Critical Evaluation and Thermodynamic Modeling of the Li-Se and Na-Se Binary Systems Using Combined CALPHAD and First-Principles Calculations Method
Abstract
:1. Introduction
2. Critical Literature Review
2.1. The Li-Se Binary System
2.2. The Na-Se Binary System
Phase | Strukturb-ericht | Pearson Symbol | Space Group | Lattice Parameters, Å | Model | |||||
---|---|---|---|---|---|---|---|---|---|---|
References | vdW Method | a | b | c | ||||||
Liquid | - | - | - | - | - | - | 3.5093 | - | - | MQMPA a |
bcc_A2 (Li) | A2 | cI2 | Experimental data | [30] | - | 3.4268 | - | - | CEF b | |
Calculated data | TW c | PBE | 3.3721 | - | - | - | ||||
TW | D3 | 3.2674 | - | - | - | |||||
TW | D2 | 3.4569 | - | - | - | |||||
TW | optB86b | 3.4741 | - | - | - | |||||
TW | optB88 | 3.4534 | - | - | - | |||||
TW | DF | 3.3920 | - | - | - | |||||
TW | DF2 | 3.5093 | - | - | - | |||||
hex_A8 (Se) | A8 | hP3 | Experimental data | [30] | - | 4.3659 | - | 4.9537 | CEF | |
Calculated data | TW | PBE | 4.6347 | - | 5.0300 | - | ||||
TW | D3 | 4.2577 | - | 5.0888 | - | |||||
TW | D2 | 4.3682 | - | 5.0609 | - | |||||
TW | optB86b | 4.1722 | - | 5.1180 | - | |||||
TW | optB88 | 4.2898 | - | 5.0986 | - | |||||
TW | DF | 4.7153 | - | 5.1036 | - | |||||
TW | DF2 | 4.5682 | - | 5.2096 | - | |||||
bcc_A2 (Na) | A2 | cI2 | Experimental data | [42] | - | 4.2906 | - | - | CEF | |
Calculated data | TW | PBE | 4.1954 | - | - | - | ||||
TW | D3 | 4.1603 | - | - | - | |||||
TW | D2 | 3.9799 | - | - | - | |||||
TW | optB86b | 4.1754 | - | - | - | |||||
TW | optB88 | 4.1841 | - | - | - | |||||
TW | DF | 4.2130 | - | - | - | |||||
TW | DF2 | 4.1336 | - | - | - | |||||
Li2Se | C1 | cF12 | Experimental data | [27] | - | 6.0014 | - | - | ST d | |
[27] | - | 6.0001 | - | - | - | |||||
[28] | - | 6.0170 | - | - | - | |||||
[29] | - | 6.0020 | - | - | - | |||||
Calculated data | TW | PBE | 6.0051 | - | - | - | ||||
TW | D3 | 5.8910 | - | - | - | |||||
Li2Se | C1 | cF12 | Calculated data | TW | D2 | 5.9999 | - | - | - | |
TW | optB86b | 6.0012 | - | - | - | |||||
TW | optB88 | 6.0186 | - | - | - | |||||
TW | DF | 6.0894 | - | - | - | |||||
TW | DF2 | 6.0890 | - | - | - | |||||
Na2Se | C1 | cF12 | Experimental data | [28] | - | 6.8230 | - | - | ST | |
[43] | - | 6.8130 | - | |||||||
Calculated data | TW | PBE | 6.8535 | - | - | - | ||||
TW | D3 | 6.7003 | - | - | - | |||||
TW | D2 | 6.7762 | - | - | - | |||||
TW | optB86b | 6.7693 | - | - | - | |||||
TW | optB88 | 6.7761 | - | - | - | |||||
TW | DF | 6.8792 | - | - | - | |||||
TW | DF2 | 6.8636 | - | - | - | |||||
NaSe | - | hP8 | Experimental data | [44] | - | 4.6850 | - | 10.5300 | ST | |
Calculated data | TW | PBE | 4.7248 | - | 10.7860 | - | ||||
TW | D3 | 4.6303 | - | 10.5777 | - | |||||
TW | D2 | 4.6715 | - | 10.4226 | - | |||||
TW | optB86b | 4.6352 | - | 10.6614 | - | |||||
TW | optB88 | 4.6392 | - | 10.7487 | - | |||||
