Microstructure Evaluation for Time Dependent Nucleation Protocols in KJMA Kinetics

1999 ◽  
Vol 580 ◽  
Author(s):  
Eloi Pineda ◽  
Daniel Crespo
Keyword(s):  
Mean Field ◽  
Quantitative Agreement ◽  
Nucleation And Growth ◽  
Time Dependent ◽  
First Order ◽  
Microstructure Evaluation ◽  
The Mean ◽  
Dependent Growth ◽  
First Order Phase

AbstractThe microstructure developed in a first order phase transformation is obtained using a populational extension of the Kolmogorov, Johnson-Mehl and Avrami (KJMA) model, PKJMA. PKJMA allows one to determine the grain size distribution resulting from nucleation and growth kinetics. PKJMA is grounded on the mean field hypothesis that the free space around the growing grains is randomly distributed, independent of the grain radius. Although this approach is perfectly valid for the case of constant nucleation, a detailed analysis of the model shows that this hypothesis does not hold in the case of time dependent nucleation protocols or pre-existing nuclei. In this work, the PKJMA model has been improved by estimating the average free surface around the grains as a function of their radius and the time elapsed since nucleation. The resulting model gives quantitative determination of the microstructure developed under a variety of nucleation and growth processes: pre-existing nuclei, constant nucleation, and the combination of both mechanisms, constant and radius dependent growth rates. Comparison with Monte Carlo simulations, showing a quantitative agreement will be presented.

A FIRST ORDER PHASE TRANSITION IN ISING FERRIMAGNETS

1995 ◽  
Vol 09 (21) ◽  
pp. 1347-1351 ◽  
Author(s):  
HASAN M. AL MUKADAM ◽  
DIMO I. UZUNOV
Keyword(s):  
Phase Transition ◽  
Order Parameter ◽  
Mean Field Theory ◽  
Mean Field ◽  
First Order ◽  
First Order Phase Transition ◽  
Exchange Constants ◽  
The Mean ◽  
First Order Phase ◽  
Ising Spins

The mean field theory is used for the analysis of a two-sublattice system of Ising spins, which describes ferro-, antiferro-, and ferrimagnetic orderings. It is proven that the phase transition in these systems is of a first order when the exchange constants of the sublattices are different. The free energy, the order parameter profiles and the latent heat of the phase transition are calculated for almost equivalent sublattices.

Notizen: Monte-Carlo Simulation of a Two-dimensional Dipolar Lattice

1977 ◽  
Vol 32 (11) ◽  
pp. 1320-1322 ◽  
Author(s):  
S. Romano
Keyword(s):  
Monte Carlo ◽  
Mean Field Theory ◽  
Mean Field ◽  
Square Lattice ◽  
Electrostatic Energy ◽  
Two Dimensional ◽  
First Order ◽  
First Order Phase Transition ◽  
The Mean ◽  
First Order Phase

Abstract Monte-Carlo calculations were carried out on a system consisting of 256 point-dipoles, whose centres are fixed in a two-dimensional square lattice with the usual boundary con­dition; the Epstein-Ewald-Kornfeld algorithm was used in evaluating the electrostatic energy. No evidence of a first-order phase transition was found, and the results suggest there might be a second-order one. Additional calculations were carrierd out using the mean-field theory, which was found to overestimate the transition temperature by about a factor two.

The Second-Order Master Equation

2019 ◽  
pp. 128-158
Author(s):  
Pierre Cardaliaguet ◽  
François Delarue ◽  
Jean-Michel Lasry ◽  
Pierre-Louis Lions
Keyword(s):  
Master Equation ◽  
Mean Field ◽  
Second Order ◽  
Well Posedness ◽  
Mean Field Game ◽  
First Order ◽  
Common Noise ◽  
System P ◽  
The Mean

This chapter investigates the second-order master equation with common noise, which requires the well-posedness of the mean field game (MFG) system. It also defines and analyzes the solution of the master equation. The chapter explains the forward component of the MFG system that is recognized as the characteristics of the master equation. The regularity of the solution of the master equation is explored through the tangent process that solves the linearized MFG system. It also analyzes first-order differentiability and second-order differentiability in the direction of the measure on the same model as for the first-order derivatives. This chapter concludes with further description of the derivation of the master equation and well-posedness of the stochastic MFG system.

