_{1}

^{*}

Molecular dynamics simulations of the phase transformation from body- centered-cubic (bcc) to face-centered-cubic (fcc) structures were performed. A Morse-type function was applied, and the parameters were determined so that both fcc and bcc structures were stable for the perfectcrystal model. When the fcc structure was superior to the bcc structure, the bcc model transformed to fcc. Two mechanisms, based on the Bain and Nishiyama- Wasserman (NW) relationships, were considered. Then, point or linear lattice defects, i.e., randomly scattered or regularly aligned vacancies, were introduced. Consequently, bcc models tended to transform to an fcc structure, whereas fcc models remained stable. The transformation process was also investigated in detail. BCC-to-FCC transformation is often considered as a homogeneous process based on changes in the axis lengths, and such a process was observed for the perfectcrystal model. Conversely, for the defect models, local heterogeneous deformation patterns, including cylindrical domain and planar interface formation, were observed. These behaviors are considered to be related to plastic deformation during phase transformation, and the validity of the presented model for further investigation was confirmed.

The microstructure of materials strongly affects the macroscopic mechanical properties, and controlling the microstructure is important for achieving required properties. With steel, heat treatment processes such as quenching, tempering, and annealing are the most effective routes that are indispensable for producing useful materials [

Alternatively, computer simulation is an indispensable tool in engineering processes. In heat treatment processes of steel, it has become possible to simulate macroscopic deformation and stress distribution, where the phase transformation is usually represented by an empirical kinetic law such as the Johnson-Mehl-Avrami-Kolmogorov equation, and the state of a phase is normally represented using the volume fraction of eachphase [

Experimental technology on a nanometer scale has achieved rapid progress using electron and atomic-force microscopy [

The crystallographic relationship between the fcc and bcc structures is usually explained as the Bain relationship.

Another relationship between fcc and bcc structures is Nishiyama-Wasserman (NW) relationship, as shown in

visualization of the expected results, the atomic configuration projected on the x-y and z-y planes when the bcc-to-fcc transformation occurs. The original (001) plane becomes the (011) plane of the fcc structure, following the Bain relationship, and a rectangular cell is prominent. However, relative motion of alternate layers, represented by black lines, occurs in the NW relationship, giving a somewhat disordered impression. The regular unit can be found by selecting a 45˚ rotated square, depicted in magenta, in which the center atom is shifted to one side. In the perpendicular (z-y) plane, the long and short edged rectangular cells are alternatively accumulated along the z direction.

A classical MD method with two-body interatomic potential function was used in this study, and the following Newton equation of motion was then solved numerically.

d 2 r i d t 2 = 1 m i F i = 1 m i ∑ j f i j , f i j = − d ϕ d r r i j | r i j | (1)

Here, r_{i} and m_{i} are the position vector and mass of the i-th atom, F_{i} is the force acting on the i-th atom, f_{ij} is the interatomic force between the i-th and j-th atoms, and ϕ is the interatomic potential energy function. In this study, the following Morse-type function is applied.

ϕ = D [ exp { − 2 α ( r − R ) } − 2 exp { − α ( r − R ) } ] (2)

Here, D, R, and α are the parameters, and the values for most major metallic elements are listed in the literature [

ϕ ∗ = exp { − 2 α ∗ ( r ∗ − 1 ) } − 2 exp { − α * ( r * − 1 ) } . (3)

In this paper, all variables are expressed as the standardized values, except for temperature, and the superscript * is omitted. Numerical integration was performed using the conventional velocity Verlet algorithm.

As a preliminary study, the potential parameter α was varied, and the stable structures were explored using the models illustrated in

Using these models, MD simulations were demonstrated at a constant temperature under a constant pressure, p = 0. The velocity scaling method was applied for temperature control with T = 10, 400, and 800 K. Total time step was set as 5000 steps, which may not be long enough to distinguish an actual stable structure, but this does not matter in this study because the transformation is the major objective.

bcc-(001) model. The model is initially cubic, and three edges have the same lengths. However, the x-edge is shortened, and the y and z edges are elongated between the 1000th and 2000th time steps. Consequently, the calculation cell becomes rectangular. The atomic configurations, shown in the magnified windows, correspond to those illustrated in

Similarly, an fcc transformation occurred for the bcc-(011) model. The initially rectangular calculation cell became cubic by stretching the shorter edge (y in this case), as shown in

The simulated results are summarized in a phase diagram shown in

Based on the results for perfect crystal models, the models with lattice defects were applied to the MD simulations. Models based on a bcc-(001) model are shown in _{a} or 3L_{a}, where L_{a} is the lattice parameter. In a full-line model, the vacancy line traverses the model, resulting in an infinite line through the periodic boundary. The defect line is set in the center of the x-y plane, as shown in

According to the phase diagram in

perfect crystal models. Typical results for α = 1.55 with Point-10 and α = 1.50 with Line-3 models are shown in

These results are summarized in a phase diagram in

higher values than that for line-defect models, but no specific effects on the phase transformation was found. Therefore, the initiation of the transformation is considered to originate in a local behavior, which is discussed in the next section.

According to both the Bain and NW relationships, the bcc-to-fcc transformation is an overall phenomenon, involving changes in the edge length and/or simultaneous sliding of the atomic layer. Therefore, if no local irregularity exists, phase transformation progresses homogeneously. However, defects may induce local irregular behavior; in some of the simulations, notable patterns, which may be related to plastic deformation, were observed.

The phase transformation is initiated around the 1500th time step, and then a circular pattern is generated on the z-y plane, as shown in

Another notable pattern is shown in

is initiated at about the 1500th timestep, which can be observed from the differences in the atomic configuration between the 1000th and 1500th time steps. Proceeding to the transformation, faint oblique lines are observed at the 1000th time step. These become sharper with the transformation at the 1500th time step and finally disappear when the transformation is completed by the 5000th time step. It is clear that the line corresponds to a plane in the 3-D view, and this is temporarily formed during the transformation. The origin of the plane can be tracked back to the defect, as seen in the 3-D view at the 3000th timestep, though this is ambiguous at the initiation period around the 1000th time step.

Similar behavior was observed for the full line models.

Overall, no specific patterns as shown in Figs 9 and 10 were observed during phase transformation for the scattered point defect models, although the total number of vacancies was much higher in a Point-10 model than that in a Line-3 model, and the increase in the potential energy was larger as shown in ^{th} time steps. Some other patterns were also observed, and detailed investigation of the universal features will continue.

Molecular dynamics simulations of the phase transformation from bcc to fcc structures were performed using a Morse-type potential, and the effects of lattice defects on the phase transformation were investigated. Consequently, it was revealed that the defects influenced the stable structure and accelerated transformation from bcc to fcc. Different types of lattice defects, such as cylindrical domain formation and planar defects, were also generated during phase transformation, which might result in the initiation of plastic deformation. Further investigation is necessary to clarify the relationship between the phase transformation and induced plastic deformation, and it is concluded that the validity of the

present model is verified. In addition, we have also reported microstructural change in polycrystalline material under severe plastic deformation [

The author declares no conflicts of interest regarding the publication of this paper.

Uehara, T. (2019) A Molecular Dynamics Study on the Effects of Lattice Defects on the Phase Transformation from BCC to FCC Structures. Materials Sciences and Applications, 10, 543-557. https://doi.org/10.4236/msa.2019.108039