XRD lab Fall 2022 Max Shapiro .docx (1)
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Single- Phase Identification via XRD Lab Report
Student Name: _________________________________________________________
Section _______________________________________________________________
Lab Session Date: ______________________________________________________
Lab Report Due Date: ___________________________________________________
TA:
Lab Report
Possibl
e Points
Points
Awarded
Questions
20
Procedure
10
Results
….
Data analysis
…
Discussion
…
Conclusion
…
SUBTOTAL
…
School of Materials Science and Engineering
Georgia Institute of Technology
Prepared
8 November 2022
1
Lab: Utilizing X-ray Diffraction to Identify Unknown Powder for single and
multi-phase structures
Abstract
An x-ray diffractometer and a Hanawalt Search Manual were used in conjunction to first identify an
unknown powder and secondly a mixture of unknown powders. For the single phase powder peak intensity
values for a range of 2θ values are analyzed, and considerations of experimental variation are discussed.
With the aid of spreadsheets, the plot/replot method will be used to separate peak intensities, allowing for
the identification of the phases present in the powder mixture.
Introduction
When incident light waves have a wavelength on the order of repeating scattering centers,
diffraction can occur.
One example is electromagnetic radiation, such as a beam of x-rays, incident on a
crystal lattice. Crystal lattices are comprised of many parallel planes of atoms (each atom is equivalent to a
scattering center). Each particular crystallographic plane (ie. 110, 100, 220) has unique spacing distances,
d
hkl
.
These interplanar spacings depend on both crystal structure and composition. At certain angles of
incidence, the diffracted parallel waves constructively interfere and create detectable peaks in intensity.
W.H. Bragg identified the relationship illustrated in
Figure 1
and derived a corresponding equation,
eqn. 1
.
Figure 1:
An illustration of Bragg’s law showing constructive interference occurs at particular angles with
respect to a lattice, constructive interference only occurs integer multiples of the incident wavelength, λ.
nλ = 2d’ sin θ
or
(
λ = 2d
hkl
sin θ
, in which ‘order’ of diffraction has been taken into account) [
eqn. 1
]
When a peak in intensity is observed,
eqn. 1
is necessarily satisfied. Consequently, one can calculate
d-spacings based on the angles at which peaks are observed. By calculating the d-spacings of the three
strongest peaks, a single-phase material can readily be identified using a Hanawalt Search Manual, which
lists d-spacings of thousands of materials in order of observed intensity. Often more than one material may
seem to fit the experimental data. One way to determine which indexed material best matches an
experimental pattern is to calculate a figure of merit. One popular figure of merit is given by
eqn. 2,
where
N
poss
is the number of independent diffraction lines listed in the powder diffraction file (pdf) for the 2θ
range scanned, Δ2θ is the average absolute discrepancy between indexed and observed 2θ values, and N is
the number of peaks in the experimental pattern. A higher figure of merit, F
N
, means a better match.
Obviously the figure of merit described does not include analysis of the relative peak heights in the pattern;
so, for complete analysis, some manual interpretation must be utilized.
2
[
eqn. 2
]
Because the possible 2θ reflections depend on crystal structure and satisfying Bragg’s law,
predicting the diffraction angle for
any
set of planes in a particular structure is possible through a general
relationship produced by combining Bragg’s law and a particular structure’s plane spacing equation.
Eqn.
3
is the plane spacing equation for cubic lattices where
d
hkl
is the interplanar spacing,
a
is the lattice
parameter and
h
,
k
, and
l
are the Miller indices for a particular plane.
[
eqn. 3
]
In this lab, we will be using the powder diffraction method, which is easily the most popular
diffraction technique. Powder diffraction requires a polycrystalline sample and monochromatic x-rays
(fixed λ). These requirements simplify how diffraction peaks are measured. If the sample were a single
crystal, it would need to be rotated until the Bragg condition is satisfied to see a spike in diffracted
intensity. Because the powder is assumed to be made up of randomly oriented grains, by chance, certain
crystals will be oriented for diffraction of one plane, while another group will be oriented for the diffraction
of another plane. As a result, we observe every possible lattice plane capable of diffraction.
