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Title: Weak crystallization theory of metallic alloys

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. In this paper, 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. Finally, as an application, we find the condition for stability ofmore » 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.« less

Authors:
 [1];  [2];  [3]
  1. Argonne National Lab. (ANL), Argonne, IL (United States)
  2. Harvard Univ., Cambridge, MA (United States). Dept. of Physics; California Inst. of Technology (CalTech), Pasadena, CA (United States). Dept. of Physics
  3. Harvard Univ., Cambridge, MA (United States). Dept. of Physics
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States); Harvard Univ., Cambridge, MA (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)
OSTI Identifier:
1356629
Alternate Identifier(s):
OSTI ID: 1258310
Grant/Contract Number:  
AC02-06CH11357; DMR-1308435
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 93; Journal Issue: 23; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Martin, Ivar, Gopalakrishnan, Sarang, and Demler, Eugene A. Weak crystallization theory of metallic alloys. United States: N. p., 2016. Web. https://doi.org/10.1103/PhysRevB.93.235140.
Martin, Ivar, Gopalakrishnan, Sarang, & Demler, Eugene A. Weak crystallization theory of metallic alloys. United States. https://doi.org/10.1103/PhysRevB.93.235140
Martin, Ivar, Gopalakrishnan, Sarang, and Demler, Eugene A. Mon . "Weak crystallization theory of metallic alloys". United States. https://doi.org/10.1103/PhysRevB.93.235140. https://www.osti.gov/servlets/purl/1356629.
@article{osti_1356629,
title = {Weak crystallization theory of metallic alloys},
author = {Martin, Ivar and Gopalakrishnan, Sarang and Demler, Eugene A.},
abstractNote = {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. In this paper, 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. Finally, 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.},
doi = {10.1103/PhysRevB.93.235140},
journal = {Physical Review B},
number = 23,
volume = 93,
place = {United States},
year = {2016},
month = {6}
}

Journal Article:

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Cited by: 1 work
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    Phase crystals
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    text, January 2019

    • Spurrier, Stephen; Cooper, Nigel
    • Apollo - University of Cambridge Repository
    • DOI: 10.17863/cam.43032