Question

Aluminum has a room temperature linear thermal expansion coefficient of α L

​
= 23μm/mK. If the linear thermal expansion coefficient is defined as: α L
​
= L
1
​
ΔT
ΔL
​
, where L is a length, then derive the shift of the position of the (220) powder diffraction peak if the Al sample is heated from room temperature to 800 K. You may assume that α L
​
does not change with temperature, and that CuK α
​
radiation is used.

Answer 1

The shift in the position of the (220) powder diffraction peak of Aluminum can be derived using the equation for linear thermal expansion.

Step-by-step explanation:

The shift in the position of the (220) powder diffraction peak of Aluminum can be derived by using the equation for linear thermal expansion: ΔL = αL * ΔT * L. In this equation, ΔL is the change in length, αL is the linear thermal expansion coefficient, ΔT is the change in temperature, and L is the original length of the Aluminum sample.

Given that αL = 23μm/mK, ΔT = 800K - 298K = 502K, and L is the length of the (220) plane, we can calculate the shift in position of the diffraction peak by substituting these values into the equation.

For example, if the initial position of the (220) peak is at a certain angle, the shift in position will be proportional to the change in length, ΔL. This shift can be measured experimentally using a diffraction technique such as X-ray diffraction.