From: rparson@spot.Colorado.EDU (Robert Parson)
Newsgroups: sci.chem
Subject: Re: Ping Uncle Al - Re: Can Hydrogen & Oxegen be frozen solid?
Date: 5 Jun 2000 15:12:55 GMT

In article <20000601133047.16347.00001176@ng-fe1.aol.com>,
JackTrax <jacktrax@aol.comn0spamm> wrote:
>>Helium-3 also cannot solidify at 1atm.
>>: And both Helium-3 and Helium-4 go >superfluid too.
>
>So does this infer that superfuids can only consist of  fluids that cannot
>solidify under thier own vapor pressure?

 No, these are distinct phenomena. Helium (either isotope) is a liquid
 at T= 0K, p=1at because the zero-point motion overwhelms the weak
 interatomic attractions - in effect, the solid melts under its own
 zero point energy. The effect is actually more pronounced in He-3
 because it is lighter and hence has more zero-point motion: He-4
 requires a pressue of about 25 atmospheres to solidify at 0K,
 whereas He-3 requires about 35 atmospheres. This is a consequence
 of one-body quantum mechanics - quantum statistics (Bose vs. Fermi)
 doesn't enter, at least not to lowest order.

 Superfluidity, in contrast, is directly related to quantum statistics.
 He-4 (bosons) goes superfluid at about 2K. He-3 (fermions) goes
 superfluid at a much lower temperature, about 1 millikelvin, via
 a pairing mechanism that is analogous to, but more complicated than,
 Cooper pairing of electrons in superconductivity. There are actually
 several (at least 3) distinct superfluid phases.

 One really cute detail about the He-3 phase diagram: at very low
 temperatures, the solid-liquid boundary has a negative slope. OK,
 this happens in water, because the liquid is denser than the
 solid, but in He-3 the liquid is less dense than the solid. So
 something else, something even stranger than water's anomalous
 volume change upon freezing, must be going on. I'll leave this as
 an exercise for anyone who's taken (or taught) P-Chem recently.
 Hint: use the Clapeyron equation.

 See L.E. Reichl, _A Modern Course in Statistical Physics_, University
 of Texas Press, 1980 (1st Edition - I don't have the 2nd edition),
 Chapter 4. Lee, Richardson and Osheroff won the 1996 Nobel Prize in
 Physics for discovering the superfluid phases of He-3 (the discovery
 took place in the early 1970's.) Their Nobel Lectures are in the
 July 1997 issue of _Reviews of Modern Physics_  (www.rmp.aps.org)
 (not free, but you should be able to get to it via a University
 library's web site.).

 -------
 Robert

From: rparson@spot.Colorado.EDU (Robert Parson)
Newsgroups: sci.chem
Subject: Re: Entropy at 0 Kelvin
Date: 5 Jun 2000 16:08:21 GMT

In article <8h4ufr$1d4qg$1@hades.csu.net>,
iotarho <iotarhorho@hotmail.com> wrote:
>> I was taught that an example of zero entropy was a perfect crystal at
>> absolute zero (as its structure is not disordered and nor is temperature
>> forcing motion within the locale). But one thing confused me. At
>> absolute zero, the kinetic energies of all particles within such a
>> crystal would be zero, and thus the momentum would have to be zero. But
><snip>
>I would like to hear more line of thought on this as I've heard from several
>physicists that this is not the case.  Specifically, I had wondered if
>electron orbits would cease at 0K; the resounding answer was no.  I'll dust
>off some old textbooks in hopes of contributing something more concrete than
>my less-than-prodigious memory serves up.  In the meanwhile, can anyone else
>comment?

 When a system is in its quantum-mechanical ground state, its entropy
 is zero. In this ground state, there is still zero-point motion.
 In an ordinary solid, this means that the atoms are still doing
 small-amplitude vibrations around their equilibrium positions at
 zero degrees K. As discussed in another thread, in Helium the
 zero-point motion results in a liquid at 0K (and pressures less
 than about 25 at). Nevertheless this liquid represents, at 0K, the
 quantum ground state of the system and has zero entropy.

 The association of temperature with average kinetic energy is a
 classical approximation which breaks down at very low temperatures.
 Ditto for the relationship between entropy and molecular motion.
 Entropy is still a measure of disorder on the molecular scale, but
 you have to express it in terms of populations of quantum states
 rather than in terms of visualizable molecular motion.

 --------
 Robert