College

For x-ray diffraction from crystalline solids, briefly explain the meaning of the terms "elastic scattering" and "scattering vector \( \mathbf{q} \)" in terms of the \( \mathbf{k} \) vectors of the incident and diffracted x-ray beams.

Sketch a diagram that describes this situation and explain the significance of elastic scattering in this diagram.

Answer :

Final answer:

Elastic scattering in x-ray diffraction refers to the scattering process where the energy of the incident x-ray beam is conserved. It is significant in x-ray diffraction as it allows for the determination of the crystal structure. The scattering vector q is a mathematical quantity that describes the momentum transfer during scattering and provides information about the arrangement of atoms in the crystal lattice.

Explanation:

In x-ray diffraction from crystalline solids, elastic scattering refers to the scattering process where the energy of the incident x-ray beam is conserved. This means that the scattered x-rays have the same energy as the incident x-rays. Elastic scattering is significant in x-ray diffraction because it allows for the determination of the crystal structure.

The scattering vector q is a mathematical quantity that describes the momentum transfer during scattering. It is defined as the difference between the wave vectors of the incident and diffracted x-ray beams. The magnitude and direction of the scattering vector q provide information about the arrangement of atoms in the crystal lattice.

A diagram illustrating this situation can be sketched as follows:

Diagram:

[Insert diagram here]

In the diagram, the incident x-ray beam is represented by a wave vector ki, and the diffracted x-ray beam is represented by a wave vector kf. The scattering vector q is defined as q = kf - ki. The magnitude and direction of q depend on the angles of incidence and diffraction, as well as the wavelength of the x-rays.

Elastic scattering is significant in x-ray diffraction because it allows for the determination of the crystal structure. When x-rays interact with a crystal, they are scattered by the atoms in the crystal lattice. The scattered x-rays interfere constructively or destructively, producing a diffraction pattern. By analyzing the diffraction pattern, information about the arrangement of atoms in the crystal lattice can be obtained.

Learn more about explanation of 'elastic scattering' and scattering vector q in x-ray diffraction from crystalline solids, along with a diagram and an explanation of the significance of elastic scattering. here:

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