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Quartz tuning fork—A potential low temperature thermometer in high magnetic fields

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Abstract

We present the performance of commercial quartz tuning forks (QTFs) operating at resonance frequencies of 32 kHz, 77 kHz, and 100 kHz in the temperature range below 1 K and in high magnetic fields up to 7.5 T. We show that characteristics of the quartz tuning forks, in particular, the normalized QTF resonance frequency, manifest a universal temperature dependence, which is independent of the magnetic field strength. This feature makes the QTFs very promising low temperature thermometers in high magnetic fields in the temperature range below 1 K having the B/T ratio up to 1000. We also discuss the physical origin of the observed dependencies.
Appl. Phys. Lett. 115, 193507 (2019); https://doi.org/10.1063/1.5124736 115, 193507
© 2019 Author(s).
Quartz tuning fork—A potential low
temperature thermometer in high magnetic
fields
Cite as: Appl. Phys. Lett. 115, 193507 (2019); https://doi.org/10.1063/1.5124736
Submitted: 17 August 2019 . Accepted: 14 October 2019 . Published Online: 06 November 2019
M. Človečko , and P. Skyba
COLLECTIONS
This paper was selected as Featured
Quartz tuning fork—A potential low temperature
thermometer in high magnetic fields
Cite as: Appl. Phys. Lett. 115, 193507 (2019); doi: 10.1063/1.5124736
Submitted: 17 August 2019 .Accepted: 14 October 2019 .
Published Online: 6 November 2019
M.
Clovecˇko and P. Skyba
a)
AFFILIATIONS
Centre of Low Temperature Physics, Institute of Experimental Physics, SAS and P. J.
Saf
arik University in Ko
sice,
Watsonova 47, 04001 Ko
sice, Slovakia
a)
Electronic mail: skyba@saske.sk
ABSTRACT
We present the performance of commercial quartz tuning forks (QTFs) operating at resonance frequencies of 32 kHz, 77 kHz, and 100 kHz
in the temperature range below 1 K and in high magnetic fields up to 7.5 T. We show that characteristics of the quartz tuning forks, in
particular, the normalized QTF resonance frequency, manifest a universal temperature dependence, which is independent of the magnetic
field strength. This feature makes the QTFs very promising low temperature thermometers in high magnetic fields in the temperature range
below 1 K having the B/T ratio up to 1000. We also discuss the physical origin of the observed dependencies.
Published under license by AIP Publishing. https://doi.org/10.1063/1.5124736
Precise low temperature measurements in a strong magnetic field
are associated with problems, since almost all measurable thermomet-
ric physical parameters at low temperatures are sensitive to the mag-
netic field. Typical examples are the presence of the magnetoresistance
in the case of resistive thermometry, the magnetic saturation in the
case of paramagnetic thermometry, etc. In order to measure the tem-
perature in high magnetic fields, an experimenter has to account for
these effects and perform a nontrivial thermometer calibration at these
conditions. Another way to solve problems with low temperature
measurements in high magnetic fields is to search and find a physical
parameter, which would be temperature dependent at low tempera-
tures, but simultaneously (more-less) magnetic field independent.
Our recent research has focused on commercially available piezo-
electric resonators in the form of quartz tuning forks (QTFs). These
devices are known very well, and they are used as experimental tools
in various low-temperature techniques, namely, in scanning probe
microscopy,
1–4
as various sensors in cryogenic fluid environments,
5–10
as probes/detectors in superfluid helium phases
11–17
and
3
He-
4
He
mixtures,
18
etc. Moreover, the quartz tuning forks are considered as
objects of interest themselves, especially in their high Q-value oscilla-
tion mode at low temperatures, where the Q-value of these devices
reaches the value up to the order of one million and even more.
6,16
To be more specific, the recent low-temperature vacuum study of high
Q-valued QTFs revealed that these devices manifest fine, but continu-
ous and reproducible temperature dependence of their resonance
frequency in the millikelvin temperature range.
19,20
We assign the
physical origin of this dependence to the presence of the van der
Waals interaction acting between induced electric dipoles inside
the quartz crystal and emerging on cooling of QTFs. Providing an
ordering effect of electric dipoles on further cooling, the van der
Waals interaction simultaneously stiffens their potential energy,
thus increasing the resonance frequency of the QTFs. Moreover,
we presume that this effect is going to be a universal one for a
broad class of piezomaterials.
