TEP
5.4.6101
TEP
5.4.6001
Energy-dispersive measurements of
K- and L-absorption edges
Related topics
Bremsstrahlung, characteristic X-radiation, absorption of Xrays, Bohr’s atom model, energy levels,
Moseley’s law, Rydberg frequency, screening constant, semiconductor energy detectors and multichannel analysers.
Principle
Thin powder samples are subjected to polychromatic X-rays. The energy of the radiation that passes
through the samples is analysed with the aid of a semiconductor detector and a multi-channel analyser.
The energy of the corresponding absorption edges is determined, and the resulting Moseley diagrams
are used to determine the Rydberg frequency, the screening constant, and the principal quantum numbers.
Equipment
1
1
1
1
1
1
1
1
XR 4.0 expert unit 35kV
XR 4.0 Goniometer for X-ray unit, 35 kV
XR 4.0 Plug-in module with W X-ray tube
Diaphragm tube d = 1 mm
Diaphragm tube d = 2 mm
Multi-channel analyser
X-ray energy detector
XR 4.0 XRED cable 50 cm
09057-99
09057-10
09057-80
09057-01
09057-02
13727-99
09058-30
09058-32
1
1
1
1
1
Screened cable, BNC, l = 750 mm
Set of chemicals for edge absorption
Universal crystal holder for the X-ray unit
Microspoon, steel, l = 150 mm
Software for the multi-channel analyser
07542-11
09056-04
09058-02
33393-00
14452-61
PC, Windows® XP or higher
Fig. 1: P2546101
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TEP
5.4.6101
Energy-dispersive measurements of
K- and L-absorption edges
Safety instructions
When handling chemicals, you should wear suitable
protective gloves, safety goggles, and suitable clothing. Please refer to the appendix for detailed safety
instructions.
Tasks
1. Calibrate the semiconductor energy detector
with the aid of the characteristic radiation of the
calibration sample.
2. Record the energy spectra of the polychromatic
X-rays that pass through the powder samples.
Fig. 2: Connections in the experimentation area
3. Determine the energy of the corresponding Kand L-absorption edges.
4. Determine the Rydberg frequency, screening
constants, and principal quantum numbers with
the aid of the resulting Moseley diagrams.
Set-up and procedure
Set-up (Fig. 1)
- Screw the adapter ring onto the inlet tube of Fig. 3: Connection at the external panel of the XR 4.0 Xray expert unit to the MCA
the energy detector.
- Connect the signal and supply cables to the
corresponding ports of the detector with the aid
X-ray energy
of the right-angle plugs.
detector
- Connect the signal and supply cables from the
MCA to the appropriate connections in the experiment chamber of the X-ray unit (signal cable: red, supply cable: green (see Fig. 2)).
- Connect the external ports for the X RED of the
x-ray unit (signal cable red, supply cable green,
see Fig. 3) to the multi-channel analyse (MCA).
Connect the signal cable via a screened BNCcable to the “Input” port of the MCA and the
supply cable to the “X-Ray Energy Det.” port of
Left position of the
the MCA.
goniometer
Universal crystal
- Secure the energy detector in the holder of the
holder with metal
swivel arm of the goniometer. Lay the two casample
bles with sufficient length so that the goniometer can be swivelled freely over the entire swivelling range.
- Connect the multi-channel analyser and computer with the aid of the USB cable.
- Insert the tube with the 2-mm-aperture.
Fig. 4: Set-up at the goniometer
2
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P2546101
TEP
5.4.6101
TEP
Bring the goniometer block and the detector to their respective end positions on the left. Bring5.4.60the de01
tector to the 90° position in the 2:1 coupling mode (Fig. 4).
Energy-dispersive measurements of
K- and L-absorption edges
-
Calibration of the multi-channel analyser
(if there is no other already existing calibration that can be used)
- Bring the goniometer block and the detector to their respective end positions on the left.
- Insert the tube with the 2-mm-aperture into the exit tube of the X-ray tube.
- Fasten the Fe- and Zn-samples on the universal sample holder so that the line where they touch is in
the middle. Insert the sample holder and bring it to the 45° position in the 2:1 coupling mode (detector at 90°).
- Operating data of the copper X-ray tube: Select an anode voltage Ua = 35 kV and an anode current ia
= 1 mA and confirm these values by pressing the “Enter” button.
- When the sliding door of the X-ray unit is closed, lock it with the red safety button. Press the safety
button again to unlock the electronic lock. Then, press the “HV-ON” button. The X-ray unit should
now emit radiation (it should light up).
- In the MEASURE program, select “Multi channel analyser” under “Gauge”. Then, select “Settings and
calibration”. After the “Calibrate” button has been clicked, a spectrum can be measured. The counting rate should be approximately 100 c/s. Energy calibration settings: - 3-point calibration, - Unit =
keV, Gain = 2 – Set the offset so that lowenergy noise signals will be suppressed (usually a few per
cent are sufficient), - Interval width [channels] = 1.
- Measuring time: approximately 5 minutes. Use the timer of the X-ray unit.
