The Correlation Factors and Mechanisms of Diffusion for P and S in the Cu Single Crystal
Abstract
:1. Introduction
2. Materials and Methods
2.1. The Effective Diffusion Model—5-Frequency Model
2.2. Computational Details
3. Results
3.1. Vacancy Formation Energies and Vacancy–Impurity Interactions
3.2. Correlation Effects: The Effective Diffusion Model or 5-Frequency Model for the Diffusion of P and S in Cu
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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ΔEP | ΔES | ΔEvac | ΔEvac_P | ΔEvac_S |
---|---|---|---|---|
−0.653 | −0.511 | 1.176 | −0.229 | −0.432 |
P | ||||
Jump | λ (Å) | ΔEa (eV) | ΔZPE (eV) | ΔHa (eV) |
w1 | 2.518 | 0.639 | 0.012 | 0.650 |
w2 | 2.501 | 0.663 | 0.005 | 0.668 |
w3 | 2.545 | 0.884 | 0.005 | 0.889 |
w4 | 2.521 | 0.626 | −0.014 | 0.611 |
w0 | 2.495 | 0.819 | 0.008 | 0.828 |
S | ||||
Jump | λ (Å) | ΔEa (eV) | ΔZPE (eV) | ΔHa (eV) |
w1 | 2.518 | 0.714 | 0.010 | 0.724 |
w2 | 2.501 | 0.315 | 0.012 | 0.327 |
w3 | 2.545 | 0.895 | 0.009 | 0.904 |
w4 | 2.459 | 0.505 | −0.008 | 0.496 |
w0 | 2.495 | 0.819 | 0.008 | 0.828 |
Jump Index i | P | S | ||
---|---|---|---|---|
ν (Hz) | wi (Hz) | ν (Hz) | wi (Hz) | |
1 | 8.982 × 109 | 0.0905146 | 9.478 × 109 | 0.0053790 |
2 | 1.313 × 1010 | 0.0665103 | 9.031 × 109 | 26661.4233049 |
3 | 1.039 × 1010 | 9.5 × 10−6 | 1.048 × 1010 | 5.3 × 10−6 |
4 | 8.701 × 109 | 0.3974227 | 8.038 × 109 | 32.2438087 |
0 | 1.023 × 1010 | 1.020 × 10−4 | 1.023 × 1010 | 1.020 × 10−4 |
Quantity | Impurity | |
---|---|---|
P | S | |
T = 298 K | ||
x | 324.53063 | 26,336.58531 |
y | 324.61396 | 26,336.66865 |
F | 0.28609 | 0.28572 |
f2 | 0.57637 | 2.0195 × 10−7 |
f0 (fcc lattice) | 0.781 | 0.781 |
D (cm2·s−1) | 1.44 × 10−29 | 2.95 × 10−28 |
D (cm2·year−1) | 4.56 × 10−22 | 9.30 × 10−21 |
D (cm2·100,000 year−1) | 4.56 × 10−17 | 9.30 × 10−16 |
Diffusion length √(Dt) (cm·year−1) | 2.13 × 10−11 | 9.64 × 10−11 |
Diffusion length √(Dt) (cm·100,000 year−1) | 0.674 × 10−8 | 3.05 × 10−8 |
T = 373 K | ||
D (cm2·s−1) | 6.61× 10−24 | 8.06 × 10−23 |
D (cm2·year−1) | 2.09 × 10−16 | 2.54 × 10−15 |
D (cm2·100,000 year−1) | 2.09 × 10−11 | 2.54 × 10−10 |
Diffusion length √(Dt) (cm·year−1) | 1.44 × 10−08 | 5.04 × 10−08 |
Diffusion length √(Dt) (cm·100,000 year−1) | 4.57 × 10−06 | 1.60 × 10−05 |
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Lousada, C.M.; Korzhavyi, P.A. The Correlation Factors and Mechanisms of Diffusion for P and S in the Cu Single Crystal. Appl. Sci. 2025, 15, 3305. https://doi.org/10.3390/app15063305
Lousada CM, Korzhavyi PA. The Correlation Factors and Mechanisms of Diffusion for P and S in the Cu Single Crystal. Applied Sciences. 2025; 15(6):3305. https://doi.org/10.3390/app15063305
Chicago/Turabian StyleLousada, Cláudio M., and Pavel A. Korzhavyi. 2025. "The Correlation Factors and Mechanisms of Diffusion for P and S in the Cu Single Crystal" Applied Sciences 15, no. 6: 3305. https://doi.org/10.3390/app15063305
APA StyleLousada, C. M., & Korzhavyi, P. A. (2025). The Correlation Factors and Mechanisms of Diffusion for P and S in the Cu Single Crystal. Applied Sciences, 15(6), 3305. https://doi.org/10.3390/app15063305