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1 SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor INTERNATIONAL of Raman Spetrosop SCHOOL - Fernando Rull & Valentín Garía Baona 4 th to 6 th JUNE, NANCY (FRANCE) RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE Theor of Raman Spetrosop Fernando Rull & Valentín Garía Baona
2 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona MOLECULAR SYMMETRY CLASSIFICATION (POINT GROUP)
3 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona CHARACTER TABLES Point Group Smmetr Operations Order C v (h) = 4 ( E, C, σ v, σ v ) C V E C σ v () σ v () A A - - B - - B - - Classes Charater: χ Irreduible Representation for B Irreduible Representation (Γ i ) In vibrational spetrosop we are ver onerned with the smmetr of eah normal mode of vibration in a moleule. Eah normal mode of vibration will (behaves like) form a basis for an irreduible representation of the point group of the moleule. The transformation of all the atomi displaements (oordinates) will result in what we shall all a Reduible Representation, whih should be epressed as a sum of Irreduible Representations (Smmetr Modes)
4 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona CHARACTER TABLES C V E C σ v () σ v () A,, A - - R B - -, R B - -, R Simmetr of Funtions
5 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona C v orbital p E C σ v () σ v () C V E C σ v () σ v () A,, A - - R B - -, R B - -, R orbital p E σ v () C σ v ()
6 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona C v R n E C σ v () σ v () C V E C σ v () σ v () A,, A - - R B - -, R B - -, R
7 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona C v d XY E C σ v () σ v () C V E C σ v () σ v () A,, A - - R B - -, R B - -, R
8 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona MOLECULAR VIBRATIONS Γ = A +E+T +T Γ VIB = A +E+T ν (A ) ν (E) 46 m - 8 m - ν (T ) ν 4 (T ) 76 m - 4 m -
9 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona MOLECULAR VIBRATIONS AND POLARIZABILITY Γ = A +E+T +T Γ VIB = A +E+T POLARIZED LIGHT SAMPLE ν (A ) ν (E) ρ = I I II 46 m - 8 m - ν (T ) ν 4 (T ) 76 m - 4 m - Wavenumber (m - ) Wavenumber (m - )
10 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona ISOTOPIC CONTRIBUTIONS CCl 5 Cl 7 CCl 5 4 CCl 5 Cl 7 ν (A ) 46 m -
11 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona CRYSTAL VIBRATIONS AND POLARIZABILITY POLARIZED LIGHT SAMPLE Celestine (SrSO 4 ) Vibrations of SO 4 - group -Smmetr group in the free state T d (4m) -Smmetr domain group C s (m) -Crstallographi fator group D h (mmm)
12 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona CRYSTAL VIBRATIONS AND POLARIZABILITY POLARIZED LIGHT SAMPLE Celestine (SrSO 4 ) Vibrations of SO 4 - group -Smmetr group in the free state T d (4m) -Smmetr domain group C s (m) -Crstallographi fator group D h (mmm)
13 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona SYMMETRY IN CRYSTALS
14 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona CRYSTAL VIBRATIONS AND RAMAN ACTIVITY Celestine (SrSO 4 ) Vibrations of SO 4 - group T d (4m) C s (m) D h (mmm)
15 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona CRYSTAL VIBRATIONS AND RAMAN ACTIVITY Celestine (SrSO 4 )
16 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona CRYSTAL VIBRATIONS AND RAMAN ACTIVITY Celestine (SrSO 4 )
17 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona CRYSTAL VIBRATIONS AND RAMAN ACTIVITY Celestine (SrSO 4 )
18 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona PHONONS IN DIAMOND: SIZE EFFECTS Phonon onfinement
19 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona PHONONS IN DIAMOND: PRESSURE AND TEMPERATURE EFFECTS Harmoni Energ = Kr K : fore onstant ω = π K µ µ : redued mass 4 Diamond ω (m - ) 9 This work: Anastassakis et al. Borer Cui et al. Herhen and Cappelli: Zoubolis and Grimsdith: Liu et al. 8 Intrinsi ontribution This work: Zoubolis and Grimsdith: T (K)
20 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona GRÜNEISEN PARAMETERS AND DAVIDOV SPLITTINGS γ j V = ν j ν j V T lnν j = lnv T γ j = B ν T j ν j p T = B T lnν j p T B T p = V V T Elementar vibrational model for Moleular Crstals Internal Modes (HIGH Frequen) Free Moleule ν(m - ) Moleular Solid Eternal Modes (LOW Frequen) Davdov Splittings ν(m - ) Moleular Solid at High Pressure ν(m - ) Chattopadha et al. (PRB, 98)
21 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona FERMI RESONANCE Two level Perturbation Model CO δ = ν + ν R= I + / I - W: Fermi Coupling Parameter W = δ (R) / / (R+) δ = [δ -4W ] / ν + = ν + /[δδ ] ν = ν +/[δδ ] Eat Degeneration: R = ( δ + δ) ( δ δ) / / R R / / + ( δ δ ) ( δ + δ ) / / δ is ero δ is minimum R =
22 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona FERMI RESONANCE
23 Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) C C B B A A F F C C B B A A F F C C B B A A F F C C B B A A F F = Φ = Φ = Φ = Φ ) ( ) ( ) ( ) ( = E E W W W W E E W W W W E E W W W W E E C BC AC FC BC B AB FB AC AB A FA FC FB FA F 8 9 ν OV ν OV ν AS (CH ) FR(ν ) FR(ν + ) Intensit (arb. units) P (GPa) RP Raman Shift (m - ) FERMI RESONANCE
24 SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor INTERNATIONAL of Raman Spetrosop SCHOOL - Fernando Rull & Valentín Garía Baona 4 th to 6 th JUNE, NANCY (FRANCE) RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE Theor of Raman Spetrosop Fernando Rull & Valentín Garía Baona
25 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona NORMAL MODES IN WATER MOLECULE Q Q Q
26 Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) C v E C σ σ A,, A - - R B - -, R B - -, R = = = = E, χ(e)=9 C, χ(c )=- σ v, χ(σ v ) = σ 'v, χ(σ 'v ) = Γ red = (9)E + (-)C + ()σ v + ()σ v Γ red = A + A + B + B
27 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona Γ tran = A + B + B R R Γ rot = A + B + B R Γ red = (9)E + (-)C + ()σ v + ()σ v Γ red = A + A + B + B Γ Vib = A + B C v E C σ σ A,, A - - R B - -, R B - -, R
28 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona Γ tran = A + B + B R R Γ rot = A + B + B R Γ red = (9)E + (-)C + ()σ v + ()σ v Γ red = A + A + B + B Γ Vib = A + B
29 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona RAMAN ACTIVITY C V E C σ v () σ v () A,, A - - R B - -, R B - -, R Γ Vib = A + B Simmetr of Funtions Ψ α i uv Ψ
30 INTERNATIONAL SCHOOL -RAMAN SPECTROSCOPY APPLIED TO EARTH SCIENCES AND CULTURAL HERITAGE4 th to 6 th JUNE, NANCY (FRANCE) Theor of Raman Spetrosop - Fernando Rull & Valentín Garía Baona PROPIEDADES DE SÓLIDOS CRISTALINOS: INTERPRETACIÓN RAMAN ACTIVITY IN CRISTALS
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