> I have read that most super-conducting materials, .... will change
> state from resistive- to super-conduction and vice versa, in
> a matter of a few degrees C.
Actually, the transition occurs over a *much* narrower temperature
interval, on the order of 10^-4 to 10^-5 degrees C or K.
> I am wondering if it can really be the case that such
> minute ammounts of energy ... as all it takes to bring
> about this rather profound change in the material characteristics?...
> Is it perhaps the case that more energy than usual is needed to heat
> (or cool) the super conductor .... as it passses through the
> temperature range where it stops (starts) super conducting?
Exactly. The thermodynamic quantity that how much energy it takes to
increase the temperature of a material by a given amount is called the
"heat capacity". Formally, the heat capacity, C, is defined as C =
dq/dT, where q is heat (energy) and T is the absolute temperature.
The quantity dT is the infinitesimal change in temperature caused by
an infinitesimal addition (or subtraction, if dq is negative) amount
of energy. In materials that become superconducting, the heat
capacity exhibits a large and abrupt (but continuous) increase right
at the superconducting transition temperature. See the first set of
figures at http://en.wikipedia.org/wiki/Superconductivity for an
illustration of this.
> If so, what law of nature explains this apparant "phase-change",
> as I understand it there is no change of crystal structure or any
> such thing, unlike when a material melts or boils)
The superconducting transition is, indeed, a phase transition;
however, there are different types of phase transitions. One way of
classifying the different types is according to the lowest order
derivative of the thermodynamic free energy that exhibits a
discontinuity at the transition. The type of phase transformations
most people are familiar with (whether they know it or not) are called
"first-order phase transitions". Such transitions typically involve
the wholesale rearrangement of atoms (like the examples of melting or
vaporization you gave). First order phase transitions are
characterized by a change in slope in a plot of free energy versus
temperature (or pressure or other controlling variable). If the slope
changes at the transition temperature, then this implies that the
first derivative of the energy (i.e., the heat capacity) with respect
to temperature is discontinuous at that point.
The nature of the phase transition occurring at the superconducting
transition temperature is more subtle than a major rearrangement of
the atoms in the material. We have a good explanation of what happens
in "ordinary" or "type 1" superconductors (i.e., all materials that
were known to become superconducting prior to the discovery of
"high-temperature superconductors in 1986), but there is still no good
theory to explain what's going on in high-temperature superconductors.
In "ordinary" superconductors, we know that at the transition
temperature, the thermal vibrations of the crystal lattice of the
material (essentially "sound" waves) "couple" with the electronic
wavefunction of the material. This coupling has the odd result of
making it energetically favorable for electrons, which normally repel
one another due to their like charges, to "pair up". (These pairs are
known as "Cooper pairs"). You can think of this coupling of the
vibrational and the electronic wavefunctions as causing a small
attractive force between the electrons. At temperatures above the
superconducting transition temperature, the lattice vibrations are too
energetic to cause this pairing, and any Cooper pairs that form are
immediately destroyed. Below the transition temperature, *all* the
conduction electrons form pairs. It is this pairing of electrons that
constitutes the superconducting phase transition (in type-1
superconductors, anyway). The phase transition in this case
(probably) involves a discontinuity in the *second* derivative of the
energy with respect to temperature (i.e., the derivative of the heat
capacity with respect to temperature), so the superconducting phase
transition for type-1 superconductors has traditionally been
classified as a "second-order" phase transition. (There is some
argument over this, however). Second-order phase transitions
typically involve a change in the "ordering" of a material that occurs
over a temperature range. Although the degree of order changes
continuously over the range, the properties of the material often
exhibit a discontinuous change at some critical value of the order
parameter. Other examples of second-order transitions include
magnetic transitions, ordering in certain minerals, Bose Einstein
condensation, and the transition to superfluidity.
Superconductors owe their superconductivity to the Cooper pairs,
which, unlike independent electrons, have integral spin and behave as
bosons. Unpaired electrons have spin 1/2, and behave as fermions. No
two fermions can have the same set of quantum numbers (i.e., they
cannot occupy the same energy state), and this is what gives rise to
all of chemistry. Bosons, on the other hand, are gregarious creatures
that have no occupancy restrictions on their party rooms. All the
bosons in a system can occupy the lowest possible energy state of the
system, and in this state, they do not interfere with one another. It
is this "interference" (really collisions) that gives rise to
resistivity in ordinary matter, and in superconductors, this
interference does not exist. |
