Summary of Difracción de rayos-X | | UPV

Summary of "Difracción de rayos-X | UPV"

This video explains the fundamental principles and applications of X-ray Diffraction (XRD), a widely used technique for studying the crystalline structure of materials. The main focus is on understanding Bragg’s Law, interpreting diffractograms, and analyzing crystal structures using XRD data.

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Main Ideas and Concepts

• Introduction to X-ray Diffraction (XRD):
  XRD is a technique where X-rays are incident on a material’s surface, and the intensity of reflected X-rays is measured at different angles to study the material’s crystalline structure.
• Bragg’s Law:
  • Developed independently by Lawrence Bragg and his son William Bragg, and also Victor Walf.
  • It relates the wavelength of incident X-rays, the angle of incidence, and the spacing between atomic planes in a crystal.
  • Formula:
    n λ = 2 d sin θ
    where:
    
    • n = integer (order of diffraction)
    • λ = wavelength of X-rays
    • d = distance between atomic planes
    • θ = angle of incidence
  • Constructive interference (diffraction peaks) occurs when the path difference between waves reflected from consecutive planes equals an integer multiple of the wavelength.
• XRD Measurement and Diffractogram:
  • A diffractogram plots intensity (y-axis) vs. 2θ angle (x-axis).
  • Each peak corresponds to a set of crystal planes fulfilling Bragg’s Law.
  • Peak positions and intensities provide information about the crystal structure.
• Miller Indices and Diffraction Peaks:
  • Miller Indices (hkl) identify crystallographic planes.
  • Not all planes produce peaks; selection rules depend on the crystal structure.
  • For example:
    • Body-Centered Cubic (BCC): Only planes where the sum of Miller Indices is even produce peaks.
    • Face-Centered Cubic (FCC): Only planes where all Miller Indices are all even or all odd produce peaks.
• Relation Between Interplanar Distance and Lattice Parameter:
  • For cubic crystals:
    d = a / √(h² + k² + l²)
    where a is the lattice parameter (cell edge length).
• Example Problem:
  • Given a cubic crystal and X-ray wavelength (λ = 0.154 nm), determine lattice parameter and crystal structure.
  • Use measured 2θ angles from diffractogram peaks.
  • Assign Miller Indices based on crystal structure rules (BCC vs FCC).
  • Calculate interplanar distances and verify assumptions by comparing calculated and observed peak angles.
  • Conclude the structure (BCC in the example).
• Clarifications on Diffraction Concept:
  • Although explained as reflection for simplicity, the phenomenon is actually diffraction caused by atomic planes acting as scattering centers.
  • Simulations show diffraction peaks matching Bragg’s Law predictions.
• Handling Non-Parallel Planes:
  • If crystal planes are not parallel to the sample surface, no peak appears in the described setup.
  • Solution: use powdered samples so that some crystallites have planes oriented properly.
  • Rotating the sample during measurement increases the chance of detecting all possible diffraction peaks.

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Methodology / Step-by-step Instructions for XRD Analysis

1. Set up XRD experiment:
   • Direct X-rays with known wavelength λ onto the material surface.
   • Measure intensity of reflected/diffracted rays as a function of angle 2θ.
2. Record Diffractogram:
   • Plot intensity vs. 2θ.
   • Identify peaks corresponding to diffraction from specific atomic planes.
3. Assign Miller Indices to Peaks:
   • Use crystal structure rules (BCC, FCC) to determine which planes produce peaks.
   • Assign Miller Indices (hkl) to each peak based on order and selection rules.
4. Calculate Interplanar Distances:
   • Use Bragg’s Law for each peak:
     d = (n λ) / (2 sin θ)
5. Calculate Lattice Parameter a:
   • For cubic structures:
     a = d × √(h² + k² + l²)
6. Verify Crystal Structure:
   • Compare calculated angles and lattice parameters with experimental data.
   • Confirm or refute assumed crystal structure.

Notable Quotes

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