XRD Notes PDF - Analytical Instrumentation

IN-201: Analytical Instrumentation (Aug-Dec 2024) Course Instructor: Dr. Manukumara Manjappa ([email protected]), Office: #113 IAP Teaching Assistants: Mr. Om Prakash Sahu ([email protected]) and Ms. Santilata Sahoo ([email protected]) Class Timings: 5:00PM-6:30PM on...

IN-201: Analytical Instrumentation (Aug-Dec 2024) Course Instructor: Dr. Manukumara Manjappa ([email protected]), Office: #113 IAP Teaching Assistants: Mr. Om Prakash Sahu ([email protected]) and Ms. Santilata Sahoo ([email protected]) Class Timings: 5:00PM-6:30PM on Mondays and Wednesdays Credit: 3:0 Venue: Instrumentation and Applied Physics (IAP) Department, Lecture hall (LH)-1 Guest Lectures: Prof. Asokan. S and Prof. Soumen Ghosh QR code to register to the IN 201 Course Teams page IN201-Analytical Instrumentation:Aug-Dec 2024 2  Course Content 1. X-Ray Methods of Analysis - TEST I 2. Electron Methods of Analysis 3. STM, TEM, AFM Techniques - TEST II 4. UV, Vis, IR and THz spectroscopy 5. Mass spectroscopy and Thermal Analysis Techniques 6. Raman Spectroscopy - TEST III 7. Polarimetry Techniques 8. Nuclear Magnetic resonance - Final Exam Mid Terms (Best of Two) 40% + Final Exam (60%) IN201-Analytical Instrumentation:Aug-Dec 2024 3  Learning Objectives Fundamental Principles of Analytical Instrumentation Instrumentation Techniques Operation and working Procedures Instrument Selection Measurement and Calibrations Data Analysis Applications IN201-Analytical Instrumentation:Aug-Dec 2024 4  References 1. Principles of Instrumental Analysis - Skoog et al 2. X-ray Methods - Clive Whiston 3. Instrumental Techniques for Analytical Chemistry – Frank Settile 4. EDXA in Electron Microscope – A.J. Garrath-Reed & Bell 5. Electron Diffraction in TEM – P.E. Champress 6. Elements of X-ray Diffraction – B D Cullity & S R Stock 7. Fundamentals of Molecular Spectroscopy – C N Banwell 8. Instrumental methods of analysis, by Willard, H H; Merritt, Jr, L L; Dean, J A. 9. Analytical Instrumentation: A Guide to Laboratory, Portable and Miniaturized Instruments, by Gillian McMahon IN201-Analytical Instrumentation:Aug-Dec 2024 5 Analytical Instruments IN201-Analytical Instrumentation:Aug-Dec 2024 6  Analytical Instrumentation: Introduction and Definition An instrument is a device that enables analytical measurements to be carried out automatically and objectively. Analytical instruments help analysts to work out composition, characterize samples, separate mixtures and yield useful results and analysis in both qualitative and quantitative way. IN201-Analytical Instrumentation:Aug-Dec 2024 7 Analytical Process: Flow Chart IN201-Analytical Instrumentation:Aug-Dec 2024 8 Analytical Process: Flow Chart ❑ The analytical process is the science of taking measurements in an analytical and logical way. ❑ An analysis is to be performed depends on experience, time, cost and the instrumentation available. IN201-Analytical Instrumentation:Aug-Dec 2024 9  Instruments for Analysis 1. Stimulus: An analytical instrument can be viewed as a Electromagnetic radiation, electrical signals, communication device between the system under mechanical force study and the investigator. Thermal energy/heat IN201-Analytical Instrumentation:Aug-Dec 2024 10  Instruments for Analysis 1. Stimulus: An analytical instrument can be viewed as a Electromagnetic radiation, electrical signals, communication device between the system under mechanical force study and the investigator. Thermal energy/heat 2. System under study Material Solutions Biological samples Devices IN201-Analytical Instrumentation:Aug-Dec 2024 11  Instruments for Analysis 1. Stimulus: An analytical instrument can be viewed as a Electromagnetic radiation, electrical signals, communication device between the system under mechanical force study and the investigator. Thermal energy/heat 2. System under study Material Solutions Biological samples Devices 3. Analytical information Nonelectrical domain Electrical domain Analogue domain signals Time or frequency domain signals Digital signals IN201-Analytical Instrumentation:Aug-Dec 2024 12 Analytical Information Principles of Instrumental Analysis, Seventh Edition Douglas A. Skoog, F. James Holler, Stanley R. Crouch IN201-Analytical Instrumentation:Aug-Dec 2024 13 Analytical Information Nonelectrical domains Performing the measurement by having the information reside entirely in nonelectrical domains Electrical domains Principles of Instrumental Analysis, Seventh Edition Douglas A. Skoog, F. James Holler, Stanley R. Crouch IN201-Analytical Instrumentation:Aug-Dec 2024 14 Analytical Information Nonelectrical domains Performing the measurement by having the information reside entirely in nonelectrical domains Electrical domains 1. Analog domain signals, 2. Time domain signals, 3. The digital domain signals, Principles of Instrumental Analysis, Seventh Edition Douglas A. Skoog, F. James Holler, Stanley R. Crouch IN201-Analytical Instrumentation:Aug-Dec 2024 15 Analytical Information and Process: A general block model for Fluorometer Involves interdomain conversions IN201-Analytical Instrumentation:Aug-Dec 2024 16 Analytical Information and Process: A general block model for Fluorometer Involves interdomain conversions IN201-Analytical Instrumentation:Aug-Dec 2024 17 Analytical Information and Process: A general block model for Fluorometer Involves interdomain conversions IN201-Analytical Instrumentation:Aug-Dec 2024 18 Analytical Information 1. Analog-Domain Signals ✓ Information encoded as the magnitude of one of the electrical quantities ✓ The measurement variables can be time, wavelength, magnetic field, temperature, … ✓ The correlations of different analog signals are important in the instrumentation techniques such as NMR, Thermal analysis, IR spectroscopy,… ▪ Susceptible to undesirable electrical noise within the measurements ▪ Some noise filtering and signal to noise optimization techniques/tools are available. IN201-Analytical Instrumentation:Aug-Dec 2024 19 Analytical Information 2. Time-domain Information IN201-Analytical Instrumentation:Aug-Dec 2024 20 Analytical Information ✓ Information is stored in the time domain as the time 2. Time-domain Information relationship of signal fluctuations, rather than as the amplitudes of the signals. ✓ The time relationships between transitions of the signal from HI to LO or from LO to HI contain the information of interest (period and pulse width). ✓ Devices such as voltage-to-frequency converters and frequency-to-voltage converters may be used to convert time-domain signals to analog-domain signals and vice versa. ✓ FTIR, NMR and THz spectroscopy employ the time- domain measurements IN201-Analytical Instrumentation:Aug-Dec 2024 21 Analytical Information 3. Digital Information ✓ Data are encoded in the digital domain in a two-level scheme ✓ The digital domain spans both electrical and nonelectrical encoding methods. ✓ Measuring the nuclear counts, gamma ray detectors, modulation/demodulation schemes, information transmission/memory devices, … IN201-Analytical Instrumentation:Aug-Dec 2024 22 Analytical Information 3. Digital Information ✓ Data are encoded in the digital domain in a two-level scheme ✓ The digital domain spans both electrical and nonelectrical encoding methods. ✓ Measuring the nuclear counts, gamma ray detectors, modulation/demodulation schemes, information transmission/memory devices, … IN201-Analytical Instrumentation:Aug-Dec 2024 23 Transducers, Sensors and Detectors Transducer: Devices that convert information in nonelectrical domains to information in electrical domains and the converse. IN201-Analytical Instrumentation:Aug-Dec 2024 24 Transducers, Sensors and Detectors Transducer: Devices that convert information in nonelectrical domains to information in electrical domains and the