(247c) Study of Tritium Solubility and Diffusivity in Lithium Aluminate and Lithium Zirconate Pellets in Tpbar Using First Principle Density Functional Theory

Study of Tritium Solubility and
Diffusivity in Lithium Aluminate and Lithium Zirconate Pellets in TPBAR Using
First Principle Density Functional Theory

Hari P. Paudel, Yueh-Lin Lee, Yuhua Duan

National
Energy Technology Laboratory, United States Department of Energy, Pittsburgh,
Pennsylvania 15236, USA

Abstract

The ceramic
materials γ-LiAlO₂ and Li₂ZrO₃ have
superior thermo-physical and thermo-chemical properties, and are highly
compatible with other blanket materials being used in the form of annular
pellets in tritium-producing burnable absorber rods (TPBARs) to produce tritium
(³H or T) by thermal
neutron irradiation of ⁶Li. These materials have an
excellent irradiation behavior at high temperatures, and are better swelling
resistant than many other Li rich materials.^1-3 However, the transport
mechanism of ³H through the ceramic pellets and the barrier is
hampered by the lack of data such as the diffusivity and solubility of hydrogen
isotope. The study of Li diffusivity in Li containing ceramics, such as γ-LiAlO₂
and Li₂ZrO₃, has also been a subject of interest in
Li-ion battery and solid oxide fuel cells. One of the powerful experimental
techniques to understand atomic diffusion in crystals is nuclear magnetic
resonance (NMR) measurement that probes the ion dynamics as a function of
temperature. With the known value of spin-lattice relaxation rate from NMR
measurements, it is possible to calculate the ionic jump rate (τ^-1)
that allows us to further calculate diffusion coefficients using the
Einstein−Smoluchowski equation.⁴ In the past, by using NMR and dc
conductivity measurements in γ- LiAlO₂, it was found that the
Li diffusion coefficient is in the range of 10^-20 to 10^-13
m²/s in temperature range of 400 K to 1000 K.⁵ In the same experiment, Li activation
energy was found to vary between 0.74 to 1.14 eV. Okuno and Kudo experimentally studied tritium diffusion
and recovery processes in ceramic breeders irradiated with neutrons.⁶ Their study revealed that the tritium
produced in the ceramic materials (Li₂O, γ-LiAlO₂,
Li₂SiO₃, Li₄SiO₄, Li₂ZrO₃,
Li₈ZrO₆) irradiated with neutrons was released mainly in
the chemical form of tritiated water (HTO) when heated in vacuum.

Despite
several experimental and theoritical efforts aforementioned here on Li ion
dynamics, roles of interaction between ³H and vacancies
on diffucivity, and its release behavior, and diffision mechanism of ³H in
pristine and radiation damaged crystal of LiAlO₂ and Li₂ZrO₃. After
recoil of ³H by
losing several hundreds of eV in neclear reaction, ³H remains
as an impurity in the material. In addition to that, higly energetic alpha
particles produced during the nuclear reaction process, sweep through the
materials and can create vacancies and interstitial ions. These vacancies and
interstitial ions can interact with a ³H, resulting a significant change
in ³H diffusion and release behavior than expected. As
a matter of fact, it is still an open question that which mechanism best
describes the activation energy barrier of ³H measured in the NMR
experiments.⁷

In order
to identify the mechanisms associated with atomic ³H formation,
diffusion, transport, deposition, and the kinetics in TPBAR pellets, in this study,
we present the results of first-principles density functional theory (DFT)
calculations of interstitial and substitutional ³H defects,
hydroxide (OT) vacancy defects, interaction of ³H with O-vacancies
in ceramics γ-LiAlO₂ and Li₂ZrO₃, and
provide an understanding of how such defects hamper the diffusivity and
solubility of ³H.^7-8 This study focuses on the diffusion of ³H
and its species (such as OT^-, T₂, T₂O) in bulk
γ-LiAlO₂ and Li₂ZrO₃ in presence of Li
and O defects. In particular, we focus on the diffusion of substitutional and
interstitial ³H, its species (such as T₂O) and Li
diffusion pathways in pristine and defective γ-LiAlO₂ and Li₂ZrO₃
crystal. We examine possible activation energy barrier of ³H
by computing several diffusion pathways. Our results show that the smallest
activation energy barrier corresponds to the substitutional ³H
diffusion with barrier height of 0.63 eV in LiAlO₂ and 0.30 eV in Li₂ZrO₃
as shown in the following figures a and b. The reported
experimental value of activation energy barrier for ³H in LiAlO₂
is 0.93 eV.⁶ The smallest OT diffusion barrier is
found to be 2.17 eV in LiAlO₂ and that of 1.05 eV in Li₂ZrO₃
crystal. DFT results are more accurate at 0 K with experimental results
obtained at low temperature. At elevated temperature, diffusion coefficient is expected
to deviate due to contribution from the entropy term. However, temperature
dependence of enthalpy and entropy is shown to be nearly cancelled out to each
other.⁹ In addition to that due to inherent
limitation in correlation treatment with DFT, there could still be error while
obtaining the diffusion barriers by subtracting transition image energy from
the final state energy. Nevertheless, our results for diffusion barriers and
diffusion coefficients in the ceramics γ-LiAlO₂ and Li₂ZrO₃
provide good estimates, and understanding of main diffusion mechanisms that
exist in defectives and pristine pellets.

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