X ray diffraction For crystal structure Analysis

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1. Find the crystal structure , the lattice parameter of the metal.
Known 2[tex]\theta[/tex] of the peaks
17
21
28
33
35
41
45
46
2. bragg's law [tex]\lambda[/tex]=2 d[tex]_{h,k,l}[/tex] /b]sin[tex]^{2}[/tex]([tex]\theta[/tex])
Also, the cubic interplanes distance d[tex]_{h,k,l}[/tex] = a0/(squr(h[tex]^{2}[/tex]+k[tex]^{2}[/tex]+l[tex]^{2}[/tex])
3. The Attempt at a Solution :
Since I didn't know the lattice parameter I just take the sin[tex]^{2}[/tex] of every theta and the divide every number between the smallest number, (the first peak one), to get integers. According to that I should know which cubic structure is( BCC FCC SC) What's happens is that I get the following numbers with all the procedure 4,6,12,14,16,22,26,28. I can't identify which one is.

Thanks for any help.

 

[Valkarie]

The numbers you have obtained correspond to the Miller indices of a cubic lattice structure. The Miller indices of a crystal structure are derived from the Bragg's law, which states that the angle of incidence for any reflection of an X-ray beam off a crystal lattice is equal to the angle of diffraction. The Miller indices can be used to identify the type of crystal structure, and in this case, it is likely that the structure is a face-centered cubic (FCC) lattice. To calculate the lattice parameter, you will need to use the Bragg's law equation, which is: λ = 2d_hkl/sinθ, where λ is the wavelength of the incident X-ray beam, d_hkl is the interplanar spacing of the crystal lattice, and θ is the angle of incidence.

 

[piercas]

I can provide some feedback and guidance on your approach to this problem.

Firstly, it is important to note that X-ray diffraction is a powerful technique for determining the crystal structure of a material. It works by directing a beam of X-rays onto a sample and measuring the diffraction pattern that is produced. This pattern is then analyzed to determine the arrangement of atoms within the crystal lattice.

In order to determine the crystal structure and lattice parameter of a metal using X-ray diffraction, the first step is to collect the diffraction data. This involves measuring the diffraction angles (2θ) at which the peaks occur. From the data provided, we can see that there are 8 peaks with corresponding 2θ values of 17, 21, 28, 33, 35, 41, 45, and 46 degrees.

Next, we can use Bragg's law to calculate the interplanar spacing (d) for each peak, using the formula \lambda=2 d_{h,k,l} /sin(\theta), where λ is the wavelength of the X-rays, and h, k, and l are the Miller indices of the crystal planes that are diffracting the X-rays. Note that the Miller indices can be determined by dividing the 2θ values by 2 and rounding to the nearest integer. For example, for the first peak at 17 degrees, the Miller indices would be (1, 0, 0).

Once we have calculated the interplanar spacing for each peak, we can then determine the lattice parameter (a) using the formula d_{h,k,l} = a0/(squr(h^{2}+k^{2}+l^{2}), where a0 is the lattice parameter for a cubic crystal structure (which is what we are assuming for this problem).

From your attempt at a solution, it seems that you have correctly calculated the interplanar spacing for each peak. However, your approach to identifying the crystal structure using the ratios of the interplanar spacings is not accurate. Instead, you should compare the calculated lattice parameter (a) to the known values for different cubic crystal structures (such as BCC, FCC, and SC) to determine the most likely crystal structure.

In summary, to determine the crystal structure and lattice parameter of a metal using X-ray diffraction, you would need to collect diffraction data, use Bragg's law to calculate