Langmuir probe diagnostics at VINETA II experimental apparatus
STM in a PTR - J. Meringa
1. STM in a PTR
Readying a pulsetube refrigerator for scanning tunnelling
microscopy experiments.
Author: Supervisor:
Jeroen Meringa Prof. dr. ir. Tjerk Oosterkamp
August 27th
2014
5. iv
Preface
When I first did a small research project on scanning tunnelling microscopy as a first-year
bachelor student, it brought a lot of fun and amazement to see how such a relatively simple
concept could yield actual pictures of atoms. Back then I used an easy setup, allowing for
quick picturing of the sample surface at atomic level, and the fact that it worked so well and
that you could literally see the atoms was quite mesmerizing. When I then got the opportunity
to engage in a more challenging low-temperature STM project as a research project, I felt like
just had to do it.
Part of this project involves creating a setup in which it would be possible to carry out STM
and related experiments in a pulsetube refrigerator, known to be very “shaky”. An experiment
as sensitive to vibrations as STM surely can’t be done in such environment, or can it? With
this challenge (amongst others) I’ve struggled throughout the project, encountering many
other difficulties throughout and learning a lot along the way. With this report I hope others
can learn something from my efforts as well.
With this I would also like to thank the many people involved who helped more than a great
deal along the way, first of all my supervisor Tjerk Oosterkamp whose support and
encouragement allowed for a very pleasant learning environment. Next a lot of thanks go to
the people of the fine mechanical department, Dian van der Zalm, Fred Schenkel and Gert
Koning. They fabricated the required equipment, and offered a lot of practical insight into the
project. I would also like to thank the people from the electronic department; especially Ko
koning and Bert Crama for all the electronics-related support. Thanks as well for the
technical and academic support from Federica Galli and Gertjan van Baarle. And lastly,
thanks to the other people active in the Oosterkamp group for helping out and creating a
pleasant atmosphere: Arthur de Haan, Tobias de Jong, Hiske Overweg, Ernst-Jan Vegter,
Marc de Voogd, Bob van Waarde, Jelmer Wagenaar, Louk Rademaker, and Lucia Bossoni.
For now, I hope the reader can learn as much from reading the report as I did when writing it.
Alkmaar, August 16, 2014
7. vi
Abstract
In this report, low temperature scanning tunnelling microscopy in a pulsetube refrigerator
will be described. PTRs are known to produce a lot of vibration making them seemingly
unsuitable for STM experiments. However, with proper vibration isolation methods these
vibrations can be reduced to a workable level making STM possible. This allows for
vibration-sensitive experiments to be done with all the benefits that the PTR brings (low
operation cost, easily accessible).
After a short general introduction of both STM and PTRs, the design and isolation measures
in the used PTR will be described, including optimal wiring and a mass-spring system
suspended in the PTR.
Next there will be some theory dealing with properly calculating and comparing vibration
levels in a setup, and finally the STM device itself will be discussed.
Using proper methods and preparation, it is possible for STM to be done in a PTR.
11. 1
Chapter 1
Introduction to STM
A Scanning Tunnelling Microscope (STM) is a device that can be used to image conducting
surfaces with atomic resolution, which is about 0.1nm lateral resolution and 0.01nm depth
resolution. Figure 1.1 shows its elements.
Figure 1.1: Diagram of a STM setup. Original image from Chen Introduction to Scanning Tunnelling
Microscopy[1]
.
A probe tip driven by a piezo motor scans the sample surface using three mutually
perpendicular piezoelectric transducers; one each for the x, y and z direction. When a voltage
is applied to a piezoelectric transducer it will expand or contract, depending on the sign of the
voltage. The scanning motion is done by applying a saw tooth like voltage on the x piezo, and
a ramp on the y piezo. This way, the probe tip will scan the xy-plane. The tip is brought to the
sample with a coarse positioner (see chapter 4.3) and a fine z-piezo. Though the tip and
sample do not touch, they are close enough for the wave functions of the electrons in the tip
and sample to overlap. When a bias voltage is now applied to the sample, a current will flow
through the quantum tunnelling effect. This tunnelling current is then amplified and
compared to a pre-set value for feedback on the z-driver. There is a negative feedback
mechanism, meaning that when the tunnelling current becomes too large, a voltage is applied
on the z-piezo to withdraw it from the surface, and vice versa. The equilibrium z positions
during the xy-plane scan are stored and this data can then be used to image the scanned
surface area.
12. 2
[1] Introduction to Scanning Tunnelling Microscopy, by C. JULIAN CHEN – Page 1.
Figure 1.2: Example surface scan of a HOPG sample. The spheres represent the graphite atoms on
the surface.[2]
In order to achieve atomic resolution, vibration isolation is vital. Therefore, a lot of time and
effort has been put into dampening vibrations in this experiment. This is done by making the
STM unit itself as rigid as possible as well as reduce the coupling of environmental vibrations
into the STM. In general, STM can be performed under a wide set of circumstances, such as
in air, in ultra-high vacuum, in inert gas or in liquids and even electrolytes. The temperatures
in which STM can be performed range from 0K to hundreds of degree Celsius.
[2] Scanning Tunnelling Microscopy; J. Meringa 2011.
13. 3
Chapter 2
Pulsetube Refrigerator Setup
2.1 Introduction to Pulsetubes
Pulse Tube Refrigerator (PTR, or PT for short) is a developing cryocooling technology which
can be made without moving parts in the part of the device which actually gets cold. This
makes it useful for a wide range of applications. Another advantage is that it does not lose its
cryogens, as it’s a closed system. This makes pulsetubes particularly useful in space-based
machinery where it is not possible to replenish the cryogens as they are depleted.
Furthermore, it is also much less expensive to operate as conventional cryostats using helium
as a cryogen are much more expensive, with the helium price being around €16,50 per litre.[3]
It would therefore be preferable to be able to do STM in a pulsetube cryostat, however there
are some challenges to overcome in order to do so.
A pulsetube consists of several components:
Component: Description:
(1) Compressor Consists of a piston moving back and forth at room temperature.
(2) Heat Exchanger 1 Releases heat into the surrounding.
(3) Regenerator Usually a porous medium with a large specific heat.
(4) Heat Exchanger 2 Delivers the cooling power at the low temperature end.
(5) Pulse Tube Tube between the heat exchangers.
(6) Heat Exchanger 3 At room temperature releasing heat into the surrounding.
Figure 2.1.1: Schematic drawing of part of a PTR. Adapted from Mbeljaars[4]
[3] Coping With The Helium Shortage; Marc S. Reisch – C&EN Volume 91 Issue 5 | pp. 18-19 Issue Date: February 4, 2013 | Web Date:
February 5, 2013, updated on Feb. 5, 2013.
[4] Mbeljaars 9-6-2007 - http://en.wikipedia.org/wiki/File:Schematic_pulstuberefridgerator.jpg
14. 4
For the working principle of the PTR, let us assume that the helium gas used as a cryogen
obeys the ideal gas law, that is:
(1)
In the PTR itself, processes are endotherm. This means they require an amount of heat.
Processes occurring before the heat exchangers happen in such way so that there is no
transfer of heat or matter between the system and its surroundings. This is one of the key
components of the PTR, where a compressed helium gas adiabatically expands.[5]
The heat required for the endotherm process which follows, is withdrawn from the helium
gas cooling it down. Figure 2.1.2 shows a diagram of such adiabatic process.