Identifying multiple phases in a particular X-ray pattern, especially when containing more than
two phases, can be quite cumbersome.
There are now many software programs that provide automated
searches of the ICDD database for matches to a particular pattern. However, these programs generally only
rank possible identification matches by some figure of merit. For complete analysis some manual
interpretation must be utilized, such as the fit of relative peak intensities.
The purpose of this lab is to
identify two separate single phase materials in a powder mixture by using an x-ray diffraction pattern,
possible matches identified in a Hanawalt search manual, and spreadsheet calculations. By performing
manual phase identification, a better understanding of identification software and its limitations will be
garnered.
It is assumed that the examined powder mixture is crystalline and randomly oriented. Often in the
case of a multiple constituent material, peaks from individual phases will add, possibly producing double
peak structures and/or single peaks with increased intensity due to overlap at particular 2θ values.
To
determine the identities of the separate phases, one can use a technique known as the plot/replot method.
An example of the final result of a plot/replot method is shown in
Figure 2
.
3
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Figure 2:
Plot generated from unknown powder diffraction pattern with overlays of identified compounds.
Generated from data in Elements of X-ray Diffraction by Cullity and Stock, 3
rd
edition, 2001. See example
spreadsheet on Canvas
Notice the two materials identified (overlays) in
Figure 2
account for all of the peaks present in the original
diffraction pattern.
Using a phase identification procedure, one can calculate d-spacings of the strongest
peaks and use a Hanawalt Search Manual to determine the first phase present in the sample. Once the first
phase is identified, the normalized intensities will be subtracted off and the result renormalized.
The
second phase will then be identified from the remaining peaks, and a residual error will be calculated.
Questions to be answered for Background/Introduction
Often what are actually diffracted beams are referred to as “reflected beams.” Diffraction of x-rays by
crystals and the reflection of light by mirrors are sometimes confused because both phenomena result in the
angle of “reflection” being equal to the angle of incidence.
1) (2 Points) Name one way in which diffraction and reflection differ. (Hint: consider the qualities of
the incident beam, any equations governing either, what is required for each to occur, etc.)
Reflection involves a change of direction off of a surface with a definite angle of reflection depending onhy
on the incident angle. Diffraction on the other hand can will change direction depending on the medium
that it hits. It is interacting with the actual material on a micro scale and bends and changes direction as it
passes through the medium. The change in medium that the xray passes through determines the angle of
change rather than a reflection that bounces of a material in the same way it comes in.
4
2) (2 Points) Because interatomic distances for most crystalline solids are on the order of __________,
x-ray wavelength beams can be used to measure lattice spacing. Knowing this, could visible light be
used for crystal diffraction? Please circle one of the following:
YES
NO
3) (2 Points) In a typical X-ray pattern, intensity is plotted versus INCREASING 2θ which
corresponds to _____________ d-spacing.
decreasing
4) (2 Points) If the atomic radius of aluminum (FCC crystal structure) is 0.143 nm, what is the d
spacing between (100) planes? (show your work)
For FCC
𝑎 = 4?/(2
1/2
) = 4(. 123??)/(2
1/2
=. 404??
? = 𝑎/(ℎ
2
+ ?
2
+ ?
2
)
1/2
for (100) d(hkl)=a=404nm
5) (3 Points) If the spacing between the (3 1 1) planes of Al is 0.122 nm, calculate the lattice
parameter (a) for Al.
? = 𝑎/(ℎ
2
+ ?
2
+ ?
2
)
1/2
.122nm=a/
(9 + 1 + 1)
1/2
𝑎 =. 122?? * (11)
1/2
=. 405 ??
6) (3 Points) Assuming the crystal structure is cubic, rearrange the list of Miller’s Indices to put them
in order of decreasing (largest -> smallest) interplanar spacing (3 1 1), (2 2 2), (2 1 1), (3 0 0).
