Solid state physics Part #2 "Diffraction phenomenon (summary)" very important to study the semiconductor compounds

carloserp-2000 (68)in #science • 7 years ago (edited)

X-rays are an electromagnetic radiation whose wavelength is of the order 1 Amstrong.

In the previous post I talked a little about the crystal structures and networks of Bravais. Now the question is: is the separation between atoms and crystalline planes of the order of several Amstrongs, how can these structures be verified and studied ?. The answer to this question was presented by scientists (Lau-Friedrich-Knipping), on June 9, 1912, at the Bavarian Academy of Sciences, in a paper entitled "Effects of interference with Röntgen rays." In the first part of the paper, In the second part, Friedrich and Knipping present the first experimental observations of the diffraction of X-rays by crystals.

The work on the one hand demonstrates that the X-rays are wave-shaped in nature because they can diffract and, in turn, that the crystals are formed by a periodic arrangement of atoms.

The first determinations of the crystalline structures by means of X-ray diffraction analysis were made by the English physicist William Henry Bragg, who published the first KCl, NaCl, KBr and KI structures.

Thus the study of the structure of matter requires the use of very small wavelength radiation, such as X-rays. One of the ways to produce X-rays is through the bombardment of atoms with that of electrons at high speeds. In general an electron strikes and excites another electron from the most intense layers of the atoms, extracting it to the upper layers, then the excited electron, it makes a transition towards the lowest state of energy, emitting the energy difference between the levels in form of X-ray radiation.

Figure 1. Scheme of the excitation of electrons inside the white atom.

The radiation emitted in this way has a wide continuous spectrum, in which is a series of discrete superimposed lines, that are the ones produced by the transitions in the different levels of energy of the atom. The continuous spectrum is due to the emission of radiation by incident electrons as they are deflected by the charges of the nucleus of the material that has served as a target.

Figure 2. Note of my physics notebook (Mo radiation spectrum).

In general, the monochromatic X-ray sources are the K-alpha and K-alpha lines of molybdenum with wavelengths of 1,541 and 0,709 Amstrongs respectively.

Bragg Law

As already mentioned, the location of the diffraction maxims was explained by William Bragg, based on a very simple model in which it is assumed that X radiation is mirrored specularly from the successive planes of the crystal, and in which the maxims of diffraction are only found for angles of incidence and reflection such that the reflections of the adjacent planes of a system interfere in a constructive way, with differences of phase 2pin radians where n is an integer.

Figure 3. Diffraction of Bragg.

So when dealing with waves, the wavelength rays will produce maximum and minimum interference whenever the path difference produces a wave offset.

From the graph it can be easily deduced that the path difference between, say, beam "a and b", is given by AB + AC.
This path difference must be equal to a whole number of waves, that is: