Скачать с ютуб Secret Behind X-rays scattering by electrons - atoms - unit cells (Crystal) || XRD analysis в хорошем качестве

Secret Behind X-rays scattering by electrons - atoms - unit cells (Crystal) || XRD analysis

Structure Factor - Scattering of x-rays from electron ⟹ atom ⟹ unit cell - Contribution in XRD Peak intensity ✍🥀 Bragg’s equation (nλ= 2dsinθ) tells us about the peaks position (2θ). However, tells nothing about the peak intensities. The intensities of the XRD peaks depend on many factors but here we only discuss the “Structure factor” When x-rays shine on a crystal can scatter in three ways: As crystal is made up of unit cells ⟹ unit cell is made up of atoms ⟹ atom is made up of electrons ✅ 1) - Scattering from electron : Polarization factor ✅ 2) - Scattering from an atom : Atomic scattering factor (f) ✅ 3) - Scattering from a unit cell : Structure factor (F) This is the structure factor formula: F = ∑f exp2πi(hx+ky+lz) To establish an exact relation between atom position and intensity, first considering how x-rays are scattered by a single electron, followed by an atom, and finally by all the atoms in the unit cell. ✅ 1- Scattering of x-rays by an electron - Polarization factor ✍🥀 X-rays are EM wave characterized by an E-field whose strength varies sinusoidally with time. Since E-field exerts a force on charged objects (in this case electron) so, the oscillating E-field of the incident x-ray sets any electron it encounters into oscillatory motion about its mean position. When any charged object (electron) is accelerating or decelerating, it emits an EM waves (i.e., x-rays). In this scenario, an electron is said to scatter x-rays. The scattered beam shows exactly the same λ and frequency as the incident x-rays and is said to be coherent with it. Here, the intensity of the scattered beam is just small fraction of the incident x-rays! Moreover, the x-rays scatter from the ONLY tightly bounded electrons NOT from the loose bounded electrons ❗ ✅ 2- Scattering by of x-rays by an atom (atomic scattering factor, f)✍🥀 As atom made up of electrons (as shown in the attached image) so the wave scattered by an atom is simply the sum of the waves scattered by its component electrons, right? Or more concisely, an atom containing Z (atomic number) electrons, the amplitude of the wave scattered is Z times the amplitude of the wave scattered by a single electron. This simply means that the scattered wave is proportional to the Z in the atom. A quantity f, shown in the “Structure factor” formula is called the atomic scattering factor, and defined as a ratio of amplitudes 🥀f = (Amplitude of the x-rays scattered by atom)/(Amplitude of the x-rays scattered by single electron)🥀 ✅ 3- Scattering by a unit cell (Structure factor, F) ✍🥀 We must now restrict ourselves to consideration of coherent scattering from all atoms of the unit cell called the structure factor, F. It is obtained by simply adding together all the waves scattered by the individual atoms. F= (Amplitude of the x-rays scattered by all atoms in a unit cell)/(Amplitude of the rays scattered by single electron) Finally, the intensity diffracted x-rays by all atoms in a unit cell is given by F = ∑f exp2πi(hx+ky+lz) or I ∝ |F|^2