Transcript d, the x-ray intensity vs. wavelength may be determined and

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 Xrays 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, Xrays 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: h max  KEmax  
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:
h max  h
 min
 min
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c
min
 KEmax  Ve


hc 6.63 10 34 J .s 3 108 m.s 1


Ve
V 1.6 10 19 J

1.24 10 6

V
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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-VISNIR 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 threedimensional gratings, the periodic atomic arrangement in the
crystals constituting the grating rulings
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Modern Physics
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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θ
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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Modern Physics
Wave Properties of Particles
• The momentum of a photon of light of frequency f:
E
hf
h
p 


c
c

h
h
 

p
mv
γ is called the
relativistic factor

1
1 v2 c2
• 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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Modern Physics
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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