converse. Sensor: The class of analytical devices that are capable of monitoring specific chemical species continuously and reversibly. IN201-Analytical Instrumentation:Aug-Dec 2024 25 Transducers, Sensors and Detectors Transducer: Devices that convert information in nonelectrical domains to information in electrical domains and the converse. Sensor: The class of analytical devices that are capable of monitoring specific chemical species continuously and reversibly. Detector: A mechanical, electrical, or chemical device that identifies, records, or indicates a change in one of the variables in its environment, such as pressure, temperature, electrical charge, electromagnetic radiation, nuclear radiation, particulates, or molecules. (Transducer + Sensor) IN201-Analytical Instrumentation:Aug-Dec 2024 26 QR code to register to the IN 201 Course Teams page IN201-Analytical Instrumentation:Aug-Dec 2024 27 Recap IN201-Analytical Instrumentation:Aug-Dec 2024 28 Analytical Methods: 1. Classical methods 2. Instrumental methods Classical methods (Chemical methods) Gravimetric Volumetric Measurement of Measurement of mass volume Quantitative analysis Quantitative analysis of analyte. using titrations Analytical chemistry Simple methods Laboratory based Cost-effective Old-style instrumentation IN201-Analytical Instrumentation:Aug-Dec 2024 Analytical Methods 1. Classical methods 2. Instrumental methods Instrumental methods Optical methods Electroanalytical methods Interaction of analyte with EM radiation Measurement of conductance, electric potential, Spectroscopic techniques current/voltage Emission and scattering measurements Potentiometry, Voltammetry, Conductometry, … Quantitative analysis using absorption Quantitative analysis using titrations Qualitative analysis using spectral fingerprint. These analytical methods involve use of instruments Provides more accurate qualitative and quantitative analysis Modern instruments are usually rapid, automated and capable of measuring more than one analyte at a time. They need calibration before performing the measurements 30 Analytical Methods Analysis can be of two types – 1. Qualitative analysis – This helps in answering the question ‘What is present‘ in the sample? In short, qualitative analysis reveals the identity of the elements/compounds in the sample. 2. Quantitative analysis– This analysis helps us to answer the question ‘How much is present‘? This analysis helps us to find out the amount of analyte in the sample. IN201-Analytical Instrumentation:Aug-Dec 2024 31 Analytical Methods Analysis can be of two types – 1. Qualitative analysis – This helps in answering the question ‘What is present‘ in the sample? In short, qualitative analysis reveals the identity of the elements/compounds in the sample. 2. Quantitative analysis– This analysis helps us to answer the question ‘How much is present‘? This analysis helps us to find out the amount of analyte in the sample. IN201-Analytical Instrumentation:Aug-Dec 2024 32 Selecting an Analytical Method Criteria for selecting an appropriate Analytical method 1. Defining the nature of the analytical problem 2. Required accuracy of the measurement/analysis 3. Knowledge about the concentration/density range of the sample 4. Required Physical/chemical property of the sample 5. Knowing the Performance characteristics of the Instrument 1. Precision 2. Sensitivity 3. Detection limit 4. Dynamic Range 5. Selectivity IN201-Analytical Instrumentation:Aug-Dec 2024 33 Performance characteristics of the Instrument Precision: Provides a measure of random or error of an analysis IN201-Analytical Instrumentation:Aug-Dec 2024 34 Performance characteristics of the Instrument Sensitivity: Ability to discriminate between small differences in analyte concentration IN201-Analytical Instrumentation:Aug-Dec 2024 35 Performance characteristics of the Instrument Detection limit: The minimum concentration or mass of analyte that can be detected at a known confidence level IN201-Analytical Instrumentation:Aug-Dec 2024 36 Performance characteristics of the Instrument Dynamic Range: Extends from the lowest concentration at which quantitative measurements can be made (Limit of quantitation, LOQ) to the concentration at which the calibration curve departs from linearity by a specified amount (limit of linearity, or LOL). IN201-Analytical Instrumentation:Aug-Dec 2024 37 Performance characteristics of the Instrument Selectivity: Refers to the degree to which the method is free from interference by other species contained in the sample matrix. IN201-Analytical Instrumentation:Aug-Dec 2024 38 Selecting an Analytical Instrument Selection of the analytical instrument is based on the measuring either of the following three parameters – 1. Physical property 2. Interaction with electromagnetic radiation – spectroscopy. 3. Electric charge/current. Physical Property Spectroscopy Electric charge/current Mass / volume Absorption Electrical conductivity Density Emission Electrical potential Refractive index Scattering Magnetization Thermal conductivity Diffraction Voltammetry Mechanical strength IN201-Analytical Instrumentation:Aug-Dec 2024 39  Selecting an Analytical Instrument Characteristic Properties Instrumental Methods Emission of radiation Emission Spectroscopy (X-ray, UV, visible, electron, Auger); Fluorescence, phosphorescence, and luminescence (X-ray, UV, and visible) Absorption of radiation Spectrophotometry and photometry (X-ray, UV, visible, IR); FTIR and THz; photoacoustic spectroscopy; nuclear magnetic resonance (NMR) Scattering of radiation Raman spectroscopy; Refraction of radiation Refractometry; interferometry Diffraction of radiation X-ray and electron diffraction methods Rotation of radiation Polarimetry; optical rotary dispersion; circular dichroism Mass-to-charge ratio Mass spectrometry Rate of reaction Kinetic methods Thermal characteristics Thermal gravimetry (TGA); differential scanning calorimetry (DSC); differential thermal analyses (DTA); thermal conductometric methods Radioactivity Activation and isotope dilution methods IN201-Analytical Instrumentation:Aug-Dec 2024 40 Selecting a Spectroscopic Analytical Instrument Interaction of Electromagnetic (EM) Radiation With Matter Analytical Methods are developed based on the interaction of EM radiation with matter Two Important Factors: Wavelength & Nature of Radiation (Ionizing or Non-Ionizing) The wavelength decides the length scale/size of matter with which the radiation will interact IN201-Analytical Instrumentation:Aug-Dec 2024 41 Interaction of EM Radiation With Matter Parameters ε + μ n Light Matter σ χ, χ(2),.. IN201-Analytical Instrumentation:Aug-Dec 2024 42 Wavelength, Frequency and Length Scale of Interaction of Electromagnetic Radiation IN201-Analytical Instrumentation:Aug-Dec 2024 43  Types of Radiations 1. Ionization Radiation 2. Non-ionization Radiation IN201-Analytical Instrumentation:Aug-Dec 2024 44  Ionization Radiation ▪ Ionizing radiation has sufficient energy to ionize atoms. ✓ Usually, this means it can remove electrons from atoms, although some types of radiation cause nuclear reactions involving protons and neutrons. ✓ Ionization is a process in which a radiation dislodges an electron from one of electronic orbitals of a target atom ✓ Generally, photons or particles with energies greater than 10 electron volts (eV) are ionizing ✓ For hydrogen atom the ionization energy is 13.6 eV IN201-Analytical Instrumentation:Aug-Dec 2024 45  Ionization processes Electron Impact Ionization: High-energy electrons collide with atoms or molecules, transferring enough energy to eject electrons and form ions. Mass spectrometry, Imaging, nano-patterning,… Photoionization: An atom or molecule absorbs energy in the form of photons, typically from EM radiation such as ultraviolet (UV) or X-ray light. Detectors (Photoionization detector, gas monitoring), Mass Spectrometry Chemical Ionization: Interaction of a sample molecule with ions of a reagent gas in a low-energy ionization process Analyzing volatile organic compounds IN201-Analytical Instrumentation:Aug-Dec 2024 46  Non-Ionization Radiation ▪ Non-ionizing radiation is a radiation with insufficient energy to ionize atoms or molecules. ✓ However, it does have enough energy for excitation - Instead of fully dislodging an electron, it can raise electrons from lower energy to higher energy states. IN201-Analytical Instrumentation:Aug-Dec 2024 47  Non-Ionization processes Absorption: Interaction of Resonant light with Atoms /molecules. Spectroscopy, Imaging, Sensors, Detectors, Emitters… NMR, UV-Vis, THz, Interferometry, Optical Microscopy Reflection/Transmission: Imaging, Scattering phenomena, Low-energy neutron scattering experiments Electromagnetic Field Meters: Cell phones, Wi-Fi routers, and power lines Thermal Imaging: Infrared cameras, Temperature sensors, … IN201-Analytical Instrumentation:Aug-Dec 2024 48  Ionizing and Non-ionizing Radiations Ionizing radiation: Non-Ionizing radiation: High-energy ultraviolet light (> 10eV) Radiofrequency (RF) Radiation X-rays Microwave Radiation Gamma rays Terahertz Radiation Alpha Particles Infrared Radiation Beta particles UV-Visible Light Neutrons Thermal High-energy protons Charged atomic nuclei from cosmic rays and the Sun Positrons and other antimatter IN201-Analytical Instrumentation:Aug-Dec 2024 49  Course Content 1. X-Ray Methods of Analysis 2. Electron Methods of Analysis 3. STM, TEM, AFM Techniques 4. UV, Vis, IR and THz spectroscopy 5. Mass spectroscopy and Thermal Analysis Techniques 6. Raman Spectroscopy 7. Polarimetry Techniques 8. Nuclear Magnetic resonance IN201-Analytical Instrumentation:Aug-Dec 2024 50 QR code to register to the IN 201 Course Teams page IN201-Analytical Instrumentation:Aug-Dec 2024 51  Recap IN201-Analytical Instrumentation:Aug-Dec 2024 52  X-Ray Methods of Analysis X-Ray Diffraction Instrumentation X-Ray Photoelectron Spectroscopy X-Ray Fluorescence Spectroscopy IN201-Analytical Instrumentation:Aug-Dec 2024 53  Electromagnetic Spectrum Frequency(Hertz) Name of the Spectrum/Radiation Photon energy Wavelength (eV) (Angstroms) (Hard X-rays) (Soft X-rays) THz IN201-Analytical Instrumentation:Aug-Dec 2024 54 https://halas.rice.edu/unit-conversions  X-Ray Methods and Analysis Basics of X-rays : Principle, Production and Properties Instrumentation Source Monochromator/Filter Detector Basics of X-ray Analysis – Interaction of X-rays with matter Absorption Fluorescence Scattering and Diffraction Applications: X-Ray Diffraction, X-Ray Fluorescence, X-Ray photoelectron spectroscopy. IN201-Analytical Instrumentation:Aug-Dec 2024 55 Accidental Discovery by Rontgen In 1895, November German physicist Wilhelm C Röntgen accidentally discovered X-rays while studying the effects of passing an electrical current through gases at low pressure. Inaugural Nobel Prize in Physics in 1901 IN201-Analytical Instrumentation:Aug-Dec 2024 56 Accidental Discovery by Rontgen IN201-Analytical Instrumentation:Aug-Dec 2024 57  Aftermath of X-rays discovery Birth of Radiology Discovery of electrons and Ionization processes in 1897 (J. J Thomson) Nobel Prize in 1906 J.J. Thomson Discovery of Radioactivity (in 1896) (H. Becquerel) (Nobel in 1903) Determining the Crystal Structures (X-Ray Henri Becquerel Diffraction) in 1912 (Laue and Bragg Family): Nobel Prize in 1914 and 1915. Imaging the DNA Structure (in 1953) IN201-Analytical Instrumentation:Aug-Dec 2024 Max Von Laue The Braggs 58  X-rays X-rays are the EM radiation of exactly same nature as light but with very short wavelengths (0.5 to 2.5 angstroms). Ionizing Radiation Radiography and Radioactivity IN201-Analytical Instrumentation:Aug-Dec 2024 59  https://halas.rice.edu/unit-conversions IN201-Analytical Instrumentation:Aug-Dec 2024 60  Production of X-rays Fast moving Charged Metal Target X-rays Particle (e-) X-rays are produced when the accelerated electrons collide with the target The emission of Radiation due to the impact of electrons are manifested as X-rays X-ray is produced in X-ray (vacuum) tube Kinetic energy of the electrons on impact is given by the equation 1 e – electron charge (1.6 x 10-19 C) 𝐾𝐸 = 𝑒𝑉 = 𝑚𝑣 2 m – mass of the electron (9.11 x 10-31 kg) 2 V – Voltage across the electrodes (V) v – velocity of the electrons (m/s) X-rays : - Continuous (Bremsstrahlung) X-rays - Characteristic X-rays IN201-Analytical Instrumentation:Aug-Dec 2024 61  Cross-section schematic of X-ray production chamber X-Ray vacuum tube, Filament, Filter, Target, High Voltage, Accelerating electrons : Production of X-Rays Bremsstrahlung (Braking) Radiation: Continuous X-Ray spectra IN201-Analytical Instrumentation:Aug-Dec 2024 62 X-Rays emission spectrum IN201-Analytical Instrumentation:Aug-Dec 2024 63 Production of X-rays The X-Ray Tube IN201-Analytical Instrumentation:Aug-Dec 2024 64  Production of X-rays High voltage supply Lead Shielding Vacuum Chamber Cathode filament Anode/Target Filter 65 IN201-Analytical Instrumentation:Aug-Dec 2024  Production of X-rays Cathode Filament Metal filament (high melting point) - Electrons Thermionic emission Rate of electron production depends on the filament current More electrons/unit time More X-rays/unit time 66 IN201-Analytical Instrumentation:Aug-Dec 2024  Production of X-rays High Voltage Field Accelerates the Electrons towards the anode High Voltage Field Electrons Accelerating electrons Strength of the volage determines the kinetic energy of the electron Anode: Heavy Metal IN201-Analytical Instrumentation:Aug-Dec 2024 67  Production of X-rays Anode/Target Electron path Anode is rotated to distribute the heat An extra cooling mechanism is used to dissipate the heat generated Upon Electron impact on at Anode: electron decelerates Converts the electron KE into Heat and X-ray photons (Conversion < 1%) IN201-Analytical Instrumentation:Aug-Dec 2024 68 IN201-Analytical Instrumentation:Aug-Dec 2024 69  Production of X-rays Z = 74 Z = 47 Z = 42 IN201-Analytical Instrumentation:Aug-Dec 2024 70 Cross-section schematic of X-ray production chamber IN201-Analytical Instrumentation:Aug-Dec 2024 71 Continuous X-Radiation- Bremsstrahlung IN201-Analytical Instrumentation:Aug-Dec 2024 72  Continuous X-Radiation- Bremsstrahlung The continuous X-ray emission is due to the deceleration of the electron due to the collision with the target atoms Energy lost by the electron in this collision process is converted into X-rays (Less than 1% energy) Incoming Electron need not loose all its energy in a single collision – Multiple collisions – X-rays emitted with a distribution in Energies / Wavelengths IN201-Analytical Instrumentation:Aug-Dec 2024 73 A simplified model of the Bremsstrahlung interaction IN201-Analytical Instrumentation:Aug-Dec 2024 74  A simplified model of the Bremsstrahlung interaction Assume that there is a space, or field, surrounding the nucleus in which electrons experience the "braking" force. This field can be divided into zones – Analogy of a “Firing target” with the actual nucleus located in the center. An electron striking anywhere within the target experiences some braking action and produces an x-ray photon. Those electrons striking nearest the center are subjected to the greatest force and, therefore, lose the most energy and produce the highest energy photons. The electrons hitting in the outer zones experience weaker interactions and produce lower energy photons. The area of a given zone depends on its distance from the nucleus. Since the number of electrons hitting a given zone depends on the total area within the zone, it is obvious that the outer zones capture more electrons and create more photons. IN201-Analytical Instrumentation:Aug-Dec 2024 75 Selection of XRD tubes according to Anode Material IN201-Analytical Instrumentation:Aug-Dec 2024 76 Continuous X-rays: Spectra Pd a IN201-Analytical Instrumentation:Aug-Dec 2024 77  Continuous X-rays- Short wavelength Limit The intensity is Zero at a certain wavelength : Short Wavelength Limit (λSWL) : Electrons transfer all the KE into the photon Electron Energy = Photon Energy 𝑒𝑉 = ℎ𝜈𝑚𝑎𝑥 (Duane-Hunt equation) 12.4 ✗ 103 % 𝑐 ℎ𝑐 2 𝜆𝑆𝑊𝐿 = = 𝜈𝑚𝑎𝑥 𝑒𝑉 6.626 × 10−34 (2.998 × 10)8 𝜆𝑆𝑊𝐿 = 1.6 × 10−19 𝑉 λSWL in angstroms 12.4 × 103 Short Wavelength Limit 𝜆𝑆𝑊𝐿 = V in Volts 𝑉 IN201-Analytical Instrumentation:Aug-Dec 2024 78  Spectral distribution of continuous X-ray radiation The spectral distribution of the ‘braking’ radiation is given by Kramer formula 𝑘1 𝑖𝑍 𝜆 𝐼(𝜆) = 2 −1 𝜆 𝜆0 I : radiation intensity, £:(¾.