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Raman Spectrum

Raman Spectrum. chi-ruei huang (2009). Fundamentally build up by Yung-Chang Lin (26 Dec, 2008) . outline. Review the history of Raman Molecular spectrum. Vibrations and Rotations. Scattering and Raman effect. Stokes and Anti-Stokes line. Molecular symmetry and Group theory.

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Raman Spectrum

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  1. Raman Spectrum chi-ruei huang(2009) Fundamentally build up by Yung-Chang Lin (26 Dec, 2008)

  2. outline • Review the history of Raman • Molecular spectrum. • Vibrations and Rotations. • Scattering and Raman effect. • Stokes and Anti-Stokes line. • Molecular symmetry and Group theory. • Carbon system. • Raman spectroscopy of graphite, graphene, and carbon nanotubes. • Reference. Additional: instrument

  3. Review the history of Raman spectrum • C. V. Raman who discovered the scattering of photon got the Nobel prize in 1930. • This scattering was named by Raman scattering. C. V. Raman http://science.scu.edu.tw/phy/M301/doc/Nb-1930%27.doc

  4. Raman spectrum Incident light (EM wave) Molecular (Symmetry & Group theory) Molecular Vibration or Rotation Phonon dispersion Raman scattering spectrum

  5. Molecular vibrations and rotations M2 x2 M1 Energies of rotation: • Selection rule: x1 且 ΔKe ~ 10-4 eV E= 10-2 eV in RT

  6. Energies of vibration: M2 M1 M2 振動量子數(n) = 0，1，2，3… M1 振頻 k=彈性係數 M=有效質量 ΔKv ~ 10-1 eV

  7. Molecular Spectrum • Vibrational energy spacings are 0.1 ~ 1 eV. • Rotational energy spacings are 0.01 ~ 0.1 eV.

  8. Molecular Vibration and group frequencies • Diatomic vibration: • Coupled oscillators: • M-M : • In-phase M1-M2-M1 (M1-∞) : • Out-of-phase M1-M2-M1 (M1-M2/2):

  9. Calculate the vibrational frequency • Force constant k (C-H): • k (Sp) : 5.9 • k (Sp2 ) : 5.1 • k (Sp3 ) : 4.9

  10. Molecular symmetry • Symmetry plays an important role in the structure of molecules. • Five symmetry elements: (standpoint of infrared and Raman spectroscopy) • A center of symmetry designated by “ i ”. • A p-fold rotation axis of symmetry designated by “ Cp ”. (360°/p)

  11. Fivesymmetry elements (3) • Planes of symmetry usually designated by “ σ”. • συ: vertical symmetry. • σh: horizontal symmetry. • σd: diagonal symmetry.

  12. Fivesymmetry elements (4, 5) • A p-fold rotation-reflection axis of symmetry designated by Sp. • The identity “ I ”, a trivial symmetry element possessed by all molecules. (purposes of mathematical group theory)

  13. Vibration types (1) • Г:The vibration types. • A: symmetric with respect to the principal axis of symmetry. • B: antsymmetric with respect to the principal axis of symmetry. • E:Doubly degenerate vibrations, the irreducible representation is two dimensional. i.e., a 2 x 2 matrix. • F:triply degenerate vibrations, i.e., a three dimensional representation.

  14. Vibration types (2) • g and u(subscripts): symmetric or antisymmetric with respect to a center of symmetry. • 1 and 2 (subscripts): symmetric or antisymmetric with respect to a rotation axis (Cp) or rotation-reflection axis (Sp) other than the principle axis or in those point groups with only one symmetry axis with respect to a plane of symmetry. • ’ and ” (subscripts): symmetric or antisymmetric with respect to a plane of symmetry.

  15. Fundamental vibrational modes of benzene

  16. Normal vibrational mode of Graphene E2g is the doubly degenerate in-plane optical vibration. Only the E2g representation is Raman active.

  17. Scattering and Raman effect (1) • When electromagnetic radiation of energy content hυ irradiates a molecules, the energy may be transmitted, absorbed, or scattered.

  18. Scattering and Raman effect (2) • Infrared absorption: • An infrared photon whose frequency is the same as the molecular frequency υm. • Reyleigh scattering: • Anelasticcollision between the incident photon and the molecule. • Raman effect: • Aninelasticcollision between the incident photon and the molecule where as a result of the collision the vibrational or rotational energy of the molecule is changed by an amount ΔEm.

  19. Scattering and Raman effect (3) • According to quantum mechanics the allowed change in the vibrational quantum number for a Raman transition is Δυ = ±1 for a harmonic vibration.

  20. Scattering and Raman effect (4) • hυi: The energy of the incident photon. • hυs: The energy of the scattered photon. • ΔEm: The changed energy. hυi hυs

  21. Scattering and Raman effect (5) • Raman Stokes: (υi >> υm) • Starting fromground state. (υ=0). • The molecule gains energythen ΔEm is positive and υiis smaller than υs. • Raman Anti-Stokes: (υi >> υm) • Starting from excited state. (υ=1). • The molecule loses energythen ΔEm is negative and υs is smaller than υi.

