Midterm1_MAE251_Fall2023
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University of California, San Diego *
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251
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Aerospace Engineering
Date
Feb 20, 2024
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Uploaded by CoachManatee3931
MAE 251 – Structure and Analysis of Solids
Midterm #1 Solutions
Name: Lucas Chiang
PID:
A59023058 Signature: Lucas Chiang
Name: Yueh-Ting Tsai
PID:
A59023525
Signature: Yueh-Ting Tsai
An AlCu
2
Mn ordered Heusler alloy is an extremely important magnetic material. Several publications describing this material can be found at:
https://doi.org/10.1016/j.jmmm.2018.02.018
Heusler alloys, in general, also have applications as thermoelectric materials and shape memory alloys, among several others. See for example, a general description in wikipedia:
https://en.wikipedia.org/wiki/Heusler_compound
And recent reviews by Prof. Marc Meyers and Prof. Kesong Yang:
https://doi.org/10.1016/j.pmatsci.2022.101017
https://doi.org/10.1016/j.jallcom.2021.158854
1.
The crystal structure of AlCu
2
Mn can be found in the prototype structures handout (Structure 9).
(a)
Determine the atomic packing factor and density of this compound.
(b)
Calculate the structure factor for this compound.
(c)
Draw in separate unit cells all the planes that correspond to the first peak in the XRD pattern.
(d)
Determine the intensities of the peaks in the XRD pattern of this compound at diffraction angles from 20 to 80 degrees 2
.
(e)
Draw the XRD pattern of this compound at diffraction angles from 20 to 80 degrees 2
. Make sure to label all the peaks with their corresponding Miller indices.
2.
Sometimes during processing, MnAl
12
separates from the AlCu
2
Mn and precipitates into a distinct phase. From microscopy, it was determined that a mixed-phase composite contained 90 wt.% AlCu
2
Mn and 10 wt.% of MnAl
12
. Draw the X-ray diffraction pattern (from 20 to 80 degrees 2
) for this composite. Clearly label which
peaks correspond to each phase. Also, make sure to normalize the pattern so that the highest peak corresponds to an intensity of 100%.
The crystal structure of MnAl
12
can be found at:
https://legacy.materialsproject.org/materials/mp-1104165/
https://next-gen.materialsproject.org/materials/mp-1104165/
3.
For MnAl
12
, determine the following:
(a)
The angles between the y
-axis and body diagonal directions. Draw in separate unit cells (for clarity) all the body diagonal directions and mark their vector coordinates.
(b)
the angle between the (0 3 1) and (0 1
1
) planes; also, draw the two planes in two separate unit cells,
(c)
the density,
(d)
the atomic packing factor.
4.
During a manufacturing process for the production of a Mn
2
O
3
compound for battery technologies, a reducing atmosphere was established such that some of the manganese ions in Mn
2
O
3
were reduced to manganese metal. This resulted in a mixed metal/insulator composite consisting of Mn+Mn
2
O
3
in amounts of 259 g and 1052 g, respectively.
The crystal structure of Mn
2
O
3
is found at:
https://next-gen.materialsproject.org/materials/mp-565203
https://legacy.materialsproject.org/materials/mp-565203/
The crystal structure of Mn is found at:
https://legacy.materialsproject.org/materials/mp-35/
(a)
Determine the wt.% of each of the two phases in the composite.
(b)
Determine the mol.% of each of the two phases in the composite.
(c)
Determine the X-ray diffraction pattern of this mixed-phase composite at diffraction angles from 20 to 80 degrees 2
. Clearly label which peaks correspond to each phase. Also, make sure to normalize the pattern so that the highest peak corresponds to an intensity of 100.
Dr. Olivia A. Graeve
Page 2
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