Here, we present the performance of the commercial QTFs oper-
ating at resonance frequencies of 32 kHz, 77 kHz, and 100 kHz in the
temperature range below 1K and in high magnetic fields up to 7.5 T.
We show that characteristics of the quartz tuning forks, in particular,
the temperature dependencies of their resonance frequencies in high
magnetic fields, make these devices potential low temperature ther-
mometers in high magnetic fields and in the temperature range below
1 K. Before their installation, the tuning forks were removed from the
original metal can and the former (magnetic) leads were replaced by
copper wires having a diameter of 120 lm. These copper wires were
electrically connected to tuning fork’s pads using a conductive silver
epoxy and glued to a small piece of Stycast 1266—epoxy impregnated
paper in order to achieve a mechanical stiffness of the setup. Cooling
of the tuning forks was ensured by clamping these copper wires
between two copper blocks, and these blocks were screwed to the
mixing chamber of the cryogen-free dilution refrigerator Triton 200.
To excite and measure response (decay) signals from tuning
forks, we applied a pulse-demodulation (P-D) (or heterodyning)
Appl. Phys. Lett. 115, 193507 (2019); doi: 10.1063/1.5124736 115, 193507-1
Published under license by AIP Publishing
Applied Physics Letters ARTICLE scitation.org/journal/apl
technique.
20–22
All decay signals (see the bottom inset of Fig. 1)being
measured were fitted using the expression
VðtÞ¼Vð0Þet
ssin ð2pft þ/Þ;(1)
where fitting parameter V(0) is the initial amplitude of the signal, sis
the relaxation time constant characterizing a damping process, fis
the signal frequency (f
sig
), and /is the phase. The tuning fork’s high
Q-value is demonstrated by a long duration of the decay signal of the
order of several tens of seconds.
Figure 1 shows the temperature dependencies of the QTFs’ reso-
nance frequencies in zero and nonzero magnetic fields, measured
using a P-D technique during continuous heating and subsequent
cooling sweeps of the dilution refrigerator in the temperature range
between 25 mK and 850 mK with the rate of the temperature sweep
being 2 mK per minute. The magnetic field was applied along the
z-axis (see the inset of Fig. 1). The presented measurements are related
to the temperature of the mixing chamber of the dilution refrigerator
because we were not able to measure the temperature of the QTFs
directly. The mixing chamber temperature was monitored using a
RuO thermometer. Calibration of the RuO thermometer in zero mag-
netic field was checked using the SQUID-noise thermometer MFFT-1
provided by Magnicon together with a homemade fix-point device.
23
The RuO thermometer measuring the temperature of the mixing
chamber is placed in a small residual field of a superconducting
magnet reaching values up to 100 mT. Based on the reproducibility of
the measurements, we assume that the tuning forks were in thermal
equilibrium with mixing chamber temperature in the whole tempera-
ture range presented and that the calibration of the RuO thermometer
has not been affected by the residual magnetic field.
As we pointed above, we interpret the temperature dependencies
of the QTF resonance frequencies in zero magnetic field using a phe-
nomenological model based on the presence of the van der Waals
interaction increasing the stiffness of the potential energy,
20
Vpot kþQ2
aðTÞ
!
x2;(2)
where the first term is related to the potential energy associated with
elastic deformation of the lattice, with kbeing the spring constant. The
second term expresses the contribution of the van der Waals interac-
tion, with a(T) being the polarizability, Qthe charge, and xthe deflec-
tion of the ions from the equilibrium position. This interpretation is
based on the fact that in piezomaterials, there are oscillating induced
electric dipoles p¼Qd¼aðTÞEloc (where dis the distance between
the charges, which is proportional to deflection of the ions from equi-
librium position x), and each of them experiences a local electric field
of intensity Eloc produced by other electric dipoles including an initial
voltage pulse (and other electric fields). The electric dipole moment p
in electric field Eloc has potential energy p:Eloc ¼pEloc cos ðhÞ,
with hbeing the angle between pand Eloc . This energy has a tendency
to orient the dipole pin the direction of local field Eloc, but on the
other hand, the thermal energy ðkBTÞviolates this dipole order. We
presume that at low temperatures, the energy of the van der Waals
interactions overwhelms the thermal energy. Polarizability of the
quartz excited by the pulse can be expressed in the form
24
aðTÞ¼ 3e0
Nhcos ðhÞi ¼3e0
NLðXÞ;(3)
where e
0
is the vacuum permittivity, Nis the density of dipoles,
and hcos ðhÞi is the mean value of Picos ðhÞi, which is equal to
the Langevin function hcos ðhÞi ¼ LðXÞ¼cothðXÞ1=X,with
X¼pEloc=ðkBTÞ¼Tc=T.Here,E
loc
is the magnitude of the electric
field intensity produced by other electric dipoles (and an initial voltage
pulse) and T
c
is the critical temperature expressed as Tc¼pEloc=kB.
