Effect of the stress field of an edge dislocation on carbon diffusion in -iron: Coupling molecular
statics and atomistic kinetic Monte Carlo
R. G. A. Veiga and M. Perez
INSA Lyon, Laboratoire MATEIS, Université de Lyon, UMR CNRS 5510, 25 Avenue Jean Capelle, F69621 Villeurbanne, France
C. S. Becquart
Unité Matériaux et Transformations (UMET), Ecole Nationale Supérieure de Chimie de Lille,
UMR CNRS 8207, Bat. C6, F59655 Villeneuve d’Ascq Cedex, France
and Laboratoire commun EDF-CNRS Etude et Modélisation des Microstructures pour le Vieillissement des Matériaux (EM2VM)
C. Domain
Recherche et Développement, Matériaux et Mécanique des Composants, EDF, Les Renardières, F77250 Moret sur Loing, France
and Laboratoire commun EDF-CNRS Etude et Modélisation des Microstructures pour le Vieillissement des Matériaux (EM2VM)
S. Garruchet
Laboratoire de Physico-Chimie des Surfaces, UMR CNRS-ENSCP 7045, Ecole Nationale Supérieure de Chimie de Paris,
11 Rue Pierre et Marie Curie, 75005 Paris, France
Received 12 April 2010; revised manuscript received 22 June 2010; published 9 August 2010
Carbon diffusion near the core of a 1111
¯
01 edge dislocation in -iron has been investigated by means of
an atomistic model that brings together molecular statics and atomistic kinetic Monte Carlo AKMC. Mo-
lecular statics simulations with a recently developed embedded atom method potential have been carried out in
order to obtain atomic configurations, carbon-dislocation binding energies, and the activation energies required
for carbon hops in the neighborhood of the line defect. Using information gathered from molecular statics,
on-lattice AKMC simulations have been performed for temperatures in the 300–600 K range, so as to study the
behavior of a carbon atom as it interacts with the edge dislocation stress field. This model can be seen as a very
first step toward the modeling of the kinetics of carbon Cottrell atmosphere formation in iron during the static
aging process.
DOI: 10.1103/PhysRevB.82.054103 PACS numbers: 66.30.-h, 05.10.Ln, 61.72.Ff, 07.05.Tp
I. INTRODUCTION
The concept of “atmospheres” tiny clouds of interstitial
impurities that might be found decorating dislocations in
crystals was introduced by Cottrell and Bilby in late 1940s.
1
According to their theory, during the static aging process,
carbon atoms in solid solution in an iron matrix diffuse to
dislocations because the strain energy is lowered thereby,
thus forming what was later called a carbon Cottrell atmo-
sphere. Since they were predicted to pin dislocations, which
requires the application of a larger external stress to make
them move, Cottrell atmospheres were pointed out as the
cause for loss in metal plasticity. Important consequences of
dislocation pinning by Cottrell atmospheres, embrittlement,
and nonuniform yielding Lüders bands may end up being a
serious hindrance to manufacture of steel and other metallic
alloys. Therefore, formation of Cottrell atmospheres still re-
mains a timely subject in metalurgy.
Cottrell and Bilby roughly estimated the binding energy
between an interstitial carbon atom and a dislocation in iron
by considering the elastic interaction of the pressure created
by the dislocation with the relaxation volume of carbon.
Thereafter, more refined analytical models were proposed to
overcome the limitations of that pioneering approach, taking
into account not only dilatation but also the shear strain as-
sociated with impurities,
2
as well as the anisotropy of the
cubic cell.
3
Nowadays, with growing computer power, per-
forming large scale numerical simulations that take into con-
sideration the atomistic details of the interaction between
both defects became possible as well,
4–10
thus completing the
set of tools available for theoretical modeling.
In recent years, three dimension atom probe techniques
allowed to obtain images of interstitial impurities distributed
around dislocations in metallic alloys,
11–15
providing the
missing experimental evidence of Cottrell atmospheres.
However, in spite of representing a substantial advance in the
experimental side, the actual i.e., atomic scale kinetics of
impurity diffusion in the neighborhood of a dislocation re-
mains a challenge for these techniques. Macroscopic mea-
surements, e.g., thermoelectric power, on the other hand,
have been successfully used to assess the long-time segrega-
tion of impurities to dislocations
16,17
but they obviously lack
any information at the atomic level. In this context, numeri-
cal modeling might come and fill this gap by offering an
atomistic view of the kinetics of impurity diffusion near and
to dislocations.
8,9
The aim of the work reported in this article was to model
the behavior of a single interstitial impurity in the neighbor-
hood of a dislocation, where the stress field created by the
line defect was expected to affect at some extent the impurity
diffusion. Given their undisputable technological importance
as the main constituents of steel the most widely used me-
tallic alloy, carbon and iron have been elected the interstitial
atom and host material candidates of our model, respectively.
PHYSICAL REVIEW B 82, 054103 2010
1098-0121/2010/825/05410311 ©2010 The American Physical Society 054103-1