Figure 2.1.2: Diagram of an adiabatic process.
The green line in figure 2.1.2 represents how the temperature of the gas decreases from TA to
TB as the pressure and volume decrease and increase respectively. The blue area beneath the
green line equals the work done during the process. Because no heat is exchanged with the
surroundings, the gas cools down. To compress and decompress the gas, a compressor with
rotating valve is used to alternately supply high and low pressure to compress and
decompress the helium gas.
[5] D.J. van der Zalm – 09055878 – Afstudeerverslag Trilling reducerend frame voor een mengkoelmachine‐ verslag; chapter 2.3
15. 5
Figure 2.1.3: Schematic view of a pulsetube system showing the compressor, rotating valve and the
top and bottom plates being cooled to 50K and 3K respectively. PH Indicates high-pressure where PL
means a lower pressure. Adapted from D.J. van der Zalm[6]
In order to reach the condensation temperature of helium gas of 4.2K two cooling plates are
necessary, where the first reaches 50K and the second bottom plate cools to 3K. The helium
contained in the closed circuit of the PTR remains a gas however, as it absorbs heat through
the heat exchanger immediately after the adiabatic expansion. The cold plates are isolated
using two Ultra High Vacuum (UHV) chambers; the Inner Vacuum Chamber (IVC) and
Outer Vacuum Chamber (OVC).
Figure 2.1.4: a) 3D View of the actual setup, with the compressor and the 50K and 3K plate and
showing breakout boxes on top of the device. b) The system mounted on a frame, with the OVC visible
as the white barrel.
The pressure differences account for lots of vibrations coupling into the cooled plates, so for
sensitive experiments like STM al lot of vibration reduction measurements have to be taken
first (see chapter 3.1).
[6] D.J. van der Zalm – 09055878 – Afstudeerverslag Trilling reducerend frame voor een mengkoelmachine ‐ Appendices
16. 6
2.2 Pulsetube Refrigerator Setup
The PTR used in this experiment was the 1401 – CF CS81-3K produced by Leiden
Cryogenics B.V.[†]
Figure 2.2.1: 3D View of the pulsetube device used in this experiment.
Many vibrations from the pulsetube couple in at the 4K plate, displayed in gold in figure
2.2.1. Hence the frame to support the machine was designed in such way to dampen the
vibrations, and is mounted on a measuring island whose foundation is separated from that of
the laboratory floor thus carrying fewer vibrations. On top of the legs, on the hexagonal part,
an air cushioning system is installed; dampening vibrations even more (see appendix C7).
Figure 2.2.2: Support for the PTR including an air-based vibration dampening system (Vision
IsoStation by Newport[‡]
, designed to reduce vibration coupling into the 4K plate.
[†] Contact Leiden Cryogenics B.V. for more information: http://www.leidencryogenics.com/contact.php.
[‡] See appendix C7.
17. 7
Further vibration isolation measures consist of a spring-mass system with low resonance
frequency. On the vibrational quiet platform, the STM gets mounted for experiments (see
chapter 2.3 for details). As a final vibration reduction measure, the PT is driven with a linear
driver.
Figure 2.2.3: PTR with a spring-platform system extending from the 4K plate, further preventing any
vibrations from coupling into the STM (see chapter 2.3).
18. 8
When all experiments are installed, the machine gets closed with two barrels acting as Ultra-
High Vacuum (UHV) chambers: the Inner Vacuum Chamber (IVC) and the Outer Vacuum
Chamber (OVC). Once the chambers are sealed, they are pumped to UHV and the pulsetube
is turned on in order to bring the plates and platform suitable for experiments to low
temperatures (4K).
Figure 2.2.4: 3D Picture of the entire PTR device with support when closed and operating at low
temperatures. The white barrel is the OVC, containing the IVC which contains the spring-platform
system and the cooled plates.
19. 9
2.3 Spring-Mass System
In order to further reduce vibrations, a platform hanging from springs attached to the 3K plate
of the pulse-tube cryostat had been designed. This way, any vibrations that are still present in
the 3K plate get dampened before reaching the measuring equipment on the platform. The
objective is to create a spring system with the lowest possible resonance frequency, as this
will dampen the vibrations most. In order to be functional, this frequency has to at least be
lower than the pulse-tube frequency of 1.4Hz, but the lower the better. The initial aim is for
the system to have a resonance frequency of <1.0Hz. For a simple harmonic motion, we
know that the motion is described by:
(2)
where ω is the angular frequency, k is the spring constant, m is the mass attached to the
spring and f the resonance frequency we want to minimize. Further, it is given that the force
exerted on the spring is equal to the extension times the spring constant, or:
(3)
Here F is the force applied on the spring, in our case in the z-direction, g the standard
acceleration due to free fall on Earth (9.807 m/s2
) and x denotes how far the springs are
extended. Combining equations (2) and (3) leads to:
(4)
Combining (2), (3) and (4) now provides us to the useful expression:
(5)
relating the length that the springs extend to the resonance frequency. This is a useful
equation, as we can immediately see that the best way of minimalizing the resonance
frequency is to use springs capable of reaching great extension lengths. From the bottom of
the 3K plate to the bottom of the IVC barrel is 1.00m of space, so ideally we would use
springs of no initial length capable of extending 1.00m. This would lead to a resonance
frequency of x = 0.498, way below the target of 1.4 Hz. Unfortunately, such ideal springs do
not exist, and instead commercial springs[†]
from Amatec have been used.
[†] We used the Amatec E0750-049-3000S springs: http://www.amatec.nl/webshop/trekveren/E0750-049-3000S.
20. 10
These have the following properties:
Amatec Springs Do d Lo L1 T P1 P/f Material
E0750-049-3000S 19.05 1.24 76.2 272.8 2.18 24.5 0.12 Stainless Steel
Units:
Do: Outer diameter (mm)
d: Wire Thickness (mm)
Lo: Unextended Length (mm)
L1: Maximally Extended Length (mm)
T: Initial Tension (N)
P1: Force (N)
P/f: Spring Constant (N/mm)
a) b)
Figure 2.3.1 a) shows a schematic view of the spring in b). Images retrieved from Amatec.[7]
Three of these springs are hung in series to make for a chain with an unextended length of
228.6mm, capable of extending 589.8mm. Three of such chains are then attached to the
platform for stability. When fully extended, the spring makes use of 0.8184m out of the 1m
available space. In the setup, we extended the springs to a total length of 0.938m however
(See appendix B6 for an explanation as to why the springs had been overextended) .
Using formula (5) it can be shown that such a system would have a resonance frequency of
0.592Hz, more than reaching the target of <1.0Hz. For this extension to be reached, the
platform including equipment should weigh 8.903kg, as can be seen using the equating for
the force needed in order to maximally extend N chains of M springs:
(6)
[7] Source: http://www.amatec.nl/webshop/trekveren/E0750-049-3000S.
21. 11
This is the initial tension times the number of chains (as each chain needs a force before it
starts extending) plus the difference in final length and initial length multiplied by the number
of chains again, as when N chains extend a length x, then a total length of N*x has been
added. This length is then multiplied by the force required to stretch one spring one unit of
length, and then divided by the number of springs in each chain, as springs in series
effectively become softer by a factor equal to the number of springs. Finally this is multiplied
by the number of chains, as the weight gets distributed over each chain. In our case, the
equation becomes:
(7)
Since the equipment varies per experiment, the platform itself weights 6.8kg and some extra
weights are used to balance out the platform and to get to the desired extension.
