Condensed Matter: Thermal Expansion coeff. using diffraction angles

AI Thread Summary
To calculate the mean coefficient of linear expansion of a cubic crystal using diffraction angles, the temperature change (ΔT) and the angles of diffraction at two temperatures (150.8° at 18°C and 141.6° at 318°C) are essential. The relationship between the diffraction angles and the crystal lattice spacing can be explored using Bragg's Law, which may help derive the necessary parameters for linear expansion calculations. The user is advised to find an expression for the change in lattice spacing (Δd) relative to the original spacing (d), as this will assist in determining the linear expansion coefficient (α). Further exploration of diffraction equations is necessary to connect the angles to the crystal dimensions. Understanding these relationships is crucial for solving the problem effectively.
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!
 
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Hello, themongrelcat. Welcome to PF!

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