-I k1 : an empirical constant, i : the tube current, Z : the atomic number of the target element, λ : Wavelength of the emitted X-ray λ0 : the cut-off wavelength (i.e. the wavelength at which I = 0). The Maximum intensity is given by Ulrey formula: Icont-spect = A i Z V2 A: Empirical Constant IN201-Analytical Instrumentation:Aug-Dec 2024 79  Effect of Tube Current and Accelerating Potential 𝑘1 𝑖𝑍 𝜆 𝐼(𝜆) = 2 −1 Icont-spect = A i Z V2 𝜆 𝜆0 At a given λ, radiation intensity increases proportionally with i and Z IN201-Analytical Instrumentation:Aug-Dec 2024 80 IN201-Analytical Instrumentation:Aug-Dec 2024 82 Characteristic X-ray emission IN201-Analytical Instrumentation:Aug-Dec 2024 83  Characteristic X-ray emission ❑ Incoming eˉ knocks off an electron from inner electronic sub-shells of the target atom. Ionization process governed by a probability factor called the cross-section ❑ This vacancy created in this process is filled by an electron residing in the higher electronic sub-shell X-ray with definite λ is emitted. IN201-Analytical Instrumentation:Aug-Dec 2024 84  Characteristic X-ray emission Incoming Ejected Electron Electron X-ray Emitted The emission of X-ray Vacancy filled by an Takes place ≈10-4 sec electron from a later higher Electronic sub shell Vacancy created in the inner electronic sub shell The energy of the Characteristic X-ray emitted depends on the difference in the binding energies of the electronic sub-shells between which the electron transfer takes place: hγ = EK ˜ E L IN201-Analytical Instrumentation:Aug-Dec 2024 85 EMISSION OF VARIOUS CHARACTERISTIC X-RAY LINES Line Transition Kα1 LІІІ - K Kα2 LІІ - K Kβ1 MІІІ - K Lα1 Mv - LІІІ Lα2 Miv - LІІІ IN201-Analytical Instrumentation:Aug-Dec 2024 86 Partial energy diagram showing common transitions producing X-rays. The most intense lines are indicated by the wider arrows Energy n Quantum Kseries e− levels I J states Lseries X-ray Nv 4 2 5/2 designation Ni 4 2 3/2 N v ІІІ 41 3/2 NІ N 4 1 1/2 І N 4 0 1/2 І Mv 3 2 5/2 Miv 3 2 3/2 M 3 1 3/2 M ІІІ MІ 3 1 1/2 ІM 3 0 1/2 І β4 η β6 L Log β3 β1 η α2 β series energy γ2 γ5 15 α1 β LІІ 2 1 3/2 γ3 γ1 2 ІL І 21 1/2 L І L 2 0 1/2 І LІ LІІ LІІІ α1 β3 γ3 α2 β1 γ1 K series K K 1 0 1/2 O IN201-Analytical Instrumentation:Aug-Dec 2024 87  Ionization Cross-section Gives the probability of an ionization event occurring leading to an X-ray emission. Depends on Energy of incident electron beam & electron current density. Example: Suppose the incident electron current density = 1 electron/m2/sec Typical electron energies ≈ 103eV Typical electron density ≈ 1028 The probability of ionization with this electron current ≈ 1/1028 / m2 Ionization cross-section (Ϭ), defined in Barns is б ≈ 10-28 /m2 = 1 Barn. 1 Barn =10-28 /m2 IN201-Analytical Instrumentation:Aug-Dec 2024 88 Ionization cross-section for K-shell electrons in Cu , as a function of incident electron energy. 400 Ionization Cross section 300 (Barns) 200 100 0 0 50 100 150 200 250 Energy (keV) As E ↑ б ↑ (Rapidly first , reaches a maximum at an energy corresponding to the B.E. of the K shell Correspondingly intensity of characteristic X-ray emitted ↑ with ↑ in incident electron energy. IN201-Analytical Instrumentation:Aug-Dec 2024 89  X-Ray Emission – Continuous and Characteristic Radiation Intensity of Characteristic K-line I K-line = B i (V - Vk)1.5 1 Work function, 𝑊𝐾 = m𝑣 2 2 A threshold volage is required to excite K characteristic radiation When the voltage applied to an X-ray tube increases, the Intensity of the Lines increases, but Wavelength will remain Constant IN201-Analytical Instrumentation:Aug-Dec 2024 90  Table 1 : Characteristics of Common Anode materials o Material At.# Kα (A ) Char Min Opt Advantages (keV) kV (Disadvantages) Cr 24 2.291 5.99 40 High resolution for large d-spacing particularly Organics (High attenuation in air) Fe 26 1.937 7.11 40 Most useful for Fe – rich materials where Fe fluorescence is a problem (Strongly fluorescence Cr in specimens) Cu 29 1.542 8.98 45 Best overall for most inorganic materials(Fluorescence Fe and Co Kα and these elements in specimens can be problematic) Mo 42 0.710 20.00 80 Short wavelength good for small unit cells, particularly metal alloys (Poor resolution of large d-spacings ;optimal kV exceeds capabilities of most HV power supplies.) IN201-Analytical Instrumentation:Aug-Dec 2024 91  Properties of Characteristic X-ray Spectrum There are several lines in the K-set: The strongest are Kα1, Kα2 , Kβ1 Kα1, is always stronger than Kα2 Usually only the K-lines are useful in X-Ray diffraction Hard X-rays (high energy X-rays from K shells) Soft X-rays (Lower Energy X-rays emitted from Outer Shells) IN201-Analytical Instrumentation:Aug-Dec 2024 92 Characteristic x-ray spectrum for Cu, silver and tungston Kα (29) (74) (47) Kα Kα Kβ Kβ IN201-Analytical Instrumentation:Aug-Dec 2024 93  Moseley’s law It relates the wavelength (λ) of the emitted characteristic X-ray line to the atomic number (Z) of the target element Helps in identifying the elements using X-ray spectroscopy 1 = 𝐾(𝑍 − 𝜎)2 OR 𝜐 = 𝐶(𝑍 − 𝜎) 𝜆 λ : the wavelength of the emitted X-ray.; ν: Frequency K : A constant specific to the X-ray tube and the order of diffraction. Z : the atomic number of the element. σ : A constant that depends on the type of X-ray transition (e.g., Kα- or K-β lines) IN201-Analytical Instrumentation:Aug-Dec 2024 94  Relationship between X-ray emission frequency and atomic number for Characteristic X-rays (holds good for all series – e.g. Kα1 and Lα1 lines As Z ↑ , λC↓ and νC ↑ Atomic number (Z) Henry Mosley In his early 20's, Moseley measured and plotted the x-ray frequencies for about 40 of the elements of the periodic table. IN201-Analytical Instrumentation:Aug-Dec 2024 95  Heat produced during X-ray emission Since Only a small fraction of the electronic energy is converted in X-radiation, it can be ignored and assumed that all of the electron energy is converted into heat. In a single exposure, the quantity of heat produced in the focal spot area is given by Heat (in Joule) = w kVp I. Where kVp is the peak kV value. I is the total quantity of electrons passing a point in a given time in seconds (s). w is the waveform factor; its value is determined by the waveform of the voltage applied to the X-ray tube. For a constant potential, w = 1.0; three-phase, 12 pulse, w = 0.99; three- phase, 6-pulse, w = 0.96; single-phase, 0.71. IN201-Analytical Instrumentation:Aug-Dec 2024 96  Heat produced during X-ray emission The X-ray tube heat is often expressed in terms of a special heat unit (HU); One Joule is equal to 1.4 heat unit (HU) For Single phase using w = 0.71 and joules-to-heat unit conversion factor of 1.4, The heat produced in heat units = kVp x I x s The rate at which heat is produced in a tube is equivalent to the electrical power and is given by kVp x I Heat Capacity: The amount of heat energy required to raise the temperature of the given entity by 1o Celsius It is a characteristic of the object. Heat Capacity = Heat/ Change