2023
X-Ray Diffraction Report
Content:
1. Brief History
1.1. Introduction
1.2. X-Ray Diffraction
1.3. How XRD works?
1.4.What information XRD can give you?
2. How to run XRD experiment:
2.1. Apparatus
2.2. Procedure
3. Results
4. Discussion
4.1.Limitations
4.2. Sample requirement
5. Example of XRD
6. References
1. Brief theory:
1.1.Introduction
X-rays are discovered by Wilhelm Conrad Roentgen in 1895. They are a form of
electromagnetic radiation that have high energies and short wavelengths ranging from 0.01 to
10 nanometers.
Fig. 1. The electromagnetic spectrum is the full range of frequencies of electromagnetic radiation.
X rays are generated when electrons are accelerated under a potential difference and turned
into electromagnetic radiation. An X-ray tube, with its respective components placed in
a vacuum, and a generator, make up the basic components of X-ray production [1].
Fig. 2. An X ray generation tube
X rays have properties that allow the occurrence of diffraction. Diffraction occurs when a wave
encounters a series of regularly spaced obstacles that are capable of scattering the wave, and
have spacings that are comparable in magnitude to the wavelength. Furthermore, diffraction is
a consequence of specific phase relationships that are established between two or more waves
that have been scattered by the obstacles. The discovery of X-rays enabled scientists to probe
crystalline structure at the atomic level.
When electromagnetic radiation is focused towards a crystal, it is scattered in a predictable
fashion; for a given radiation wavelength (similar to the atomic spacings, i.e. X-rays), certain
angles of incidence lead to constructive interference of the reflected waves. This is known as
Bragg’s Law, and is a foundation in X-ray crystallography. The Braggs were awarded the
Nobel Prize in physics in 1915 for their work in determining crystal structures beginning with
NaCl, ZnS and diamond. The Bragg equation for constructive interference is given by
nλ = 2dsinθ
where n is the order of diffraction, λ is the wavelength of the incident radiation, d is the spacing
between the lattice planes of the crystal, and θ is the angle of incidence of the radiation.
Fig. 3. Diffraction of X rays by crystal lattice according to Brag’s law
Although Bragg's law was used to explain the interference pattern of X-rays scattered by
crystals, diffraction has been developed to study the structure of all states of matter with any
beam, e.g., ions, electrons, neutrons, and protons, with a wavelength similar to the distance
between the atomic or molecular structures of interest [2].
1.2.X Ray Diffraction:
“The atomic planes of a crystal cause an incident beam of X-rays to interfere with one
another as they leave the crystal. The phenomenon is called X-ray diffraction.”
X-ray diffraction can be used to determine a materials crystalline structure and lattice
parameter. This information can then be used to identify the material being analysed since each
metallic element in the periodic table has a unique combination of lattice structure and
parameter at room temperature.
1.3.
How XRD works:
X-ray diffractometers consist of three basic elements: an X-ray source, a sample holder, and an
X-ray detector. X-rays were generated by heating a filament to produce electrons, accelerating
the electrons toward the sample target by applying a voltage, and bombarding the sample with
electrons. When electrons have sufficient energy to dislodge inner shell electrons of the target
material, characteristic X-ray spectra are produced. These spectra consist of several
components, the most common being Kα and Kβ. These X-rays were collimated and directed
onto the sample.
Fig. 4. XRD instrument schematic
As the sample and detector were rotated, the intensity of the reflected X-rays and the detector
position (2-theta angle) were recorded. When the geometry of the incident X-rays impinging
the sample satisfied the Bragg Equation, constructive interference occurs and a peak in
intensity occurs. A detector recorded and processed this X-ray signal and converted the signal
to a count rate which is then output to the computer as a plot of intensity vs. 2-theta diffraction
angle.
Fig. 5. Single Crystal XRD reflections.
Bragg's law is used to determine a crystal parameters from its characteristic x-ray pattern. The
x-rays that strike a crystal have a wavelength of about the same length as the space between
atoms in the crystal lattice. Bragg's law can be derived by considering a cubic crystal lattice
that consists of parallel planes of atoms. If each plane is assumed to act as a surface which is
struck by the incident x-ray beam, we see the beam reflected in some cases and not reflected
in others. In the case of reflection, it is seen that the beams exiting the crystal are in phase and
act to reinforce each other. This occurs when the incident beam hits the parallel planes at certain
angles known as Bragg Angles,  In the non-reflecting case, the waves leaving the crystal are
out of phase and cancel each other. Non-reflectance occurs when the incident beam strikes at
arbitrary angles [3].
1.4. What information XRD can give you:
X-ray powder diffraction is most widely used for the identification of unknown crystalline
materials (e.g. minerals, inorganic compounds). Determination of unknown solids is critical to
studies in geology, environmental science, material science, engineering and biology.