Nonzero potential energy produces the restoring force Fres ¼rVpot .
This force divided by the effective mass of the fork oscillating prong
m
eff
determines the frequency of the fork oscillations f
tf
,
ftf ðTÞ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
f2
0þbLðTc=TÞ
q;(4)
FIG. 1. Resonance frequencies of measured quartz tuning fork exemplars as func-
tions of mixing chamber temperature and external magnetic field. Red solid lines
represent the fits to experimental data obtained at zero magnetic field (red dots)
using Eq. (4). The inset to the upper graph shows the dependence of the 100 kHz
fork’s resonance frequency on the magnetic field. The blue line is a guide to the
eye (for details, see the text). The inset to the middle graph shows the direction of
the applied magnetic field with respect to the coordinate system related to the tun-
ing fork’s base. The bottom inset shows an example of the QTF free-decay signal
being fitted using Eq. (1).
Applied Physics Letters ARTICLE scitation.org/journal/apl
Appl. Phys. Lett. 115, 193507 (2019); doi: 10.1063/1.5124736 115, 193507-2
Published under license by AIP Publishing
where f
0
corresponds to the temperature-independent term deter-
mined by the elastic properties of quartz. The second term reflects the
temperature contribution to the resonance frequency due to the rising
stiffness of the potential energy provided by the van der Waals interac-
tion with decreasing temperature, where b¼ðQ2NÞ=ð12p2e0meff Þ.
The red lines shown in Fig. 1 represent the fits to the experimental
data measured in zero magnetic field using Eq. (4).
Figure 1 also shows the temperature dependencies of the tuning
fork resonance frequencies measured for the different values of mag-
netic fields. There is a slight rise in the resonance frequencies as the
value of the magnetic field grows up. The origin of this effect seems to
be a consequence of the presence of the free electric charges in the
metal electrodes on fork’s surface. As the tuning fork prongs oscillate
with velocity vin magnetic field B, so do the metal electrodes. Fork’s
oscillating motion generates the Lorentz force FL¼qðvBÞacting
on free electric charges qin the metal electrodes and redistributes
them. The amount of electric charge qin metal electrodes varies with
time and depends on the voltage across the tuning fork as qðtÞ
¼q0þCPV0sin ðxtÞ,whereq
0
is the free charge in fork’s electrodes,
C
P
is the fork capacitance (the capacitance of electrodes), and V
0
is the
voltage amplitude. Simultaneously, the fork velocity vis a harmonic
function of the time [v¼v0sin ðxtþuÞ], where uis the phase
between velocity vand voltage V(t).
21
It turns out that due to the time dependence of the velocity v(t)
and charge q(t), the Lorentz force FLis a multicomponent force. This
can be seen from the expression FL¼qðvBÞ, and substituting
all the above-mentioned expressions for q(t) and fork velocity v(t)
including the relation between fork’s velocity vand fork’s current I
F
as
v0¼IF0=a(where ais the fork constant
6
), one gets the resulting
expression for the Lorentz force amplitude in the form
25
FLðtÞ¼q0IF0B
asinðxtþuÞþCpV0IF0B
2acosucosð2xtþuÞðÞ:(5)
The resulting expression for F
L
has three components: the first one is
constant, the second one oscillating at fundamental fork frequency,
and the third one oscillating at twice the fork’s resonance frequency.
Thus, the time dependent Lorentz force FLðtÞgenerates additional
induced electric field Eind ¼vB, simultaneously modifying the
intensity of local electric field Eloc (and potential energy V
pot
).
