Open-system elasticity: experimental verification of the Larché-Cahn theory and application in functional materials with switcheable stiffness
Thermodynamics and Kinetics as well as Properties of Phases and Microstructure of Materials
Final Report Abstract
Many material phenomena are critically determined by the interaction between chemistry and mechanics. The general formulation of a theory for this interaction goes back to a groundbreaking work on the elasticity of open systems by Francis Larché and John W Cahn in the 1970s. A central conclusion of the theory is that the coupled chemo-elastic equilibrium in the small strain limit can be reduced to a classical problem of continuum mechanics if the classical elastic constants for fixed composition in Hooke's law are replaced by new elastic parameters of open systems. These parameters include the information about the interaction between the chemical composition and the mechanical stress in thermodynamic equilibrium at constant chemical potential. The Larché-Cahn theory is an explicit or implicit component of many modern modeling approaches in materials science; however, there is no direct experimental verification in the literature, and in particular the theory's predictions for the elastic parameters of open systems have not yet been verified in experiments. These parameters, however, can be highly interesting, since they can deviate strongly from those at constant concentration, since they are highly nonlinear in strain and concentration, and since their numerical values can also diverge at critical points in the miscibility gap of the alloy phase diagram. In view of the above, the research program in this project aimed to consolidate the experimental evidence for the theory and to apply it to the design of optimized functional materials. Nanoporous Pd-Pt should serve as the experimental basis, since at room temperature, continuous solubility for the highly mobile interstitial atom H and a rapid equilibration for the dissolution of hydrogen in exchange with H2 gas at controlled partial pressure or with protons at controlled effective chemical potential are possible here. In addition, it should be demonstrated that in nanoporous Pd – a material with a miscibility gap at room temperature – the phase transition between the dilute and concentrated metal hydride can be excited by mechanical load. The preparation of the nanoporous Pd-Pt proved to be unexpectedly challenging; however, reproducibly successful protocols have now been established and the material characterized. With regard to the properties as functional materials, the incorporation of the mobile impurity H enabled the modulus of elasticity to be switched by up to a factor of three. The relationship between elasticity and hydrogen content follows the theory prediction well over the entire concentration range. The mechanical excitation of the phase transition has not yet been demonstrated. A theory of the elastic behavior for the open system in the entire concentration interval has been published. In a further publication, it was shown that metal hydrides or battery electrodes as energy storage materials – another example of functional materials with mobile impurities – are directly and decisively influenced by the elasticity of open systems in key characteristics. In particular, the theory of open-system elasticity offers a qualitatively new approach to understanding and predicting coherent phase transitions, which are crucial for the behavior of the storage material during charging and discharging cycles.
