XRD lab Fall 2022 Max Shapiro
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1040
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Material Science
Date
Jan 9, 2024
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10
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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
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Discussion
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Conclusion
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SUBTOTAL
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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
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
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