Due to the inherent complexity of the task and the vast configuration space, as well as experimental and real-world limitations, however, material design and discovery based on experiments alone is extremely difficult and time-consuming. With the advent of the scientific method, however, such discovery has been based increasingly on hypothesis-guided experimentation. In past ages, material design and discovery have relied on trial and error methods. The deformation behavior of planetary crusts 11 or that of polar ice caps leading to calving 12, 13 are specific examples of much larger-scale material behavior where multiple physical processes and lengthscales come together. Multi-scale and multi-physics phenomena are not limited to microscopic and macroscopic lengthscales. These are often in form of configurational defects in the solid structure and therefore, non-conservative. Note that although the spatial distribution of composition, depending on lengthscale, can be regarded as a type of microstructure, in this work, the microstructure is defined as structural variations at small scales. microstructure) for optimal materials, process, and performance design. This opens up a theory-based design pathway into a competition between the exploitation of conserved parameters (e.g. Improved models that consider both composition and microstructure can be employed to investigate the trade-off between these in the optimization of material properties. Superalloys 8, modern Al alloys 9, and semiconductors 10, are examples of such systems. Most of the current technologically important materials have therefore complex chemical compositions and carefully designed microstructures, however, often with high costs for expensive alloy ingredients and reduced compatibility when subject to recycling. This trend is observed in generations of alloys, where typically the number of alloying elements has increased in the quest to improve material properties and behavior. A complex system (either in terms of composition or microstructure) has a higher potential for exhibiting interesting, unusual, and surprising behavior compared to a simple system. The number of microstructural and compositional parameters, processes, and configurations to combine to invent a new material is enormous. Ni-based superalloys are another example where carefully tuned chemical composition and processing results in a complex microstructure which ultimately gives rise to the high performance of these alloys at elevated temperatures 7. There are numerous other examples where inelastic deformation features and damage are initiated or accelerated due to harsh environmental conditions such as hydrogen embrittlement 4, stress corrosion cracking 5, and radiation-inflicted damage 6. The interplay of chemistry and mechanical failure, for example, is important for the longevity of rechargeable batteries 2, 3 microscopic cracks which form over time as the electrodes are mechanically deformed during load cycles result in electrical disconnections and loss of capacity. Designing improved materials requires an in-depth understanding of several intertwined metastable configurations and intertwined, hierarchical and self-organized networks of defects that influence each other through various interactions across multiple lengths- and timescales 1. The diversity and complexity of materials and their behavior are rooted in the complex, generally nonlinear interplay between microstructural features such as voids, cracks, phases, grains, dislocations, and local chemical composition with each other and with environmental conditions.
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