Bragg Microwave Diffraction Experiment

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Synchrotron Workshops for Students in September
3:15
4:15
5:15
6:15
6:50
7:30
Australian Synchrotron: Its physics and technology: Synchrotron speaker (Banquet Room 1, 1st floor, Union Building, Monash University)
Group 1: Site tour
Group 2: Practical activities (Banquet Room 3)
Group 1: Practical activities
Group 2: Site tour
Dinner (Banquet Room 2)
Synchrotron radiation: Its properties and uses: Synchrotron speaker (Banquet Room 1)
Finish
Practical activities: 10 groups of 3: A, B, C, D, E, F, G, H, I, J
0 - 10 min
11 - 20 min
21 - 30 min
Microwave Bragg Diffraction Experiment: Station 1
A
B
Microwave Bragg Diffraction Experiment : Station 2
C
Microwave Bragg Diffraction Experiment: Station 3
D
Microwave Bragg Diffraction Experiment: Station 4
E
Microwave Bragg Diffraction Experiment: Station 5
Modelling Bragg
diffraction Station 6
G Laser diffraction
activities: Station 10
H CD Line Spacing:
Station 8
I Modelling Bragg
diffraction Station 7
J Laser diffraction
activities: Station 11
F
CD Line Spacing:
Station 8
Modelling Bragg
diffraction Station 6
Laser diffraction
activities: Station 10
CD Line Spacing:
Station 9
Modelling Bragg
diffraction Station 7
Laser diffraction
activities: Station 10
CD Line Spacing:
Station 8
Modelling Bragg
diffraction Station 6
Laser diffraction
activities: Station 11
CD Line Spacing:
Station 9
31 - 40 min
41 - 50 min
51 - 60 min
Modelling Bragg
CD Line Spacing:
Laser diffraction
diffraction: Station 6
Station 8
activities: Station 10
Laser diffraction
Modelling Bragg
CD Line Spacing:
activities: Station 10
diffraction Station 6
Station 8
CD Line Spacing:
Laser diffraction
Modelling Bragg
Station 8
activities: Station 10
diffraction Station 6
Modelling Bragg
CD Line Spacing:
Laser diffraction
diffraction Station 7
Station 9
activities: Station 11
Laser diffraction
Modelling Bragg
CD Line Spacing:
activities: Station 11
diffraction Station 7
Station 9
Microwave Bragg Diffraction Experiment: Station 1
Microwave Bragg Diffraction Experiment: Station 2
Microwave Bragg Diffraction Experiment: Station 3
Microwave Bragg Diffraction Experiment: Station 4
Microwave Bragg Diffraction Experiment: Station 5
Bragg Microwave Diffraction Experiment: Stations: 1 - 5
Background Theory
Bragg’s Law derived in 1913 by the English physicists Sir W.H. Bragg and his son Sir W.L. Bragg
to explain why crystals appear to reflect X-ray beams at certain angles of incidence.
n = 2d sin
Bragg's Law:
Where d is the distance between atomic layers in a crystal,
 is the wavelength in metres of the incident beam,
 is the angle of incidence; and
n is an integer representing the number of wavelengths required for constructive interference to
occur. At the smallest angle of incidence () for a maxima n = 1, at the next smallest angle n = 2,
etc.
Bragg’s Law is an example of X-ray wave interference or X-ray diffraction (XRD), and is used to
determine the atomic structure of crystals.
The Braggs were awarded the Nobel Prize in physics in 1915 for their work in determining crystal
structures (NaCl, ZnS and diamond).


dsin
d
dsin
Extra distance travelled by
photon that enters the second
layer is twice dsin = 2dsin.
If this equals a whole number
of wavelengths of the incident
beam then constructive
interference occurs.
The reflected beam will be
detected at a higher intensity.
Although Bragg's law was used to explain the interference pattern of X-rays scattered by crystals,
diffraction has been developed to study the structure of all kinds of matter with a beam, as long as
the wavelength used is comparable to the spacing of the molecules (or atoms) within the object
under investigation.
In this experiment microwaves will be used with a frequency roughly 1/50,000th lower than the Xrays the Bragg’s used. This will allow the measurement of crystal spacings 50,000 times greater
than those found in compounds such as diamond or sodium chloride (NaCl).
APPARATUS
Microwave transmitter and receiver, wavelength = 2.85 cm (freq = 10.525 GHz)
‘Foam Crystal’
2  1 metre ruler
Multimeter
Aluminium barrier
Large Protractor
METHOD
1. Align one straight edge of the ‘foam crystal’ along the base of the large protractor as shown
in figure 1 below. Record the number of the face towards the transmitter.
2. Place the aluminium sheet barrier on the 90o line of the protractor so that the cones of the
transmitter and receiver can ‘see’ the ‘foam crystal’, but that any direction radiation from
transmitter to receiver is blocked.
3. Place the microwave transmitter and receiver on the small blocks provided to raise them off
the desk surface.
4. Point the microwave transmitter toward the face of the ‘foam crystal’ at an initial angle of
~30o. Similarly align the receiver at 30o to the face of the ‘foam crystal’ to detect the
reflected beam. See figure 1. (Hint: using 1 metre rulers to align the receiver and transmitter
can save considerable time in setting up)
5. Switch on the power to the transmitter and receiver and set the multimeter to a 0 – 20 V
range.
CAUTION: Never allow the transmitter to be directed towards a person’s eyes at any time.
Damage to the retinas is possible!
Foam
Crystal


