Diapositiva 1

1

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

by Giorgio Benedek, Dipartimento Scienza dei
Materiali Università di Milano-Bicocca
2
Helium a brief biography of a superatom
- 18 Aug 1868 solar eclipse Pierre Janssen ?
587.49 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 a rays are 4He nuclei
Sir Ernest Rutherford
3
Helium gets condensed

• 1908 Heike Kamerlingh Onnes liquifies He, but
  attempts
• to solidify He are unsuccesful

• 1926 Kamerlinghs student Willem Hendrik Keesom
  
• succeeds in solidifying 4He at 25 atm

- 1938 Pyotr Leonidovich Kapitsa discovers
superfluidity of 4He

• 1969 Andreev Lifshitz predict a superfluidity
  in solid 4He
• (? supersolid)

• 1972 Douglas D. Osheroff, D. M. Lee R. C.
  Richardson
• observe superfluidity in 3He as an
  effect of Cooper pairing

• 2001 C. Cohen-Tannoudji et al obtain
  Bose-Einstein condensation in 4He

4
4He nuclear structure
? Big Bang nucleosynthesis predicts an
abundance of 23 of 4He (by mass) This is
due to (a) helium-4 is very stable and most
neutrons combine with protons to form 4He (b)
two 4He atoms cannot combine to form a stable
atom 8Be is unstable
? Carbon can be produced within stars
(triple-alpha process), thus making life
possible
5
Helium a protected species

• ? Nearly all helium on Earth from radioactive
  decay (0.0034 m3/km3/year) most helium comes
  from natural gas. Concentrations
• - in rocks 810-9
• - in seawater 410-12
• - in atmosphere 5.210-6

?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.
?In 1958 John Bardeen and other influential
scientists warned the Congress that all our
helium would be gone by 1980. Congress reacted by
spending 1 billion on a separation plant in
Amarillo, Texas, and began stockpiling helium in
empty gas wells.
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?Thanks to the conservation measures, helium
supplies were not exhausted by 1980. 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 2095--without
any Mickey Mouse balloons.
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4He vs 3He
3He 0.000137 4He 99.999863
Nucleus Spin Magnetic moment µN
proton p 1/2 2.79278
neutron n 1/2 -1.91315
deuterium d 1 0.85742
3He 1/2 -2.1276
4He 0 0
? 3He hyperfine structure
? 3He nuclear magnetic resonance
? 3He spin-echo spectroscopy
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He electronic structure I
9
He electronic structure II
He(23S)
Refractive index of liquid He 1.026 (!)
Atomic radius 0.31 Å VdW radius 1.40 Å
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He an ideal gas?
? Van der Waals equation of state
? Joule-Thomson effect
? Thermal conductivity 151.310-3 W / mK (300 K)
? Diffusivity in solids 3 times that of air
2/3 that of H2
? Solubility in water smaller than for any other
gas
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He a nobleman?

• ? Helium in an electric glow discharge can form
  unstable compounds and molecular
• ions like HeNe, HgHe10, WHe2, He2, He2,
  HeH, HeD and even He2 ..
• or form otherwise a plasma ? supersonic
  cluster beam deposition

? Endohedral fullerenes (by heating under a
high pressure of the gas) C60_at_He The
neutral molecules formed are stable up to high
temperatures.
? If 3He is used, it can be readily observed by
helium NMR spectroscopy Fullerenes
compounds, nanotubes, supramolecular compounds
can be studied in this way. 3He sneaks
into everywhere and tells about the electronic
environment (a nobleman?)
? The largest wdW cluster! 4He2 is a giant, gt
50 Å wide!
End of lecture 1
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Helium the only substance which doesnt freeze
at absolute zero and normal pressure
ordinary substances
P. Kapitza (1938)
Lee, Osheroff, Richardson
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log scale!
from D. Vollhardt P Wölfle 1990
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? line specific heat
W. H. Keesom et al (1932)
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(No Transcript)
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4He solid vs. liquid II
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4He a quantum solid fighting against
Heisenbergs indetermination principle
r0
pressure needed!
in solid Helium unfavorable conditions -
attractive forces (Epot) are weak - both m and r0
are small
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Classical (Maxwell-Boltzmann) statistics
A
B
Quantum Bose-Einstein statistics
A
B
4He
Quantum Fermi-Dirac statistics
3He
B
A
Fermions (3He) also fight against Paulis
esclusion principle!
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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. ...
the supersurface film H. Kamerlingh Onnes (1922)
This observation seemes to indicate an enormous
drop of viscosity when liquid helium passes the
?-point. Fritz London, Superfluids, Vol. II
(John Wiley Sons, New York 1954)
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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
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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)
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simple ideas about BoseEinstein condensation
(BEC)
density of states
V,N
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total energy
average energy per atom
atom density
condensation on the ground state
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BEC critical temperature conditions
de Broglie wavelength ? 2 x interatomic distance
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Micromégas, bien meilleur observateur que son
nain, vit clairement que les atomes se parlaient
(Voltaire, Micromégas)
?de Broglie
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.
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• ?(even L)?(singlet)
• ?(odd L)?(triplet)

3He condensation
L 0 S 0 s-wave Cooper pair unfavoured
?
L 1 S 1 p-wave Cooper pair favoured
? J L S J 0 (3P0), J 1 (3P1),
J 2 (3P2) but
spin-orbit interaction is below the mK range
and can be neglected 9-fold
degeneracy ? mixing of Sz 1, 0,-1 states
(like the ground state of ortho-H2 !)
L 2 S 0 d-wave Cooper pair less
favoured ?
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the superfluid phases of 3He
B-phase Balia-Werthamer state (isotropic gap
?(T)) ? ??gt 2-1/2 ??gt ??gt
??gt A-phase Anderson-Brinkham-Morel axial
state ? ??gt ??gt
anisotropic gap ?(k,T) ?0(T)1 (kL)21/2

• a third phase (A1) is induced by a magnetic field
  with spin wavefunction
• ??gt
• a magnetic superfluid!

End of lecture 2