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					                          UNIVERSITY OF SURREY

                        DEPARTMENT OF PHYSICS

             Level 1 Laboratory: General Physics Experiment



      THE ABSORPTION, DIFFRACTION AND EMISSION OF

                                  X-RAY RADIATION

1       AIMS

1.1     Physics

These experiments are intended to give some experience of the generation and properties of X-
rays. The very short wavelength of X-rays will be exploited to cause Bragg diffraction from a
NaCl crystal. The emission of X-rays will be studied and used to calculate a value for Planck's
constant.


1.2     Skills

The particular skills you will start to acquire by performing this experiment are:


                 Use of a low power, biologically safe, X-ray source.


                 Use of a Geiger-Müller tube and appropriate equipment to detect and measure
                 X-rays.


                 Use of a Sodium Chloride crystal as a diffraction grating for short wavelengths.


                 Adjustment of an X-Ray spectrometer to measure small angles accurately.


                 Graphing and calculating skills.



                                                                        Last updated by AL 27th Feb 2009
                                            Page 1   of 11
                                   Experiment 2F - X-ray Diffraction


2       X-RAY PRODUCTION, DETECTION, ABSORPTION AND
        DIFFRACTION

2.1     Production of X-rays

X-rays are generated when fast moving              n=∞                                          0 eV
electrons are slowed down rapidly on
collision with a metal target[1]. In the Tel-      n=4                                          N
X-Ometer equipment the electrons are                                                    Mα
accelerated through 20kV or 30kV in a              n=3                                          M
vacuum tube and then collide with a copper                                            Lα
target. The accelerating voltage is selected       n=2
by a switch on the top of the instrument.                                                       L
The current carried by the electron beam is
typically 60-80µA, as can be observed on               Kα2      Kα1    Kβ      Kγ
the meter provided.
                                              n=1                                         K
The spectrum of radiation produced
consists of sharp lines characteristic of the
target material superimposed on a Figure 1:                K, L and M energy levels in
background of continuous radiation. For a                  the copper atom.
copper target the most intense lines are the Kα and Kβ lines, corresponding to the transitions
indicated in Figure 1.

2.2     X-Ray Detection

Photographic methods are frequently used particularly when observing X-ray diffraction patterns.
However, when quantitative measurements of intensity are required either an ionisation chamber
together with a sensitive current detector, or a Geiger-Müller (GM) tube connected to a ratemeter
or counter, are more suitable.

2.3     Absorption

When X-rays pass through matter they lose energy both by scattering and by true absorption, the
net effect is termed the total absorption. The true absorption is the larger effect and varies as the
cube of the wavelength of the radiation.

If a beam of intensity I traverses a layer of thickness dx the intensity decreases according to the
relationship
                                           dI
                                              = − µdx                                          (1)
                                            I
where µ is the absorption coefficient for the material through which the rays have passed.
Integrating the above relation gives:

                                        I = I 0 exp(− µx )                                      (2)




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                                      Experiment 2F - X-ray Diffraction


The true absorption coefficient is
a function of wavelength and
changes      abruptly    at     the
characteristic absorption edges.
For example, the transmission of
Ni varies with the wavelength of
the radiation as shown in Figure
2. By using a thin layer of nickel
in the X-ray beam it is possible to
have the absorption edge just on
the short wavelength side of the
Kα line, hence producing much            Figure 2: Transmitted X-radiation through a thin Ni foil,
more nearly monochromatic                showing strong absorption at an angle corresponding to a
radiation.                               characteristic Kβ absorption energy.


2.4     Diffraction
The wavelength of X-rays is so short that in order to produce diffraction patterns a grating with a
spacing of the order of a nanometer would be required. While such a grating would be difficult to
manufacture artificially, this value is typical of the interplanar spacing in crystal lattices, and
therefore a crystal of known lattice structure can be used as a grating to determine X-ray
wavelengths. Alternatively, if the wavelength of the radiation is known, then the lattice spacing
can be found. This technique is of great importance in crystallography[2].