  22. Scattering and Raman effect (6) • According to the Boltzmann distribution. • ThereforeStokes lines have greater intensitiesthan anti-Stoke lines which originate from an excited level with lower population. 10 1

  23. Phonon dispersion relation (1) • Force constant model. (N atom in the unit cell) • Inter-atomic forces are represented by spring constants. • ui=(xi, yi, zi): the displacement of the ith atom. • Mi: the mass of the ith atom. • k(ij): the 3 x 3 (x, y, z) force constant between ith and the jth atoms.

  24. Phonon dispersion relation (2) Fourier expencion Phonon dispersion of Graphene

  25. Raman spectroscopy of graphene C-C伸缩振动在拉曼光谱中是强谱带 G’ , 2D G 633 Red Laser 1583 2635 D 1320 monolayer monolayer bilayer HOPG

  26. 右圖是一組鑽石薄膜光譜圖。鑽石薄膜是碳原子以 混成軌域與其他四個碳原子所組成。(a)是一很好的鑽石薄膜，(b) 、(c) 、及(d)所對應的薄膜則是漸次變差。 無定型的碳固體的拉曼光譜(e)所示，有兩個很寬的譜線。(f)為晶形石墨的拉曼光譜。在1580 處也有訊號出現，也就是部分碳是成非均質態方式出現。

  27. Phonon dispersion of Graphene G D G’ , 2D

  28. Relation between Electron and phonon Electrons g0=3.033eV K¢ k k K¢ Phonons q q

  29. b a c  K Double resonance model Double resonance: Two terms in the denominator go to zero simultaneously Thomsen and Reich, Phys. Rev. Letters 85, 5214 (2000)

  30. Double resonance Raman process G peak • Resonant Raman process • 1st order: q<k, k~0 • q~0 (only nearГpoint) • 2nd order:(1 phonon, 2 phonons) • q>>1 (depend on Elaser) One phonon emission D peak 1st order Raman Double resonance condition C. Thomsen and S. Reich, Phys. Rev. Lett.85 5214 (2000)R. Saito et al., Phys. Rev. Lett.88, 027401 (2002) 2nd order Raman

  31. Defect induced Raman D mode • Excitation of an electron-hole pair. • Inelastic scattering of electron by a phonon. • Elastic scattering of the electron by a defect. • Recombination of the excited electron and hole.

  32. G’,2D peak (1) • Excitation of an electron-hole pair. • Inelastic scattering of electron by a phonon. • Inelastic scattering of the electron by a phonon. • Recombination of the excited electron and hole. The Raman shift of 2D will be twice of D peak. monolayer

  33. G’,2D peak (2) bilayer Resonant with incident photon energy Resonant with scattered photon energy

  34. G’,2D peak (3)

  35. Laser energy and D peak Blue 488 (2.54 eV) Green 532 (2.33 eV) Red 633 (1.95 eV)

  36. Conclusion • Raman spectrum can detect the particular phonon scattering frequency by a incident Laser, which is very sensitive to the crystal structure.

  37. Reference • N. B. Colthup, L. H. Daly, and S. E. Wiberley, “Introduction to Infrared and Raman Spectroscopy” Third Edition, Academic Press. • RICHARD L. McCREERY, “Raman spectroscopy for chemical Analysis”, WILEY-INTERSCIENCE. • “Solid state physics” • K. Krane, “MODERN PHYSICS” second edition, WIELY. • R. Saito, G. Dresselhaus, and M. S. Dresselhaus, “Physical Properties of Carbon Nanotubes”, Imperial College Press. • Andrea C. Ferrari and John Robertson “Raman Spectroscopy in Carbons: from nanotubes to Diamond”. (碳材料的拉曼光譜)

  38. Group theory – point group (1) • Cp: A molecule possessing only Cp rotation axis of symmetry. • Sp: A molecule having only a p-fold rotation reflection axis of symmetry. • Cpυ: Molecules have a vertical rotation axis of order p with p vertical planes of symmetry lying in the rotation axis. • Cph: Molecules have a rotatin axis of order p and a horizontal plane of symmetry perpendicular to the axis.

  39. Group theory – point group (2) • Dp:The D stands for dihedral. Molecules have a p-fold axis, Cp, and perpendicular to this axis p-twofold axes at equal angles to each other. • Dpd: Molecules have a p-fold axis, Cp, and perpendicular to this axis p-twofold axes plus p-planes of symmetry (σd) passing through the p-fold axis and bisecting the angles between the two consecutive twofold axes. • Dph: Molecules with a p-fold axis and p-vertical planes of symmetry lying in the rotation axis plus a horizontal plane of symmetry perpendicular to the Cp axis.

  40. Group theory – point group (3) • T: The T stands for tetrahedral (四面體). Molecules have four threefold axes and three mutually perpendicular two-fold axes. • Td: Point group T + two mutually perpendicular planes of symmetry through each twofold axis. • O: The O stands for octahedral(八面體).Molecules have three mutually perpendicular fourfold axes and four threefold axes. • Oh: Point group O + a center of symmetry and nine planes of symmetry.

