ISSN 10628738, Bulletin of the Russian Academy of Sciences: Physics, 2010, Vol. 74, No. 5, pp. 650–652. © Allerton Press, Inc., 2010. Original Russian Text © L.E. Kar’kina, I.N. Kar’kin, Yu.N. Gornostyrev, 2010, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2010, Vol. 74, No. 5, pp. 686–688.
Computer Simulation of the Interaction between an Edge Dislocation and Cu Precipitates in bcc Iron L. E. Kar’kina, I. N. Kar’kin, and Yu. N. Gornostyrev Institute of Metal Physics, Urals Division, Russian Academy of Sciences, ul. S. Kovalevskoi 18, Yekaterinburg, 620049 Russia email:
[email protected] Abstract—The molecular dynamics method was used to determine the energy of the interaction between a 1/2 [ 111 ] (110) edge dislocation and a Cu precipitate in bcc Fe. It was shown that three ranges of precipitate dimensions, characterized by different types of hardening, can be distinguished as a dislocation crosses over a precipitate. It was found that maximum hardening was due to the structural instability of the particles rela tive to the bcc–9R transformation, with this instability resulting from the stress fields produced by a disloca tion. DOI: 10.3103/S1062873810050187
INTRODUCTION Dispersed precipitates are important for the forma tion of the structure and properties of lowalloyed steels. Special interest has recently been stirred by the use of superfine particles 10–100 nm in size (nanopre cipitates) for the control of structural states. It was recently proposed that the traditional alloying of fer ritic steels with Nb and V be replaced with the addition of Cu [1]. The nanosized copperenriched particles formed in αFe upon cooling lead to the precipitation hardening of steels, ensuring high plasticity and frac ture toughness. While the hardening effect of copper precipitates has long been known [2], the mechanism of this phenomenon and the factors that control the formation of nanosized copper precipitates are still open to discussion. Studies on the kinetics of decom position of supersaturated FeCu solid solutions have shown that Cu precipitates are formed in the bcc Fe matrix in several stages. Nanoprecipitates with a bcc lattice containing up to 50–70% copper appear first. As their size increases, the precipitates rearrange themselves into a closely packed phase with a 9R lat tice (an fcc lattice twinned in each ninth plane). Finally, fcc Cu precipitates are formed as the holding time increases. The marked effect of bcc Cu precipi tates on the mechanical properties of αFe has gener ated interest among researchers studying the structural state and thermodynamic and elastic properties of Fe–Cu solid solution. The mechanism by which cop perenriched nanosized precipitates provide consider able improvement in mechanical properties is still poorly understood, however. To clarify the mechanism responsible for the hard ening of Cualloyed lowcarbon steels, the interaction of dislocations with copperenriched precipitates was explored in this work by the molecular dynamics (MD) method, with which it is possible to perform
numerical experiments with a large number of atoms (up to 106), as is necessary in studying such mesolevel phenomena as dislocations and grain boundaries. Manybody potentials constructed by the embedded atom method (EAM) have been used to describe the interaction between atoms of two species in a Fe–Cu alloy. The Farkas [3] and Mishin [4] potentials were taken for bcc Fe and Cu, respectively. Notice the very small difference between the lattice parameters of the bcc phases of Fe and Cu (aFe = 2.866 Å and aCu = 2.868 Å), and the considerably larger difference between the elastic moduli (μFe = 0.859 Pa and μCu = 0.499 Pa). A comparison of the shear moduli shows that the phase of the bcc Cu precipitates is softer than the Fe matrix. A pair Fe–Cu interaction functions was constructed as a superposition of the contributions from individual elements, taking into account the dependence of the mixing energy on the Cu concen tration in the solid solution of an Fe–Cu alloy with a bcc lattice. The concentration dependence of the lat tice parameter and the volume and shear elastic mod uli were also tested. The MD method was used to determine the energy of interaction between a Cu precipitate and an edge dislocation with the Burgers vector 1/2[ 111 ] sliding in the (110) plane. A relaxation procedure (Т = 0 K) was performed to calculate the energy of a crystallite with Cu precipitate of a preset size Ep in each of the 15 posi tions of the dislocation axis on the slip plane. Figure 1a shows the dependence Ed(x) for Cu precipitates with the number of atoms N = 511–10890 the radius of which varied within the limits R = 1.25–3.50 nm (curves 2–9). Curve 1 shows the change in the disloca tion energy in a crystallite without a precipitate. Depending on the position of the dislocation in the slip plane, Ed(x) changes weakly under the action of
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COMPUTER SIMULATION OF THE INTERACTION Ed, eV Å−1 5.5
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Fig. 1. Energy per unit length of a dislocation in a crystal lite with a precipitate (a); the dependence of hardening ΔE on precipitate radius R (b).