- Make the three coloured calibration lines congruent with the line centres of the three characteristic Xray lines. The corresponding energy values Fe(Kα) = 6.40 keV, Zn(Kα) = 8.64 keV, and Zn(Kβ) = 9.57
keV are entered into the corresponding fields, depending on the colour. Name and save the
calibration.
Figure 5 shows the calibration spectrum.
Kα (zinc)
Kα (iron)
Kβ (zinc)
Kβ (iron)
Fig. 5: Calibration spectrum
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TEP
5.4.6101
Energy-dispersive measurements of
K- and L-absorption edges
Sample preparation
The thickness of the powder samples is very important for obtaining clear absorption edges. If the samples are not thick enough, the edge effect cannot be made visible. On the other hand, samples that are
too thick do absorb the entire primary beam intensity. This is why the following method is recommended
for preparing samples in the thickness range between 0.2 and 0.4 mm: Use an office punch and punch
several sheets of paper of a suitable thickness (approximately 3 layers of standard writing or printing paper that are glued together). Then, seal the hole on one side with some transparent adhesive tape (Fig.
6a). The result is a little “pot”. Fill the sample powder into the pot with a spatula and smooth the surface.
Seal the pot with another piece of transparent adhesive tape (Fig. 6b and c). Then, fasten the strip of
Fig. 6a-d: Sample preparation; a: perforated paper (3 layers) with adhesive tape; b: filling in the powder; c: smoothing the surface; d: fastening on the diaphragm tube
paper that has been cut to size in front of the tube
with the 1mm-aperture with some transparent adhesive tape (Fig. 6d).
Spectrum recording
- The goniometer block and detector (0° position)
are now in their respective end positions on the
right.
- Adjust an anode voltage Ua = 35 kV and an anode current so that the counting rate is ≤ 400
c/s.
- Measuring time: 3 to 5 minutes (use the timer
of the X-ray unit).
Evaluation of the measurement curves
Fig. 7: Determination of the position of the absorption
- In order to determine the edge energy, switch
edges.
from the bar display to the curve display. To do
so, click “Display options” and then “Interpolation and straight lines”.
- Then, smoothen the curve to a medium extent
with
.
- Extend the relevant edge section with the zoom
function
.
- Determine the extreme values Imax and Imin of the
edge intensity with the function “Survey”
.
- On the measurement curve, find the energy value that belongs to the intensity middle of the Fig. 8: Schematic course of the transmission T as a
edge (see Fig. 7).
function of the quantum energy E in the range
of absorption edges.
4
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5.4.6101
TEP
5.4.60Theory and Evaluation
When X-rays interact with matter, they lose energy due to Compton scattering, pair production, and01
phoEnergy-dispersive measurements of
K- and L-absorption edges
toelectric effects. In the range of energy that is available during this experiment, the photoelectric effect
plays the most important role.
Figure 8 shows the schematic course of the transmission T as a function of the radiation energy E. At
certain energy levels, the absorption (decrease in the transmission) increases drastically. In this case,
the energy of the X-ray quanta is only sufficient for removing electrons from certain energy levels of the
absorber atoms. As a result, the measurement of the absorption edges in X-ray spectra enables the determination of the energy levels of the inner atomic shells.
If relativistic and spin-orbit coupling effects are neglected, the binding energy En of an electron on the nth
shell of an atom can be described in an approximative manner by Bohr's atom model:
En  
me e 4
Z   2 12
2 2
8 0 h
n
Electron mass
me
Elementary charge
e
Planck’s constant
h
Dielectric constant
e
Atomic number
Z
Screening constant
σ
Principal quantum number n
(1)
= 9,109∙10-31 kg
= 1,602∙10-19 J
= 6,626∙10-34 Js
= 8,854∙10-12 N-1m-2C2
With the introduction of the Rydberg frequency
me e 4
R  2 3  3,29  1015 s 1
8 0 h
(1) leads to
E n   R  hZ   
2
1
n2
(2)
The function √E = f(Z) provides a so-called Moseley diagram, which can be used to determine either R,
n, or σ.
Evaluation of the K-absorption edges
Figure 9 shows the X-ray spectra with the K-absorption edges for various elements.
Column C of Table 1 shows the energy values of the K-edges, which have been determined with the aid
of the spectra. Column E shows the corresponding literature values (taken from the “Handbook of Chemistry and Physics”, CRC-Press, Inc., USA).
Table 1: K-edge absorption
A
B
Element
Ge
Se
Br
Rb
Sr
Z
32
34
35
37
38
C
E(K) exp. / keV
D
σ
E
E(K) lit. / keV
11,09
12,62
13,44
15,13
16,04
2,67
2,72
2,72
2,75
2,74
11,103
12,658
13,474
15,200
16,105
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TEP
5.4.6101
Energy-dispersive measurements of
K- and L-absorption edges
without
Abs
E (K)
Ge
Se
Br
Rb
Sr
Fig. 9: X-ray spectra with the K-absorption edges.
