Calorimetric Glass Transition Yuanzheng Yue Wuhan University of Technology, China Aalborg University, Denmark Joint ICTP-IAEA Workshop, Trieste, Italy, Nov. 6-10, 2017
Outline • Background and motivation • Case 1: Borosilicate and phosphate glasses – Dulong Petit Law The C p m relation – – Pressure effect on fictive temperature Structural source of the C p change – – Prediction of T g by topological model • Case 2: Hyperquenched (HQ) glasses – Relaxation in multi-component oxide systems – Relaxation in metallic glasses – T g of SiO 2 – Relaxation in HQ strong glass formers (SiO 2 and GeO 2 ) • 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
Outline • Background and motivation • Case 1: Borosilicate and phosphate glasses – Dulong Petit Law The C p m relation – – Pressure effect on fictive temperature Structural source of the C p change – – Prediction of T g by topological model • Case 2: Hyperquenched (HQ) glasses – Relaxation in multi-component oxide systems – Relaxation in metallic glasses – T g of SiO 2 – Relaxation in HQ strong glass formers (SiO 2 and GeO 2 ) • 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
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.
Calorimetric glass transition is reflected by a sudden change in heat capacity 1.8 q h = q c =10 K/min 1.6 C p (Jg -1 K -1 ) upscan 1.4 downscan 1.2 T g 1.0 0.8 400 500 600 700 800 900 C p = (d H /d T ) p C v T (K) • Glass transition temperature ( T g ) is a dynamic temperature, measured as the onset temperature of glass-liquid transition. • Melting temperature ( T m ) is a thermodynamic temperature.
Key values for glass transition: Heat capacity ( C pg ) and its jump at T g ( C p ) for a normally cooled glass 1.8 q h = q c =10 K/min 1.6 -1 ) C pl -1 K C p (PO 3 ) 2 glass 1.4 C p (Jg C p d 1.2 C pg T g 1.0 0.8 400 500 600 700 800 900 T (K)
Heat capacity for a hyperquenched glass (rockwool glass at ~10 6 K/s) The hatched area: 1.6 energy released from 1g fiber T g 1.4 C p (Jg -1 K -1 ) 1.2 upscan 2 1.0 64 J/g upscan 1 0.8 T c 0.6 400 600 800 1000 T (K)
Determination of the glass transition ( T g ) and the fictive temperatures ( T f ) 1.8 T g =941 K T f =1141 K T f =1141 K T g =941 K = 1.6 C pl C p (Jg -1 K -1 ) 1.4 A B = B 1.2 C pg C p2 1.0 A C p1 0.8 900 950 1000 1050 1100 1150 400 600 800 1000 1200 T (K) T (K) T T eq f Basic equation: ( C C ) dT ( C C ) dT p 2 p 1 pl pg T T c g C pg = a + bT + c / T 2 + d / T 0.5 Y. Z. Yue, et al., Chem. Phys. Lett. 2002; J. Chem. Phys. 2004
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
Outline • Background and motivation • Case 1: Borosilicate and phosphate glasses – Dulong Petit Law The C p m relation – – Pressure effect on fictive temperature Structural source of the C p change – – Prediction of T g by topological model • Case 2: Hyperquenched (HQ) glasses – Relaxation in multi-component oxide systems – Relaxation in metallic glasses – T g of SiO 2 – Relaxation in HQ strong glass formers (SiO 2 and GeO 2 ) • 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
Dulong Petit Law applies when the unit of Cp is converted to J/mol of atoms? 45 *Jouls per mole of atoms, not per mole of molecules 25 C pg at T g (Jmol -1 K -1 )* 40 24 35 C p (J mol -1 K -1 )* 23 30 0 20 40 60 80 B 2 O 3 (mol%) 25 3 R 20 Dulong Petit Law B 2 O 3 increases 15 works at T g 400 500 600 700 800 900 T (K)
C p ≈3 R law works for oxide glasses at T g 50 borosilicate 45 basaltic 40 Diopsite NaPoLi C p (J mol -1 K -1 )* 35 CMP 35Al 2 O 3 65SiO 2 30 SiO 2 3 R 25 20 *Jouls per mole of atoms 15 400 600 800 1000 1200 1400 1600 T (K)
C p as a function of composition 170 60 1.6 175 75B C pl 63B-12Si 150 51B-24Si 50 1.5 140 125 37B-37Si C p (J mol -1 K -1 ) -1 ) 24B-51Si C pg 100 -1 K C p,l / C p,g (-) 12B-63Si 40 T g 6B-69Si 75 C p (J mol 400 450 500 550 600 110 1.4 75Si 30 Experiment ( C p ) 80 1.3 20 Model ( C p ) Experiment ( C p,l / C p,g ) 10 1.2 50 100 200 300 400 500 600 0 20 40 60 80 o C) T ( [B 2 O 3 ] (mol%) Configurational heat capacity ( C p ) increases with increasing the B 2 O 3 /SiO 2 Smedskjaer et al. J. Phys. Chem. B. 115 (2011) 12930
Relation between C p and kinetic fragility 60 50 C p (J mol -1 K -1 ) 40 30 20 10 0 20 30 40 50 60 m (-) 0 A m C ( 1 ) p T m g Implication : There is a link between C p to the kinetic fragility for the same series of glasses.