(2 1 1)
(3 0 0)
(3 1 1)
(2 2 2)
7) (2 Points) What are some of the difficulties associated with the identification of multiple phases in
a mixture?
The peaks may be mixed together and cause broadening of the peaks that will skew the data. Some of
these phases could be left out due to extinction depending on the crystal type. This woul dmena
certain phases that are present would be left out of the data.
8) (2 Points) Repacking a powder sample for an additional scan (repacked because the scan varied
from expected relative peak heights) resulted in drastically different relative intensities, which
eliminated the primary source of _____________as the primary source of relative intensity error.
(Hint: how might repacking affect the orientation of the crystals?)
preferred orientation
9) (2 Points) You produced an extremely thin coating (phase X) on a small amount of powder
material (phase Y). Because phase X is black and phase Y is white you know you were successful in
forming a coating because the resulting material was black and SEM/EDS analysis revealed a
5
continuous coating containing the coating elements was present; however, only phase Y was detected
in a diffraction pattern of this material. How would you set up a subsequent scan to detect phase X?
(Hint: how would you reduce the influence of the bulk in your collected signal?)
In order to find just one of the phases you would change the diffraction angle to more speciifialy target the
phase you want to find. You would do this by opening up the filter slits to allow more xrays to interact with
your sample. You would lose resolution but gain more dta points and then e able to filter out the bulk issue.
Procedure
It is assumed that the unknown powder sample is homogeneous in composition, crystalline in structure, and
randomly oriented. Different sample holders may be required for different specimen volumes (e.g. if you
only have a small amount of sample).
1) (5 Points) In your own words, briefly describe the sample preparation procedure. Name the two
types of sample holders used in this lab. What is the primary reason for choosing one sample holder
over the other? What affect does sample volume have on the diffracted beam intensity?
sample must be a fine powder
1.
Clean holder with acetone
2.
fill holder with sample enough to cover the full space
3.
pat down
4.
put sample in the machine with correct parameters
The two types of holders were 16 and 27 named so for their size. The larger holder allows more
x-rays to interact with the material and therefore a higher intensity overall to the reader. This allows
for better data accuracy. There are also sample holders that are visible and invisible to the scanner.
The invisible ones are made of a material that xrays will pass thorugh completly. So they will not
show up in your scan data. This is important for accuracy and if you have a very low amount of the
sample in the holder.
2) Please watch the video below and answer questions:
https://www.jove.com/science-education/10446/x-ray-diffraction
3). Use the data provided for the single phase and do the analysis below
Results
Insert a plot showing the diffraction pattern generated with your instrument settings (and the data
provided). Normalize the intensity in your plot such that the most intense peak has an intensity of “100.0”
and all other intensities are relative to this value. Use the provided label below with your sample name
inserted in the blank space.
Answer the following questions for the set up in the lab that the single phase and multi-phase was
performed:
3a) (5 Points) Provide the instrument parameters used for data for the lab Performed.
6
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Monochromatic x-ray source: K(alpha 1) with wavelength 1.5406 A (include units).
X-ray tube operating settings: 45 kV , _____40___ mA
Start 2 θ: 10.0064 degrees
End 2 θ: 109.998
Incident Soller Slit: .8709
Mask Size:20 mm
Incident Divergence Slit: .8709 degrees
Incident Anti-scatter Slit: 1 degree
Diffracted Soller Slit:
NONE
Diffracted Anti-scatter Slit: 10mm
Detector:
X’celerator
3b) (10 Points) Figure 3: Diffraction Profile for the Single Phase Sample (Insert Figures Below):
3c) (10 Points) List each observed peak for the single phase sample in the Tables 1a, b and c
.
In the
space below, show your work for the conversion of the observed 2θ value to the corresponding value
of d-spacing. State any assumptions needed for this calculation.
