NASA/CR--2003-212122

Atomic-Scale Modeling of the Structure and

Dynamics of Dislocations in Complex Alloys

at High Temperatures

Murray S. Daw

Clemson University, Clemson, South. Carolina

Michael J. Mills

Ohio State University, Colu.mbt_.s, Ohio

February 2003

https://ntrs.nasa.gov/search.jsp?R=20030019248 2018-05-15T15:38:02+00:00Z
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NASA/CR--2003-212122

Atomic-Scale Modeling of the Structure and

Dynamics of Dislocations in Complex Alloys

at High Temperatures

Murray S. Daw

Clemson University, Clemson, South. Carolina

Michael J. Mills

Ohio Sta te University, Columbt_.s, Ohio

Prepared under Grant NAG3----2675

N ational Aeronautics and

Spa ce Ad.minis tration

Glelm Research Center

February 2003
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Available electronically at bttp: //gltrs.grc.nasa.gov
Atomic-scale Modeling of the structure and dynamics of

dislocations in complex alloys at high temperatures

Murray S. Daw

Clemson University

Clemson, South Carolina 29634

Michael J. Mills

Ohio State University

Columbus, Ohio 43210

Abstract

We report on the progress made during the first year of the project. Most of the

progress at this point has been on the theoretical and computational side. Here are

the highlights:

• A new code, tailored for high-end desktop computing, now combines modern Accelerated Dynamics (AD) with the well-tested Embedded Atom Method (EAM).

• The new Accelerated Dynamics allows the study of relatively slow, thermallyactivated processes, such as diffusion, which are much too slow for traditional

Molecular Dynamics.

• We have benchmarked the new AD code on a rather simple and well-known

process: vacancy diffusion in copper.

• We have begun application of the AD code to the diffusion of vacancies in ordered

intermetallics.

NASA/CR 2003-212122 1
1 Project Description

Developing a complete understanding of dislocation-level processes at high temperatures is

crucial to the physically-based modeling of the creep performance of structural materials such

as superalloys and intermetallics. However, there are presently several significant challenges

which stand in the way of employing dislocation modeling concepts to the problem of hightemperature deformation in these complex alloys. First, the dislocation configurations at

the atomic level can be far more complex at higher temperatures because of the additional

degree of freedom offered by diffusion-mediated climb processes. Second, the diffusion paths

are not accurately known, and are affected by the presence of the dislocation's core and strain

field. Third, though alloying additions and deviation from stoichiometry can have dramatic

effects on mechanical properties, their effects on fundamental dislocation configurations and

microscopic diffusional processes are largely unknown.

In this program, we intend to develop a modeling capability at the atomic scale whereby

we can rigorously treat the non-conservative motion of complex dislocation configurations,

and obtain quantitative estimates of dislocation velocities - an essential first step toward the

prediction of high temperature performance of structural materials. This effort is inspired

by recent advances in these distinct areas:

• Improved understanding of dislocation processes controlling high-temperature deformation in complex intermetallics

• Revolutionary advances in the computation of the dynamics of thermally-activated

processes

Specifically, the goals stated in our proposal were to develop a modeling capability which

can:

• Compute atomic structures and mobilities of point defects and dislocations

• Flexibly employ and compare energy functions from a variety of models (particularly

EAM and the more recently developed BFS method)

• Benchmark energetics of important processes from first principles

• Simulate atomic movement via diffusional processes near dislocations and obtain realistic rate information

• Treat the effects of alloying on the rates of diffusion and dislocation motion

The progress this year has concentrated on the modeling challenge. In particular, we

have made significant advances in the computational tools used to study diffusion and have

begun to use these tools in the study of vacancy diffusion in intermetallics.

NASA/CR 2003-212122 2
2 This Year's Progress

We have combined modern accelerated dynamics with the Embedded Atom Method (EAM)

to provide an advanced tool for investigating thermally activated processes (diffusion and

dislocation climb) on an atomic scale. A new code, tailored for the current high-end desktop

computing environment, now includes the accelerated dynamics.

When applied to diffusion, traditional Molecular Dynamics is constrained to follow the

high-frequency vibrations of all the atoms in the system (with a typical period of picoseconds)

which only rarely results in an atomic hop. By contrast, Accelerated Dynamics allows the

study of relatively slow, thermally-activated processes, such as diffusion, in a inuch quicker

and more revealing way. Our project has combined a robust algorithm which searches for

saddlepoints (Dimer Method) with kinetic Monte Carlo, thereby integrating out the highfrequency motion and concentrating on the interesting atomic hops. Because the new method

is so robust, it can be applied even to the dynamics of very complex processes.

