# Applications and Thermodynamic Analysis of Equilibrium Solution for Secondary Phases in Ti–N–C Gear Steel System with Nano-Particles

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## Abstract

**:**

_{1}increases with the temperature decreases, and increases with the higher content of Ti or C, while it decreases with the higher N content under the same temperature. Thermodynamic analysis shows that nitrogen has been precipitated largely as TiN micron-particles above 1400 °C in gear steels. Then, titanium precipitated mainly as TiC nano-particles, thus this secondary phase can hinder grain coarsening during heat treatment.

## 1. Introduction

## 2. Thermodynamic Analysis

_{1}, M

_{2}) (C, N). Valid for small element concentrations, the microalloying elements M

_{1}and M

_{2}, as well as the interstitial elements C and N form dilute solutions in the matrix and their activities obey the Henry’s law. In this case, the effective activity coefficients of the components M

_{1}C, M

_{2}C, M

_{1}N and M

_{2}N are assumed to be k

_{1}, k

_{2}, m

_{1}and m

_{2}, respectively, and the total molar fraction of the M

_{1(k1+m1)}M

_{2(k2+m2)}C

_{(k1+k2)}N

_{(m1+m2)}carbonitride formed in the steel is t moles [14,15]. This carbonitride can be seen as a mixture of the following amounts of pure binary carbides and nitrides: k

_{1}t mole M

_{1}C, k

_{2}t mole M

_{2}C, m

_{1}t mole M

_{1}N and m

_{2}t mole M

_{2}N. Therefore, based on the chemical equilibrium, the thermodynamic analysis model and computing method of the equilibrium solution for the multivariable secondary phase in steels have been developed, according to the mass balance and solubility product equations for the quarternary secondary phase, or more. Therefore, the solid solution precipitation of the secondary phases formed in steel is Ti(C

_{k}

_{1}N

_{m}

_{1}) in the Ti–N–C microalloy steel system, and the coefficient of solid solubility of the product is taken as in the reference [14]. Therefore,

_{1}, C and N are the mass percentages of Ti, C and N, respectively; A

_{m}

_{1}, A

_{C}and A

_{N}are the atomic weights of Ti, C, and N, respectively; and A

_{Ti}= 47.9, A

_{N}= 14, A

_{C}= 12, [M

_{1}], [C] and [N] are the concentrations (in wt. %) of the respective elements dissolved in the solution; T is the temperature; and t is the total molar fraction of the carbonitride Ti(C

_{k}

_{1}N

_{m}

_{1}) formed in the steel; thus, these ternary secondary phases can be seen as a mixture of the following amounts of pure carbides and nitrides: k

_{1}t mole TiC, m

_{1}t mole TiN. Equations (1)–(6) have six unknowns, which are solved for numerically to determine the equilibrium state. For a given steel at any appropriate temperature, the equilibrium matrix composition, precipitate composition, and precipitate volume fraction can be determined (i.e., [M

_{1}], [C], [N], k

_{1}, m

_{1}and t).

_{1}and m

_{1}constants, as well as the total molar fraction of carbonitrides have been investigated. The complete dissolution temperatures for different Ti–N–C system microalloyed steels are shown in Table 1. The carbonitride complete dissolution temperature increases with higher C, N, or Ti levels in Ti–N–C system microalloyed steels. It should be noted that the effects of N and Ti additions on the complete dissolution temperature are expected to be greater compared with C. As is known for microalloyed gear steels, if the complete dissolution temperature is above the liquidus temperature, constitutional liquation of the carbonitrides would occur, so it is important to scientifically optimize the content of Ti, N and C elements in the actual production.

_{1}increases as the temperature decreases, and at a given temperature, the coefficient k

_{1}increases with the content of C or Ti increasing, while it decreases obviously with the content of N increasing. Therefore, in engineering application, for higher [Ti] dissolved in Ti-bearing microalloyed steels, the addition of N should be decreased during the microalloy composition design, which is significant to control the secondary phase precipitate at the required temperature.

## 3. Engineering Applications

_{1}and m

_{1}, strongly depends on the steel composition. The real content change of the TiC and TiN components with the temperature can be approximated, based on Figure 4b. The thermodynamic analysis shows that the dissolved Ti content is 0.03915%, the dissolved C content is 0.21843%, while the dissolved N content is only 0.00067% in the gear steel, and the coefficient k

_{1}is 0.23238, and the coefficient m

_{1}is 0.76762 at 1400 °C, thus nitrogen has been precipitated primarily in the TiN micro-particles above 1400 °C. The complete dissolution temperature is calculated to be 1915.02 °C by the model, which is 400 °C higher than the corresponding liquidus temperature of 1514.89 °C [16]. It is obvious that constitutional liquation of the strong carbonitrides would occur in this sample.

