# Microstructural and Mechanical Properties of Binary Ti-Rich Fe–Ti, Al-Rich Fe–Al, and Ti–Al Alloys

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Preparation of Disc Surfaces for Mechanical Characterization

#### Configuration with Piezoelectric Discs

## 4. Ingredients for Estimating Alloy-Disc-Sample Elastic Modulus

#### 4.1. First Model for Solving Direct Problem

#### 4.2. Second Model for Solving Direct Problem

#### 4.3. Solving the Inverse Problem of Vibrational Spectroscopy

#### 4.4. Identification and Classification of Vibration Modes in the Response Spectrum

## 5. Results

#### 5.1. XRF Analysis

#### 5.2. Energy Dispersive Spectrometer (EDS) Analysis

#### 5.3. Phase Identification

#### 5.4. Metallography

#### 5.5. Vibration Modes

## 6. Discussion

#### 6.1. Fe–Ti Binary Alloys

#### 6.2. Fe–Al Binary Alloys

#### 6.3. Ti–Al Binary Alloys

#### 6.4. Retrieved Young’s Modulus Values

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Diagram and (

**b**) photography of the setup employed for the vibration spectroscopy experimental setup.

**Figure 4.**Scanning electron microscopy (SEM) micrographs of binary alloys of respective compositions (percent by weight): (

**a**) ${\mathrm{Fe}}_{60}{\mathrm{Ti}}_{40}$, (

**b**) ${\mathrm{Fe}}_{50}{\mathrm{Ti}}_{50}$, (

**c**) ${\mathrm{Ti}}_{45}{\mathrm{Al}}_{55}$, (

**d**) ${\mathrm{Fe}}_{60}{\mathrm{Al}}_{40}$.

**Figure 5.**Natural vibration mode shapes of the thick discs: (

**a**) first flexural mode (≈70 kHz—Table 4); (

**b**) first compressional mode (≈110 kHz); (

**c**) second flexural mode (≈134 kHz); (

**d**) first wine-glass mode (≈165 kHz).

**Figure 6.**Vibration spectrum obtained using piezoelectric-disc transducers for the binary disc sample ${\mathrm{Fe}}_{50}{\mathrm{Ti}}_{50}$ composition (percentage by weight).

**Table 1.**Existing mechanical (elastic modulus) data in the literature for the studied alloys and methods employed to obtain them.

Alloy | Composition (at. %) | Young’s Modulus (GPa) | Characterization Method | Reference |
---|---|---|---|---|

TiAl | 154 | dynamic indentation | [16] | |

160–176 | [5] | |||

$\gamma $ TiAl | ${\mathrm{Ti}}_{44}$${\mathrm{Al}}_{56}$ | 182 | Resonant ultrasound spectroscopy Rectangular parallelepiped sample, sides (a, b, c) → (4.173, 3.993, 3.260) mm | [17] |

B19 TiAl | 161.99 159.24 | (DFT) Strain–stress method (DFT) Energy density method | [18] | |

FeTi | (310, 86, 74.9)- > (${c}_{11}$, ${c}_{12}$, ${c}_{44}$) Elastic constants ${c}_{ij}$ | Ultrasonic measurement method Acoustic Resonance and velocity | [19] | |

FeAl | Fe${\mathrm{Al}}_{40}$ | 205 | Tensile test | [2] |

FeAl | 48.71Al-50.87Fe | 261 | PZT ultrasonic composite oscillator-cylindrical specimens 3 mm diameter, 44 mm length | [20] |

Fe${\mathrm{Al}}_{2}$ | 204.5 | Embedded-atom method simulation | [21] |

**Table 2.**Effective compositions of the studied binary alloys obtained by X-ray fluorescence (XRF) analysis.

The Studied Alloys (w%) | ${\mathrm{Fe}}_{50}{\mathrm{Ti}}_{50}$ | ${\mathrm{Fe}}_{60}{\mathrm{Ti}}_{40}$ | ${\mathrm{Ti}}_{55}{\mathrm{Al}}_{45}$ | ${\mathrm{Ti}}_{45}{\mathrm{Al}}_{55}$ | ${\mathrm{Fe}}_{60}{\mathrm{Al}}_{40}$ | ${\mathrm{Fe}}_{80}{\mathrm{Al}}_{20}$ |
---|---|---|---|---|---|---|

Effective composition (Fe, Al, Ti) | 51.12–48.88 | 58.71–41.29 | 54.67–45.33 | 46.25–53.75 | 58.64–41.36 | 81.71–18.29 |

