Materials Chemistry III [IC 300] Course Outline PDF

Materials Chemistry III [IC 300] 1  Course Timings Instructor: Dr. Satyajit Gupta Monday: 12:30-1:25 PM Grading: Relative Course Credit: 1...

Materials Chemistry III [IC 300] 1  Course Timings Instructor: Dr. Satyajit Gupta Monday: 12:30-1:25 PM Grading: Relative Course Credit: 1 Mode: Offline Total 14 days; weekly 1 h; total 14 h mid-semester break-05/10/2023-13/10/2024; Last teaching day 27/11/2024 1. Assignment 2. Quiz Mid Semester exam (23/09/2024-27/09/2023) and Final Exam (28/11/2024- 4/12/2024) 2   Class representative? Please write your Name and ID number in all the pages of: -Assignment -Quiz -Exam 3  The broad syllabus…. Light-matter interaction (black body radiation, photo-electric effect, wave-particle duality, concept of wave function, particle in 1D/2D box), concept of chemical bonding. (Detail Theory and Interpretation) Applications of semiconductor systems in 3G solar-cells, LEDs. Introduction to light harvesting materials (conjugated polymers, quantum dots and dyes and introduction to some advanced materials), electron-mater interaction. (Introductory Level) Objective of 14 h!!! Theory (5L) Application (4L) Text-book In real life? 4  Course Objective  To learn how certain quantum mechanical principles translates into applications in the area of materials science and advanced applications.  The course will start with Pre-Quantum theory and then will move towards application of quantum mechanics in macroscopic world and in sub-atomic world. 5  Basic Mathematics ∞ 𝑿𝟑𝒅𝒙 Standard Integration ‫𝒙𝒆 𝟎׬‬−𝟏= (π4/15) Differentiation Differential Equation  λ×ν=c Operator Algebra ν=(c/λ) dν = - c(dλ/λ2) Physical interpretation of the results will be important for this course! 6  Physical Constants Planks constant (h)=6.62618 × 10-34 J-sec Speed of light in vacuum (c): 2.99 ×108 m/s Electron rest mass (me): 9.10953×10-31 Kg Boltzmann constant (KB): 1.38066×10-23 J/K 7 1) Black body radiation (~solar spectrum), ‘Photoelectric effect’-Light/Mater nteraction. (Concept of Work Function and Fermi level). UPS measurement. 2) Wave-particle Duality, de Broglie’s equation: Application in real world and microscopic world. Emerging nanomaterials. Heisenberg’s experiment and Uncertainty Principle. 3) Understanding the Electron wavelength and principle of SEM. (Electron mater interaction) Nano Particles 4) Particle in 1D Box and its implication in Materials world and the regime of nanoscale/Quantum dots, rainbow concept. (Light mater interaction) 5) Conjugated Polymer Based Systems, Lead halide perovskites and Flexible Devices. 8 n  Day-Wise Plan Day 1/Problem day 2: Introduction and Black-body Radiation Day 3: Photo-electric effect, Application Day 4/Problem day 5: Wave-Particle Duality Day 6: Concept of wave function, Postulates, Operator Algebra Day 7/Problem day 8: Particle in 1D box (2D box and 3D box) Day 9: Electronic Transition Day 10: Quiz (Announced) Day 11/Problem day 12: Simple Harmonic Oscillator Day 13: Quantum Confinement Effect Day 14: Applications 9  Study Materials 1. Quantum Chemistry, D. A. McQuarrie, Viva Books, New Delhi, 2003. 2. P. W. Atkins and R. Friedman, Molecular Quantum Mechanics, Oxford University Press, 2005. 3. K. L. Kapoor, A text book of Physical Chemistry. 4. A.K Chandra, Introductory Quantum Chemistry. 