- It is a universal wave phenomenon and is characterized by the same laws when observing wave fields of different natures, including light waves, sound waves, water waves, and even matter waves like electrons.
- Diffraction is related with the phenomenon of interference, which is formulated in The Huygens–Fresnel principle - the main postulate of wave theory, describing and explaining the mechanism of wave propagation.
A diffraction minimum is observed if the number of zones is even: $$ a\sin\varphi = \pm m \lambda $$ In this case, the amplitude of the resulting oscillation at the point is zero since the oscillations from a pairs of neighboring zones cancel each other out.
If the number of Fresnel zones is odd, a diffraction maximum is observed: $$ a\sin\varphi = \pm (2m + 1)\frac{\lambda}{2}$$ where \(m = 1,2,3...\) order of diffraction, \(a\) - width of a slit, \(\varphi\) - a diffraction angle and \(\lambda\) is a wavelength.
In the case of Fraunhofer diffraction approximation (a screen is positioned far from the slit) the intensity of the light is determined by equation: $$ I(\varphi) = I_0\left(\frac{sin(\beta)}{\beta}\right)^2$$ where: \( \beta = \frac{\pi a}{\lambda} sin(\varphi)\), \(I_0\) is the intensity of the incident wave, \(\varphi\) is the angle between the direction of observation and the normal to the diffracting aperture or obstacle, that depend on the width of the slit \(a\) and the wavelength of the wave \(\lambda\).
Using the "Diffraction Visualizer," observe how light diffracts when passing through a single slit. Adjust the wavelength of the beam with the "Wavelength" slider on the left and the aperture size with the "Aperture" slider on the right. This setup allows for easy exploration and observation of the dependencies between wavelength, aperture size, and the resulting diffraction pattern.
In this section, wave propagation (the initial state of which is given by the Gaussian profile in the previous section) through the barrier is simulated. In other words, here we can analyze the temporal evolution of the wave packet in the barrier system.
Laser diffraction analysis is a widely used technique for measuring particle size, especially in powders, suspensions,
and emulsions, used in the development of new materials or for quality control.
This technique leverages the principle of diffraction to determine the size distribution of particles within a sample over a wide measurement range (10 nm to 4 mm).
The method is based on the deflection of a laser beam by an ensemble of particles dispersed in either
a liquid or an air stream. Where the angles of diffraction or scattering are dependent on the particle size .
MICROTRAC,
PTL.
The Mie theory (in the case of light scattering) considers spherical, transparent particles that absorb part of the light, with a size comparable to the laser's wavelength.
For particles that are spherical, opaque, and have a diameter much larger than the wavelength of the laser beam, we can applied the Fraunhofer model for diffraction light in sferical apperture:$$ \sin\theta = \frac{1.22 \lambda} {d}$$ where \(d\) is the diameter of the particle, \(\lambda\) - a wavelength of light, and \(\theta\) is the angle observation of the first diffraction minimum.
The method of Light Diffraction is suitable for a variety of materials, easy to operate, and offers high accuracy and reproducibility.
Today, electron diffraction is an integral technique of transmission electron microscopy (TEM) systems that is widely employed in materials science, nanotechnology, and other fields for analyzing the structures of materials, including metals, semiconductors, and biological specimens. MyScope Nanoscience Instruments.
This methodology is based on the idea that:
- Atomic planes within a crystal act as a diffraction grating for electrons, similar to how optical diffraction occurs with light passing through a slit or grating. This principle is described by Bragg’s Law: $$n\lambda = 2d\sin\theta$$ where \(n\) is the order of diffraction, \(\lambda\) is the wavelength of the electrons, \(d\) is the spacing between atomic planes, and \(\theta\) is the angle of diffraction.
- Any material object with momentum \(p\) possesses both corpuscular and wave properties, known as wave-particle duality principle: $$ \lambda = \frac{h}{p}$$ where \(\lambda\) is the correponding wavelenth and \(h\) is Planck's constant.
The experiment was conducted using the Ultrafast Electron Diffraction technique, and the pattern was recorded with approximately \(3.87 × 10^7\) electrons at a beam energy of \(58 \text{keV}\) (\(\lambda = 0.0495 \text{Å}\))
To demonstrate the correspondence of the diffraction maxima in the two figures, a section marked by a white rectangle has been made.
