Page 442 - Handbook of Battery Materials

414 14 Lithium Alloy Anodes

The primary question is the rate at which the mobile guest species can be added to,
or deleted from, the host microstructure. In many situations the critical problem is
the transport within a particular phase under the influence of gradients in chemical
composition rather than kinetic phenomena at the electrolyte/electrode interface.
In this case, the governing parameter is the chemical diffusion coefficient of the
mobile species, which relates to transport in a chemical concentration gradient.
Diffusion has often been measured in metals by the use of radioactive tracers. The
resulting parameter, D T , is related to the self-diffusion coefficient by a correlation
factor f that is dependent upon the details of the crystal structure and jump
geometry. The relation between D T and the self-diffusion coefficient D self is thus
simply
D T = D self ∗ f (14.3)
Whereas in many metals with relatively simple and isotropic crystal structures the
parameter f has values between 0.5 and 1, it can have much more extreme values in
materials in which the mobile species move through much less isotropic structures
with one-dimensional (1-D) or two-dimensional (2-D) channels, as is often the case
with insertion reaction electrode materials. As a result, radiotracer experiments can
provide misleading information about self-diffusion kinetics in such cases.
More importantly, the chemical diffusion coefficient D chem , instead of D self ,isthe
parameter that is relevant to the behavior of electrode materials. They are related
by
D chem = D self ∗ W (14.4)
where W is an enhancement factor. This is sometimes called the ‘thermodynamic
factor,’ and can be written as
W = dlna i /dlnc i (14.5)
in which a i and c i are the activity and concentration of the neutral mobile species
i, respectively. Experimental data have shown that the value of W can be very
large in some cases. An example is the phase Li 3 Sb, in which it has a value of
◦
70 000 at 360 C [38].
It is thus much better to measure the chemical diffusion coefficient directly. De-
scriptions of electrochemical methods for doing this, as well as the relevant theoreti-
cal background, can be found in the literature [39, 40]. Available data on the chemical
diffusion coefficient in a number of lithium alloys are included in Table 14.3.

14.8
Examples of Lithium Alloy Systems

14.8.1
Lithium–Aluminum System
Because of the interest in its use in elevated-temperature molten salt elec-
trolyte batteries, one of the first binary alloy systems studied in detail was the