5. A textbook of nanoscience and nanotechnology, T. Pradeep [All course materials/tutorials will be sent via email] 10  Materials Chemistry III thus ‘its’ Chemistry of Materials Science 11  Quantum Mechanics 12 Newton’s laws of motion: Solution of dynamic systems. Lagrange’s eqn, Hamilton’s eqn are fundamental of classical mechanics, useful for complicated dynamical systems. Carnot, Gibbs’s Thermodynamics. (Maxwell, Boltzmann) These can’t explain certain properties of microscopic systems. Newton 1st beginning was at German Physical Society by Max Plank 2nd stage initiation by Heisenberg and de Broglie Erwin Schrödinger Plank Noble Prize-1933 Noble de Broglie Heisenberg (Prize-1918) 13 Noble Prize-1929 Noble Prize-1932  Quantum Mechanics: the beginning… Newton’s laws of motion are the elementary equations of classical mechanics and these laws are suitable for the description motion of macroscopic bodies. However, when we deal with very tiny particles (subatomic world - electrons) then these equations fail. Quantum mechanics deals with the systems, that are not part of every day's macroscopic systems. 14 S.P Singh, M.K. Bagde, Quantum Mechanics, Published by S. Chand & Company. The followings are the example, where classical mechanics fails is Black-body radiation  Black body radiation  Photoelectric effect  Compton effect Quantum mechanics…. 15  Black Body Radiation (Experimental data to Quantum theory) 16  Black body radiation A black body is a body, which completely absorbs all the radiations falling on it and the radiation emitted by it called black body radiation. A perfectly black-body absorbs all the radiations incident on it. [ideal condition] Remember: There is no available surface that can absorb 100%! S= Porcelain sphere S A A= opening Maintained at constant temperature The emissive power is measured by means of ‘Bolometer’ and ‘IR spectrophotometer’. ‘Burner in an electrical stove-Red-White-Yellow’ 17  Why black-body is important? As the radiation level of a blackbody only depends on its temperature, blackbodies are used as optical reference sources for optical sensors. That’s why blackbodies are also known as Infrared Reference Sources. The main applications are of course IR sensors calibration. Applications in solar energy collectors Anti-reflection surfaces (Telescope and cameras) https://www.hgh-infrared.com/FAQ/Blackbody/What-are-the-applications-of-a-blackbody 18  Lummer and Pringsheim - 1899 Wien’s displacement law E(λ)dλ is the ‘energy density’ radiated, for wavelength in the range λ to λ+dλ. [J/m3] Area under the curve: Total radiated energy 19 1) As T increases, E(λ) - emissive power for every wavelength increases. 2) At constant temperature, E(λ) increases and becomes maximum at a certain λmax and then with further increase in λ, E(λ) decreases. 3) At higher temperature, E(λ) shifts towards shorter wavelength. 20  Features and the Laws…….. 𝜆𝑚𝑎𝑥 and the corresponding temperature are related by Wien’s Displacement Law 𝝀𝒎𝒂𝒙 𝐓 = 𝐜𝐨𝐧𝐬𝐭𝐚𝐧𝐭 = 𝟐. 𝟖𝟗𝟖 × 𝟏𝟎−𝟑 𝐦. 𝐊 The maximum value of 𝐸𝜆 is directly proportional to the fifth power of temperature: Em/T5 = constant = 2.188 ×10-11 J K The area enclosed between the curve at temperature T and the 𝜆-axis represents the total radiation emitted per unit area per unit time over all wavelengths The total radiation emitted per unit area per unit time is directly proportional to the fourth power of temperature. This is called Stefan’s law. ∞ Total radiation from black body: RB=‫𝑬 𝟎׬‬ 𝝀 𝒅 𝝀=σT4; σ=Stefan’s constant 21 1) Calculate the temperature of Sun, considering its radiation of the peak occurs at 500 nm. 2) Star Sirius appears blue, having a surface temperature of 11000 K. Find out its wavelength of radiation. 22 Solar Radiation C=λ×ν E=h×ν 23  Understanding Radiation Radiation consists of electromagnetic waves. Electric field is perpendicular to magnetic field and they are perpendicular to the direction of propagation. Diffraction and interference strongly evidenced that they have wave nature. Classical mechanics: Energy is proportional to Amplitude2 And its Independent of frequency 24 Theoretical Laws of Black Body Radiation Wien’s displacement Law Stefan’s law or Stefan-Boltzmann Law Wien’s radiation Formula Rayleigh-Jeans Law Planck’s Law 25  Wien’s Law and Radiation Formula Wien’s displacement law: 𝜆𝑚𝑎𝑥 T = constant = 2.898 × 10−3 m. K Wien’s radiation formula (derived in 1896): 𝑪𝟏 −𝑪𝟐 𝑬𝝀 𝒅𝝀 = 𝟓 𝒆 𝝀𝑻 𝒅𝝀 𝝀 𝑪𝟏 and 𝑪𝟐 are constants Arbitrary assumptions: 1) The radiation is produced by resonator of molecular dimensions. 