Thermal Diffraction and Expansion

[rannasquaer]

Does anyone know how I can relate the diffraction in a circular crack to the thermal expansion of that crack?

Something that I relate the gap radius with the distances between the light and dark fractions of the diffraction figure.

 

[jvicens]

Yes, there is a direct relationship between the diffraction in a circular crack and the thermal expansion of that crack. This is known as the Bragg equation, which states that the spacing between the light and dark fringes in a diffraction pattern is inversely proportional to the distance between the crack edges.

The Bragg equation is given by:

nλ = 2d sinθ

where n is the order of the diffraction pattern, λ is the wavelength of the incident light, d is the spacing between the crack edges, and θ is the angle of diffraction.

If we rearrange this equation to solve for d, we get:

d = nλ / 2sinθ

This equation shows that the spacing between the crack edges is directly proportional to the wavelength of the incident light, and inversely proportional to the sine of the angle of diffraction. The angle of diffraction can be related to the thermal expansion of the crack by considering the thermal strain in the material.

When a material undergoes thermal expansion, its dimensions change due to the increase in temperature. This leads to a change in the spacing between the crack edges, which in turn affects the diffraction pattern. As the crack expands, the spacing between the edges increases, resulting in a larger angle of diffraction and a corresponding decrease in the spacing between the light and dark fringes in the diffraction pattern.

Therefore, by measuring the change in the spacing between the light and dark fringes in the diffraction pattern, we can determine the amount of thermal expansion that has occurred in the crack. This can be used to monitor the thermal stability of materials and to predict the behavior of cracks under different temperature conditions.

In summary, the diffraction in a circular crack can be related to the thermal expansion of that crack through the Bragg equation. By measuring the spacing between the light and dark fringes in the diffraction pattern, we can determine the amount of thermal expansion that has occurred in the crack and use this information to study the behavior of materials under different temperature conditions.