3409
J . Phys. Chem. 1992, 96, 3409-3412
Adsorptlon Potential of Hydrogen Atom on Zirconium Masahiro Yamamoto,* Shizuo Naito, Mahito Mabuchi, and Tomoyasu Hashino? Institute of Atomic Energy, Kyoto University, Uji, Kyoto 611, Japan (Received: August 28, 1991)
The adsorption potential of hydrogen atom on zirconium(0001) surface has been calculated by an effective medium theory. The adsorption energy is found to be -3.0 eV for both the overlayer sites above the tetrahedral site and the octahedral site, The hydrogen vibrational energy and the potential energy including an effect of lattice relaxation at the subsurface tetrahedral site are in good agreement with experiments.
Introduction Zirconium has a high affinity for hydrogen and physical properties of the zirconium-hydrogen system have been widely studied. The reaction of hydrogen with zirconium at its surface, e.g. chemisorption or transport of hydrogen atom from the surface to the bulk, determines the hydrogen absorption which is of importance in hydrogen storage applications. Few e~perimentall-~ and t h e o r e t i ~ a lstudies ~ , ~ on the hydrogen chemisorption on zirconium have been reported, although a lot of investigators have studied chemisorption of hydrogen on transition-metal surfaces experimentally and theoretically.6 Naito, one of the present authors, has measured the absorption rate of hydrogen by polycrystalline a-zirconium and has determined some kinetic parameters for the adsorption of hydrogen on ~ i r c o n i u m .It~ has been found that the adsorption energy of hydrogen on zirconium is -2.84 eV, the adatom at the surface site is more tightly bound by 0.06 eV than the atom a t the subsurface site, the activation energy of the dissociative adsorption is 0.02 eV, and the activation energy of the diffusion in the bulk is 0.475 eV. The chemisorption energies of hydrogen on transition metals have been obtained by the use of some theoretical models, e.g., Newns-Anderson models, cluster models, effective medium models, and slab models based on a b initio self-consistent band calculations.6 Nordlander et al. calculated the heat of hydrogen chemisorption and absorption of all the 3d, 4d,5d transition metals by using the effective medium theory and showed good agreement with the experimental result^.^*^ The chemisorption sites, bond lengths, vibrational frequencies, and surface diffusion energies for the hydrogen-Ni(lll), -Ni(llO), -W(lOO), and -W(110) systems were also evaluated and were in good agreement with experiments. They evaluated the chemisorption energy of hydrogen on zirconium as 3.0-3.2 eV. However, the specification of the chemisorption site of hydrogen on zirconium and the variation of the potential along absorption paths have not reported. In this study we have calculated the hydrogen chemisorption potential along absorption paths by using the effective medium theory, and the chemisorption potential and the hydrogen vibrational energy have been compared with the experimental results. Metbod We have calculated the hydrogen chemisorption energy by considering the following three contribution^:^*^,^ 1. Interaction between Hydrogen Atom and Electron Cas. The valence electrons of the metal are regarded as an inhomogeneous electron gas. The interaction energy between the hydrogen atom and the electron gas is given by Nsrskov as a function of the electron density.’ The interaction energy of this contribution is the greatest in the three contributions considered here. The interaction energy has a minimum -2.45 eV at the electron density 0.01 a c 3 and increases with the density because of the kinetic energy repulsion. whom correspondence should be addressed. ’*To Prescnt address: Department of Industrial Chemistry, Faculty of Engi-
neering, Chubu University, Kasugai, Aichi 487, Japan.
