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

许多材料现象是由化学和力学之间的耦合所控制的。20世纪70年代，弗朗西斯·拉奇（Francis Larché）和约翰·W·卡恩（John W. Cahn）关于开放系统弹性的开创性工作揭示了材料中耦合作用的一般理论。作为该理论的一个中心结论，在小应变极限下的化学-力学耦合平衡可以被投影到连续介质力学的经典问题上，只要虎克定律的恒定组成的经典弹性常数被新的开放系统弹性参数所取代。这些参数包含在热力学平衡和恒定化学势下的组成和应力之间相互作用的信息。无论是明示还是暗示，Larché-Cahn理论都包含在许多现代材料建模方法中。然而，没有直接的实验验证已经公布。具体而言，开放系统的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，因为它们可能在恒定成分下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，并且因为它们的数值可能在合金相图中的相容性间隙的临界点处发散。着眼于上述陈述，拟议的研究追求以下双重目标：首先，利用模型合金，通过实验测定开放体系弹性参数随成分的变化，验证了Larché和Cahn的理论。其次，我们的目标是证明材料设计，利用理论的结果，实现-第一次-在一个很宽的区间内的弹性刚度的操作调谐。理想情况下，应该可以可逆地切换刚度几乎所有的方式为零，并返回到纯金属value.As一个原始的方法，我们建议使用纳米多孔钯作为模型材料。外部载荷在限定微结构的纳米级支柱上引起弯矩。Pd晶格中的氢在支柱的拉伸纤维和压缩纤维之间在毫秒内重新分布。动态力学分析将用于测量有效的宏观杨氏模量，并且电化学电势控制提供对氢含量的快速、精确和可逆的控制。

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.