MANTENIMIENTO

As the normalized atomic density ρT GA

a is identical to the atomic fraction measured by

the TGAαT GA

r the recombination probability per wall collisionhbiγr can be obtained by

eq. 2.45: hb_iγr = 1 αT GA r −1, (5.13) 76

The ground state is then identical to the completely bound state.

77_{In case of the measurement of fig. 5.2 (left graphs), a low temperature behavior of the form of eq. 5.12 fits}

the data as well. The prefactor is of course different and one obtains for the exponent 223.6 ±2.5K instead of 271±2K. 0.4 0.5 0.6 0.7 0.8 0.9 1 102 T/K αr TGA 119.8 / 20 P1 1.391 P2 -366.1 P3 0.7967E-03 P4 271.3 0.4 0.5 0.6 0.7 0.8 0.9 1 102 T/K αr TGA 177.4 / 17 P1 0.3974E-06 P2 462.7 P3 0.1784E-01 10-2 10-1 1 10 1 2 3 100K/T < b >γ 117.2 / 20 P1 1.393 P2 -3.670 P3 0.8003E-03 P4 2.711 10-2 10-1 1 10 1 2 3 100K/T < b >γ 167.1 / 17 P1 0.5668E-06 P2 4.507 P3 0.1704E-01

Fig. 5.2: Measured atomic frac- tion αT GA_r (upper figures) and scaled recombination probabili- ty (lower graphs) versus storage cell temperature for a fresh Dri- film coated surface (left figures) and a aged surface (right figu- res), which was exposed for so- me weeks to the HERA beam. The measurements were perfor- med with hydrogen. The inlets show the resulting parameters of a fit with eq. 5.14. For the left graph, one hasT1= 271.1Kand T2 = 367K, in the right graph one obtains onlyT2= 450.7K.

5.3 The Temperature Dependence of Recombination 59

Fig. 5.2 shows the measured behavior of the atomic fraction αT GA

r as a function of the

storage cell temperature (upper graphs) and an Arrhenius plot of the derived value of hb_iγr in the lower graphs for a fresh Drifilm coated surface (left plots) and for an aged

Drifilm surface after a longer time of operation under HERMES running conditions (right plots). The temperature dependence of the recombination probability γr(T) was fitted

with the following function:

γr(T) =k1exp (T1/T) +k2exp (−T2/T) . (5.14) The temperature model matches the data reasonably well. The fact, that γr has to be

described by a sum of two exponentials indicates, that (at least) two different processes are involved in recombination. The second term on the right side of eq. 5.14 has likely to be interpreted as reactions with chemically bond atoms, as the value of T2 represents an activation barrier. Only atoms with a thermal energy above kbT2 are able to react with the surface atoms. The process, which is represented by the first term on the right side of eq. 5.14 can be interpreted by reactions with physisorbed atoms [Ko 98]. The increase of γr at low temperatures is then caused by the sticking time of the physisorbed

atoms on the surface - following the Arrhenius law k1exp (T1/T) - while the increase at high temperatures results from an activation barrier for reactions with atoms, which are chemically bound to the surface, resulting in a term k2exp (−T2/T).

5.3.1 High Temperature Behavior of Recombination

Even though the bond strength of a hydrogen atom with Drifilm (H₋CH2SiO3) is not precisely known, it can assumed to be close to the bond strength of the chemically similar

H₋CH2Si(CH3)3, which is 415.1kJ/mol [Lid 98]. This is just below the bond strength of a hydrogen molecule H₋H, which is 435.99kJ/mol 78_{. Recombination of a hydrogen} atom of the gas phase with a hydrogen atom, which is chemically bound to a CH3-group of the Drifilm coating, is therefore likely an exothermic process79. As shown in fig. 5.2, the recombination probability increases exponentially with the inverse temperature for temperatures above 120K, indicating a thermally activated reaction80.

Koleske and Gates [Kol 94] obtained similar results for the reaction between gaseous atomic hydrogen and deuterium, which was chemisorbed on a single crystal silicon surface and vice versa. Their results showed only little dependence of the reaction rate on the surface temperature. They concluded, that the impinging atoms do not thermalize with the surface in advance to the reaction, which indicates reactions of the E-R type. The re- action rate however had a measurable dependence on the energy of the impinging atoms - indicating an activation energyEa (as illustrated in fig. 5.3) of about 48meV for abstrac-

tion of chemisorbed hydrogen by deuterium atoms and about 25meV for chemisorbed deuterium abstracted by gaseous atomic hydrogen. Similar results have - for example - been observed for hydrogen chemisorbed on Ni(110) [Eil 96], on Ni(100) [Kam 95], on Ru(001) [Jac 94] and on Al(100) [Boh 98]. Theoretical calculations of the isotope effect have been performed by Kratzer and Brenig [Kra 96].

78

1kJ/mol = 0.010364eV /molecule

79_{Of course, one has to take other contributions of the binding into account, as the heat of condensation of}

the Drifilm coating etc. The total energy balance is not precisely known and likely differs from site to site on the surface.

80

The missing hydrogen atom in the methyl group can assumed to be replaced soon by an impinging hydogen atom.

-125 -100 -75 -50 -25 0 25 50 75 1.5 2 2.5 3 3.5 4 4.5 5 z/Å U(z)/meV E_b E_a H₁ H₂ E_kin A B C D E F G

Fig. 5.3: Surface potential scheme for reactions with the surface. The curve DEF represents the physisorption po- tential for atoms as in fig. 5.1. The curve ABGEF is the potential energy curve, if the possibility of chemical reacti- ons with the H/D atoms of the Methyl groups of Drifilm are taken into account. The curve ABC represents the potential energy for molecules after the reaction.Ea is the activation

energy for E-R reactions with atoms impinging from the gas phase of thermal energy E > Ea. Physisorbed atoms,

that are sticking at position E, may enter the second poten- tial minimum and thus react with the surface by tunneling as indicated by the arrow. The desorbing molecule has an average additional energyEkinby the exothermic reaction,

indicated by a lowered energy base line at₋75meV.

In case of the HERMES storage cell, the kinetic energy of the impinging atoms is determined by the surface temperature81_{. The measurement of fig. 5.2 results an activation} energy of T2 =Ea/kb = 367K for hydrogen abstraction on Drifilm by atomic hydrogen,

corresponding to 31.6meV and of about 786K, corresponding to 68meV, for deuterium as shown by fig. 5.4. These values are close to the results of Koleske and Gates, which may be considered as a consequence of the similar covalent binding between hydrogen and silicon in one case and hydrogen with carbon in Drifilm in the other case. If one assumes, that the mechanism is the same, then the activation energies depends on the type (or mass) of the impinging atom and not on the type of the abstracted atom. The fact, that the activation energies are higher in case of a Drifilm coated surface compared to a silicon surface, can be explained by the higher bond strength with the carbon of Drifilm compared to Si. The beam rates of mass 3 (HD) and mass 4 (D2) shown in fig. 5.5, measured during the first exposure of a new storage cell, are in good agreement with this interpretation.