tuning fork viscometry in liquid helium matt jachowski aj kumar naveen sinha aaron ligon john...
TRANSCRIPT
Tuning Fork Viscometry in Liquid Helium
Matt JachowskiAJ KumarNaveen SinhaAaron LigonJohn RutherfordEd Fei
TA: Charis Quay
Physics 108, Group 4
Why Liquid Helium?
Superfluid transition Viscosity goes to zero
Existing LHe viscometers Vibrating wire Torsional oscillator MEMS cantilever
Why Tuning Forks?
Advantages of tuning forks Crystal acts as both
actuator and sensor No optical
measurements necessary
Crystals are inexpensive and easy to obtain
Study properties of piezoelectric crystals at low temperatures
5 mm
Design and Construction
Three environments Open in LHe Sealed in LHe Open in vacuum
Two stages One stick
The Stick and Vacuum Chamber
The Inner Stage
The Outer Stage
Design and Construction
Three open forks Thermal contact to
walls of can Si diode thermometer In vacuum
Mixture of open and sealed forks
DIP socket for modularity
In direct contact with LHe
Electronics
Excite tuning fork crystal with random noise
Measure tuning fork spectral response
Preamp
Resonant Frequency
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
32695.2
32695.6
32696.0
32696.4
32696.8
Sealed Tuning Fork
Reso
nan
t F
req
uen
cy [
Hz]
Temperature [K]
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
32695.2
32695.6
32696.0
32696.4
32696.8
Sealed Tuning Fork
Reso
nan
t F
req
uen
cy [
Hz]
Temperature [K] 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
31920
31940
31960
31980
32000
Open Tuning Fork
Reso
nan
t F
req
uen
cy [
Hz]
Temperature [K]
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
31920
31940
31960
31980
32000
Open Tuning Fork
Reso
nan
t F
req
uen
cy [
Hz]
Temperature [K]
Resonance Width
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
5
10
15
20
25
30
Open Tuning Fork
Reso
nan
ce W
idth
[H
z]Temperature [K]
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
5
10
15
20
25
30
Open Tuning Fork
Reso
nan
ce W
idth
[H
z]Temperature [K]
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Sealed Tuning Fork
Reso
nance
Wid
th [H
z]
Temperature [K]
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Sealed Tuning Fork
Reso
nance
Wid
th [H
z]
Temperature [K]
Quality Factor
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.520000
30000
40000
50000
60000
70000
Sealed Tuning Fork
Qu
ality
Facto
r
Temperature [K]
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.520000
30000
40000
50000
60000
70000
Sealed Tuning Fork
Qu
ality
Facto
r
Temperature [K]1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
Sealed Tuning Fork
Qu
ality
Facto
rTemperature [K]
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
Sealed Tuning Fork
Qu
ality
Facto
rTemperature [K]
Applications
Already shown to be an indicator for passing Tλ
2.175 +/- 0.04 K Viscometry and density measurement Several theories
Kanazawa and Gordon (1985): Zhang (2001):
f 2
0f f
Applications (cont’d)
There are (complicated) functional forms for density of liquid helium: Donnelly and Barenghi (1998):
Practicality of tuning fork viscometry 2
ln ma T T b T T T T P T T
DensityViscosity
Conclusions
Demonstration of novel LHe viscometry technique
Clear indicator of lambda transition Future work:
Closer examination of lambda transition regime
Determination of proper theoretical model
Real-time extraction of resonance characteristics