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By Giorgio Benedek, Dipartimento Scienza dei Materiali Università di Milano-Bicocca 1.He: a superatom 2.Superfluid helium 3.Supersonic helium 4.A surface.

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Presentation on theme: "By Giorgio Benedek, Dipartimento Scienza dei Materiali Università di Milano-Bicocca 1.He: a superatom 2.Superfluid helium 3.Supersonic helium 4.A surface."— Presentation transcript:

1 by Giorgio Benedek, Dipartimento Scienza dei Materiali Università di Milano-Bicocca 1.He: a superatom 2.Superfluid helium 3.Supersonic helium 4.A surface superprobe 5.Helium clusters 6.Flying refrigerators 7.From fountains to geygers 8.Supersolid helium

2 Helium: a brief biography of a superatom - 18 Aug 1868 solar eclipse : Pierre Janssen  nm: Na? - 20 Oct 1868: Norman Lockyer  same line (D3) in solar spectrum. Proposal with Edward Frankland of a new atom: Helium! - 26 Mar 1895: William Ramsay looks for Ar in rocks but finds something else; Lockyer and William Crookes confirm: Helium! William F. Hillebrand (US) found it earlier but…. - later in 1895: Teodor Cleve & Abraham Langlet (Uppsala) determine the atomic weight of He with great accuracy -1907: Ernest Rutherford & Thomas Royds prove that α rays are 4 He nuclei Sir Ernest Rutherford

3 - 1908: Heike Kamerlingh Onnes liquifies He, but attempts to solidify He are unsuccesful : Kamerlingh’s student Willem Hendrik Keesom succeeds in solidifying 4 He at 25 atm : Pyotr Leonidovich Kapitsa discovers superfluidity of 4 He : Douglas D. Osheroff, D. M. Lee & R. C. Richardson observe superfluidity in 3 He as an effect of Cooper pairing : Andreev & Lifshitz predict a superfluidity in solid 4 He (  supersolid) : C. Cohen-Tannoudji et al obtain Bose-Einstein condensation in 4 He* Helium gets condensed

4 4 He: nuclear structure  Carbon can be produced within stars (triple-alpha process), thus making life possible  Big Bang nucleosynthesis predicts an abundance of ~23% of 4 He (by mass) This is due to: (a) helium-4 is very stable and most neutrons combine with protons to form 4 He; (b) two 4 He atoms cannot combine to form a stable atom: 8 Be is unstable

5 Helium: a protected species  Nearly all helium on Earth from radioactive decay (~ m 3 /km 3 /year): most helium comes from natural gas. Concentrations: - in rocks: 8· in seawater: 4· in atmosphere: 5.2·10 -6  In 1958 John Bardeen and other influential scientists warned the Congress that all our helium would be gone by Congress reacted by spending $1 billion on a separation plant in Amarillo, Texas, and began stockpiling helium in empty gas wells.  Most helium in the Earth's atmosphere escapes into space due to its inertness and low mass. In a part of the upper atmosphere, He and other lighter gases are the most abundant elements.

6  Thanks to the conservation measures, helium supplies were not exhausted by Still worldwide consumption of helium has increased by 5 to 10 % a year in the past decade. Presently it is about 100 million cubic metres, and is predicted to rise by 4 to 5 % a year.  No one is claiming that we are in imminent danger of running out of helium-- there should be at least 20 years supply left. However, new sources of the gas will have to be found to meet the ever-growing demand.  If not, God forbid, we may have to celebrate helium's 200th birthday in the year without any Mickey Mouse balloons.