2. Interaction between Hydrogen Atom and Core Electrons of the Metal. When the hydrogen atom is located at a near position of the substrate atom, the strong repulsive interaction between the atoms becomes significant due to a wave function overlapping. In this study we approximate this interaction energy as the kinetic energy repulsion. By addition of the full core electron density to the valence electron density, the interaction energies of hydrogen with the core and the valence electrons are calculated simultaneously in the following way. The interaction energy between the hydrogen atom and the substrate electron gas can be written as U(r) = U[e(r)]
(1)
where A(r) is the weighted average of the electron density n(r) of the metal substrate with a hydrogen-induced potential vH(r) of electron. n(r) = i d r ‘ n(r’) uH(r’- r ) / i d r ‘ vH(r’)
(2)
The average has been taken over a sphere of radius 2.5 au around the hydrogen atom. uH(r) is chosen as the hydrogen atomic potentiala7 The electron density of the metal substrate is approximated to be a superposition of the atomic electron density. (3) The atomic density of zirconium is calculated self-consistently using a modified Herman-Skillman computer program.* The Perdew-Zunger local density approximation for the electron exchange and correlation was used.9 Latter’s modification for the electron is not carried out in our numerical calculation.I0 The configuration of the valence electron of hcp zirconium metal is chosen as 4d35sl, which was shown to be agreement with the configuration determined by the Compton-scattering measurement.lI The contour plot of the electron density of the Zr(0001) surface was shown previously.l* 3. Hybridization between the Hydrogen 1s Level and tbe d Electrons of the Substrate. When the hydrogen 1s level hybridizes with the valence d band, the 1s level shifts downward and makes ( I ) Veal, B. W.; Lam, D. J.; Westlake, D. G. Phys. Reu. B 1979, 19,2856. (2) Tapping, R. L. J . Nucl. Mater. 1982, 107, 151. (3) Naito, S. J . Chem. Phys. 1983, 79, 3113. (4) Nordlander, P.; Holloway, S.; Nsrskov, J. K. Surf. Sci. 1984, 136, 59. (5) Nordlander, P.; Nsrskov, J . K.; Basenbacher, F. J . Phys. F 1986, 16,
1161. (6) Christmann, K . Surf. Sci. Rep. 1988, 9, I . (7) Nsrskov, J. K. Phys. Reo. E 1982, 26, 2875. (8) Herman, F.; Skillman, S.Atomic Structure Calculation; Prentice-Hall: New York, 1963. (9) Perdew, J . P.; Zunger, A. Phys. Reo. E 1981, 23, 5048. (IO) Slater, J. C. The Calculation of Molecular Orbitals; Wiley: New York. 1979. (11) Sharma, B. K.; Ahuja, B. L. Phys. Reu. E 1980, 21, 3148. (12) Maeno, Y.; Yamamoto, M.; Naito, S.; Mabuchi, M.; Hashino, T. J . Chem. Soc., Faraday Trans. 1991, 87, 1399.
0022-3654/92/2096-3409$03.00/00 1992 American Chemical Society
3410 The Journal of Physical Chemistry, Vol. 96, No. 8, 1992
Yamamoto et al.
I -4.06
I
-2.43
I
I
1
0.00
2.43
4.86
D I S T W E FRMl THE SURFACE
U
Figure 1. Adsorption and absorption path of hydrogen atom on Zr(0001) surface. Along path 1 (2) hydrogen atom adsorbs the overlayer hcp (fee) site above the tetrahedral (octahedral) site and incorporatesto the subsurface T (0)site.
(a")
Figure 2. Calculated hydrogen potential along path I, Le., from vacuum to the subsurface T site. Positive values of the distance from the surface z > 0 indicate the interior of the metal. The open squares are the calculated points and the solid line is a guide for eye.
a bonding state. If we assume that the energy difference between the 1s level and the d-band center is much larger than the d-band width, the hybridization energy is given by the perturbation theory' wherefis the degree of filling of the d band (f= 0.25 in the case of ~irconium),~ Vd is the ls-d hopping matrix element, C, is the d-band center (-2.2 eV from the v a c u ~ m ) , land ~ ' ~E, is the energy of the 1s level of the hydrogen adatom. We have approximated that the level E,(r) in the region far from the surface (>4.1 au from the surface) is shifted upward by the image potential and follows the potential of the substrate in the near region from the surface.I6 The energy level a t the distance --m from the surface may lie at the first ionization level I . (N~rrskovcalculated this energy to be 13.4 eV.)" This level and the H- level which lies amount 4-A higher in energy than the level I ( + , work function of metal; A, affinity level of hydrogen) are shifted upward and downward by the image potential, respectively.16 Both the levels cross each other a t the distance 4.1 au from the surface if the image plane is coincident with the surface. The potential followed by the level E,(r) in the near surface region (
