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Weak crystallization theory of metallic alloys

Martin, Ivar and Gopalakrishnan, Sarang and Demler, Eugene A. (2016) Weak crystallization theory of metallic alloys. Physical Review B, 93 (23). Art. No. 235140. ISSN 2469-9950. https://resolver.caltech.edu/CaltechAUTHORS:20160620-122457585

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Abstract

Crystallization is one of the most familiar, but hardest to analyze, phase transitions. The principal reason is that crystallization typically occurs via a strongly first-order phase transition, and thus rigorous treatment would require comparing energies of an infinite number of possible crystalline states with the energy of liquid. A great simplification occurs when crystallization transition happens to be weakly first order. In this case, weak crystallization theory, based on unbiased Ginzburg-Landau expansion, can be applied. Even beyond its strict range of validity, it has been a useful qualitative tool for understanding crystallization. In its standard form, however, weak crystallization theory cannot explain the existence of a majority of observed crystalline and quasicrystalline states. Here we extend the weak crystallization theory to the case of metallic alloys. We identify a singular effect of itinerant electrons on the form of weak crystallization free energy. It is geometric in nature, generating strong dependence of free energy on the angles between ordering wave vectors of ionic density. That leads to stabilization of fcc, rhombohedral, and icosahedral quasicrystalline (iQC) phases, which are absent in the generic theory with only local interactions. As an application, we find the condition for stability of iQC that is consistent with the Hume-Rothery rules known empirically for the majority of stable iQC; namely, the length of the primary Bragg-peak wave vector is approximately equal to the diameter of the Fermi sphere.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevB.93.235140DOIArticle
http://journals.aps.org/prb/abstract/10.1103/PhysRevB.93.235140PublisherArticle
ORCID:
AuthorORCID
Martin, Ivar0000-0002-2010-6449
Additional Information:© 2016 American Physical Society. (Received 25 June 2015; revised manuscript received 1 June 2016; published 20 June 2016) uthors would like to thank P. Goldbart, Z. Nussinov, D. Levine, P. Steinhardt, J. Vinals, and A. Rosch for useful discussions. I.M. acknowledges support from Department of Energy, Office of Basic Energy Science, Materials Science and Engineering Division. S.G. and E.A.D. acknowledge support from Harvard-MIT CUA, NSF Grant No. DMR-1308435, and AFOSR Quantum Simulation MURI. S.G. acknowledges support from the Walter Burke Institute at Caltech. E.A.D. acknowledges support from the Humboldt Foundation.
Group:Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)UNSPECIFIED
Harvard-MIT Center for Ultracold AtomsUNSPECIFIED
NSFDMR-1308435
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Alexander von Humboldt FoundationUNSPECIFIED
Issue or Number:23
Record Number:CaltechAUTHORS:20160620-122457585
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160620-122457585
Official Citation:Weak crystallization theory of metallic alloys Ivar Martin, Sarang Gopalakrishnan, and Eugene A. Demler Phys. Rev. B 93, 235140
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:68529
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:20 Jun 2016 20:00
Last Modified:03 Oct 2019 10:14

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