  41. Additional: Raman apparatus and application Raman 光譜的實驗裝置

  42. 雷射光源 • 為了激發 Raman Raman 光譜，對光源的最主要求是應當具有相當好的單色性，即線寬要窄，並且光的強度必須足夠。 • 氣體雷射能滿足這些要求，準直性良好， 並且是平面偏振的。 • 有多種氣體雷射可以提供許多條功率不同 的單頻雷射光。最常用的是氬離子雷射， 波長為 波長為 514.5 nm 和 488.0 nm 的譜線最強。輸出功率可在 0.2 mW ~ 2 W 之間

  43. 雷射光源 (2) 通常所謂具有一定波長的雷射，實際上是由許多 通常所謂具有一定波長的雷射，波數略有差異的縱模所組成，這些模的集合構成 一個波包，其寬度決定這個雷射波數的觀測寬度。 以氬離子雷射的 514.53 nm（19430cm-1）這條線為 這條線為 例，通常它的線寬為 0.15 cm-1。如果採用腔內選模器後，線寬變得極窄，可達 0.001 cm-1。 此時，單模輸出功率約降到多模輸出的二分之一。 單模工作的雷射器對於高分辨光譜研究很重要。

  44. 二、外光路系統及樣品裝置 (1) 在雷射之後到分光儀之前的部分為外光路 系統和樣品裝置。 功用有： • (1) 最有效的照射樣品。 • (2) 最大量的收集散射光 • (3) 適合作各種不同條件下的量測。

  45. 二、外光路系統及樣品 (2) 由於 Raman 散射的效率很低，樣品裝置要能以最有效，樣品裝置要能以最有效 的方式使雷射光照射樣品和聚集散射光，所以光學設 計是非常重要的。 􀂄 通常將雷射光束聚焦照射到樣品上，以提高樣品上的照度，利於產生 Raman 散射。 􀂄 一般用 L1 聚焦雷射光束，使其最集中的區域（光 斑直徑可達 10μm）照射到試樣上，試樣上的照度大約 可增大一千倍。如功率密度太高會損壞樣品時，則不 用此透鏡。 透鏡 L2 是聚集樣品的散射光，並準確地入射至分光儀 的狹縫上，以最佳的立體角收集散射光，並使之與分 光儀的集光立體角相匹配。

  46. 外光路系統及樣品裝置 (3) 樣品室內的凹面鏡M1和M2是用以提高散射強度。 􀂄 M1 把透過樣品的雷射光束反射而來回多次通過樣 品，以增強雷射對樣品的激發效率。對於透明樣品照射光的強度可增大五倍以上。 M2 則把反方向的散射光收集起來反射回去，可將進入分光儀的散射光的立體角增加一倍。 在做單晶體Raman 散射實驗時，由於 M1 和 M2 會改變散射的幾何配置，所以不用這兩個反射鏡。

  47. 三、分光系統 分光系統是Ｒaman光譜儀的核心部分，它的主要作用 是把散射光分光並減弱雜散光。 分光系統要求有高的解析度和低的雜散光，一般採用串聯 兩個單光儀。當兩個單光儀耦合起來，其色散是相加的，所以可得到較高的解析度（約1cm cm-1 ） 兩個串聯的單光儀的雜散光（在50cm cm-1 處）可以降低到可以降低到 10*-11 為了進一步降低雜散光，有時再加一個連動的第三單光儀， 此時解析度提高了，但譜線強度也相應減弱。

  48. 四、偵測裝置 (1) Raman 光譜儀的偵測器為光電倍增管。用不同波 長的激發光，散射光在不同的光譜區，要選用適的光譜回應的光電倍增管。 為了減少其暗電流降低雜訊，以提高信噪比，需用致冷器冷卻光電倍增管。 處理光電倍增管輸出的電子脈衝的方法有直流放大法，交流放大法和光子計數法。 • 當輸出電流大於 當輸出電流大於 10*-9A 時用直流放大器， 10*-10 A 時用光子計數器。交流放大法目前已較少採用。

  49. 四、偵測裝置 (2) 在直流測量法中，增大光電倍增管的回應時間，使其倒數大於光子到達速率，則與各個光子對應的脈衝不可分辨，流向光電倍增管的負載電阻的電流是連續的，電流的大小與射到光電陰極的強成正比，經過直流放大後，可用記錄儀器記錄。 • 光子計數器適合於探測微弱信號。它的計數範圍為每秒10～10*5 個脈衝，相鄰的兩個脈衝的時間間隔為0.1s～10μs，而光電倍增管內光電子脈衝形成的時間 0.1～10μs，因此光電倍增管中所產生的電脈衝信號是分立的。光子計數器就是要算 出這些脈衝數目。

  50. 使用 Raman 光譜儀應注意的事項 • 在 Raman Raman光譜實驗中，為了得到精確的光譜圖，除了選用性能優異的光譜儀外，準確地使用光譜儀，控制和提高儀器解析度 和信噪比是很重要的。 • 1. 狹縫的調整。 • 2. 孔徑角的匹配。 • 3. 激發功率。 • 4. 激發波長。

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