Table 1: PEAK DATA FOR SAMPLE _________
2
θ
I
d
I/I
max
37.0509
2.42441
43.0436
69.89
2.09974
2.53
7
62.469
74.8862
78.9915
2762
2189
106.8
138.4
1.48560
1.26700
1.21112
100
79.25
3.866
5.0108
Data Analysis
Use the Hanawalt Search Manual to select at least 2 possible matches for your single phase sample. Report
the values of d-spacing, relative intensity and corresponding hkl values for each entry in the tables below.
Then, calculate the figure of merit for each possible match to determine which possible match is the best
candidate for the unknown sample. Show an example calculation for figure of merit in the space below.
1) (5 Points) Table 2 PDF for GaMgNi
d
I
hkl
2θ
pdf
2θ
exp
∆2θ
|
|
1.211
1.12
1.04
1.002
.988
.9381
1.2
.4
100
.6
.1
12.1
.2
.2
(111)
(200)
(220)
(311)
(222)
(400)
(331)
(420)
78.994
84.84
94.519
102.335
110.394
26.022
30.156
43.23
51.01
53.45
62.55
68.9
71.98
78.96
86.86
95.5
102.4
110.33
.142
0
.10
.20
.3
.991
.03
nλ = 2dsinθ
d= nλ/2sinθ
8
?𝑖?
−1
𝛌/2? = ?ℎ??𝑎
?𝑖?
−1
1. 54/23. 42 = 26. 022
F
N
=
only for 2theta between 37 and 78
(1/ ∆2θ
|
|)(
𝑁
𝑁????
)
(1/.3466)(6/8)=2.16
2) (5 Points) Table 3 PDF for MgO
d
I
hkl
2θ
pdf
2θ
exp
∆2θ
|
|
2.42
2.1000
1.484
1.266
1.212
1.05
.96355
.93915
.85732
.80829
11.4
100
45.7
5.1
11.3
4.2
1.6
10.6
8.1
1.2
(111)
(200)
(220)
(311)
(222)
(400)
(331)
(420)
(422)
(511)
37.044
43.038
62.497
74.931
78.889
94.381
106.154
110.212
127.922
144.727
37.106
43.02
62.51
74.921
78.886
94.333
106.09
110.14
127.8313
144.5875
.62
.028
.004
.01
.003
F
N
=
… only for 2 theta between 37 and 78
(1/ ∆2θ
|
|)(
𝑁
𝑁????
)
=1/.133(5/10)
=3.75
Discussion
1) (8 Points) Bragg’s Law gives us discrete values for diffraction peaks. However in the lab, we find
that diffraction peaks have width. Why?
This is from Scatted beams that are
not parallel and create width to the peak. This
is because of defects in the material causing a lattice strain Other defects include
stacking faults within the material. Also purely reflected-rays that are not difracted
could result in data skewing.
2) (8 Points) In this lab we assumed that the sample grains were randomly oriented. How would the
measured diffraction pattern change if they were preferentially oriented? (For example, in a textured
polycrystalline thin film).
The peaks would be increased due to the preferential orientation of those peaks in the sample. There
would e over and under represented data from the orientations.
9
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3) (8 Points) Draw what would your data look like if instead of a crystalline material, we looked at an
amorphous material? Why does it look this way? (Remember proper axis labels!)
This is due to an extremely wide range of scattering form the sample that all blends together. They
have so many different types of peaks and are all so scattered that the intensity is low and
indistinguishable.
Conclusions
(18 Points) Summarize your results and explain what the analysis of your data shows for the single
phase analysis.
I used the given peak data of 5 peaks to fit with the given pdf data and I could find the best math for
the sample. The highest figure of merit tells me that this is the greatest likelihood of a math in the
experiment. I found the unknown powder to be MgO. This seems likely because several of the D
spacings and 2theta values were very similar between the given pdf and the single phase sample. It
had a figure of merit of 3.75 according to my calculation.
References
B. D. Cullity and S. R. Stock.
Elements of X-Ray Diffraction
, 3
rd
edition. Prentice Hall, 2001. Chapters 3, 4,
and 9.
10