VETRO  0 <  C SINTESI DI UN VETRO DAL CORRISPONDENTE CRISTALLO CRISTALLO  =  C Fusione con successivo super-raffreddamento e conseguente.

Presentazione sul tema: "VETRO  0 <  C SINTESI DI UN VETRO DAL CORRISPONDENTE CRISTALLO CRISTALLO  =  C Fusione con successivo super-raffreddamento e conseguente."— Transcript della presentazione:

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7 VETRO  0 <  C SINTESI DI UN VETRO DAL CORRISPONDENTE CRISTALLO CRISTALLO  =  C Fusione con successivo super-raffreddamento e conseguente risolidificazione

8 DIAGRAMMA DI FASE DI UN LIQUIDO GLASS-FORMING Poiché il volume del vetro è maggiore di quello del corrispettivo cristallo gli atomi costituenti il vetro avranno un maggior numero di gradi di libertà da cui l’eccesso di stati vibrazionali di bassa energia.

9 Fragilità dei Liquidi Glass-forming (C. A. Angell, JNCS 1985, Science 1995; De Benedetti and Stillinger, Nature 2001) La fragilità di un liquido glass-forming misura la degradazione termica della struttura vetrosa nella regione di transizione vetrosa, considerando lo scostamento da un comportamento Arrheniano della viscosità. Andamento della viscosità di shear o del tempo di rilassamento strutturale  s ( η=G ∞  s ) al variare della temperatura nella regione T ≥ T g : Differentemente dai sistemi “fragile”, i liquidi “strong” preservano l’ordine strutturale a medio range nel passaggio liquido ↔ solido.

10 Elevati valori di m (  100) individuano i deboli liquidi molecolari semplici (CKN, OTP), mentre piccoli valori di m (  20-30) corrispondono ai liquidi caratterizzati da forti legami covalenti (SiO 2, GeO 2, BeF 2 ).

11 Stretta relazione tra le proprietà di trasporto e le proprietà termodinamiche dei liquidi glass- forming : I liquidi “fragile” esibiscono un elevato salto,  C p (=C p,l -C p,g ), nella capacità termica alla T g, contrapposto ad una ridotta variazione  C p esibita dai liquidi “strong”.

12 Correlation between fragility and the ratio of longitudinal and transversal sound velocities in glassy state (Novikov and Sokolov, Nature 2004)

13 Correlation between fragility and anharmonicity in glassy state (Carini et al JPC 2000, PRB 2005, JPC 2006)

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15 Conducibilità termica a basse T in un vetro Se-Te e nel corrispondente cristallo (Rosenberg and Carini, 1990)

16 ATTENUAZIONE ACUSTICA NEI VETRI a) Attenuazione acustica in quarzo (SiO 2 ) vetroso a 930 MHz b) Attenuazione acustica in quarzo vetroso a 507 MHz c) Attenuazione acustica in quarzo cristallino a 1 GHz

17 Dynamics of Strong and Fragile Glass-Formers: Correlation between Fragility and Low Temperature Properties (Sokolov et al PRL 1993)

18 ULTRASONIC ATTENUATION AND SOUND VELOCITY IN BORATE GLASSES: DEPENDENCE ON THE CATIONIC FIELD STRENGTH (M 2 O) 0.14 (B 2 O 3 ) 0.86

19 (ADWP) ASYMMETRIC DOUBLE WELL POTENTIAL MODEL (Gilroy and Phillips, Phil. Mag 1984; Hunklinger et al, PRB 1995) The application of an asymmetric double-well potential model allows for a quite coherent linking between high temperature classical relaxation processes and low temperature quantum effects observed in the acoustic behaviours of these borate glasses. T < 20 K T > 20 K

20 Dynamics of two-level tunneling systems in glasses: Coherent and incoherent tunneling (T< 20 K)

21 Classical Thermal Activation in glasses (T > 20 K)

22 CLASSICAL ACTIVATION: COMPARISON BETWEEN THE EXPERIMENTAL DATA AND THE ADWP THEORETICAL FIT

23 SPECTRAL DENSITIES OF TLSs AND ASYMMETRIES vs CATION FIELD STRENGTH At variance with the tunnelling strength C, the relaxation strength C* decreases with decreasing cation size also exhibiting values which are more than one order of magnitude larger than those of C.

