Crystallography, diffraction, identifying the pure element

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SUMMARY

The discussion focuses on identifying a pure element from a crystalline sample with a cubic lattice using X-ray diffraction data. The relevant equations include Bragg's Law (n λ = 2dhklsin θ) and the relationship between interplanar spacing and lattice parameters (d = a/√(h²+k²+l²)). Distances from Bragg peaks provided are d1 = 0.2037 nm, d2 = 0.1746 nm, and d3 = 0.1244 nm, which can be used to determine the lattice type (FCC or BCC) and subsequently identify the element. Resources such as periodic tables of elements and X-ray diffraction basics are recommended for further assistance.

PREREQUISITES
  • Understanding of cubic lattice structures (FCC and BCC)
  • Familiarity with X-ray diffraction principles
  • Knowledge of Bragg's Law and its application
  • Ability to interpret interplanar spacing calculations
NEXT STEPS
  • Research the properties of elements with FCC and BCC structures
  • Learn how to calculate interplanar distances for various crystal systems
  • Explore the use of X-ray diffraction in material identification
  • Study the periodic table of elements for lattice parameters and atomic radii
USEFUL FOR

Students in materials science, crystallographers, and researchers involved in solid-state chemistry who are looking to identify elements through X-ray diffraction techniques.

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Homework Statement


The only things you know about the sample are: (i) it has some kind of cubic lattice, and (ii) it is a pure element. Identify the element in the crystalline sample.
SC: R = 0.5a
FCC: R = 0.25a√2
BCC: R = 0.25a√3

Distances from Bragg peaks:
d1 = 0.2037 nm
d2 = 0.1746 nm
d3 = 0.1244 nm

Homework Equations


n λ = 2dhklsin θ

d = a/√(h2+k2+l2)

The Attempt at a Solution


Assuming the above is correct, I'm stuck.
I think I need a table or something of each element. Extra
Related questions
Related complete problems
  • https://ocw.mit.edu/courses/materials-science-and-engineering/3-091sc-introduction-to-solid-state-chemistry-fall-2010/crystalline-materials/self-assessment-crystalline-materials/MIT3_091SCF09_sa4_supp_sol.pdf
  • https://ocw.mit.edu/courses/materials-science-and-engineering/3-091sc-introduction-to-solid-state-chemistry-fall-2010/crystalline-materials/16-crystallographic-notation-x-rays/MIT3_091SCF09_hw16_sol.pdf
 
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