# Bragg Reflection

1. An X ray beam having a wavelength $\lambda =1.537*10^{-10} m$ is diffracted by a family of parallel plans from a crystal. Knowing that the Bragg reflection of the $n=3$  order is observed when the angle between the incident and reflected rays is $\phi =60 degree$, find the distance between two consecutive crystal plans.

2. Same order Bragg reflection on an Ag crystal is observed at two temperatures $t_1 =18 deg C$ and $t_2 =630 deg C$, under the angles $\theta_1 =80 deg 9’$ and $\theta_2 =76 deg 54’$. Find the linear thermal expansion coefficient for Ag.

1.

The angle between the incident X beam and the family of parallel plans is

$\theta =(180-\phi)/2 =60 deg$

The condition of diffraction is

$2*d*sin(\theta) =n*\lambda$

therefore

$d = 2.662*10^{-10} m$

2.

Using the diffraction conditions in the two cases:

$d_1*sin(\theta_1) = d_2*sin(\theta_2)$

and the thermal expansion equations:

$d_1 =d_0*(1+\beta*t_1)$

$d_2 =d_0*(1+\beta*t_2)$

where $d_0$ is the distance between two parallel plans at $t =0 deg C$

we obtain

$\beta = [sin(\theta_1)-sin(\theta_2)]/[t_2*sin(\theta_2) -t_1*sin(\theta_1)] =1.8935*10^{-5} (1/deg)$