So the total path difference between path AHGF and BCDE is CD - HG.To observe a wave of high intensity (one created through constructive interference), the difference CD - HG must equal to an integer number of wavelengths to be observed at the angle psi, \(CD - HG = n\lambda\), where \(\lambda\) is the wavelength of the light.Applying some basic trigonometric properties, the following two equations can be shown about the lines: \[CD = x \cos(θ o)\] and \[HG = x \cos (θ) \] where \(x\) is the distance between the points where the diffraction repeats.
X-ray crystallography remains to this day the primary tool used by researchers in characterizing the structure and bonding of organometallic compounds.
Diffraction is a phenomena that occurs when light encounters an obstacle.
Due to the periodic crystalline structure of a solid, it is possible to describe it as a series of planes with an equal interplaner distance.
As an x-ray's beam hits the surface of the crystal at an angle ?
The x-ray beams travel different pathlengths before hitting the various planes of the crystal, so after diffraction, the beams will interact constructively only if the path length difference is equal to an integer number of wavelengths (just like in the normal diffraction case above).
In the figure below, the difference in path lengths of the beam striking the first plane and the beam striking the second plane is equal to BG GF.
So, the two diffracted beams will constructively interfere (be in phase) only if \(BG GF = n \lambda\). Bragg; who discovered this geometric relationship in 1912.
Basic trigonometry will tell us that the two segments are equal to one another with the interplaner distance times the sine of the angle \(\theta\). Bragg's Law relates the distance between two planes in a crystal and the angle of reflection to the x-ray wavelength.
, some of the light will be diffracted at that same angle away from the solid (Figure 2).
The remainder of the light will travel into the crystal and some of that light will interact with the second plane of atoms.