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"Entropy"
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(Multiscale) Cross-Entropy Methods: A Review
Cross-entropy was introduced in 1996 to quantify the degree of asynchronism between two time series. In 2009, a multiscale cross-entropy measure was proposed to analyze the dynamical characteristics of the coupling behavior between two sequences on multiple scales. Since their introductions, many improvements and other methods have been developed. In this review we offer a state-of-the-art on cross-entropy measures and their multiscale approaches.
Journal Article
Tunable stacking fault energies by tailoring local chemical order in CrCoNi medium-entropy alloys
High-entropy alloys (HEAs) are an intriguing new class of metallic materials due to their unique mechanical behavior. Achieving a detailed understanding of structure–property relationships in these materials has been challenged by the compositional disorder that underlies their unique mechanical behavior. Accordingly, in this work, we employ first-principles calculations to investigate the nature of local chemical order and establish its relationship to the intrinsic and extrinsic stacking fault energy (SFE) in CrCoNi medium-entropy solid-solution alloys, whose combination of strength, ductility, and toughness properties approaches the best on record. We find that the average intrinsic and extrinsic SFE are both highly tunable, with values ranging from −43 to 30 mJ·m−2 and from −28 to 66 mJ·m−2, respectively, as the degree of local chemical order increases. The state of local ordering also strongly correlates with the energy difference between the face-centered cubic (fcc) and hexagonal close-packed (hcp) phases, which affects the occurrence of transformation-induced plasticity. This theoretical study demonstrates that chemical short-range order is thermodynamically favored in HEAs and can be tuned to affect the mechanical behavior of these alloys. It thus addresses the pressing need to establish robust processing–structure–property relationships to guide the science-based design of new HEAs with targeted mechanical behavior.
Journal Article
Entropy : a very short introduction
Entropy is an idea that is no less important than energy, but it is not widely understood. We are surrounded by free energy: what we value is energy that's not too polluted with entropy. This book explains how the concepts of energy and entropy were separated from one another over half a century.
BOOK
Short-range order and its impact on the CrCoNi medium-entropy alloy
Traditional metallic alloys are mixtures of elements in which the atoms of minority species tend to be distributed randomly if they are below their solubility limit, or to form secondary phases if they are above it. The concept of multiple-principal-element alloys has recently expanded this view, as these materials are single-phase solid solutions of generally equiatomic mixtures of metallic elements. This group of materials has received much interest owing to their enhanced mechanical properties
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. They are usually called medium-entropy alloys in ternary systems and high-entropy alloys in quaternary or quinary systems, alluding to their high degree of configurational entropy. However, the question has remained as to how random these solid solutions actually are, with the influence of short-range order being suggested in computational simulations but not seen experimentally
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. Here we report the observation, using energy-filtered transmission electron microscopy, of structural features attributable to short-range order in the CrCoNi medium-entropy alloy. Increasing amounts of such order give rise to both higher stacking-fault energy and hardness. These findings suggest that the degree of local ordering at the nanometre scale can be tailored through thermomechanical processing, providing a new avenue for tuning the mechanical properties of medium- and high-entropy alloys.
Metal alloys consisting of three or more major elemental components show enhanced mechanical properties, which are now shown to be correlated with short-range order observed with electron microscopy.
Journal Article
Permutation Entropy: New Ideas and Challenges
Over recent years, some new variants of Permutation entropy have been introduced and applied to EEG analysis, including a conditional variant and variants using some additional metric information or being based on entropies that are different from the Shannon entropy. In some situations, it is not completely clear what kind of information the new measures and their algorithmic implementations provide. We discuss the new developments and illustrate them for EEG data.
Journal Article