Nucleation and growth of a stable phase in an Ising-type system

Shneidman, Vitaly A.; Jackson, K. A.; Beatty, Kirk M.

doi:10.1103/physrevb.59.3579

Cited by 66 publications

(68 citation statements)

References 46 publications

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“…This simply reflects the time needed for the quasi-steady state gas to fully form (finally resulting in the distribution of subcritical clusters), and also for stable clusters to grow to a certain size. More sophisticated analysis methods would allow to fit also the lag time and the transition period, 58 but here we focus our analysis on the much simpler steady-state regime.…”

Section: Discussionmentioning

confidence: 99%

Large scale molecular dynamics simulations of homogeneous nucleation

Diemand

Angélil

Tanaka

et al. 2013

The Journal of Chemical Physics

118

163

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We present results from large-scale molecular dynamics (MD) simulations of homogeneous vapor-to-liquid nucleation. The simulations contain between 1 × 109 and 8 × 109 Lennard-Jones (LJ) atoms, covering up to 1.2 s (56 × 106 time-steps). They cover a wide range of supersaturation ratios, S = 1.55-104, and temperatures from kT = 0.3 to 1.0 (where is the depth of the LJ potential, and k is the Boltzmann constant). We have resolved nucleation rates as low as 1017 cm-3 s-1 (in the argon system), and critical cluster sizes as large as 100 atoms. Recent argon nucleation experiments probe nucleation rates in an overlapping range, making the first direct comparison between laboratory experiments and molecular dynamics simulations possible: We find very good agreement within the uncertainties, which are mainly due to the extrapolations of argon and LJ saturation curves to very low temperatures. The self-consistent, modified classical nucleation model of Girshick and Chiu [J. Chem. Phys. 93, 1273 (1990)] underestimates the nucleation rates by up to 9 orders of magnitudes at low temperatures, and at kT = 1.0 it overestimates them by up to 105. The predictions from a semi-phenomenological model by Laaksonen et al. [Phys. Rev. E 49, 5517 (1994)] are much closer to our MD results, but still differ by factors of up to 104 in some cases. At low temperatures, the classical theory predicts critical clusters sizes, which match the simulation results (using the first nucleation theorem) quite well, while the semi-phenomenological model slightly underestimates them. At kT = 1.0 , the critical sizes from both models are clearly too small. In our simulations the growth rates per encounter, which are often taken to be unity in nucleation models, lie in a range from 0.05 to 0.24. We devise a new, empirical nucleation model based on free energy functions derived from subcritical cluster abundances, and find that it performs well in estimating nucleation rates. We present results from large-scale molecular dynamics (MD) simulations of homogeneous vapor-toliquid nucleation. The simulations contain between 1 × 10 9 and 8 × 10 9 Lennard-Jones (LJ) atoms, covering up to 1.2 μs (56 × 10 6 time-steps). They cover a wide range of supersaturation ratios, S 1.55-10 4 , and temperatures from kT = 0.3 to 1.0 (where is the depth of the LJ potential, and k is the Boltzmann constant). We have resolved nucleation rates as low as 10 17 cm −3 s −1 (in the argon system), and critical cluster sizes as large as 100 atoms. Recent argon nucleation experiments probe nucleation rates in an overlapping range, making the first direct comparison between laboratory experiments and molecular dynamics simulations possible: We find very good agreement within the uncertainties, which are mainly due to the extrapolations of argon and LJ saturation curves to very low temperatures. The self-consistent, modified classical nucleation model of Girshick and Chiu [J. Chem. Phys. 93, 1273 (1990)] underestimates the nucleation rates by up to 9 orders of magnitudes at l...

