Lec. No. (4)
The Characteristic Spectrum
*Discovered by W.H. Bragg and systematized by H.G. Moseley .
*The characteristic peak is created in when a hole in the inner shell,
created by a collision event, is filled by an electron from higher energy
shell.
*Let a K-shell electron be knocked out -- the vacancy can be filled by an
electron from the L-shell (Kα radiation) or the M-shell (K β radiation).
Properties of the Characteristic Spectrum
*The intensity of any characteristic line depends both on the tube
current (i) and the amount by which the applied voltage V exceeds the
critical excitation voltage for that line. For a K-line.
*Characteristic lines are also very narrow, most of them less than 0.001 Å
wide (Full Width At Half Maximum).
*High intensity and narrow K-lines makes x-ray diffraction possible,
since it generally requires the use of monochromatic radiation.
Absorption coefficients of lead
Properties of the Absorption Coefficient
*There is a sharp discontinuity in the dependence of the absorption
coefficient on energy (wavelength) at the energy corresponding to the
energy required to eject an inner-shell electron.
*The discontinuity is known as an absorption edge.
*Away from an absorption edge, each “branch” of the absorption curve is
given by:
μ /ρ=k λ3 Z3
k : a constant.
Z :atomic number of absorber.
Lec. No. (6)
Question (1) X-rays are generated by making the electrically charged
particles (electrons) with sufficient kinetic energy in vacuum collide with
cathode, as widely used in the experiment of an X-ray tube. The
wavelength distribution and intensity of continuous X-rays are usually
depending upon the applied voltage. A clear limit is recognized on the
short wavelength side.
(1) ) Find the relation of the shortest wavelength limit (SWL) of X-rays
generated with the applied voltage V , when an electron loses all
energy in a single collision.
(2) Estimate the speed of electron before collision when applied voltage
is 30,000V and compare it with the speed of light in vacuum.(H.W)
Answer
1)λSWL = c/νmax = c e V/h = 1.602 * 10_19 * 2.998 * 108 * V /6.626 *
10_34
=0.7248 *1023 V
2)
EK=eV=1/2 mg2
Question (2) Kα1 radiation of Fe is the characteristic X-rays emitted
when one of the electrons in L shell falls into the vacancy produced by
knocking an electron out of the K-shell, and its wavelength is 0.1936 nm.
Find the energy difference related to this process for X-ray emission?
Sol.
Consider the process in which an L shell electron moves to the vacancy
created in the K shell of the target (Fe) by collision with highly
accelerated electrons from a filament. The wavelength of the photon
released in this process is given by λ , (with frequency ν). We also use
Planck’s constant h of (6.626 *10_34 Js) . Energy per photon is given by
E= hν= hc/λ
Using Avogadro’s number NA( 0.6022 * 1024), one can obtain the energy
difference ΔE related to the X-ray release process per mole of Fe.
ΔE = NA h c / λ
ΔE = 6.1979 *108 J/mole
Question (3) There is a substance of linear absorption coefficient.
(1) Obtain a simple relation to give the sample thickness x required to
reduce the amount of transmitted X-ray intensity by half.
(2) Calculate also the corresponding thickness of Fe-17 mass % Cr alloy
.density( D= 7.76 * 106 g/m3 ) for Mo-K˛ radiation.
x = 0.693/µ
The values of mass absorption coefficients of Fe and Cr for the Mo-K˛
radiation are 37.6 and 29.9 cm2/g obtained from Appendix, respectively.
The concentration of Cr is given by 17 mass %, so that the weight ratio of
two alloy components can be set as wFe = 0.83 and wCr = 0.17. Then, the
mass absorption coefficient of the alloy is expressed in the following
Next, note that the unit of the density of the Fe–Cr alloy is(7.76 g/cm3)
(H.W) Calculate the mass absorption coefficient of lithium niobate
(LiNbO3) for Cu-K˛ radiation.
Lec. No. (7)
Filters
When the energy of a photon beam is just above the excitation potential
or absorption edge of a material, that material strongly absorbs the given
photon beam. If another substance can be found that has an absorption
edge between the Kα and Kβ lines of the incident photon beam, this other
substance can be used to significantly reduce the intensity of the Kβ line
relative to the Kα line. The absorption edges of elements with
Z
Filter
= ZTarget - 1 (or - 2) meet this requirement. The thickness of the
filtering material is usually chosen to reduce the intensity of the Kβ line
by a factor of 100 while reducing the intensity of the Kα line by a factor
of 10 or less .the propose from filter to absorb the Kβ component much
more strongly than Kα component ,because of the abrupt change in its
absorption coefficient between two wavelengths .
