Diffraction of X-rays by crystals

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1. Diffraction of X-rays by crystals Presented By :- Danyal Akram Ist YEAR

2. What is Diffraction ? A scattering of  X - rays  by the atoms of a crystal that produces an interference effect so that the  diffraction pattern gives information on the structure of the crystal or the identity of a crystalline substance.

3. Introduction of X-rays : X ray,  invisible, highly penetrating electromagnetic radiation of much shorter wavelength (higher frequency) than visible light. The wavelength range for X rays is from about 10  - 8  m to about 10 - 11   m, or from less than a billionth of an inch to less than a trillionth of an inch; the corresponding frequency range is from about 3 × 10 16  Hz to about 3 × 10 19 Hz (1 Hz = 1 cps).

4. History of X-Rays crystallography   The study of atomic structure of crystals by X-rays was initiated in 1914 by W.H. Bragg and W.L Bragg with remarkable achievements. They found that a monochromatic beam of X-rays was reflected from a crystal plane as if it acted like mirror. To understand this effect, a series of atomic planes of constant interplanar spacing d parallel to a crystal face are shown by lines PP’, P 1 P’ 1 , P 2 P’ 2 , and so on, in Fig below.

5. Diffraction of x-rays by crystals : X-ray crystallography  is a tool used for identifying the atomic and molecular structure of a  crystal , in which the crystalline atoms  cause a beam of incident  X-rays  to  diffract  into many specific directions. By measuring the angles and intensities of these diffracted beams, a  crystallographer  can produce a three-dimensional picture of the density of  electrons  within the crystal. From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical bonds , their  disorder  and various other information.

6. Suppose that a single monochromatic wave (of any type) is incident on aligned plane of lattice points, with separation d, at angle θ . Points A and C are on one plane, and B is on the plane below. Points ABCC’ form a quadrilateral. (AB + BC) – (AC’) The tow separate waves will arrive at a point with the same phase, and hence undergo constructive interference, if and only if this path difference is equal to any integer value of the wavelength, i.e. (AB + BC) – (AC’) = n λ , Where the same definition of n and λ apply as above. Therefore, AB = BC = and AC = From which it follows that AC’ = AC . cos θ = cos θ = cos θ ) cos θ = θ . Putting everything together, n λ = (1-cos θ ) = sin θ , Which simplify to n λ = 2d sin θ , Which is Bragg’s Law.   Heuristic derivation

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