X-Ray Diffraction Homework: Deriving (2theta) Values

In summary, the conversation discusses the calculation of the angular position of (2theta) for (100) and (110) planes using X-ray diffraction with Cu k-alpha and Mo k-alpha radiation on a crystal composed of two fractions with different cell parameters. The equations used include Bragg's law and the formula for calculating d. The speaker mentions finding different values for a and the need to repeat the calculation multiple times for each peak. They also mention that the different cell parameters may refer to different crystals or crystal structures within the sample.
  • #1
Lemenks
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Homework Statement



A crystal composed of two fractions, one having the a cell parameters of 4.123A and the other of 3.997A are subjected to X-ray diffraction using both Cu k-alpha and a Mo k-alpha radiation. Derive the angular position of (2theta) for (100) and (110) planes.
Explain the procedure you used for the calculation.

Homework Equations



Bragg's law: n*lambda = 2*d*sin(theta)

d = a/(h^2 + k^2 + l^2)^(1/2)

The Attempt at a Solution



I found both equations - I understand them but I don't know why a is different for both ions. I know that the ions radius will be different but when we scan the crystal, the value of a should be the same?

Anyway I will show one calculation, I know the method but I am not sure I can fully explain it.

d = a/(1+0+0) = a

n = 1

lambda = 1.542A for the Cu k-alpha radiation

1.542 = 4.123 sin(theta)

theta = 21.96

2*theta = 43.92 degrees.

I would repeat this 7 more times to find every peak for the two planes, the two forms of ka radiation and the two atomic radii. ~ I don't know why a is different for both atoms, if the lattice repeats infinitely and there are equal numbers of both atoms, then it seems like there should be equal distances between both atoms.
 
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  • #2
I think the different cell parameters refer to different crystals or crystal structures - your sample has both, but not at the same place.
 
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FAQ: X-Ray Diffraction Homework: Deriving (2theta) Values

1. What is X-Ray Diffraction?

X-Ray Diffraction is a technique used to study the structure of materials by analyzing the diffraction patterns produced when a beam of X-rays is directed at the material. This technique provides information about the arrangement of atoms and molecules in a material.

2. What is the purpose of deriving (2theta) values in X-Ray Diffraction Homework?

(2theta) values are derived in X-Ray Diffraction Homework in order to determine the angles at which the X-rays are diffracted by the material. These values are used to calculate the spacing between atoms in the material, which can provide valuable information about its structure and composition.

3. How are (2theta) values derived in X-Ray Diffraction Homework?

(2theta) values can be derived using the Bragg's Law, which states that the angle of diffraction is equal to twice the angle of incidence when X-rays are diffracted by a regular crystal lattice. This can be calculated using the wavelength of the X-rays and the spacing between atoms in the material.

4. What factors can affect the (2theta) values in X-Ray Diffraction?

The (2theta) values in X-Ray Diffraction can be affected by several factors, including the wavelength of the X-rays, the spacing between atoms in the material, and the angle of incidence of the X-rays. Additionally, the crystal structure and orientation of the material can also impact the (2theta) values.

5. How are (2theta) values useful in X-Ray Diffraction analysis?

(2theta) values are useful in X-Ray Diffraction analysis because they can provide information about the crystal structure and composition of a material. By comparing the (2theta) values obtained from a sample with known values for different materials, scientists can identify and characterize unknown materials.

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