TW | DF | 4.7253 | - | 11.0405 | - | |||||
TW | DF2 | 4.7088 | - | 11.0724 | - | |||||
Na2Se3 | - | - | - | - | - | - | - | - | - | ST |
NaSe2 | - | tI48 | Experimental data | [43] | - | 10.1926 | - | 12.2177 | ST | |
Calculated data | TW | PBE | 4.7248 | - | 10.7860 | - | ||||
TW | D3 | 10.0389 | - | 12.2162 | - | |||||
TW | D2 | 10.2005 | - | 11.7552 | - | |||||
TW | optB86b | 10.1190 | - | 11.9942 | - | |||||
TW | optB88 | 10.2042 | - | 12.0233 | - | |||||
TW | DF | 10.5358 | - | 12.2918 | - | |||||
TW | DF2 | 10.5920 | - | 12.1594 | - | |||||
NaSe3 | - | - | - | - | - | - | - | - | - | ST |
Phase | Method | Enthalpy of Formation, (kJ/mol-atoms) | Reference |
---|---|---|---|
Li2Se | PBE | −120.3 | [32] |
emf | −139.3 | [35] | |
calorimetry | −147.4 ± 1.3 | [37] | |
electrochemical and calorimetry | −141.97 ± 3 | [38] | |
PBE | −123.2 | FTW a | |
D3 | −128.4 | FTW | |
D2 | −134.4 | FTW | |
optB86b | −129.8 | FTW | |
optB88 | −131.5 | FTW | |
DF | −130.7 | FTW | |
DF2 | −136.1 | FTW | |
PBE | −142.1 | [21,22] | |
CALPHAD | −143.6 | CTW b | |
Na2Se | PBE | −109.6 | [32] |
electrochemical and calorimetry | −114.2 | [38] | |
emf | −131.9 | [50] | |
calorimetry | −114.3 | [51] | |
the NBS tables | −113.8 | [52] | |
PBE | −106.3 | FTW | |
D3 | −108.5 | FTW | |
D2 | −116.7 | FTW | |
optB86b | −108.5 | FTW | |
optB88 | −114.1 | FTW | |
DF | −115.1 | FTW | |
DF2 | −119.6 | FTW | |
PBE | −125.1 | [21,22] | |
CALPHAD | −121.8 | CTW | |
NaSe | PBE | −84.5 | [32] |
emf | −100.0 | [50] | |
calorimetry | −97.0 | [51] | |
PBE | −82.6 | FTW | |
D3 | −87.5 | FTW | |
D2 | −94.7 | FTW | |
optB86b | −85.5 | FTW | |
NaSe | optB88 | −89.8 | FTW |
DF | −90.7 | FTW | |
DF2 | −93.2 | FTW | |
PBE | −110.8 | [21,22] | |
CALPHAD | −106.0 | CTW | |
Na2Se3 | emf | −93.4 | [50] |
−88.7 | CTW | ||
NaSe2 | PBE | −58.3 | [32] |
emf | −86.6 | [50] | |
PBE | −56.9 | FTW | |
D3 | −62.1 | FTW | |
D2 | −65.4 | FTW | |
optB86b | −58.3 | FTW | |
optB88 | −61.0 | FTW | |
DF | −61.6 | FTW | |
DF2 | −62.8 | FTW | |
PBE | −94.6 | [21,22] | |
CALPHAD | −74.5 | CTW | |
NaSe3 | CALPHAD | −56.3 | CTW |
3. Thermodynamic Models
3.1. Liquid Phase
3.2. Solid Solutions
3.3. Stoichiometric Phases
3.4. Gaseous Phase
4. First-Principles Calculations
5. Results and Discussions
5.1. Thermodynamic Modeling and Evaluation of the Li-Se Binary System
5.2. Thermodynamic Modeling and Evaluation of the Na-Se Binary System
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Coordination Numbers a | Gibbs Energies of Pair Exchange Reactions (J/mol-atoms) | |||
---|---|---|---|---|
i | j | |||
Li | Se | 3 | 6 | |
Na | Se | 3 | 6 |
Phase, Model, and Thermodynamic Parameters (J/mol or J/(mol·K)) |
---|
hex_A8 phase, format (Li, Na, Se): |
; |
bcc_A2 phase, format (Li, Na, Se): |
; |
Li2Se phase, format (Li)2(Se): |
; |
Na2Se phase, format (Na)2(Se): |
; |
NaSe phase, format (Na)(Se): |
; |
