X-Ray Diffraction

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  • Topic: Atom, Photon, Electron
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PHYS 3P91
X-ray fluorescence Electron Diffraction

Professor: Dr. F. Razavi Lab Demonstrator: J. Korobanik Lab Partner: Adam Kober

Author : Jasper D’Agostino SN : 4656534

Contents
1 Introduction 1.1 X-ray fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Electron diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Discussion 2.1 X-ray fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Electron diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 3 4 4 7

1
1.1

Introduction
X-ray fluorescence

X-ray fluorescence is a technique for investigating the elemental and chemical properties of a given physical sample. When X-rays are incident on the surface of a crystalline lattice, some of the x-rays are absorbed by atoms present in the sample. This results in a production of X-rays with a characteristic energy that depends on the atomic property of the element. An incident X-ray with energy hν0 will be absorbed by some atom and emitted with some new energy hνj , in which this new energy is directly related to the absorber atoms in the sample. A photoelectric effect occurs when an X-ray photon is incident with an atom present in the sample where photon is annihilated and the atom becomes ionized. The atom undergoes a de-exitation to its ground level energy state when the atom binds with a nearby electron. This effect can be described by an energy equation given by K − hν0 − B where K is the kinetic energy of the photoelectron, and B is its binding energy. During the de-exitation of the atom to its ground state, characteristic X-ray photons are produced directly related to the properties of the atom undergoing energy change. To obtain accurate spectroscopic data for unkown samples, known samples must be used as a cailbration guide. Using the Molybdenum source X-ray emitter, detector, and programmable MCA (Multi Channel Analyzer), we were able to smash known samples with X-rays to obtain a fluorescence spectrum.

1.2

Electron diffraction

The first physicist to describe the motion of particle using a wave equation was de Broglie in 1924 with the advancement of the de Broglie wave, with wavelength λ. Each particle was associated with a wave whose wavelength depended on the momentum of the particle given by the following equation h λ= p where h is Planck’s constant. When an electron is accelerated through a potential difference V , then it’s kinetic energy is described by 1 2 mv = eV 2 where m is the electron mass, v is the speed of the electron after accelerating through the potential v, and e is it’s charge. From this we can deduce that the electron has momentum p = mv = (2meV )1/2 The electron also has a de Broglie wavelength given by the normal prescription: λ= h (2meV )1/2

In our experiment, the electron is accelerated by leaving a cathode with some potential V and travels towards a crystal. When it smashes against the crystal, the de Broglie

wave will be diffracted by the lattice structure of the crystal. The electron will only pass through the crystal in directions where the de Broglie wave is strongly diffracted. This can be modelled by Bragg’s law: 2d sin θ = nλ If the d values for the crystal are known then the wavelength can be obtained by measuring the directions in which the incoming de Broglie waves are strongly diffracted.

2
2.1

Discussion
X-ray fluorescence

The de-exitation of an ionized atom to it’s electrically neutral ground state energy level can be better understood using an energy level diagram. Each energy level is related to the exitation of the atom within the sample when an individual electron is missing from the usually full atomic subshell (nlj). The zero energy level corresponds to the ground level energy of the neutral atom. K level energy transitions correspond to the binding energy BK of an electron in the K shell. The same goes for subsequent shells and energy transitions. If...
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