in Temperature (ΔT). IN201-Analytical Instrumentation:Aug-Dec 2024 97  Heat capacities Energy Conversion Percentage IN201-Analytical Instrumentation:Aug-Dec 2024 98 IN201-Analytical Instrumentation:Aug-Dec 2024 100 IN201-Analytical Instrumentation:Aug-Dec 2024 101  Other Sources of X-rays - Radioactive Sources - -Synchrotron Sources (Free electron laser sources) IN201-Analytical Instrumentation:Aug-Dec 2024 102  Radioactive Sources X-rays are also produced in certain radioactive decay α , β emission process → excited nuclei → Ground State with X/ γ-ray Emission ELECTRON CAPTURE K-shell electron (captured by nucleus) → Element of lower Z X-ray ← Electronic transitions to fill the Vacancy Artificially produced Radio isotopes → mono λ X-rays : 55Fe 26 → 55Mn25 + hγ ( λ = 2.1Aº) IN201-Analytical Instrumentation:Aug-Dec 2024 103  Common Radioisotope sources of X-ray Spectroscopy source Decay Process No of Life Type of Radiation Energy keV 3 - a βֿ 12.3yrs continuum 3-10 1H Ti Ti-K X-rays 4-5 55 1 26Fe ECb 2.7yrs Mn-K Xrays 5.9 57 27Co EC 270days Fe-K Xrays 6.4 γrays 14,122,136 109 Ag-K Xrays 48Cd EC 1.3years 22 γ rays 88 125 53I EC 60days Te-K Xrays 27 γ rays 35 147 61Pm-Al βֿ 2.6years continuum 12 - 45 210 82Pb βֿ 22years Bi-L Xrays 11 γrays 47 IN201-Analytical Instrumentation:Aug-Dec 2024 104  Synchrotron Radiation – Production and Energy Range Synchrotron radiation is produced when electrons (charged particles) accelerated to relativistic velocities are caused to change direction by an electromagnet while traveling at nearly light speed. IN201-Analytical Instrumentation:Aug-Dec 2024 105  Synchrotron Radiation: Generation Synchrotron radiation (also known as magnetobremsstrahlung radiation) is EM radiation emitted when charged particles are accelerated radially, i.e., when they are subject to an acceleration perpendicular to their velocity (a ⊥ v) Any accelerated charged particle emits electromagnetic radiation with power specified by Larmor’s formula : P=⅔E⅔ˢ It implies that any charged particle radiates when it is accelerated and that the total radiated power is proportional to the square of the acceleration. The lightest charged particles (electrons, positrons) are accelerated more than relatively massive protons and heavier ions. Radiation from electrons is typically 4×106 times stronger than radiation from protons. IN201-Analytical Instrumentation:Aug-Dec 2024 106  Synchrotron Radiation: Generation Electrons are generated and accelerated in a Linac and sent to the storage ring In the presence of Magnetic field, the circulating electrons emit intense beam of Synchrotron radiation : Relativistic Process Components: 1. Bending Magnet 2. Wiggler 3. Undulator Synchrotron Storage ring 107  Synchrotron Radiation: Generation Bending Magnet: Accelerates the electrons and creates the Synchrotron Radiation: Broadband Source IN201-Analytical Instrumentation:Aug-Dec 2024 108  Synchrotron-Wiggler B-Fields in the Halbach Array A series of magnets designed to periodically laterally deflect ('wiggle') a beam of charged particles (invariably electrons or positrons) inside a storage ring of a synchrotron. These deflections create a change in acceleration which in turn produces emission of broad synchrotron radiation tangent to the curve X-ray Intensity is higher due to the contribution of many magnetic dipoles in the wiggler A wiggler has a broader spectrum of radiation (Highly in-coherent) IN201-Analytical Instrumentation:Aug-Dec 2024 109  Synchrotron Undulators 𝜆 Brightness  N2 N: number of periods ∆𝑇 = 𝑛 𝑐 Consists of a periodic structure of dipole magnets, The static magnetic field alternates along the length of the undulator with a wavelength λU Electrons traversing the periodic magnet structure are forced to undergo oscillations and thus to radiate energy Highly Intense (due to higher magnetic flux amplitude and constructive Interference) A Very Narrow band (Highly coherent due to interference) IN201-Analytical Instrumentation:Aug-Dec 2024 110  SYNCHROTRON RADIATION - Properties ❑High brightness: synchrotron radiation is extremely intense(hundreds of thousands of times higher than conventional X-ray tubes) ❑Highly collimated: High degree of angular collimation ❑Synchrotron radiation is highly polarized ❑It is emitted in very short pulses, typically less that a nanosecond(a billionth of a second) ❑Wide energy spectrum: synchrotron radiation is emitted with a wide range of energies, allowing a beam of any energy to be produced. ❑Ultra-high vacuum environment and high beam stability ❑Intense Coherent (Undulators) and Incoherent (Wiggler) X-ray beams IN201-Analytical Instrumentation:Aug-Dec 2024 111 IN201-Analytical Instrumentation:Aug-Dec 2024 112 X-ray Beam Profile – Conventional Tube And Synchrotron IN201-Analytical Instrumentation:Aug-Dec 2024 113 COMPARISON OF X-RAY SOURCES IN201-Analytical Instrumentation:Aug-Dec 2024 114 IN201-Analytical Instrumentation:Aug-Dec 2024 115 INDIAN SYNCHROTRON (INDUS II) Source RRCAT Indore 2.5GeV IN201-Analytical Instrumentation:Aug-Dec 2024 116 IN201-Analytical Instrumentation:Aug-Dec 2024 1  X-Ray Detectors ↓ ↓ Intensity Energy ◼ Photographic Films ◼ Semiconductor Detectors ◼ Gas-filled (Proportional or Geiger) Detectors ◼ Scintillation Detectors (Solid state detectors) IN201-Analytical Instrumentation:Aug-Dec 2024 2 X-RAY PHOTOGRAPHIC FILMS IN201-Analytical Instrumentation:Aug-Dec 2024 3  FILM PHOTOGRAPHY: Detection Process A typical photographic film contains tiny crystals of very slightly soluble silver halide salts such as Silver Bromide (AgBr), Silver Iodide (AgI) or Silver Chloride (AgCl) commonly referred to as "grains." The grains are suspended in a gelatin matrix and the resulting gelatin dispersion, is applied as a thin coating on a polymer base or, on a glass plate. When light or radiation of appropriate wavelength strikes one of the silver halide crystals, a series of reactions begins that produces a small amount of free silver in the grain: Chemical Reduction Process. Initially, a free bromine atom is produced when the bromide ion absorbs the photon IN201-Analytical Instrumentation:Aug-Dec 2024 4  FORMATION OF AN IMAGE Ag+Br- (crystal) + hγ (radiation) --> Ag+ + Br + e- The electron then migrates to a silver + ion, a shallow “trap” (called a sensitivity site). Ag + + e - → Ag (Chemical Reduction Process) The atom is not stable; it can decompose back into a silver ion and a free electron. Ag → Ag + + e - However, silver ion again can trap another electron if available. If this second electron remains trapped until the arrival of a second silver ion, a two- atom cluster (Ag2o) forms. This build-up of a silver cluster can continue as long as photoelectrons are available. The smallest cluster corresponding to a stable latent image speck is believed to consist of three or four silver atoms. IN201-Analytical Instrumentation:Aug-Dec 2024 5  DEVELOPMENT OF FILM The grains containing silver ions are readily reduced by chemicals referred to as "developers" forming relatively large amounts of free silver which produce a dark area in that section of the film. The developer under the same conditions does not significantly affect the unexposed grains. Ag+ ions +e- Neutral Ag atoms IN201-Analytical Instrumentation:Aug-Dec 2024 6 IN201-Analytical Instrumentation:Aug-Dec 2024 7  GAS FILLED/PROPORTIONAL DETECTORS (COUNTERS) X-rays Gas Filled volume ion pairs Number of Ion Pairs Formed The incident radiation should transfer an Energy at least equal to the Ionization Energy of least Tightly Bound electron. ( EI )min (work function) = 10 – 30 eV The Energy required to create an ion pair = W > EI  30 eV W Depends on : - Type of gas / species of gas - Type of Radiation - Energy of Incident Radiation  GAS FILLED DETECTOR (~ 200V) Ionization chamber Used air gas type: Inert gases (He, Ne, Ar, …) There