaxations.
Cp(sub-Tg)=Cp2-Cp1
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Contrast in relaxation behavior between the two glasses
400 420 440 460 480 500
0.00
0.05
0.10
0.15
GFEDCB
Cp (
JK
-1g
-1)
T (K)
Tmax
(K)
A As-milled
B 400
C 413
D 423
E 440
F 459
G 471
A
Energy release of both the as-milled Ag3PS4 glass (curve A) and the dynamically heated Ag3PS4 (curves B to G)
Y. Z. Yue, et al, Appl. Phys. Lett. 81 (2002) 2983
A. Qiao, et al. J. Am. Ceram. Soc. 100 (2017) 968-974
The milling-derived Ag3PS4 glass has similar relaxation feature to that of HQ glasses. But the former is structurally more heterogeneous.
Energy release of basalt glass wool after annealing at various Ta
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Outline• Background and motivation• Case 1: Borosilicate and phosphate glasses
– Dulong Petit Law – The Cp m relation– Pressure effect on fictive temperature– Structural source of the Cp change– Prediction of Tg by topological model
• Case 2: Hyperquenched (HQ) glasses– Relaxation in multi-component oxide systems– Relaxation in metallic glasses– Tg of SiO2
– Relaxation in HQ strong glass formers (SiO2 and GeO2)
• Case 3: Mechanically vitrified glasses• Case 4: Metal-organic framework glasses
– Evidence for polyamorprphism in ZIF-4– Melting and glass transition of ZIFs– Ultrahigh glass-forming ability of ZIF-62
48
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MOF glass family has emerged…
• Concerning chemical bonds, melt-quenched glasses have
3 families:
– Inorganic non-metallic glasses (e.g. oxide,
chalcogenide glasses, fluride…)
– Organic glasses (polymer, molecular glasses…)
– Metallic glasses
• A new family: Organic-inorganic hybrid glasses:
– ZIF glass, coordination polymers
49
Bennett, Tan, Yue, et al., Nature Com. 6 (2015) 8079Bennett, Yue, Li, et al., J. Am. Chem. Soc. 138 (2106) 3484Tao, Bennett, Yue, et al. Adv. Mater. 29 (2017) 1601705Umeyama, et al. J. Am. Chem. Soc. 137 (2015) 864.Zhao, et al. J. Am. Chem. Soc. 138 (2016) 10818
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We have succeeded in vitrifyingseveral Zeolitic imidazolate frameworks (ZIFs)
- ZIF is a subset of MOFse.g., ZIF-4, structurally analogous to SiO2
Zeolitic topology
Bondingunit for SiO2
Bonding unit for ZIF-4
SiO2 network
But their properties differ significantly.
Zn(C3H3N2)2
50
Coordinating bonds!Covalent+ionic mixed bonds!
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Observe fascinating transitions in ZIF-4 by DSC
400 500 600 700 800 900 1000 1100-4
-2
0
2
4
6
Cp (
Jg
-1K
-1)
T (K)
20 K/min upscan
crystallization
melting
foaming
onset of gas release
lattice collapse
amorphisation
LDA to HDL
solvent release
80
85
90
95
100
Ma
ss (
%)
51
350 400 450 500 550 600 650
1.0
1.2
1.4
1.6
Cp (
Jg
-1K
-1)
T (K)
ZIF-42nd upscan at 20 K/min
Tg=570 K
Crystal ZIFdesolvation-LDA HDAHDL phasecrystal ZIF-zni MeltBulk glass Foam glass!
LDA: Low density amorphous phase HAD: High density amorphous phase
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Crystal ZIF-4 Amorphisation Crystal ZIF-zni
a) b) c)
350 400 450 500 550 600 650 7000.8
1.0
1.2
1.4
1.6
350 400 450 500 550 600 650 700
1.0
1.2
1.4
1.6
Cp
Tg of HDA
Cpl
Cp (
Jg
-1K
-1)
T (K)
Cpg
Upscan 2
LDL-HDL
liquid transition
Cp (
Jg
-1K
-1)
T (K)
123
Tg of HDA=563 K
Cp=0.14 Jg-1K
-1
Cpl/Cpg=1.1
release of
solvent
collapse into LDA
Glass transition of HDA
upscan rate:
10 K/min
400 500 600 700 800 900 1000 1100-4
-2
0
2
4
6
Cp (
Jg
-1K
-1)
T (K)
20 K/min upscan
crystallization
melting
foaming
onset of gas release
lattice collapse
amorphisation
solvent release
80
85
90
95
100
Ma
ss (
%)
Calorimetric evidence for polyamorphic transitionsand glass formation
52
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Potential energy landscape of ZIF-4
ZI
ZIF-4
LDA
HDA/MQG
ZIF-zni
kBTm
kBTgLDA
kBTgHDA/MQG
Pote
nti
al E
ner
gy
Configurational Coordinate
exo endo
HmAmorphization
Quench-vitrifying
53
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Co-existence of LDA and HDA phases!
480 520 560 600 640 680
LDA
300 400 500 600 7001.0
1.2
1.4
1.6 HG
F
E
D
CB
Cp (
Jg
-1K
-1)
T (K)
A
A: 529 K
B: 563 K
C: 578 K
D: 588 K
E: 601 K
F: 608 K
G: 613 K
H: 673 K
G
H
FEDCB
Heat flow
(A
U)
T (K)
A
Rescans of ZIF-4 after the sample
was scanned to different T
Scan rate: 10 K/min
HDA
Polyamphic transition in ZIF-4 54
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Fragilities of LDA and HDA phases
LDA phase is superstrong!
It is stronger than HDA phase and melt-quenched glass!
0.90 0.92 0.94 0.96 0.98 1.00 1.02
9
10
11
12
13
HDA: m=41
LDA: m=18
log
(
in
Pa
s)
Tg/T
ZIF-4DSC data to viscosity datalog = 11.35 – logqh (Tf)
Yue, von der Ohe, Jensen, JCP (2004)
Dashed line: MYEGA fit
Mauro, Yue, Ellison, Gupta, Allan,PNAS (2009)
11
15exp153log
T
Tm
T
T gg
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Compare with other systems
0.4 0.5 0.6 0.7 0.8 0.9 1.0
-4
-2
0
2
4
6
8
10
12
log (
Pa
s)
Tg/T (K/K)
SiO 2 (m
=20)
Anorthite
(m=53)
ZIF-4 LDA (SAXS) (m=14)
ZIF-4 LDA (DSC) (m=18)
ZIF-4 HDA (D
SC) (m=41)
Triphe
nyle
thylen
e (m
=101
)
56
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Summary
Glass transition is an fascinating complex problem. Investigation of
glass transition is continuing…..
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I thank
all my co-authors and collaborators.
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Thank you for your attention!