7 4 He vs 3 He NucleusSpinMagnetic moment [μ N ] proton p1/ neutron n1/ deuterium d He1/ He00  3 He nuclear magnetic resonance  3 He hyperfine structure  3 He spin-echo spectroscopy 3 He: % 4 He: %

8 He: electronic structure I

9 He: electronic structure II Atomic radius: 0.31 Å VdW radius: 1.40 Å He*(2 3 S) Refractive index of liquid He: (!)

10 He: an ideal gas?  Van der Waals equation of state  Joule-Thomson effect  Thermal conductivity: 151.3·10 -3 W / mK (300 K)  Diffusivity in solids: ~3 times that of air; ~ 2 / 3 that of H 2  Solubility in water: smaller than for any other gas

11  Helium in an electric glow discharge can form unstable compounds and molecular ions like HeNe, HgHe 10, WHe 2, He 2 +, He 2 ++, HeH +, HeD + and even He 2 ….. or form otherwise a plasma  supersonic cluster beam deposition  The largest wdW cluster! 4 He 2 is a giant, > 50 Å wide! He: a nobleman?  Endohedral fullerenes (by heating under a high pressure of the gas): C The neutral molecules formed are stable up to high temperatures.  If 3 He is used, it can be readily observed by helium NMR spectroscopy: Fullerenes compounds, nanotubes, supramolecular compounds can be studied in this way. 3 He sneaks into everywhere and tells about the electronic environment (a nobleman?) End of lecture 1

12 Helium: the only substance which doesn’t freeze at absolute zero and normal pressure ordinary substances P. Kapitza (1938) Lee, Osheroff, Richardson

13 from D. Vollhardt & P Wölfle 1990 log scale!

14 λ – line specific heat W. H. Keesom et al (1932)


16 4 He solid vs. liquid II

17 4 He: a quantum solid fighting against Heisenberg’s indetermination principle in solid Helium unfavorable conditions: - attractive forces (E pot ) are weak - both m and r 0 are small r0r0 pressure needed!

18 Classical (Maxwell- Boltzmann) statistics A B B B A A Quantum Bose- Einstein statistics Quantum Fermi-Dirac statistics 4 He 3 He Fermions ( 3 He) also fight against Pauli’s esclusion principle!

19 “Keesom and van den Ende (1930) observed quite accidentally that liquid helium II passed with very annoying ease through certain extremely small leaks which at a higher temperature were perfectly tight for liquid helium I and even for gaseous helium.... … This observation seemes to indicate an enormous drop of viscosity when liquid helium passes the λ-point.” Fritz London, Superfluids, Vol. II (John Wiley & Sons, New York 1954) the supersurface film H. Kamerlingh Onnes (1922)

20 a Helium fountain “At any rate the fountain effect experiments show that, in liquid helium, heat transfer and matter transfer are inseparably interconnected”. F. London, ibidem

21 Two-fluid model of the superfluid state (L. Tisza) a normal (viscous) component with atoms having different excited-state velocities a superfluid component with all atoms having the same ground state velocity (BEC  no dissipation  zero viscosity)

22 simple ideas about Bose–Einstein condensation (BEC) V,N density of states

23 total energy average energy per atom atom density condensation on the ground state

24 BEC critical temperature & conditions de Broglie wavelength  2 x interatomic distance

25 Micromégas, bien meilleur observateur que son nain, vit clairement que les atomes se parlaient … (Voltaire, Micromégas) atoms “talk” each other if their average mean distance is smaller than their de Broglie wavelength but the boson attitudes are totally different from fermion attitudes…. de Broglie

26  (even L)  (singlet)  =  (odd L)  (triplet) L = 0 S = 0 s-wave Cooper pair: unfavoured  L = 1 S = 1 p-wave Cooper pair: favoured  J = L + S J = 0 ( 3 P 0 ), J = 1 ( 3 P 1 ), J = 2 ( 3 P 2 ) but spin-orbit interaction is below the mK range and can be neglected: 9-fold ~ degeneracy  mixing of S z = 1, 0,-1 states (like the ground state of ortho-H2 !) L = 2 S = 0 d-wave Cooper pair: less favoured  3 He condensation

27 B-phase: Balia-Werthamer state (isotropic gap  (T))  = |  > /2 [ |  > + |  >] + |  > A-phase: Anderson-Brinkham-Morel “axial” state  = |  > + |  > anisotropic gap  (k,T) =  0 (T)[1 – (k·L) 2 ] 1/2 ^^ the superfluid phases of 3 He a third phase (A 1 ) is induced by a magnetic field with spin wavefunction  = |  > a magnetic superfluid! End of lecture 2

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