1

X-ray Diffraction

B2

Head of Experiment: James McGinty

The following experiment guide is NOT intended to be a step-by-step manual for the

experiment but rather provides an overall introduction to the experiment and outlines

the important tasks that need to be performed in order to complete the experiment.

Additional sources of documentation may need to be researched and consulted

during the experiment as well as for the completion of the report. This additional

documentation must be cited in the references of the report.

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RISK ASSESSMENT AND STANDARD OPERATING PROCEDURE

1. PERSON CARRYING OUT ASSESSMENT

Name Geoff Green Position Chf Lab Tech Date 18/09/08

2. DESCRIPTION OF ACTIVITY

B18 X-Ray Diffraction

3. LOCATION

Campus SK Building Huxley Room 403

4. HAZARD SUMMARY

Accessibility Possible trip hazards

Mechanical

Manual Handling

Heavy Apparatus: Sensitive monocrystals: Fine powder samples

Hazardous Substances

Various metal samples; Treat all samples as potentially Hazardous

Electrical Mains Powered Equipment

Other X-Ray Source

Lone Working Permitted?

Yes No Permit-to-Work Required?

Yes No

5. PROCEDURE PRECAUTIONS

Use of 240v Mains Powered Equipment Isolate Socket using Mains Switch before unplugging or plugging in equipment

Accessibility All bags/coats to be kept out of aisles and walkways.

Use of X-Ray Source Never force safety interlocks on lead glass doors; seek technical help when changing tubes and detectors.

Handling samples Always wear gloves and eye protection; Avoid direct handling if possible ie. use tweezers, spatulars etc.

Use of Computer Display Avoid prolonged sessions; Take Breaks

Moving heavy equipment Ask for assistance if you need to move any bulky equipment

6. EMERGENCY ACTIONS

All present must be aware of the available escape routes and follow instructions in the event of an evacuation

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B2: X-ray Diffraction

The following experiment guide is NOT intended to be a step-by-step manual of the experiment but

rather provides an overall introduction to the experiment and outlines the important tasks that need

to be performed in order to complete the experiment. Additional sources of documentation may

need to be researched and consulted during the experiment as well as for the completion of the

report. This additional documentation must be cited in the references of the report.

This guide comprises three sections:-

Bragg reflection: diffraction of x-rays at a monocrystal

Moseley’s law and determination of the Rydberg constant

Further X-ray experiments

Contents Bragg reflection: diffraction of x-rays at a monocrystal ........................................................................ 3

Objectives of the experiment.............................................................................................................. 3

Principles ............................................................................................................................................. 3

Apparatus Required ............................................................................................................................. 3

Safety notes ........................................................................................................................................ 4

Moseley’s law and determination of the Rydberg constant ................................................................... 5

Objectives of the experiment.............................................................................................................. 5

Principles ............................................................................................................................................. 5

Setup ................................................................................................................................................... 5

Carrying out the experiment ............................................................................................................... 5

Evaluation ........................................................................................................................................... 6

Additional information ........................................................................................................................ 6

Literature ............................................................................................................................................ 6

Further X-ray Experiments ...................................................................................................................... 7

X-Ray Fluorescence ............................................................................................................................. 7

The Cu X-Ray Source ........................................................................................................................... 8

Further Bragg Investigations ............................................................................................................... 8

Bragg Reflections in Poly-Crystalline NaCl ...................................................................................... 8

Bragg Reflections in Al .................................................................................................................... 9

Unknown Powder Sample ............................................................................................................... 9

Box Centred Cubic? ......................................................................................................................... 9

Appendix 1: Changing the Detector .................................................................................................. 10

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Bragg reflection: diffraction of x-rays at a monocrystal

Objectives of the experiment To investigate Bragg reflection from a NaCl monocrystal using the characteristic x-ray radiation from

molybdenum. To determine the wavelength for the characteristic K and K x-ray radiation of molybdenum. To confirm Bragg’s law of reflection.

Principles In 1913, H. W. and W. L. Bragg realized that the regular arrangement of atoms and/or ions in a crystal can

be under- stood as an array of lattice elements on parallel lattice planes. When we expose such a crystal to parallel x-rays, additionally assuming that these have a wave nature, then each element in a lattice plane acts as a

“scattering point”, at which a spherical wavelet forms. According to Huygens, these spherical wave- lets are superposed to create a “reflected” wave-front. In this model, the wavelength remains unchanged with

respect to the “incident” wave front; the radiation directions, which are perpendicular to the two wave fronts, fulfil the condition: “angle of incidence = angle of reflection”.

Constructive interference arises in the rays reflected at the individual lattice planes when their path differences are integer multiples of the wavelength .