24 SPECTRAL DENSITIES OF TLSs AND ASYMMETRIES vs INCREASING CONCENTRATION OF METAL OXIDE At variance with the tunnelling strength C, the relaxation strength C* decreases with increasing metal oxide concentration also exhibiting values which are more than one order of magnitude larger than those of C.

25 0.019512.6819.19.552702186196135782484(Cs 2 O) 0.14 (B 2 O 3 ) 0.86 0.01710.5322.5811.063312567230142282088(K 2 O) 0.14 (B 2 O 3 ) 0.86 0.0146.530.5916.83427317228515060.32071(Li 2 O) 0.14 (B 2 O 3 ) 0.86 0.02615.112.266.4426720841871.53367.41838B 2 O 3 (our data) ll  th,298 (10 -6 K -1 ) B (GPa) G (GPa)  D (K) v D (m s -1 ) v t (m s -1 ) v l (m s -1 )  (kg m -3 ) Samples The different magnitude of C and C* leads to the conclusion that only a small fraction of the relaxing particles are involved in tunneling local motions. 3.33.381.86.376503.440.633.56.61 (Li 2 O) 0.14 (B 2 O 3 ) 0.86 7.25.604.115.06852.240.551.743.74 (K 2 O) 0.14 (B 2 O 3 ) 0.86 9.15.172.216.27281.760.471.03.79 (Cs 2 O) 0.14 (B 2 O 3 ) 0.86 15.3 1.73 1.08.287254.5 a 0.21 a 0.52 a 2.4 a B2O3B2O3 f 0 (10 46 J -1 m -3 ) (10 8 J m -3 ) (10 13 s -1 ) C l * x 10 3 V 0 /k B (K) (10 45 J -1 m -3 )  l (eV) (10 7 J m -3 ) C l x 10 4 Samples G =  B =  - G

26 SOUND VELOCITY IN BORATE GLASSES: CLASSICAL ACTIVATION AND VIBRATIONAL ANHARMONICITY Classical activation also regulates the sound velocity between 20 and 120 K, whereas the vibrational anharmonicity results to be the dominant mechanism for higher temperatures.

27 DEPENDENCES ON THE CATION FIELD STRENGTH OF COMPRESSIBILITY, LINEAR THERMAL EXPANSION COEFFICIENT  th, SPECTRAL DENSITY OF ASYMMETRY f 0, AND ANHARMONICITY COEFFICIENT  I B =  - G G =  Compressibility = 1/B The anharmonicity of the glassy network decreases with increasing field strength of the modifier ion, in close correlation with the parallel reduction of the local molecular mobility.

28 Hypersonic and Ultrasonic Attenuation

29 Arrhenius plot T peak,hyper WELL FIT THE ARRHENIUS PLOTS DETERMINED BY T peak,ultra

30 Hypersonic vs Ultrasonic THE HYPERSONIC ATTENUATION EVALUATED BY THE ULTRASONIC RELAXATION PROCESS IS MARKEDLY SMALLER THAN THE EXPERIMENTAL OBSERVATION. Akhiezer mechanism: “phonon viscosity”

31 The fragility of glass-forming liquids scales with the average global anharmonicity of their glassy state. The spectral density of relaxing defects decreases with increasing cation field strength and is more than one order of magnitude larger than the spectral density of tunnelling states. The anharmonicity of the glassy network decreases with increasing field strength of the modifier ion, in close correlation with the parallel reduction of the local molecular mobility. Tunnelling TLS’s confirm their universal character, as inherent to the glassy state: they cause an internal friction which lies in the range between 10 -4 and 10 -3, independent of structural changes and of bond strengths characterizing the glassy network. The hypersonic attenuation arises from the contributions of classical relaxation processes and of anharmonic interactions of phonons (Akhiezer mechanism or “phonon viscosity”). CONCLUSIONS