X-Ray Diffraction
A Report For the 2004 Nanotechnology Teachers Workshop
The University of Tulsa
Pamela Diaz
X-ray Diffraction
X-rays were discovered in 1895 by Wilhelm Roentgen while he was experimenting with
a Crookes tube. A Crookes tube is a vacuum tube through which a high voltage is passed causing
the streaming of electrons between the cathode and anode. Fluorescent materials paced in the
tube glowed when the current was present. Roentgen noticed that a card painted with fluorescent
material that was laying on the table near the tube, glowed when the tube was turned on. The
card would glow even if the Crookes tube was covered in black paper . It also didn’t matter if
the fluorescent coated side of the card was placed up or down. Roentgen soon discovered that if
a hand was placed between the X(unknown)-rays and a fluorescent screen, shadows of the bones
of the hand could be discerned. This discovery was immediately applied to the medical field for
diagnostic purposes.
Diffraction occurs when waves pass over an object that has approximately the same
repeat distance as the wave. Thist is seen when light is passed through a grating with repeat
distances of approximately 1000 Angstroms. X-rays were thought to be much smaller than light,
having a size of approximately 1 Angstrom – about the same as the distance between atoms.
In 1910 scientists working with Max van Laue conducted an experiment to see if x-rays could
be diffracted by a crystal of sodium chloride. They were successful in getting a diffraction
pattern captured on photographic film. The structure of the crystal lattice of sodium chloride was
no longer a secret.
In 1912 W.L. Bragg, working with his father, determined the mathematical relationship
between the angle of diffraction, the wavelength, and the distance between layers of atoms in a
crystal. If the wavelength was known, and the angle of diffraction was known, the distance
between the atom in a crystal could be determined according to the following equation:
nλ = 2dsinθ
where n = an integer, (we use 1 for most calculations)
λ = the wavelength of the x-ray ( this is 1.54Ǻ if copper is the target metal)
d = the distance between atoms in angstroms, Ǻ
θ = the diffraction angle in degrees
By knowing the distance and angles between the atoms of a substance, the structure of the crystal
could be determined.
Today X-ray diffraction is used to identify corrosion products on the surface of a metal as
well as the pigments used in wall paintings. XRD is used by many museums to evaluate
paintings to determine their age and artist by the pigments that were popular at a given time.
It is almost non-destructive in regards to the sample being analyzed.
In nanotechnology, XRD is a useful tool since x-rays are in the nano-scale. At the University of
Tulsa it is used to evaluate the deposition of one metal onto the surface of a substrate.
How it Works
A high voltage is applied across electrodes causing electrons to be propelled towards a
metal target – the anode. Electrons bombarding the metal cause the expulsion of x-rays with a
wavelength characteristic of the metal. Copper is very commonly used metal. X-rays with a
wavelength of 1.54Ǻ are emitted from copper. The x-rays are passed through a slit that
collimates the x-rays before they reach the sample chamber. Upon hitting the sample the x-rays
are diffracted in all directions. Both constructive and destructive interference occur.
Constructive interference occurs where the waves are in phase with one another. The waves can
be detected by a scintillation counter after they are monochromatized by passing through a
graphite crystal. The scintillation counter which measures x-ray intensity is mounted to an angle
measuring device called a goniometer. The goniometer is motorized and is controlled by a
computer. Thus the angle and intensity of the diffracted x-ray beam are measured according to
the parameters set in the computer. (The diffractometer records the x-ray intensity as a function
a 2-theta angle. Therefore to find the diffracted angle to use in Braggs equation, you must divide
the angle by 2.)
Electronic signals from the goniometer and scintillation counter are sent to a computer
where they are translated before being displayed on an output device such as a strip chart or
computer monitor where a diffraction pattern is recorded. A diffraction pattern is the fingerprint
of a mineral or other sample. It records the x-ray intensity at various 2 theta angles. By dividing
the angle from the strip readout by two and applying Braggs Law, we can now calculate the
distance between the atoms in the crystal. The smaller the angle of diffraction the larger the
distance between atoms. The peaks are prioritized according to their height from tallest to
shortest. By consulting a handbook of mineral diffraction patterns, the sample can be identified.
Figure 1
Quartz Diffractogram - TU XRD
Figure 2:
Jones, E.R. and Childers, R.L. Contemporary College Physics 2nd Edition, Addison Wesley
Publishing Co., 1993.
USGS Open-File Report 10-041; A Laboratory Manual for X-ray Diffraction
basic information and current applications
Concise, well written explanation of how the XRD works
Cornell, Winton. Power Point Presentation on XRD
A tutorial on XRD

X-Ray Diffraction - TU Department of Mathematical and Computer

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