Material Science- x-ray diffraction and metal densities

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SUMMARY

The discussion focuses on calculating the density of a metal with a Body-Centered Cubic (BCC) crystal structure and an atomic weight of 92.91 using X-ray diffraction data. The wavelength of the monochromatic X-radiation is 0.14 nm, and the angle of diffraction for the (211) planes is 41.148° for first-order reflection. Key equations include the relationship between lattice parameter 'a', atomic radius 'R', and the density formula involving the number of atoms 'n', area 'A', volume 'V', and Avogadro's number 'N'. The user seeks assistance in determining the radius needed to compute the lattice parameter 'a' for density calculation.

PREREQUISITES
  • Understanding of Body-Centered Cubic (BCC) crystal structures
  • Familiarity with X-ray diffraction principles
  • Knowledge of the density formula in crystallography
  • Ability to convert angles from degrees to radians
NEXT STEPS
  • Learn how to calculate atomic radius from atomic weight for BCC metals
  • Study the derivation of the density formula in crystallography
  • Explore the use of the sin function in diffraction calculations
  • Research the significance of Miller indices in X-ray diffraction
USEFUL FOR

This discussion is beneficial for students in materials science, physicists studying crystallography, and engineers involved in metal properties and applications.

maiad
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Homework Statement



Consider a metal with an BCC crystal structure and atomic weight 92.91. When monochromatic x-radiation having a wavelength of 0.14 nm is used, the angle of diffraction (2*theta) for the (211) set of planes in this metal occurs at 41.148 ° (first-order reflection).


Compute the density of this metal in g/cm^3


The sin function requires input in radians.


Use decimal notation, digits after decimal: 2

Homework Equations



a=4R/sqrt(3)

p=n*A/V*N

n*lamba=2d(hkl)sin(theta)

d(hkl)=a/sqrt(h^2 +k^2 + l^2)


The Attempt at a Solution



i basically broke down the equation into P=(2Asin(theta)) / ((a^2)(sqrt(h^2+k^2+l^2))

but for the vaule of a... i don't have the radius to find the vaule of a soo any hints would be nice :)
 
Physics news on Phys.org
maiad said:
n*lamba=2d(hkl)sin(theta)

What is known, what is unknown?
 

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