von Fraunhofer, that result from the
absorption by elements in the solar
chromosphere of some of the wave-
lengths of the visible radiation emit-
ted by the hot interior of the sun.
free electron See electron.
free-electron approximation
The approximation resulting from
the assumption that electrons in
metals can be analysed using the
kinetic theory of gases, without tak-
ing the periodic potential of the
metal into account. This approxima-
tion gives a good qualitative account
of some properties of metals, such as
their electrical conductivity. At very
low temperatures it is necessary to
use quantum statistical mechanics
rather than classical statistical me-
chanics. The free-electron approxi-
mation does not, however, give an
adequate quantitative description of
the properties of metals. It can be im-
proved by the nearly free electron ap-
proximation, in which the periodic
potential is treated as a perturbation
on the free electrons.
free energy A measure of a sys-
tem’s ability to do work. The Gibbs
free energy (or Gibbs function), G, is
deÜned by G = H – TS, where G is the
energy liberated or absorbed in a re-
versible process at constant pressure
and constant temperature (T), H is
the enthalpy and S the entropy of
the system. Changes in Gibbs free en-
ergy, ∆G, are useful in indicating the
conditions under which a chemical
reaction will occur. If ∆G is positive
the reaction will only occur if energy
is supplied to force it away from the
equilibrium position (i.e. when ∆G =
0). If ∆G is negative the reaction will
proceed spontaneously to equilib-
rium.
The Helmholtz free energy (or
Helmholtz function), F, is deÜned by F
= U – TS, where U is the *internal en-
ergy. For a reversible isothermal
process, ∆F represents the useful
work available.free radical An atom or group of
atoms with an unpaired valence elec-
tron. Free radicals can be produced
by photolysis or pyrolysis in which a
bond is broken without forming ions
(see homolytic fission). Because of
their unpaired valence electron, most
free radicals are extremely reactive.
See also chain reaction.
freeze drying A process used in
dehydrating food, blood plasma, and
other heat-sensitive substances. The
product is deep-frozen and the ice
trapped in it is removed by reducing
the pressure and causing it to sub-
lime. The water vapour is then re-
moved, leaving an undamaged dry
product.freezing mixture A mixture of
components that produces a low
temperature. For example, a mixture
of ice and sodium chloride gives a
temperature of –20°C.
freezing-point depression See
depression of freezing point.
Frenkel defect See crystal defect.Frenkel–Kontorowa model A
one-dimensional model of atoms,
such as xenon, adsorbed on a peri-
odic substrate, such as graphite. This
model, which can be used to investi-
gate the nature of the lattice formed
by the adsorbed gas, was invented in
1938 by Y. I. Frenkel and T. Kon-
torowa and independently in 1949 by
F. C. Frank and J. H. Van der Merwe.
The Frenkel–Kontorowa model can
be used to investigate the phase tran-
sition between a *commensurate lat-
tice and an *incommensurate lattice.
freon See chlorofluorocarbon.Freundlich isotherm An isotherm
for adsorption with the form θ=
c 1 P1/c^2 , where the fractional coverage235 Freundlich isotherm
f