Re-Examination of A1 → L10 Ordering: Generalized Bragg-Williams Model with Elastic Relaxation

2011 ◽  
Vol 172-174 ◽  
pp. 608-617 ◽  
Author(s):  
William A. Soffa ◽  
David E. Laughlin ◽  
Nitin Singh
Keyword(s):  
Nearest Neighbor ◽  
Binary Solution ◽  
Mean Field ◽  
Lattice Relaxation ◽  
Two Phase ◽  
First Order ◽  
Tetragonal Lattice ◽  
Wide Range ◽  
Third Law Of Thermodynamics ◽  
The Mean

The tetragonal lattice relaxation has been included in the thermodynamics of the fcc→L10ordering to produce a first-order character of the transition within the mean field description of the binary solution energetics. In view of growing interest in such systems e.g. Fe-Pd and Co-Pt alloys, which display a wide range of applications relevant to current and futuristic technologies, the fcc→L10two-phase field is re-examined utilizing a generalized Bragg-Williams approach including first and second nearest neighbor interactions. The thermodynamic behavior is examined in the limit of T→0K and discussed in terms of the implications of the Third Law of Thermodynamics.

scholarly journals Topological signature of first-order phase transitions in a mean-field model

2003 ◽  
Vol 62 (6) ◽  
pp. 775-781 ◽  
Author(s):  
L Angelani ◽  
L Casetti ◽  
M Pettini ◽  
G Ruocco ◽  
F Zamponi
Keyword(s):  
Phase Transitions ◽  
Field Model ◽  
Mean Field ◽  
Mean Field Model ◽  
First Order ◽  
First Order Phase

Magnetic Anisotropy Constants of Epitaxial (110) Fe/GaAs Films from 77k To 293k Studied by Magneto-Resistance

1989 ◽  
Vol 151 ◽  
Author(s):  
Daniel K. Lottis ◽  
G. A. Prinz ◽  
E. Dan Dahlberg
Keyword(s):  
Phase Transition ◽  
Uniaxial Anisotropy ◽  
Epitaxial Films ◽  
Effective Anisotropy ◽  
First Order ◽  
First Order Phase Transition ◽  
Gaas Films ◽  
First Order Phase ◽  
Magneto Resistance

ABSTRACTA first-order phase transition in the magnetization of Fe films, driven by an applied magnetic field, was first reported by Hathaway and Prinz [1]. Further studies were performed on this phase transition using anisotropic magnetoresistance measurements by Riggs and Dahlberg [2]. Here we report the extension of these studies to include temperatures between 77K and 293K. Emphasis is on a determination of the fourth-order and uniaxial anisotropy constants (K1 and Ku). It is shown that the temperature dependence of the anisotropy energies in these films varies with thickness, which may be useful in sorting out the origin and magnitude of different contributions to the total effective anisotropy. The present study suggests that similar studies of (110) iron on other substrates might contribute to achieving a better understanding of in-plane anisotropies in epitaxial films.

An analytical method for determining rate constants using a periodical irradiation technique

1969 ◽  
Vol 47 (24) ◽  
pp. 4531-4535 ◽  
Author(s):  
W. Kawakami ◽  
H. S. Isbin
Keyword(s):  
Rate Constants ◽  
Analytical Method ◽  
Apparent Rate Constant ◽  
Chloral Hydrate ◽  
Life Time ◽  
First Order ◽  
Radical Concentration ◽  
Γ Rays ◽  
The Mean

A new analytical method is presented for the determination of rate constants using a periodical irradiation technique. This method is applicable to reactions which have both a first and a second order termination for the chain radical concentration, and is illustrated for the radiolysis of aqueous solutions of chloral hydrate by 137Cs γ rays. The apparent rate constant of first order termination, and the mean chain life time of the chain radical were determined to be 1.10 s−1, and 0.25 s for 400 rad/min, at 22 °C, respectively.

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