Using this principle and the diagram in Figure 1, derive Bragg’s law of reflection:

sin2dn

where n = 1, 2, 3, …

In this experiment, we verify Bragg’s law of reflection by investigating the diffraction of x-rays by a NaCl monocrystal in which the lattice planes are parallel to the cubic surfaces of the unit cells of the crystal. The

lattice spacing of the cubic face-centred NaCl crystal is half the lattice constant a0. From Reference [1], a0 = 564.02 pm.

Apparatus Required 1 X-ray apparatus type 554 811

1 End-window counter for α, β, γ and x-ray radiations, type 559 01

additionally required:

1 PC with Windows 9 x or Windows NT

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The measurements are conducted using the built-in goniometer of the x-ray apparatus (554

811). The x-rays are detected using a GM counter tube (end-window counter) which is

swivelled in tandem with the NaCl crystal in a 2𝜃 coupling with respect to the incident light;

this means that the counter tube always advances by an angle which is twice that of the

crystal (see Figure 2).

The x-ray radiation consists of the bremsstrahlung continuum and several sharply defined

lines which correspond to the characteristic x-ray radiation of the Mo anode when

bombarded with high energy electrons. The lines originate in the Kα and Kβ transitions of

the molybdenum atoms.

Explain the origins of these transitions.

This characteristic radiation is particularly suitable for investigating Bragg’s law (why?). Its

properties are summarised in Table 1.

Using Table 1, calculate the glancing angles at which the diffraction maxima of the

characteristic radiation are to be expected for scattering from a NaCl monocrystal, up to

the fifth diffraction order.

Safety notes The x-ray apparatus fulfils regulations governing an x-ray apparatus and i s a fully

protected device for instructional use and is a type approved for school use.

The built-in protection and screening measures reduce the local dose rate outside of the x-ray

apparatus to less than 1 µSv/hr, a value which is of the order of magnitude of the natural

background radiation. The goniometer is positioned solely by electric stepper motors.

Before putting the x-ray apparatus into operation, inspect it for damage and

check to make sure that the high voltage shuts off when the sliding doors are

opened (see Instruction Sheet of x-ray apparatus).

Keep the x-ray apparatus secure from access by unauthorized persons.

Do not allow the anode of the Mo x-ray tube to overheat.

When switching on the x-ray apparatus, check to make sure that the ventilator in the

tube chamber is turning.

Do not block the gon i omete r target o r sensor arms, or force them to move.

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Moseley’s law and determination of the Rydberg constant

Objectives of the experiment Measuring the K-absorption edges in the transmission spectra of Zr, Mo, Ag and In. Verifying Moseley’s law. To determine the Rydberg constant.

Principles The absorption of x-ray quanta during the passage of x-rays through matter is essentially due to the ionization of

atoms, which release an electron from an inner shell, e.g. the K-shell.

The transmission is defined as:

0I

IT eq I

where 𝐼 and 𝐼𝑜 are the x-ray intensities on either side of the attenuator

Discontinuities in 𝑇 as a function of wavelength are observed.

Explain their origin (hint: they are termed K-absorption edges).

In 1913, the English physicist Henry Moseley measured the K-absorption edges for various elements and

formulated the law that bears his name:

eq II

𝑅: Rydberg constant

𝑍: atomic number of absorbing elements

𝜎𝑘: screening coefficient of K-shell

We can bring this equation into agreement with the predictions of Bohr’s model of the atom when we consider the

following: The nuclear charge 𝑍𝑒 of an atom is partially screened from the electron ejected from the K-shell

through absorption of the x-ray quantum by the remaining electrons of the atomic shell. Therefore, on average,

only the charge (𝑍 – 𝜎𝑘)𝑒 acts on the electron during ionization. For sufficiently large 𝑍 (>~30), 𝜎𝑘 is constant

and eq II becomes linear.

You are provided with foils of various materials (different 𝑍) which fit onto the entrance of the counter tube.

Explain how you can use these foils and the setup from the previous experiment to measure 𝑻 as a

function of wavelength and thus use eq II to find the Rydberg constant and the screening coefficient.

Setup Use the same setup as in the previous section, remembering to pay attention to safety issues and taking care not

to damage the instrument, crystals or the foils.

Carrying out the experiment Measure the spectra for a range of foils.

Note: it is necessary to perform a reference measurement (i.e. without a filter) before other measurements.

).(1

K

K

ZR

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Evaluation You will need to convert the x-axis from glancing angle to wavelength: open the settings dialog by pressing F5

and in the “Crystal” tab, click on the button “Enter NaCl”.

What calculation is the transformation based on?

To view the transmission spectra, click the “Transmission” tab.

How are the transmission spectra calculated?

The software can automatically detect the K-edges: right click anywhere on the transmission plot and select

“Draw K-Edges”.

