Condensed Matter: Thermal Expansion coeff. using diffraction angles

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SUMMARY

The discussion focuses on calculating the mean coefficient of linear expansion (α) of a crystal using diffraction angles from monochromatic x-rays at two temperatures: 18°C and 318°C. The angles observed are 150.8° and 141.6°, respectively. The relevant equations include α=Δl/lΔT and possibly nλ=2dsinθ, with a suggestion to explore Bragg's Law for further insights. The user seeks a method to relate the diffraction angles to the linear dimensions of the crystal.

PREREQUISITES
  • Understanding of Bragg's Law in x-ray diffraction
  • Familiarity with the concept of thermal expansion coefficients
  • Basic knowledge of cubic crystal structures
  • Ability to manipulate equations involving temperature changes and linear dimensions
NEXT STEPS
  • Research Bragg's Law and its application in determining crystal dimensions
  • Study the relationship between diffraction angles and interplanar spacing
  • Explore methods for calculating linear expansion coefficients in materials
  • Investigate the effects of temperature on crystal lattice parameters
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Students and researchers in materials science, physicists studying crystallography, and anyone involved in thermal analysis of crystalline materials.

themongrelcat
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Homework Statement



At a temperature of 18°C a beam of diffracted monochromatic x-rays is observed at an angle of 150.8° to the incident beam after being diffracted by a crystal with cubic structure. At a temperature of 318°C the corresponding beam makes an angle of 141.6° with the incident beam. What is the mean coefficient of linear expansion of the crystal in the given temperature range?

Homework Equations



α=Δl/lΔT

possibly nλ=2dsinθ

The Attempt at a Solution



I already have ΔT and the equation for thermal expansion, but I have no idea how to get l and Δl. I know it must have something to do with the diffraction angles, maybe Bragg's Law? I've scoured the entire internet looking for an equation to relate the two, and I just can't find it. Even just an equation relating those would be helpful. Thank you!
 
Last edited by a moderator:
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Hello, themongrelcat. Welcome to PF!

See if you can find an expression for Δd/d.
 

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