3       EXPERIMENTAL EQUIPMENT

In the Tel-X-Ometer the entire experimental zone is enclosed in a transparent plastics scatter
shield. It is impossible to turn on the extra high voltage (EHT) supply, and thus to generate X-
radiation, unless this shield is locked down in the safe position. In addition this shield is fitted with
an Aluminium and Lead back-stop directly in line with the X-ray source. The EHT may be set to
either 20kV or 30kV, and the tube current may be adjusted with a screwdriver - do not exceed
80µA.

You are advised to spend about half an hour becoming familiar with the Tel-X-Ometer and its
controls.

Connect the Tel-X-Ometer to the mains supply and switch on at the POWER ON switch. Note
that nothing will happen unless the timer knob on the front panel is rotated clockwise to start a
timed period. Throughout the experiment, keep an eye on the timer. When it gets close to zero,
increase the time, so that the X-ray source does not switch off during an experiment. The X-ray
tube filament and power on indicators will then illuminate. The equipment should be allowed to
warm-up for 3 minutes after initial switch on to eliminate any condensation.

During this period examine the functioning of the scatter shield interlocks. To release the shield
displace it sideways in either direction at its hinge. To close the shield lower it until the ball ended
spigot engages with its locking plate and then displace the shield at the hinge to centralise this
spigot. Note that the directions of displacement should suit the position of the carriage arm.
                                                Page 3 of 11
                                Experiment 2F - X-ray Diffraction




                                                                                 carriage arm
                                                                                  ES spring clip
  clutch plate




                                Al/Pb Back Stop

          Figure 3: Photograph of the Tel-X-ometer showing all important components.


With the shield closed depress the X-Rays ON button. The EHT will now be applied to the tube
and the red indicator lamp
will illuminate. Observe
that the tube current is in
the 60-80µA range. If not,
adjust the current using a
screwdriver.          Should
depressing the button have
no effect check carefully
that the shield is centralised
in its locked position.




                                 Figure 4: Figure showing the reflecting crystal face against the
                                             chamfered post of the Tel-X-ometer.




                                          Page 4 of 11
                                  Experiment 2F - X-ray Diffraction

To turn off the EHT simply displace the shield sideways at the hinge.

The X-ray beam from the tube is circular with a diameter of 5mm. This beam can be collimated by
fitting either the 1mm circular collimator, TEL 580.002, or 1mm slot collimator 582.001, to the
tube port, where they will be retained by their O-ring seals. Further collimation may be produced
by fitting 1mm or 3mm slot collimators at the appropriate experimental station (ES) on the
carriage arm.

Crystals can be mounted on the central crystal post using the screw clip provided, as shown in
Figure 4.

The tube is mounted by slotting the square flange of the tube holder into the spectrometer arm,
usually at ES 26. The tube can be connected to the GM inputs of either the ratemeter or the
Digicounter, and the power supply should be set to about 480 V.

4      EXPERIMENTAL PROCEDURE

4.1    Experiment 1: Absorption of X-rays by Aluminium
When X-rays strike an absorbing material, the “softer” longer wavelength radiation of the
continuous spectrum is absorbed more easily. The mean wavelength of the transmitted radiation
therefore progressively decreases, and the X-rays “harden”.

For this experiment the Digicounter and GM tube will be used to measure the intensity of the X-
rays.

A      Mount the auxiliary slide carrier over the basic port using the 1mm circular collimator
       582.002 to hold it in position.

B      Mount the GM tube at ES22. If this is not possible due to space constraints, choose the
       nearest slot to ES22 that is possible and make a note of the position. Connect the GM tube
       to the Digicounter. Set the Digicounter function switch to radioactivity and the range
       switch to 10s. Set the tube voltage to 480 V and the reading switch to continuous.

C      Mount a 2mm thick Aluminium slide at ES2. This slide will remain in position during the
       experiment and its thickness is not to be included in the values of absorber thickness x
       below.

D      Locate the carriage arm in the straight through position, switch on the EHT, set to 30kV,
       and record the count rate, tabulating three ten second counts and calculating their mean and
       the standard error in the mean. If you record more than 14000 counts in 10s, then please
       insert an additional aluminium slide in the auxiliary slide carrier until the number of counts
       has dropped below 14000 in 10s.