Figure 2.3.2: Scheme of the spring-platform system. The STM will be placed on the platform, for
which the springs dampen environmental vibrations by having such a low resonance frequency.
The next challenge lies in thermalizing the copper platform. In order to do so, a copper rod of
0.976m is extended from the 4K plate to reach the platform. Heat-links are then placed
between the rod and the platform to transfer heat from the platform to the actively cooled 4K
plate. However, this can’t be done without taking the stiffness of the heat-links into account,
as when these are stiffer than the springs, vibrations will just couple into the STM through the
heat-links, bypassing our carefully designed spring-platform system.
22. 12
Figure 2.3.3: Section of the OVC and IVC to see how the plate and rod are implemented. From the
bottom of the 4K plate to the bottom of the IVM measures 1.00m.
Stiffer heat-links generally transport heat better, so it is necessary to know how well this link
has to perform. After running a quick test, consisting of cooling down without any heat-links
at all, it was clear that radiation alone seems to be enough to properly cool the platform. For
this reason, we have chosen to use plain copper tape as heat-links since the stiffness,
especially when put in a curled-up configuration, should be about two orders of magnitude
lower than that of the springs.
Figure 2.3.4: Copper tape is curled up and used as a heat-link between the copper platform and the
rod. The stiffness of the tape is much lower than that of the springs, so the dampening function doesn’t
get bypassed through the heat-link. Though the heat conductivity is low by using copper tape like this,
it is still sufficient to cool down the plate.
23. 13
2.4 Low Temperature Effects on the Spring-Mass
System in Liquid Nitrogen
Because the spring system has been designed at room temperature, it is necessary to look at
what the low-temperature effects are on the springs and platform. As heat-links normally
aren’t very flexible like the copper tape used in this experiment (they can usually extend in
the order if one or two millimetres), it’s not possible to just connect them to the copper rod
and the platform to thermalize it. At low temperatures, the springs will shrink and their
stiffness will increase, so a carelessly placed heat-link might get damaged in the process.
Thermal expansion goes as the original length times the change in temperature times the
thermal expansion coefficient, which differs per material:
(8)
For stainless steel, α = 16.0*10-6
K-1
. With an initial temperature of 296.25K and the springs
extending to 0.938m, cooling down to 4.6801K means a contraction of about 0.004376m:
(9)
To make sure the heat-links won’t get damaged, or damage the IVC (by snapping and
swinging the copper platform against the sides for example…) it is necessary to know the end
position of the platform with respect to the copper rod. When cooling down, this rod will
shrink as well, so a problem will arise when the difference in thermal expansion between the
two is too big. For a solid copper rod of 0.938m the difference on length will be:
(10)
This means that the platform and the copper rod will move 0.2735mm further apart. While
this seems to be a reassuring result, thermal expansion is not the only effect playing a role
when cooling down. The stiffness of the springs will change as well. To see if this effect is
more worrisome, a small test it devised. In this test, a glass tube is filled with liquid nitrogen,
cooling the contents down to 77K. Extending the chain (consisting of two springs in series for
this test) into the tube, it reaches a length 0.642m. Using (8) the final length after cooling
down is expected to be 0.640m. Experimentally, an equilibrium length of 0.618m was found
after cooling with liquid nitrogen. However, thermal expansion does not tell the complete
story yet.
24. 14
Figure 2.4.1: Scheme of a chain of three springs in liquid nitrogen. This test shows how much the
springs will contract when cooled down. However, the chain shrunk to 0.618m as opposed to the
expected 0.640m. This is due to the effective weight being lower when “floating” in the liquid than in
air. Also, the slightly boiling top layer of the liquid nitrogen exerts a small upwards force.
In order to know the real effects of thermal expansion and contraction, it is necessary to take
the buoyant force into account as well. The weight of 0.78kg on the springs is effectively
different in liquid nitrogen. To calculate the apparent immersed weight, the following
formula is used:
(11)
The density of the pure copper weight near room temperature is 8.96 g·cm−3
and that of
liquid nitrogen near its boiling point is 0.807 g/ml. Using a mass of 0.78kg for the copper
weight we can now calculate the apparent immersed weight, and see its effects on the spring:
(12)
The weight acting on the spring submersed in liquid nitrogen is 0.710kg. Based on this force
and the thermal contraction however, we expect the final length of the spring to be 0.592m
rather than the measured 0.618m. These final centimetres should be explained by the change
in stiffness of the springs when cooling the stainless steel down.
From this simple test we can conclude that the temperature effects on the extended plate
system do play an important role, and regular heat-links cannot compensate for the variation
in length occurring. The attached ends move too far apart during the cooling process. Now
that we know this, an accurate test needs to be done in the cryostat to see exactly how much
difference there will be, so that it can be compensated for.
25. 15
2.5 Testing 4K Effects on Spring-Mass System using a
Capacity Sensor
Because the vacuum chambers are closed, it is nontrivial to “see” how much the platform will
displace while cooling down. For this, a small experiment is devised in the form of a
capacitance test. Two copper cylinders are taken, where one is slightly smaller in diameter
than the other. These are slit into each other without making electrical contact. A capacitor is
now created, where if the smaller cylinder moves further into the larger outer one, the
capacity of the system goes up, as more area of the cylinders overleap. By attaching one
cylinder to the platform, and the other to the copper rod extended from the 4K plate, the
capacitance gives a measure of the relative displacement between the two:
Figure 2.5.1: Schematic view of the capacitor. The top hollow cylinder is attached to the 4K plate
while a solid smaller cylinder inside of it gets attached to the copper platform, extending from
springs. The capacity changes according to the relative movement of the platform and the 4K plate.
26. 16
In the actual system it is implemented as follows:
Figure 2.5.2: Inside view of the capacitor placed on the platform and attached to the copper rod
which in turn is attached to the 4K plate. When the springs increase in stiffness due to the drop in
temperature, the platform will move up relative to the copper rod, resulting in the smaller copper
cylinder on the platform sliding into the other, increasing capacitance.
First it is necessary to calibrate the capacitor in order to know precisely what displacement
corresponds to which change in capacity. To have a sense for the order of magnitude to
expect, we look at the formula for a cylindrical capacitor:
(13)
Here, C is the capacitance, L the length of which the two cylinders overleap, k the dielectric
constant and b the outer radius and a the inner radius:
Figure 2.5.3: Schematics of a cylindrical capacitor.[8]
[8] Original image from http://hyperphysics.phy-astr.gsu.edu/hbase/electric/imgele/ccyl.gif.
27. 17
The used capacitor has an inner radius of a = 0.198m and outer radius b = 0.200m. Having
the two overleap for example 0.05m and with the dielectric constant of air being k = 1.00059
we obtain:
(14)
(15)
Note that during the actual height measurement, it is done in vacuum so a dielectric constant
of k = 1 is used. A capacitance of a couple hundred pico farad is to be expected from the
device. Looking at how the capacity changes as a function of the overleap, the following
dataset is obtained:
Figure 2.5.4: Capacity as a function of the length over which the inner and outer cylinder overleap.