Figure 1
Transmitter
Aluminium
shield
Receiver
6. Gradually move both the transmitter and receiver around on the angle. Ensure both devices
are at the same angle at the same time and pointing directing to the centre of the protractor.
7. Record the multimeter reading in the table over the page.
8. Now decrease the angle of both the transmitter and receiver by two or five degrees and
record the data in the table. Continue this down to about 5 degrees. The data in the table
will give you an indication of where the maxima are.
9. Reset the apparatus as in step 4 and repeat step 5 - 7 but gradually increase the angle.
10. Take extra measurements to precisely locate the angles for various maxima.
11. Each maxima represents a value for n. The smallest angle at which a maximum occurs will
have a value of n= 1, with subsequent angles n =2, etc. Use Bragg’s Law to determine the
spacing of the molecules in the ‘foam crystal’ for each angle.
RESULTS
Station No: ______
Record the angle () at which maximum readings were recorded.
Angle
Value of n
Average
Spacing
Spacing
(cm)
a)
What is the uncertainty in the average spacing due to the different calculated values? ______
CONCLUSION The spacing for face no: ____ is _________ +/- ________ cm.
Angle
Reading
Angle
Reading
Modelling Bragg Diffraction with Microwave Apparatus: Stations 6 & 7
Equipment: A microwave transmitter and receiver, a multimeter, two strips of foam about 10 –
15 cm long, each with three equally spaces flat metal objects such as thumb tacks,
coins, metal washers, one foam mount and one large protractor.
Procedure
1.
Place the foam mount at the centre of the protractor and the transmitter and the receiver at
angles of 45 degrees,
2.
Place one of the foam strips on the top of the foam mount near the edge closest to the
transmitter and receiver. The reflected beam from the metal objects on the foam strip should
be picked up by the receiver and shows a strong signal.
3.
Place the second foam strip above and behind the first strip, but parallel to it and positioned so
that it will also receive the signal. Now two signals, each travelling a different path will be
arriving at the receiver.
4.
Set the spacing between the two rows of flat metal objects to be as small as possible. Now
very slowly pull the second foam strip back. You should observe that the signal drops. This
is due to cancellation because of the path difference.
5.
Continue pulling the foam strip back very slowly. You should observe that the signal begins
to increase. Find the position where the signal is a maximum. At this spacing between the
two rows, then path difference will be a full wavelength, because the waves are reinforcing
each other.
6.
As you continue to pull the foam strip back the signal will move between maximum and
minimum values, as the path difference moves between odd and even multiples of the
wavelength.
7.
Record the spacing of the two rows for a series of successive maxima. The average distance
between readings will give you a value for ‘d’ to substitute into the Bragg’s Law to find the
wavelength  = 2d sin
Angle = 450
Results:
Successive spacings: ________, _________, _________, ________, _________
Distance between 1st and 2nd =
Distance between 2nd and 3rd =
Distance between 3rd and 4th =
Average distance = ______________
Wavelength = __________
Line Spacing on a CD: Stations 8 and 9
Aim:
To measure the line spacing on a CD
Equipment: Laser (lab or pointer, wavelength must be known), CD, DVD, tape measure, ruler,
retort stands & clamps, room which can be darkened.
Method:
1.
Clamp the CD in a vertical position and clamp laser to produce a horizontal beam onto a left
or right edge of the CD.
2.
Reflect the light to a suitable screen (white board etc). If set up correctly, there should be a
line of red dots on the screen, where the diffraction pattern has formed.
3.
Measure accurately the distances: CD to screen and the dot spacing.
4.
The spacing is calculated from / D = x/L, where D = CD groove spacing, x = dot spacing
on the screen , laser wavelength
5.
Repeat the experiment with a DVD and observe the difference in the diffraction effect due
to the different groove spacing.
Screen
x
CD
Laser
L
Data: Wavelength of laser light = ____________+/- _____ __ = ____ +/- ____ cm
Measurements: L = ____ +/- ____ cm, x = ____ +/- ____ cm
Calculated value of D = = _________ +/- _______ cm
Laser diffraction activities: Stations 10 and 11
Modelling synchrotron radiation using visible light
Student investigations: Diffraction effects
Warning
Keep direct laser light out of your eyes. Point the laser away from you and from other people.
Look away from bright reflections. Keep lasers at waist height and don’t sit at benches.
A. Fibres and wires
Use laser light to observe the diffraction pattern formed by different fibres. Sketch each pattern and
take any measurements that you could use to calculate the diameter of each fibre.
object
screen
laser
1. Put the objects in order of fibre diameter from thickest to thinnest. Sketch the diffraction
patterns relative to the first fibre that you test or measure the dimensions of the pattern that
you observe.
Object
Paint brush
Feather
hair
Single strand of
insect screen
wire
Order:
Diffraction pattern : sketch or measurements
Relative diameter of one
fibre
B.
Two Dimensional Grids
Use laser light to observe the diffraction pattern formed by different materials. Sketch each pattern
and take any measurements that you could use to calculate the spacing of strands in the material.
object
scree
screen
n
laser
Object
Top bend of a needle
threader
Insect screen mesh
Observations
Gauze ribbon 1
Gauze ribbon 2
Artificial flower petal
Tea strainer
Other: …….
2.
What is the effect of turning the material or object in front of the laser?
3.
__________________________________________________________________________
What is the effect of two layers of the material?
4.
__________________________________________________________________________
For each material, what conclusions can you make about

the structure of the material? ______________________________________________

the size of the fibres in the material? ________________________________________
C. Two dimensional helix model
Use a pair of bolts or screws as in the diagram below. The laser beam must line up with the gap
between the threads.
Two
Two bolts
bolts
screen
screen
laser
Blu-tack
Object
Pair of bolts or screws
5.
Observations
What does the pattern remind you of? ___________________________________________
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