are two parallel plates that are applied electric field Incident X-ray produces photoelectrons, Auger Electrons and Fluorescence X-rays: Gas atoms are Ionized IN201-Analytical Instrumentation:Aug-Dec 2024 9 The out put of a gas filled detector depends on the number of ions reaching the respective electrodes n = h / Eo “n” depends on the energy of the incident radiation; Where Eo is the energy required to create one electron – and +ve ion pair No of ions reaching the respective electrodes & consequently the output varies with the applied electric field between the cathode and the anode If the detector dimensions and the gas type are selected correctly, the efficiency of these counters approaches 100% IN201-Analytical Instrumentation:Aug-Dec 2024 10  DIFFERENT DETECTION REGIMES OF GAS COUNTER Five regimes of Detection (amplification) depending on the applied voltage Region I –Recombination Region – All ions produced by the ionization process recombine and Pulse height no ions reach the electrodes – negligible out put Region II – Ionization Region- The ions get enough energy due to the accelerating potential so that they reach the respective electrodes – n is a constant and equal to the number of ions produced by the incoming radiation Applied Voltage IN201-Analytical Instrumentation:Aug-Dec 2024 11 PROPORTIONAL REGION - SECONDARY IONIZATION BY ELECTRONS – GAS MULTIPLICATION Region III -Proportional Region- n increases rapidly due to secondary ionization – gas multiplication – Threshold field around 600-900V The Multiple Ionization (Gas amplification) Eventually leads to a Cascade or Avalanche (Townsend Avalanche) - “α” Townsend Coefficient Applied Voltage IN201-Analytical Instrumentation:Aug-Dec 2024 12  TOWNSEND AVALANCHE: CASCADING IONIZATION Though there is gas amplification and avalanche there is still a proportionality retained between the number of primary ionizations and number of electrons/ions reaching the electrodes IN201-Analytical Instrumentation:Aug-Dec 2024 13  Region IV- GEIGER REGION – Gas Amplification is enormous, and ‘n’ is independent of primary ionization Arc Discharge IN201-Analytical Instrumentation:Aug-Dec 2024 14 Ionization chamber: No Amplification Smaller Currents : 10-13 _ 10-16 A Relatively Independent of V Seldom used in X-ray Spectroscopy Proportional Counters Amplification : 500 – 10,000 Also, largely dependent of ‘V’, Gas pressure, and Chamber Geometry The Dead time : 1.25 μsec (Dissipation of space charge) Extremely high Counting rates are possible 50,000 – 2,00,000 counts /sec. IN201-Analytical Instrumentation:Aug-Dec 2024 15 Geiger Counter Amplification > 109 Larger Dead time 50 - 200μsec (Quenching agent – methane) Counting rate : 15,000 counts / min After 106 – 109 counts Quench agent to be replaced IN201-Analytical Instrumentation:Aug-Dec 2024 16  GASES MEDIUM USED IN THE GAS-COUNTER W-value is defined as the average energy lost by the incident particle per ion pair formed. Due to the competing mechanisms of the energy loss, i.e. excitation, W-value is always greater than the ionization energy IN201-Analytical Instrumentation:Aug-Dec 2024 17 GAS FILLED DETECTORS VS. SOLID STATE DETECTORS Solid State Detectors Scintillation Detector Semiconductor Detector IN201-Analytical Instrumentation:Aug-Dec 2024 18  SCINTILLATION DETECTOR: SCHEMATIC Thallium Activated NaI, Sodium Activated CsI or Bismuth Germanate (BGO): Scintillating Materials: emit fluorescence X-rays Increasing Voltages in the subsequent Dynodes (PMT) Energy Resolution is 2-3 times better than Proportional Counters Number of electrons detected are proportional to incident X-rays IN201-Analytical Instrumentation:Aug-Dec 2024 19 SCINTILLATION DETECTOR: WORKING PRINCIPLE IN201-Analytical Instrumentation:Aug-Dec 2024 20 Inorganic Scintillator: Band Structure and light emission process IN201-Analytical Instrumentation:Aug-Dec 2024 21  (NaI (Tl) ) IN201-Analytical Instrumentation:Aug-Dec 2024 22 IN201-Analytical Instrumentation:Aug-Dec 2024 23 IN201-Analytical Instrumentation:Aug-Dec 2024 24 SCINTILLATION MATERIALS: ORGANIC AND INORGANIC IN201-Analytical Instrumentation:Aug-Dec 2024 26  SEMICONDUCTOR DETECTORS Silicon detectors Germanium detectors Why semiconductor detectors? Low Ionization energy: High Signal Long mean free path: Good charge collection efficiency High Mobility: Fast Charge Collection ( 2keV) 2. Absorption effects: Photoelectric emission (> 10keV) 3. It can interact and be scattered or deflected from its original direction and deposit part of its energy.: Compton effect (> 10keV) 4. Interaction with the nuclear fields: Pair-production (> 1MeV) 5. It can interact with the matter and be completely absorbed by depositing its energy: Photo Disintegration (10MeV) IN201-Analytical Instrumentation:Aug-Dec 2024 34 TRANSMISSION/PENETRATION PROCESS IN201-Analytical Instrumentation:Aug-Dec 2024 35 TRANSMISSION/PENETRATION PROCESS IN201-Analytical Instrumentation:Aug-Dec 2024 36  ABSORPTION PROCESS Depends on the Radiation x as well as the absorbing medium X-ray Sample I I0 I (x) = I0 exp-µx µ = linear absorption Co- efficient β: Absorption index Beer-Lambert law: Absorption/Attenuation of light in a medium IN201-Analytical Instrumentation:Aug-Dec 2024 37  ABSORPTION OF X-RAYS The absorption is often expressed in terms of the mass of the material (linear absorption coefficient) encountered by the photons rather than in terms of distance. Here, the quantity that affects attenuation rate is not the total mass of an object but rather the area mass. Area mass is the amount of material contained in 1-unit surface area. The area mass is the product of material thickness and density Area Mass (g/cm2) = Thickness (cm) x Density (g/cm3). Mass Absorption Co-efficient = µ /ρ = µm IN201-Analytical Instrumentation:Aug-Dec 2024 38  Compare two pieces of material with different thicknesses and densities but the same area mass. Since both absorb the same fraction of photons, the Mass Absorption Coefficient (µ /ρ) is the same for the two materials. They do not have the same linear attenuation coefficient ( µ) values. I = I0 e-(µmρx) Mass attenuation coefficient values are actually normalized with respect to material density, and therefore do not change with changes in density. IN201-Analytical Instrumentation:Aug-Dec 2024 39 ABSORPTION DEPENDS ON THE WAVELENGTH/ENERGY OF INCIDENT RADIATION IN201-Analytical Instrumentation:Aug-Dec 2024 40 ABSORPTION DEPENDS ON THE WAVELENGTH/ENERGY OF INCIDENT RADIATION Absorption generally increases with increase in λ. Longer λ (less Energy) has less penetration & are more readily absorbed 𝜇 = 𝑘𝜆3 𝑍 3 𝜌 k: Constant Z: Atomic number of absorber 1 erg = 10-7 Joules IN201-Analytical Instrumentation:Aug-Dec 2024 41  WORKING PRINCIPLE OF X-RAY FILTERS ✓ Cut-down the Kβ characteristic peak of Copper ✓ Not a 100% filtering: Will have a fraction of other X-ray energies IN201-Analytical Instrumentation:Aug-Dec 2024 42 CHOOSING THE IDEAL FILTER MATERIAL FOR THE X-RAY TRAGET (Z) (Z) (42) (40) (29) (28) (27) (26) (26) (25) (24) (23) IN201-Analytical Instrumentation:Aug-Dec 2024 43 MULTIPLE THRESHOLDS Line Transition Kα1 LІІІ - K Kα2 LІІ - K Kβ1 MІІІ - K Lα1 Mv - LІІІ Lα2 Miv - LІІІ IN201-Analytical Instrumentation:Aug-Dec 2024 44  EMISSION PROCESS The Absorption of X-ray at various thresholds lead to (a) Emission of photoelectrons (& Compton Scattering) (b) Emission of Characteristic (Fluorescent X-rays) (c) Emission of Auger Electrons eֿ =(E0-E) e (KLL Auger) M E (BEK ~ BEL ) –EBEL2 L X-Ray Photon E0 Ch. x-ray E (BEK ~ BEL ) K E (BE ) k 45 IN201-Analytical Instrumentation:Aug-Dec 2024  PHOTOELECTRON (PE) EMISSION The X-ray photon transfers all its energy to an electron located in one of the atomic shells. The electron is ejected from the atom having the energy (E-E0); E0 = work function Photoelectric interactions