Lec. No. (8)
Production of x-rays
x-ray tube: any x-ray tube must contain :
1)a source of electrons .
2)high accelerating voltage.
3)metal target.
The most of kinetic energy of the electrons is converted into heat in the
target ,and must be cooled by water to prevent its melting.
x-ray tubes can be divided into two types according to provide electrons :
filament tubes , in which source of electrons is a hot filament , and gas
tubes in which electrons are produced by ionization of a small quantity of
gas in the tube.
The x-ray tube is a relatively simple electrical device typically containing
two principle elements: a cathode and an anode. As the electrical current
flows through the tube from cathode to anode, the electrons undergo an
energy loss, which results in the generation of x-radiation.
X-ray tube consist from:
1)Anode
The anode is the component in which the x-radiation is produced. It
is a relatively large piece of metal that connects to the positive side of the
electrical circuit.
The anode has two primary functions: (1) to convert electronic energy
into x-radiation, and (2) to dissipate the heat created in the process.
Figure show cross section of an x-ray tube.
*The fraction of the total electronic energy that is converted into xradiation (efficiency) depends on two factors: the atomic number (Z) of
the anode material and the energy of the electrons. Most x-ray tubes use
tungsten, which has an atomic number of 74, as the anode material. In
addition to a high atomic number, tungsten has several other
characteristics that make it suited for this purpose. Tungsten is almost
unique in its ability to maintain its strength at high temperatures, and it
has a high melting point and a relatively low rate of evaporation.
2) Focal Spot
Not all of the anode is involved in x-ray production. The radiation is
produced in a very small area on the surface of the anode known as the
focal spot. The dimensions of the focal spot are determined by the
dimensions of the electron beam arriving from the cathode. In most x-ray
tubes, the focal spot is approximately rectangular. The dimensions of
focal spots usually range from 0.1 mm to 2 mm. X-ray tubes are designed
to have specific focal spot sizes; small focal spots produce less blurring
and better visibility of detail, and large focal spots have a greater heatdissipating capacity.
Most x-ray tubes have two focal spot sizes (small and large), which can
be selected by the operator according to the imaging procedure.
3)Cathode
The basic function of the cathode is to expel the electrons from the
electrical circuit and focus them into a well-defined beam aimed at the
anode. The typical cathode consists of a small coil of wire (a filament)
recessed within a cup-shaped region, as shown below.
The filament of the cathode is heated in the same way as a light bulb
filament by passing a current through it. This heating current is not the
same as the current flowing through the x-ray tube that produces the xradiation. During tube operation, the cathode is heated to a glowing
temperature, and the heat energy expels some of the electrons from the
cathode.
4) Envelope
The anode and cathode are contained in an envelope. The majority of
x-ray tubes have glass envelopes, although tubes for some applications
have metal and ceramic envelopes.
The primary functions of the envelope are to provide support and
electrical insulation for the anode and cathode and to maintain a vacuum
in the tube. The presence of gases in the x-ray tube would allow
electricity to flow through the tube freely, rather than only in the electron
beam. This would interfere with x-ray production and possibly damage
the circuit.
Lec. No. (9)
Detection of x-ray
1)Photographic film: is affected by x-ray in much the same way as by
visible light ,and film is the most widely used means of recording
diffracted x-rays beams. However, the emulsion on ordinary film is too
thin to absorb much of the incident x-radiation ,and only absorbed x-rays
Can be effective with rather thick layers of emulsion on both sides in
order to increase the total absorption . the grain size is also made large for
the same purpose . this has the unfortunate consequence that x-ray films
are grainy , do not resolve fine detail , and cannot stand much
enlargement.
2)fluorescent screen: are made of a thin layer of Zinc sulfide containing a
trace of (Ni ) mounted on cardboard backing .under the action of x-rays ,
this compound fluoresces in the visible region , i.e. emits visible light ,
in this case yellow light.
3)Ionization devices : measure the intensity of x-ray beams by the amount
of ionization they produce in a gas . x-ray quanta can cause ionization
just as high –speed electrons can namely , by knocking an electron out of
gas molecule and leaving behind a positive ion this phenomenon can be
made this basis of intensity measurements by passing the x-ray beam
through a chamber containing a suitable gas and two electrodes having a
constant potential difference between them.
The electrons are attracted to the anode and the positive ions to the
cathode and a current is thus produced in an external circuit . in the
ionization chamber, this current is constant for constant x-ray intensity ,
and the magnitude of the current is a measure of the x-ray intensity.