Single crystal XRD

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Single crystal XRD. Energy as a function of wavelength. X-rays – High energy, highly penetrative electromagnetic radiation Energy E = h n = hc / λ Because n = c/ λ is the frequency c is the speed of light in a vacuum λ is the wavelength h is Planck’s constant
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Single crystal XRDEnergy as a function of wavelength
  • X-rays – High energy, highly penetrative electromagnetic radiation
  • Energy E = hn = hc/λ
  • Because n = c/λ
  • is the frequency
  • c is the speed of light in a vacuum
  • λ is the wavelength
  • h is Planck’s constant
  • λ(X-rays) = 0.02-100Å (avg. ~1 Å)
  • λ(visible light) = 4000-7200Å
  • As λgets smaller, energy E gets bigger.Powder X-ray Diffraction
  • When the geometry of the incident X-rays impinging the sample satisfies the Bragg Equation, constructive interference occurs and a peak in intensity occurs. The powder improves the chance that all possible planes are sampled. The sample rotates through angles θ while the detector counts photons.
  • Kb would make confusing double peaks
  • The Copper anode makes two strong peaks, Ka and Kb. The Kb would cause confusing double peaks, so we filter it out with a Nickel filter.
  • Calculations
  • Recall last time we had a homework problem
  • A strong peak is recorded at a 2q = 28.29 degrees. Calculate d using Bragg’s Law. Assume a l = Ka for copper of 1.54 Å. and use n=1
  • Hint: 2q is given, you need q.
  • a. 1.625 angstromsb. 3.15 angstromsWe used Braggs Equation nλ = 2d sin θInstrument Plots
  • Here is a typical plot with a strong reflection at
  • 2q = 28.29. Lets look at the other reflections
  • The next stronger peak
  • There is another reflection at
  • 2q = 47.12. Calculate d. nλ = 2d sin θ
  • The next stronger peak
  • There is another reflection at
  • 2q = 55.74. Calculate d. nλ = 2d sin θ
  • Identification
  • A mineral with d - spacings of 3.15, 1.93, 1.65
  • is Fluorite, CaF2After we have the d-spacings, we want to calculate the dimensions of the unit cell, and decide which planes are giving strong reflections. This will allow us to check our model building ideas.Calculating Unit Cell Size
  • A formula exists for calculating the dimensions of the unit cell for each crystal system.
  • For Isometric crystals such as Fluorite or Halite, the formula is simple
  • a2 = d2 (h2 + k2 + l2) where the (hkl) are the Miller indices
  • Let’s try it with Halite, where the XRD reports d = 2.8, 1.98, 1.62, 1.404
  • Halite NaCld d2x (h2 + k2 + l2) for the zones zones[100] [110] [111] [200] [210] [211]sum of squares 1 2 3 4 5 62.8 7.847.84 15.08 23.52 31.36 39.20 47.041.98 3.923.927.84 11.76 15.68 19.6 23.521.62 2.622.62 5.24 7.86 10.48 13.1 15.72 1.40 1.971.97 3.96 5.94 7.86 9.9 11.88 Discussion: which is a2 ?Which zones made which reflections?Homework and Lab
  • Now complete the last question on HW8-9, then do the lab using your data printouts from your unknown.
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