The rise of the fork’s resonance frequencies with the rising mag-
netic field (see Fig. 1) seems to be a consequence of the growing stiff-
ness of the potential energy due to the presence of the magnetic field
[the second term in Eq. (5)]. The upper inset of Fig. 1 shows the
dependence of the fork resonance frequencies on the magnetic field
determined for the 100 kHz fork at a temperature of 25 mK. Although
the line presented is a guide to the eye, there is a linear dependence
between the fork resonance frequency and magnetic field, except the
first point measured at zero field. We presume that a slight shift to the
lower frequencies is caused by a small overheating of the fork due to
its motion in the magnetic field.
Now, let us discuss the influence of the intrinsic damping process
on tuning forks’ resonance frequencies expressed as the temperature
dependence of the measured relaxation time constants sMðTÞ.Figure 2
shows the temperature dependencies of s
M
for individual tuning
forks. There are two important features presented: different temper-
ature dependencies of the time constants for individual forks
(32 kHz, 77 kHz, and 100 kHz) and a significant shortage of the
time constants with the rising value of the magnetic field. We pre-
sume that the time constant s
M
consists of two terms,
1
sM
¼1
si
þ1
sB
;(6)
where s
i
is the intrinsic time constant characterizing the intrinsic pro-
cesses of energy dissipation and s
B
is the time constant related to those
connected with the magnetic field. The presence of the extremums in
the temperature dependencies of sMðTÞsuggests that there are ther-
mally activated dissipation processes, especially at the interface
between piezocrystals and metallic electrodes. As individual quartz
tuning forks are covered by the metal electrodes made of various alloys
(tin, silver, etc.), this allows the formation of Schottky barriers due to
the difference in energy spectra between metals and quartz.
20,26
These
barriers open channels for the electric charge injection through the
interface, causing the energy dissipation. However, precise mecha-
nisms of the energy dissipation acting in QTFs need to be elucidated.
A shortage of the time constant s
M
occurs when a fork oscillates
in magnetic field B, which we relate to an effect of “the magnetic
brake.” Harmonic oscillations of the QTFs in the magnetic field gener-
ate the eddy currents in metallic electrodes, and these currents act
against the fork motion causing additional damping and subsequently
the signal shortage. Using expression (6),itiseasytoestimates
B
as a
function of the magnetic field Bamplitude, assuming that s
i
is field
independent. At the condition of experiment, the amplitude of the
eddy currents is expected to be proportional to B
2
,andtheriseofthe
FIG. 2. Relaxation time constants as functions of the mixing chamber temperature
and external magnetic field.
Applied Physics Letters ARTICLE scitation.org/journal/apl
Appl. Phys. Lett. 115, 193507 (2019); doi: 10.1063/1.5124736 115, 193507-3
Published under license by AIP Publishing
eddy current amplitude reduces the value of s
B
.Figure 3 shows a
dependence of 1=sBas a function of the magnetic field squared for all
three QTFs. This supports the presence of the magnetic brake caused
by the eddy currents flowing in metallic electrodes of the QTFs.
Finally, Fig. 4 shows the temperature dependencies of the QTF
resonance frequencies scaled to their maximum value. All the mea-
sured curves collapse on each other, creating a universal dependence,
thus giving the possibility to determine only one value of the reduced
frequency for given temperature, but independent of the magnetic field
magnitude. This unique property makes the quartz tuning forks
potential low temperature thermometers below 1 K in high magnetic
fields. Table I summarizes the parameters of the tuning forks used.
In summary, we have shown that motion of the tuning fork in
high magnetic fields (and in vacuum) is associated with generation of
the Lorentz force FL, which acts on free electric charges presented in
its metal electrodes. The time dependent Lorentz force FLðtÞgenerates
additional induced voltage on the fork’s electrodes, and the corre-
sponding induced electric field Eind simultaneously modifies the inten-
sity of local electric field Eloc (and potential energy V
pot
). This gives
rise to the additional stiffness of the potential energy V
pot
manifested
as the increase in the fork’s resonance frequency with the magnetic
field. We also demonstrated the presence of the “magnetic brake,” a
dampingforce created due to eddy currents flowing in metallic electro-
des of the QTFs and being responsible for the signal shortage. A cru-
cial property we have shown is a universal temperature dependence of
the normalized QTF resonance frequency, which is independent of the
magnetic field strength. This feature makes the QTFs very promising
low temperature thermometers in high magnetic fields. Another
important physical consequence of the tuning fork motion in the mag-
netic field is a possibility of its excitation as a parametric resonator. In
fact, as its potential energy V
pot
consists of a term cos ð2xtÞcaused
by the Lorentz force, there is a possibility to excite these forks paramet-
rically by applying a rf-pulse on twice the fork’s resonance frequency
in nonzero magnetic field.
