Materials Characterization
Lab Report
Submitted to:
Dr. Mohsin Ali Raza
Submitted by:
17MME-S1-313
USMAN LIAQAT
Dept. of Metallurgy and Materials Engineering
7th Semester
University of the Punjab
“To study the working of Diffractometer and to perform Powder XRD analysis of two
unknown samples using X-ray Diffractometer”
Objective
The objective of this experiment is to perform diffraction by using X-ray diffractometer and
identification of unknown samples by using match software.
Principle
XRD of a powder and a metal sample is performed to obtain real time data.
Theory of XRD
Working and various parts of diffractometer
A diffractometer is used to perform diffraction of the samples in order to find the planes and d-
spacing in the samples for studying their behaviors.
Parts of x-ray diffractometer
It has a cabinet in which there are 3 main parts of the diffractometer
Figure 1. Scheematic arrangement of x-ray diffractometer components
1. X-ray tube
An X-ray diffractometer must have an x-ray tube for generation of x-rays that fall on the sample
for diffractions. Mostly, copper tube is used and in our lab we also have copper tube x-ray. It
consists of a copper anode and water circulation for cooling the copper anode in order to prevent
it from melting.
Figure 2. Schematic of x-ray gun in diffractometer
2. Sample holder and monochromator
An arm is attached with x-ray tube which consists of two things, one is monochromator and the
other is sample holder. The monochromator is attached to pass the only monochromatic x-rays
generated in x-ray tube. Now, as we have studied that there are two monochromatic x-rays are
produced known as Kα and Kβ. We required only Kα to pass and fall on sample while Kβ to stop.
For this purpose, monochromator consists of a germanium crystals set at an angle of 20-22° this
will allow only Kα to pass on the sample. Then a sample holder is attached at the end of the arm
for holding sample. Samples may be of two types either in the form of a powder or may be in the
form of bulk material. The sample holder is attached on fixed goniometer head. Sample holder
also contain a screw for adjusting the height of the sample.
3. Detector
In cabinet, the third part is the detector which is located in the arc form above the holder. The
detector used in our lab diffractometer is proportional counter detector but also known as curved
position sensitive detector due to its shape. The detector is at 2θ w.r.t incident beam. On the
detector part that is straight front to the sample a lead sheet is attached because sometimes, the x-
rays passed without diffraction so in order to protect the detector from damaging effect of x-rays
the lead piece is attached on it.
External components
Outside the cabinet following are some components or parts of diffractometer used
4. Generator
For producing high voltage, a generator is used and located at the back chamber of
diffractometer. High voltage required for the production of x-rays. The voltage and current of the
generator is controlled by the software.
5. Gas cylinder
Gas cylinder consists of argon gas is also attached with the equipment, as we have a proportional
counter detector it requires gas to be purged in it. The gas in the cylinder is 99.9% pure Argon. It
may consist of ethane in some percentage in order to control the ionization process by electrons.
The gas is purged at a pressure of 6 bar.
6. Cables
There are two types of cables at the back of x-ray diffractometer one is power cable for
providing power to the equipment and second is data cable that attaches the equipment to the
computer for controlling parameters and obtaining real time data.
7. Chiller
A chiller is also attached to cool the water that is circulating in the x-ray tube as the temperature
of the equipment should not increase more than 20°C, the chiller consists of a pump also for
circulating water through the x-ray tube and the pressure at which water is pump is 3 bar.
Working of diffractometer
Before starting the diffractometer, it should be calibrated or set, for calibration of the
diffractometer Y2O3 is used as a standard sample. And as germanium crystal in monochromator
allow only Kα to pass, but further the Kα consists of two rays i.e. Kα1 and Kα2 for preventing Kα2
to fall on sample a fluorescence screen is used which is placed on the place of sample and the
security of the equipment is by-pass by pressing the key and then by shutting the light off the X-
rays are started and then by adjusting the slit on the sample holder the opening of r
ays is set such that only Kα1 will pass. Then after preparing the sample either powder or bulk the
sample with its cup is placed in the sample holder in the cabinet of the diffractometer and by
using the screw of the sample holder the height of the sample is adjusted because low height or
high height will not produce good results. After adjusting the height of the sample the cabinet is
closed and water circulation is started and the voltage and current of generator is increased
slowly to a required value then x-rays are fall on the sample and get diffracted and real time
data is ojbtained on the computer. This is how the x-ray diffractometer works.
Experimental procedure
As the sample 1 was a metal strip, for metal strip sample a sample holder prior to cabinet
holding was used on which the sample was placed by using a double side scotch-tape. The
sample was firmly hold on that and then placed in the sample holder of the cabinet by using
screw the height of the sample was adjusted and then further test was performed on the sample.
As sample 2 is a powder sample it is prepared by using a sample cup having a depth of 1 to 2
mm. The powder was placed on the cup and then a clean glass strip was used which was placed
on the cup and pressed and rotated for uniform distribution of the sample. There should be no
moisture either in the cup or in the powder otherwise the powder will get stick to the glass strip.
After uniform distribution of the sample the cup with powder was placed in the sample holder
and again a glass strip was placed on it and the height of the sample was adjusted by rotating the
screw and then the sample was ready for the test and further test was performed.
