Diffraction and Spectroscopy PDF

### 03/01/25 ### Friday - 2dsinθ=nλ - E=E₀ei(kx-wt) - (Semiconductors) - Spectroscopy & Diffraction? - Study of spectrum - Plot btw intensity/amplitude (vs) Energy. - I/A - Structure - Energy levels - Spectrum - H+ - +H+ - +H - Diffractio...

### 03/01/25 ### Friday - 2dsinθ=nλ - E=E₀ei(kx-wt) - (Semiconductors) - Spectroscopy & Diffraction? - Study of spectrum - Plot btw intensity/amplitude (vs) Energy. - I/A - Structure - Energy levels - Spectrum - H+ - +H+ - +H - Diffraction pattuen (Solids) - XRD - Electron - CD (Visible light) - H₂O ice - Amorphous (T<0^oC) - Crystalline ### 7/01/25 ### Tuesday ### Waves - E=E₀ei(kr-wt) - Frequency. - K - wave vector, which shows direction. - Re(E) at t=0 - E - electric field - H=H₀e^i(kr-wt) - Plane wave - H⊥E⊥k - <S>= ±(ExH*) - Pointing vector - <S> gives the energy flow. - Reason why waves imp in spectroscopy - Wave interact with material - 1. Molecular atoms. - 2. Bonding H bond/covalent - 3. Special arrangment. - Solid, liquid, Gas. - Contribute final - x band structure (λ) - Electronic structure in a material. ### - Energy levels lump together - Transition (excitation) - Emission - n=2 (emission process) - n=1 (Ground state) - 1^st excited state - Coord (in Four Space) - Inelastic process - Typically represented by K - Elastic process - Comes from a quantum - E_lev - Visible range - Elastic - Inelastic - Not belong to absorption - Either release a photon(or) phonon (deexcitation) - Happen based on - 1. hv photon - 2. phonon - Thermal (N/0e^V ~ 3-4 eV) enough energy - - Plot bed. - Photon comes and hits the molecule & then - Out put intensity - Which is not absorbed. - I_oe^-αx ; x-unit length. - Comes in term of a curve. ### - At t=0 - E=E₀e^i(kz) - n - refractive index - n=n_o+n₁, - amount of absorption we have in a material - Spectrum - Depend of absorption, n_o+n₁ - Inversely proportional. - When products of n_o+n₁ and absorption are increased, the spectrum also becomes broadened. - Case 2 - As multiple level are increased, spectrum also broaden, where it was narrow time ### - n₁ & a are independent in concentration. - How do we calculate the absorption co-efficient? - How do you find transition probability of the given level to the other level? - For ex: based on the equation n=∫f(E)D(E) dE - Total(S₁) (emp S₂)(ΔE) - (E) - limits matters. - Emplaty (empty state) - Total(S₁) (D_Os) (Cmps) (ΔE) - Total(S₁) - Density - States - e^r - Change in transition. - 1 mole = 1 mole/L=6×10²³ mole/L - V=V₂= 2.5×10^-3 m calculate no.d. molecules/cm³ - 10^-3A 10^-3 moles = 1.17×10¹⁷ - 1mM - Beam, 5mm, 1x10^-2m - What decides height of peaks/absorption co-efficient? - If you have more eo which conduct, there will be more absorption. - How do you find probability / "(E) =∫f(E) P(E) dE for a transition to happen? - (No.q.es in ground state) (Empty State in 1st Excited State)(ΔE) ### - Can we do absorption in spectroscopy for a single crystal? - No. It's 10⁵-10⁷ 1mM - No. It's 10⁹-10¹¹ 1nM. How do we reduce this no? - Let have arbitrary sample. - Difficult to calculate inelastic - Backward scattering - (I/I₀)NAbsorption - No scatt - Pointless - Extinctiom = Absorptiom + Scattering - (elastic) - Energy Consumption purely - d - (dipole approximation ) - Based on this we can categorize spectroscopy into two types: - Absorption spectroscopy - Ex: absorption spectra - Scattering Spectroscopy - Ex: Raman effect - Sometimes called - Holoramission Spectroscopy. - (small) dipole absorption - If very small, the scattering looks like - Assuming particle is so small (f), scattering happens in a similar way to dipole. - So, how dipole scatters? ### - Im=1$/mole/L = 6.023×10²³. MM=1 - Let's say beam of 5mm circle, solution of concentration 1mM. - In measurement volume, how many molecules? - Cylinder = πr²h - π(5x10^-3)² - π(5x10^-3)² - π(5x10^-3)² - π(5x10^-3)² - 5x10^-3 cm - 1x10^-2m - Beam Cylinder. - 6×10²³. - 6×10²³ - x = 6×10²³/25 - (6×10²³)/25 - X = 4×10⁹ - 2 = 6×10²³ x 3.14 x 25 x 10^-6 - 6x3.14x25 - 117.75x10⁵ - 1.1775x10¹⁷ - (10⁵-10⁷)- 1mM ### - Distance blw person & wall = 100 cm. - Distance blw points on wall= 15 cm. - Periodicity-? - Gravity - (mmmmf) Periodicity- - (mm) - K 100cm. - Density (height, wt they say) - 0 - AE → - EELS and EDS - Xray - cathode luminascence - Input (light (e)) - Output (spectroscopy) (light(e)) ### - By Sairam Sir. - Infrared - causes heating (~700 nm) - UV - energy higher than visible light (~400 nm) - UV-Vis Spectroscopy - Based on the energy range peak. - Energy related to some events happening in atom - Emission - Absorption - Scattering - Electron - Electron energy loss spectroscopy - Sing signal coming - (From the sample) - Which means visible light going in and coming out - I vs λ - How do we do it? - "Prism" spectrum ### - Other points in α for a sample. - Red shift - Blue shift - Spectroscopy - quantifying, but looking at displacement (t). - Inelastic scattering event energy lost. - Electron energy lost spectroscopy: with the help of energy lost. - During it with photoemission by using x-rays (e's out) - 1. σ-(typical ) λ_out - 2. - (k-1) - K(1-1/π) - 2 - 2 - 2 - 3. - ΔE - Virtual energy band ### - 28/01/25 ### Tuesday - Raman -no (s₀) - Inelastic - E₀ ≠E₁ - Rayleigh scattering. - - ΔE - E₀,₃ - E₀,₂ - - ΔE=hc( ) - E₀,₁ = (Anti-stokes) - (Phonones supplies energy ) - E₀,₁ < E₁ = (Stokes) - (Phonons take energy) - - Antistokes - Stokes - Higher energy - Lower energy → Rayleigh wavenumber ### - Why is Raman so special? - How does Raman tell you about bond into? - EELS - Quiz on ### - Scattered lig - (sunlight) white - Raylight scattered - Raman scattered. - violet - Green - Green filter - Observe - violet - Stokes of Antistokes in graph au mirror images. - Intensities of Stokes are higher than antistokes, why? - Strong spectrum = [ ]^1/2cm^-1 - E₁=532nm - E₂=633nm (red) - I ### - Depends on laser we use, same positions of Raman peaks, but intensity varies. - v² =(1-/λ_s) - This remains same. - G₂ - G₁ - What is the different b/w fluorescence of Raman. - What leads to laser emission. How is it beneficial? - Gas Lasers has narrow line width - Diode Lasers. Why is it important in terms of Raman speciality? - (bar) am&ad = ξ