**Table 3.**Effective compositions of the studied alloys obtained by Energy Dispersive Spectrometer (EDS) analysis.

Studied Alloys (w%) | ${\mathrm{Fe}}_{50}{\mathrm{Ti}}_{50}$ | ${\mathrm{Fe}}_{60}{\mathrm{Ti}}_{40}$ | ${\mathrm{Ti}}_{55}{\mathrm{Al}}_{45}$ | ${\mathrm{Ti}}_{45}{\mathrm{Al}}_{55}$ | ${\mathrm{Fe}}_{60}{\mathrm{Al}}_{40}$ | ${\mathrm{Fe}}_{80}{\mathrm{Al}}_{20}$ |
---|---|---|---|---|---|---|

Effective composition (Fe, Al, Ti) | 50.60–49.40 | 61.96–38.04 | 55.29–44.71 | 45.75–54.25 | 58.64–41.36 | 79.66–20.34 |

Alloy Studied (w%) | Phases Formed | Crystal Structure | Prototype | Space Group | Reference |
---|---|---|---|---|---|

${\mathrm{Fe}}_{50}{\mathrm{Ti}}_{50}$ | FeTi | B2 | CsCl | Pm-3m | [34,35,36,37] |

${\mathrm{Fe}}_{2}$Ti | C14 | Mg${\mathrm{Zn}}_{2}$ | $\mathit{P}{\mathit{6}}_{\mathit{3}}\mathit{6}$/mmc | ||

${\mathrm{Fe}}_{60}{\mathrm{Ti}}_{40}$ | FeTi | B2 | CsCl | Pm-3m | |

${\mathrm{Fe}}_{2}$Ti | $\mathrm{C}14$ | Mg${\mathrm{Zn}}_{2}$ | $\mathit{P}{\mathit{6}}_{\mathit{3}}\mathit{6}$/mmc | ||

${\mathrm{Ti}}_{55}{\mathrm{Al}}_{45}$ | TiAl | $\mathrm{L}{1}_{0}$ | AuCu | P4/mmm | [34,35,36,37] |

Ti${\mathrm{Al}}_{2}$ | - | Hf${\mathrm{Ga}}_{2}$ | $\mathit{I}{\mathit{4}}_{\mathit{1}}$/amd | ||

${\mathrm{Ti}}_{45}{\mathrm{Al}}_{55}$ | TiAl | $\mathrm{L}{1}_{0}$ | AuCu | P4/mmm | |

Ti${\mathrm{Al}}_{2}$ | - | Hf${\mathrm{Ga}}_{2}$ | $\mathit{I}{\mathit{4}}_{\mathit{1}}$/amd | ||

${\mathrm{Fe}}_{60}{\mathrm{Al}}_{40}$ | FeAl | B2 | CsCl | Pm-3m | [34] |

Fe${\mathrm{Al}}_{2}$ | - | Fe${\mathrm{Al}}_{2}$ | P1 | ||

${\mathrm{Fe}}_{80}{\mathrm{Al}}_{20}$ | FeAl | B2 | CsCl | Pm-3m |

**Table 5.**Mechanical properties calculated by an ab initio method (density functional theory), and resonance frequencies of single-crystal metals computed using the 3D finite-element method (${F}_{1}$, ${F}_{2}$). ${E}_{1}^{r}$ and ${E}_{2}^{r}$ are the recovered Young’s moduli (in GPa) using synthetic resonance frequencies (${F}_{1}$, ${F}_{2}$) and the second interaction model (Equation (2)).

Element | Density (kg/m${}^{3}$) | Young’s Modulus (GPa) | Poisson Ratio ($\mathit{\nu}$) | ${\mathit{F}}_{1}$ (Hz) | ${\mathit{F}}_{2}$ (Hz) | ${\mathit{E}}_{1}^{\mathit{r}}$ (GPa) | ${\mathit{E}}_{2}^{\mathit{r}}$ (GPa) |
---|---|---|---|---|---|---|---|

Fe | 7874 Ref. [38] | 212 Ref. [39] | 0.27 | 70,480 | 110,577 | 213.27 | 210.05 |

Ti | 4500 Ref. [40] | 114.6 Ref. [38,41] | 0.3 | 67,932 | 109,053 | 111.14 | 114.60 |

Al | 2707 Ref. [38] | 69.3 Ref. [38,42] | 0.3 | 68,230 | 109,530 | 67.27 | 69.36 |

**Table 6.**Resonance frequencies (${f}_{1}$, ${f}_{2}$) recovered from vibration spectra obtained using piezoelectric-disc transducers and the corresponding Young’s moduli (${E}_{1}$, ${E}_{2}$), retrieved using Equation (2). Final 3D finite-element method (FEM) Young’s moduli (E) after adjustment to fit experimental resonance frequencies. The difference between ${E}_{2}$ and E is given as a percentage. The ${}^{\u2020}$ indicates ab initio calculated results found in the literature. Values of ${K}_{1}$ = 4.6356, ${K}_{2}$ = 7.3284, and initial $\nu $ = 0.27.

