X-ray diffraction (XRD) is a powerful analytical technique used for determining the atomic arrangement and molecular structure of a crystal. X - RAY DIFFRACTOMETER P OWDER CRYSTALLINE AMORPHOUS
Why x-ray ? X-rays are a form of electromagnetic radiation with high energy and short wavelengths. X-rays have the ability to penetrate materials and interact with the electrons in atoms. Wilhelm Conrad Roentgen
Diffraction: - Diffraction is the bending of waves as they pass through an aperture or around obstacles. - X-ray diffraction occurs when X-rays encounter a crystalline material, leading to constructive and destructive interference.
Principle XRD is based on the interaction between X-rays and electron clouds of atoms. THE BRAGG EQUATION is crucial here, describing how X-rays are diffracted by crystal lattice planes. When the X-ray is incident onto a crystal surface, its angle of incidence, θ , will reflect with the same angle of scattering, θ. And, when the path difference, d is equal to a whole number, n , of wavelength, λ , constructive interference will occur. CONSTRUCTIVE INTERFERENCE DESTRUCTIVE INTERFERENCE λ d
P R Q S Derivation of Braggs law Lets consider, PQ is first plain surface of crystal & RS is second surface. Surface 1 Surface 2
θ θ B A P R Q S Lets consider, PQ is first plain surface of crystal & RS is second surface. Two parallel beam (AX & BO) of X-rays incident on plain surface with angle ‘ θ ’. O X ∠AXR = ∠ BOP d Incident beam Θ : angle between incident ray and lattice planes d : Distance between successive crystal lattice planes
θ θ θ θ O B A C D X P R Q S Lets consider, PQ is first plain surface of crystal & RS is second surface. Now, parallel beam scatter from the point of incidence with angle ‘ θ ’. ∠AXR = ∠ DXS ∠BOP = ∠ COQ d ∠AXR = ∠ BOP Incident beam diffracted beam
θ θ θ O B A C D X P R Q S E F Lets consider, PQ is first plain surface of crystal & RS is second surface. Now, parallel beam scatter from the point of incidence with angle ‘ θ ’. AE = BO , But second beam travels extra Extra travel = EX + XF As per constructive interference, extra path travelled is integral multiple of the waveleanth . So, Extra travel = n λ EX + XF = n λ 2EX = n λ as (EX = XF) ∠BOE = 90° d Incident beam diffracted beam
θ θ θ (90- θ ) O B A C D X P R Q S E F EX + XF = n λ 2EX = n λ ∠BOE = 90° i.e. ∠POE = (90°- θ ) d eq.01 Lets consider, PQ is first plain surface of crystal & RS is second surface. Now, parallel beam scatter from the point of incidence with angle ‘ θ ’. Incident beam diffracted beam
θ θ θ O B A C D X P R Q S E F ∠BOE = 90° i.e. ∠POE = (90°- θ ) ∠POX = 90° d Lets consider, PQ is first plain surface of crystal & RS is second surface. Now, parallel beam scatter from the point of incidence with angle ‘ θ ’. EX + XF = n λ 2EX = n λ eq.01
θ θ θ θ θ O B A C D X P R Q S E F i.e. ∠EOX = θ ∠POX = 90° d Lets consider, PQ is first plain surface of crystal & RS is second surface. Now, parallel beam scatter from the point of incidence with angle ‘ θ ’. EX + XF = n λ 2EX = n λ eq.01 Incident beam diffracted beam
θ θ θ θ θ O B A C D X P R Q S E F IN △ EOX, d , (OX = d) Lets consider, PQ is first plain surface of crystal & RS is second surface. Now, parallel beam scatter from the point of incidence with angle ‘ θ ’. EX + XF = n λ 2EX = n λ eq.01 EX = d sin θ eq.02 ∠EOX = θ Incident beam diffracted beam
θ θ θ θ θ O B A C D X P R Q S E F d Lets consider, PQ is first plain surface of crystal & RS is second surface. Now, parallel beam scatter from the point of incidence with angle ‘ θ ’. 2EX = n λ eq.01 EX = d sin θ eq.02 ∠EOX = θ Substitute eq.02 in eq.01 2d sin θ = n λ BRAGG’S LAW EXPRESSION Incident beam diffracted beam
Instrumentation and Working of XRD Instrument: - XRD instruments include X-ray sources, monochromators, sample stages, and detectors. - They operate by measuring the intensity of diffracted X-rays at various angles. G oniometer - It measures an angle or permits the rotation of an object to a definite position. Specimen Holder THE BRAGG-BRENTANO GEOMETRY
INSTRUMENTATION AND WORKING OF XRD INSTRUMENT: DETECTORS: Photographic method Laue method Counter methods Geiger-Muller tube counter Proportional counter Scintillation detector Semi conductor detector Laue Method Scintillation Detector Geiger-Muller tube counter
XRD graph interpretition Sharp peak Broad peak
Peak Intensity Peak Position Qualitative Phase Analysis (Identification of Phases) This involves comparing the X-ray pattern of an unknown sample with patterns of known reference materials. Computer-aided comparisons use data like 2θ diffraction angles and d-spacings. Organic crystals are typically analyzed in a 2θ range up to 30°. Reference peak Sample peak
ERRORS in Qualitative phase analysis Sample displacement - Misalignment of sample.
TiO 2 defract X ray more efficiently so it has more intense peak Intensity of peak cannot define the amount of phase present. Its need proper calibration Phase analysis of Mixture of titanium oxide and Aluminium oxide by comparision with database
Quantitative Phase Analysis If a sample contains multiple phases, quantitative analysis determines the percentage of each phase. This can be done by comparing integrated intensities or peak heights with reference materials. External standard – Diffraction intensity of a phase in a mixture compare against the diffraction intensity of a pure phase. Internal standard- Diffraction intensity of a phase in sample is compare against the pure phase which is spiked in sample in known proportion. Rietveild refinement- instead of focusing particular peaks , whole diffraction pattern must take under consideration for the interpretation.
Applications in Pharmaceuticals : - XRD is used to identify polymorphism in drug compounds. - Different polymorphs have distinct XRD patterns, helping in drug development and quality control. Polymorphism is the ability of solid materials to exist in two or more crystalline forms with different arrangements or conformations of the constituents in the crystal lattice. P olymorphic forms affects Dissolution Solubility Chemical nature Physical stability Flowability Hygroscopicity D rug efficacy hampered B ioavailability compromised Toxicity may occur
XRD can detect different polymorphs based on their unique diffraction patterns. Small changes in the X-ray powder patterns can imply the presence of a new polymorph such as, The appearance of new peak(s), Additional shoulders or Shifts in the peak position