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Title: Weak crystallization theory of metallic alloys

Journal Article · · Physical Review B
 [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

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.

Research Organization:
Argonne National Laboratory (ANL), Argonne, IL (United States); Harvard Univ., Cambridge, MA (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)
Grant/Contract Number:
AC02-06CH11357; DMR-1308435
OSTI ID:
1356629
Alternate ID(s):
OSTI ID: 1258310
Journal Information:
Physical Review B, Vol. 93, Issue 23; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

References (27)

First-principles order-parameter theory of freezing journal March 1979
Density functional theory of freezing: Analysis of crystal density journal November 1987
Weak crystallization theory journal June 1993
Simple Views on Condensed Matter book June 1998
Should All Crystals Be bcc? Landau Theory of Solidification and Crystal Nucleation journal September 1978
The phase boundaries in binary alloys, part 2: the theory of the  ,   phase boundaries journal May 1937
Metallic Phase with Long-Range Orientational Order and No Translational Symmetry journal November 1984
Quasicrystals: A New Class of Ordered Structures journal December 1984
Quasicrystals book November 1999
Electronic structure of complex Hume-Rothery phases and quasicrystals in transition metal aluminides journal August 2005
Icosahedral clusters, icosaheral order and stability of quasicrystals—a view of metallurgy journal January 2008
Electron transport properties of thermodynamically stable Al-Cu-Ru icosahedral quasicrystals journal July 1990
Pseudopotentials and quasicrystals journal September 1987
Phenomenological Theory of Icosahedral Incommensurate ("Quasiperiodic") Order in Mn-Al Alloys journal April 1985
Long-Range Icosahedral Orientational Order and Quasicrystals journal August 1985
Mean-Field Theory of Quasicrystalline Order journal April 1985
Mean-field-theory study of the energetics of icosahedral, decagonal, and dodecagonal quasicrystals journal January 1988
Order in metallic glasses and icosahedral crystals journal October 1985
Amplitude equation and pattern selection in Faraday waves journal July 1999
Pattern Selection for Faraday Waves in an Incompressible Viscous Fluid journal January 2007
Inhomogeneous Electron Gas journal November 1964
Theory of the formation of metallic glasses journal January 1980
Density-functional theory of freezing and properties of the ordered phase journal September 1991
Interpretation of the Hume–Rothery rule in complex electron compounds: γ-phase Cu5Zn8 Alloy, FK-type Al30Mg40Zn30 and MI-type Al68Cu7Ru17Si8 1/1–1/1–1/1 approximants journal January 2004
Indirect Exchange Coupling of Nuclear Magnetic Moments by Conduction Electrons journal October 1954
A Theory of Metallic Ferro- and Antiferromagnetism on Zener's Model journal July 1956
Magnetic Properties of Cu-Mn Alloys journal June 1957

Cited By (2)

Phase crystals journal January 2020
Theory of quantum oscillations in quasicrystals: Quantizing spiral Fermi surfaces text January 2019

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