Composition (wt.%) | Composition (at.%) | ${\mathit{f}}_{1}$ (Hz) | ${\mathit{f}}_{2}$ (Hz) | Density (kg/m${}^{3}$) | ${\mathit{E}}_{1}$ (GPa) | ${\mathit{E}}_{2}$ (Gpa) | E (Gpa) 3D FEM | ${\mathit{F}}_{1}$ (Hz) 3D FEM | ${\mathit{F}}_{2}$ (Hz) 3D FEM | Difference Percentage ${\mathit{E}}_{2}$-E (%) | Previous Studies—Ref. E (GPa), $\mathit{\nu}$ |
---|---|---|---|---|---|---|---|---|---|---|---|

${\mathrm{Fe}}_{80}{\mathrm{Al}}_{20}$ | ${\mathrm{Fe}}_{66}{\mathrm{Al}}_{34}$ | 70,400 | 110,200 | 7412 | 200.03 | 196.30 | 200.03 | 70,650 | 110,800 | 1.86 | 200 Ref. [2] |

${\mathrm{Fe}}_{60}{\mathrm{Al}}_{40}$ | ${\mathrm{Fe}}_{42}{\mathrm{Al}}_{58}$ | 82,400 | 130,200 | 5330 | 197.30 | 197.10 | 197.30 | 82,840 | 130,000 | 0.10 | |

${\mathrm{Fe}}_{60}{\mathrm{Ti}}_{40}$ | ${\mathrm{Fe}}_{56}{\mathrm{Ti}}_{44}$ | 70,400 | 111,400 | 7050 | 190.50 | 190.80 | 190.50 | 70,740 | 111,000 | 0.16 | 191.66, $\nu $ = 0.287 Ref. [40] ${}^{\u2020}$ |

${\mathrm{Fe}}_{50}{\mathrm{Ti}}_{50}$ | ${\mathrm{Fe}}_{46}{\mathrm{Ti}}_{54}$ | 69,200 | 10,800 | 6950 | 181.47 | 179.16 | 181.47 | 69,174 | 108,700 | 1.27 | 182.38, $\nu $ = 0.28 Ref. [52] ${}^{\u2020}$ |

${\mathrm{Ti}}_{55}{\mathrm{Al}}_{45}$ | ${\mathrm{Ti}}_{40}{\mathrm{Al}}_{60}$ | 88,700 | 139,800 | 3880 | 166.45 | 165.40 | 166.45 | 88,521 | 139,270 | 0.63 | 160–176 Ref. [5] |

${\mathrm{Ti}}_{45}{\mathrm{Al}}_{55}$ | ${\mathrm{Ti}}_{32}{\mathrm{Al}}_{68}$ | 90,800 | 145,700 | 3609 | 162.60 | 166.90 | 162.60 | 91,460 | 143,000 | 2.64 | 161.99, $\nu $ = 0.265 Ref. [18] ${}^{\u2020}$ |

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**MDPI and ACS Style**

Chanbi, D.; Adnane Amara, L.; Ogam, E.; Amara, S.E.; Fellah, Z.E.A.
Microstructural and Mechanical Properties of Binary Ti-Rich Fe–Ti, Al-Rich Fe–Al, and Ti–Al Alloys. *Materials* **2019**, *12*, 433.
https://doi.org/10.3390/ma12030433

**AMA Style**

Chanbi D, Adnane Amara L, Ogam E, Amara SE, Fellah ZEA.
Microstructural and Mechanical Properties of Binary Ti-Rich Fe–Ti, Al-Rich Fe–Al, and Ti–Al Alloys. *Materials*. 2019; 12(3):433.
https://doi.org/10.3390/ma12030433

**Chicago/Turabian Style**

Chanbi, Daoud, Leïla Adnane Amara, Erick Ogam, Sif Eddine Amara, and Zine El Abiddine Fellah.
2019. "Microstructural and Mechanical Properties of Binary Ti-Rich Fe–Ti, Al-Rich Fe–Al, and Ti–Al Alloys" *Materials* 12, no. 3: 433.
https://doi.org/10.3390/ma12030433