Condensed Matter: Thermal Expansion coeff. using diffraction angles

In summary, the conversation discusses the observation of diffracted monochromatic x-rays at different angles and temperatures in a crystal with cubic structure. The goal is to determine the mean coefficient of linear expansion of the crystal in the given temperature range. The relevant equations are α=Δl/lΔT and possibly nλ=2dsinθ, and the key is to find an expression for Δd/d.
  • #1
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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  • #2
Hello, themongrelcat. Welcome to PF!

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

1. What is condensed matter?

Condensed matter refers to a state of matter in which particles are densely packed together. This includes solids and liquids, but not gases or plasmas.

2. What is thermal expansion?

Thermal expansion is the tendency of a material to expand or contract in response to changes in temperature. This is due to the increase or decrease in the kinetic energy of its particles.

3. How is thermal expansion coefficient determined using diffraction angles?

Thermal expansion coefficient is determined by measuring the change in diffraction angles of a material as it undergoes a change in temperature. This is done by using X-ray or neutron diffraction techniques.

4. Why is thermal expansion coefficient important?

Thermal expansion coefficient is important because it affects the physical properties of materials, such as their size, shape, and volume. This can have practical implications in industries such as construction and engineering.

5. Can thermal expansion coefficient be negative?

Yes, thermal expansion coefficient can be negative for certain materials. This means that as the temperature increases, the material actually contracts instead of expanding. This is known as negative thermal expansion or thermal contraction.

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