27
We would like to acknowledge the support from the following
grants: European Microkelvin Platform (H2020 Project No.
824109), APVV 16-0372, VEGA 2/0086/18, and Project Promatech
No. 26220220186. We wish to thank F. Vavrek for his technical
assistance. Support provided by the U.S. Steel Ko
sice s.r.o. is also
much appreciated.
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Appl. Phys. Lett. 115, 193507 (2019); doi: 10.1063/1.5124736 115, 193507-5
Published under license by AIP Publishing
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In this paper, we investigate the potential of using quartz tuning fork (QTF) sensing system for detection of specific metal ions in aqueous solutions with sample volume of $1~\mu \text{L}$ . Functionalized self-assembled monolayers (SAMs) of L-glutathione (LG) on gold-coated QTFs were used to sense specific analytes of CaCl <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and HgCl <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , whereas functionalized L-cysteine based SAMs used to sense PbCl <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> . The resonance frequency undergoes a shift in response to the interaction between functionalized QTF and target analyte. X-ray photoelectron spectroscopy was used to study the interaction of thiol groups between the functionalized SAM and gold coated on QTF surface. Our analysis revealed that active QTFs functionalized with LG are more sensitive to detection of CaCl <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> compared with HgCl <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> . The SAM-based QTF sensors were found to be capable of detecting low concentrations ( $10^{- {12}}$ M) of divalent analyte solutes with high sensitivity.
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We present the measurements of a parametrically excited quartz tuning fork in vacuum at very low temperatures (\(\sim 20\) mK) and magnetic field of 1.5 Tesla. We show that if a quartz tuning fork is exposed to a high static magnetic field, the motion of the tuning fork in this field modifies its potential energy forming a time-dependent term oscillating at twice of its fundamental frequency. This phenomenon gives an opportunity to study and use the quartz tuning forks as the parametric resonators. Here, we present the technique of the parametric excitation of the quartz tuning forks, and we discuss the results of the measurements.
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We present the measurements of a parametrically excited quartz tuning fork in vacuum at very low temperatures (\(\sim 20\) mK) and magnetic field of 1.5 Tesla. We show that if a quartz tuning fork is exposed to a high static magnetic field, the motion of the tuning fork in this field modifies its potential energy forming a time-dependent term oscillating at twice of its fundamental frequency. This phenomenon gives an opportunity to study and use the quartz tuning forks as the parametric resonators. Here, we present the technique of the parametric excitation of the quartz tuning forks, and we discuss the results of the measurements.
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We present the properties of the standard, commercial 100 kHz quartz tuning forks at very low temperatures and high magnetic fields up to 8 Tesla. We show that the resonance frequency of the tuning forks depends weakly on the strength of magnetic field. This makes the quartz tuning forks a promising low-temperature thermometer having the B/T ratio up to 1000. We discuss the physical origin of the observed experimental results.
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We present experimental observation of a phenomenon that we interpret as a NMR-like effect on an anisotropic magnetic moment of the surface Andreev bound states in topological superfluid He3−B at zero temperature limit. We show that an anisotropic magnetic moment formed near the horizontal surface of a mechanical resonator due to symmetry violation of the superfluid He3−B order parameter by the resonator's surface may lead to anomalous damping of the resonator motion in magnetic field. In difference to the classical NMR technique, here NMR was excited using own harmonic motion of the mechanical resonator and nuclear magnetic resonance was detected as a maximum in damping when the resonator's angular frequency satisfied the Larmor resonance condition.
