Bragg Angles and Thermal Expansion

  1. Problem statement:

    The Bragg angles of a certain reflection from copper is 47.75◦ at 20◦C but is 46.60◦ at 1000◦C.
    What is the coefficient of linear expansion of copper? (Note: the Bragg angle θ is half of the
    measured diffraction (deflection) angle 2θ).

    Attempt at solution:


    Using \begin{equation} 2d sin( \theta )= n \lambda \end{equation} to find the ratio of d(T=1000) and d(T=20) and saying that this is equal to the lattice constant ratio for those temperatures I found that:

    \begin{equation}

    \frac{a(T=1000)}{a(T=20)}=\frac{sin( \theta (T=20) )}{sin( \theta ( T= 1000))}

    \end{equation}

    Which when used in the equation for the linear expansion coefficient, kappa:

    \begin{equation}

    \kappa = \frac{a(T=1000)}{a \Delta T}

    \end{equation}

    gives a value of 10^{-3} per kelvin, which is about 100 times too large when I compared it to the actual data. I know this is a basic question, but I can't see what I'm wondering what I'm doing wrong.

    Thanks in advance!

    \end{equation}
     
  2. jcsd
  3. The coefficient of thermal expansion is not given by that last formula.
    You should have a (Δa) in the formula, the difference between the lattice constants at the two temperatures.
     
    1 person likes this.
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