Open-system elasticity: experimental verification of the Larché-Cahn theory and application in functional materials with switcheable stiffness

许多物质现象是由化学和力学之间的耦合所支配的。20世纪70年代，弗朗西斯·拉奇和约翰·W·卡恩关于开放系统弹性的开创性工作揭示了材料中这种耦合作用的一般理论。作为该理论的一个核心结论，只要用新的开放系统弹性参数代替胡克定律恒定组成的经典弹性常数，小应变极限下的化学-机械耦合平衡就可以投射到连续介质力学的经典问题上。这些参数包含了在热力学平衡和恒定化学势的情况下，组成和应力之间相互作用的信息。无论是明确的还是含蓄的，Larché-Cahn理论都包含在许多现代材料建模方法中。然而，还没有发表直接的实验验证。具体地说，开放系统弹性参数的理论预测尚未得到实验验证。根据理论，这些参数可能非常有趣，因为它们在恒定组成时可以强烈偏离经典的弹性常数，因为它们在应变和浓度方面是高度非线性的，而且在合金相图中混溶间隙的临界点上，这些数值可能会发散。考虑到上述陈述，拟议的研究追求以下两个目标：首先，使用一个模型合金，我们的目的是通过实验确定开放系统弹性参数作为组成的函数来验证Laché和Cahn的理论。其次，我们的目标是展示一种材料设计，它利用该理论的结果来实现-第一次-在很大范围内弹性刚度的可调性。理想的情况是，可以可逆地将硬度几乎一直切换到零，然后再回到纯金属的值。作为一种新颖的方法，我们建议使用纳米孔钯作为模型材料。外部载荷会在定义微结构的纳米级支柱上产生弯矩。Pd晶格中的氢在几毫秒内重新分布在支柱的拉伸纤维和压缩纤维之间。动态力学分析将用于测量有效的宏观杨氏模数，而电化学电位控制将提供快速、精确和可逆的氢含量控制。

Many materials phenomena are governed by the coupling between chemistry and mechanics. The general theory of the action of that coupling in materials was exposed in the 1970s through the seminal work by Francis Larché and John W Cahn on the elasticity of open systems. As a central conclusion of that theory, the coupled chemo-mechanical equilibrium in the limit of small strain can be projected onto a classic problem of continuum mechanics, provided that the classic elastic constants for constant composition of Hooke’s law are replaced by new, open system elastic parameters. These parameters contain the information on the interaction between composition and stress at thermodynamic equilibrium and subject to constant chemical potential. Explicitly or implicitly, the Larché-Cahn theory is contained in many modern approaches at materials modeling. Yet, no direct experimental verification has been published. Specifically, the theory predictions for the elastic parameters of open systems have not been verified by experiment. These parameters can – according to the theory – be highly interesting because they can deviate strongly from the classic elastic constants at constant composition, because they are highly nonlinear in strain and concentration, and because there numerical values can diverge at critical points of the miscibility gap in alloy phase diagrams.With an eye on the above statements, the proposed research pursues the following twofold aim: Firstly, using a model alloy, we aim at verifying the theory of Larché and Cahn through experimental determination of the open system elastic parameters as the function of the composition. Secondly, we aim to demonstrate a materials design which exploits the results of the theory for achieving – for first time – operando tuneability of elastic stiffness in a wide interval. Ideally, it should be possible to reversibly switch the stiffness almost all the way to zero and back to the pure-metal value.As an original approach, we propose to use nanoporous palladium as the model material. External load induces bending moments on the nanoscale struts that define the microstructure. Hydrogen in the Pd crystal lattice redistributes within milliseconds between the tensile and compressive fiber of the struts. Dynamic mechanical analysis will be used for measuring the effective, macroscopic Young’s modulus, and electrochemical potential control affords fast, precise and reversible control over the hydrogen content.