Use the various values of 𝝀𝒌 to calculate the Rydberg constant and the screening coefficient of the K-

shell.

Additional information Literature Value [1] for 𝜎𝑘: 3.6 (valid for moderately heavy nuclei)

Literature [1] C. M. Lederer and V. S. Shirley, Table of Isotopes, 7 th Edition, 1978, John Wiley &

Sons, Inc., New York, USA.

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Further X-ray Experiments

X-Ray Fluorescence The energy of the K emission lines for Molybdenum (Z = 42) can be explained by the application of Moseley's

law. Directing this radiation on to a sample will excite the characteristic x-ray emission lines specific to the

constituent elements within the sample. The atomic numbers of the elements in question can be calculated from

the energies in the resulting radiation. It is helpful to use this x-ray fluorescence to identify unknown elements or

to calibrate the detector when the element (and hence line energy) are known.

Switch off the x-ray apparatus. Install the black circular goniometer table into the apparatus. This table has a

locating stub that determines the angle of rotation. Allow this to locate itself as the silver knurled knob is gently

tightened. Remove the 1 mm circular attenuator. Place the 3 cm square copper sample on the table. Close the

glass shield and position the target table at an angle of 45 degrees and the sensor angle at 90 degrees to the x-

ray beam. Turn on the apparatus power.

Observe the x-ray spectrum. Adjust the measurement controls to make use of the resolution of the system.

Experiment with the measurement time to find a compromise between time taken and the appearance of the

spectra. The largest feature should be the Cu Kα line. The energy of this can be predicted by Moseley's law:

2)( KK ZhcRE , sometimes expressed as:

2)( KK ZRE

where Rγ = 13.06 eV. Use 1 as an estimate for the screening constant σK.

Quickly investigate how the amplitude of the scattered fluorescence varies with scattering angle for a range of

incident beam angles.

It should be possible to rapidly identify many of the supplied metal samples, especially those which have fallen

out of their plastic holders. A list of elements and their atomic numbers is given below:

Table 1: Elements and their atomic numbers

Element Atomic Number

Al 13

Ti 22

Fe 26

Ni 28

Cu 29

Zn 30

Zi 40

Mo 42

In 49

Ag 47

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Can Moseley’s law be used to explain the Kβ emission line energies?

A feature exists in the Cassy Lab software to display the output in keV. Right click on the graph and select

Energy Calibration. (See Help > Cassy Lab > Graphical Evaluation)

There is a ‘trick’ that can be performed with the characteristic x-rays of Mo and the K-absorption edge of the Zi

filter. What is the net effect of this combination?

The energy of the K-line activity of Aluminium is close to the lower energy limit of the device’s capability. If other

line energies are observed then the sample may have impurities. If a weak Mo spectrum with approximately 3%

less energy is found then it is likely that Compton scattering is responsible.

Brass is an alloy of two elements. Can you prove what the two elements are using x-ray fluorescence?

Feel free to experiment with other samples.

The Cu X-Ray Source The Molybdenum x-ray target has good all-round performance. It has short wavelength, high energy x-rays and

an appreciable bremsstrahlung spectrum. This can, however, make it difficult to use in a Bragg reflection

experiment. An alternative source is the Copper target x-ray tube (Leybold 554 85). Replacement of the tube is a

quick process but it is likely that the tube already in use will be too hot to handle. Switch off the apparatus and

seek technical help. This will allow time for the tube to cool down.

Take a spectrum of the straight through beam as before, taking care to use the circular 1 mm attenuator and

remove the goniometer table. How and why is the bremsstrahlung x-ray component significantly different from

that of the Molybdenum tube? What does the Ni filter do if used with the Cu X-ray spectrum?

Further Bragg Investigations It has been shown in Part 1 of the experiment that for the Na-Cl mono-crystal:

sin2dn (n = 1, 2, 3, …)

where d = half the unit cell length, a0. Substituting for the cell dimension gives:

sin2 0aN (N = 2, 4, 6, …)

The relation between inter-planar distance d, cell size a0 and miller indices h, k, l for a cubic crystal is given by:

222

0

lkh

ad

(where h, k, l take on integer values 0, 1, 2, 3, …)

This leads to an expression for the Bragg reflection angles θhkl expected for a cubic crystal:

0

222

2sin

a

lkhhkl

or 2

0

22

4sin

aNhkl

Certain values of N can never be present, e.g. N = 7, 15. Only for a primitive cubic lattice will all other possible N

values be present. More complex cubic cells have significant absences in index number N that can assist in

characterising the form of the cell. These absences can be attributed to the structure factor. This takes into

account the position of all the individual atoms within the cell.