As expected, a linear correlation is found between the overleaping area and the capacity.
28. 18
For an accurate calibration curve, the datasets are averaged and a linear fit is made:
Figure 2.5.5: a) Linear fit through the calibration data points. b) Fit of the averaged results.
29. 19
Based on formula (13) a linear function was used to fit the data. The obtained parameters
were:
Value Standard Error
Intercept 107.42863 5.11025
slope 23.25694 0.6653
Table 2.5.6: Linear fit curve parameters.
From this the calibration formula is obtained to relate the measured capacity to the height ,
and the actual test can be done:
(16)
Where h is the height in cm and C the capacitance in pF. Based on the largest deviation of the
calibration data from the fit curve (-9.96605pF), we obtain an accuracy of ±0.4cm. When
cooling the spring-platform system down from 296.25K to 4.6801K, a corresponding
capacitance of 148.8pF and 357.4pF respectively is measured, having a difference of 208.6Pf.
Using formula (16) a displacement of 9.0cm ± 0.4cm is found:
(17)
We’ve now obtained that the change in stiffness of the feathers results in the spring-platform
system displacing 9.0cm ± 0.4cm when cooling down:
Figure 2.5.7:The capacitance test results in a measured displacement of 9.0cm ± 0.4cm. This is
mostly due to change in stiffness of the feathers when exposed to low temperatures (~4K).
30. 20
2.6 Wiring and Wire Vibration Sensitivity
It is important to read out a clean signal outputted by the STM tip. To minimize noise due to
microphonics (mechanical vibrations that are transformed into an undesired electrical signal
(noise)), the right choice of wire must be made. Three candidates are tested for microphonics
sensitivity, namely a silver coated copper wire, and a graphite coated phosphor-bronze cable
and a phosphor-bronze wire without graphite coating. In order to compare these, as well as
measure the sensitivity of copper-nickel coated copper-nickel wire which is readily mounted
in the pulse-tube, a simple test it devised. The wires are connected to an amplifier, which is
then read out using a DAQ (see appendix C1). The other end of the wire is left open, so the
changes in output that are measured are those due to microphonics. To see how sensitive the
wires are to vibrations, every second the wires receive a gentle tap which should be visible in
the signal. By comparing the output when the wires are at rest with that of when tapping, it
should be possible to determine how sensitive to microphonics each individual wire is, and
compare it to the others.
Figure 2.6.1: a) Signal of the copper-nickel coated copper-nickel wire in rest. b) The signal
when tapping on the wires once per second.
From the example in Figure 2.6.1 it is clear that the cables show a lot of microphonics, as the
peak voltages reach over a factor 102
higher when vibrating due to the taps compared to the
rest state. On the next page an overview of how the four wires behaved.
32. 22
Figure 2.6.2: Microphonics measurement of four wires in rest (A, C, E, G) and when tapped against
(B, D, F, H) every second. A and B are of a phosphor-bronze wire, C and D show a silver coated
copper wire, E and F are of a graphite coated copper wire and G and H are done with copper-nickel
coated copper-nickel wire. At first sight the silver coated copper wire seems to show the least
microphonics, but the wires were of different lengths, so more factors need to be taken into account
before drawing any hard conclusions.
The effects of vibrations due to tapping on the wires can be seen clearly in figure 2.6.2. It
would be unwise however to judge the silver coated copper wire as optimal based on this.
More sample sets have to be taken and then averaged over. Moreover, not all the cables are of
exact equal length, ranging between ±0.9m and ±1.7m. To obtain more accurate results, we
look at the Fourier transforms of the plots in order to know how the wires perform in our
interested frequency range of 1-200Hz. The (relative) increase in integrated area of the
Fourier spectra in this range between rest and taps should be a more reliable indicator. The
figure on the next page shows the Fourier spectra of the tested wires with the 1-200 Hz
integrated area.
34. 24
Figure 2.6.3: Fourier transforms of the voltage output of four wires when in rest and when tapped
against once per second. The 50Hz peaks are due to electronic noise and should be ignored. Though
the absolute voltage outputs cannot be compared, the relative difference in integrated area over a set
range does give a measure of microphonics sensitivity of the wires.
Now it is possible to conclude which cable performs best under the microphonics test, by
looking at the relative increase in integrated area under the Fourier spectra. The results are
displayed in the table below:
Table 2.6.4: Integrated area under Fourier spectrum while the wires are in rest and when disturbed.
The factor difference is a measure for the sensitivity to microphonics.
It is immediately obvious that the wire without graphite coating performs by far the worst,
increasing noise by a factor of 653.4 when stressed. The coated wires are all less sensitive for
microphonics, as one would expect. By far the best in this test is the copper wire coated in
silver. With only a nominal increase of 1.027 under stress, it is the wire of our choice to lead
the signal from the STM tip out of the pulse-tube.
35. 25
Chapter 3
Vibration Measurements
3.1 Vibration Reduction Measures Taken
As stated, several vibration reduction measures have been taken in order to make an
experimental environment which is isolated from vibrations. This includes a frame, air
suspension system, linear driver and a spring-platform system (see chapter 2.2). In order to
accurately know the effects of these measures, geophones were installed in different setups
and used to measure the displacement before and after taking vibration reducing measures.
3.2 Calculating Displacement from Geophone
Measurements
Geophones were used to measure vibrational stability in the STM setup. A geophone converts
a ground movement (displacement) into a voltage. Vibrations set a conductor or coil in
motion, which in turn generates a magnetic field from which a voltage signal is obtained.
Schematics of a geophone.[8]
The geophone produces data in the form of a voltage as a function of time. This can then be
converted to useful plots through some simple steps.
[8] Image adapted from Seismic Reflection Method: http://principles.ou.edu/seismic_explo/reflect/reflect.html
36. 26
Step 1: Read Geophone Output
Figure 3.2.1: The geophone’s output as a function of time.
The plot above shows an example, with the correct units shown along the axis.
Next we want to go from the time domain to the frequency domain. To do this, a Fast Fourier
Transformation (FFT) is taken of the raw V(t) data. We have used a Hanning window for the
transformation. We can now plot the voltage amplitudes versus the frequency. Note that in
the example below, the peaks at 50Hz are due to electronic noise. This and other noise can be
reduced by amplifying the geophone's signal. In this case, divide the voltages by the
amplification factor before taking the FFT. During the actual measurements, a pre-amplifier
was used (See appendix B2 and C4).
37. 27
Step 2: FFT the V(t) data
Figure 3.2.2: Result after taking a FFT.
Now we involve something called the “geophone response curve” which we call C(f), a curve
depending on frequency. This curve shows the sensitivity of the geophone at different
frequencies. Since the geophone is not equally sensitive at each frequency, we divide by the
response curve. These curves are usually supplied by the manufacturer. In our case a GS-11D
geophone (see appendix C5) was used. The response curve has units of volts per meter per
second [V/m/s] so if we divide we end up with units of m/s: [V] / ([V]/[m]/[s]) = [m]/[s].
Note that some manufacturers might have their devices calibrated in inches or some other
unit. In this case, if wanted it is possible to convert to meters now by multiplying the
amplitudes by a conversion factor. Let's say we want to have units of μm but our geophone
response curve is in inches. We first multiply our voltage amplitudes by 25400 (inch –> μm
conversion factor) before dividing by the response curve.
