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Title: Self-consistent phonon theory of the crystallization and elasticity of attractive hard spheres

Abstract

We propose an Einstein-solid, self-consistent phonon theory for the crystal phase of hard spheres that interact via short-range attractions. The approach is first tested against the known behavior of hard spheres, and then applied to homogeneous particles that interact via short-range square well attractions and the Baxter adhesive hard sphere model. Given the crystal symmetry, packing fraction, and strength and range of attractive interactions, an effective harmonic potential experienced by a particle confined to its Wigner-Seitz cell and corresponding mean square vibrational amplitude are self-consistently calculated. The crystal free energy is then computed and, using separate information about the fluid phase free energy, phase diagrams constructed, including a first-order solid-solid phase transition and its associated critical point. The simple theory qualitatively captures all the many distinctive features of the phase diagram (critical and triple point, crystal-fluid re-entrancy, low-density coexistence curve) as a function of attraction range, and overall is in good semi-quantitative agreement with simulation. Knowledge of the particle localization length allows the crystal shear modulus to be estimated based on elementary ideas. Excellent predictions are obtained for the hard sphere crystal. Expanded and condensed face-centered cubic crystals are found to have qualitatively different elastic responses to varying attraction strengthmore » or temperature. Furthermore, as temperature increases, the expanded entropic solid stiffens, while the energy-controlled, fully-bonded dense solid softens.« less

Authors:
 [1];  [1]
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  1. Univ. of Illinois, Urbana, IL (United States)
Publication Date:
Research Org.:
Univ. of Illinois at Urbana-Champaign, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1876183
Grant/Contract Number:  
FG02-07ER46471
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 138; Journal Issue: 8; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Statistical mechanics models; Elastic modulus; Shear modulus; Crystallography; Crystallization; Free energy; Einstein model of solids; Self-consistent phonon theory; Statistical thermodynamics; Phase transitions

Citation Formats

Shin, Homin, and Schweizer, Kenneth S. Self-consistent phonon theory of the crystallization and elasticity of attractive hard spheres. United States: N. p., 2013. Web. doi:10.1063/1.4792440.
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Shin, Homin, & Schweizer, Kenneth S. Self-consistent phonon theory of the crystallization and elasticity of attractive hard spheres. United States. https://doi.org/10.1063/1.4792440
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Shin, Homin, and Schweizer, Kenneth S. Wed . "Self-consistent phonon theory of the crystallization and elasticity of attractive hard spheres". United States. https://doi.org/10.1063/1.4792440. https://www.osti.gov/servlets/purl/1876183.
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@article{osti_1876183,
title = {Self-consistent phonon theory of the crystallization and elasticity of attractive hard spheres},
author = {Shin, Homin and Schweizer, Kenneth S.},
abstractNote = {We propose an Einstein-solid, self-consistent phonon theory for the crystal phase of hard spheres that interact via short-range attractions. The approach is first tested against the known behavior of hard spheres, and then applied to homogeneous particles that interact via short-range square well attractions and the Baxter adhesive hard sphere model. Given the crystal symmetry, packing fraction, and strength and range of attractive interactions, an effective harmonic potential experienced by a particle confined to its Wigner-Seitz cell and corresponding mean square vibrational amplitude are self-consistently calculated. The crystal free energy is then computed and, using separate information about the fluid phase free energy, phase diagrams constructed, including a first-order solid-solid phase transition and its associated critical point. The simple theory qualitatively captures all the many distinctive features of the phase diagram (critical and triple point, crystal-fluid re-entrancy, low-density coexistence curve) as a function of attraction range, and overall is in good semi-quantitative agreement with simulation. Knowledge of the particle localization length allows the crystal shear modulus to be estimated based on elementary ideas. Excellent predictions are obtained for the hard sphere crystal. Expanded and condensed face-centered cubic crystals are found to have qualitatively different elastic responses to varying attraction strength or temperature. Furthermore, as temperature increases, the expanded entropic solid stiffens, while the energy-controlled, fully-bonded dense solid softens.},
doi = {10.1063/1.4792440},
journal = {Journal of Chemical Physics},
number = 8,
volume = 138,
place = {United States},
year = {Wed Feb 27 00:00:00 EST 2013},
month = {Wed Feb 27 00:00:00 EST 2013}
}
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