Characteristics of a cryogenic fluid Critical, normal boiling, and triple point temperatures of cryogenic fluids

1. Critical, normal boiling, and triple point temperatures of cryogenic fluids 2. Vapor pressure of liquids 3. Liquid Helium 4. Superfluids

Note log temperature scale

Figure adapted from Cryogenic Engineering by Thomas M. Flynn, Dekker:NY (1997), p. 80

Vapor pressure of liquids Helium • Spherical shape • Two isotropic forms: 3He and 4He • Low mass • Van der Waals forces
low critical and boiling points • Remains a liquid even at absolute zero (unless external pressure is applied)

Figure adapted from Cryogenic Engineering by Thomas M. Flynn, Dekker:NY (1997), p. 81

Spelling Bee Name that man

How do you spell the word for making a gas In whose laboratory was helium first into a liquid? liquefied?

A. liquify A. Sir James Dewar B. liquefy B. Cailletet C. liquafy C. Wroblewski D. liquifi D. Onnes E. liquiphy E. Van der Waals

1 1882-Helium liquefied at Leiden University • In 1882, Onnes was appointed Professor of Experimental Physics at H. Kamerlingh Onnes was Leiden University. In one of the first professors in 1895, he established experimental physics at Leiden Laboratory Leiden University. His lab first • His researches were to liquefy helium (1908), for mainly based on the which he was awarded the theories of J.D. van der Waals and H.A. Lorentz Nobel prize in 1913, and he discovered superconductivity • Was able to bring the temperature of helium in 1911. He liquefied down to 0.9 °K, justifying hydrogen to pre-cool the the saying that the coldest helium gas in his liquefier. spot on earth was situated Heike Kamerlingh Onnes (left) at Leiden. and Van der Waals in Leiden at the helium 'liquefactor' (1908)

Who would have ever thought… Why Not A Solid?

• Zero-Point Energy 2 = 3h • energy of a free particle in a small box E 2 3 • E decreases as V increases
the effect 8mV of the Zero-Point to raise molar volume • Kinetic energy exceeds the interaction potential energy

Heike Kamerlingh Onnes , his stamp, and ( right ) showing his helium liquefier to passers-by: Niels Bohr (visiting from Kopenhagen), Hendrik Lorentz, and Paul Ehrenfest (far left ).

Superconductivity -1911 Regular substance Phase Diagrams Heike Kamerlingh Onnes discovered superconductivity, 4He the total lack of dc electrical resistance in certain materials when cooled to a temperature near absolute zero. 3He

2 Why so low? Helium-4 Phase Diagram

4 Superfluidity occurs in He at about 4.2 K but only • At 2.17K 4He below about 0.002 K in 3He. Why? undergoes a transition to the A. 3He is rarer than 4He in nature superfluid state B. 3He is always in smaller containers than is 4He • The lambda line separates He I and 3 4 C. He has different chemical properties than He He II 4 D. He superfluidity is an electronic process while • 3He does not become 3He superfluidity is a nuclear process a superfluid until E. 3He superfluidity is an electronic process while below 2mK 4He superfluidity is a nuclear process

Helium Mixtures 1931: Keesom discovered lambda shaped- specific heat in helium at Leiden Allen and Misener and Kapitza (1939) Density

4He (Boson)

He II He I

Heat Capacity

Tλ=2.17K

Temperature [Frank Pobell, 1992]

Superfluidity in Helium 4 in 1938 Superfluidity of the Quantum Fluid, 4He

Science 24 • Superfluidity is a dramatic Thermal de Broglie wavelength of 4He at October 1997: visible manifestation of 2K: Vol. 278. no. quantum mechanics, being the 5338, pp. 664 - result of Bose–Einstein 666 condensation in which a h 8.9Å 4 λ = ≈ macroscopic number of He T atoms occupy the same, single- 3mkT particle quantum state. It was ≥ mean interparticle distance discovered simultaneously by of 4He ≈ 3.6 Å Kapitza, Allen and Misener Fig. 2. (A through C) Microscope Figure 3. Microscope Breaker experiment: images showing an edge-on view of image of a superfluid drop working separately, though superfluid drops on a horizontal Cs on a Cs substrate inclined at substrate. The dark bar in the upper 10° to the horizontal. A only Kapitza received the half of the image is the capillary drop hanging off of the Nobel prize. It is also amusing tube. The pictures show the outline capillary is also seen in the of the drop as well as its mirror upper right. The drop on the to note that Allen was a image in the reflective substrate. As inclined substrate is “classical physicist” at heart, the volume of the drop increased stationary. The downhill from (A) to (B), the contact angle edge of the drop has the who didn’t much care for the remained constant. When fluid was same contact angle as subatomic world. He withdraw as in (C), the contact angle shown in Fig. 2B, whereas decreased but . the uphill edge has a discovered superfluidity with a the diameter remained constant vanishing contact angle. pen light. [Frank Pobell, 1992]

