# Dislocations Help Initiate the α–γ Phase Transformation in Iron—An Atomistic Study

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## Abstract

**:**

## 1. Introduction

## 2. Simulation Method

## 3. Results

#### 3.1. The Austenitic Transformation

#### 3.2. The Martensitic Transformation

#### 3.3. Dislocations in the Transformed Phase

## 4. Conclusions

- The presence of dislocations alleviates the transformation in the sense that the martensitic transformation temperature is increased and the austenitic transformation temperature is decreased. For the martensitic transformation, a dislocation-free crystal would not transform at all under the simulation conditions (system size and cooling rate); here the presence of dislocations is essential in inducing the transformation.
- For the martensitic transformation, a roughly linear dependence of the transformation temperature on the dislocation density was found. For the austenitic transformation, on the other hand, a saturation of the transformation temperature at dislocation densities above around $\rho =2\times {10}^{12}$ cm${}^{-2}$ was observed. These trends correlate well with the potential energy stored in the dislocations, which exhibits the same dependence on dislocation energy as the transition temperature.
- In all cases, the new phase nucleated at the dislocations. In the absence of dislocations, the new phase would nucleate at the surface (if at all). Nucleation at the dislocations is in agreement with previous MD findings for NiAl alloys [49], which show that the lattice distortion induced by the stress exerted by the dislocation configurations assists in the nucleation of the new phase, and also with other studies of defective pure Fe crystals that report phase nucleation in the vicinity of defects, such as grain boundaries [21] and phase boundaries [22]. However, Karewar et al. [23] found a more complex nucleation pattern in their study of the influence of planar defects on the martensitic transformation, depending on the resolved shear stresses in the available slip systems; depending on the configuration of the planar defects, these may increase or decrease the barrier for slip and hence for the coordinated atomic movement necessary for the martensitic transformation.
- The orientation relationships governing the transformation in the nuclei at the dislocations are governed by the Burgers path and the Kurdjumov–Sachs and Nishiyama–Wassermann paths; these pathways have also been identified to dominate the transformation behavior of pure iron in other simulational studies [50]. However, when, after growth and coalescence of the nuclei, the entire sample has transformed, a simple microstructure results. After the martensitic transformation, the bcc-phase is characterized by a homogeneous phase consisting of only few twinned grains separated by twin boundaries; the austenitic phase, on the other hand, is single-crystalline, containing planar defects such as stacking-fault planes and plates of hcp material. This simple microstructure is the consequence of the free surfaces of the thin film, which tend to form conserved planes under the transformation [39]. As a consequence, the final orientation relationships of the transformed sample are characterized by the Bain and the Pitsch pathway.
- While the new phase nucleates earlier when dislocations are present, the duration of the transformation is slowed down, as multiple nuclei compete in their growth.
- The transformed crystal contains abundant dislocations. The dislocation density becomes reduced in the case of the martensitic transformation but may even increase during the austenitic transformation. A detailed analysis demonstrates that the dislocations in the novel structure are ‘inherited’ from the original phase.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Examples of dislocation-filled samples used in the simulation. (

**Top row**) bcc sample used for studying the austenitic transformation: $\rho =4.5\times {10}^{12}$ cm${}^{-2}$. (

**a**) The local lattice structure: bcc (green), fcc (dark blue), hcp (light blue), and unidentified (red); (

**b**) the dislocation network: $1/2\langle 111\rangle $ (green) and $\langle 100\rangle $ (pink). (

**Bottom row**) fcc sample used for studying the martensitic transformation: $\rho =13.6\times {10}^{12}$ cm${}^{-2}$. (

**c**) The local lattice structure as in (

**a**); (

**d**) the dislocation network: $1/6\langle 112\rangle $ (green), $1/6\langle 110\rangle $ (pink), $1/2\langle 110\rangle $ (blue), $1/3\langle 100\rangle $ (yellow), and other (red).

**Figure 2.**Transition temperature ${T}_{c}$ as a function of the dislocation density $\rho $ for the (

**a**) austenitic and (

**b**) martensitic transformations; potential energy of the crystallites ${E}_{\mathrm{pot}}$ as a function of the dislocation density $\rho $ for the (

**c**) bcc and (

**d**) fcc crystals.

**Figure 3.**Snapshots of a dislocation-free bcc sample before, during, and after the austenitic transformation at temperatures of 10, 919, and 1250 K, respectively. The colors denote the local lattice structure as in Figure 1.

**Figure 4.**Snapshots of a bcc sample with low dislocation density, $\rho =1.72\times {10}^{12}$ cm${}^{-2}$, before, at the start, during, and after the austenitic transformation at temperatures of 645, 728, 730, and 1250 K, respectively. The colors denote the local lattice structure as in Figure 1.

**Figure 5.**Snapshots of a bcc sample with high dislocation density, $\rho =4.5\times {10}^{12}$ cm${}^{-2}$, (

**a**) before, (

**b**) at the start, and (

**c**) after the austenitic transformation at temperatures of 543, 753, and 1250 K, respectively. Snapshots show a view on a ${\left(110\right)}_{\mathrm{bcc}}$ plane; (

**d**) a perspective view of the dislocation structure in (

**b**). The colors denote the local lattice structure and the dislocations (in the bcc-phase) as in Figure 1.

**Figure 6.**Nucleation of the (

**a**) austenitic and (

**b**) martensitic phase in the corresponding transformations. Sample (

**a**) with a dislocation density of $\rho =4.5\times {10}^{12}$ cm${}^{-2}$ corresponds to Figure 5b at the start of the austenitic transformation process; sample (

**b**) with a dislocation density of $\rho =10.34\times {10}^{12}$ cm${}^{-2}$ corresponds to Figure 8c at the start of the martensitic transformation process. The colored lines denote the dislocation type in the original phase, the green (blue) atoms, the nucleating bcc (close-packed (cp))-phase as in Figure 1.

