Understanding Bragg's Law in X-Ray Diffraction

In summary, the Bragg's law states that the path difference between two incident rays is equal to n times the wavelength, where n is an integer, and is equal to 2dsinθ, where d is the distance between the reflecting planes and θ is the angle of incidence. In the derivation of this formula, the two incident rays are assumed to be parallel, but the reflected rays are also assumed to be parallel. This may seem contradictory since the reflected rays should meet in order for superposition to occur. However, this assumption is valid because the distance between the reflecting planes is effectively infinite, or a lens can be used to simulate this distance. This is similar to the assumption made in Fraunhofer diffraction. In
  • #1
manofphysics
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We all know, Bragg's law , [tex]n\lambda=2dsin\theta[/tex]
where [tex]2dsin\theta=path difference[/tex].
In the derivation of the path difference we take the two incident rays to be parallel which is perfect BUT we take reflected rays also to be parallel.How can this be since the reflected rays have to MEET for superposition to take place.
This is the same as in FRAUNHOFER diffraction, where we CAN take parallel rays due to the distance being effectively infinity or due to the use of LENS.
But we are not using a lens nor is the distance supposed to be very large(infinity) in the experimental methods of Xray diffraction ( rotating crystal, powder photograph etc.).
So, how is it that this formula works?
 

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  • #2
I'm missing something here.

You have parallel incident waves reflecting from parallel planes...why wouldn't the reflected rays also be parallel?

Or are you trying to treat the wavefront as a single point rather than a plane?
 
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  • #3
when an EM wave strikes an atom, a spherical wave front is emitted. ie waves are emitted in ALL directions . Now we are considering the emitted rays by two atoms which are parallel,
But the parallel rays will not meet for interference, we need to use a lens...
(I am using an analogy of diffraction in optics here. as both are almost similar, I think)
 
  • #4
The rays do meet because the rays are not exactly parallel. They are only approximately parallel. And the approxmation is good enough because the place where they meet is "far" away.
 
  • #5
So, I guess it is the same assumption that we take in Fraunhofer diffraction.
Thanks for the reply ,Edgardo.
 

1. What is Bragg's Law in X-Ray Diffraction?

Bragg's law in X-ray diffraction is a fundamental principle that explains the relationship between the angle of incidence of an X-ray beam on a crystal and the resulting diffraction pattern. It states that when X-rays are incident on a crystal at a specific angle, the scattered X-rays will constructively interfere, resulting in a diffraction pattern. This law is essential in understanding the structure and properties of crystals.

2. How is Bragg's Law derived?

Bragg's law is derived from the principles of constructive interference and the properties of waves. When X-rays are incident on a crystal, they interact with the atoms within the crystal lattice, causing them to scatter in all directions. However, at certain angles, the scattered rays will have a path difference that is a multiple of the wavelength, resulting in constructive interference and a strong diffraction signal. This angle is known as the Bragg angle and is given by the equation nλ = 2dsinθ, where n is the order of diffraction, λ is the wavelength of the incident X-rays, d is the distance between crystal planes, and θ is the Bragg angle.

3. What is the significance of Bragg's Law in X-Ray Diffraction?

Bragg's law is essential in X-ray diffraction as it allows scientists to determine the atomic and molecular structure of crystalline materials. By measuring the angle and intensity of the diffracted X-rays, the distances between crystal planes can be calculated, providing information about the arrangement of atoms within the crystal lattice. This information is crucial in fields such as material science, chemistry, and biology, as it helps in understanding the properties and behavior of materials at the atomic level.

4. How does Bragg's Law relate to the properties of crystals?

The properties of crystals, such as their strength, hardness, and optical properties, are directly related to their atomic and molecular structure. Bragg's law allows scientists to determine this structure by analyzing the diffraction patterns produced by X-rays interacting with the crystal lattice. By understanding the arrangement of atoms within a crystal, scientists can also predict and manipulate its physical and chemical properties.

5. How is Bragg's Law used in practical applications?

Bragg's law is used in various practical applications, including material analysis, crystallography, and medical imaging. It is commonly used in X-ray crystallography to determine the structure of proteins and other complex molecules, which is crucial in drug development and understanding biological processes. It is also used in material science to analyze the crystal structure and properties of new materials, and in medical imaging techniques such as X-ray diffraction imaging and X-ray computed tomography (CT) to create detailed images of internal structures in the human body.

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