111907-3
Borgschulte et al.
Appl. Phys. Lett. 94, 111907 ͑2009͒
This work was financially supported by the European
Commission ͓Contract Nos. MRTN-CT-2006-032474 ͑Hy-
drogen͒ and MRTN-CT-2006-032474 ͑COSY͔͒.

Ediff
ln
= −
+ C,
͑6͒
ͩ ͪ
T21/2
kT1/2
where C is a not further defined constant. The great advan-
tage of this method is its model independency. Errors from
geometry uncertainties, etc., do not enter Eq. ͑6͒. Figure 1
shows temperature programmed hydrogen deuterium ex-
change in NaH at various constant heating rates. From this,
the peak temperatures T21/2 are determined. T21/2/ is plotted
as a function of the reciprocal temperature in the bottom
panel of Fig. 1, a so-called Kissinger plot. From the slope an
activation energy of diffusion of Ediff=͑1.0Ϯ0.1͒ eV is de-
rived. For diffusion in stoichiometric hydrides, the probabil-
ity of finding a vacant site is as important as the barrier
height Ediff. In ionic crystals, charge fluctuations can accom-
pany vacancies, e.g., a hydrogen vacancy can be charged
neutral, i.e., V0H, or positively, respectively, negatively
charged ͑V+H, V−H͒. DFT calculations of hydrogen diffusion
in NaH give diffusion barrier heights of 0.94, 0.57, and 1.17
eV for V0H, VH+ , and V−H vacancies, respectively.4 The value of
1.0 eV and the absolute value of the diffusion parameter are
in excellent agreement with the calculated values of hydro-
gen diffusion via V0H vacancies and thus a corroboration of
this model.
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1997͒.
In conclusion, we have demonstrated the use of HD-
exchange experiments to derive the diffusion parameters of
deuterium in NaH. The measurements confirm recent DFT
calculations and thereby the hypothesis of hydrogen diffu-
sion mediated by charge neutral hydrogen vacancies in NaH.
13T. Akahira and T. Sunose, Transactions of the Joint Convention of Four
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155.33.120.209 On: Thu, 04 Dec 2014 06:30:19