**Figure 7.**Pathway during the austenitic transformation of a sample with a dislocation density of $1.72\times {10}^{12}$ cm${}^{-2}$; cf. Figure 4. Snapshot (

**a**) during the phase transition at 728 K (corresponding to Figure 4b) provides a view on the ${\left(0\overline{1}1\right)}_{\mathrm{bcc}}\parallel {\left(0001\right)}_{\mathrm{hcp}}$ plane; the red arrows show the conserved directions, ${\left[\overline{1}11\right]}_{\mathrm{bcc}}\parallel {\left[11\overline{2}0\right]}_{\mathrm{hcp}}$. The black hexagons highlight the transformation of the relevant atoms in the bcc crystal into the hcp unit cell. Snapshots (

**b**,

**c**) compare the structures before (

**b**, 10 K) and after (

**c**, 1300 K) the transformation by a view on the ${\left(001\right)}_{\mathrm{bcc}}\parallel {\left(001\right)}_{\mathrm{fcc}}$ plane; the red arrows show the conserved directions, ${\left[100\right]}_{\mathrm{bcc}}\parallel {\left[110\right]}_{\mathrm{fcc}}$ and ${\left[010\right]}_{\mathrm{bcc}}\parallel {\left[1\overline{1}0\right]}_{\mathrm{fcc}}$. The black rectangle in (

**b**) shows the bcc unit cell, the white rectangle in (

**c**), the fcc unit cell. The colors denote the local lattice structure as in Figure 1.

**Figure 8.**Martensitic transformation process in a sample with a dislocation density of $\rho =10.34\times {10}^{12}$ cm${}^{-2}$. (

**a**) The temporal evolution of the sample temperature during the martensitic transformation; the times of the snapshots (

**b**–

**f**) are marked in (

**a**); (

**g**) the final state after completion of the transformation. The colors denote the local lattice structure as in Figure 1.

**Figure 9.**Pathway during the martensitic transformation of a sample with a dislocation density of $10.34\times {10}^{12}$ cm${}^{-2}$; cf. Figure 8. (

**a**): View on the close-packed plane ${\left(111\right)}_{\mathrm{fcc}}\parallel {\left(110\right)}_{\mathrm{bcc}}$ during the phase transition; the figure shows a detail in the nanotwinned structure in the top left part of Figure 8e. The white arrows denote the conserved directions, ${\left[\overline{1}10\right]}_{\mathrm{fcc}}\parallel {\left[\overline{1}11\right]}_{\mathrm{bcc}}$; the black rectangles highlight the twin structure; (

**b**) view on the x–z plane displaying a transformation state between Figure 8e,f; the red arrows emphasize the connection between the global phase nucleating at the surface and the nanotwinned structure; snapshots (

**c**,

**d**) compare the structures before (

**c**) and after (

**d**) the transformation by providing a view on a ${\left(001\right)}_{\mathrm{fcc}}\parallel {\left(1\overline{1}0\right)}_{\mathrm{bcc}}$ plane. Arrows indicate the conserved direction, ${\left[110\right]}_{\mathrm{fcc}}\parallel {\left[111\right]}_{\mathrm{bcc}}$. Red rectangles in (

**c**) highlight the twin structure built around the twin ${\left(11\overline{2}\right)}_{\mathrm{bcc}}$ boundaries. The colors denote the local lattice structure as in Figure 1.

**Figure 10.**(

**a**): Comparison of the dislocation density before and after the austenitic phase transition. Green data points marked by ‘GB’ denote cases of abundant dislocation production organized in grain boundaries; (

**b**,

**c**) snapshots of a specimen with a dislocation density of $3.63\times {10}^{12}$ cm${}^{-2}$ before (

**b**) and after (

**c**) the transformation. The colors denote the dislocation type as in Figure 1. Pink areas highlight corresponding regions before and after the transformation.

**Figure 11.**(

**a**): Comparison of the dislocation density before and after the martensitic phase transition; (

**b**,

**c**) snapshots of a specimen with a dislocation density of $10.34\times {10}^{12}$ cm${}^{-2}$ before (

**b**) and after (

**c**) the transformation. The colors denote the dislocation type as in Figure 1. Pink areas highlight corresponding regions before and after the transformation. In (

**c**), gray vertical structures denote twin boundary ${\left[1\overline{1}2\right]}_{\mathrm{bcc}}$ planes in the transformed bcc structure.

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**MDPI and ACS Style**

Meiser, J.; Urbassek, H.M.
Dislocations Help Initiate the *α*–*γ* Phase Transformation in Iron—An Atomistic Study. *Metals* **2019**, *9*, 90.
https://doi.org/10.3390/met9010090

**AMA Style**

Meiser J, Urbassek HM.
Dislocations Help Initiate the *α*–*γ* Phase Transformation in Iron—An Atomistic Study. *Metals*. 2019; 9(1):90.
https://doi.org/10.3390/met9010090

**Chicago/Turabian Style**

Meiser, Jerome, and Herbert M. Urbassek.
2019. "Dislocations Help Initiate the *α*–*γ* Phase Transformation in Iron—An Atomistic Study" *Metals* 9, no. 1: 90.
https://doi.org/10.3390/met9010090