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ABSTRACT Any thermodynamically stable or metastable phase corresponds to a local minimum of a potentially very complicated energy landscape. But however complex the crystal might be, this

energy landscape is of parabolic shape near its minima. Roughly speaking, the depth of this energy well with respect to some reference level determines the thermodynamic stability of the

system, and the steepness of the parabola near its minimum determines the system’s elastic properties. Although changing alloying elements and their concentrations in a given material to

enhance certain properties dates back to the Bronze Age1,2, the systematic search for desirable properties in metastable atomic configurations at a fixed stoichiometry is a very recent tool

in materials design3. Here we demonstrate, using first-principles studies of four binary alloy systems, that the elastic properties of face-centred-cubic intermetallic compounds obey certain

rules. We reach two conclusions based on calculations on a huge subset of the face-centred-cubic configuration space. First, the stiffness and the heat of formation are negatively

correlated with a nearly constant Spearman correlation4 for all concentrations. Second, the averaged stiffness of metastable configurations at a fixed concentration decays linearly with

their distance to the ground-state line (the phase diagram of an alloy at zero Kelvin). We hope that our methods will help to simplify the quest for new materials with optimal properties

from the vast configuration space available. Access through your institution Buy or subscribe This is a preview of subscription content, access via your institution ACCESS OPTIONS Access

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subscriptions * Read our FAQs * Contact customer support SIMILAR CONTENT BEING VIEWED BY OTHERS A MAP OF SINGLE-PHASE HIGH-ENTROPY ALLOYS Article Open access 19 May 2023 FIRST PRINCIPLES

COMPUTATION OF COMPOSITION DEPENDENT ELASTIC CONSTANTS OF OMEGA IN TITANIUM ALLOYS: IMPLICATIONS ON MECHANICAL BEHAVIOR Article Open access 07 June 2021 MULTIFUNCTIONAL HIGH-ENTROPY

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Chem._ 187, 211–218 (2012) Article  ADS  CAS  Google Scholar  Download references ACKNOWLEDGEMENTS Funding by the DFG (Deutsche Forschungsgemeinschaft) grant Mu1648/5 is acknowledged. We

also thank the RRZ-Hamburg super-computing site for a generous amount of computational time and E. Kahnert and her team for support and advice related to the computing facilities. Additional

computing resources from the German super-computing alliance HLRN are acknowledged. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Hamburg University of Technology, Institute of Advanced

Ceramics, Denickestraße 15, 21073 Hamburg, Germany, Sascha B. Maisel, Michaela Höfler & Stefan Müller Authors * Sascha B. Maisel View author publications You can also search for this

author inPubMed Google Scholar * Michaela Höfler View author publications You can also search for this author inPubMed Google Scholar * Stefan Müller View author publications You can also

search for this author inPubMed Google Scholar CONTRIBUTIONS S.B.M. performed the density functional theory calculations for the NiW, NiTa and CuAl alloys, and M.H. for the NiAl alloy.

S.B.M. calculated the cluster expansion Hamiltonians, performed the data post processing and wrote the paper. S.M. formulated the original problem and supervised the investigation. All

authors participated in the manuscript preparation during all stages of the process. CORRESPONDING AUTHOR Correspondence to Stefan Müller. ETHICS DECLARATIONS COMPETING INTERESTS The authors

declare no competing financial interests. SUPPLEMENTARY INFORMATION SUPPLEMENTARY FIGURES This file contains additional ground-state diagrams. (PDF 6916 kb) POWERPOINT SLIDES POWERPOINT

SLIDE FOR FIG. 1 POWERPOINT SLIDE FOR FIG. 2 POWERPOINT SLIDE FOR FIG. 3 POWERPOINT SLIDE FOR FIG. 4 RIGHTS AND PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE

Maisel, S., Höfler, M. & Müller, S. A canonical stability–elasticity relationship verified for one million face-centred-cubic structures. _Nature_ 491, 740–743 (2012).

https://doi.org/10.1038/nature11609 Download citation * Received: 28 June 2012 * Accepted: 11 September 2012 * Published: 21 November 2012 * Issue Date: 29 November 2012 * DOI:

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