## 4. Conclusions

- (1)
- Thermodynamic calculation results show that the complete dissolution temperature increases with higher levels of either C, N, or Ti, and the effects of Ti and N are more significant compared with C. At a given temperature, the amount of dissolved Ti increases naturally as the content of Ti microalloyed element increases, while it decreases obviously with more N. It will decline rapidly in the complete dissolution temperature range, until 1100 °C in steels. The coefficient k
_{1}increases as the temperature decreases, and increases with the higher content of Ti or C, but decreases with the higher N content under the same temperature. - (2)
- For the 20CrMnTi gear steels produced by Fangda Special Steel Technology Co., Ltd., the heat treatment shows that when the temperature is above 950 °C, the grains begin to coarsen in this steel. When the temperature is 1000 °C, the grains coarsen sharply, the grain size is No. 5.0 grade, and the phases are ferrite and bainite, containing a small amount of pearlite.
- (3)
- Thermodynamic analysis shows that the nitrogen has been precipitated largely as TiN micron-particles above 1400 °C in the gear steels, and then the titanium is precipitated mainly as TiC nano-particles, so this secondary phase hinders grain growth during heat treatment, consistent with experimental results.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**C-0.0065N-0.02Timicroalloy steel: (

**a**) Ti content changes with temperature; (

**b**) k

_{1}coefficient changes with temperature.

**Figure 2.**0.20C-N-0.02Ti microalloy steel: (

**a**) Ti content changes with temperature; (

**b**) k

_{1}coefficient changes with temperature.

**Figure 3.**0.20C-0.0065N-Ti microalloy steel: (

**a**) Ti content changes with temperature; (

**b**) k

_{1}coefficient changes with temperature.

**Figure 4.**The 0.22%C-0.0067%N-0.066%Ti gear steel: (

**a**) Solid solution contents change with temperature; (

**b**) k

_{1}, m

_{1}and t change with temperature.

**Figure 5.**The 20CrMnTi steel microstructure: (

**a**) Optical image after etching; (

**b**) Optical image without etching.

**Figure 6.**(

**a**) scanning electron microscope (SEM) image of the secondary phase in 20CrMnTi; (

**b**) Energy dispersive spectroscopy (EDS) results.

**Figure 7.**Microstructure of 20CrMnTi under different heat treatment temperatures: (

**a**) 850 °C; (

**b**) 900 °C; (

**c**) 950 °C.

**Figure 8.**Secondary phase in 20CrMnTi gear steel: (

**a**) transmission electron microscopy (TEM) image; (

**b**) energy dispersive spectroscopy (EDS) results.

**Table 1.**Complete dissolution temperature changes with C, N and Ti composition variation in the Ti–C–N system steels.

Variation of C (0.0065N-0.02Ti) | Variation of N (0.20C-0.02Ti) | Variation of Ti (0.20C-0.0065N) | |||
---|---|---|---|---|---|

C (wt. %) | T_{AS} (°C) | N (wt. %) | T_{AS} (°C) | Ti (wt. %) | T_{AS} (°C) |

0.05C | 1630.69 | 0.0025N | 1470.73 | 0.01Ti | 1507.28 |

0.10C | 1632.35 | 0.005N | 1586.74 | 0.03Ti | 1719.72 |

0.20C | 1635.65 | 0.01N | 1722.56 | 0.045Ti | 1811.57 |

0.35C | 1640.54 | 0.015N | 1812.61 | 0.08 Ti | 1957.49 |

Steel | C | Si | Mn | Cr | Ti | N | P | S |
---|---|---|---|---|---|---|---|---|

Standard | 0.17–0.23 | 0.17–0.37 | 0.80–1.15 | 1.00–1.35 | 0.04–0.10 | ≤0.01 | ≤0.035 | ≤0.035 |

Sample | 0.22 | 0.22 | 0.88 | 1.14 | 0.066 | 0.0067 | 0.023 | 0.003 |

Element | Weight % | Atomic % |
---|---|---|

C K1 | 0.22 | 0.60 |

N K1 | 21.27 | 48.36 |

Ti K1 | 65.22 | 43.35 |

Cr K1 | 2.85 | 1.75 |

Fe K1 | 10.43 | 5.95 |

Material | Heat Treatment Temperature | Phases | Grain Size | Hardness, (HBW) |
---|---|---|---|---|

20CrMnTi | 850 °C | Ferrite, Pearlite | No. 11.5–12.0 grade | 172 |

900 °C | Ferrite, Pearlite | No. 11.5–12.0 grade | 170 | |

950 °C | Ferrite, Pearlite and Bainite | No. 8.5–10.0 grade | 217 | |

1000 °C | Ferrite, Bainite and a small amount of Pearlite | No. 5.0 grade | 234 |

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**MDPI and ACS Style**

Wang, Y.; Zhou, M.; Pang, X.; Volinsky, A.A.; Chen, M.; Gao, K. Applications and Thermodynamic Analysis of Equilibrium Solution for Secondary Phases in Ti–N–C Gear Steel System with Nano-Particles. *Metals* **2017**, *7*, 110.
https://doi.org/10.3390/met7040110

**AMA Style**

Wang Y, Zhou M, Pang X, Volinsky AA, Chen M, Gao K. Applications and Thermodynamic Analysis of Equilibrium Solution for Secondary Phases in Ti–N–C Gear Steel System with Nano-Particles. *Metals*. 2017; 7(4):110.
https://doi.org/10.3390/met7040110

**Chicago/Turabian Style**

Wang, Yanlin, Meng Zhou, Xiaolu Pang, Alex A. Volinsky, Mingwen Chen, and Kewei Gao. 2017. "Applications and Thermodynamic Analysis of Equilibrium Solution for Secondary Phases in Ti–N–C Gear Steel System with Nano-Particles" *Metals* 7, no. 4: 110.
https://doi.org/10.3390/met7040110