It is not sufficient to eliminate one or two of these weak links because all it takes is one of them to cause brittle fracture. Any one of multiple factors can result in brittleness, including complex crystal structure, insufficient number of slip systems, low mobile-dislocation density, high stress to move dislocations, weak grain boundaries, harmful segregants, lack of sustained strain hardening (or worse, strain softening), porosity, and cracks. Consider the case of fracture which is a “weakest-link” phenomenon. Second, even if we suppose that only a single property is a critical requirement, that property may nevertheless be affected by multiple factors, none of which can exhibit deficiencies, or failure will occur. An alloy that has sufficient strength but is too expensive is unlikely to be practical in most cases. For example, in structural applications, strength, toughness, ductility, density, corrosion resistance, and cost are just some of the factors that may have to be simultaneously optimal. First, it is rare for just one property to be a critical requirement rather, an optimal balance of several different properties is usually needed. Similar constraints bedevil the discovery, development, and deployment of new and useful materials. Not unlike happy families, therefore, successful domestication is foiled if even a single relevant factor is lacking. Take zebras and horses, for instance: they appear to be identical-except obviously for the stripes yet only one has been domesticated (for a variety of reasons). Diamond uses domestication of animals to demonstrate that, despite the large number of candidate animals, only a small fraction have been successfully domesticated. Briefly, the principle states that when success can be undermined by deficiencies in any one of multiple governing factors, the likelihood of failure increases dramatically. However, as one of us has on occasion pointed out, 5 the so-called Anna Karenina principle-all happy families are alike each unhappy family is unhappy in its own way, popularized by Jared Diamond in his book Guns, Germs and Steel 6- should give us pause, or at least temper some of the prevailing unbridled optimism. This vast unexplored compositional space is assumed to contain rich veins of useful materials just waiting to be mined. One often-cited reason is the mind bogglingly large number of distinct compositions that can be created by combining multiple different elements together, 4 only a tiny fraction of which have been investigated. Additionally, for the sake of brevity and to avoid having to introduce various confusing nomenclatures, HEMs in this article include multiphase variants of these materials (i.e., we do not restrict ourselves to solid solutions). To be inclusive of all these different classes of materials, we use the term high-entropy materials (HEMs) here. In the future, it would not be surprising to witness similar growth in high-entropy polymeric and glassy materials. From 2015 onward, high-entropy ceramics (HECs) have entered the fray 3 and are garnering increasing interest. 1, 2 Variously referred to as high-entropy alloys (HEAs), compositionally complex alloys (CCAs), or multi-principal element alloys (MPEAs), the field has seen explosive growth recently, especially since 2013 judging by the number of published papers and citations in Web of Science and is now a “hot topic” in materials science. Alloys consisting of multiple elements in which no single element can be considered the principal (or base) element have been the focus of considerable research since 2004.
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