# Impact of Alloying on Stacking Fault Energies in γ-TiAl

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Geometry of Planar Defects in $\gamma $-TiAl

#### 2.2. Modeling of SFs

#### 2.3. Computational Details

## 3. Results and Discussion

#### 3.1. SFE in $\gamma $-TiAl

#### 3.2. Impact of Alloying Elements

#### 3.3. Comparison with Experiment

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

APB | anti-phase boundary |

CASTEP | Cambridge Serial Total Energy Package |

CPA | coherent potential approximation |

CSF | complex stacking fault |

DFT | density functional theory |

ESF | extrinsic stacking fault |

FP-LAPW | full-potential linearized augmented plane-wave (method) |

FP-LMTO | full-potential linear muffin-tin orbital (method) |

GGA | generalized gradient approximation |

GSFE | generalized stacking fault energy |

LDA | local density approximation |

ISF | intrinsic stacking fault |

SF | stacking fault |

SFE | stacking fault energy |

SISF | superlattice intrinsic stacking fault |

TEM | transmission electron microscopy |

TM | transition metal |

VASP | Vienna Ab initio Simulation Package |

xc | exchange and correlation (potential, effects) |

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**Figure 1.**Schematic drawing demonstrating the two possible modeling approaches to SFs in the $\gamma $-TiAl with the L${1}_{0}$ structure.

**Figure 2.**Energy profile along the dissociation path according to (

**a**) Equation (2) and (

**b**) Equation (3). The right panels show the dissociation path overlayed on the calculated $\{111)$ GSFE surface of the $\gamma $-TiAl lattice.

**Figure 3.**Impact of alloying on $\gamma $-TiAl with a composition Ti-48Al-2X (X = transition metal element): (

**a**) SFs fixed to their geometrically-dictated configurations and relaxed only in the perpendicular direction and (

**b**) atomic positions fully relaxed.

**Figure 4.**Dependence of SFEs on the location of the substitutional atom (here, Ti). N labels the layer number away from the fault plane (located at $N=0$), and the dashed line represents a reference value for the stoichiometric TiAl (Table 1).

**Figure 5.**GSFE profile for Ti-48Al-2Nb along the (

**a**) Equation (2) and (

**b**) Equation (3) dissociation paths.

**Table 1.**Calculated SF energies (in mJ/m${}^{2}$) compared with available literature data for $\gamma $-TiAl. Differences in calculation methods are noted.

APB | CSF | SISF | Note | |
---|---|---|---|---|

present work | 717 | 415 | 188 | GGA-PW91, VASP, tilted supercells |

635 | 370 | 173 | GGA-PW91, VASP, tilted supercells, fully relaxed | |

711 | 414 | 188 | GGA-PW91, VASP, displaced supercells | |

694 | 392 | 179 | LDA, VASP, tilted supercells | |

[10] | 710 | 314 | 134 | LDA, FP-LMTO, tilted supercells(?) |

[11] | 756 | 420 | 184 | LDA, FP-LAPW, tilted supercells |

[12] | 499 | 329 | 137 | GGA-PW91, CASTEP, tilted supercells |

[13] | 355 | 184 | GGA-PW91, VASP, displaced supercells | |

[14] | 663 | 400 | 170 | GGA-PW91, VASP, displaced supercells |

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**MDPI and ACS Style**

Dumitraschkewitz, P.; Clemens, H.; Mayer, S.; Holec, D.
Impact of Alloying on Stacking Fault Energies in *γ*-TiAl. *Appl. Sci.* **2017**, *7*, 1193.
https://doi.org/10.3390/app7111193

**AMA Style**

Dumitraschkewitz P, Clemens H, Mayer S, Holec D.
Impact of Alloying on Stacking Fault Energies in *γ*-TiAl. *Applied Sciences*. 2017; 7(11):1193.
https://doi.org/10.3390/app7111193

**Chicago/Turabian Style**

Dumitraschkewitz, Phillip, Helmut Clemens, Svea Mayer, and David Holec.
2017. "Impact of Alloying on Stacking Fault Energies in *γ*-TiAl" *Applied Sciences* 7, no. 11: 1193.
https://doi.org/10.3390/app7111193