Physical structure of matter
X-ray Physics
Absorption of X-rays 5.4.11-00
What you can learn about …
Bremsstrahlung
Characteristic radiation
Bragg scattering
Law of absorption
Mass absorption coefficient
Absorption edges
Half-value thickness
Photoelectric effect
Compton scattering
Pair production
Principle:
Polychromatic X-rays are to be energy selected using a monocrystal analyzer. The monochromatic radiation
obtained is to serve as the primary
radiation source for examination of
the absorption behaviour of various
metals as a function of the absorber
thickness and the wavelength of the
primary radiation.
What you need:
10
9
8
7
6
X-ray basic unit, 35 kV
09058.99
1
Goniometer for X-ray unit, 35 kV
09058.10
1
Plug-in module with Cu x-ray tube
09058.50
1
4
Counter tube, type B
09005.00
1
3
Lithium fluoride crystal, mounted
09056.05
1
Absorption set for X-rays
09056.02
1
Recommended accessories:
Software X-ray unit, 35 kV
14407.61
1
RS232 data cable
14602.00
1
I/I0
2
5
2
1
10
9
8
7
6
5
4
PC, Windows® 95 or higher
3
Complete Equipment Set, Manual on CD-ROM included
Absorption of X-rays
P2541100
2
3
1
0.02
Tasks:
1. The intensity attenuation of the
primary radiation is to be measured for aluminium and zinc as a
function of the material thickness
and at two different wavelengths.
The mass absorption coefficients
are to be determined from the
graphical representation of the
measured values.
3. The absorption coefficients for
copper and nickel are to be determined as a function of the wavelength and the measured values
plotted. The energies of the K levels are to be calculated.
4. The validity of m/r = f(Z3) is to
be proved.
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
d/mm
Semi-logarithmic representation of the pulse rates as a function of the absorber thickness.
Ua = 35 kV, Ia = 1 mA.
Curve 1: Al (Z = 13); l = 139 pm
Curve 2: Al (Z = 13); l = 70 pm
Curve 3: Zn (Z = 30); l = 139 pm.
2. The mass absorption coefficients
for aluminium, zinc and tin foils of
constant thickness are to be determined as a function of the
wavelength. It is to be shown from
the graphical representation that
m/r = f(l3).
PHYWE Systeme GmbH & Co. KG · D - 37070 Göttingen
Laboratory Experiments Physics 247
LEP
5.4.11
-00
Absorption of X-rays
Related topics
Bremsstrahlung, charateristic radiation, Bragg scattering, law of
absorption, mass absorption coefficient, absorption edge, halfvalue thickness, photoelectric effect, Compton scattering, pair
production.
Principle
Polychromatic X-rays are to be energy selected using a
monocrystal analyzer. The monochromatic radiation obtained is
to serve as the primary radiation source for examination of the
absorption behaviour of various metals as a function of the
absorber thickness and the wavelength of the primary radiation.
Equipment
X-ray basic unit, 35 kV
Goniometer for X-ray unit, 35 kV
Plug-in module with Cu x-ray tube
Counter tube, type B
Lithium fluoride crystal, mounted
Absorption set for X-rays
2. The mass absorption coefficients for aluminium, zinc and tin
foils of constant thickness are to be determined as a function
of the wavelength. It is to be shown from the graphical representation that m/r = f(l3).
3. The absorption coefficients for copper and nickel are to be
determined as a function of the wavelength and the measured values plotted. The energies of the K levels are to be
calculated.
4. The validity of m/r = f(Z3) is to be proved.
Set-up and procedure
Set up the experiment as shown in Fig. 1.
With the X-ray unit switched off, connect the goniometer and the
counter tube to the appropriate sockets in the base plate of the
experimenting area. Set the goniometer block with mounted
analyzing crystal to the left stop and the counter tube to the right
stop.
09058.99
09058.10
09058.50
09005.00
09056.05
09056.02
1
1
1
1
1
1
14407.61
14602.00
1
1
The following settings are recommended for the recording of the
spectra:
— Auto and Coupling mode
— Gate time 50 s or longer
— Angle step width 0.1°
— Anode voltage UA = 25-35 kV: Anode current IA = 1 mA
Tasks
1. The intensity attenuation of the primary radiation is to be
measured for aluminium and zinc as a function of the material thickness and at two different wavelengths. The mass
absorption coefficients are to be determined from the graphical representation of the measured values.
Note
Never expose the counter tube to primary radiation for a longer
length of time.
To keep the relative error to a minimum, always use a gate time
of 50 seconds or longer, so that the total number of pulses is
always higher that 1000. At small pulse rates, the background
radiation must be taken into account, and must first be carefully
determined at an accelerating voltage of Ua = 0 V.
Recommended accessories:
Software X-ray unit, 35 kV
RS232 data cable
PC, Windows® 95 or higher
Fig. 1:
Experimental set-up for the determination of X-ray absorption.