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Section: Discussionmentioning

confidence: 99%

Large scale molecular dynamics simulations of homogeneous nucleation

Diemand

Angélil

Tanaka

et al. 2013

The Journal of Chemical Physics

118

163

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“…VII.) The effects of the dependence of the proportionality factor ν on the droplet radius, which are remarkably minor, are discussed by Shneidman and collaborators [86,87]. Equation (5.1) with d = 2 and K = 3 in Eq.…”

Section: Derivation Of M (T ) From Avrami's Lawmentioning

confidence: 99%

Kinetic Ising model in an oscillating field: Avrami theory for the hysteretic response and finite-size scaling for the dynamic phase transition

1999

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Hysteresis is studied for a two-dimensional, spin-1/2, nearest-neighbor, kinetic Ising ferromagnet in a sinusoidally oscillating field, using Monte Carlo simulations and analytical theory. Attention is focused on large systems and moderately strong field amplitudes at a temperature below Tc. In this parameter regime, the magnetization switches through random nucleation and subsequent growth of many droplets of spins aligned with the applied field. Using a time-dependent extension of the Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory of metastable decay, we analyze the statistical properties of the hysteresis-loop area and the correlation between the magnetization and the field. This analysis enables us to accurately predict the results of extensive Monte Carlo simulations. The average loop area exhibits an extremely slow approach to an asymptotic, logarithmic dependence on the product of the amplitude and the field frequency. This may explain the inconsistent exponent estimates reported in previous attempts to fit experimental and numerical data for the low-frequency behavior of this quantity to a power law. At higher frequencies we observe a dynamic phase transition. Applying standard finite-size scaling techniques from the theory of second-order equilibrium phase transitions to this nonequilibrium transition, we obtain estimates for the transition frequency and the critical exponents (β/ν ≈ 0.11, γ/ν ≈ 1.84 and ν ≈ 1.1). In addition to their significance for the interpretation of recent experiments on switching in ferromagnetic and ferroelectric nanoparticles and thin films, our results provide evidence for the relevance of universality and finite-size scaling to dynamic phase transitions in spatially extended nonstationary systems. PACS number(s): 05.40.+j, 77.80.Dj, 64.60.Qb

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“…(8), (12) and (13) are valid in the phase-field model using cell dynamics method. A similar study to test the validity of KJMA picture in Ising-type spin model was conducted by Shneideman et al [17] and Ramos et al [18].…”

Section: Classical Kjma Picture Of Nucleation and Growthmentioning

confidence: 99%

Direct numerical simulation of homogeneous nucleation and growth in a phase-field model using cell dynamics method

Iwamatsu

2008

The Journal of Chemical Physics

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Homogeneous nucleation and growth in a simplest two-dimensional phase field model is numerically studied using the cell dynamics method. Whole process from nucleation to growth is simulated and is shown to follow closely the Kolmogorov-Johnson-Mehl-Avrami (KJMA) scenario of phase transformation. Specifically the time evolution of the volume fraction of new stable phase is found to follow closely the KJMA formula. By fitting the KJMA formula directly to the simulation data, not only the Avrami exponent but the magnitude of nucleation rate and, in particular, of incubation time are quantitatively studied. The modified Avrami plot is also used to verify the derived KJMA parameters. It is found that the Avrami exponent is close to the ideal theoretical value m = 3. The temperature dependence of nucleation rate follows the activation-type behavior expected from the classical nucleation theory. On the other hand, the temperature dependence of incubation time does not follow the exponential activation-type behavior. Rather the incubation time is inversely proportional to the temperature predicted from the theory of Shneidman and Weinberg [J. Non-Cryst. Solids 160, 89 (1993)]. A need to restrict thermal noise in simulation to deduce correct Avrami exponent is also discussed.

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Nucleation and growth of a stable phase in an Ising-type system

Cited by 66 publications

References 46 publications

Large scale molecular dynamics simulations of homogeneous nucleation

Large scale molecular dynamics simulations of homogeneous nucleation

Kinetic Ising model in an oscillating field: Avrami theory for the hysteretic response and finite-size scaling for the dynamic phase transition

Direct numerical simulation of homogeneous nucleation and growth in a phase-field model using cell dynamics method

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