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The results of a newly developed pulse-demodulation (P-D) technique introduced to determine the resonant characteristics of a high Q value quartz tuning forks in vacuum and millikelvin temperature range are presented. Applying P-D technique to a standard 32 kHz quartz tuning fork with extremely low excitation energy of the order of a few femtojoules, we were able to measure the resonance frequency of the fork’s decay signal with resolution better than 10 \(\upmu \)Hz. Using this highly sensitive measurement technique, we found a continuous and reproducible temperature dependence of the tuning fork’s resonance frequency in the millikelvin temperature range. The observed dependence suggests a potential application for the quartz tuning forks to be used as thermometers in the millikelvin temperature range. We also discuss the physical origin of the observed phenomenon.
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We have investigated the influence of the damping force acting on high quality tuning forks (Q∼106) of different sizes and geometries in superfluid 3He-B at temperatures below 200 μK and a pressure of 0.1 bar. The measurements show that at low velocities, the damping of the largest fork expressed in terms of its resonance characteristic width Δf 2 rises up as its velocity increases. This is in contradiction to the damping of the fork due to Andreev reflection and it may be caused by the interaction of this fork with excitations trapped in the Andreev bond states. We present our preliminary experimental results.
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This paper explores the fundamental limits of the use of quartz tuning forks as force detectors in scanned probe microscopy. It is demonstrated that at room temperature, pressure, and atmosphere these force sensors have a noise floor of 0.62 pN/ and exhibit a root mean square Brownian motion of only 0.32 pm. When operated as a shear force sensor both dissipative and reactive forces are detected on approach to the sample. These forces are sufficient to reduce the amplitude of motion of the probe nearly to zero without physically contacting the surface. It is also demonstrated that conventional proportional-integral feedback control yields closed loop responses at least 40 times faster than their open loop response. © 2000 American Institute of Physics.
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We present the design, properties of a very simple and very easy to make fix-point device (FPD) for temperature scale definition below 1 K. The FPD consists of five superconductors Mo, Zn, Zr, Ti and AuIn2 allowing thus to fix the temperature scale from 0.915 K down to 200 mK.
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A principle of operation and electrical characteristics of a high frequency current-to-voltage (I/V) converter are presented. The I/V converter measures the electric current with selectable gains of 10(5), 10(4), and 10(3) V/A in the frequency range from DC to 500 kHz, 1.2 MHz, and 2.4 MHz, respectively. These properties make this I/V converter suitable for wide range of applications such as tuning forks, torsion oscillators, ultrasound transducers measurements, detection of the piezoelectric transducers used in STM techniques, etc., in low temperature physics. The influence of the input impedance of a I/V converter on the precision of alternating current measurements is also discussed.
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We have developed the use of quartz tuning forks for thermometry in normal liquid 3He. We have used a standard 32 kHz tuning fork to measure the viscosity of liquid 3He over a wide temperature range, 6 mK<T<1.8 K, at SVP. For thermometry above 40 mK we used a calibrated ruthenium oxide resistor. At lower temperatures we used vibrating wire thermometry. Our data compare well with previous viscosity measurements, and we give a simple empirical formula which fits the viscosity data over the full temperature range. We discuss how tuning forks can be used as convenient thermometers in this range of temperatures with just a single parameter needed for calibration.
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We have measured the damping on a quartz tuning fork in the B-phase of superfluid 3He at low temperatures, below 0.3T c. We present extensive measurements of the velocity dependence and temperature dependence of the damping force. At the lowest temperatures the damping is dominated by intrinsic dissipation at low velocities. Above some critical velocity an extra temperature independent damping mechanism quickly dominates. At higher temperatures there is additional damping from thermal quasiparticle excitations. The thermal damping mechanism is found to be the same as that for a vibrating wire resonator; Andreev scattering of thermal quasiparticles from the superfluid back-flow leads to a very large damping force. At low velocities the thermal damping force varies linearly with velocity, but tends towards a constant at higher velocities. The thermal damping fits very well to a simple model developed for vibrating wire resonators. This is somewhat surprising, since the quasiparticle trajectories through the superfluid flow around the fork prongs are more complicated due to the relatively high frequency of motion. We also discuss the damping mechanism above the critical velocity and compare the behaviour with other vibrating structures in superfluid 3He-B and in superfluid 4He at low temperatures. In superfluid 4He the high velocity response is usually dominated by vortex production (quantum turbulence), however in superfluid 3He the response may either be dominated by pair-breaking or by vortex production. In both cases the critical velocity in superfluid 3He-B is much smaller and the high velocity drag coefficient is much larger, compared to equivalent measurements in superfluid 4He.