38. 28
Step 3: Divide by Response Curve
Figure 3.2.3: Velocity is obtained after dividing by the response curve.
The following step involves going from speed to displacement. In order to do this we simply
divide by 2*π*f, where f is the frequency. Since this carries units of [Hz]-1
we obtain our
amplitude in meters [m].
39. 29
Step 4: Go from Speed to Displacement
Figure 3.2.4: From the velocity, the displacement is calculated.
Next we calculate the power spectrum, by squaring our displacement and dividing by two.
Remember to also square the units.
40. 30
Step 5: Take Power Spectrum
Figure 3.2.5s: Power spectrum of the displacement.
Now we have to take into account the frequency resolution with which the data was taken.
This affects the area under the peaks in the spectra. The frequency resolution is calculated
with:
(18)
where is the frequency resolution, is the total measurement time, is the sampling
rate and is the total number of samples taken. A higher resolution means narrower, better-
defined peaks. When we later want to integrate the area under these peaks, we should thus
take our frequency resolution effects into account. Some mathematical programs
automatically compensate for this. There are some simple methods to check whether this is
the case (see appendix B3). To make sure the area stays the same, we divide by the frequency
resolution which was 0.1 in our example case.
41. 31
Step 6: Divide by Frequency Resolution
Figure 3.2.6: The power spectrum gets divided by the frequency resolution as to compensate for
frequency resolution effects, see appendix B3.
Usually, a lot of measurements should be taken for better precision. Now that we have the
power spectra of all those measurements, we can simply add them together and divide by the
number of measurements to average the data.
42. 32
Step 7: Average the Data
Figure 3.2.7: For better accuracy, a lot of datasets should be taken and then averaged over at this
point.
Finally, from this plot we can obtain both the total displacement over the required frequency
range, and create the “displacement per sqrtHz” plot. For the latter, just take the square root
of the averaged data.
43. 33
Step 8: Create Displacement per sqrtHz Plot
Figure 3.2.8s: Displacement per √Hz at each frequency.
We can now also calculate the total displacement over a frequency range. In order to do so,
integrate the average data as obtained in Step7 over the desired range, then take the square
root.
44. 34
Step 9: Calculate Total Displacement over a Frequency Range
Figure 3.2.9: The total integrated displacement in meters at each frequency.
In the example case we integrated from 1 to 200 Hz, resulting in a total displacement of
2.54935*10-4
meters.
Following these steps with the geophone in various setups, our results are obtained.
45. 35
3.3 Results of Vibration Reduction Measures
For a full view of the vibration reduction measures taken, the factory performance is
compared to that in the laboratory. This starts by comparing the floors of the factory with
those of the lab, and includes the measuring island:
Figure 3.3.1 a): Vibration levels of the Leiden Cryogenics[†]
factory floor compared to the laboratory
floor and the measuring island, which is isolated of the lab floor.
Figure 3.3.1 b): Integrated displacement of the setups from 1Hz to 200Hz.
[†] See http://www.leidencryogenics.com/contact.php.
46. 36
The floor at the laboratory is much more stable than that in a factory environment, as would
be expected. The isolated island however, does not seem to have much additional value
though. Next the addition of the linear driver is inspected:
Figure 3.3.2 a): Vibrations at the 4K plate when cooled to 4K. “PT” stands for the Pulse-Tube,
“LinD” is the Linear Driver and “Air” or “RemovedAir” stands for whether the air suspension
system is in place or removed. The “+” or “-” sign means whether the indicated system is on or off.
“Cold” or “RT” stands for whether the system had been cooled to 4K or is at Room Temperature.
Note that this sample had been taken without preamplifier, so the noise contributes a lot to the
integrated displacement. For comparison purposes however, this is not a problem as the only
difference between the two setups is whether the linear driver is on or off. The air-dampening system
is turned off as well for this test.
Figure 3.3.2 b): Showing integrated displacement of the setup with and without linear driver.
47. 37
The linear driver contributes a lot in the reduction of vibrations, reducing levels by a factor of
nearly one-third. In order to test the performance of the frame, the 4K-plates are compared in
default factory settings from Leiden Cryogenics, and with the special frame in place.
Figure 3.3.3 a): Geophones on the 4K-plates at room temperature using the default frame from
Leiden Cryogenics, and the specially designed isolating frame. The noise at 50Hz is shown next to the
total integrated area under the curves.
Figure 3.3.3 b): Integrated displacement.
48. 38
The frame performs well as an anti-vibration measures. Next the performance of the air-
suspension (see appendix C7) system is tested. Tests are ran with geophones on top of the
frame and on top of the cryostat with the pulsetube running, both with the air suspension
system in place and removed:
Figure 3.3.4 a): Displacement on top of the frame and the cryostat, with the Air system in place and
removed.
Figure 3.3.4 b): Integrated displacement comparing the setups with and without air suspension
system.
49. 39
The air suspension system also performs well, significantly reducing vibrations in the 100Hz
– 200Hz range, as can be seen in Figure 3.3.4 a). Finally, the effects of the suspended
platform are put to the test, directly comparing the vibrations found on the 4K plate with that
on the spring-platform system:
Figure 3.3.5 a): Performance of the spring-mass platform system.
Figure 3.3.5 b): Integrated area.
The isolation effect of the spring-platform system is definitely notable, especially in the low-
frequency regime of 1Hz – 10Hz. For its design, see chapter 2.3.
50. 40
Chapter 4
STM
4.1 STM Design
The STM used for this experiment consists of a custom made titanium body, containing a
sapphire slider being held in place by three piezo stacks, used for the coarse approach. The
slider contains a piezoceramic tube produced by the company EBL (see appendix C6) which
is used to move the platinum tip for scanning purposes. The sample is mounted on a rotating
platform, driven by a third piezo motor.
Figure 4.1.1: 3D Schematic picture of the used STM with its components. The green scale indicates
10mm. Not shown here are the three piezo stacks holding the sapphire slider. These are used for the
coarse approach, and positioned on alternating sides of the hexagonal slider, with one positioned on
the very top face. This top piezo motor is pressed to the top of the sapphire slider through a spring
plate pressing a ruby ball against the piezo stack.
4.2 Sample Rotator
The sample rotator was specially designed by G. Koning[†]
and has many uses. By placing
two different samples on the rotating plate, the tip can be cleaned on one then proceed to scan
on the other. This also ensures that there are no topological defects on the sample, as when
there’s an improper area in the scan range, the sample can be moved to a clean spot.
[†] See for contact details: http://www.physics.leidenuniv.nl/index.php?option=com_content&view=article&id=240&PID=892.
51. 41
Figure 4.2.1: 3D Half-section of the sample rotator. The green scale indicates 10mm. The piezo motor
on the left rotates the plate holding the samples on the right.
4.3 Coarse Approach and Stick-Slip Motor
For the course approach, a piezoelectric motor based on the stick-slip principle is used. The
drawing in figure 4.3.1 on the next page shows its working principle. Three piezo legs hold
the sapphire slider in place. When a voltage is applied to one leg, it slides back along the
slider, while friction of the remaining two legs hold the slider stationary. After a short delay,
the same voltage is then applied to the remaining legs, one at a time. The slider won’t move
due to friction, as two piezo legs always keep the slider from moving. After all three legs
have been moved to the back, the voltages of all piezo legs are restored smoothly and
simultaneously. This results in the sapphire slider being moved slightly forward. One such
cycle is what is referred to as a “step”. It is useful to know the size of such as step, as the
fine-stage should have a bigger reach than the coarse approach. This is to make sure the tip
will not crash during the approach (see appendix B4).
