Bragg’s Law Is Given By: Reports Example

Abstract:

The following experiment was performed in order to demonstrate the usage of Bragg’s law in determining the structure of a model crystal. Bragg’s law gives a relation between the wavelength of radiation, the angle of incidence and the lattice spacing. When two of the variables are known, the third can be determined with the help of the law. Microwave radiation is used to find out the angle of reflection. With the value of angle and the wavelength of the radiation known, the value of the lattice spacing of the metal sphere lattice was found out to be‘d’. By direct measurement, the lattice spacing of the metal sphere lattice was found out to be ‘d1’.

Introduction:

Propagation of a wave even after it encounters an obstruction is known as ‘diffraction’. This experiment is Bragg diffraction, which occurs when an electromagnetic wave hits an obstruction and refracts. As mentioned above, it draws out a relation between three entities. This relation was drawn by William Lawrence Bragg and William Henry Bragg in 1913. Their work confirmed the existence of lattice structure at the atomic level. They received Nobel Prize in the year 1915 for their work.

n λ = 2 d sin θ
where

λ is wavelength of the incident radiation

d is the lattice distance

θ is the angle of refraction.

Diagram 1: Bragg Diffraction
Derivation:
As seen in the figure,
BD is ‘d’.
Hence AB is ‘d sin θ’. (1)
Similarly,BC= ‘d sin θ’ (2)
Now, ABC= AB+BC
= 2d sin θ (3)

We also know that,

For constructive interference, path difference is equal to the integral number of wavelengths.
Hence, ABC=n λ (4)
n λ = 2 d sin θ
It is a general rule that Bragg’s experiments are performed using X-rays as the wavelength of X-rays are of the same order as that of the crystal structure. Since we use, metal spheres in ethafoam cube, which has a similar structure as that of lattice, we use microwaves to perform this experiment. The macroscopic lattice structure requires the use of microwaves in the experiment. There is a transmitter and a receiver set up used in this experiment. The transmitter transmits the microwaves and the receiver receives them. The angle of incidence is equal to the angle of refraction. The planes in this experiment are denoted by means of the 3-D coordinates.

References:

John M. Cowley (1975) Diffraction physics (North-Holland, Amsterdam) ISBN 0-444-10791-6.
 H. P. Myers (2002). Introductory Solid State Physics. Taylor & Francis. ISBN 0-7484-0660-3.
 Barden, S.C.; Williams, J.B.; Arns, J.A.; Colburn, W.S. (2000). "Tunable Gratings: Imaging the Universe in 3-D with Volume-Phase Holographic Gratings (Review)". ASP Conf. Ser. 195: 552.