Other applications include:
•
characterization of crystalline materials
•
identification of fine-grained minerals such as clays and mixed layer clays that
are difficult to determine optically
•
determination of unit cell dimensions
•
measurement of sample purity
With specialized techniques, XRD can be used to:
•
determine crystal structures using Rietveld refinement
•
determine of modal amounts of minerals (quantitative analysis)
•
characterize thin films samples by:
•
o
determining lattice mismatch between film and substrate and to
inferring stress and strain
o
determining dislocation density and quality of the film by rocking
curve measurements
o
measuring superlattices in multilayered epitaxial structures
o
determining the thickness, roughness and density of the film using
glancing incidence X-ray reflectivity measurements
make textural measurements, such as the orientation of grains, in a
polycrystalline sample [4].
2. How to run an XRD experiment (steps):
2.1.Apparatus:
• Sample material, and
• XRD Machine
2.2.Procedure:
Sample preparation:
Grind the sample material into a fine powder and Place the
powdered sample onto a sample holder and then take pressing
block and press down firmly. Removed the extra powder. Then we
take the bottom of sample holder with face down and press down.
Flipped the whole block and separated the plate sample from
block.
Calibration:
Fig.6. Sample preparation
The first step in the experiment was to calibrate the goniometer which measures the θ and 2θ
values accurately. The sample used for calibration was a reference (001) crystal. The
goniometer was calibrated by iteratively coupling and decoupling θ and 2θ knobs on the
goniometer
Load into XRD machine:
Placed the samplein the sample stage was placed between the clips so that the surface flushed
with the clip. All the doors of the X-ray unit were closed. It is worthwhile to note that when the
doors were opened, the beam did not turn on to prevent exposure to radiation. It was taken into
consideration that the door was only opened when the beam was turned off or the shutter to the
tube was closed so that no X-rays were coming out.
Set parameters on software:
Set the parameters on software as per sample.
Run Scan:
The X-ray tube was turned on by slowly increasing the voltage to the allowed value and the
current to the allowed value. Run the scan, the peak position showed the highest counts. Sample
is rotated and detector recorded the data.
Analyse Result:
The software collected the data of intensity versus 2θ. The data were analysed using an excel
file. Use the Braggs Law to calculated the d-spacing for each diffraction peak. And identify the
sample by comparing its diffraction pattern with database reference
Fig.7. Experimental setup of XRD
3. Results:
Calculate the inter planar spacing d:
λCopper = 1.315Å = 1.315 × 10−10 m
n=1
Formula:
nλ = 2dsinθ
d=
No.
Peak Position
𝟐𝛉°
nλ
2sinθ
Relative
intensities
𝐈⁄ %
𝐈
𝛉°
.
1
2
3
4
5
6
7
21.89
29.05
31.88
33.03
39.9
50.50
51.38
1166
5223
1423
9406
3932
1207
4128
10.945
14.525
15.94
16.515
19.95
25.25
25.69
Intra planer
spacing Å
𝐧𝛌
𝐝=
𝟐𝐬𝐢𝐧𝛉
3.463
2.622
2.394
2.313
1.927
1.541
1.517
4. Discussion
4.1.Limitations:
•
Only Homogeneous and single-phase material is best for identification of an
unknown
•
Not suitable for amorphous structures
•
Must have access to a standard reference file of inorganic compounds (dspacings, hkls)
•
Requires tenths of a gram of material which must be ground into a powder
•
For mixed materials, detection limit is ~ 2% of sample
•
For unit cell determinations, indexing of patterns for non-isometric crystal
systems is complicated
•
High intensity X ray may cause damage to sensitive samples
•
Peak overlay may occur and worsens for high angle 'reflections'
4.2.Sample requirement:
• Sample should be as pure as possible
• Sample must exhibit crystalline structure.
• Sample should be in solid form not in liquid state.
5. Example of real XRD results:
In this research paper, the structural properties of synthesized CuONPs were explored using
XRD. The XRD patterns of CuONPs are shown in Fig. 7 which showed diffraction peaks at
angle 38.30°, 47.90° and 66.10° indicating the existence of CuONPs with (111), (200) and
(220) planes of face centred cube (FCC) structure
(JCPDS No. 48-1548). Two smaller peaks are also
observed at angle 36.33° and 60.56° corresponding to
cuprous oxide (Cu2O) NPs having (111) and (220)
planes of FCC (JCPDS No. 05-667). The crystallite
size of green synthesized material was found in the
range of 16–43 nm.
Reference:
Rafique, M., Shaikh, A. J., Rasheed, R., Tahir, M. B.,
Gillani, S. S. A., Usman, A., ... & Rabbani, F. (2018).
Aquatic biodegradation of methylene blue by copper
oxide nanoparticles synthesized from Azadirachta
indica leaves extract. Journal of Inorganic and
Organometallic Polymers and Materials, 28, 24552462.
Fig.7. XRD spectra of CuONPs synthesized
using Azadirachta indica leaves extract
6. References:
1. Callister Jr, William D. Materials science and engineering an introduction. 2007.
2. L. Reynolds, Characterization of Materials MSE 210 Lab Manual, 2008.
3. Cullity, Bernard Dennis. Elements of X-ray Diffraction. Addison-Wesley Publishing,
1956.
4. Khan, Hayat, et al. "Experimental methods in chemical engineering: X‐ray diffraction
spectroscopy—XRD." The Canadian journal of chemical engineering 98.6 (2020):
1255-1266.