Page 272 - Handbook of Battery Materials

242 9 Metal Hydride Electrodes

Thermodynamic quantities for a system may be determined from the van’t Hoff
equation, which defines the equilibrium constant, K, in terms of the reaction
enthalpy, H, and the temperature, T.
d ln K H
= (9.3)
dT RT 2
For reaction (9.2),
a MHx
K = (9.4)
) x/2
a M (f H 2
Under ideal conditions the activity of a solid may be taken as unity and the fugacity
as the pressure, then Equation 9.3 may be rewritten as
) −x/2
d(ln P H 2 H
= (9.5)
dT RT 2
which upon integration yields,
2
= ( H/RT) + C (9.6)
ln P H 2
x
The enthalpy of the phase conversion can be determined via Equation 9.6 by
plotting the log of the absorption or desorption plateau pressure, P plateau ,vsthe
reciprocal temperature as indicated in Figure 9.2. When the solubility of hydrogen
in the metal (α) phase is small, then H plat ≈ H f , where H f is essentially the
enthalpy of formation of the hydride from the metal [4]; the intercept, C,isequal
to 2/x( S/R). Equation 9.6 is commonly presented as
A
ln P plateau = + B (9.7)
T
where the constants A and B are specified. Thermodynamic data for some repre-
sentative compounds are given in Table 9.1.

9.2.2
Electronic Properties

Switendick was the first to apply modern electronic band theory to metal hydrides
[11]. He compared the measured density of electronic states with theoretical results
derived from energy band calculations in binary and pseudo binary systems.
Recently, the band structures of intermetallic hydrides including LaNi 5 H x and
FeTiH x have been addressed; the results for these more complicated systems have
been summarized in a review article by Gupta and Schlapbach [12]. All exhibit
certain common features upon the absorption of hydrogen and the formation of
a distinct hydride phase. These are (i) the density of states versus energy function
is changed, (ii) new low -lying states having an s-like character appear and are
associated with hydrogen, and (iii) to the extent that the hydrogen electrons cannot
be accommodated in the new low-lying states they are inserted into empty states
near the Fermi level, which in turn shifts.