Phase field theory of interfaces and crystal nucleation in a eutectic system of fcc structure: I. Transitions in the one-phase liquid region

Tóth, Gyula I.; Gránásy, László

doi:doi:10.1063/1.2752505

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Tight-binding molecular dynamics study of the role of defects on carbon nanotube moduli and failure

We performed tight-binding molecular dynamics on single-walled carbon nanotubes with and without a variety of defects to study their effect on the nanotube modulus and failure through bond rupture. For a pristine (5,5) nanotube, Young’s modulus was calculated to be ∼ 1.1 TPa, and brittle rupture occurred at a strain of 17% under quasistatic loading. The predicted modulus is consistent with values from experimentally derived thermal vibration and pull test measurements. The defects studied cons...

Phase field theory of interfaces and crystal nucleation in a eutectic system of fcc structure: II. Nucleation in the metastable liquid immiscibility region

In the second part of our paper, we address crystal nucleation in the metastable liquid miscibility region of eutectic systems that is always present, though experimentally often inaccessible. While this situation resembles the one seen in single component crystal nucleation in the presence of a metastable vapor-liquid critical point addressed in previous works, it is more complex because of the fact that here two crystal phases of significantly different compositions may nucleate. Accordingly,...

The phase field theory (PFT) has been applied to predict equilibrium interfacial properties and nucleation barrier in the binary eutectic system Ag–Cu using double well and interpolation functions deduced from a Ginzburg-Landau expansion that considers fcc (face centered cubic) crystal symmetries. The temperature and composition dependent free energies of the liquid and solid phases are taken from CALculation of PHAse Diagrams-type calculations. The model parameters of PFT are fixed so as to recover an interface thickness of ∼ 1 nm from molecular dynamics simulations and the interfacial free energies from the experimental dihedral angles available for the pure components. A nontrivial temperature and composition dependence for the equilibrium interfacial free energy is observed. Mapping the possible nucleation pathways, we find that the Ag and Cu rich critical fluctuations compete against each other in the neighborhood of the eutectic composition. The Tolman length is positive and shows a maximum as a function of undercooling. The PFT predictions for the critical undercooling are found to be consistent with experimental results. These results support the view that heterogeneous nucleation took place in the undercooling experiments available at present. We also present calculations using the classical droplet model [classical nucleation theory (CNT)] and a phenomenological diffuse interface theory (DIT). While the predictions of the CNT with a purely entropic interfacial free energy underestimate the critical undercooling, the DIT results appear to be in a reasonable agreement with the PFT predictions.

Article Outline

INTRODUCTION
APPLIED MODELS
1. Phase field theory (PFT)
  1. Specific double well and interpolation functions
    1. The “standard” set (PFT/S)
    2. Ginzburg-Landau form for fcc structure (PFT/GL)
  2. Equilibrium interfaces
    1. Solid-liquid interfaces
    2. Solid-solid interfaces
  3. Barrier for crystal nucleation
  4. Tolman length
2. Classical nucleation theory (CNT)
3. Diffuse interface theory (DIT)
4. Steady state nucleation rate
PHYSICAL PROPERTIES
RESULTS AND DISCUSSION
1. Equilibrium interfaces
  1. Solid-liquid interfaces
  2. Solid-solid interfaces
2. Crystal nuclei
  1. Nucleation in PFT with GL free energy
  2. Comparison with other models
SUMMARY

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KEYWORDS and PACS

Keywords

nucleation, crystallisation, undercooling, interface phenomena, free energy, Ginzburg-Landau theory, critical fluctuations, eutectic alloys, molecular dynamics method, silver alloys, copper alloys

PACS

64.60.Q-

Nucleation
64.70.D-

Solid-liquid transitions
68.08.-p

Liquid-solid interfaces
68.35.Md

Surface thermodynamics, surface energies
61.50.Ah

Theory of crystal structure, crystal symmetry; calculations and modeling

ARTICLE DATA

Digital Object Identifier

http://dx.doi.org/10.1063/1.2752505

PUBLICATION DATA

ISSN

0021-9606 (print)

1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef

American Institute of Physics

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