Atomistic simulations of grain boundary pinning in CuFe alloysLuis A. Zepeda-Ruiz, George H. Gilmer, Babak Sadigh, Alfredo Caro, Tomas Oppelstrup, and Alex V. Hamza Citation: Applied Physics Letters 87, 231904 (2005); doi: 10.1063/1.2137871 View online: http://dx.doi.org/10.1063/1.2137871 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/87/23?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Modeling the first stages of Cu precipitation in α-Fe using a hybrid atomistic kinetic Monte Carlo approach J. Chem. Phys. 135, 064502 (2011); 10.1063/1.3622045 High B s Fe84−x Si4B8P4Cu x (x=0–1.5) nanocrystalline alloys with excellent magnetic softness J. Appl. Phys. 109, 07A303 (2011); 10.1063/1.3535290 Low core losses and magnetic properties of Fe85-86Si1-2B8P4Cu1 nanocrystalline alloys with high B for powerapplications (invited) J. Appl. Phys. 109, 07A302 (2011); 10.1063/1.3535169 Magnetic force microscopy study on the effect of Cu in melt-spun Sm–Fe–Si–C ribbons J. Appl. Phys. 87, 2061 (2000); 10.1063/1.372138 Thermal stability of the nanocrystalline Fe–Co–Hf–B–Cu alloy J. Appl. Phys. 85, 4424 (1999); 10.1063/1.369805

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Atomistic simulations of grain boundary pinning in CuFe alloysLuis A. Zepeda-Ruiz,a� George H. Gilmer, Babak Sadigh, Alfredo Caro,Tomas Oppelstrup,b� and Alex V. HamzaChemistry and Materials Science Directorate, Lawrence Livermore National Laboratory,Livermore, California 94550

�Received 7 June 2005; accepted 21 October 2005; published online 29 November 2005�

We apply a hybrid Monte Carlo-molecular dynamics code to the study of grain boundary motionupon annealing of pure Cu and Cu with low concentrations of Fe. The hybrid simulations accountfor segregation and precipitation of the low solubility Fe, together with curvature-driven grainboundary motion. Grain boundaries in two different systems, a �7+U-shaped half-loop grain and ananocrystalline sample, were found to be pinned in the presence of Fe concentrations exceeding3%. © 2005 American Institute of Physics. �DOI: 10.1063/1.2137871�

The stabilization of grain boundaries �GBs� in nanocrys-talline materials has received much attention in recentyears.1–5 The Hall–Petch relation predicts that the hardnessof polycrystalline materials increases with decreasing grainsize, due to inhibited dislocation motion. But, the possibilityof taking full advantage of restricted dislocation motion inthese materials seems to be limited to grain sizes above acritical size �10–30 nm�; below this value, the strength de-creases with decreasing grain size. Grain sliding, or othertypes of GB accommodation, are thought to predominate inthis regime. In this work, we study the inhibition of GBmotion by impurity drag or precipitation mechanisms. Theability to pin the boundaries in this way may extend theregion of normal Hall–Petch behavior to smaller grain sizes,and allow the fabrication of materials with greater hardness.

Early models of impurity drag are based on continuumdescriptions of the GB structure that tacitly assume either adiffuse interfacial region, which can “drag” an impuritycloud along, or a mechanism analogous to impurity drag dueto a Cottrell atmosphere of impurities around a dislocation.6,7

Neither of these models is very accurate, since the diffuseinterface description is not consistent with the fact that theactual GB “thickness” is only a few lattice spacings, and thestress field surrounding the GB has a very short range.8

Atomic interactions and configurations are essential for ac-curate modeling. Atomistic models have clearly shown thatthe mismatch of the two orientations produces sites at theGB that are in strong tensile stress, and others in compres-sive stress, and that these highly localized sites are usuallythe major players in the binding of impurity atoms.9 For thisreason, we have used molecular dynamics �MD� and MonteCarlo �MC� techniques in this study, since the atomic struc-ture and local stresses are then fully represented.

