The Röntgen Radiation and its application in studies of ... - Mansic

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Bragg’s Law was used to explain the interference pattern of X-rays scattered by crystals, diffraction has been developed to study the structure of all states of matter with any beam, e.g., ions, electrons, neutrons, and protons, with a wavelength comparable to the distance between the atomic or molecular structure. Bragg’s Law: n ⋅ λ = 2 ⋅ d ⋅ sinθ Figure 1. The reflection of the X-rays on the crystal planes Constructive interference occurs only when difference of between rays is proportional to the wavelength: n ⋅ λ = AB + BC AB=BC n ⋅ λ = 2 ⋅ AB sin θ = AB / d AB = d ⋅ sinθ n ⋅ = 2 ⋅ d ⋅ λ sinθ λ = 2 ⋅ d ⋅ sinθ hkl P.P. Ewald published in 1916 a more simple and more elegant theory of the Xray diffraction, by introducing the concept of reciprocal network. Comparison of Bragg’s Law (left), Bragg Modified Law (middle) and Ewald Law (right): ⋅ λ = 2 ⋅sinθ n d Physics of Advanced Materials Winter School 2008 4 hkl 1/ d sinθ = 2 / λ σ sinθ = 1 2 ⋅ λ
2. The production of X-rays The X rays, that are currently being used for different purposes, can be obtained with help of the X-ray tube. The X-ray tube is a vacuumed space (10 -6 torr) inside of which there are two electrodes, a hot cathode (tungsten filament) and an anode between which a 10 ÷ 200 kV voltage is applied. The electrons emitted by the filament are accelerated due to the voltage differential and when they hit the anode X radiation is emitted. Because through the collision with the anode over 98% from the energy of incoming electrons is turned into heat (the rest consist of energy radiated as X-rays), the anode has to be water cooled (Figure 2) [2]. For higher power (5 ÷ 60 kW) of X-ray radiation, the tube equipped with rotating anode is in use. On the X-ray tube used for structural studies, the electrons emitted by the filament are focused, only on a rectangular surface of the anode (tubes with Gotze linear focal point). Figure 2. The scheme of the tube with rotating anode Figure 3. The principle of X-ray diffraction [3] 3. X-ray spectrum - continuous and characteristic Roentgen radiation, produced with the help of X-ray tubes, is the result of the accelerated electrons interaction with the atoms from surface of the anode. There are two types of interactions that lead to the apparition of a continuous spectrum or a characteristic spectrum [4]. a. The continuous spectrum. An electron that moves at a high speed can be decelerated when pass near of atom nuclei. As a result of this interaction the Physics of Advanced Materials Winter School 2008 5
Page 1 and 2: The Röntgen Radiation and its appl
Page 3: The next improvement was introduced
Page 7 and 8: Due to the fact that Kβ and Kα2 a
Page 9 and 10: Crystal net is built from planes of
Page 11 and 12: Figure 10. A Modern Automated X-ray
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Page 15 and 16: technique is used for determination
Page 17 and 18: In te ns it y Temperature 0 C 2θ F

The Röntgen Radiation and its application in studies of ... - Mansic

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