Thermionic Emission

• Long before Einstein, photoelectric effect, it was observed that the electric conductivity of air surrounding a very hot object significantly increases. This effect was attributed to emission of electrons

• Like photoelectrons, thermoelectrons need minimum energy to escape. Measurements revealed that this value is always close to the work function, φ, for the same surface indicating that φ of a particular surface does not depend on the perturbing source

• Applications include CRT devices in which metal filaments (or recently developed coated cathodes) at high temperatures supply dense streams of electrons

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The X-Rays• Just before the discovery of the photoelectric effect, it was

discovered that part or all of the KE of a moving electron can be converted into photon, which is the “inverse” photoelectric effect

• In 1895, Roentgen (a German physicist) incidentally discovered the creation of EM radiation of unknown nature when fast electrons fall on matter. He called them X-rays

• The faster the falling electrons, the higher energy of X-rays, and the greater the number of these electrons the greater the intensity of the X-rays

• Roentgen received the 1st Nobel price in physics in 1902. However, he refused to benefit financially from his work and died in poverty in the German inflation that followed the WW1

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X-Rays Production

• X-rays are produced by bombarding a metal target (copper, tungsten, and molybdenum are common) with energetic electrons having energies of 50 to 100 keV. The higher the accelerating voltage, the faster the electrons and the shorter the wavelengths of the X-rays produced

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Bremsstrahlung!• EM theory, formulated by Maxwell, predicts that an accelerated

charged particle that are moving near nuclei will radiate EM radiation

• These radiation is given the German phrase “bremsstrahlung”, or in English “braking radiation”

• Energy loss due to bremsstrahlung is more important for electrons than for heaver charged ions because electrons are lighter and hence undergo more violent acceleration when passing near nuclei in their path

• The greater the energy of an electron and the greater atomic number of the nuclei it encounters, the more energetic the bremsstrahlung, which accounts for, in general, X-rays produced by an X-ray tube

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X-Rays Production

• However, the agreement between theory and experiment is not satisfactory in certain important respects

• For Mo target, the spectrum consists of spectral lines superimposed on background continuum radiation. These spectral lines peaks occur at specific wavelengths. The occurrence of these lines is in clear contradiction with the EM theory which, as mentioned, predicts a continuous radiation (bremsstrahlung)

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X-Rays Production

• In the case of W target, the X-rays produced at a given accelerating potential not only differ in intensity but also in wavelength. As the potential increases, the peak of the curve shifts towards shorter wavelengths (see Planck Blackbody curves). Also, the minimum wavelength is different

• However, for both Mo and W at the same potential, λmin is the same (see previous slide)

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X-Rays Production

• Most of the electrons energy in the electron beam is lost on the form of heat upon collision with the target. Therefore, X-rays are produced from few electrons in the beam

• In order to increase the efficiency of the X-rays production process, W is preferred to Mo since it has a higher melting point. In addition, the target is cooled down by a circulating oil/water system to quickly carry the heat away through a heat exchanger

• X-rays produced this way have wavelengths covering the range 0.01–10 nm, with the range 1–10 nm called soft X-rays while the other range called hard X-rays

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Inverse Photoelectric Effect

• In the photoelectric effect, we got:Since φ is in the order of some eV, it can be ignored with respect

to the accelerating potential of value tens of hundreds of thousands volts, so the X-rays production equation is:

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X-rays Diffraction (Scattering)

• In 1912, a diffraction experiment was recognized as an ideal for determining (measuring) X-rays wavelengths.

• Recalling the physical optics course, the spacing between adjacent lines (grooves) on a diffraction grating must be of the order of magnitude as the wavelength of the light falling on it. As this can be done readily with wavelengths in the UV-VIS-NIR spectral regions, a grating can not be ruled with the tiny spacing required by X-rays

• Max von Laue in Germany and William Henry Bragg and William Lawrence Bragg (a father and son team) in England suggested using single crystals such as calcite as natural three-dimensional gratings, the periodic atomic arrangement in the crystals constituting the grating rulings

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X-rays Diffraction (Scattering)

• Atoms in successive planes (A and B) will scatter constructively at an angle Ѳ if the path length difference for rays (1) and (2) is a whole number of wavelengths, nλ. From the diagram, constructive interference will occur when:

AB+BC = nλ, n = 1, 2, 3, …And since AB = BC = d(sinѲ) → nλ = 2d(sinѲ) which is called Bragg Equation

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X-rays Diffraction (Scattering)

where n is the order of the intensity maximum, d is the spacing between planes, and Ѳ is the angle of the intensity maximum measured from plane A. Note that there are several maxima at different angles for a fixed d and corresponding to n = 1, 2, 3, . . The previous equation was used with great success to determine atomic positions in crystals. A diagram of a Bragg x-ray spectrometer is shown. The crystal is slowly rotated until a strong reflection is observed. If λ is known, d can be calculated and, from the series of d values found, the crystal structure may be determined. If measurements are made with a crystal with known d, the x-ray intensity vs. wavelength may be determined and the x-ray emission spectrum examined.

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Wave Properties of Particles

• The momentum of a photon of light of frequency f:

• This equation is called the de Broglie’s wavelength for photons as well as material particles

• The wave and particle aspects of moving objects can never be observed at the same time. In certain situations, a moving object resembles a wave and in others it resembles a particle.

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Wave Properties of Particles: What is waving in matter waves?

• In sound waves, the quantity that varies periodically with time is the pressure. In light waves, electric and magnetic fields vary with time

• For matter waves, the quantity whose variations make up matter waves is called the wave function (Ψ). The value (i.e. amplitude) of Ψ that is associated with a moving body at a particular point in space (x, y, z) at a certain time t is related to the probability of finding the body there at this time

• Ψ, however, has no physical significance (i.e. cannot be observed experimentally) since it can be negative as well as positive quantity. The German physicist Max Born in 1926 suggested the quantity |Ψ|2 to replace Ψ and called it the probability density.

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Transmission Electron Microscope (TEM)

• It makes use of the fact that electron wavelengths are much shorter than those of light and hence have more ability to resolve fine details. They are also controlled by electric and magnetic fields because of their charge. X-rays also have short wavelengths, but it is not yet possible to focus them adequately

• The resolving power of any optical instrument, which is limited by diffraction, is proportional to the wavelength of whatever is used to illuminate the specimen

• The best optical microscopes using ultraviolet light have a magnification of about 2000 and can resolve two objects separated by 200 nm, but a TEM using electrons accelerated through 100 kV has a magnification of as much as 1,000,000 and a maximum resolution of 0.2 nm

• Increasing electron energy above 100 keV does not improve resolution—it only permits electrons to sample regions deeper inside an object.

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Scanning Electron Microscope (SEM)

• Another type of electron microscopes with less resolution and magnification than the TEM, but capable of producing outstanding three-dimensional images and does not require that the specimen be ultra thin

• Such a device is typically operated with 20-keV electrons and have a resolution of about 10 nm and a maximum magnification of 100,000. An electron beam is sharply focused on a specimen by magnetic lenses and then scanned across a tiny region on the surface of the specimen. The primary high energy electrons scatter lower-energy secondary electrons out of the object, depending on specimen composition and surface topography, where they detected and amplified

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