1. Reversible Hydrogen Storage Battery Materials: Non-Destructive Sensor Development
A.N. Lasseigne-Jackson1, B. Mishra2, D.L. Olson2, and J.E. Jackson2
National Institute of Standards and Technology
Colorado School of Mines

2. Outline Introduction Investigations
Free Electron Theory
Thermoelectric Power
Hydrogen Storage Materials
Investigations
Characterization of LaNi5 Utilizing Thermoelectric Power
Characterization of NaAlH4 Utilizing Thermoelectric Power
Optimization of Thermoelectric Power Measurements
Final Conclusions

3. Free Electron Theory
The free electron model assumes valence electrons of constituent atoms become conduction electrons and move freely through the volume of the metal
A conduction electron is scattered by perturbations in periodicity like lattice defects, impurities, phonons, etc.
Certain properties of a metal can be determined from the electron gas properties
The properties of metals are determined from:
The occupation of the valence and conduction bands
The spacing between the valence and conduction bands
Relative location of the Fermi energy
A conduction electron is scattered only infrequently by other conduction electrons, which is a consequence of the pauli-exclusion principle, which states that no two electrons in a single atom can occupy the same set of quantum numbers.
A conduction electron is scattered by perturbations in periodicity like lattice defects, impurities, phonons, etc.

4. Free Electron Theory
The highest electronic energy state assumed by an electron at absolute zero is the Fermi energy:
Where the available electronic states are determined from solutions to the schrodinger equation.

5. Fermi-Dirac Energy Distribution
The kinetic energy of the free electron gas increases as temperature increases. Some energy levels which are empty at absolute zero become occupied with a temperature increase, while some energy levels which were occupied at absolute zero may become empty.
The fermi-dirac distribution gives the probability that an electronic state will be occupied in an ideal electron gas at thermal equilibrium. The chemical potential is the fermi energy level at all temperatures.

6. Thermoelectric Power Measurements
The developing voltage of each element is dependent upon the Seebeck coefficient, where the potential difference between two metals AB= A-B. The emf between the two metals, VAB=VA-VB can be expressed by following:

7. Thermoelectric Power Measurements
S Thermoelectric power
r Scattering parameter
h Planck constant
K Boltzmann's constant
n Free electron concentration
me Effective mass (m*)
S = S(n, me, r)

8. Use of the Effective Mass of an Electron
Electron wave function is modified by localized potentials
Free Electron Wave (-----)
+ Localized Potential
Ref: Wilkes, 1973
LCAO Model
If a lattice atom is a solute atom or is situated in a strain field, the localized potential will be altered and will offer a different interaction to the nearly-free conduction electron wave function. In the free electron model, the potential is V=0, the electron’s energy is given as E = 1/2mv2 = P2/2m, where P is the electron’s momentum, the deBroglie expression is P = k, and the energy is expressed as E = 2k2/2m, where m is the mass of an electron. For situations where there are localized lattice potential interactions, the conduction electron’s energy could be described as E = 2k2/2m + V, where V is associated with the potential energy experienced by the conduction electron in the vicinity of the lattice atom. Now, allowing the value of the mass of the electron to be altered to quantitatively incorporate the effect of V, the effective mass, me, is introduced to describe the total energy as E = 2k2/2me. In this manner the free electron formulation can be used to derive the electron properties of an alloy, thus making the effective mass a valuable parameter to assess the microstructure and alloy stability through electron property measurements.

9. Thermoelectric Power
When hydrogen enters the metal lattice it dissociates into a proton and an electron. The proton occupies the interstitial site in ferrous alloys and the electron is donated to the host metal electronic d-band. The proton is very small when compared to the size of the interstitial site. The positive charge of the proton must be screened to maintain the electrical neutrality [Pepperhoff and Acet, 2001]. The electrical neutrality is preserved by the formation of an atomic sized electron cloud, however this process is not perfect so that repulsive forces occur between the proton and the neighboring positively charged metal nuclei. These repulsive forces result in a local expansion and lattice distortion.

10. Electronic Nature of Hydrogen

11. Schematic Pressure-Composition-Temperature Diagram

12. Comparison of Thermoelectric Power and Activity Diagrams

13. Pressure-Composition Isotherms for LaNi5
Van Vucht et al., 1970

14. Hydrogen Charging System

15. Thermoelectric Power Powder Measurement System
Powder Sample

16. Thermoelectric Power as a Function of H/LaNi5

17. Thermoelectric Power as a Function of H/LaNi5

18. Sodium Alanates 5.6 % Hydrogen by Weight $50 per kg Slow Kinetics
Reversible only at ~600 K
Bogdanovic and Sandrock, 2002

19. PCT Diagram for NaAlH4
Bogdanovic et al., 2000

20. Thermoelectric Power as a Function of H/Al

21. Thermoelectric Power as a Function of H/Al
Bogdanovic et al., 2000

22. Optimization of Thermoelectric Power Measurements
Equipment
Design of Probes
Calibration and Standardization
Temperature Difference

23. Determination of Optimum Temperature Difference
1.7 ppm
0.9 ppm
0.3 ppm

24. Outlook
Resistivity is also dependent upon effective mass allowing inductive impedance to be used to assess hydrogen content and to obtain thermodynamic data.
Magnetic properties, especially for transition metal containing hydrogen storage materials, has a strong correlation to hydrogen content.

25. Conclusions
The use of electronic and magnetic properties will give new insight into the behavior of hydrogen storage materials.
Advanced elastic property measurements will also give insight into the behavior of hydrogen storage materials.
Since these properties are dependent on many physical variables, it will require a combination of techniques to develop a reliable, rapid measurement system.

26. Acknowledgements
The authors would like to thank and acknowledge the support of the Naval Research Laboratories and the University of Hawaii