E      Mount the 0.25mm, 0.50mm, 0.75mm, 1.0mm and 2.0mm aluminum slides, singly or in
       combination the available slots in front of the GM tube, and repeat the measurements
       above to record count rates for absorber thickness x from 0.25mm to 3mm.

F      Plot a graph of count rate I against x. This graph should be an exponential curve since I is
       related to x by the equation (2), where µ is the linear absorption coefficient.
                                            Page 5 of 11
                                   Experiment 2F - X-ray Diffraction

G       Find from your plot of I against x the “half-value” thickness of aluminium for 30kV
        radiation, i.e. the value of x required to reduce the intensity to Io/2. Find also the “tenth-
        value” thickness. Tabulate and plot ln(I) against x. The equation above implies that this
        graph should be a straight line. (Do you understand why?) Is it a straight line? Find the
        value of µ from this graph. What is the meaning of the y-intercept?

H       Try to answer the following questions.

        Why do you think that the first 2mm (or more, if needed to drop the count rate) of
        aluminium needs to be placed near to the basic port? What happens if it is omitted? Try it.
         (See the Appendix for more information about the effect of filters.)

        Does the fact that the X-ray spectrum contains characteristic lines as well as the continuous
        spectrum make any difference?

        Radiographers concerned with the medical effects of soft radiation on outer body tissues
        commonly work with “half-values”, while those working with hard radiation more often
        use “tenth-values”. Why is this sensible?


4.2     Experiment 2: Bragg diffraction of X-radiation and the Determination
        of the NaCl Crystal Lattice Spacing

When an incident wavefront strikes a series of
reflecting layers separated by a distance d the first
condition for Bragg “reflection” is that the angles of
incidence and reflection are equal, and therefore the
detector of reflected rays must move through an
angle of 2θ, where θ is the angle between the
incident rays and the reflecting layers. This is shown
in Figure 5.

Scattering from atoms in a crystal occurs in all
directions.     The second condition for Bragg
reflection is that reflections from several layers must
combine constructively. The diagram at the bottom
of Figure 5 shows that if two rays reflect from
parallel planes (such as planes of atoms in a crystal)
separated by a distance of d, then constructive
interference will occur only when the lower ray
travels an "extra" distance exactly equal to 2dsinθ.
This simple geometric argument can thus be used to
derive the Bragg equation for diffraction:

2d sin θ = nλ                (3)                             Figure 5. Constructive interference leading to
                                                                         the Bragg condition.




                                             Page 6 of 11
                                   Experiment 2F - X-ray Diffraction

This equation tells us that for a certain wavelength λ, constructive interference will occur, and we
will see a peak in a diffraction pattern, only at values of θ where Equation 3 applies. If λ is known
(or can be calculated), and if θ is measured in an experiment, then the spacing between the planes
may be found. The variable n is called the “order” of the diffraction and it takes a positive integer
value. It should not be confused with the n values in Figure 1! Think about how n will affect the
angles where you see diffraction.

The Tel-x-ometer uses a copper target to generate the X-rays. Consequently, the energies of the X-
rays and their wavelengths can be related to the energy levels in the copper atom. There are a pair
of emission lines, called the Kα and Kβ1 lines, that you will use for your diffraction experiment.
You can calculate the wavelengths of the Cu Kα and Kβ1 radiation by using the mean energies of
the K, L, and M levels of the copper atom: -8979 eV, -951 eV, and -120 eV, respectively. As seen
in Figure 1, Cu Kα radiation is caused by a transition from the L to K level, whereas K β1 radiation
is caused by a transition from the M to the K level. (You should note on Figure 1 that there are
actually two transitions that lead to the α radiation, leading to two different wavelengths for α 1 and
α 2 emission lines, but you will not be able to resolve these in this experiment, and so it is
sufficient to calculate a single wavelength for Kα.)

In this experiment, you will use a crystal of NaCl as a diffraction grating. The structure of NaCl is
shown in Figure 6. It is commonly known that the crystal structure of NaCl is face-centred cubic.
The edge length of the cubic repeat unit (e on the Figure) is referred to as the lattice constant.