Phywe series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
25411-00
1
LEP
5.4.11
-00
Absorption of X-rays
Due to counter dead time t, high pulse rates N* should be corrected to the true pulse rates N by means of the relation:
N
N*
1 tN*
(with t = 90 msec)
(1)
To determine the absorption of two different materials (Al and Zn)
as a function of the thickness of the absorbers, first measure the
intensity for two different glancing angles (wavelengths) without
an absorber, then with an absorber. The combination of two
metal foils can be used. Plot the measured values as in Fig. 2.
Now determine the absorption for aluminium (d = 0.08 mm), then
for tin (d = 0.025 mm), in the range 6° < q < 16° in steps of
∆q = 1°-2°, and plot the results as shown in Fig. 3.
In order to assure a sufficiently high precision in the evaluation of
the measurements on nickel and copper (d = 0.025 mm),
increase the number of points measured near the absorption
edges, and also increase the measuring interval at large wavelengths (Figs 4 and 5).
Theory and evaluation
If X-rays with intensity I0 penetrate matter of layer thickness d,
then the intensity behind the layer is given by:
I = I0 e-m(l)d
In order to be able to directly compare the absorptivities of various materials, it is advantageous to use the so-called half-value
thickness d1/2. This symbolizes the material thickness that
reduces the intensity of primary radiation by one half. On applying the half-value thickness, equation (2) becomes:
d1>2 0.69
1
m
(3)
Since the attenuation coefficient is proportional to the mass, the
mass absorption coefficient m/r (where r = the mass density in
the unit cm2/g) is often used.
Intensity attenuation is caused by the following processes:
1. The photoelectric effect
2. Scattering
3. Pair production
Number 3 pertains to gamma radiation, due to the minimum
energy required, equal to twice the amount of the electron rest
energy.
2E0 = 2m0c2 = 1.02 MeV
The absorption coefficient for X-rays therefore comprises of the
following components:
(2)
m=t+s
The quantity m in the unit cm-1, is called the linear attenuation
coefficient and is dependent on the wavelength l of the primary
radiation and the atomic number Z.
Fig. 2: Semi-logarithmic representation of the pulse rates as a
function of the absorber thickness.
Ua = 35 kV, Ia = 1 mA.
Curve 1: Al (Z = 13); l = 139 pm
Curve 2: Al (Z = 13); l = 70 pm
Curve 3: Zn (Z = 30); l = 139 pm.
10
9
8
7
6
2
(4)
t = The photoelectric absorption coefficient
s = The scattering coefficient
Fig. 3:
3
2
m>r for aluminium and tin as a function of the primary radiation wavelength; Ua = 25 kV.
5.0
3
2
m>r
4.5
g 1>3cm2>3
I/I
05
4.0
4
3
Sn
3.5
2
1
3.0
10
9
8
7
6
2.5
5
2.0
4
Al
3
1.5
2
3
1.0
1
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
d/mm
2
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0.20
30
40
50
60
70
80
90
100
110
l/pm
Phywe series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
LEP
5.4.11
-00
Absorption of X-rays
For the wavelength range used here, the photoelectric effect is
of primary account for absorption. Thus: t > s
The following equation (derived empirically) applies with sufficient precision:
m
t
k 1l3·Z3 2
r
r
(5)
where Z = the atomic number.
The above numeric factors of the constant k only pertain to
wavelengths l < lK, whereby lK is understood to be the wavelength corresponding to the absorption edge of the K energy
level. Other numeric factors apply for lK < l.
It becomes accordingly evident that the absorption increases
drastically with the wavelength of the primary radiation, as well
as with the atomic number of the absorbing element.
Since absorption is an entirely atomic characteristic, it follows
that a molecular absorption is compiled from the addition of the
absorption coefficients of the elements concerned.
In order to produce the monochromatic radiation necessary for
absorption analysis from the copper X-ray spectrum, a
monocrystal is used as monochromator. The wavelength l is
determined by the Bragg equation:
2d sin q = nl
(6)
q
= the glancing angle
n (1, 2, 3...) = the scattering order
d
= 201.4 pm = the lattice constant of the LiF crystal
Fig. 2 shows the measured pulse rates for different absorber
thicknesses and two different wavelengths plotted on a semilogarithmic scale. Curves 1 and 2 apply to aluminium (Z = 13,
r = 2.7 g/cm3) and curve 3 to zinc (Z = 30, r = 7.14 g/cm3).
It is apparent from Fig. 2 that absorption increases with both the
wavelength of the primary radiation and the atomic number. The
results from Fig. 2, obtained using (2) to (6), are listed in Table 1.
The wavelength dependency of aluminium absorption according
to (5) is apparent. A check on the Z dependency of the mass
absorption coefficients for aluminium and zinc according to (5) is
not possible here, since the primary radiation wavelength lies
within the K absorption edge of zinc.
(5) is only valid outside of the absorption edges.
Fig. 3 shows that the experimentally determined dependence of
aluminium and tin (Z = 50, r = 7.28 g/cm3) on the wavelength
corresponds well with the l3 relationship wavelength given in (5).
