Read before class: Textbook section 8.3.1 and 8.3.4
A short discussion of X-ray Diffraction from crystals such as NaCl
I. Introduction
From diffraction patterns, one can measure the average spacings between layers or rows of atoms; determine the orientation of a single crystal or grain; find the sub-atomic (crystal) structure of an unknown material and measure the size, shape and internal stress of small crystalline regions.
In this experiment you will use apparatus consisting of a Copper target X-ray tube and power supply, a photon detecting Geiger-Muller tube and associated electronics. You will determine the crystal structure and lattice constant (a_0) of ordinary table salt (NaCl) and LiF by X-ray diffraction.
II. Crystal Structure of NaCl and LiF
The angles and intensities of x-ray diffraction from a regular crystal structure are determined by the locations and atomic structure factors of the atoms in the unit cell. The possible angles of diffraction are determined by the spacings of planes of atoms within the structure of the crystal. See the attached pages for the method used to calculate the expected angles of diffraction from a crystal plane defined by the Miller indices (h,k,l). For the NaCl lattice the primitive vectors are given in many textbooks.
To operate the X_ray source, the system must be INTERLOCKED. The red light must be illuminated. This may require some horizontal adjustment of the lead glass casing.
Connect the Geiger-Mueller counter to the high voltage power supply. The output of the GM counter goes to the pre-amplifier and then to the amplifier. The positive output pulses from the amplifier then go to input B of the scaler. [Alternatively, the amplifier can be used in the negative input mode, the pulses can be send to a NIM discriminator and to channel A of the scaler.]
Initially set the Geiger-Muller tube high voltage to a POSITIVE value in the range between 0.30 kV and 0.45 kV.
Since the black box (RC circuit) has an impedance that is not well matched to 50 Ohms, we first send the signal to the pre-amplifier/amplifier and then count the positive pulses with channel B of the scaler module.
First, plateau the HV for the counter and then after verifying all the signals are present at each intermediate step with the scope, begin taking data.
There is considerable background from scattered X-rays. Try to reduce this constant background by shielding with the small pieces of lead that are available near the apparatus. Unfortunately, this background cannot be completely eliminated.
The X-ray lines from the Copper target in the X-ray generator are:
- K_alpha1 : 0.1540 nm
- K_alpha2 : 0.1544 nm
- K_beta : 0.1392
Here alpha designates the first level above the vacancy, etc. The K-absorption-edge (K-to-continuum threshold) for nickel is at 0.1488 nm As a result, nickel absorbs Cu Kbeta radiation much more strongly than it absorbs Cu Kalpha radiation. A Nickel foil filter is often used to attenuate Cu Kbeta radiation. (For some x-ray diffraction devices, a nickel filter is a permanent part of the apparatus).
Starting from a small angle, plot the number of counts versus angle for the two crystal samples (NaCl and LiF). Take data with and without the nickel filter to distinguish the K_alpha and K_beta lines. Note that the apparatus measures 2 x theta_B. (Why is this the relevant angle ?). The crystal should be properly aligned in the holder with the mark on the bottom.
In your data analysis, the results for the angles of the n=1 and n=2 lines can be combined using a weighted average.
Note that for these two crystals a_0 = 2 d, where d is the spacing determined from Bragg’s Law.
Clean up after performing the experiment ! Remove the crystals from the holder and replace in the storage box (!) The LiF crystal is quite corrosive and can damage the apparatus if left for long periods of time.
Technical Notes:
a) The output pulse from the Geiger-Muller tube is a long negative pulse but is not impedance matched to 50 \Ohms. Therefore you will not see the signal clearly on the oscillscope if it is terminated in 50\Ohms.
b) There is a warming up effect for the X-ray tube. Please allow it to run for 15 minutes before taking data.
c) Some students have found a large shadowing effect for the background level due to the geometry of collimators.
d) The X-ray tube can operate for a maximum of 2 hours. (the timer mechanism is designed to prevent longer operation).
e) The X-ray tube can operate with 20 kV or 30 kV. The 20 kV appears to be better for LiF data taking.
f) Do not forget the pre-amplifier. The chain should be GM tube->preamplifier-amplifier-scalar.
g) The universal counter can also be used in the TOT (time over threshold mode) as a scaler. h) The crystal should be properly aligned in the holder. The mark on the crystal should be facing downwards.
Self-Study Questions:
1) What is the Bragg condition ?
2) What are the Miller indices of a crystal ?
3) Explain the origin of the K_alpha and K_beta lines from the X-ray tube ? (Note that as a result, there are pairs of diffraction maxima.)
4) What are the wavelengths for the K_alpha and K_beta lines of copper ? Which one has higher intensity ?
5) Explain why the nickel filter is used ? (see self-study question 3).
Last updated Feb 26, 2015, Tom Browder, teb#phys.hawaii.edu
(Adapted from Mike Peter’s original writeup in the 1990’s. Extensively modified.)