Supplemental Material
Unique Effects of Thermal and Pressure Histories on Glass Hardness:
Structural and Topological Origin
Morten M. Smedskjaer1, Mathieu Bauchy2, John C. Mauro3, Sylwester J. Rzoska4,5, Michal Bockowski4
1
Section of Chemistry, Aalborg University, 9000 Aalborg, Denmark. 2Department of Civil and Environmental
Engineering, University of California, Los Angeles, California 90095, USA. 3Science and Technology Division,
Corning Incorporated, Corning, New York 14831, USA. 4Institute of High Pressure Physics, Polish Academy of
Sciences, Warsaw 00-142, Poland.
5
Institute of Physics, University of Silesia, Chorzow 41-500, Poland.
Correspondence and requests for materials should be addressed to M.M.S. (email: mos@bio.aau.dk).
1
Supplementary Table S1. Pressure history dependence of interatomic distances. Data are predicted by
the MD simulations for the glasses subjected to pressure-quenching from different pressures (P).
P (GPa)
0
0.5
1.0
1.5
2.0
2.5
Si-O
1.635
1.635
1.635
1.635
1.635
1.635
Al-O
1.765
1.765
1.765
1.755
1.775
1.775
Interatomic distance (Å)
Ca-O
Si-Si
Si-Al
Al-Al
2.325 3.195 3.205
3.115
2.325 3.225 3.145
3.075
2.315 3.215 3.105
3.035
2.325 3.215 3.295
3.035
2.315 3.205 3.195
3.195
2.325 3.215 3.165
3.015
2
Ca-Ca
3.325
3.365
3.325
3.295
3.415
3.455
O-O
2.655
2.655
2.655
2.665
2.645
2.655
Supplementary Table S2. Thermal history dependence of interatomic distances. Data are predicted by
the MD simulations for the glasses subjected to annealing for different durations (ta).
ta (ps)
0
1
10
1000
Si-O
1.635
1.635
1.635
1.635
Al-O
1.765
1.765
1.765
1.765
Interatomic distance (Å)
Ca-O
Si-Si
Si-Al
Al-Al
2.325 3.195 3.205
3.115
2.325 3.195 3.115
3.035
2.315 3.155 3.105
3.145
2.325 3.215 3.205
3.225
3
Ca-Ca
3.325
3.275
3.415
3.465
O-O
2.655
2.645
2.645
2.655
Supplementary Figure S1. O–Si–O bond angle distribution. Dependence of the standard deviation (σθ) of
the intra-tetrahedral O–Si–O bond angle distribution on density (ρ) for both annealing and pressurequenching as predicted by MD simulations. Inset: dependence of the average value of the O–Si–O bond
angle on ρ for both annealing and pressure-quenching.
7.5
7.0
109.5
Angle (o)
Standard deviation  (o)
8.0
O-Si-O
109.4
109.3
109.2
2.60
2.65
2.70
2.75
 (g/cm3)
6.5
6.0
5.5
Annealing
Pressure-quenching
2.60
2.65
2.70
 (g/cm )
3
4
2.75
Supplementary Figure S2. Schematic illustration of bond constraints. (a) Intact and (b) broken bondbending (BB) and bond-stretching (BS) constraints as generated by molecular dynamics from atomic
trajectories. Small radial and angular excursions correspond to intact BS and BB constraints (a), while large
radial and angular excursions correspond to broken BS and BB constraints (b).
5
Supplementary Figure S3. O–Al–O bond angle distribution. Dependence of the standard deviation (σθ) of
the intra-tetrahedral O–Al–O bond angle distribution on density (ρ) for both annealing and pressurequenching as predicted by MD simulations. Inset: dependence of the average value of the O–Al–O bond
angle on ρ for both annealing and pressure-quenching.
15
14
Angle (o)
Standard deviation  (o)
109.1
O-Al-O
109.0
108.9
108.8
108.7
2.60
2.65
2.70
2.75
 (g/cm3)
13
12
Annealing
Pressure-quenching
2.60
2.65
2.70
 (g/cm )
3
6
2.75
Supplementary Figure S4. Al–O–Al bond angle distribution. Dependence of the standard deviation (σθ)
of the inter-tetrahedral Al–O–Al bond angle distribution on density (ρ) for both annealing and pressurequenching as predicted by MD simulations. Inset: dependence of the average value of the Al–O–Al bond
angle on ρ for both annealing and pressure-quenching.
Annealing
Pressure-quenching
Al-O-Al
20
128
127
18
Angle (o)
Standard deviation  (o)
22
126
125
124
123
2.60
2.65
2.70
2.75
 (g/cm3)
16
2.60
2.65
2.70
 (g/cm )
3
7
2.75
Supplementary Figure S5. Si–O–Al bond angle distribution. Dependence of the standard deviation (σθ) of
the inter-tetrahedral Si–O–Al bond angle distribution on density (ρ) for both annealing and pressurequenching as predicted by MD simulations. Inset: dependence of the average value of the Si–O–Al bond
angle on ρ for both annealing and pressure-quenching.
Annealing
Pressure-quenching
Si-O-Al
16.5
16.0
15.5
140
Angle (o)
Standard deviation  (o)
17.0
139
138
137
136
2.60
2.65
2.70
2.75
 (g/cm3)
15.0
2.60
2.65
2.70
 (g/cm )
3
8
2.75