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#1/16
FSU Jena
Nawrodt 10/06
Ronny Nawrodt
ILIAS/STREGA Annual Meeting
London, 27 October 2006
Friedrich-Schiller-Universität Jena, Germany
Cryogenic Q-measurementson Calcium Fluoride
#2/16
FSU Jena
Nawrodt 10/06
Calcium fluoride research
• manufacturer: Schott1
• polishing: surface + circumference (Hellma-Optik2)
• (100) orientation
• 75 mm 75 mm
• mass: ~ 1100 g
1 www-schott.de, 2 www.hellmaoptik.com
#3/16
FSU Jena
Nawrodt 10/06
CaF2 – Measuring Setup
special cryostat1 (5…300 K, p<10-3 Pa)
suspension: polished tungsten wire2 ( 75 µm)
electroststic exciter (~ 1.2 kV)
interferometric read-out3 (1 point)L < 0.2 nmup to 500 kHz
1 Nawrodt et al., Cryogenics 46 (2006) 718-723, 2 Advent Research Materials, 3 www.sios.de
#4/16
FSU Jena
Nawrodt 10/06
CaF2 – Mode Scan
20 40 60 80 1000
5
10
15
20
25
Frequency [kHz]
Am
plit
ud
e [n
m]
mode excitation: high voltage ~ 1.2 kV
33 modes found within 25 kHz – 100 kHz interferometerspot
CaF2, (100) orientation, 75 mm 75 mm
#5/16
FSU Jena
Nawrodt 10/06
CaF2 – Ring-Down Experiment
0 1000 2000 3000 4000 50000
5
10
15
20
25
30
Time [s]
Am
plitu
de [n
m]
CaF2, (100) orientation, 75 mm 75 mm
T = (79.5 0.2) K
f0 = (42017.3 0.1) Hz t = (1490 10) s
Q = (1.97 0.01) 108
reproducibility ~ 20%
Q = (2.0 0.4) 108
#6/16
FSU Jena
Nawrodt 10/06
CaF2 – Measured Q-values
5 10 20 30 50 100 200 30010
6
107
108
109
Temperature [K]
Q-f
acto
r
41302 Hz
40310 Hz
57421 Hz
influence of thesuspension
maximum Q @ 64 K: Q = 3.2 108, = 3.1 10-9
@ 300 K
ongoing work(defects? similar to crystalline quartz)
intrinsic limitthermoelastic ?
CaF2, (100) orientation, 75 mm 75 mm
#7/16
FSU Jena
Nawrodt 10/06
CaF2 – Interaction with Suspension (1)
50 100 150 200 250 30010
5
106
107
108
109
Temperature [K]
Q-f
acto
r
41302 Hz
40310 Hz
@ 300 KCaF2, (100) orientation, 75 mm 75 mm
~140 K ~196 K
#8/16
FSU Jena
Nawrodt 10/06
CaF2 – Interaction with Suspension (2)
0 50 100 150 200 250 30041.3
41.4
41.5
41.6
41.7
41.8
41.9
42
42.1
Temperature [K]
Res
onan
t Fre
quen
cy [k
Hz]
41010.6 Hz41720.5 Hz
0 50 100 150 200 250 30040.2
40.4
40.6
40.8
41
41.2
41.4
Temperature [K]R
eson
ant F
requ
ency
[kH
z]
~140 K
~196 K
#9/16
FSU Jena
Nawrodt 10/06
CaF2 – Interaction with Suspension (3)
50 100 150 200 250 30010
5
106
107
108
109
Temperature [K]
Q-f
acto
r
41302 Hz
40310 Hz
@ 300 K
41010.6 Hz 41720.5 Hz
Difference fits to a harmonic of the suspension!
CaF2, (100) orientation, 75 mm 75 mm
At lower temperaturesno resonances are possible!
#10/16
FSU Jena
Nawrodt 10/06
CaF2 – Impurities? (1)
• temperature dependence
41302 Hz
40310 Hz
57421 Hz
@ 300 K20 30 40 50 60
107
108
109
Temperature [K]
Q-f
acto
r
• no Arrhenius-law?ongoing work
CaF2, (100) orientation, 75 mm 75 mm
#11/16
FSU Jena
Nawrodt 10/06
CaF2 – Impurities? (2)
• substrate: crystalline quartz, Q(T) understood
0 20 40 60 80 100 120 140 160 180 20010
-10
10-9
10-8
10-7
10-6
10-5
10-4
Temperature [K]
Da
mp
ing
Q-1
0 20 40 60 80 100 120 140 160 180 20010
-10
10-9
10-8
10-7
10-6
10-5
10-4
Temperature [K]
Da
mp
ing
Q-1
phonon-phonon
large contribution
crystalline quartz, c-axis orientation, 75 mm 12 mm
impurities
sum
#12/16
FSU Jena
Nawrodt 10/06
CaF2 – Low Temperature Limits (1)
5 10 20 30 50 100 200 30010
6
107
108
109
1010
1011
1012
Temperature [K]
Q-f
act
or
• Thermoelastic limit
Braginski1:
longitudinal mode of a bar
20
2
TE c9
T
Q
1
CaF2, (100) orientation, 75 mm 75 mm
- thermal conductivity
- thermal expansion
c – heat capacity per unit volume
- mass density
0 - resonant frequency
1 Braginski et al., Systems with Small Dissipation
#13/16
FSU Jena
Nawrodt 10/06
CaF2 – Low Temperature Limits (2)
5 10 20 30 50 100 200 3000
500
1000
1500
2000
2500
3000
Temperature [K]
[W
/m K
]
thermal conductivity
0 50 100 150 200 250 3000
200
400
600
800
1000
Temperature [K]
C [J
/kg
K]
heat capacity - 30 … 320 K, Batchelder et al., The Journal of Chemical Physics 41 (1964)
- 3 … 500 K, Slack et al., Phys. Rev. 122 (1961)
C – 3 … 30 K, Huffman et al., Phys. Rev. 117 (1960)
53 … 300 K, Todd et al., Journal of the American Chemical Society 71 (1949)
0 50 100 150 200 250 3000
0.5
1
1.5
2x 10
-5
Temperature [K]
[K
-1]
thermal expansion
#14/16
FSU Jena
Nawrodt 10/06
Grating Research
0 50 100 15010
4
105
106
107
108
Temperature [K]
Q-f
act
or
pure substrate
1 mm grating
crystalline quartz, c-axis orientation, 75 mm 12 mm
#15/16
FSU Jena
Nawrodt 10/06
Silicon research
• new substrates
- doping: boron, phosphorus- electron / hole - different doping concentration (1014 … 1017 cm-3 for n-doped,
1014 … 1018 cm-3 for p-doped)- CZ / floating zone
• 100 mm 100 mm (~2 kg)
• 150 mm 90 mm (~4 kg)
#16/16
FSU Jena
Nawrodt 10/06
Summary
• calcium fluoride research: 3.2108 @ 64 K lower Q‘s at lower temperatures
• solid-state basic research ongoing (phonon-phonon interaction)
• further steps in Jena: silicon bulk research (doping!) tantala research all-reflective components