In this letter, we measure curvature-driven GB migrationfor systems with different concentrations of Fe. The initialdistribution of the impurities is an important issue for thisstudy, since the time scale feasible for MD simulations isrelatively short, on the order of nanoseconds, and solid-statediffusion of Fe atoms is quite small. The fabrication of nano-crystalline materials occurs on a much longer time scale andusually involves either deposition, with rapid interfacial

and/or surface diffusion, or high-temperature deformations.Both methods involve high mobility and are likely to allowequilibration of impurities between the bulk and GB. There-fore, we start our simulations with an equilibration run basedon the Metropolis MC algorithm that produces the initialdistribution of impurities.

To describe alloy properties, two major issues have to beaddressed. One is the adequacy of the potentials to describethe materials properties, and the second is to develop theright tools to prepare the samples in representative initialstates, in particular addressing the GB segregation issue. Forthe first point, we have analyzed, in detail, the properties ofthe Cu–Fe potentials available in the literature10,11 and foundthat the Ludwig et al.12 potential reproduces the miscibilitygap most accurately. For the second point, we have devel-oped a parallel MC code in the transmutation ensemble. Thiscode performs sequences of MC events and MD time steps.In this way, the equilibrium concentrations in the GB andbulk are obtained. Details of the code will be publishedelsewhere.

Two samples with different microstructures were used inour study as shown in Fig. 1. The first one, a nanocrystallinesample, was created using a Voronoi construction, with ran-dom location and orientation of the grains. It consists of fivegrains with a mean size of 5 nm and has dimensions of40a0�40a0�40a0, where a0 is the Cu lattice constant.Periodic boundary conditions are used in the three directions.The color scheme for the atoms indicates the crystallo-graphic orientation of the grains. The second sample, aU-shaped half-loop bicrystal, is created by rotating Grain 2through 38.2° about the z direction �a common �111�direction�.13–15 This value of rotation corresponds to high

a�Electronic mail: zepedaruiz1@llnl.govb�Also at: NADA, Royal Institute of Technology �KTH�, 10044 Stockholm,

Sweden. FIG. 1. �Color online� Nanocrystalline and half-loop samples.

APPLIED PHYSICS LETTERS 87, 231904 �2005�

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symmetry �7 GB along the straight branches shown in Fig.1. These boundaries provide the driving force for motion.The average mobility of the curved segment is measuredduring annealing. The dimensions are: 17�6a0�48�2a0

�6�3a0 along x, y, and z, respectively �x, y, and z corre-spond to �112�, �110�, and �111�, respectively�. Periodicboundary conditions are used in the x and z directions, andfree surfaces in the y direction. A layer of static atoms isintroduced at the left surface in the y direction to avoid grainrotation. In both cases, the simulations are performed in acanonical ensemble after a short thermalization and volumerelaxation under zero pressure.

We now consider the annealing of nanocrystallinesamples with various concentrations of Fe; namely, 0%,0.6%, and 3%. After loading the samples with Fe and relax-ing them at the chosen annealing temperature of 950 K, MDannealing runs of 100 ps were performed. A representativeslice through the configuration with 3% Fe is shown in Fig.2. The majority of the Fe impurities �shown in red� is locatedin the GB, and small precipitates are formed there also.

Figure 3 shows cross sections of the Cu samples beforeand after the MD annealing run. The same initial configura-tion, shown in Fig. 3�a�, was used for different concentra-tions of Fe. Since the same color scheme shown in Fig. 1 isused here, color indicates orientation alone, and Fe atoms are

not differentiated from Cu atoms. It is clear that during an-nealing GBs in pure Cu exhibit considerable migration, asshown by comparing Figs. 3�a� and 3�b�. The shrinkage ofthe central grain and the growth of its neighbors is clearlyvisible. Smaller GB displacements are observed when thesystem contains 0.6% Fe, as shown in Fig. 3�c�. The samplewith 3% Fe exhibits very small displacements for all grains.This result shows that impurities that segregate to theboundaries are able to stabilize the grain structure duringannealing.