                                                                             d


                              e




    Figure 6. The NaCl crystal structure. The small spheres represent Cl ions; the large spheres
                                         represent Na ions.

Only certain planes in a crystal allow X-ray diffraction, however, because in some cases, there are
other planes that cause interference of the diffraction. In NaCl, diffraction does not occur between
the top and bottom planes of the repeat unit (separated by a distance of e), because of this effect.
Can you see why by looking at Figure 6? Diffraction does occur, however, from the planes
separated by a distance of e/2. In your Solid State Physics lectures in the Second Year, you will
learn that crystallographers use Miller indices to refer to these planes as (020) planes. In this
experiment, you will find e for NaCl.

A       Mount the NaCl crystal, 582.004, colour coded yellow, in the crystal post, ensuring that the
        face containing the major planes is in the reflecting position, i.e. against the chamfered
        post. Refer to Figure 4. The crystal is now mounted so that diffraction will occur from the

                                             Page 7 of 11
                              Experiment 2F - X-ray Diffraction

    (020) planes.

B   Mount the collimator 582.001 on the tube port with its slot vertical, without attaching the
    auxiliary slide carrier. Mount the GM tube at ES 26, the 3mm collimator 562.016 in ES
    13 and the 1mm collimator 562.015 in ES 18. If this is not possible due to space
    constraints, choose the nearest slots possible and note the used positions.

C   Set the carriage arm carefully to zero and then release the drive to the crystal post by
    unscrewing the clutch plate. Push the slave plate (the inner rotating plate engraved with
    two datum lines) round until the datum lines are accurately aligned with the zeros on the
    scale. Check that the carriage arm is still at zero and then screw down the clutch plate to
    engage the 2:1 drive mechanism between crystal and carriage arm positions. Rotate the
    carriage arm through 90° and verify that the slave plate has moved through 45°.

D   Connect the GM tube to the ratemeter. Set the GM tube supply voltage to 480V and the
    EHT to 30kV and turn it on.

E   Track the carriage arm from its minimum angle (2θ = 11°) to its maximum angle (2θ
    =120°) noting the count rate as a function of θ. The idea is to obtain a "survey" of how
    intensity varies as a means of finding the diffraction peaks. Angular increments of 5° in 2θ
    should be sufficient, but you could try larger or smaller increments. Your aim here is to
    discover the general position of the diffraction peaks; you will later "hone in" on the
    angular regions of the peaks. In the initial survey, there is no need to take three
    measurements. Alter the ratemeter time as appropriate to obtain a sufficient number of
    counts. Angular settings between 11° and 15° degrees can be obtained by indexing the
    cursor to 15° and using the thumb wheel indications between 0° and minus 4°.

F   Plot a graph of count rate against 2θ over the whole range you have measured.

G   Wherever the count rate appears to peak, plot the count rate at intervals of only 10 minutes
    of arc by using the thumb wheel. At each peak, measure and record the maximum count
    rate and angle 2θ as accurately as possible.

H   Tabulate values of θ where you observe a peak. Use the values of λ that you have
    calculated for Kα and Kβ radiation. As the wavelengths for the two types of radiation are
    similar, their peaks should occur closely together. You should think about which type of
    peak (Kα or Kβ) will occur at lower angles. (You will also need to think about the values of
    n.)

I   Determine values of d using Bragg's equation. The two X-ray lines should give the same
    values for d. Do they? Estimate the error in your results for d. What is the largest source
    of error?

J   Now check your result by estimating the atomic spacing between Na and Cl in the NaCl
    crystal. This distance will equal the spacing between the planes that lead to diffraction.
    For your calculation, you should make use of the fact that the molar mass of NaCl is 58.44
    g/mole, and its density is 2.17 gcm-3. You should also try to find a value of the lattice
    constant for NaCl in the literature and compare it to the value that you obtain in this
    experiment.

