ABSTRACT
In the previous chapter, we mentioned that X-ray diffraction is essentially a scattering phenomenon in which a large number of atoms are involved. Since the atoms in a crystal are periodically arranged, the X-rays scattered by these atoms can be in phase and constructively interfere in a few directions. If the atoms were not arranged in a regular, periodic fashion, the rays scattered by them would have a random phase relationship to one another. Under this condition, neither constructive nor destructive interference takes place, and the scattering intensity in a particular direction will be simply the sum of the intensities of all the rays scattered in that direction. The intensity of electromagnetic radiation is proportional to the square of its amplitude. If there are N scattered rays, each of amplitude E o $ E_{\text{o}} $ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315365282/9eb5b991-20db-4936-bcd8-0d892254b15f/content/ilm4_1.tif"/> , the total amplitude is N E o $ NE_{\text{o}} $ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315365282/9eb5b991-20db-4936-bcd8-0d892254b15f/content/ilm4_2.tif"/> when they are all in phase. Then, the intensity of the scattered beam becomes N 2 E o 2 $ N^{2} E_{\text{o}}^{2} $ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315365282/9eb5b991-20db-4936-bcd8-0d892254b15f/content/ilm4_3.tif"/> . On the contrary, when the scattered rays have a random phase relationship, the scattering intensity is N E o 2 $ NE_{\text{o}}^{2} $ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315365282/9eb5b991-20db-4936-bcd8-0d892254b15f/content/ilm4_4.tif"/> , which is N times smaller than the former case. Since solid materials contain 1022 –1023 atoms/cm3, N is a very large number in X-ray diffraction.
