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Braggs law

Braggs Law was first derived by physicist Sir W.H. Bragg ( [link] ) and his son W. L Bragg ( [link] ) in 1913.

British physicist, chemist, mathematician and active sportsman Sir William H. Bragg (1862 - 1942).
Australian-born British physicist William L. Bragg (1890 - 1971).

It has been used to determine the spacing of planes and angles formed between these planes and the incident beam that had been applied to the crystal examined. Intense scattered X-rays are produced when X-rays with a set wavelength are executed to a crystal. These scattered X-rays will interfere constructively due the equality in the differences between the travel path and the integral number of the wavelength. Since crystals have repeating units patterns, diffraction can be seen in terms of reflection from the planes of the crystals. The incident beam, the diffracted beam and normal plane to diffraction need to lie in the same geometric plane. The angle, which the incident beam forms when it hits the plane of the crystal, is called 2θ. [link] shows a schematic representation of how the incident beam hits the plane of the crystal and is reflected at the same angle 2θ, which the incident beam hits. Bragg’s Law is mathematically expressed, [link] , where,n= integer order of reflection, λ= wavelength, d= plane spacing.

Bragg’s Law construction.

Bragg’s Law is essential in determining the structure of an unknown crystal. Usually the wavelength is known and the angle of the incident beam can be measured. Having these two known values, the plane spacing of the layer of atoms or ions can be obtained. All reflections collected can be used to determine the structure of the unknown crystal material.

Bragg’s Law applies similarly to neutron diffraction. The same relationship is used the only difference being is that instead of using X-rays as the source, neutrons that are ejected and hit the crystal are being examined.

Neutron diffraction

Neutrons have been studied for the determination of crystalline structures. The study of materials by neutron radiation has many advantages against the normally used such as X-rays and electrons. Neutrons are scattered by the nucleus of the atoms rather than X-rays, which are scattered by the electrons of the atoms. These generates several differences between them such as that scattering of X-rays highly depend on the atomic number of the atoms whereas neutrons depend on the properties of the nucleus. These lead to a greater and accurately identification of the unknown sample examined if neutron source is being used. The nucleus of every atom and even from isotopes of the same element is completely different. They all have different characteristics, which make neutron diffraction a great technique for identification of materials, which have similar elemental composition. In contrast, X-rays will not give an exact solution if similar characteristics are known between materials. Since the diffraction will be similar for adjacent atoms further analysis needs to be done in order to determine the structure of the unknown. Also, if the sample contains light elements such as hydrogen, it is almost impossible to determine the exact location of each of them just by X-ray diffraction or any other technique. Neutron diffraction can tell the number of light elements and the exact position of them present in the structure.

Questions & Answers

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Source:  OpenStax, Physical methods in chemistry and nano science. OpenStax CNX. May 05, 2015 Download for free at http://legacy.cnx.org/content/col10699/1.21
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