the boundary conditions. In Fig. 1a, the position of the center of a particle is marked with a vertical dotted line. Energy Ed(x) decreases upon entering a particle, remains at approximately the same level at the posi tions of the dislocation axis within the particle, and rises again as the dislocation leaves the particle. If the radius of a precipitate is small, the energy of a disloca tion within a particle decreases primarily due to the modulus effect, since the shear modulus of bcc Cu is smaller than that of bcc Fe. In Fig. 1a, quantity ΔЕ is the energy gain per unit length of a dislocation that is required for the disloca tion to cross a particle. Quantity ΔЕ was taken to be a quantitative characteristic of hardening as a disloca tion crosses a particle. A comparison of curves 2–9 in Fig. 1a shows that the hardening level increases with the radius of the precipitates. Figure 1b presents the dependence of ΔЕ on precipitate radius R. It is possi ble to distinguish three ranges of particle sizes, in which the character of dependence ΔЕ(R) changes qualitatively. In the range I (R < ~2.2 nm), the size dependence is quite weak. In this range of sizes, a par ticle is constrained by the environment of the Fe
Fig. 2. Configuration of particles depending on the size of precipitates in the ranges I (a), II (b), and III (c).
matrix, and its equilibrium configuration corresponds to a bcc lattice (Fig. 2a). The introduction of a dislo cation causes just a slight distortion of a particle near the dislocation slip plane. In range II (Fig. 1b), depen dence ΔЕ(R) increases sharply. In this range of sizes a particle retains a bcc structure in the equilibrium con figuration in the matrix (Fig. 2b). A dislocation within a particle, however, leads to its structural instability. Displacements appear in the planes parallel to the dis location slip plane. The stress fields produced by a dis location within a particle affect its structural state and provide a higher level of ordering. In range III of par ticle sizes (Fig. 1b), the energy of a particle exhibits a nonmonotonic dependence on the dislocation posi tion in the particle. In this range of sizes, an equilib rium configuration of a dislocationfree particle already has a structural instability (Fig. 2c). In this case, any additional dislocationinduced instability depends on the position of the dislocation relative to the regions of the intrinsic instability of the particle. This is probably the reason for the nonmonotonic dependence of energy Ed(x) relative to the position of the dislocation line within a particle. Our calculations
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thus showed that the sharp increase in the hardening of Fe–Cu alloy with Cu particles of radius R > ~2 nm is due to the structural instability of the particles caused by dislocations. CONCLUSIONS 1. EAM potentials of the interatomic interaction in the Fe–Cu alloy were constructed. They describe well the lattice parameters and the elastic and energy prop erties of an Fe–Cu solid solution. 2. The energy of the interaction between a 1 / 2 〈111〉(110) edge dislocation and Cu precipitates was determined using the MD method. 3. It was found that the dislocation–precipitate interaction depends on the size of the precipitates. At R < 2, the interaction is modulous in character; in the range 2.0 ≤ R ≤ 3.0 nm, the dislocation initiates shear structural instability of the particle, accompanied by a
sharp increase in hardening. At R ≥ 3.0, the stresses induced by the particle interact with the dislocation. ACKNOWLEDGMENTS This work was supported in part by the Program for the Support of Leading Scientific Schools (project no. NSh3706.2010.3) and by the Russian Foundation for Basic Research (project no. 080200022_a). REFERENCES 1. Vaynman, S., Guico, R.S., Fine, M.E., and Manga nello, S.J., Metall. Trans. A, 1997, vol. 28, pp. 1274– 1276. 2. Lahiri, S.K. and Fine, M.E., J. Met. A, 1969, vol. 21, p. 132. 3. http://www.ims.uconn.edu/centers/simul/pot/fefarkas.pot 4. http://cstwww.nrl.navy.mil/ccm6/ap/eam/index.html
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