X-ray Diffraction (new)

X-Ray Diffraction
Introduction (From University of Florida Advanced Physics Laboratory Manual)
When an electron beam of energy around 20 keV strikes a metal target, two different
processes produce x-rays. In one process, the deceleration of beam electrons from
collisions with the target produces a broad continuum of radiation called bremsstrahlung
having a short wavelength limit that arises because the energy of the photon hc/ λ ¸can be
no larger than the kinetic energy of the electron. In the other process, beam electrons
knock atomic electrons in the target out of inner shells. When electrons from higher
shells fall into the vacant inner shells, a series of discrete xrays lines characteristic of the
target material are emitted. In our machine, which has a copper target,only two emission
lines are of appreciable intensity. Copper K α x-rays (λ = 0:1542 nm) are produced when
an n = 2 electron makes a transition to a vacancy in the n = 1 shell. A weaker K β xray
with a shorter wavelength (λ = 0:1392 nm) occurs when the vacancy is filled by an n = 3
electron.
Thus, the spectrum of x-rays from an x-ray tube consists of the discrete lines
superimposed on the Bremsstrahlung continuum. This spectrum can be analyzed in much
the same way that a visible spectrum is analyzed using a grating. Because x-rays have
much smaller wavelengths than visible light, the grating
spacing must be much smaller. A single crystal with its regularly spaced, parallel planes
of atoms is often used as a grating for x-ray spectroscopy. The incident x-ray wave is
reflected specularly as it leaves the crystal planes, but most of the wave energy continues
through to subsequent planes where additional reflected waves are produced. The path
length difference for waves reflected from successive planes is 2d sin θ, where d is the
distance between atomic planes. Note that the scattering angle (the angle between the
original and outgoing rays) is 2θ. Constructive interference of the reflected waves occurs
when 2d sin θ is equal to an integer number of wavelengths nλ.
For more detail about the theory, the Tel-X-Ometer manual has a lengthy explanation, as
does the Art of Experimental Physics (excerpt from the textbook is linked here), which is
available in hardcopy in the classroom. The first two chapters of C. Kittel, Introduction to
Solid State Physics, or an equivalent text such as Fundamentals of Modern Physics by
Eisberg also have good background on diffraction.
In the Tel-X-Ometer, the x-rays from the tube are collimated to a thick line and reflected
from the crystal placed on the sample table. The detector, a Geiger-Muller (GM) tube, is
placed behind collimating slits on the detector arm which can be placed at various
scattering angles 2θ. In order to obey the Bragg condition, the crystal must rotate to an
angle θ when the detector is at an angle 2 θ. This θ : 2 θ relationship is maintained by
gears under the sample table.
Equipment

• X-ray diffraction system (Tel-X-Ometer) experiment manual and its setup manual
• Geiger-Müller tube and stepping motor
• Computer and interface ( Labview software)
• Alkali halide large single crystals
• Radiation safety guide (just in case you want to know more)
Theory Questions:
What does the x-ray spectrum look like that is emitted from the x-ray tube?
How does the Geiger-Müller tube work?
Procedure
1. Please read the Tel-X-Ometer setup manual (particularly sections 10.1-12.5), and
any sections regarding safety features. Realize, you are working with a
radioactive source, and thus should be aware of any possible hazards.
2. Also read the Tel-X-Driver manual which explains how to use the software.
3. To operate the Tel-X-Ometer:
a. To open or close the scatter shield (the main cover), the whole shield must
be displaced to the right or the left of center, depending on the position of
the detector.
b. To turn on the power to the unit, turn POWER ON key on the control
panel; the unit will only function when the TIME SWITCH is rotated
away from zero, and when the key is turned ON. This is to ensure that the
x-rays only turn on when enclosed within the leaded glass. The filament of
the x-ray tube should then be illuminated. Wait 5 minutes, then depress the
X-RAYS ON switch (the red light will turn on). If it does not turn on,
wiggle the lid to ensure the metal pin is in the exact center.
c. The Tel-atomic software (Tel-X-Driver v2.32 shortcut link on the
Desktop) measures the counts from the Geiger-Mueller tube, the Geiger-
Mueller tube’s voltage, and the current through the x-ray tube filament
(this should be set to

maximum allowed angle should be about 115 degrees and the minimum
should be 12.5 degrees (the arm cannot go below this angle).
i. If the spectrum is shifted, decide the best course of action. Confirm
this with your TA/Instructor BEFORE carrying out this action.
b. When inserting the vertical collimating slits, you may adjust the
number/position of these slits, but you should understand and describe in
your report the consequence of the adjustments (both positive and negative
consequences arise when slits are moved). Also, consider then angular
accuracy possible given the size of the collimating slit closest to the
Geiger-Mueller tube.
c. When setting up the Carriage Arm you need to check two things:
i. Make sure θ (written below the central gear) = ½ (2 θ) (which is
written on the outer edge of the Tel-X-Ometer. If it doesn’t, rotate
the sample holder using pliers (gently!)
ii. Make sure that the set-angle in the software = 2θ written on the
edge of the Tel-X-Ometer.
5. Single Crystal Diffraction Experiments:
For four of the large single crystal alkali halide samples provided (LiF,NaCl, KCl,
or RbCl), collect the x-ray spectra using the Tel-X-Driver Software on the
computer. Plot the spectra, and then determine in detail how the observed
reflections relate to the real space structure of the crystal A detailed procedure for
this is described in the Tel-X-Ometer manual, sections D.22-D.26. For purposes
of plotting and analyzing your data you may wish to use one of the graphics
packages available on the lab computers.
Goals:
References
a. Quantify how the crystal spacing d changes with atomic number.
i. What does the d spacing mean in terms of the crystal’s lattice
constant?
ii. Draw the crystal structure and label the d-spacing.
iii. Compare the experimental value of the lattice constant to the
published value.
iv. If you rotated the crystal by 90°, would you get the same result? If
you have time, try this experiment (D.25).
v. What are the possible sources of error in this experiment?
C. Kittel, Introduction to Solid State Physics, 6 th edition, Wiley, New York (1985).
D. W. Preston and E. R. Deitz, The Art of Experimental Physics Wiley, New York
(1991).
R. Eisberg, Fundamentals of Modern Physics, Wiley, New York (1961).

R. Eisberg and R. Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei and
Particles, 2 nd edition, Wiley, New York (1985).
B. E. Warren, X-Ray Diffraction, Addison-Wesley, Reading, MA (1969).
International Tables for X-Ray Crystallography, Vol. 3, Reidel, Boston (1962).
L. V. Azaroff and M. J. Buerger, The Powder Method in X-Ray Crystallography,
MacGraw-Hill, New York (1958).
P. J. Barry and A. D. Brothers, Am. J. Phys. 54, 186 (1986).