In Kinetic Monte Carlo (kMC), the system begins in a local valley of the potential

energy surface. For the system to move to a neighboring valley requires it to pass over one

of possibly several saddlepoints. If the list of possible saddlepoints is known (and also the

energy barrier Q for each), the kMC procedure picks one at random based on a Boltzmann

weighting exp (-@/kT). The system is then moved over that saddlepoint to the next valley,

and the simulated time is calculated as proportional to exp (@/kT).

The Dimer Method is a scheme for finding saddlepoints on a high dimensional potential

energy surface. To understand the scheme, consider that an arrangement of N atoms forms a

point in 3N-dimensional configuration space. From such a point in configuration space, one

could calculate the curvature of the energy in all directions. A saddlepoint is a configuration

which has exactly one direction with negative curvature, in contrast to a minimum where

all directions have nonnegative curvature. When searching for a saddlepoint from a starting

configuration, complete knowledge of the curvature in all directions would enable one to move

toward the saddlepoint by focusing on the direction with the lowest (eventually negative)

curvature.

The "Dimer" in the Dimer Method is formed by taking two neighboring points in configuration space (that is, two configurations which are slightly different). If the Dimer is

allowed to rotate freely without translating in configuration space, the energy of the Dimer

will be minimized when it points along the direction of lowest curvature in the energy. In the

region near a saddlepoint, this is the direction of negative curvature, in contrast to all other

directions which have positive curvature. In the simplest case, the dimer acts like a compass, pointing from a valley toward a saddlepoint. Even in more complex cases, the dimer

direction can be used to move the dimer toward the saddlepoint. The numerical advantage

of the dimer scheme is that some second derivative information is obtained, but only first

derivatives are explicitly calculated from the potential surface.

The saddlepoint search in the Dimer Method must be started by selecting some initial

orientation of the Dimer, and this should then lead to a saddlepoint. Once one saddlepoint

is found, the Dimer Method must be started again with a different initial direction to locate

another saddlepoint. Clearly, it is best to find some efficient means of providing profitable

initial orientations for the dimer search. Also, to be efficient, the successive applications of

NASA/CR 2003-212122 3
the Dimer Methodshouldavoidrediscoveringpreviouslyidentifiedsaddlepoints.With these

thoughtsin mind, wehavemadesomeimprovementsto the efficiencyof the Dimer Method.

Consideras an example,the hop of a V in Cu, shownin the followingfigure. In FCC

metals, there are 12 nearest neighbors to the vacancy. Applying the Dimer Method 12

times in succession comes up (in our code) with a new saddlepoint each time. This table

of saddlepoints can then be used in the Kinetic Monte Carlo to decide which of the 12

neighbors will exchange places with the vacancy. In this fashion, we have combined kMC

with the Dimer Method, and this has been implemented in flame.

Which neighbor will hop? Dimer points the way!

V

Here is a summary of our key accomplishments for this year:

• new code (flame) for doing accelerated dynamics with EAM, tailored to Pentium architecture

• new functionalities are critical for current interests:

- Dimer Method (robust saddlepoint search)

- kinetic Monte Carlo (uses Dimer Method to find saddlepoints)

- new Hyper-Dimer (original with this work)

• successful benchmark application to simple, well-known case (V in Cu)

• first runs for Ni vacancy in Ni3Al

3 Code Description

The new code (flame) should replace commonly used but dated Sandia dynamo code, which

was written (by Daw & Foiles in the late 80's and early 90's) for the Cray. Dynamo and its

related codes have become commonly used throughout the community. The new code retains

the easy usability that characterized the dynamo suite. In addition, flame's execution of the

NASA/C_2003-212122 4
traditional functionalities (energyminimization, moleculardynamics,Langevindynamics)

is muchfasterthan dynamo. There are several advances which give flame advantages in the

current computing environment:

• The old code was targetted for smaller problems than are feasible today. The target

systems are now larger.

A significant improvement in the speed is attained by utilizing a "linklist" strategy

for finding neighbors when calculating interactions. The code stores the neighbor lists

from one iteration to the next, updating them only when necessary.

Larger memories makes it possible to store several configurations simultaneously in

memory. This is very convenient for constructing chains-of-state for saddlepoint searches,

or tables of saddlepoints for kMC.

A working version of flame will be made available with this report to our contacts at

NASA.

4 Plans for the coming year (2003)

4.1 Theoretical Portion

For the theoretical work, the target application of this project in the coming year will be:

1. the diffusion of vacancies in ordered intermetallics, and

2. the interaction of those vacancies with dislocations

Progress has been such that we anticipate reporting on the first round of results at the

Intermetallic Symposium of the 2002 Fall Meeting of the MRS in Boston.