If the wavelength of the X-rays is reduced, so that their energy is
equal to one of the energies of the atomic levels of the absorber,
a sudden increase in absorption is observed. Fig. 4 shows this
situation for copper (Z = 29, r = 8.96 g/cm3).
Thus, according to (5), the value decreases linearly up to a critical wavelength lK, then increases suddenly for before again
decreasing linearly. From this experiment, l > lK = 138 pm, so
that using this and the equation:
EK h·c
elK
(7)
where
h = 6.6256 · 10-34Js Planck's quantum of action
(Plancks constant)
c = 2.9979 · 108 m/s-1 the velocity of light
e = 1.6021 · 10-19 C as the elementary charge
the following value for the energy of the copper K level is
obtained:
Cu - EK = 8.98 keV (literature value; 8.98 keV).
The deviation of the absorption from linearity in front of the
absorption edge is produced by the gain in short waved photons produced by 2nd order of diffraction scattering.
Fig. 5 shows the absorption curve for nickel (Z = 28, r =
8.99 g/cm3). Since the atomic number of nickel is smaller than
that of copper, EK (Ni) < EK (Cu) also applies here, as well as
lK(Ni) > lK(Cu). This is actually true in the case of lK(Ni) =
149 pm.
Using this value for lK(Ni) in (7) we obtain:
EK (Ni) = 8.32 keV (literature value; 8.33 keV).
Table 1: The dependence of absorption on wavelength
m
cm
1
d1>2
cm
m>r
2 1
cm g
m1>r
m2>r
a
l1 3
b
l2
Al (Z = 13)
r = 2.7 g/cm-3
l = 139 pm
112
6.2 · 10-3
41.5
l = 70 pm
14.1
20.4
5.2
7.98
7.83
Zn (Z = 30)
r = 7.14 g/cm-3
l = 139 pm
280
2.5 · 10-3
39.2
Phywe series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
25411-00
3
LEP
5.4.11
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Absorption of X-rays
Nickel filters are used to monochromatize the radiation from
copper X-ray tubes. When this is done, only the characteristic
Ka copper radiation E(Ka) = EK - EL2,3 = (8.98 - 0.95) keV =
8.03 keV is allowed to pass, while the Kb line E(Kb) = EK - EM2,3
= (8.98 - 0.074) keV = 8.9 is absorbed (see also Experiment
5.4.06). The reduction in the absorption curve at l < 100 pm is
the result of 2nd order of diffraction scattering.
A short calculation might be helpful here to help emphasize this
fact.
The beginning of the X-ray spectrum at high energy is determined by the acceleration voltage of the X-ray tube (see also
Experiment 5.4.09) According to (7), an acceleration voltage of
25 kV complies with a wavelength of lc = 49.6 pm. If this value
is inserted in the Bragg equation for the 2nd order of diffraction
(n = 2), then scattering is expected to be under glancing angle
q = 14.3°.
Under this glancing angle, X-rays of wavelength l = 99.2 pm are
emitted from the 1st order of diffraction, so that the primary radiation colliding with the absorber under a glancing angle of
q > 1.3° (q > 99.2 pm) contains a percentage of shorter wavelength photons. As a consequence, the absorber appears to be
more transparent than it really is. This disturbing effect does not
appear as drastically in Fig. 5. Due to the conscious choice of a
reduced primary voltage of Ua = 20 kV, the bremsstrahlung is
only activated under larger glancing angles.
Furthermore, the intensity of the bremsstrahlung at Ua = 35 kV is
less than at Ua = 20 kV.
Finally, Fig. 6 shows the dependence of the absorption on the
atomic number Z. Keeping in mind that the absorption behaviour
is different for the ranges l < lK and l > lK, the Z dependence
of absorption coefficients can only be compared within equivalent absorption ranges. Literature values marked by a cross are
additionally used to support the measured values.
Fig. 4: Absorption edge of copper; Ua = 25 kV; lK = 138 pm.
Fig. 5: Absorption edge of nickel; Ua = 25 kV; lK = 149 pm.
Literature
Energy level values have been taken from:
"Handbook of Chemistry and Physics", CRC-Press Inc, Florida.
3
2
m>r
g 1>3cm2>3
2m>r
g 1>3cm2>3
Cu
5.5
5.5
5.0
5.0
4.5
4.5
4.0
4.0
3.5
3.5
3.0
3.0
2.5
2.5
2.0
2.0
lK = 138 pm
1.5
20
40
60
80
100
120
140
160
l/pm
4
Ni
6.0
3
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180
lK = 149 pm
1.5
20
40
60
80
100
120
140
160
180
l/pm
Phywe series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
Absorption of X-rays
LEP
5.4.11
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3
2
m>r
g 1>3cm2>3
8.0
7.0
l>lK
6.0
5.0
4.0
3.0
l<lK
2.0
1.0
10
20
30
40
50
60
Z
3
Fig. 6: 2m>r = f (Z); values marked with a circle are literature
values.
Phywe series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
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Absorption of X-rays
25411-00
Phywe series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen