Ichak rentgenografiyasi: natijani ko'rsatadigan tayyorgarlik

Intuitive understanding by Bragg's law

An intuitive understanding of X-ray diffraction can be obtained from the Bragg model of diffraction. In this model, a given reflection is associated with a set of evenly spaced sheets running through the crystal, usually passing through the centers of the atoms of the crystal lattice. The orientation of a particular set of sheets is identified by its three Miller indices (h, k, l), and let their spacing be noted by d. William Lawrence Bragg proposed a model in which the incoming X-rays are scattered specularly (mirror-like) from each plane; from that assumption, X-rays scattered from adjacent planes will combine constructively (konstruktiv aralashuv ) when the angle θ between the plane and the X-ray results in a path-length difference that is an integer multiple n of the X-ray wavelength λ.
A reflection is said to be indekslangan when its Miller indices (or, more correctly, its o'zaro panjara vector components) have been identified from the known wavelength and the scattering angle 2θ. Such indexing gives the unit-cell parameters, the lengths and angles of the unit-cell, as well as its kosmik guruh. Beri Bragg qonuni does not interpret the relative intensities of the reflections, however, it is generally inadequate to solve for the arrangement of atoms within the unit-cell; for that, a Fourier transform method must be carried out.

Scattering as a Fourier transform

The incoming X-ray beam has a polarization and should be represented as a vector wave; however, for simplicity, let it be represented here as a scalar wave. We also ignore the complication of the time dependence of the wave and just concentrate on the wave's spatial dependence. Samolyot to'lqinlari bilan ifodalanishi mumkin to'lqin vektori k_yilda, and so the strength of the incoming wave at time t = 0 is given by
At position r within the sample, let there be a density of scatterers f(r); these scatterers should produce a scattered spherical wave of amplitude proportional to the local amplitude of the incoming wave times the number of scatterers in a small volume dV haqida r
qayerda S mutanosiblik doimiysi.
Consider the fraction of scattered waves that leave with an outgoing wave-vector of k_chiqib and strike the screen at r_ekran. Since no energy is lost (elastic, not inelastic scattering), the wavelengths are the same as are the magnitudes of the wave-vectors |k_yilda|=|k_chiqib|. From the time that the photon is scattered at r until it is absorbed at r_ekran, the photon undergoes a change in phase
The net radiation arriving at r_ekran is the sum of all the scattered waves throughout the crystal
which may be written as a Fourier transform
qayerda q = k_chiqib – k_yilda. The measured intensity of the reflection will be square of this amplitude