Spectroscopie vibrationnelle applique la dtermination de la - PowerPoint PPT Presentation

Spectroscopie vibrationnelle appliquée à la détermination de la structure locale des verres silicatés B. Hehlen 1,2 1 Laboratoire Charles Coulomb (L2C), University Montpellier II, France. 2 CNRS, UMR5221, Montpellier, France.

Outline I- Vibrational spectroscopies - Infrared, Raman and hyper-Raman scattering - Nature of the vibrations in the glass formers SiO 2 and B 2 O 3 Atomic displacements, polar or not polar,… → Quantitative description of the structural modifications in binary and ternary glasses II- Hyper-Raman scattering: Coherent vs incoherent excitations III- Si-O-Si angle distribution in silicates and borosilicates IV- Signature of network modifier cations in the Raman spectra of aluminosilicate glasses

Vibrational spectroscopies { ) } ( ) ( ( , ) , 0 , 0 ω ∝ I q TF P r t P Scattered intensity: Hyper-Raman Raman • Polarization : Induced polarization ω i ω ω ω ω ω ω ω d ω ω ω ω d ω ω i ω ω Dipole Polarizability Hyper-Polarizability moment P T (r,t) = µ µ µ (r,t) + α µ α ( r ,t) E i α α + β β β ( r ,t) E i E i + ... β ω i ω ω ω ω ω ω v ω ω ω v ω ω ω ω ω ω ω ω ω v ω v Raman Raman Hyper-Raman Hyper-Raman Infrared Infrared (RS) (HRS) (IR) Different selection rules in IR, RS, and HRS Only polar modes in IR Polar and non-polar excitations in RS and HRS Their exist excitations active in HRS not active in RS, and vice versa ⇒ ⇒ HRS complements IR and Raman techniques ⇒ ⇒

Le spectromètre Hyper-Raman I 6 10 − ≈ → Nécessité d’un spectromètre très lumineux !! → → → HRS I RS CCD Diffractomètre Diffractomètre Diffractomètre : Laser pulsé ns - Haute résolution ( ∼ 2cm -1 ) - Haute luminosité Y CCD : A -Très Sensible + faible bruit G Polariseur Polariseur - Spectres VV et VH CCD λ λ λ λ =1064 nm Atténuateur Microscope confocal λ λ ≅ λ λ ≅ ≅ ≅ 532 nm - Résolution spatiale qqes µ m Polariseur Doubleur de fréquence échantillon µ scope µ µ µ Doubleur de fréquence → → Spectromètre Raman très lumineux → → Hyper-Raman Raman

v- SiO 2 : Vibrational spectroscopy Only Polar modes Polar modes + BP Polar modes (but not TO4!) + BP Selection rules partly apply !!

The vibrations of v -SiO 2 Stretching of Ring modes R-band Raman 1500 SiO 4 tetrahedra D 1 [Galeener et al. 70’s-80’s] n [Pasquarello et al. PRL2003] 1000 D 2 I RS ( ω ) n F1 F2s F2b F2s F2b F1 500 [Taraskin et al. PRB 1997] 0 Hyper-Raman Hyper-Raman 0 0 1000 1000 500 500 Frequency (cm -1 ) -1 Rocking Si-O-Si Libration of rigid SiO 4 tetrahedra [Kirk JPC1988] [Hehlen et al. Motions of rigid Deformation of Deformation of PRL 2000] SiO 4 tetrahedra Si-O-Si units SiO 4 tetrahedra Weak bonds Weak bonds Hard bonds Hard bonds

– II – Hyper-Raman spectroscopy in v -SiO 2 : Localized vs delocalized excitations [B.Hehlen and G. Simon, JRS2012]

Hyper-Raman scattering 2 d order polarization fluctuation: β = β Av + β Loc In glasses [Denisov et al. Phys. Rep. 1987] Fluctuations from Local fluctuations the average media • β β Loc in liquids and gases β β T d - Depends on the symmetry (point group) of the molecular units - Isotropic averaging over all orientation → Incoherent D 3h → Scattering is independent on the wave vector q (intensity and depolarization ratio ρ ρ ρ ρ =I VH /I VV )

HRS selection rules for β β β β • β β Av : Isotropic average media → → ( ∞∞ ∞∞ m) symmetry group β β → → ∞∞ ∞∞ No LOs Only LOs ⇒ The scattering depends on q, intensities and depolarization ratios !! - LOs owing to their coupling with the long range electric field - Strongly delocalized vibrations • β β β β in glasses: A complicated mixture of β β β β Av and β β β β Loc

q-dependence of the HRS spectra I ρ = VH Depolarization ratio I VV [B.Hehlen and G. Simon, JRS2012] � TO4-LO4 : k S q k i ρ and I HRS depend on q → → HRS efficiencies controled by β → → β β β Av ? q q k k S k i k � HRS Boson peak : k S 0 . 63 0 . 1 ρ = ± k i BP whatever the scattering geometry !!! q → HRS efficiency controled by β β β Loc β

O HRS efficiencies of the (TO-LO) 4 doublet Si • LO4 : fullfil the ( ∞∞ ∞∞ m) average media selection rules ∞∞ ∞∞ Si → Collective motions du to the coupling with the macroscopic E-field • TO4 : intermediate between ( ∞∞ ∞∞ m) and local selection rules ∞∞ ∞∞ ( ∞∞ m) Expe. → β = β Loc + β Av 180 180 ° ° I I 9 5.9 VV VH → Delocalized excitation !! 90 ° 90 ° ∼ 10 ∼ 10 I I I I 18 18 VV VH [M. Wilson et al. PRL 1996] 90 ° 180 ° I I ∼ 5.4 9 VV VH Density fluctuations in v -SiO 2 [A.M. Levelut and A. Guinier, ∆ρ / ρ ≅ 1.2% in a volume of ∼ (2 nm) 3 → ∼ 235 SiO 2 units Bull. Soc. Fr. Miné. Crist. 1967] → Up to ∼ ∼ ∼ ∼ 100 Si-O-Si units could be involved !! …

The Boson Peak • The HRS Boson Peak • Scattering independent on q • Constant depolarization ratio ρ = I VH /I VV = 0.63 → Local or quasi-local excitations Librations of rigid SiO 4 tetrahedra [B. Hehlen etal., PRL 2000] • Importance of librations at low-frequency in v-SiO 2 - Soft mode of the α - β transition of α -quartz - Soft mode of the α - β transition of α -quartz [Y. Tezuka et al. , PRL 1991] [Y. Tezuka et al. , PRL 1991] - Its frequency extrapolate to that of the glass at Tg [B. Hehlen et al., JNCS 2002] - Supported by numerical simulations [B. Guillot et al., PRL1997] - They participate to the total excess of low- ω vibrations [U. Buchenau et al. , PRL 1984] [K. Trachenko et al. , PRL 1998] - Compatible with the Rigid Units Model (RUM) Boson Peak (excess of Cp/T 3 at low-T) : Rigid librations + Translations

– III – -O- bond angle of silicates extracted from their Raman spectra [B.Hehlen, JPCM2010] 1500 1500 D 1 R 1000 I RS ( ω ) 500 D 2 Bending Bending Si-O-Si Si-O-Si 0 0 500 1000 Frequency (cm -1 )

Raman is highly sensitivity to local structural modifications and very simple to operate but,… it hardly provides quantitative estimates !! One example : Bending modes R, D1, D2 What has to be known : → Si-O-Si angle θ θ C( ω ) ∝ ω 2 Coupling to light coefficient C( ω ) 1 2 2 Coherent or incoherent scattering Coherent or incoherent scattering No No 3 Relation between the frequency or/and cos ( θ /2) = 7.33 10 -4 ω intensity and the structural property 4 Effect of the surrounding on points 1-3 No - After normalization by C( ω ), the frequency of the R, D1 and D2 bands relates to the Si-O-Si angle through 3 - The transformation is however an approximation du to the unknowns 2 and 4

Raman Scattering in permanently densified silicas, d -SiO 2 O Si • Permanent densification θ - Reduction of the Si-O-Si angle θ in the network Si - SiO 4 tetrahedra remain unchanged [Y.Inamura et al. JNCS 2001] → → → → Puckering of the ring network + bond redistribution θ • Density of states of bending modes Raman Intensity O ( ) ( ) Si RS ω 1 I ω ω ∝ g B 3 ρω ω ( ω ) [n( ω ) + 1 ] C Si i s B Glass density Coupling function For those C B ( ω ) ∝ ω 2 [B.Hehlen, JPCM2010] ( ) ( ) Boson Boson RS ω 1 I peak peak ω ∝ g B 3 [n( ) 1 ] ρω ω ω ⋅ ω + i s

Raman is highly sensitivity to local structural modifications and very simple to operate, but… it hardly provides quantitative estimates !! One example : Bending modes R, D1, D2 What has to be known : → Si-O-Si angle θ θ C( ω ) ∝ ω 2 Coupling to light coefficient C( ω ) 1 ⇒ ∼ ⇒ ∼ VDOS g( ω ∼ ∼ ω ω ω ) ⇒ ⇒ 2 2 Coherent or incoherent scattering Coherent or incoherent scattering No No 3 Relation between the frequency or/and cos ( θ /2) = 7.33 10 -4 ω intensity and the structural property 4 Effect of the surrounding on points 1-3 No - After normalization by C( ω ), the frequency of the R, D1 and D2 bands relates to the Si-O-Si angle through 3 - The transformation is however an approximation du to the unknowns 2 and 4

Si-O-Si angle θ θ in d -SiO 2 θ θ θ Small rings : θ [B. Hehlen, J.Phys.: Cond Matter 2010] n = 3 n = 4 θ Network angle : n n ≅ n ≅ ≅ ≅ 6 ≅ ≅ ≅ ≅ 6 Max. of the distribution Max. of the distribution R-band Average angle n > 6

Si-O-Si angle θ θ in d -SiO 2 θ θ θ Small rings : θ [B. Hehlen, J.Phys.: Cond Matter 2010] n = 3 n = 4 θ Network angle : n n ≅ n ≅ ≅ 6 ≅ ≅ ≅ 6 ≅ ≅ Max. of the distribution Max. of the distribution R-band RMN RMN RMN (Devine et al. 1987) (Devine et al. 1987) (Devine et al. 1987) Average angle n > 6

Si-O-Si angle θ θ in d -SiO 2 θ θ θ Small rings : θ [B. Hehlen, J.Phys.: Cond Matter 2010] n = 3 n = 4 θ Network angle : n n ≅ n ≅ ≅ ≅ ≅ ≅ 6 ≅ 6 ≅ Max. of the distribution Max. of the distribution R-band RMN (Devine et al. 1987) Average angle n > 6 Simulations [Rahmani et al. PRB,2003] [ Matsubara , Ispas, Kob, 2009]