# X-Ray Diffraction: Solving for θ Using nλ=2dsinθ

• dawud
In summary, the conversation discusses a homework problem involving diffraction and a thin film. The equations involved are nλ=2dsinθ and the attempt at a solution involves considering the effect of the thin film and deducing the angle of the crystal planes responsible for the observed interference. The conversation also mentions making assumptions and using the values of λ and θ to determine the plane spacing.
dawud

## Homework Statement

It's got a diagram in it so I have just attached a picture of it.

nλ=2dsinθ

## The Attempt at a Solution

I've really got no idea how to proceed with this one. I think you have to consider the effect of the thin film as well. Any ideas?

#### Attachments

• 20140211_183605.jpg
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From a quick reading up on the subject (of which previously I was blissfully ignorant), I would say that the incoming and outgoing beams must make the same angle to the planes in the crystal. Since it's powdered, the planes will be at every angle, but diffraction is only going to observed in those crystals with planes at the bisecting angle. So given the geometry of the source, sample and observed interference, you can deduce the angle of the crystal planes responsible.
Having done that, you can compute the plane spacing.

3. But you can make some assumptions. You have a ##\lambda##, there are 2 ##\theta##s. If n= 1, what is d for each of these ?

Once again, even quick replies cross. But there is a starting point.

Thanks a lot guys! I've got it now!

X-ray diffraction is a powerful technique used in materials science to determine the crystal structure of a material. It works by shining a beam of X-rays onto a sample and measuring the angles at which the X-rays are diffracted. The equation nλ=2dsinθ is known as Bragg's law and is used to calculate the angle θ at which the X-rays are diffracted.

In this equation, n is the order of the diffraction peak, λ is the wavelength of the X-rays, d is the spacing between crystal planes, and θ is the diffraction angle. The spacing between crystal planes, d, is a characteristic of the crystal structure and can be calculated using the Miller indices of the planes.

To solve for θ, we can rearrange the equation to θ=sin^-1(nλ/2d). This means that by measuring the diffraction angle, θ, and knowing the wavelength of the X-rays and the crystal structure, we can determine the spacing between the crystal planes.

In order to take into account the effect of the thin film, we can use the equation nλ=2ntsinθ, where t is the thickness of the film. This takes into account the additional path length the X-rays travel through the film before reaching the crystal planes.

Overall, X-ray diffraction is a complex but powerful technique for studying the atomic structure of materials. By understanding the principles behind Bragg's law, we can use X-ray diffraction to solve for θ and gain valuable insights into the crystal structure of a material.

## 1. What is X-Ray Diffraction?

X-Ray Diffraction is a scientific technique used to determine the structure of crystals by analyzing the diffraction pattern of X-rays passing through them. This method is commonly used in fields such as material science, chemistry, and geology.

## 2. How is θ calculated in X-Ray Diffraction?

The angle θ is calculated using the equation nλ=2dsinθ, where n is the order of the diffraction, λ is the wavelength of the X-rays, d is the distance between the crystal lattice planes, and θ is the angle of diffraction.

## 3. What does the value of θ represent in X-Ray Diffraction?

The value of θ represents the angle at which the X-rays are diffracted by the crystal lattice planes. This angle is used to determine the spacing between the lattice planes, which in turn provides information about the crystal structure.

## 4. How is X-Ray Diffraction used in determining crystal structures?

X-Ray Diffraction is used to determine crystal structures by measuring the diffraction pattern of X-rays passing through a crystal. This pattern is then analyzed to determine the angles and intensities of the diffracted beams, which can be used to calculate the positions of atoms within the crystal lattice.

## 5. What are the limitations of X-Ray Diffraction?

One limitation of X-Ray Diffraction is that it can only be used to study crystalline materials, as they have a regular lattice structure. It is also limited in its ability to determine the positions of light atoms, such as hydrogen, within a crystal lattice. Additionally, X-Ray Diffraction requires specialized equipment and expertise to perform, making it a complex and expensive technique.

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