4.2 Complementary Experiments

Our success in the development of the accelerated molecular dynamics should enable us to

begin treating diffusion and defect interactions with dislocations in systems of interest. We

believe that a problem of significant interest from a fundamental and technological viewpoint

is that of dislocation motion in the ordered 7' phase of Ni3A1. Based on previous creep

studies IT. S. Rong, I. P. Jones and R. E. Smallman, Acta Metall. Mater., vol. 43, (1995),

pp. 1385-1393], deformation of single crystals of the 7' phase at intermediate temperature

(500-700C) occurs by motion of a(ll0) superdislocations. These dislocations are reported

to adopt climb-dissociated configurations under these conditions, such that the a/2(110)

superpartials lie on top of one another relative to the overall glide plane. An APB links the

two superpartials together in the ordered structure. It is the inotion of such configurations

that appears to limit deformation under these creep conditions.

We will perform detailed TEM investigation of such dislocation configurations to determine overall glide planes, dissociation distances and dislocation densities. Initial efforts

NASA/C_2003-212122 5
are plannedto creepdeforma limited numberof Ni3(Al, Ta) crystals that are available,

although additional compositions may be pursued in consultation with NASA personnel.

This information will be used to obtain estimates of dislocation velocities that will enable us

to benchmark the accelerated dynamics modeling of appropriate dislocation configurations

using flame.

NASA/C_2003-212122 6
5 Bibliography

Dimer Method

• G. Henkelman and H. Jonsson, "A dimer method for finding saddlepoints on high

dimensional potential surfaces using only first derivatives", J Chem Phys, v111 p7010

(1999).

• R. Elber and M. Karplus, Chem Phys Lett, v139, p375 (1987)

Other schemes for Accelerated Dynamics

• A. F. Voter, "A method for accelerating the molecular dynamics simulation of infrequent events", J Chem Phys, v106, p4665 (1997).

• A. F. Voter, "Hyperdynamics: Accelerated molecular dynamics of infrequent events",

Phys Rev Lett v78 p3908 (1997).

• M. R. Sorensen and A. F. Voter, "Temperature-accelerated dynamics for simulation of

infrequent events", J Chem Phys, v112, p9599 (2000)

Embedded Atom Method (EAM)

• M. S. Daw and M. I. Baskes, "Embedded-atom method: derivation and application to

impurities, surfaces, and other defects in metals", Phys Rev B29, p6443 (1984).

• M. S. Daw, S. M. Foiles, and M. I. Baskes, "The embedded-atom method: a review of

theory and applications", Mat Sci Reports v9 p251 (1993)

BFS (Bozzolo, Ferrante, & Smith)

• G. Bozzolo, J. Ferrante, & J. Smith, "Method for calculating alloy energies", Phys Rev

B, v45 p493 (1992).

• G. Bozzolo, R. Noebe, J. Ferrante, & C. Amador, "An introduction to the BFS method

and its use to model binary NiA1 alloys", J Comp-Aided Mat Des, v6 pl (1999).

NASA/CR 2003-212122 7
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February 2003 Interim Contractor Report

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Atomic-Scale Modeling of the Structure and Dynamics of Dislocations in

Complex Alloys at High Temperatures

6. AUTHOR(S)

Murray S. Daw and Michael J. Mills

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESN(ES)

Ohio State University

190 N. Oval Mall

Columbus, Ohio 43210

WBS-22-708-87-23

NAG3-2675

8. PERFORMING ORGANIZATION

REPORT NUMBER

E----13774

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AGENCY REPORT NUMBER

National Aeronautics and Space Administration

Washington, DC 20546-0(101 NASA CR-------2003-212122

11. SUPPLEMENTARY NOTES

Murray S. Daw, Clemson University, Clemson, South Carolina 29634; and Michael J. Mills, Ohio State University,

Columbus, Ohio 43210. Project Manager, Ronald Noebe, Materials Division, NASA Glenn Research Cenmr,

organization code 5 ] 20, 216---433---2093.

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Unclassified- Unlimited

Subject Categories: 26 and 65 Distribution: Nonstandard

Available electronically at http://_ltrs.grc.n_sa.gov

][his pub]ication is available from the NASA Center for AeroSpace lnfonnatiom 301-621-0390.

12b. DISTRNBUTION CODE

13. ABSTRACT (Maximum 200 words)

We report on the progress made during the first yea*" of the project. Most of the progress at this point has been on the

theoretical and computational side. t[ere are the highlights: (1) A new code, tailored for high-end desktop computing,

now combines modern Accelerated Dyna*I_ics (AD) with the well-tested Embedded Atom Method (EAIvl); (2) The new

Accelerated Dynaraics _lows the study of relatively slow, thermally-activated processes, such as diffusion, which are

much too slow for traditional Molecular Dynamics; (3) We have benchmarked the new AD code on a rather simple and

well-known process: vacancy diffusion in copper; and (4) We have begun application of the AD code to the diffusion of

vacancies in ordered intermetallics.

14. SUBJECT TERMS

Atomistic modeling; Dislocation; Kinetic-Monte-Carlo; Accelerated dynamics;

Embedded atom method

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