Analysis of the Diffusion in a Multilayer Structure under a Constant Heating Rate: The Calculation of Activation Energy from the In Situ Neutron Reflectometry Measurement

Understanding mass transport in micro- and nanostructures is of paramount importance in improving the performance and reliability of the micro- and nanostructures. In this work, we solve the diffusion problem in a multilayer structure with periodic conditions under a constant heating rate via a Fourier series. Analytical relation is established between the coefficients of eigenfunctions and the intensity of X-ray or neutron Bragg peak. The logarithm of temporal variation of the intensity of X-ray or neutron Bragg peak is a linear function of the nominal diffusion time, with the nominal diffusion time being dependent on the heating rate. This linear relation is validated by experimental data. The Taylor series expansion of the linear relation to the first order of the diffusion time yields an approximately linear relation between the logarithm of temporal variation of the intensity of X-ray or neutron peak and the diffusion time for small diffusion times, which can be likely used to calculate the activation energy for the diffusion in a multilayer structure. The validation of such an approach is subjected to the fact that the characteristic time for heat conduction is much less than the characteristic time for the ramp heating as well as the characteristic time for diffusion.

Tracer diffusion in proton-exchanged congruent LiNbO3 crystals as a function of hydrogen content

The proton-exchange process is an effective method of fabricating low-loss waveguides based on LiNbO₃ crystals. During proton-exchange, lithium is replaced by hydrogen and Li_1-xH_xNbO₃ is formed. Currently, mechanisms and kinetics of the proton-exchange process are unclear, primarily due to a lack in reliable tracer diffusion data. We studied lithium and hydrogen tracer diffusion in proton-exchanged congruent LiNbO₃ single crystals in the temperature range between 130-230 °C. Proton-exchange was done in benzoic acid with 0, 1, 2, or 3.6 mol% lithium benzoate added, resulting in micrometre thick surface layers where Li is substituted by H with relative fractions between x = 0.45 and 0.85 as determined by Nuclear Reaction Analysis. For the diffusion experiments, ion-beam sputtered isotope enriched ⁶LiNbO₃ was used as a Li tracer source and deuterated benzoic acid as a H tracer source. Isotope depth profile analysis was carried out by secondary ion mass spectrometry. From the experimental results, effective diffusivities governing the lithium/hydrogen exchange as well as individual hydrogen and lithium tracer diffusivities are extracted. All three types of diffusivities can be described by the Arrhenius law with an activation enthalpy of about 1.0-1.2 eV and increase as a function of hydrogen content nearly independent of temperature. The effective diffusivities and the lithium tracer diffusivities are identical within a factor of two to five, while the hydrogen diffusivities are higher by three orders of magnitude. The results show that the diffusion of Li is the rate determining step governing the proton-exchange process. Exponential dependencies between diffusivities and hydrogen concentrations are determined. The observed increase of Li tracer diffusivities and effective diffusivities as a function of hydrogen concentration is attributed to a continuous reduction of the migration enthalpy of diffusion by a maximum factor of about 0.2 eV. Simulations based on the determined diffusivities can reproduce the step-like profile of hydrogen penetration during proton-exchange.

Slow Lithium Transport in Metal Oxides on the Nanoscale

This article reports on Li self-diffusion in lithium containing metal oxide compounds. Case studies on LiNbO3, Li3NbO4, LiTaO3, LiAlO2, and LiGaO2 are presented. The focus is on slow diffusion processes on the nanometer scale investigated by macroscopic tracer methods (secondary ion mass spectrometry, neutron reflectometry) and microscopic methods (nuclear magnetic resonance spectroscopy, conductivity spectroscopy) in comparison. Special focus is on the influence of structural disorder on diffusion.

Influence of defects and domain walls on dielectric and mechanical resonances in LiNbO3

Monodomain and periodically poled LiNbO3 crystals (congruent composition) show dielectric and piezoelectric resonances between 100 K and 900 K. Dielectric measurements show resonances in some samples between 10-100 kHz. These resonances vanish under thermal anneal in monodomain crystals while they remain stable in periodically poled samples with high domain wall densities. The low activation energy of 0.18 eV suggests their electronic (bi-polaronic) origin. Resonant piezoelectric spectroscopy, RPS, shows two features in virgin samples: a relaxation peak at 420 K and a rapid hardening when the sample was slowly heated to ~500 K. The dynamic relaxation and the hardening are related to excitations and reorientations of Li defects. The relaxations and hardening are irreversibly suppressed by high temperature anneal. We do not observe domain wall related RPS resonances in annealed samples, which excludes the existence of highly charged walls. We suggest that domain walls stabilize polaronic states with (bi-)polarons located inside or near to the ferroelectric domain walls.