52. 42
Figure 4.3.1: a) The piezo legs shown in green are sheered one by one ( 2, 3 and 4) from their
starting position (1), where the friction of the other two hold the slider (shown in blue) in place. Then
all three legs move simultaneously back to their initial position (5), moving the slider forward. b)
Shows the output voltage in order to move the piezo legs in the described fashion.
4.4 Calculating the Coarse Approach Step Size
Before approaching the sample with the STM tip, it should be checked that the fine stage (the
piezo tube steering the tip, as opposed to the coarse approach, which is driven by the three
piezo stick-slip motors) has a bigger reach than the step size of the coarse approach. This is to
prevent the tip from crashing. After ear course step, the fine stage probes for a tunnelling
current. If no current flows, another course step is taken and the process is repeated until a
tunnelling current is established. The reach that the piezo tube (see appendix C6) is capable
of, is determined by:
(19)
Here S is our reach, d31 the piezoelectric coefficient and h the wall thickness of the tube.
When a voltage of 180 volt is applied and with the piezo-tube having a wall thickness of
0.000762m and a d31 constant of -0.31*10-10
at 4.2K, this leads to a reach of:
(20)
53. 43
For the coarse approach steps, the stick-slip motor is set to run 5500 steps. Measuring a
displacement at room temperature of 0.0019m, this means that a single step is:
0.0019m / 5500 = 345nm (21)
Since this is well within the fine stage reach, no problems should arise when approaching. It
is important to always check this first before engaging an approach.
54. 44
4.5 Ground Loop Prevention by Optical Disconnection
Ground loops are a major source of electrical noise, and should be prevented. This occurs
when there is a current in a conductor connecting two points which are supposedly connected
to the same (ground) potential. If in reality these two points are at different potentials, noise
and interference arises. In our case, the LPM electronics and the computer are at risk of
creating a ground loop, inducing noise in the tip signal. In order to solve this, we place an
optical usb extender between the PC and the DAQ, which is connected to the LPM
electronics. The PC and the LPM electronics have their own grounds, which is why the
extender is placed.
Figure 4.5.1: Circuit illustrating a ground loop.[9]
A simple example would be that of two circuits sharing a common ground. Let’s call the
resistance of that ground RG. In the ideal case, this would be zero with a voltage drop across it
of zero as well. This isolates the point at which the circuit connect at constant ground
potential. If this is the case, Vout = V2. A problem arises though, when the ground resistance
RG is nonzero. Now, in the case of a current I1 flowing through the left circuit, there will be a
voltage drop proportional to RG*I1 through RG resulting in neither of the ground connections
of the circuits actually being at ground potential and they are no longer isolated:
(22)
[9] Image by Chetvorno and taken from http://en.wikipedia.org/wiki/File:Ground_loop.svg. The image is freely released into the public
domain for any use whatever. It was made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
55. 45
Interference can now be seen as a ground loop is created. In the setup used for our
experiment, a ground loop can most likely be created when current leaks through the
insulation in grounded devices. Ground potentials at different sockets can differ in the order
of 10 volts because of voltage drops from currents. In the used setup, all different power
supplies have been optically disconnected in order to avoid ground loops (see appendix A).
56. 46
Appendix
Appendix A – LPM Electronics Setup
Below is a crude scheme of the electronics used. A description and clarification follows.
Figure A.1: Scheme of the LPM modules and electronics as connected in the setup.
SPM Rack
From To Device
(1) X-gen Out X-Mixer In1 SPM Rack
(2) X-gen Out Y-Mixer In1 SPM Rack
(3) Y-gen Out X-Mixer In2 SPM Rack
(4) Y-gen Out Y-Mixer In2 SPM Rack
(5) X-Mixer Out X In1 HV Driver Rack 2
(6) X-Mixer Out Z Mixer In1 SPM Rack
(7) Y-Mixer Out Y In1 HV Driver Rack 2
(8) Y-Mixer Out Z Mixer In2 SPM Rack
(9) Z-Mixer Out Z-Driver In Z-mix HV Driver Rack 2
(10) U-Sample Out Sample bias In STM
57. 47
(11) Wave Gen DAQ In DAQ
(12) SPM Bus 1/0 1 PC PC
(13) SPM Bus 1/0 2 ADC Bus 1/0 2 ADC Rack
(14) Dig. Com. 1/0 1 PI-regulator 1/0 1 Feedback Rack
(15) Dig. Com. 1/0 2 PI-regulator 1/0 2 Feedback Rack
Feedback Rack
From To Device
(16) STM Converter Out1 ADC2 In ADC Rack
(17) PI-Regulator Out2 Monitor In2 Feedback Rack
(18) PI-Regulator Out3 Z-Driver in Z-fb HV Driver Rack 2
(19) PI-Regulator Out4 ADC 1 In ADC Rack
DAQ
From To Device
(20) Out0 In Z-fb HV Driver Rack 1
21) Out0 In Z-Mix HV Driver Rack 1
(22) Out1 In Y HV Driver Rack 1
(23) Out1 In Y-Wave HV Driver Rack 1
(24) Out2 In X HV Driver Rack 1
(25) Out2 In X-Wave HV Driver Rack 1
HV Driver Rack 1
From To Device
(26) X+ Out X-In Approach Piezo
(27) X- Out X-In Approach Piezo
(28) Y+ Out Y-In Approach Piezo
(29) Y- Out Y-In Approach Piezo
(30) Z+ Out Z-In Approach Piezo
(31) Z- Out Z-In Approach Piezo
58. 48
HV Driver Rack 2
From To Device
(32) X+ Out In-X Tip Piezo
(33) X- Out In-X Tip Piezo
(34) Y+ Out In-Y Tip Piezo
(35) Y- Out In-Y Tip Piezo
(36) Z Out In-Z Tip Piezo
ADC Rack2
From To Device
(37) ADC Bus 1/0 1 PC PC
From the SP rack, the X and Y generators are both connected to the X and Y mixer through
(1-4). The reason for also connecting the X generator to the Y mixer, and likewise for the Y
generator, is so that there is rotational invariance while scanning. If the sample would be
rotated, the same scanning path can be done still because of these connections. The Z-mixer
also receives input from both the X and Y mixer (6, 8), so that it’s possible to scan under a
tilted sample. Connection (12) and (37) are done with fibre cables to the computer. In
between the DAQ and the HV Driver Rack 1 connections (20-25) we have used units to split
the BNC from the DAQ into two separate X, Y and Z cables (the plus and minus had been
separated). We have used a similar way to connect HV Driver Rack 2 to the STM tip piezo
(26-31). In order to connect the DAQ to the PC, an usb-detacher has been used in order to
avoid ground loops. For connection (19), we've used a cable that reverses positive and
negative voltages. This is because when the STM tip goes over a bump while scanning, it has
to retract as the tunnelling voltage is kept constant. The Z-voltage will thus lower, but we
want it to appear on our screen as a peak rather than a gap, as that is true to the topology of
the material. Therefore, we have to convert the negative voltage that the PI-Regulator outputs
in order to retract the tip, into a positive voltage and vice versa to reflect the topology of the
scanned surface. We use the output from the PI-regulator of the feedback rack to do feedback
on the Z of our fine stage (18). The X and Y fine stage piezo both receive their input from the
SPM rack (5, 7). HV Driver rack 1 is driven with the output controlled by the pc in order to
drive the coarse approach piezos (20-25). The sample bias is set with U-sample out (10). The
sine generator from the SPM rack is connected to the DAQ (11) and sends a signal once there
is sufficient tunnelling current and the coarse approach should stop.
