Abstract：When the size of a particle is reduced then the excess free energy due to the surface and to internal interfaces diminishes more slowly than the free energies of the bulk phases. In transformations where the area of the interfaces or the crystallography of the phases varies, the interfacial excess will therefore affect the equilibrium at small system size. This is the origin of the well-explored phenomenology of size-dependent melting in nanoparticles. Much less is known about the size-dependent shifts in the chemical equilibrium arising from the interface energy or from elastic interactions between interfaces, and the bulk. These effects can be important even when the (referential) area and the crystallography of the interfaces are invariant, for instance when a solid solution is equilibrated with a reservoir of solute at controlled chemical potential. Here, changes in the local composition give rise to forces at surfaces, which must be balanced by stress in the bulk. The associated changes in the pressure can reach values of several GPa, resulting in reversible deformation that can be visible to the naked eye, and in a Clausius-Clapeyron type shift in the chemical potential as well as a change in the apparent solute-solute interaction energy. Metal hydrides provide ideal model systems for experimental studies of these phenomena, since hydrogen can be exchanged reversibly with the solid. General balance of force equations which apply to arbitrary microstructures can be derived, both for the local stress tensors at interfaces as well as for the mean stress in the bulk. By combining the analysis of simultaneous chemical and mechanical equilibrium with experimental data for nanoscale metal hydrogen systems, one can derive the value of the interface stress as a function of the local solute concentration or of the chemical potential, and one can measure the interfacial ‘stretch’, a normal mode of deformation. In agreement with experiment, the analysis suggests that the terminal solubilities and the critical temperature of the miscibility gap of nanoscale solid solutions with an attractive solute-solute interaction energy are strongly affected by the long range elastic interactions.

Brief CV：Joerg Weissmüller studied Materials Science at the Universities of Saarbrücken, Germany, and Dundee, Scotland. He holds a PhD in Engineering, also from Saarbrücken. Weissmüller has worked as a Postdoctoral Fellow at the National Institute of Standards and Technology in Gaithersburg, MD, USA and at the Institute of New Materials in Saarbrücken. Presently he is a staff scientist and group leader at the Institute of Nanotechnology, a department of the new Karlsruhe Institute of Technology. He is also a Privatdozent in the Technical Physics Department of Saarbrücken University. He has been awarded the Feodor Lynen Fellowship and the Heisenberg Fellowship. Weissmüller’s research is focused on nanomaterials, with emphasis on thermodynamics and continuum mechanics of interfaces, phase transformations, magnetism, magnetic neutron scattering, and plastic deformation mechanisms. He is the author of about 90 publications in peer-reviewed journals, including Science, Physical Review Letters and Nano Letters, etc. He has given about 50 invited lectures, and holds several patents.