The network connectivity increases with increasing B 2 O 3 , but the fragility increases. 0.8 60 1.6 0.6 50 1.5 C p (J mol -1 K -1 ) C p,l / C p,g (-) 40 0.4 NBO/T 1.4 30 0.2 Experiment ( C p ) 1.3 20 Model ( C p ) 0.0 Experiment ( C p,l / C p,g ) 10 1.2 0 20 40 60 80 0 20 40 60 80 [B 2 O 3 ] (mol%) B 2 O 3 (mol%) Implication : The network connectivity is not the main controlling factor for liquid fragility.
Raman on 75 q B 2 O 3 - 75(1- q ) SiO 2 - 15Na 2 O - 10CaO q = [B 2 O 3 ]/([B 2 O 3 ]+[SiO 2 ]) B 3 -O- IRO SiO 4 Relative Intensity (A.U.) q =1.0 B 2 O 3 mol% increase q =0.08 400 600 800 1000 1200 1400 1600 -1 ) Wavenumber (cm The IRO band is greatly enhanced by increasing B 2 O 3 content
Link between C p,conf and IRO units 56 50 52 -1 ) -1 K 40 fragility m 48 C p,conf (J mol 30 44 40 20 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Total Area of IRO bands Total Area of IRO Bands IRO units increase C p,conf and m The content of IRO units has a dominant contribution to the evolution of C p,conf with composition in borate-silicate glasses. H. Liu, et al., PCCP , 18 (2016) 10887
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 Se Se Se Se Se Se Ge Ge Ge Ge Ge Ge Ge Ge Gupta & Mauro: Temperature dependent constraint theory • (a) (a) • network constraints vs. composition Ge Ge Ge Ge Predicting glass properties, e.g .,T g , m , H v Se Se Se Se (b) (b) Phillips & Thorpe, Sol .State Commun . (1985) Gupta & Mauro, J. Chem. Phys. (2009)
Type and counting of Constraints • type : B-O and M NB -O linear constraints Two constraints at each oxygen • Β type : O-B-O angular constraints − Five β constraints at each Q 4 unit. − Three at each Q 3 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
Ranking of Constraints T T T T g Each type of constraint has its onset temperatures, which is the temperature where constraints become rigid as temperature is lowered. Atomic degrees of freedom 3 T > T B-O NB -O M T < T < T 2 - O - O + Na + Na Cooling T < T < T + Na - 1 O B O O T g < T < T 0 O T < T g B B 0 10 20 30 40 [Na 2 O] (mol%)
Predicting T g by using temperature dependent constraint theory Good prediction, but challenge for complex systems Smedskjaer, Mauro, Sen, Yue, Chem. Mater . 22 (2010) 5358 Smedskjaer, Mauro, Youngman, Hogue, Potuzak, Yue, J. Phys. Chem. B 115 (2011) 12930.
Pressure induced enhancement of the C p overshoot for CaP 2 O 6 glass 220 P (MPa) 200 a: 500 a 200 1st DSC upscan after b: 300 c: 200 500 MPa compression b 180 d: 100 c 180 C p (Jmol -1 K -1 ) -1 ) e: 20 d 160 -1 K 0.1 e C p (Jmol 2nd DSC upscan 160 140 120 140 100 120 80 780 790 800 810 820 830 500 600 700 800 900 T (K) T (K) Why? Pressure drives glass deep in the potential energy landscape. When being heated, glass absorb energy from the surrounding, and hence enhances C p ’.
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