1. A compact and versatile capacitive dilatometer
George Schmiedeshoff
Occidental College
September 2007
Supported by NSF-DMR , , , and

2. Thanks to (in quasi-chronological order):
Jim Smith (LANL)
Alex Lacerda (NHMFL)
Jason Cooley (LANL)
Jason Lashley (LANL)
John Neumeier (Montana State)
Paul Canfield (Ames/ISU)
Sergey Bud’ko (Ames/ISU)
Mike Hundley (LANL)
Victor Correa (NHMFL)
Stan Tozer (NHMFL)
Eric Palm (NHMFL)
Scott Hannahs (NHMFL)
Tim Murphy (NHMFL)
Eric Bauer (LANL)
Shawna Hollen (Oxy→JPL→Brown)
Winston Okraku (Oxy→JPL→NASA/Langley)
David Luna (Oxy)
Sally Tracy (Oxy)
Amanda Lounsbury (Oxy)
Cy Opeil (BC)
A. deVisser (Amsterdam)
Roy Rockage (LANL)
NSF & DOE
The NHMFL for hosting this workshop.
And all of you for coming!

3. Dilation: ΔV (or ΔL) Intensive Parameters:
T: thermal expansion: β = dln(V)/dT
H: magnetostriction: λ = ΔL(H)/L
P: compressibility: κ = dln(V)/dP
E: electrostriction: ξ = ΔL(E)/L
etc.
Volume is a quintessential extensive parameter

4. A (very) Brief History
Heron of Alexandria (0±100): Fire heats air, air expands, opening temple doors (first practical application…).
Galileo (1600±7): Gas thermometer.
Fahrenheit (1714): Mercury-in-glass thermometer.
Mie (1903): First microscopic model.
Grüneisen (1908): β(T)/C(T) ~ constant.
Fahrenheit: First precision thermometric instrument.
Gruneisen: All the original papers are in German. Translators???

5. Phase Transition: TN
TbNi2Ge2 (Ising Antiferromagnet) after gms et al. AIP Conf. Proc. 850, 1297 (2006). (LT24)
2nd Order Phase Transition, Ehrenfest Relation(s):
Pc = uniaxial pressure along c-axis
1st Order Phase Transition, Clausius-Clapyeron Eq(s).:

6. Grüneisen Theory (one energy scale: Uo)
Gruneisen Parameter. Einstein Solid, Schottky system, ideal Fermi gas.
e.g.: If Uo = EF (ideal ) then:

7. Grüneisen Theory (multiple energy scales: Ui each with Ci and i)
e.g.: phonon, electron, magnon, CEF, Kondo, RKKY, etc.
Examples: Simple metals: ~ 2

8. Example (Noble Metals):
After White & Collins, JLTP (1972).
Also: Barron, Collins & White, Adv. Phys. (1980).
(lattice shown.)
T-dependence finite but small.

9. Example (Heavy Fermions):
1- Significant temperature dependence.
2- Big at T=0.
HF(0)
After deVisser et al. (1990)

10. Dilatometers Mechanical (pushrod etc.) Optical (interferometer etc.).
Electrical (Inductive, Capacitive, Strain Gauges).
Diffraction (X-ray, neutron).
Others (absolute & differential).
See Neumeier (this workshop) and Refs at end for details.

11. Capacitive Dilatometer (Cartoon)
Capacitor Plates D
Cell Body L
Sample

12. D3 Rev. Sci. Instrum. 77, 123907 (2006) Cell body: OHFC Cu.
(cond-mat/ has fewer typos…) D3
Cell body: OHFC Cu.
BeCu spring (c).
Stycast 2850FT (h) and Kapton (i) insulation.
Sample (d).

13. Calibration Operating Region CMAX  65 pF
Use sample platform to push against lower capacitor plate.
Rotate sample platform (θ), measure C.
Aeff from slope (edge effects).
Aeff = Ao to about 1%?!
“Ideal” capacitive geometry.
Consistent with estimates.
CMAX >> C: no tilt correction.
Ao is the physical, machined, or directly measured area.
Change Cmax w/ trivial rebuild.
CMAX  65 pF

14. Cell Effect
Cell Effect vanishes below about 2K.
Feature near 240K: Kapton?
Much smaller cell effect, above 10K, using quartz (or sapphire?) instead of Cu for cell body. See, for example, Neumeier et al. (2005) and references therein.

16. Tilt Correction Pott & Schefzyk (1988).
If the capacitor plates are truly parallel then C →  as D → 0.
More realistically, if there is an angular misalignment, one can show that C → CMAX as D → DSHORT (plates touch) and that
Pott & Schefzyk (1988).
For our design, CMAX = 100 pF corresponds to an angular misalignment of about 0.1o.
Tilt is not always bad: enhanced sensitivity is exploited in the design of Rotter et al. (1998).

17. Kapton Bad (thanks to A. deVisser and Cy Opeil)
Replace Kapton washers with alumina.
New cell effect scale.
Investigating sapphire washers.
“enormous feature” equivalent to ΔL of about 10 microns!

18. Torque Bad
The dilatometer is sensitive to magnetic torque on the sample (induced moments, permanent moments, shape effects…).
Manifests as irreproducible magnetostriction (for example).
Best solution (so far…): glue sample to platform.
Duco cement, GE varnish, N-grease…
Low temperature only. Glue contributes above about 20 K.

19. Hysteresis Bad
Cell is very sensitive to thermal gradients: thermal hysteresis. But slope is unaffected if T changes slowly.
Magnetic torque on induced eddy-currents: magnetic hysteresis. But symmetric hysteresis averages to “zero”:

20. Lashley PRL Ce
Structural phase transitions: big signal!

21. Bud’ko JPhysCondMat
dHvA (related) oscillations coexisting with superconducting state (magnetic hysteresis).

22. Correa, PRL Extreme Conditions Group
FFLO state just below Hc2 in CeCoIn5
Dilatometer rotates in-situ.
Extreme Conditions Group

23. The Good & The Bad Cell effect (T ≥ 2K). Small (scale up or down).
Open architecture.
Rotate in-situ (NHMFL/TLH).
Vacuum, gas, or liquid (magnetostriction only?).
Sub-angstrom precision.
Cell effect (T ≥ 2K).
Magnetic torque effects.
Thermal and magnetic hysteresis.
Thermal contact to sample in vacuum (T ≤ 100mK ?).

24. Recommended:
Book: Heat Capacity and Thermal Expansion at Low Temperatures, Barron & White, 1999.
Collection of Review Articles: Thermal Expansion of Solids, v.I-4 of Cindas Data Series on Material Properties, ed. by C.Y. Ho, 1998.
Book (broad range of data on technical materials etc.): Experimental Techniques for Low Temperature Measurements, Ekin, 2006.
Book: Magnetostriction: Theory and Applications of Magnetoelasticity, Etienne du Trémolet de Lacheisserie, 1993.
Book: Thermal Expansion, Yates, 1972.
Review Article: Barron, Collins, and White; Adv. Phys. 29, 609 (1980).
Review Article: Chandrasekhar & Fawcett; Adv. Phys. 20, 775 (1971).
…and references therein.