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Study of kinetics and thermodynamics in thin films at the limit between coherent and semi-coherent phasetransformation

Subject Area Thermodynamics and Kinetics as well as Properties of Phases and Microstructure of Materials
Term from 2013 to 2020
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 250278176
 
Final Report Year 2021

Final Report Abstract

The project addresses the complex interplay of the coherency state and mechanical stresses arising upon hydrogen absorption, for the model case of epitaxial Nb-H thin films adhered to sapphire substrates. Below a critical temperature TC, bulk Nb-H shows a first-order phase transition with a two-phase field separating a hydride phase and the solid solution. For Nb-H thin films, the lattice expansion accompanying hydrogen absorption and the films’ adherence to the (rigid) substrate result in mechanical stresses in the GPa range. These stresses contribute to the systems’ Gibbs Free Enthalpies and change the related phase stabilities. The stress state does not necessarily depend linearily on the hydrogen concentration cH, as it can change by plastic deformation. This, again, depends on the film thickness d where, at a critical thickness dC, a change in the lattice coherency between the two phases was expected. Hence, the project aimed at a comprehensive understanding of the film’s coherency state and its impact on thermodynamics and kinetics regarding the stability of the phases, phase boundaries as well as reversibility of the phase transformation. By combining in-situ STM, XRD, EMF and stress measurements results, we deduced two different critical film thicknesses dC for the suppression of hydrogen-related dislocation formation. Below dC,1 = 39 (2) nm Nb film thickness the hydrides stay coherently linked to the α-phase matrix while above this this value, the hydrides appear semi-coherently linked. Stress release happens via dislocation formation and mechanical stress reaches -2 to -4 GPa. Below dC,2 = 5 nm we even found absence of any hydrogen-related dislocations in the film and at the film-substrate interface. Below this thickness dC,2, the mechanical stress increases linearly upon hydrogen concentration yielding a maximum measured value of -8.1 GPa in the film. This measured value meets the maximum limit calculated by using the theory of linear elasticity on H-loaded Nb films. The film stress arises fully reversible upon H-unloading and second H-loading. The concentration width of the two-phase field was also found to depend on the film thickness d. EMF isotherms and XRD measurements on Nb-H films show a shrinkage of the miscibility gap with decreasing d. The isotherms show a sloping plateau as conventionally found only for samples measured above TC in single-phase regions. However, STM and XRD confirm the coexistence of two phases and, thus, two-phase region. We successfully developed a thermodynamic σ-model that bases on the measured EMF and on the measured stress curves. It gives the width of the two-phase region and a drop of TC. The model predicts TC < 294 K for films with d < 7.2 nm. This fairly matches the STM observation on 8 nm films, that did not show any two-phase coexistence and on 15 nm films, still revealing phase transition. A refined σDOS-model includes microstructural contributions. STM and XRD measurements show strong changes of the hydride formation mode at dC,1. For d > dC,1, large hydrides are detected. They grow in lateral, elastically soft directions of the Nb thin films. The hydride formation is growth dominated. Surprisingly, the kinetics is found to be slower than for films below dC,1 , that possess coherent phases. There, the hydride formation appears by nucleation of small hydrides. Faster kinetics might be explained by the nucleation as the dominant process. Unloading experiments show stress hysteresis for all samples excluding those without hydrogen-related dislocation formation (dC,2 = 5 nm). However, these samples do not show phase transformation (d < 8nm) at 294K, as well. Hence, the predictions of the model of Schwarz et al. on thermodynamic hysteresis in coherent systems could not be tested with the Nb-H films, at the available temperature. To study thermodynamics of fully coherent systems, measurements either at reduced temperature or on 3D confined systems are required. Unloading STM measurements reveal 1-2 nm left-over surface corrugations at the film surface. They are considered to act as hydride formation centers in subsequent cycles. To conclude, manifold changes in thermodynamics and kinetics have to be considered when system sizes are reduced. Vanishing two-phase regions limit hydrogen storage applications, and high-stress states allow destabilizing too stable hydrides.

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