usually occur with electrons that are firmly bound to the atom, that is, those with a relatively high binding energy. Photoelectric interactions are most probable when the electron binding energy is only slightly less than the energy of the photon. IN201-Analytical Instrumentation:Aug-Dec 2024 46 If the binding energy is more than the energy of the photon, photoelectron emission cannot occur. This Emission is possible only when the photon has sufficient energy to overcome the binding energy and remove the electron from the atom. PE Emission can be succeeded by either fluorescent X-ray emission or Auger X-ray emission IN201-Analytical Instrumentation:Aug-Dec 2024 47 X-RAY AND AUGER ELECTRON EMISSION Characteristic X-ray Emission IN201-Analytical Instrumentation:Aug-Dec 2024 48 X-RAY AND AUGER ELECTRON EMISSION IN201-Analytical Instrumentation:Aug-Dec 2024 49 IN201-Analytical Instrumentation:Aug-Dec 2024 50  SCATTERING OF X-RAYS Scattering is a processes that can happen when a photon impinges on an atom/ molecule. The incoming X-ray photons are scattered by the orbital electrons. The scattering can be an elastic scattering or an inelastic scattering. whereas the inelastic scattering occurs with change in photon energy. IN201-Analytical Instrumentation:Aug-Dec 2024 51  SCATTERING OF X-RAYS Elastic Scattering: Occurs with no change in photon energy (Coherent scattering) Inelastic scattering: Both Energy and Momentum of the scattered photon change. i. Compton Scattering: A portion of the energy is absorbed, and the photon is deflected, with reduced energy. IN201-Analytical Instrumentation:Aug-Dec 2024 52  RAYLEIGH SCATTERING (ELASTIC) In Rayleigh Scattering, the photon penetrates into a medium composed of particles whose sizes are much smaller than the wavelength of the incident photon. In this scattering process, the energy (and therefore the wavelength) of the incident photon is conserved and only its direction is changed. The scattering intensity is proportional to the fourth power of the reciprocal wavelength of the incident photon IN201-Analytical Instrumentation:Aug-Dec 2024 53  COMPTON SCATTERING (INELASTIC) The Electron recoils at an angle φ Photon scatters in different direction with angle  Both energy and momentum are changed IN201-Analytical Instrumentation:Aug-Dec 2024 54  COMPTON SCATTERING (INELASTIC) A Compton interaction is one in which only a portion of the energy is absorbed, and the photon is deflected, with reduced energy. This photon leaves the site of the interaction in a direction different from that of the original photon (at angle θ). Because of the change in photon direction, this type of interaction is classified as a scattering process. It depends on the wavelength of photons, and independent of atomic number. In effect, a portion of the incident radiation "bounces off' or is scattered by the material. IN201-Analytical Instrumentation:Aug-Dec 2024 55 PHOTO ELECTRIC EMISSION & COMPTON SCATTERING Depends on X-ray energy and Atomic number Depends on X-ray energy And independent of Atomic number IN201-Analytical Instrumentation:Aug-Dec 2024 56  PAIR PRODUCTION Pair production is a photon-matter interaction that can occur only with photons with energies in excess of 1 MeV. In a pair-production interaction, the photon interacts with the nucleus. The interaction produces a pair of particles, an electron and a positively charged positron. These two particles have the same mass, each equivalent to a rest mass energy of 0.51 MeV. IN201-Analytical Instrumentation:Aug-Dec 2024 57 Photo Electric Emission, Compton Scattering and Pair Production e.g: 𝟐𝟏𝑫 + 𝐗 𝐨𝐫 𝜸 𝐫𝐚𝐲𝐬 → 𝟏𝟏𝑯 + 𝒏 IN201-Analytical Instrumentation:Aug-Dec 2024 58 IN201-Analytical Instrumentation:Aug-Dec 2024 59 INTERACTION X-RAYS – MATTER - SUMMARY IN201-Analytical Instrumentation:Aug-Dec 2024 60  INTERACTION X-RAYS – MATTER - SUMMARY Pair production h > 1MeV Photon disintegration Photoelectric absorption h > 10MeV h h MATTER Transmission X-rays Scattering h'  h h Compton Thomson Decay processes Rayleigh h f Fluorescence Auger electrons Primary competing processes and some radiative and non-radiative decay processes IN201-Analytical Instrumentation:Aug-Dec 2024 61 IN201-Analytical Instrumentation:Aug-Dec 2024 1  CRYSTAL STRUCTURE DETERMINATION USING X-RAY DIFFRACTION What is Diffraction? What are Crystals? What is X-ray Diffraction? Max Von Laue William Henry Bragg and William Lawrence Bragg X-Ray Diffraction Instrumentation IN201-Analytical Instrumentation:Aug-Dec 2024 2  DIFFRACTION Laser diffraction pattern from a single slit The process by which a beam of light is bent/spread out as a result of passing through a narrow aperture or across an edge. The slit behaves as a secondary source of light from which secondary waves emerge. This is typically accompanied by interference between the secondary wave forms produced. IN201-Analytical Instrumentation:Aug-Dec 2024 3 DIFFRACTION Condition for Diffraction a sin(θ) = m  ; m = 1, 2... λ: Wavelength of light a: Slit width Intensity of Diffraction IN201-Analytical Instrumentation:Aug-Dec 2024 4 X-ray Diffraction is the consequence of scattering/reflection of X-rays from the atomic planes of a crystals and their subsequent interference IN201-Analytical Instrumentation:Aug-Dec 2024 5 What are crystals? Crystals are Solids with a periodic arrangements of atoms. What is periodicity? Periodicity (or symmetry) is a quality of occurring at regular intervals or periods. It can occur in Time or space IN201-Analytical Instrumentation:Aug-Dec 2024 6  CONSEQUENCE OF PERIODICITY Reduction of a macroscopic crystal into a unit cell – a small building block which dictates the overall symmetry of the crystal Each unit cell is characterized by six-unit cell parameters (3 length and 3 angle) a ,b, c and α, β, γ 7 crystal classes based on a ,b, c and α, β, γ IN201-Analytical Instrumentation:Aug-Dec 2024 7  7 Crystal Classes Triclinic, Monoclinic, Orthorhombic, tetragonal, Cubic, Trigonal & Hexagonal. IN201-Analytical Instrumentation:Aug-Dec 2024 8  BRAVAIS LATTICES Possible arrangements of the atoms in the crystal: 14 Bravais Lattices in 3D Crystals. IN201-Analytical Instrumentation:Aug-Dec 2024 9 CRYSTALLOGRAPHIC PLANES: DESIGNATING VARIOUS PLANES IN CRYSTALS MILLER INDICES (hkl) 1. Identify the plane intercepts on the x, y and z-axes. 2. Specify intercepts in fractional coordinates. 3. Take the reciprocals of the intercepts. 4. Clear Fractions & Reduce to lowest Terms This plane is parallel to x and z axes – therefore the intercept is infinity. It has ½ unit intercept along y axis. Therefore the intercepts are ∞, ½, ∞. The reciprocals are 1/∞, 2, 1/∞ (0,2,0) IN201-Analytical Instrumentation:Aug-Dec 2024 10  Planes in a crystal: denoted in terms of the Miller indices (hkl) which are the inverse intercepts that the planes make with the crystallographic axes If a plane is parallel to an axis, the intercept is taken to be at infinity (∞); the reciprocal of infinity is 1/∞ = 0 IN201-Analytical Instrumentation:Aug-Dec 2024 11 TYPES OF SOLIDS IN201-Analytical Instrumentation:Aug-Dec 2024 12  HOW CRYSTALS DIFFRACT X-RAYS? Crystals have Periodic Distribution of atoms Behaves like a 3-d grating, diffracting X- rays just as a diffraction grating diffracts light. Carries Important information regarding the crystallography of material Approx. 