Observations and calculations
Following are the observations of both samples and their identification and calculation by using
match software:
1400
Sample 1
1200 1178
1000
800
Intensity
600
474
400
203
200 169
50
0
-20 0 20 40 60 80 100 120 140
2θ
Figure 3. XRD analysis of sample 1
The above XRD analysis of the sample#1 showed that it is Copper Cu, as predicted by Match
software with following parameters
Bravais lattice = Cube (Face centered Cubic) as (hkl) for all possible reflections are unmixed
Lattice parameter = a = 3.61300 Å
Table 1. Diffraction results of sample 1 (Copper)
Sample #1 (Copper Cu)
Angle (2θ) D-spacing (Å) Planes (hkl)
43.42 2.0825 (111)
50.63 1.8013 (200)
74.23 1.2765 (202)
90.07 1.0887 (311)
95.30 1.0423 (222)
Manual calculations
Calculating d-spacing
As we know that
𝒏𝝀 = 𝟐𝒅𝒔𝒊𝒏θ (n=1)
𝝀= 1.54 Å (for Cu Kα)
By putting these values
d= 1.54/2𝒔𝒊𝒏θ
for all values of θ the d-spacing is calculates as below:
from table 1,
2θ= 43.43 θ= 43.42/2 = 21.71
d= 1.54/2sin(21.71) = 2.08 Å
Similarly, for all values of 2θ from table 1, the d-spacing is calculated as given below:
For 2θ= 50.63 d= 1.800 Å
For 2θ= 74.23 d= 1.2760 Å
For 2θ= 90.07 d= 1.088 Å
For 2θ= 95.30 d= 1.041 Å
Determining bravais lattice
Above all values of (hkl) planes shows that they are unmixed, so the given sample 1 has face-
centered cubic structure.
Calculating lattice parameter
For any above plane the lattice parameter can be calculated as:
a = d √ h 2+k 2+l 2
for (111) plane
a= 2.08 √ 1+1+ 1
a= 3.60 Å
Similarly, for every plane with its respective d spacing value the lattice parameter will be same.
Sample 2
1600 1522
1400
1200
1000
800
586
600
379 357
400
200 166
0
-20 0 20 40 60 80 100 120 140
Figure 4. XRD analysis of sample 2
The above XRD analysis of the sample#2 showed that it is yttrium oxide Y2O3, as predicted by
Match software with following parameters
Bravais lattice = Cube
Lattice parameter = a = 10.58180 Å
Table 2. Diffraction results of sample 2 (yttrium oxide)
Sample #2 (Yttrium oxide Y2O3)
Angle (2θ) D-spacing (Å) Planes (hkl)
20.43 4.343 (211)
29.23 3.0525 (222)
33.78 2.6516 (400)
46.69 1.8689 (440)
57.77 1.5947 (622)
Manual calculations
Calculating d-spacing
As we know that
𝒏𝝀 = 𝟐𝒅𝒔𝒊𝒏θ (n=1)
𝝀= 1.54 Å (for Cu Kα)
By putting these values
d= 1.54/2𝒔𝒊𝒏θ
for all values of θ the d-spacing is calculates as below:
from table 2,
2θ= 20.43 θ= 20.43/2 = 10.215
d= 1.54/2sin(10.215) = 4.341 Å
Similarly, for all values of 2θ from table 2, the d-spacing is calculated as given below:
For 2θ= 29.23 d= 3.0516 Å
For 2θ= 33.78 d= 2.6502 Å
For 2θ= 46.69 d= 1.9431 Å
For 2θ= 57.77 d= 1.594 Å
Determining bravais lattice
Above all values of (hkl) planes shows that their sum (h+k+l) is even so the given sample 2 has
body-centered cubic structure.
Calculating lattice parameter
For any above plane the lattice parameter can be calculated as:
a = d √ h 2+k 2+l 2
for (211) plane
a= 4.341 √ 4 +1+1
a= 10.633 Å
Similarly, for every plane with its respective d spacing value the lattice parameter will be same.
Results
All above calculations and observations showed that the sample 1 is copper metal havig FCC
crystal lattice and with planes indexing as shown above in figure 3, having lattice parameter of
3.60 Å. While the second sample that is powder sample is yttrium-oxide Y 2O3 having body-
centered crystal lattice with lattice parameter of 10.633 Å and plane indexing is shown above in
figure 4.
Comparison of the results
As the match software indicated that the sample 1 and sample 2 are cubic but manual calculation
further indicated that the sample 1 is FCC while the sample 2 is BCC. Moreover, the calculation
of lattice parameter and d-spacing is almost same as done manually and predicted by the match
software.
Williamson-Hall plot for sample 2
Sometimes, the size calculated of crystal is larger than the size calculated by the XRD spectra,
this happens due to presence of strain in the sample. By finding the FWHM value of the XRD
spectra obtain we can plot the values to obtain the straight line. Then the slope of the fitted line
gives the strain as it has no units as that of slope and intercept gives the value of crystallite size.
-2
6.5x10
W illiam son-H all plo t
6.5x10
-2
linear fit
B (cos (theta)/ lem da)
-2
6.5x10
-2
6.5x10
-2
6.5x10
-2
6.5x10
-3 -3 -3 -3 -3 -3 -3 -3 -3 -3
1.5x10 2.0x10 2.5x10 3.0x10 3.5x10 4.0x10 4.5x10 5.0x10 5.5x10 6.0x10
sin(theta)/lemda
Figure 5. Linear fitting of Williamson plot for sample 2
Table 3. Slope and intercept for williamson_hall plot of sample 2
Discussion
As the slope indicates 6.0355x10-4 it showing the the strain in the sample and size of crystallite is
shown by the intercept i.e. 0.06494 angstrom. The negative sign indicates that the strain is
compressive strain. The sample 2 is of Yttrium oxide and the crystallite size and strain is
indicated by willamson-hall plot. In the above graph of Williamson-hall the y-axis contains the
Beta i.e. the value of full width half maximum (FWHM), it is obtained by finding the length of
the peak and dividing it by 2 and then finding its width from that and that is divided by two.