2) Frequency of radiation is proportional to Kinetic Energy of the resonator. Outcome: It explained the experimental results at low values of λ. 26  Stefan Boltzmann Law The area enclosed between the curve at temperature T and the axis of λ represents total radiation: ∞ ‫𝑬 𝟎׬‬ 𝝀 𝒅𝝀 The total radiation emitted /unit area/sec at temperature T is called black body radiant emittance RB (Stefan’s law for the total radiation from black body) ∞ RB=‫=𝝀 𝒅 𝝀 𝑬 𝟎׬‬σT4; σ=Stefan’s constant σ=5.6697 ×10-8 w/m2 K4 27 Rayleigh-Jeans Law (1900) 28  Rayleigh-Jeans Law (1900) 8𝜋ν2𝑘𝑇 𝐸ν 𝑑ν = 3 𝑑ν 𝑐 8𝜋𝑘𝑇 𝐸𝜆 𝑑𝜆 = 4 𝑑𝜆 𝜆 This formula was derived by applying equipartition of energy of the electromagnetic vibration (classical treatment-each vibration mode posses on an average energy Eavg=KT; all oscillator have mean energy of this KT). If there are dn number of modes of oscillation in the wavelength λ and λ + dλ; 8π dn= 4 𝑑λ λ 8𝜋𝑘𝑇 The energy density (𝐸𝜆 𝑑𝜆) =dn×Eavg = 𝑑𝜆 𝜆4 29 It describes the black-body radiation in longer wavelength region but fails in shorter wavelength region as λ→0, E approaches infinite. This is called ultraviolet catastrophe 30 Total energy of radiation per unit volume of the enclosure of all wavelength: ∞ E= ‫׬‬0 𝐸𝜆 𝑑𝜆 ∞ 8𝜋𝑘𝑇 𝐸=න 4 𝑑𝜆 0 𝜆 ∞ 1 =8𝜋𝑘𝑇 ‫׬‬0 4 𝑑𝜆 𝜆 = 8𝜋𝑘𝑇[-1/3𝜆3]0∞ =∞ Thus opening of shutter of the black body will lead to bombardment of shorter wavelength (X-ray/gamma ray). This is called as UV catastrophe. This absurd result is due to the assumption energy can be absorbed/emitted by the oscillators continuously by any amount. Also in dark, all mater should emit radiation? 31  Ultraviolet Catastrophe 𝟖𝝅𝒌𝑻 Rayleigh-Jeans Law: 𝑬𝝀 𝒅𝝀 = 𝟒 𝒅𝝀 𝝀 It describes the black-body radiation in longer wavelength region but fails in shorter wavelength region as λ→0, E approaches infinite without passing through the maxima. Thus, the equation predicts that oscillators of very short wavelength (high frequency-ν→high energy) radiation such as UV, X-Ray, γ-Ray will come out even at room temperature. [It is impossible to generate UV/X-Ray at room temperature. This absurd result , which implies that a huge amount of energy will be irradiated as we decrease λ is called Ultraviolet catastrophe. What is the significance of ‘infinite’? 32  According to classical physics a cool object should radiate in visible/UV region. Thus the object should glow in dark- signifying there is no darkness? 33 KL Kapoor 34  Planck’s Law (1900) 8𝜋ℎ𝑐 𝐸𝜆 𝑑𝜆 = 𝑑𝜆 ℎ𝑐 −1 𝜆5 𝑒 𝜆𝑘𝑇 It perfectly describes the black-body radiation in whole range of wavelength All the laws (Wien, Rayleigh-Jeans and Stephan) can be arrived from this law. (Tutorial) Energy of the oscillator has to be integral multiple of hν; E=nhν 35  S= Porcelain sphere S A A= opening Atoms in the walls are like simple harmonic oscillators having a fixed frequency v. 1901 Planks proposed the oscillator emits radiation in discrete amount. (The electrons are pictured as oscillators like they oscillates in antenna to give radiowaves. But in black body they oscillates at a much higher frequency that why we see emission in visible/UV/IR ranges) Assumptions: 1) Oscillators of black body can’t have any amounts of energy but have a discrete energy. It can have only those values of total energy E, which satisfy the relation E=nhν. (n=0,1,2…) hν is the basic unit of energy. [h=6.625×10-34 J s] 2) The oscillator does not emits continuously. The emission/absorption only occurs when 36 they jumps from one energy level to another.  Unit of radiant energy density 8𝜋𝑘𝑇ν2 𝐸ν 𝑑ν = 3 𝑑ν 𝑐 =[(J K-1) (K)/(m s-1)3] ×(s-1)2×(s-1) =J m-3 8𝜋ℎ𝑐 𝐸𝜆 𝑑𝜆 = 𝑑𝜆 ℎ𝑐 −1 𝜆5 𝑒 𝜆𝑘𝑇 =J m-3 (Radiant energy density has units of energy per unit volume)