59. 49
B – Mistakes and Tips for the Future
Appendix B1 – Sending Signals through the Shielding of
a BNC Connector
Let us look at the LPM electronics again (see Figure A1, appendix A). Both the outputs from
the driver racks were first connected to a connecting-piece before going to the DAQ-output
and the STM-tip piezzos for HV driver rack 1 and 2 respectively. This connection piece
serves for nothing else but to make the multiple outputs from the driver racks connect with
the BNC connectors attached to the DAQ and tip piezzos. However, in order to send both the
+ and – signals, we sent one signal through the inside ov the BNC, and one through the outer
shell.
Figure B1.1: A BNC connector. The inner pin
(visible here in a gold like colour) is shielded, but the
outer shell lies bare. Putting a voltage on it is dangerous,
as it can cause shortage or deliver a shock when touched.
This means that at the connector parts, a voltage is applied on an exposed piece of metal.
There were three such connectors lying right next to each other, so it is easy to imagine the
exposed parts touching and causing a shortage. This is exactly what happened, causing the
HV driver racks to break down. In hindsight it was somewhat lucky that nobody touched the
exposed connectors, as human damage is not as easily repaired.
The lesson to be learned here is to never send a signal to the exposed outer shell of the BNC
connector, as it may yield a high voltage, can easily cause short-circuiting and deliver a shock
when accidentally touched.
Appendix B2 – Using a Pre-Amplifier with Geophones
When reading out a geophone, it does indeed matter a lot whether or not a preamplifier and
filter are used. These help reducing electronic and other noise, which otherwise might get
wrongly interpreted as actual signal. In the case of the geophone, the effects become clear
once the same measurement is done twice; once with and once without the use of a filter and
preamplifier. Do be careful not to filter out the actual signals though, by setting the cut-offs
either too low or too high. The results of a quick test performed by measuring the vibrations
of the regular laboratory floor twice (with and without preamplifier and low-pass filter) are
below:
60. 50
Figure b2.1: The integrated displacement as a function of frequency, showing vibration levels on the
laboratory floor. Without using a preamplifier the vibration levels seem to be much higher than they
actually are due to the noise. Filtering out this noise gives a much more realistic picture of the actual
vibration levels, though some 50Hz electronic noise remains.
It is now clear that the effects of a low-pass filter and preamplifier are nontrivial. It is
important to have an as clean as possible signal to avoid inaccurate conclusions.
Appendix B3 - Frequency Resolution Effects on a FFT
When calculating the FFT using mathematical programs like Origin, it might be handy to
check whether the program automatically takes frequency resolution effects into account. The
frequency resolution is calculated with:
(23)
where is the frequency resolution, is the total measurement time, is the sampling
rate and is the total number of samples taken. A higher resolution means narrower, better-
defined peaks with less area underneath it. When integrating the data, it might thus be
necessary to divide by the resolution to get the proper integrated area.
One way to check this is by generating two identical pure sine wave of different, but having
one with more data points. Below are plots of the FFT of two sine waves (a Hanning window
function was used). The left plot has 1000 Data points and the right has 100000 points.
61. 51
Figure B3.1: Left: FFT of a sine with 1000 data points. Right: FFT of the same sine, but with 100000
data points. A Hanning was window used for the FFT.
Although it is the same pure sine, we do not see a delta peak at one frequency when using
Origin to generate the data and plots. This is due to our frequency resolution. Because both
sets have different resolutions, the area under the peaks differs as well. The integrated area
under the left, lower-resolution plot is 0.00102, while the area under the higher resolution one
is .0000106045. If we divide by the frequency resolution (of 1/1000 and 1/100000
respectively) we obtain 1.01892 for the low-resolution peak, and 1.06045 for the high-
resolution one. Although still not identical, we have at least compensated for the resolution
effects. The remaining difference is mostly due to the data-sets not being infinite.
When calculating FFTs using mathematical programs like Origin or Wolfram alpha, always
check if it automatically compensates for frequency resolution effects, and divide by the
resolution when it doesn’t. In the case of Origin Pro 9 (see appendix C2) which we used,
frequency resolution effects need to be taken into account manually, as the program does not
automatically compensate for it.
Appendix B4 – Coarse Approach Tip Crashes
Upon doing the coarse approach, patience truly is a virtue. The tip can only be brought so
close to the sample by eye, before it’s necessary to switch over to the coarse approach. As
calculated in section 4.4, each coarse step reaches 345nm. This means that if the tip is still
1mm away from the sample, it will take about
(24)
2899 steps to complete. With the approach method taking approximately 1 step per second,
this would mean an approach time of 49 minutes. In reality it might take much longer even. It
might be very tempting to just take bigger steps or multiple steps per fine-stage sense at a
time, though this will most likely just result in a crash, ruining the experiment. Another way
to speed thing up would be to approach automatically, and check back every half hour or so,
though unfortunately that’s no option either. There can be many false-approach signals along
the way, where the tunnelling current is read to be at the set value, but upon closer inspection
(sensing again) it might just have been a false alarm, and the approach needs to be continued.
62. 52
Even worse would be when there indeed has been a successful approach, but due to thermal
drifting or flakes on the sample the tip crashes anyway when the feedback is not initiated
quickly enough. This means that the only way to know for sure things will go all right is to
stay alert throughout the entire coarse approach, no matter how many hours it might take.
Either take my word on it, or find out the hard way (like I did).
Appendix B5 – Using an Optical USB-Extender to
prevent Ground Loops
As explained in section 4.5, ground loops can introduce unwanted noise in the signals.
Looking at the LPM electronics (Figure A.1), there are two separate grounded systems. The
LPM electronics has its own ground, and the PC is itself grounded as well. At first, this was
left unchecked and a ground loop was created. The electronic noise of 50Hz causes a lot of
disturbance, though the solution is easy. The two circuits are disconnected using an optical
USB extender, the USB 2.0 Ranger 2224 from Icron (see Appendix C3). The circuits are
disconnected by an optical fibre cable.
Figure B5.1: Connecting the DAQ to the PC with and without USB detacher. This is done in order to
break ground loops, as can be seen in the entire setup in figure A.1.
Appendix B6 – Spring-Mass System Overextended
According to chapter 4.3 the best springs to hang the vibration-isolation-platform on would
make use of the full available 1.0m of space, as the resonance frequency of the system goes
down with the extension:
(25)
Yet only 0.8184m of space is used when the used springs are maximally extended. This was
due to a miscommunication letting me believe there would only be 0.85m available in the
IVC barrel. Actually, even less than the theoretical 0.8184m would be used, as the spring
chain was not extended perfectly vertically, but under a slight angle for stability. However,
due to a miscalculation (by yours truly) of the weight needed, the platform was heavier than it
should be and the springs got extended further than the expected 0.8184m, namely to 0.938m.
