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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 Inst. of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); National Science Foundation (NSF)
OSTI Identifier:
1356629
Grant/Contract Number:
AC02-06CH11357; DMR-1308435
Resource Type:
Journal Article: 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. doi:10.1103/PhysRevB.93.235140.
Martin, Ivar, Gopalakrishnan, Sarang, & Demler, Eugene A. Weak crystallization theory of metallic alloys. United States. doi:10.1103/PhysRevB.93.235140.
Martin, Ivar, Gopalakrishnan, Sarang, and Demler, Eugene A. 2016. "Weak crystallization theory of metallic alloys". United States. doi: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
  • The crystallization behavior of amorphous Fe{sub 84{minus}X}Si{sub 6}B{sub 10}M{sub X} (M = Nb, Zr, V, or Cu) alloys was examined using differential scanning calorimetry (DSC) and transmission electron microscopy (TEM) with the aim of clarifying the effect of additional M elements. The compositional dependence of the first crystallization temperature T{sub x1} increased in the order of Zr > Nb > V; however, the addition of 1 at. pct Cu caused a decrease in T{sub x1}. Such an effect of the M elements on the thermal stability of an amorphous phase was interpreted in terms of the difference in the atomicmore » size. These alloys were composed of a mixed structure of {alpha}-Fe phase. However, their particles possessed dendritic morphology with a grain size of 0.1 to 0.3 {micro}m, when the Nb or Zr content was less than 2 at. pct. Further addition of these elements brought about the formation of spherical {alpha}-Fe particles. The average grain size, for instance, was as small as 20 nm in the aged alloy containing 6 at. pct Nb, which shows that a remarkable grain refinement occurs with increasing Nb content.« less
  • Cited by 6
  • In-situ transmission electron microcopy and time-resolved neutron diffraction were used to study crystallization kinetics of two ternary bulk metallic glasses during isothermal annealing in the supercooled liquid region. It is found that the crystallization of Zr 56Cu 36Al 8, an average glass former, follows continuous nucleation and growth, while that of Zr 46Cu 46Al 8, a better glass former, is characterized by site-saturated nucleation, followed by slow growth. Possible mechanisms for the observed differences and the relationship to the glass forming ability are discussed.
  • In-situ transmission electron microcopy and time-resolved neutron diffraction were used to study crystallization kinetics of two ternary bulk metallic glasses during isothermal annealing in the supercooled liquid region. It is found that the crystallization of Zr{sub 56}Cu{sub 36}Al{sub 8}, an average glass former, follows continuous nucleation and growth, while that of Zr{sub 46}Cu{sub 46}Al{sub 8}, a better glass former, is characterized by site-saturated nucleation, followed by slow growth. Possible mechanisms for the observed differences and the relationship to the glass forming ability are discussed.