Comparison and Analysis of Diffusion Models: Growth Kinetics of Diiron Boride Layers on ASTM A283 Steel
Abstract
:1. Introduction
2. Materials and Methods
2.1. Materials and Boriding Treatment
2.2. Description Tools
2.3. First Approach: Steady-State Diffusion Model
- (i)
- Once the threshold value of the boron concentration () at the surface is reached, the formation of layers in flat fronts begins;
- (ii)
- An initial Fe2B layer () is formed after a given incubation period ();
- (iii)
- The boride layer grows as a consequence of the perpendicular diffusion of boron atoms on the substrate surface;
- (iv)
- Fe2B layer formation occurs under thermodynamic equilibrium conditions;
- (v)
- The growth kinetics are regulated by the diffusivity of boron atoms in the composition of the boride layer;
- (vi)
- The flow of boron atoms is one-dimensional;
- (vii)
- The boron concentration at the surface and growth interface remains constant in the Fe2B layer during the process;
- (viii)
- The Fe2B layer is narrow in comparison with the thickness of the sample;
- (ix)
- The temperature at each point of the sample is identical during the whole process;
- (x)
- The chemical potential does not vary with time.
2.4. Second Approach: The Integral Diffusion Model
3. Results
3.1. SEM Examinations of the Cross-Sectional Views of Borided Coatings
3.2. Peak Profile Analysis in X-ray Diffraction
3.3. Microhardness Vickers Profile
3.4. Rockwell-C Cohesion Indentation Tests
3.5. Pin-on-Disc Tests
3.6. Assessing the Minimum Boron Energy Value in Diiron Boride for ASTM A283 Steel
4. Discussion
Analysis of Mathematical Diffusion Models
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Boriding Temperature T (K) | Incubation Period (s) | |
---|---|---|
1123 | 2.3 × 10−13 | 1798 |
1173 | 4.7 × 10−13 | 1796 |
1223 | 1.1 × 10−12 | 1796 |
1273 | 1.8 × 10−12 | 1795 |
Type of Steel | Boriding Process | Activation Energy (kJmol−1) | Temperature Range of Investigation (K) | Approach for Calculation | References |
---|---|---|---|---|---|
AISI 8620 | Plasma-paste boriding | (FeB + Fe2B) 99–108 | 973–1073 | Parabolic growth law | [9] |
ASTM A1011 | Powder | (Fe2B) 159 | 1123–1273 | Mean diffusion coefficient method | [13] |
Hardox–450 | Powder | (Fe2B) 158 | 1123–1223 | Parabolic relation | [37] |
PM Iron alloy at 3 wt.%C | Powder | (FeB + Fe2B) 164 | 1123–1223 | Parabolic relation | [40] |
AISI 1018 | Electrochemical boriding | (FeB + Fe2B) 173 ± 8 | 1123–1273 | Parabolic relation | [41] |
AISI 5140 | Salt bath | (FeB + Fe2B) 223 | 1123–1273 | Parabolic relation | [42] |
Low carbon steel | Pulse current integrated CRTD-Bor | Dominant Fe2B 38 | 1123–1323 | Parabolic relation | [43] |
C45 steel | Powder | (FeB + Fe2B) 199 | 1143–1243 | Parabolic relation | [44] |
AISI 1045 | Powder | (FeB + Fe2B) 198–137 with wt.% Nd2O3 | 1053–1213 | Parabolic relation | [45] |
ASTM A283 | Powder | (Fe2B) 168 | 1123–1273 | Steady-state diffusion model and Integral method | This work |
Boronizing Conditions T (K) | Experimental Values of Fe2B Layers’ Thicknesses (μm) | Calculated Fe2B Layers’ Thicknesses (μm) |
---|---|---|
1223 K for 9 h | 181 ± 27 | 175 |
1273 K for 9 h | 241 ± 38 | 246 |
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Ortiz-Domínguez, M.; Gómez-Vargas, O.A.; Bárcenas-Castañeda, M.; Castellanos-Escamilla, V.A. Comparison and Analysis of Diffusion Models: Growth Kinetics of Diiron Boride Layers on ASTM A283 Steel. Materials 2022, 15, 8420. https://doi.org/10.3390/ma15238420
Ortiz-Domínguez M, Gómez-Vargas OA, Bárcenas-Castañeda M, Castellanos-Escamilla VA. Comparison and Analysis of Diffusion Models: Growth Kinetics of Diiron Boride Layers on ASTM A283 Steel. Materials. 2022; 15(23):8420. https://doi.org/10.3390/ma15238420
Chicago/Turabian StyleOrtiz-Domínguez, Martín, Oscar Armando Gómez-Vargas, Mariana Bárcenas-Castañeda, and Víctor Augusto Castellanos-Escamilla. 2022. "Comparison and Analysis of Diffusion Models: Growth Kinetics of Diiron Boride Layers on ASTM A283 Steel" Materials 15, no. 23: 8420. https://doi.org/10.3390/ma15238420