Figure 10 shows the corresponding Moseley diagram. Equation (2) is converted in order to calculate the
Rydberg constant R using the Moseley diagram:
En 
1
R h  Z 
n
Note: convert the energy values of the K-absorption edges form keV to eV before evaluating the straight
line. Form the slope of the regression line in Fig. 10, R is calculated:
3,6 eV 
1
Rh
n
(3)
Conversion of eV to J (1 eV = 1.602 · 10-19 J)
3,6 2 eV  1,602  10 19 
1
Rh
n2
20,76  10 19 J
 R  3,13  1015 s 1
34
6
,
626

10
and as n = 1
6
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TEP
5.4.6101
TEP
15 -1
5.4.60gives the following result for the Rydberg frequency: R = 3.13 · 10 s .
01
Column D of Table 1 shows the values of the screening constant σ that were calculated with the aid of
(2). However, in accordance with Bohr's atom model, σ should be 1 for the K shell, since the attenuation
Energy-dispersive measurements of
K- and L-absorption edges
of the nuclear field is only caused by a 1s electron that is not involved in the ionisation process. A
screening value of σ ≈ 2.7 emphasises the limited validity of Bohr’s atomic model. More detailed calculations (Hartree) shows that the electrons of higher shells (e.g. the 3p electron) also have secondary maxima near the nucleus in the radial charge density distribution.
Fig. 10: Moseley diagram for the K-edge absorption.
Evaluation of the L-absorption edges
Figure 11 shows the X-ray spectra with L-absorption edges. An L1 edge cannot be proven here, due to
the fact that the intensity is too low.
Columns C and D of Table 2 show the energy values of the L-edges that were determined based on the
spectra. For comparison, columns E to G show the corresponding literature values.
Table 2: L-edge absorption
A
Element
W
Pb
Bi
B
Z
C
D
E
F
G
E(L2) exp. / keV
E(L3) exp. / keV
E(L1) lit. / keV
E(L2) lit. / keV
E(L3) lit. / keV
74
82
83
11,76
15,33
15,70
10,15
13,00
13,37
12,100
15,861
16,388
11,544
15,200
15,711
10,207
13,035
13,419
Figure 12 shows the corresponding Moseley diagrams. The gradients of these diagrams are used to determine the principal quantum number n.
1
Rh
n
L1:
with Rh = 13.6 eV (Ek of the hydrogen atom), the following results:
n = 1.94 ≈ 2; accordingly, the straight line for L2 leads to: n = 2.16 ≈ 2.
1,9 eV 
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TEP
5.4.6101
Energy-dispersive measurements of
K- and L-absorption edges
E (L3)
W
E (L2)
E (L3) E (L2)
Pb
E (L3)
E (L2)
Bi
Fig. 11: X-ray spectra with the L-absorption edges.
Y1= 1,9x – 31,5
L2 →
L3 →
y2 = 1,7x – 21,9
Fig. 12: Moseley diagram for the L-edge absorption.
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Energy-dispersive measurements of
K- and L-absorption edges
Disposal
Do not dispose of heavy-metal-containing waste via household waste.
TEP
5.4.6101
TEP
5.4.6001
Appendix
Hazard symbol, signal word
Hazard statements
Precautionary statements
--
-
H302: Harmful if swallowed
H332: Harmful if inhaled
-
-
-
H301: Toxic if swalloed
H331 Toxic if inhaled
H373: Causes damage to
organs through prolonged
or repeated exposure
H413: May cause long
lasting harmful effects to
aquatic life
-
H315: Causes skin irritation
H319: Causes serious eye
irritation
H335: May cause respiratory irritation
P261: Avoid breathing
dust/fume/gas/mist/vapo
urs/spray.
P305 + P351 + P338: IF
IN EYES: Rinse cautiously with water for
several minutes. Remove contact lenses, if
present and easy to do.
Continue rinsing.
-
-
H272: May intensify fire;
oxidiser
H302: Harmful if swallowed
P201: Obtain special instructions before use.
P220: Keep/Store away
from clothing/…/combustible mate-
Rubidium chloride (RbCl)
Germanium(IV) oxide (GeO2)
Zinc
Selenium
Danger
Potassium bromide (KBr)
Strontium sulphate (SrSO4)
Lead(IV) oxide (PbO2)
Danger
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TEP
5.4.6101
Energy-dispersive measurements of
K- and L-absorption edges
H332: Harmful if inhaled
H360: May damage fertility or the unborn child
H373: Causes damage to
organs through prolonged
or repeated exposure
H410: Very toxic to aquatic life with long lasting effects
rials.
P273: Avoid release to
the environment.
P308 + P313: IF exposed or concerned: Get
medical advice/attention.
Tungsten(IV) oxide (WO2)
H335: May cause respiratory irritation
-
H315: Causes skin irritation
H319: Causes serious eye
irritation
H335: May cause respiratory irritation
P261: Avoid breathing
dust/fume/gas/mist/vapo
urs/spray.
P305 + P351 + P338: IF
IN EYES: Rinse cautiously with water for
several minutes. Remove contact lenses, if
present and easy to do.
Continue rinsing.
Warning
Bismuth(III) oxide (Bi2O3)
Warning
10
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