Calculations of Diffusion in FCC Binary Alloys Using On-the-fly Kinetic Monte Carlo

117 Pages·2016·2.45 MB·English

by  Erdi Bleda

Clemson University
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12-2008
Calculations of Diffusion in FCC Binary Alloys
Using On-the-fly Kinetic Monte Carlo
Erdi Bleda
Clemson University, [email protected]
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Calculations of diffusion in FCC binary alloys
using on-the-fly kinetic Monte Carlo
A Dissertation
Presented to
the Graduate School of
Clemson University
In Partial Fulfillment
of the Requirements for the Degree
Doctor of Philosophy
Physics and Astronomy
by
Erdi Ata Bleda
December 2008
Accepted by:
Dr. Murray S. Daw, Committee Chair
Dr. Joseph R. Manson
Dr. Chad E. Sosolik
Dr. Sean Brittain
Abstract
Withtherecentadvancementsincomputertechnologiesandtheimprovements
in simulation algorithms, along with the theories, has allowed scientists to carry
out diffusion calculations more efficiently, especially for the cases where either the
diffusion itself takes longer, or there is no available isotope to carry out the diffusion
experiments such as tracer diffusion.
In this work, we present a systematic approach to diffusion in intermetallic
alloys such as weakly clustered Cu − Ni and weakly ordered Au − Ag. We use
AcceleratedMolecularDynamics(AMD)combinedwiththeEmbeddedAtomMethod
(EAM) to find the necessary saddlepoint energies. With this technique, we calculate
the tracer diffusivity coefficients for Cu−Ni (temperature range 700−1300K) and
for Au − Ag (temperature range 800 − 1300K) as a function of composition and
temperature. We assume that the vacancy-assisted diffusion mechanism is governing
the whole process. In our calculations we keep the vacancy concentration fixed. We
observe that the results are in agreement with Arrhenius behavior as discussed in
detail in Chapter 4: Results. However closer to critical temperature, the results are
overwhelmed by statistical fluctuations.
During the simulations at low temperatures, we sometimes find that the va-
cancyspendsalargenumberofstepsmovinglocallywithoutaccomplishingsignificant
displacements or accumulating much simulated time. To overcome this “sandtrap”
ii
problem, we develop a systematic approach which is discussed in Chapter 5: Sandtrap
Limitation and How to Overcome it in detail.
We also analyze the motion and the “width” of the Anti-Phase Boundary
(APB) perpendicular to its slip plane for Ni Al using the same approach mentioned
3
above for various temperatures (1000,1200 and 1500K) under no driving force. We
create the APB in the center of the sample and observe its motion. In addition, we
create the APB farther away from the center and fix the atoms at the end of each side.
This puts a bias on the motion of the APB by limiting the number of possible escapes
in a certain direction, thus “forcing” it to move towards the center. We observe the
motion of the APB and the results are discussed in detail in Chapter 4: Results.
iii
Dedication
This work is dedicated to my mother for her tremendous support and in loving
memory of my grandfather.
iv
Acknowledgments
First, I would like to express my deepest gratitude to my adviser, Dr. Daw for
his advices and support on my studies towards ph.D. I also would like to thank each
one of my committee members for accepting being in my committee. And finally, I
would like to thank Xing Gao for her help in the calculations of Au − Ag, and her
patience in our countless discussions.
This project is carried out with the support from NSF-ITR.
v
Table of Contents
Title Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.1 Embedded Atom Method (EAM) . . . . . . . . . . . . . . . . . . . . 16
3.2 Saddlepoint Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3 On-the-fly kinetic Monte Carlo Simulation . . . . . . . . . . . . . . . 23
4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.1 Bulk Tracer Diffusivity for Cu−Ni . . . . . . . . . . . . . . . . . . . 30
4.2 Bulk Tracer Diffusivity for Au−Ag . . . . . . . . . . . . . . . . . . . 52
4.3 Mobility of Anti-Phase Boundary in Ni Al . . . . . . . . . . . . . . . 68
3
5 Sandtrap Limitation and How to Overcome it . . . . . . . . . . . . 90
6 Conclusions and Discussion . . . . . . . . . . . . . . . . . . . . . . . 97
6.1 Diffusion in Binary Alloys . . . . . . . . . . . . . . . . . . . . . . . . 97
6.2 Translation of an APB . . . . . . . . . . . . . . . . . . . . . . . . . . 98
7 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
vi
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
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List of Tables
4.1 Parameters obtained by a global fit to all of the presented kMC results
for scaled tracer diffusivity in Cu−Ni . . . . . . . . . . . . . . . 34
4.2 Parameters obtained by a global fit to all of the presented kMC results
for scaled tracer diffusivity in Au−Ag . . . . . . . . . . . . . . . 54
4.3 Histogram of sites Al atoms occupy per layer for the initial configura-
tion. There are total 32 Al atoms per layer. Due to phase shift
(remember, APB) after the fifth layer, Al atoms now reside on site
three. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.4 The averaged histogram of sites Al atoms occupy per layer over inter-
mediate configurations after the third run at T = 1000 K. Initially
the APB was positioned in the middle (between the fifth and the
sixth layer). The histogram for the first two and the last two layers
are not allowed to change due to the non-movable region. . . . . . 75
4.5 The averaged histogram of sites Al atoms occupy per layer over inter-
mediate configurations for the final configuration at T = 1000 K.
Initially the APB was positioned in the middle (between the fifth
and the sixth layer). The histogram for the first two and the last
two layers are not allowed to change due to the non-movable region. 76
4.6 The averaged histogram of sites Al atoms occupy per layer over inter-
mediate configurations for the final configuration at T = 1200 K.
Initially the APB was positioned in the middle (between the fifth
and the sixth layer). The histogram for the first two and the last
two layers are not allowed to change due to the non-movable region. 77
viii
4.7 The averaged histogram of sites Al atoms occupy per layer over inter-
mediate configurations for the final configuration at T = 1500 K.
Initially the APB was positioned in the middle (between the fifth
and the sixth layer). The histogram for the first two and the last
two layers are not allowed to change due to the non-movable region. 78
4.8 Histogram of sites Al atoms occupy per layer for the initial configura-
tion. There are total 32 Al atoms per layer. Due to phase shift
(remember– APB) after the seventh layer, Al atoms now reside on
site three. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.9 The averaged histogram of sites Al atoms occupy per layer over interme-
diate configurations for the third run at T = 1000 K. The histro-
gram for the first two and the last two layers are not allowed to
change due to the non-movable region. . . . . . . . . . . . . . . . 81
4.10 An early snapshot of the configuration of the simulation running at
T=1000K under no driving force. . . . . . . . . . . . . . . . . . . 81
4.11 AlatersnapshotoftheconfigurationofthesimulationrunningatT=1000K
under no driving force. . . . . . . . . . . . . . . . . . . . . . . . . 82
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