On Agreement of Experimental Data and Calculated Results in Grain Boundary Segregation
Abstract
:1. Introduction
2. Determination of Grain Boundary Composition
3. Calculations of Segregation Energies
4. Fundamentals of the Comparison of Theoretical and Experimental Results
5. Comparison of Experimental and Theoretical Data on Grain Boundary Segregation
5.1. System Fe—5 at.% Si
5.2. System Fe—2.3 at.% V
5.3. System Fe—0.065 at.% Sn
6. Discussion
7. Conclusions
- An excellent agreement between experiment and calculation can be obtained when the solid solubility of the solute is high enough, i.e., well above 1 at.%;
- Experimental and calculated data can be compared on basis of averaged values of the segregation energy;
- Averaged values of the segregation energy must be determined using all sites, including the ‘anti-segregation’ ones;
- To predict the value of the segregation entropy, the approach of Scheiber and Romaner [12] distinguishing the upper and bottom branches of the enthalpy–entropy compensation effect seems to be valuable.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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GB Site | DFT ΔESi [24] (kJ mol−1) | PRED (DFT) ΔSSi [11] (J mol−1 K−1) | AES ΔHSi [23] (kJ mol−1) | AES ΔSSi [23] (J mol−1 K−1) | PRED [11] (kJ mol−1) | PRED [11] (J mol−1 K−1) |
---|---|---|---|---|---|---|
0 | −6.8 | −2.5 | - | - | - | - |
+1, −1 | −17.4 | −14.3 | - | - | - | - |
+2, −2 | −3.9 | +0.7 | - | - | - | - |
+3, −3 | −1 | +3.9 | - | - | - | - |
AVE | −7.3 | −3.1 | −8 | −3 | −8.4 | −4.4 |
GB Site | DFT ΔEV [26] (kJ mol−1) | PRED (DFT) ΔSV [11] (J mol−1 K−1) | PRED [11] (kJ mol−1) | PRED [11] (J mol−1 K−1) |
---|---|---|---|---|
0 | −16.4 | −13.2 | - | - |
+1, −1 | +6.8 | +12.5 | - | - |
+2, −2 | −12.5 | −8.9 | - | - |
AVE {111} | −5.6 | −1.2 | −5.5 | −1 |
GB Site | ML ΔESn (kJ mol−1) | PRED (ML) ΔSSn [11] (J mol−1 K−1) | PRED (ML) ΔSSn [12] (J mol−1 K−1) | DFT ΔESn (kJ mol−1) | PRED (DFT) ΔSSn [11] (J mol−1 K−1) | PRED (DFT) ΔSSn [12] (J mol−1 K−1) |
---|---|---|---|---|---|---|
0i | +166.6 | +239.1 | +239.1 | +31.3 | +88.8 | +88.8 |
1 | −104.4 | −111.0 | −62.0 | −78.0 | −81.7 | −32.7 |
+2, −2 | −57.1 | −58.5 | −9.5 | −66.5 | −68.9 | −19.9 |
+3, −3 | −32.6 | −31.2 | +17.8 | −37.2 | −36.3 | +12.7 |
+4, −4 | +5.1 | +10.7 | +59.7 | −9.0 | −5.0 | +44.0 |
+5, −5 | −2.3 | +2.4 | +51.4 | −11.2 | −7.4 | +41.6 |
+6, −6 | −2.3 | +2.4 | +51.4 | - | - | - |
+7, −7 | −3.5 | +1.1 | +50.1 | −4.5 | 0 | 49.0 |
AVE ΔSSi [11] | −8.8 | −1.3 | - | −25.3 | −19.0 | - |
AVE ΔSSi [12] | −8.8 | - | +44.2 | −25.3 | - | +25.9 |
PRED [11] | −7 | - | +46 | −7 | - | +46 |
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Černý, M.; Šesták, P.; Všianská, M.; Lejček, P. On Agreement of Experimental Data and Calculated Results in Grain Boundary Segregation. Metals 2022, 12, 1389. https://doi.org/10.3390/met12081389
Černý M, Šesták P, Všianská M, Lejček P. On Agreement of Experimental Data and Calculated Results in Grain Boundary Segregation. Metals. 2022; 12(8):1389. https://doi.org/10.3390/met12081389
Chicago/Turabian StyleČerný, Miroslav, Petr Šesták, Monika Všianská, and Pavel Lejček. 2022. "On Agreement of Experimental Data and Calculated Results in Grain Boundary Segregation" Metals 12, no. 8: 1389. https://doi.org/10.3390/met12081389