NaSe2 phase, format (Na)(Se)2: |
; |
NaSe3 phase, format (Na)(Se)3: |
. |
Reaction | Reaction Type | Temperature (°C) | Composition (Se at.%) | References | ||
---|---|---|---|---|---|---|
Liquid ↔ bcc_A2 | Melting | 180.6 | - | 0 | - | [27] |
180.4 | ~0 | 0 | - | This work | ||
Liquid ↔ bcc_A2 +Li2Se | Eutectic | ~180.6 | ~0 | 0 | 33.3 | [27] |
180.4 | ~0 | 0 | 33.3 | This work | ||
Liquid ↔ Li2Se | Congruent | 1302 ± 25 | - | 33.3 | - | [27] |
1302 | ~0 | 33.3 | - | This work | ||
Liquid#1 ↔ Li2Se + Liquid#2 | Monotectic | 350±5 | 70 ± 2 | 33.3 | 99.5 ± 0.3 | [27] |
353.8 | 69.1 | 33.3 | 99.6 | This work | ||
Liquid ↔ Li2Se + hex_A8 | Eutectic | ~221 | 100 | 33.3 | 100 | [27] |
- | 100 | 33.3 | 100 | This work | ||
Liquid ↔ hex_A8 | Melting | 221 | - | 100 | - | [27] |
224.7 | ~0 | 100 | - | This work |
Reaction | Reaction Type | Temperature (°C) | Composition (Se at.%) | References | ||
---|---|---|---|---|---|---|
Liquid ↔ bcc_A2 | Melting | 97.8 | - | 0 | - | [42] |
97.7 | ~0 | 0 | - | This work | ||
Liquid ↔ bcc_A2 + Na2Se | Eutectic | ~97.8 | ~0 | ~0 | 33.3 | [42] |
97.5 | 0 | 0 | 33.3 | This work | ||
Liquid ↔ Na2Se | Congruent | >875 | - | 33.3 | - | [42] |
1087 | ~0 | 33.3 | - | This work | ||
Liquid+ Na2Se ↔ NaSe | Peritectic | ~495 | ~52 | 33.3 | 50 | [42] |
496.7 | 50.1 | 33.3 | 50 | This work | ||
Liquid+ NaSe ↔ Na2Se3 | Peritectic | 313 | ~64 | 50 | 60 | [42] |
316.4 | 62.9 | 50 | 60 | This work | ||
Liquid+ Na2Se3 ↔ NaSe2 | Peritectic | 290 | ~69 | 60 | 66.7 | [42] |
288.5 | 66.9 | 60 | 66.7 | This work | ||
Liquid+ NaSe2 ↔ NaSe3 | Peritectic | 258 | ~77 | 66.7 | 75 | [42] |
255.9 | 75.6 | 66.7 | 75 | This work | ||
Liquid#1 ↔ Liquid#2 + NaSe3 | Monotectic | ~255 | 78 | ~99.95 | 75 | [42] |
255.2 | 76.6 | 99.96 | 75 | This work | ||
Liquid ↔ hex_A8 + NaSe3 | Eutectic | ~221 | 99.98 | ~100 | 75 | [42] |
224.7 | 99.95 | 100 | 75 | This work | ||
Liquid ↔ hex_A8 | Melting | 221 | - | 100 | - | [42] |
224.8 | ~0 | 100 | - | This work |
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Ma, J.; Ji, C.; Wang, J.; Han, D.; Cui, Z.; Sa, B.; Cui, S. Critical Evaluation and Thermodynamic Modeling of the Li-Se and Na-Se Binary Systems Using Combined CALPHAD and First-Principles Calculations Method. Metals 2022, 12, 1349. https://doi.org/10.3390/met12081349
Ma J, Ji C, Wang J, Han D, Cui Z, Sa B, Cui S. Critical Evaluation and Thermodynamic Modeling of the Li-Se and Na-Se Binary Systems Using Combined CALPHAD and First-Principles Calculations Method. Metals. 2022; 12(8):1349. https://doi.org/10.3390/met12081349
Chicago/Turabian StyleMa, Jie, Chen Ji, Jian Wang, Dong Han, Zhou Cui, Baisheng Sa, and Senlin Cui. 2022. "Critical Evaluation and Thermodynamic Modeling of the Li-Se and Na-Se Binary Systems Using Combined CALPHAD and First-Principles Calculations Method" Metals 12, no. 8: 1349. https://doi.org/10.3390/met12081349