Energy dispersive x-ray spectroscopy (EDX) is a commonly used characterization technique in Materials Science to determine the elemental composition of materials. To do this, EDX measures the emitted characteristic x-rays from materials (e.g. Kα), generated due to the excitation of electrons from a lower energy shell to a higher energy one.
Assume that you are working as a Materials Engineer in a company that produces cars. Your company has purchased 1 ton of Ni-Cr-Co alloy to fabricate a certain part of the car. Your boss asks you to determine whether the material your company purchased is, in fact Ni-Cr-Co alloy. If it there is another element present in the material, you will return the purchased material and stop production. So, you perform EDX analysis on your material and you see that three x-ray energies are detected: 5416, 6406 and 7479 eV. Determine which elements are present in your material and decide whether you should send the purchased material back or continue production. (Speed of light: 3 x 108 m/sec, Planck’s constant: 6.63 ×10−34J⋅s =4.136×10−15 eV.sec)
I have an issue with the 6.406 keV energy. Check the chart of EDX analysis. https://www.unamur.be/services/microscopie/sme-documents/Energy-20table-20for-20EDS-20analysis-1.pdf
To determine the elements present in the material, we need to analyze the detected x-ray energies and match them to the characteristic x-rays of different elements. The detected x-ray energies can be correlated with the energy difference between different electron shells in the atoms of the elements.
In this case, the detected x-ray energies are 5416, 6406, and 7479 eV. We will calculate the energy differences between the K and L shells for various elements using the given formula:
ΔE = E_L - E_K
where ΔE is the energy difference, E_L is the energy of the L shell, and E_K is the energy of the K shell.
Let's calculate the energy differences for a few elements:
For Nickel (Ni):
ΔE = 7500 - 5320 = 2180 eV
For Chromium (Cr):
ΔE = 6400 - 5820 = 580 eV
For Cobalt (Co):
ΔE = 6900 - 6320 = 580 eV
Comparing these energy differences with the detected x-ray energies, we find that the energy difference of 580 eV matches with the detected energy of 6406 eV. This indicates that Chromium (Cr) is present in the material.
No other energy difference matches the detected energies of 5416 eV and 7479 eV. Therefore, we can conclude that only Nickel (Ni), Chromium (Cr), and Cobalt (Co) are present in the material.
Since we have identified all the expected elements in the material (Ni, Cr, Co), we can proceed with production and fabricate the desired part for the car. There is no need to send the purchased material back.
To determine the elements present in the material, we need to analyze the detected x-ray energies using the principles of energy dispersive x-ray spectroscopy (EDX).
The x-ray energy levels detected (5416, 6406, and 7479 eV) correspond to the characteristic x-rays emitted by different elements in the material. These energies are specific to each element and are a result of electron transitions within the atoms of those elements.
To determine which elements are present, we need to compare the detected energies with the characteristic x-ray energies of various elements. These characteristic energies can be calculated using the equation:
E = ΔE = hc/λ
Where:
E = Energy (in eV)
ΔE = Change in energy
h = Planck's constant (4.136×10^−15 eV.sec)
c = Speed of light (3 x 10^8 m/s)
λ = Wavelength of x-rays
First, let's convert the given x-ray energies to wavelengths. Since we know the speed of light, we can use the equation:
λ = c/f (where f = frequency)
Given that energy (E) is related to frequency (f) by the equation:
E = hf
We can rearrange the equations to solve for wavelength (λ) using:
λ = hc/E
Using Planck's constant (h = 4.136×10^−15 eV.sec) and the speed of light (c = 3 x 10^8 m/s), we can solve for wavelength:
For the first x-ray energy level of 5416 eV:
λ = (4.136×10^−15 eV.sec * 3 x 10^8 m/s) / (5416 eV)
For the second x-ray energy level of 6406 eV:
λ = (4.136×10^−15 eV.sec * 3 x 10^8 m/s) / (6406 eV)
For the third x-ray energy level of 7479 eV:
λ = (4.136×10^−15 eV.sec * 3 x 10^8 m/s) / (7479 eV)
Now we can convert the wavelengths to their corresponding x-ray elements using the characteristic x-ray energies.
By referring to a database or table of characteristic x-ray energies, we find that the closest characteristic energy levels to the calculated wavelengths correspond to the following elements:
For the first x-ray energy level:
- The closest characteristic energy (in eV) is for Chromium (Cr) at approximately 5415.6 eV.
For the second x-ray energy level:
- The closest characteristic energy (in eV) is for Nickel (Ni) at approximately 6403.9 eV.
For the third x-ray energy level:
- The closest characteristic energy (in eV) is for Cobalt (Co) at approximately 7484.3 eV.
Based on this analysis, the detected x-ray energies suggest that Chromium (Cr), Nickel (Ni), and Cobalt (Co) are present in the material. Therefore, the material purchased by the company is indeed a Ni-Cr-Co alloy, and production can continue as planned.