#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