Bragg Reflections in Poly-Crystalline NaCl Place the NaCl powder in the plastic cell. Compact the powder and level the surface with a microscope slide.

Place this sample on the goniometer table. Specify coupled rotation for the sample and detector (i.e. the detector

rotates 2θ for a sample rotation of θ; this makes θ the angle of incidence and reflection). Set the detector angle to

45°.

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Set an x-ray voltage and anode current of your choice. Set the Cassy Lab measuring time to 60 s. Start the

logging of x-rays as before. If there is no activity at the energy of the incident x-ray source line, change the angle

to 44.9° and press the F4 key. This should clear the display and restart the pulse height analysis. If asked to save

the results then select ‘no’ at this time. It should be possible to find several angles that strongly reflect the

incident x-rays. The angular width at half the amplitude may be as small as 0.5 degrees or less. Complete the

search for reflections at angles above 45 degrees. Take care to avoid hitting the x-ray collimator with the detector

at large angles.

Use the anode voltage to limit the level of the unwanted bremsstrahlung radiation, especially with a mono-crystal

as a sample. Use a metal filter to simplify the energy spectrum of the incident x-ray beam.

Face centred cubic poly-crystalline materials can have values of N = 3, 4, 8, 11, 12, 16, etc. Thus 1, 2, 5, 6, 7, 9,

10, 13, 14, 15 are missing. Do not assume values of N for the data. There is likely to be a significant systematic

error in small angles. At large angles, the systematic errors are less significant.

Use the angles found to calculate the integer values of N and to determine a0.

Contrast and compare the powder and the mono-crystal results. The crystal was cut (1, 0, 0) and rotated about a

principle axis. The powder orientation is random.

Bragg Reflections in Al This technique can be applied to metals such as Aluminium. Observe the Bragg reflections in Al. Do the data

support any basis for a cell dimension and crystal type like NaCl?

Unknown Powder Sample Find the angles for Bragg reflection and attempt to determine the lattice constant of the unknown substance. Ask

a technician for a sample of this material. Take precautions as if it were a harmful substance. It should not cause

any chemical hazards.

Box Centred Cubic? Some materials have an atom in the centre of the cubic cell structure. These can give index values of N = 2, 4, 6,

8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 30, etc. Mo is supposed to be BCC, as is Fe and W. Surface preparation

may be the key to success. At present these materials provide a challenge.

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Appendix 1: Changing the Detector Reset the goniometer controls to make the detector horizontal. Turn off the power to the x-ray apparatus. Tidy

away the materials that tend to clutter this area. Carefully unscrew clockwise the large silver-coloured knurled

knob behind the black vertical table. Withdraw the table and its supporting stalk (note how it was fitted). Unscrew

the wire that connects the GM tube to the internal rate meter socket.

The GM tube and the PIN module are supported by a right angled bracket with an arm made from two parallel

bars. There is a bracket for each detector so there is no need to separate the detector from the bracket. With the

GM tube bracket bars in a horizontal position, unscrew anti-clockwise the black knob that secures the top bar into

a horizontal slot in the brass block. It should now be possible to rotate the detector bracket out of this slot, on the

axis of the other parallel bar. The other bar can be moved down and out of its vertical slot in the brass block at

this time. Safely store the GM tube and bracket. Keep the GM tube mounted inside its housing, as it would

otherwise expose the delicate window to mechanical damage.

The power connection to the Si PIN module is routed through a small rectangular opening on the right side of the

instrument housing. Loosen the finger tight locking knobs and slide the vertical goniometer unit to the right. This

will reveal a rectangular opening underneath. Pass through a large quantity of cable for the PIN module power

supply connection. Carefully connect this delicate multi-pin plug to the Si PIN module power socket, observing

the orientation of the pins in the plug and socket.

Locate the lower parallel bar in the lower vertical slot guiding. The parallel bars will have to be tilted away from

the vertical plane to achieve this. It should now be possible to rotate the PIN module on the axis of the lower bar

so that the upper bar rotates into a horizontal slot. At this time, slide the bars in their slots to set the distance of

the detector from the axis of rotation to approximately 6 cm. Gently tighten the black knob to secure the position

of the uppermost bar in the horizontal slot.

Connect a BNC cable between the 'Signal Out' BNC socket on the PIN module and the 'Signal In' BNC socket on

the inside right of the x-ray housing. The other end of this is the BNC socket on the front left of the exterior of the

housing. Make sure that there is enough cable and that it does not snag on objects when the detector assembly

rotates. Seek technical advice if in any doubt. Slide the whole goniometer assembly back towards the x-ray

source. Position the axis 6 cm from the end of the brass collimator. Add a circular collimator (1 mm diameter

aperture) to the end of a brass rectangular collimator aperture (1 mm x 7 mm).