                                        Page 8 of 11
                                   Experiment 2F - X-ray Diffraction

A final word on the X-ray diffraction experiment: take care when analysing your data. You
should see diffraction from both Kα and Kβ emission lines. Plus, you should observe higher order
diffraction (n = 2 and n = 3). Do not confuse the two. As you know the relevant values of
wavelengths, when you find one diffraction peak, you should know where to look for the others.

4.3 Experiment 3: X-Ray emission and the measurement of Planck’s
constant.
When the accelerated electrons in the X-ray tube strike the target the majority of them lose their
energy by undergoing sequential glancing collisions with particles of the target material, thus
simply raising the temperature of the target.

A minority of the electrons will be involved in glancing impacts in which some of their energy is
imparted to the target particle while some is emitted in the form of quanta of electromagnetic
radiation equivalent to the loss of energy on collision.

These collisions usually occur at slight depths within the target material, so that the longer, less
energetic wavelengths are absorbed in the target and so are not emitted.

The “braking radiation” (or “bremsstrahlung”,) as it is known, is thus a continuous spread of
wavelengths, not characteristic of the target material, whose maximum possible quantum energy
will be equal to the kinetic energy of the accelerated electrons. Since few, if any, quanta will have
this maximum energy, it is necessary to find the wavelength of maximum energy by extrapolation.

A      Mount the auxiliary slide carriage 582.005 over the basic port using the 1mm slot primary
       beam collimator to hold it in position. Ensure that the slot in the collimator is vertical.
       Position the 1mm slide collimator 562.015 at ES4.

B       Mount the NaCl crystal to the crystal post as in experiment 2.

C      Mount the GM tube at ES26 and the 3mm slide collimator 562.016 at ES13. If this is not
       possible due to space constraints, choose the nearest slots possible and note the used
       positions. Connect the GM tube to the Digicounter. Set the function switch to radioactivity
       and the range switch to 1s. Adjust the GM tube supply to 480V and set the reading switch
       to continuous.

D      With the EHT set to 20kV measure, tabulate and plot the count rate at every 30’ of arc
       from 11 30’ until after the “whale back” of the curve appears to fall off. For low count
       rates it is sensible to use the 100 s range on the Digicounter in order to obtain
       sufficient statistics. These readings are not easy to take accurately - take your time and be
       as careful as you can.

E      Extrapolate your curve to zero count rate and note the angular settings at which the curve
       crosses the horizontal axis. Your results should look something like Figure 7. These angles
       correspond to the minimum wavelengths (and therefore maximum energies) of the X-
       radiation.




                                             Page 9 of 11
                                Experiment 2F - X-ray Diffraction




 Figure 7: Scattering obtained (at two EHT voltages) from NaCl. The broad peaks indicate the
 broad range of wavelengths produced.


F     Use your calculated value for the lattice spacing d for NaCl from experiment 2 to find the
      minimum wavelengths (and hence the maximum frequencies) of X-radiation emitted for
      both settings of the EHT supply. This minimum wavelength will be produced when all of
      the energy of the electrons accelerated through the EHT voltage V is converted into quanta
      of energy hν, where h is Planck’s constant and ν is the frequency of the X-radiation. The
      energy of the accelerated electrons is merely the product of their charge e and the
      accelerating voltage V. We can therefore use the relationship
                                             Ve = hν                                        (4)
      to calculate a value for h. You can determine ν from your measurements of the minimum
       X-ray wavelength. Estimate the error in your results. What is the largest source of error?



5 REFERENCES
1)    D. Halliday, R. Resnick and J. Walker, J. Wiley & Sons (1997). Ch 41.8.
2)    D. Halliday, R. Resnick and J. Walker, J. Wiley & Sons (1997). Ch 37.9.




                                         Page 10 of 11
                                   Experiment 2F - X-ray Diffraction


                                           APPENDIX

                                              K lines




                             Effect of a filter on an X-ray spectrum.


A filter has the following effects on the spectrum:

(1) A change in shape with preferential removal of lower energies (beam hardening)

(2) A shift in the peak of the spectrum towards higher energies

(3) An overall reduction in X-ray output

(4) A shift in the minimum photon energy (Emin) to higher energies

(5) No change on the maximum photon energy (Emax).




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