(a)
Interpretation:
The crystal structure of the metal is to be determined from the given x-ray diffraction results.
Concept Introduction:
X-ray diffraction (XRD) is a rapid analytical technique which is primarily used to identify phase of a crystalline material and it can provide information about the dimensions of the unit cell. The material to be analyzed is finely ground, homogenized, and its average bulk composition is determined.
Answer to Problem 3.98P
The crystal structure of the metal is FCC.
Explanation of Solution
Given information:
The figure which shows the results of the x-ray diffraction experiment is in the form of the intensity of the diffracted peak versus the
The graph between intensity of the diffracted peak versus the
It is required to tabulate the different values of lattice parameter
The table with different values is as follows:
Peak | Planar indices | ||||
1. | 17.5 | 0.023 | 3 | 111 | |
2. | 20.5 | 0.032 | 4 | 4 | 200 |
3. | 28.5 | 0.061 | 8 | 8 | 220 |
4. | 33.5 | 0.083 | 11 | 311 | |
5. | 35.5 | 0.093 | 12 | 222 | |
6. | 41 | 0.123 | 16 | 16 | 400 |
7. | 45 | 0.146 | 19 | 331 | |
8. | 46.5 | 0.156 | 20 | 420 |
The values of
Observe the sequence of
(b)
Interpretation:
The indices of the planes which produce each of the given peaks in the figure are to be determined.
Concept Introduction:
X-ray diffraction (XRD) is a rapid analytical technique which is primarily used to identify phase of a crystalline material and it can provide information about the dimensions of the unit cell. The material to be analyzed is finely ground, homogenized, and its average bulk composition is determined.
Answer to Problem 3.98P
The planar indices are
Explanation of Solution
Given information:
The figure which shows the results of the x-ray diffraction experiment is in the form of the intensity of the diffracted peak versus the
From part (a), the tabulated data for the lattice parameter
Peak | Planar indices | ||||
1. | 17.5 | 0.023 | 3 | 111 | |
2. | 20.5 | 0.032 | 4 | 4 | 200 |
3. | 28.5 | 0.061 | 8 | 8 | 220 |
4. | 33.5 | 0.083 | 11 | 311 | |
5. | 35.5 | 0.093 | 12 | 222 | |
6. | 41 | 0.123 | 16 | 16 | 400 |
7. | 45 | 0.146 | 19 | 331 | |
8. | 46.5 | 0.156 | 20 | 420 |
The planar indices are indicated on the
(c)
Interpretation:
The lattice parameter of the metal is to be determined.
Concept Introduction:
In a crystal lattice, the physical dimension of unit cells is indicated by Lattice Parameter. It is also called Lattice Constant. Lattices in three dimensions generally have three lattice parameters, they are h, k, and l.
Bragg's Law equation is as follows:
Here,
The formula to calculate the lattice parameter
Answer to Problem 3.98P
The lattice parameter of the metal is
Explanation of Solution
Given information:
The figure which shows the results of the x-ray diffraction experiment is in the form of the intensity of the diffracted peak versus the
From part (a), the tabulated data for the lattice parameter
Peak | Planar indices | ||||
1. | 17.5 | 0.023 | 3 | 111 | |
2. | 20.5 | 0.032 | 4 | 4 | 200 |
3. | 28.5 | 0.061 | 8 | 8 | 220 |
4. | 33.5 | 0.083 | 11 | 311 | |
5. | 35.5 | 0.093 | 12 | 222 | |
6. | 41 | 0.123 | 16 | 16 | 400 |
7. | 45 | 0.146 | 19 | 331 | |
8. | 46.5 | 0.156 | 20 | 420 |
To calculate the lattice parameter, it is required to choose any peak from the table. Choose peak 6 which has 400 planar indices.
The lattice parameter,
Here,
Substitute the above values in the equation 1,
Using this value of
Hence, the Lattice Parameter is
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