With Bragg diffraction the angle used in the analysis is the angle between the crystal surface and the diffracted beams,...NOT the angle between the normal and the diffracted beams (you are probably more familiar with that one...Sin theta)Mohammed Shoaib said:The spacing between atomic planes in a crystal is 0.120 nm . 15.0 keV x rays are diffracted by this crystal What is the angle of first-order diffraction?What is the angle of second-order diffraction?My question is that the manual says to use 2dcosΘ=mλ instead of 2dsinΘ=mλ( bragg diffraction condition). Why?
Bragg Diffraction is a phenomenon in which electromagnetic radiation, such as X-rays, is diffracted by a crystal lattice. This is due to the interference of the radiation with the regularly spaced atomic planes in the crystal. The diffracted waves constructively interfere at specific angles, known as Bragg angles, resulting in a diffraction pattern.
The formula for calculating the 1st order Bragg angle is given by θ = arcsin(nλ / 2d), where θ is the angle of diffraction, n is the order of diffraction (1 for 1st order), λ is the wavelength of the radiation, and d is the distance between atomic planes in the crystal lattice. Similarly, the 2nd order Bragg angle can be calculated using θ = arcsin(2nλ / 2d).
The Bragg angle is affected by the wavelength of the radiation, the distance between atomic planes in the crystal, and the order of diffraction. It is also dependent on the type of crystal and its orientation, as well as the incident angle of the radiation.
The Bragg angle is significant in diffraction experiments as it allows for the determination of the atomic structure of a crystal. By measuring the angles at which diffraction occurs, researchers can determine the distance between atomic planes and the arrangement of atoms in the crystal lattice, providing valuable information about the material's properties.
Bragg Diffraction is used in various real-world applications, such as X-ray crystallography for determining protein structures, analyzing crystal structures of minerals in geology, and non-destructive testing in materials science. It is also used in X-ray diffraction techniques for identifying substances in chemistry and in medical imaging for detecting bone fractures and analyzing the composition of materials in the body.