Our GB studies on nanocrystalline samples provide aqualitative indication of the mobility of the GB as a functionof Fe concentration. As in experiments on nanocrystallinesamples, it is difficult to extract precise mobilities from theseresults, since they are derived from grains with various crys-tallographic parameters and a distribution of sizes thatchange continuously during annealing. A solution to thisproblem is to study such properties using individual well-defined GBs. The U-shaped half-loop geometry shown inFig. 1 has been used both experimentally and computation-ally to extract individual properties of a variety of GBs.13–15

In this geometry, the driving force and the shape of themoving boundary segment remain constant during annealing.

Figure 4�a� shows a �111� projection of the final configu-ration after a 400 ps MD run of a �7 GB �straight segments�plus the half-loop in pure Cu at T=667 K. Only the higherpotential energy atoms are shown to mark the location of theGB. After a short initial transient, a steady-state migration isobserved. The driving force �GB energy per unit area� re-mains constant during anneal. Figure 4�b� shows,in turn, the final configuration after a 400 ps anneal atT=1000 K of a sample loaded with 0.91% Fe using theMC-MD run. Although this concentration value is below thesolubility limit for this potential,11 we can observe a weaksegregation of Fe �depicted in red in the figure online� at theGB. It can also be observed that there is no impurity dragunder these conditions, but depinning from the initial segre-gated Fe atoms occurs.

By monitoring the evolution of the half-loop during MDannealing, we can obtain a measure of the effect of Fe im-purities on GB motion primarily caused by pinning due toimpurity segregation at GBs. Figure 5 shows a plot of thedepinning time, �, as a function of temperature for threedifferent impurity concentrations: 0.0%, 0.34%, and 0.91%

FIG. 2. �Color online� Configuration obtained after loading 3% Fe.

FIG. 3. �Color online� Cross sections of the nanocrystalline samples. �a�represent the initial configuration for three different cases: �b�, �c�, and �d�.The resulting configuration after 100 ps anneal at 960 K are shown in �b� forpure Cu, �c� for 0.6% Fe, and �d� for 3% Fe.

FIG. 4. �Color online� Snapshots of the final configurations of a �7 half-loop GB for �a� pure Cu and �b� Cu with 0.91% Fe. Samples were annealedfor 400 ps at a temperature of 667 and 1000 K for �a� and �b�, respectively.The dashed line represents the initial position of the GB.

231904-2 Zepeda-Ruiz et al. Appl. Phys. Lett. 87, 231904 �2005�

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Fe. We observe that as T decreases and Fe impurity concen-tration increases, � increases and for some of the cases stud-ied here is beyond 400 ps �the length of our simulations�.The inset to Fig. 5 shows an Arrhenius plot of the depinningtime for the three samples studied. A substantial variation ofthe activation energy with impurity content is clearly ob-served: 0.05 eV for pure Cu and 0.15 eV for Cu 0.34% Fe.This result highlights the strong effect of impurities on mo-bility, even at low concentrations. GB depinning is the ratelimiting process that controls GB mobility in a polycrystal-line sample �GB motion in the solid solution does not play asignificant role in determining the overall mobility�. A GBmoving through the polycrystalline sample will encounterimpurity clusters left behind from segregation to other GBs.

In summary, we have simulated curvature-driven GBmotion using a hybrid MC-MD simulator. We obtain initialconfigurations of polycrystalline samples with segregation ofimpurities to the GB. We find that Fe additions stabilize GBmotion in both configurations studied. Our simulations show

that small concentrations of low solubility impurities are ca-pable of causing drastic reductions in GB mobilities. Thepresence of 1% Fe caused an order of magnitude increase inthe barrier for GB motion, and 3% Fe essentially immobi-lized GBs in our nanocrystalline sample. Our newly devel-oped tools allow us to explore the important process ofimpurity segregation at GB and its effect on pinning, openingthe possibility of modeling and designing extremelyhard materials.

This work was performed under the auspices of the U.S.Department of Energy by the University of California,Lawrence Livermore National Laboratory under ContractNo. W-7405-ENG-48.

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FIG. 5. �Color online� Dependence of the depinning time, �, on temperaturefor different impurity concentrations for the half-loop geometry shown inFig. 4. The inset shows an Arhhenius plot of � for the same systems.

231904-3 Zepeda-Ruiz et al. Appl. Phys. Lett. 87, 231904 �2005�

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