3 The Fountain Effect -1938 Two Fluid Model– Landau in 1941 (oscillating disc viscometer) Two Fluid model density viscosity entropy • In february 1938 J.F. Allen and Superfluids Viscosity Super- ρ η =0 S =0 H. Jones had found that when (µP) Two s s s they heated superfluid helium fluids fluid 4He on one side of a porous normal ρ η η medium or a thin capillary, the n = n Sn=S He The viscosity of liquid pressure increased sufficiently fluid helium 4 vanishes below to produce a fountain effect at Two-fluid equations for He II: 2.17 K [W.H. Keesom, 1938] the end of the tube which ∂ρ r r Fluid density + ∇ ⋅ ρυ = 0 (mass conservati on) The thermal conductivity contained the liquid. The ∂t becomes very large “fountain effect” was a ρ=ρ +ρ ≈ 0.14g/cm 3 ∂ρs r r n s + ∇ ⋅ ρsυ = 0 (entropy conservati on) spectacular phenomenon that ρ ∂ n A spectacular thermo- t r r was impossible to understand ρ D υ ∂υ r r r r mechanical effect: the s s s ≡ s + (υ ⋅ ∇)υ = −∇µ within classical ∂ s s "fountain effect" 56 % ρ Dt t thermodynamics. ∂J ∂P i + iα = 0 (momentum conservati on) ρ ∂t ∂rα n = δ + ρ υ υ + ρ υ υ stress tensor Pij p ij n n,i n, j s s,i s, j T (K) r r r r total mass flow J ≡ ρυ = ρ υ + ρ υ 0 2.0 T n n s s λ [S.J. Putterman, 1974]

Quantization of Superfluid Circulation Quantization of superfluid circulation: Rotating bucket of Superfluid r r nh − κ = υ ⋅dl = ≈ 97.9 ×10 4 n cm 2 /s ∫ s m

(postulated separately in 1955 by Onsager and Feynman) The angular velocity Ω is (a) 0.30 /s, (b) 0.30 /s, All superfluid vortex lines align along (c) 0.40 /s, (d) 0.37 /s, the rotation axis with ordered array of areal density= length of quantized (e) 0.45 /s, (f) 0.47 /s, vortex line per unit volume= (g) 0.47 /s, (h) 0.45 /s, r r 2Ω ∇×υ = s ≈ Ω 2 (i) 0.86 /s, (j) 0.55 /s, κ κ 2000 lines/cm (k) 0.58 /s, (l) 0.59 /s. 1. Circulation round any circular path of radius r concentric with the axis of rotation=2 πr2 Ω π 2 [Yarmchuk, 1979] 2. Total circulation= r n0h/m (n 0: # of lines per unit area) ∴ Ω Ω κ 3. n0=2 m/h=2 /

Properties of Superfluids 1962 Nobel – Lev Landau

• All of their atoms are in the same quantum • Constructed the state
they have identical momentum; if complete theory of one moves, they all move quantum liquids at very low temperatures • Ordinary Sound • He developed theories • Second Sound (Temperature Waves) on both the Bose and • Third Sound (Surface Waves) Fermi type liquids • Fourth Sound

http://www.nobel.se/physics/laurea tes/1962/index.html

4 1972 1971 – Superfluidity discovered in 3He (US) Discovery of superfluidity in helium-3 Douglas D. Osheroff, David M. Lee, and Robert C. Richardson (US) - Super fluidity was first discovered in helium-3 by American physicists David The experiment M. Lee , Douglas D. Osheroff , and Robert C. Richardson . It occurs at temperatures a few thousandths of a degree above absolute zero and is In a cryostat, figure 1, a container of 3He was cooled to about 2mK. While the 3He was being slowly distinguished by either an A phase or a higher-pressure, lower-temperature B compressed at a constant rate, the inner pressure was measured and when 3.4 MPa was reached, the phase. Helium-3 is anisotropic, which means it displays different properties helium was allowed to expand. when measured in different directions, and as such, its study has become As the volume decreased and then increased, small changes in the valuable to scientists in the fields of big-bang theory and superconductivity. slope of the pressure curve were observed, and also small kinks. These observations were the first evidences of transitions to superfluid phases in 3He. Two superfluid phases were discovered, “A” and “B”, figure 2.

Figure 2 . Pressure inside a sample David M. Lee Douglas D. Osheroff Robert C. Richardson containing a mixture of liquid 3He and solid 3He Cornell University Stanford University Cornell University ice. Ithaca, NY, USA Stanford, CA, USA Ithaca, NY, USA Figure 1. Schematic diagram of the Pomeranchuck cell used in the discovery. Pictures taken from:http://www.nobel.se/physics/laureates/1996/osheroff-lecture.pdf MN-09/09/03

Ways to the Superfluid State Microscopic Picture of Superconductivity

• 4He (even number of elementary particles (6) each with intrinsic angular momentum ½
integral angular momentum: BOSON; Bose Statistics • 3He (odd number of elementary particles (5)
half-integral spin: FERMION; Fermi Statistics

Helium 3 Length Scales in Superfluid 3He

5