Page 441 - Handbook of Battery Materials

14.7 Kinetic Aspects 413

local) composition of the solid solution, rather than the formation of additional
phases.
From a thermodynamic viewpoint, there is selective, rather than complete,
equilibrium under conditions in which this type of reaction occurs. We can assume
equilibrium in the sublattice of the mobile solute species, but not in the host
substructure, as strong bonding makes atomic rearrangements relatively sluggish
in that part of the crystal structure.
In general, equilibrium within the guest species sublattice results in their
being randomly arranged among the various interstitial locations within the host
structure. There are, however, a number of cases in which the guest species are
distributed among their possible sites within the host structure in an ordered, rather
than random, manner. There can be different sets of these ordered sites, each having
the thermodynamic characteristics of a separate phase. Thus, as the concentration
of guest species is changed, such materials can appear thermodynamically to go
through a series of phase changes, even though the host structure is relatively
stable. This type of behavior was demonstrated for the case of lithium insertion
into a potassium tungsten oxide [36].
The thermodynamic properties of topotactic insertion reaction materials with
selective equilibrium are quite different from those of materials in which complete
equilibrium can be assumed, and reconstitution reactions take place. Instead of
flat plateaus related to polyphase equilibria, the composition-dependence of the
potential generally has a flat S-type form.
Under near-equilibrium conditions the shape of this curve is related to two
contributions: the compositional dependence of the configurational entropy of the
guest ions and the contribution to the chemical potential from the electron gas [37].
The configurational entropy of the mobile guest ions, assuming random mixing
◦
and a concentration x, residing in x lattice sites of equal energy, is
0
S =−R ln[x/(x − x)] (14.1)
There is also a small contribution from thermal entropy, but this can be neglected.
If we can assume that the electrode material is a good metal and the electronic
gas is fully degenerate, the chemical potential of the electrons is given by the Fermi
level, E F , which can be written as

E F = [Constant][(x) 2/3 /m ] (14.2)
∗
∗
where m is the effective mass of the electrons.

14.7
Kinetic Aspects

In addition to the questions of the potentials and capacities of electrodes, which
are essentially thermodynamic considerations, practical utilization of alloys as
electrodes also requires attractive kinetic properties.