Diffusivity determination in bulk materials on nanometric length scales using neutron reflectometry

Abstract

An approach based on neutron reflectometry and isotope heterostructures is presented in order to determine self-diffusivities in bulk materials on small length scales of 1-10 nm. The method is demonstrated for lithium self-diffusion in LiNbO 3 single crystals at low temperatures of 200 and 250 • C using 6 LiNbO 3 (amorphous film)/ nat LiNbO 3 (single crystal) structures for analysis. Lithium diffusivities are derived from neutron reflectivity patterns in good agreement with results obtained by secondary ion mass spectrometry on the same type of samples but on larger length scales up to 90 nm, as given in literature. In addition, neutron reflectivity simulations were performed in order to investigate the influence of diffusion length and scattering length density on the quality of the results. The limitation of the method is discussed.

Slow Lithium Transport in Metal Oxides on the Nanoscale

“…The dc plateau The space coordinate is set to zero at the film/crystal interface. The diffusion length of the annealed sample is 2.5 nm (for details see also [28]). …”

“…Due to the complexity of the analysis and for a deepened understanding it is referred to Ref. [28] for further reading. The NR method described allows to determine diffusion lengths in the range between 1 and 10 nm, i.e.…”

“…We investigated Li self-diffusion in congruent single crystals (48.6 % Li 2 O) close to room temperature between 379 and 523 K by NR [27,28], between 423 and 773 K by SIMS [34] and between 473 and 1073 K by impedance spectroscopy [37] (conversion of conductivity by the Nernst Einstein equation). SAE-NMR measurements were not possible due to the very low ionic mobility.…”

“…The differences in the two patterns are clearly visible. In order to derive diffusivities, the reflectivity patterns were computer modeled and least-squares fitted by the parratt32 [36] software tool [28]. This results in a scattering length density (SLD) profile based on a layer model as shown in Figure 2b.…”

“…Literature work is mainly on the investigation of selfdiffusion in thin metallic, semiconducting and ceramic films in form of isotope multilayers [1,[22][23][24][25][26]. One of the main achievements of the present work was to implement an improvement of the classical multilayer technique [27,28], where self-diffusion in bulk materials was measured by NR for the first time and to transfer the method to the application to lithium.…”