Joe Berg

Luwa Matthews

Determining the Properties of the NaCl Crystal Via Bragg Diffraction

Abstract:The purpose of this lab was to determine the spacing between the planes of the NaCl Crystal

and the wavelength given off by Molybdenum when bombarded with electrons accelerated through a potential difference of 30,000V. An x-ray detector was used to determine the transmission of a copper film, which was then used to determine the wavelength of the x-rays emitted. This was knowledge was used with Bragg diffraction to determine the lattice spacing in a crystal plane of NaCl. The transmission of Copper was found to 0.12±0.08 and the wavelength 62.5±0.9, and the spacing between the planes is approximately 2.89 x 10-10 m.

Experimental Procedure:

Using an x-ray apparatus, electrons were accelerated through a potential difference of about 30,000V and shot at a sample of molybdenum. This excited electrons in molybdenum which, upon returning to ground state, released x-rays. The x-rays were shone through a calumniator onto an aluminum slab angled 20o to the normal. A sensor at 110o then detected the reflected x-rays from the aluminum slab.

To determine the transmission of copper at the angle specified above, a copper foil of 0.07mm was placed in front of the calumniator and tests were run with and without the copper. The number of x-rays reflected from the aluminum slab was measured with and without the copper foil. The transmission was to be 0.12±0.08 using the equation below:

T=Rwithout foil−RbackgroundRwith foil−Rbackground

equation 1

Where T= transmission and Rbackground = background x-ray in the room without the x-ray apparatus running.

Using the formula below, the wavelength, λ , of the x-rays emanating from the molybdenum was found to be 62.5±0.9 pm.

T= e

−a ( λ100 pm )

n

¿¿ equation 2

Where a=7.6 and n=2.75.

Finding the Spacing between Lattice Planes of the NaCl Crystal:

The NaCl crystal was set up such that the angle between the crystal and the x-rays was equal to the angle between the crystal and the detector. Then, the electrons were accelerated through a voltage of 30,000V and the angle of the crystal was varied by 0.1o every 13 seconds, after which the detector would record the average rate of x-rays over that period. These average values are plotted against the angle they were obtained at as shown in figure 1. There are visible peaks at 6.2 and 12.8 degrees. From the value of these peaks and equation 3 below it was found that the spacing between lattice planes in the NaCl crystal is 2.89 angstums and 2.82 angstrums for the 6.2 and 12.8 degree peak respectively.

2d∗sin (θ )=nλ equation 3

Where d is the spacing between lattice plans, θ is the angle collected at, n is the peak number, and λ is the wavelength of x-ray shown on the crystal.

The overall curve of the rate of x-rays against the angle of collection was also inspected and its interaction with the Voltage of acceleration the electrons go through before hitting the molybdenum was observed (see figure 2). For lower acceleration voltages of the electrons, the overall curve tended to be lower and began later and the peaks were less pronounced. This is explained by the fact that with lower voltages, the accelerated electrons have less kinetic energy and hence, fewer electrons on the molybdenum are excited to release x-rays.

Conclusion:

The wavelength of the x-rays emitted was found to be 62.5±0.9m The spacing between the planes of the NaCl Lattice corresponding to the 6.2o peak was

approximately 2.89 x 10-10 m and that corresponding to the 12.8o peak was found to be 2.82 x 10-

10 m. The reason the larger peaks were used to determine the spacing is that they had more clearly defined maximums and were thus more reliable.