63. 53
In the end, these two mistakes roughly balanced each other out, with the danger of the springs
being overexerted and undergoing plastic deformation. Though as long as they hold, the
platform functions perfectly. Theoretically, not optimizing the available space would increase
the resonance frequency of the platform by 0.069H assuming 0.580Hz when extended 0.15m
more, as opposed to the 0.649Hz achieved when maximally extending the current springs.
This effect is minimal, and as it is the platform well fulfils its purpose. As long as the
accidental overextension does not lead to any problems, 0.938m extension leads to a
resonance frequency of 0.592Hz, maximally utilizing the available amount of space due to
the accidental overweight hung on the springs (we should have used a platform weighing
7.88kg rather than the used 8.90kg).
What’s to learn here is that a miscalculation of the system is easily made. In this case, the
initial tension of the springs was taken into account three times per chain. However, when
hanging a weight on some springs in series, each spring separately feels the weight. Thus the
initial tension of 2.18N only has to be applied once per chain, not once per spring.
Figure B6.1:Three springs in series each with an initial tension. T. This is the force that needs to be
exerted before the spring starts to expand. No matter how many springs are chained together, the
required force will always be F = T as each spring feels the same force tugging from below due to the
weight.
64. 54
Appendix C - Equipment Specifications
Appendix C1 - NI USB-6343 DAQ
We have used a National Instruments DAQ, the NI USB-6343, for data acquisition. It is
capable of reading 500k samples per second with a 16-bit resolution and a range of ±10 V.
The output capabilities are 900k samples per second, also with a 16-bit resolution. The
maximal AO update rate caps at 2.86M samples/second.
Picture C1.1: Picture of the NI USB-6343
DAW, used to read out various data throughout the described
experiments.
Appendix C2 - ORIGIN pro 9 (academic) 64 bit
As the mathematical program of choice, the 64-bit version of Origin Pro 9 (academic) had
been used. All data analyses, FFTs (see appendix B3) and most graphs and plots have been
done using this program. For a complete feature list, see their website[†]
.
[†] http://cloud.originlab.com/pdfs/FeatureList91.pdf
65. 55
Appendix C3 - USB 2.0 Ranger 2224 Four-port Multi-
mode Fiber 500 meter extender
To avoid ground loops, the USB 2.0 Ranger 2224 Four-port Multi-mode Fiber 500 meter
extender had been used. The Ranger® 2224 is a four port USB 2.0 high speed extension
solution, allowing USB 2.0 connections at up to 480Mbps over 500m of multi-mode fibre
optics. The Ranger 2224 runs an integrated remote four port USB 2.0 powered hub delivering
standard 500mA power.[†]
Picture C3.1: The used Icron USB 2.0 Ranger 2224.
Appendix C4 – Preamplifier and Low-pass Filter
The Stanford Research Systems SR560 was used as preamplifier. This is a low-noise voltage
preamplifier, with the following specifications:
4 nV/√Hz input noise
1 MHz bandwidth
Variable gain from 1 to 50,000
AC or DC coupled
Two configurable signal filters
Differential and single-ended inputs
Line or battery operation
RS-232 interface
For more information, see the Stanford Research Systems website.[‡]
[†] For more information, see the Icron website: http://www.icron.com/products/icron-brand/usb-extenders/fiber/usb-2-0-ranger-2224/.
[‡] http://www.thinksrs.com/products/SR560.htm
66. 56
Appendix C5 - Geophones
For vibration measurements, the Geospace Geophones GS-11D had been used. These are
high output, rotating coil geophones with gold plated contacts. Its natural frequencies are 4.5,
8, 10 and 14 Hz, with standard coil resistance of 380 ohms.
Figure C5.1: The Geophone GS-11D from Geospace, used for the various vibration measurements.
GS-11D Specifications[†]
Natural Frequency
4.5 ±
.75 Hz
8 ± .75
Hz
10 ± .75
Hz
14 ± .75
Hz
Coil Resistance @ 25°C ± 5% ——380 Ohms ——
Intrinsic Voltage Sensitivity with 380 Ohm Coil ± 10% ——.81 V/in/sec (.32 V/cm/sec) —
Normalized Transduction Constant (V/in/sec) ——042 (sq.root of Rc) ——
Open Circuit Damping
.34 ±
20%
.39 ±
10%
.32 ±
10%
.23 ±
10%
Damping Constant with 380 Ohm Coil 762 602 482 344
Optional Coil Resistances ± 5% ——4,000 Ohms ———
Moving Mass ± 5% 23.6 g 16.8 g 16.8 g 16.8 g
Typical Case to Coil Motion P-P
.07 in
(.18 cm)
.07 in
(.18 cm)
.07 in
(.18 cm)
.07 in
(.18 cm)
Harmonic Distortion with Driving Velocity of 0.7
in/sec (1.8 cm/sec) P-P
N/S
——0.2% or less ——
@ 12 Hz @ 12 Hz @ 12 Hz
Dimensions
Height (less terminals*) ———1.32 in (3.35 cm) ———
Diameter ———1.25 in (3.18 cm) ———
Weight ———3.9 oz (111 g) ———
*Terminal height is .135 inches
[†] Source: http://www.geospace.com/geophones-gs-11d/.
67. 57
Appendix C6 - EBL Piezo Tube
The piezo tube of choice was the EBL#2 Piezoceramic Tube from the company EBL. It has
been custom made with the following dimensions:
Outside Dimension: 0.00635m
Wall Thickness: 0.000762m
Length: 0.0127m
Figure C6.1: Overview of the
Piezoceramic Tube provided by
EBL.[†]
We have used silver Electrodes with a radial Polarization and 4=90 Degree Quadrants on OD.
On the used tube, an electrode removal on OD at one end had been requested, 0.002032m.
[†] See the EBL website: http://www.eblproducts.com/piezotube.html for the complete set of specifications.
68. 58
EBL#2 specifications:
Material Properties EBL #2
d31Å/V@293°K -1.73
d33Å/V@293°K 3.80
d31Å/V@4.2°K -0.31
d33Å/V@4.2°K 0.69
Dielectric constant KT
3 1725
AC depoling field kV/cm rms 7
Young's modulus 1010
N/m2
6.3
Curie Temperature °C 350
Thermal Conductivity W/m°C 1.5
Thermal expansion coefficient ppm/°C ---
Density g/cm3
7.5
Mechanical Q 100
Poisson's ratio 0.31
Industry Type PZT-5A
All values are nominal: actual production values may vary up to 20%.
Appendix C7 - Air Dampening System
Between the frame and fridge of the pulse-tube, an air-based vibration dampening device was
placed. This is the Vision IsoStation by Newport. It provides a working platform for vibration
influenced devices, and is designed to perform in the 10-50Hz floor vibration frequency
range corresponding to dominant ambient vibration frequencies common to multi-floor
buildings. It is a laminated honeycomb panel and pneumatic isolation, providing a rigid yet
lightweight mounting platform. For further specifications, see their website.[†]
[†] http://www.newport.com/Vision-IsoStation-Series-Vibration-Isolation-Work/947081/1033/info.aspx#tab_Specifications
