The solid state recrystallization and grain boundary migrations in an iron nanoparticle Fe2616 with three grains were studied by a molecular dynamics simulation. It was found that nucleation rates could be determined as the smaller grains were consumed by the larger ones. Moreover, the grain disorder was more important than the misorientation angle in governing the rates. Suggestions about the critical nuclei for the recrystallization are proposed. No obvious interaction between the grain boundaries was observed in the example studied in this report.
Recrystallization is the formation of a new grain structure in a solid material by the migration of grain boundaries that results in larger grains. This spontaneous process is considered to be driven by the excess energy in grain boundaries [
In the past decade, we have used the MD technique to study nucleation in the crystallization of molten materials and in phase transitions between different solid phases of nanometer size. To explore recrystallization in solids, we began an MD study on the simplest system, an iron nanoparticle Fe1436 with only two grains, and observed the thermal annealing process [
Molecular dynamics simulations were performed on a solid state polycrystalline iron nanoparticle Fe2616. The program XMD [
The studied quasispherical iron particle containing 2616 iron atoms was first cut from a body-center cubic (BCC) lattice of iron (Figure
Images of the nanoparticles from various processing stages and different quenching runs.
Starting point
Molten droplet at 1680 K
One of 18 molten particles with different thermal history
Polycrystal after quenching to 850 K
Polycrystal after quenching to 850 K
Polycrystal after quenching to 850 K
One image of molten particles is given in Figure
To observe the stochastic behavior of the recrystallization, it is necessary to generate ensembles of systems with different thermal histories. Therefore the selected three-grain polycrystalline particle shown in Figure
Recrystallization is said to be initiated by nucleation. What is observed to happen is that the crystalline planes of the smaller grains become disrupted, making the grain appear to become amorphous. Then some stochastic, first-order process begins to form crystalline planes coincident with those of the larger, adjacent crystal. While this process has some of the earmarks of nucleation, regrettably we so far lack an adequate knowledge of the characteristics defining nuclei for recrystallization.
The recrystallization of grain structure is accompanied by energy changes. Therefore a transition in a given particle can be recognized by a sudden change in the slope of energy as a function of temperature during an annealing run. Monitoring structural changes is an effective alternative analysis method to energy, during freezing and recrystallization. Structural changes were followed by observing the linearity in the arrays of atoms corresponding to BCC cell edges. Deviations from linearity disclosed dislocations.
For an ideal BCC lattice, each atom and its nearest 8 coordination atoms, the corner atoms, form a body-centered cubic unit cell. Each atom in an array along cell edges is located at the crossing point of three orthogonal axes that connect the corners of the cells. Taking this crossing of central atoms as an origin, at the ends of the three orthogonal cell edges are 6 atoms appearing as sharp spots for a perfect crystal. For the sake of simplicity, we only consider the lines connecting an array of three atoms, with the central atom at the corner of a BCC cell, which is shared by BCC cells in the bulk case. For imperfectly packed nanoparticles these six spots may be diffuse.
Line of three atoms along a cell edge may be far from linear because of a surface or other imperfections, and if there are fewer than three nearly orthogonal lines crossing a cell corner, we will refer to these cases as having fewer than three “cross-overs” and use these in an analysis of dislocations and surfaces. In determining the number of “cross-overs” we considered neighboring atoms within the range of 2.76–2.96 Å lying along directions within 4° of perfect orthogonality [
Inasmuch as the recrystallization rate was observed to evolve into a first-order process, it is possible to interpret results in terms of classical nucleation theory as follows. The fraction of particles, in which a postulated nucleation site for recrystallization has not yet formed, obeys the first-order rate law
Figure
Images of nanoparticle at various times during the annealing run.
(Begin)
(220 ps)
(322 ps)
(336 ps)
(356 ps)
(528 s)
(536 ps)
(538 ps)
(556 ps)
(872 ps)
As seen in Figure
Figure
The total energy as a function of time during the quenching run at 850 K in unit of J/mol.
Figure
The total energy as a function of time during the annealing run in unit of J/mol.
The time between when the tricrystalline particle was put into the heat bath of 850 K and the onset of the first sharp energy drop from Figure
Figure
Most of the experimental work in recrystallization research described in the literature begins with a plastically deformed phase, followed by the processes of recovery, recrystallization, and grain growth. At present there is an incomplete understanding of the various rates encountered between deformation and the processes of recovery and recrystallization. This complicates the development of quantitative models of recrystallization. On the other hand, there is a great deal of information about the formation of boundaries during deformation, but theories of annealing are limited. In MD simulations there is no deformation stage because the metal particles are directly annealed from the state in which they were generated. This eliminated certain complications encountered experimentally, allowing us to concentrate on the steps after recovery. The greatest advantage of MD simulation is that the structure changes can be seen at the atomic level and followed during the grain migration.
A grain boundary is formed where two single-crystal grains in a polycrystalline aggregate meet and is characterized by five degrees of freedom; these include the misorientation of the grains on either side of the boundary (two degrees of freedom for the axis of misorientation and one for the misorientation angle) and the plane of the interface (two degrees of freedom). Once the boundary plane and the rotation axis are determined, then the smallest rotation angle around the rotation axis can be used for the misorientation between two crystal grains. Conventionally, grain boundaries are often grouped into low angle and high angle with the delimiting angle separating low from high angle boundaries of 15°.
Our selected sample was annealed at constant temperature in a bath at 850 K, and recrystallization events were analyzed at the atomic level. Figure
Grain boundary misorientation angles of an Fe2616 particle at the beginning of an annealing run.
The recrystallization rates for these two different grains were different. One interesting thing is that the transformation rate for the right grain is higher despite its smaller grain boundary misorientation angle. The factor discriminating between the two rates can be attributed to the greater disorder in the smaller particle despite its lower misorientation angle.
As mentioned before, once a grain boundary starts to move, the time to complete the consumption of the left grain is less than the time used for the right grain despite the slower rate. This counterintuitive effect seems to stem from the fact that, for reasons unknown, the smaller grain takes a longer time in its transformation to develop into first-order kinetics.
Presumably any critical nucleus is in the disordered grain and is immediately adjacent to the grain boundary. It must contain atoms in planes with the orientation of the larger grain. Such a nucleus was not conspicuous in our simulation and, regrettably, such a nucleus was not intensively searched for, so it remains speculative.
The solid state recrystallization and grain boundary migrations in an iron nanoparticle Fe2616 with three grains were studied by a molecular dynamics simulation. Rates were not inconsistent with what would be expected for a process of nucleation though no direct evidence of nuclei was observed. It was found that first-order transformation rates could be determined as the smaller grains were consumed by the larger one. In comparing subgrains, the conclusion that grain disorder was more important than the misorientation angle in governing the rates was reconfirmed in this study. Suggestions about the critical nuclei for the recrystallization are proposed. No obvious interactions between the subsidiary grains boundaries were observed in the example studied in this report.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported in part by the Social Security Administration.