1% of intensity in the diffracted beam All the scattering events will take place: Special circumstances/ conditions lead to diffraction effects IN201-Analytical Instrumentation:Aug-Dec 2024 13  X-RAY DIFFRACTION : X-RAY CRYSTALLOGRAPHY →Scattering of X-rays by atoms and subsequent interference of Scattered X-rays → Scattering of X-rays by atoms electrons nucleus → Scattering by a row of atoms → Scattering by a set of planes Diffraction & Bragg’s Law IN201-Analytical Instrumentation:Aug- 14 Dec 2024 X-RAY DIFFRACTION X-Rays d IN201-Analytical Instrumentation:Aug-Dec 2024 15 X-RAY DIFFRACTION: SET OF PLANES X-Rays X-Rays d IN201-Analytical Instrumentation:Aug-Dec 2024 16 X-RAY DIFFRACTION: SET OF PLANES X-Rays X-Rays d Path Difference: ML + LN = d sin + d sin = 2d sin IN201-Analytical Instrumentation:Aug-Dec 2024 17 Condition for Diffraction to occur Scattered rays 1’ and 2’ will be completely in phase if the path difference is equal to integer multiple of wavelengths i.e. Path Difference = nλ, n = 1, 2, 3,… 2d sin = nλ Bragg’s condition for Diffraction (Bragg’s Law) Geometrical facts for Bragg’s law: 1. The incident beam, the normal to the diffraction plane, and the diffracted beam are always coplanar 2. The angle between the diffracted beams and the transmitted beam is always 2. This is known as the diffraction angle. It is this angle which is usually measured experimentally. IN201-Analytical Instrumentation:Aug-Dec 2024 18  X-RAY DIFFRACTION: A ROW OF ATOMS d Path difference of rays 1-1’ and 1a-1a’ is equal to QK – PR = PK cos - PK cos = 0 The diffracted X-rays by atoms in the same plane have the same phase and mutually add-up to the diffraction intensity IN201-Analytical Instrumentation:Aug-Dec 2024 19  APPLICATIONS OF X-RAY DIFFRACTION X-Ray = Peak + Peak → Crystal structure determination Diffraction Positio Intensiti n es → Estimation of lattice parameters → Crystallite size determination Crystal = Lattice + Atoms Position → Identification of unknown materials. Structure s → Film thickness determination, etc. IN201-Analytical Instrumentation:Aug-Dec 2024 20 INTERACTION OF X-RAY WITH MATERIAL IN201-Analytical Instrumentation:Aug-Dec 2024 21 INTENSITY OF THE SCATTERED X-RAYS Scattering by a crystal A Electron Scattering by individual electrons Scattering by an atom (group of electrons) - B Atom Atomic scattering factor (f) Group of C Atoms Scattering by the Unit cell - Structure Factor F IN201-Analytical Instrumentation:Aug- 22 Dec 2024  THOMSON INTENSITY FORMULA: Thomson Scattering The total intensity of the coherently scattered X-rays is given by Thomson formula 𝐾 = 𝐼0 2 cos 2 (2𝜃) (Polarized X-ray light) 𝑟 𝐾 = 𝐼0 2 (1 + cos 2 (2𝜃)) 2𝑟 (Unpolarized incident X-ray light) 2 = diffraction angle IN201-Analytical Instrumentation:Aug-Dec 2024 23 THE SCATTERING POWER OF AN ATOM The atomic scattering factor : Out of phase f = atomic scattering factor = efficiency of scattering in a particular direction In phase IN201-Analytical Instrumentation:Aug-Dec 2024 24  THE SCATTERING POWER OF AN ATOM. The atomic scattering factor : Out of phase f = atomic scattering factor = efficiency of scattering in a particular direction In phase ◼ The total scattering from an atom is the sum scattered by all the electrons, in the forward direction. ◼ In other directions, electrons at different positions around nucleus scatter waves in out-of phase which interfere with each other with the net amplitude of the wave less than that of the wave scattered in Forward direction. ◼ Intensity scattered is strongly dependent on scattering angle θ “f” is maximum at the forward direction, corresponds to all the waves scattered are in phase; “fmax” = total number of electrons in an atom (Z, atomic number) IN201-Analytical Instrumentation:Aug-Dec 2024 25  scattering factor of different atoms * For O, it starts at 8 and decreases thereafter. * At zero scattering angle all 8 electrons of oxygen atom scatter in phase As sin(θ/λ) increases the scattering from all 8 electrons become progressively out of phase. Similarly for carbon and hydrogen the atomic scattering curves start at 6 and 1, respectively the number of electrons for C and H atoms. For iron, the curve starts at 26, corresponding to 26 electrons. The graph shown is for Fe2+ which represents a cationic state of Fe in which it has lost 2 electrons,; therefore f for Fe2+ starts at 24. IN201-Analytical Instrumentation:Aug-Dec 2024 26  INTENSITY OF X-RAY SCATTERED - THE CRYSTAL STRUCTURE FACTOR Amplitude of X−rays scattered by all the atoms in a unit cell F= Amplitude of X−rays scattered by a single electron fn : atomic scattering factor (Electronic property of the atom); n: number of atoms; (h, k, l) : Miller Indices (u, v, w) : Fractional coordinates: Structural property (position of atoms) 𝑛𝜋𝑖 h, k, l are integers 𝑒 = −1 𝑛 for 𝑛 = 1, 2, 3, … Fhkl : Real F2 : Intensity For a single atom (primitive cubic), (u,v,w) = (0,0,0)  F = f  intensity F2 = f2 IN201-Analytical Instrumentation:Aug-Dec 2024 27  THE STRUCTURE FACTOR - Example The fractional coordinates for atoms position (0,0,0) and ( ½ , ½, 0) ℎ 𝑘 2𝜋𝑖( 2 +2 +0) 𝐹=𝑓 𝑒 2𝜋𝑖 (0) +𝑓𝑒 𝐹 = 𝑓(1 + 𝑒 𝜋𝑖 ℎ+𝑘 ) If h and k are both even or both odd, then (h+k): even (unmixed)  F = 2f and F2 = 4f2 If h is odd and k is even or visa versa, then (h+k): odd (mixed)  F = 0 and F2 = 0 Inferences: The l-index has no contribution to the structure factor/intensity Reflections from (h,k,l) planes such as (1,1,1), (1,1,2), (1,1,3) and (0,2,1), (0,2,2), (0,2,3) all have same value of F and hence same scattering intensity Reflections from (h,k,l) planes such as (0,1,1), (0,1,2), (0,1,3) and (1,0,1), (1,0,2), (1,0,3) all have zero structure factor and hence are systematically absent IN201-Analytical Instrumentation:Aug-Dec 2024 28  FACTORS AFFECTING THE RELATIVE INTENSITY OF BRAGG REFLECTIONS Structure factor (F) : Depends on the position of the atoms in crystal Polarization factor (): Arises because of the X-rays are unpolarized (so different intensity of scattered beams in different direction) Temperature factor : Change in temperature alters the periodicity of the Crystal Absorption factor (A): Attenuation of X-rays in the diffracted path Multiplicity Factor (P) and Lorentz factor : The diffracted intensity also has appreciable contribution from the nearly parallel atomic planes OR nearby Bragg angles (Angular dispersion) : Results in the finite Linewidth of the intensity peak: Integrated Intensity (Area under the peak) Crystal Sizes and Strains (Nonuniform crystal sizes and uneven stress contribute to the broadening of linewidth) IN201-Analytical Instrumentation:Aug-Dec 2024 29  X-Ray Diffraction Methods Laue Rotating Crystal Powder Orientation Lattice constant Lattice Parameters Single Crystal Single Crystal Polycrystal (powdered) Polychromatic Beam Monochromatic Beam Monochromatic Beam Fixed Angle Variable Angle Variable Angle IN201-Analytical Instrumentation:Aug-Dec 2024 30 SINGLE CRYSTAL DIFFRACTION – POLYCHROMATIC AND MONOCHROMATIC X-RAYS Rotating Crystal Laue Diffraction method method IN201-Analytical Instrumentation:Aug-Dec 2024 31 LAUE DIFFRACTION METHODS: Transmission Method of Laue diffraction (Schematic) IN201-Analytical Instrumentation:Aug-Dec 2024 32  TRANSMISSION LAUE METHOD Continuous Polychromatic wavelengths are required to satisfy the Bragg’s condition (Since the crystal orientation IS FIXED) 2d sin = nλ The crystal material should be thin for the Transmission mode IN201-Analytical Instrumentation:Aug-Dec 2024 33 BACK-REFLECTION LAUE METHOD IN201-Analytical Instrumentation:Aug-Dec 2024 34 BACK-REFLECTION LAUE METHOD For measurements of thick crystals IN201-Analytical Instrumentation:Aug-Dec 2024 35  SYMMETRY OF THE DIFFRACTED SPOTS Conical Shape Hyperbola shape IN201-Analytical Instrumentation:Aug-Dec 2024 36  TRANSMITTED DIFFRACTED IMAGE The diffraction planes (parallel to each other) in the crystal form a Zone: Laue Diffractions from planes of the same zone all lie on the surface of an imaginary cone whose axis is the zone axis. They emit the diffracted radiation in the Conical shape on the Photographic Film IN201-Analytical Instrumentation:Aug-Dec 2024 37  BACK-REFLECTED DIFFRACTED IMAGE The interaction of the conical emission on the photographic plate form the Hyperbolic curves IN201-Analytical Instrumentation:Aug-Dec 2024