High-Throughput Computation of New Carbon Allotropes with Diverse Hybridization and Ultrahigh Hardness
Abstract
:1. Introduction
2. Computational Procedure and Methods
- Step 1: Initially, the RG2 code generated 1598 carbon allotropes in total with different hybridization states.
- Step 2: We perform first-principles calculations to fully optimize those structures with low Monkhorst-pack k-mesh. The k-mesh in low-resolution DFT calculations depends on total number of atoms in the cell. Specifically, for numbers of atoms , , , and , the k-mesh was , , , and , respectively. After this step, we had 1576 carbon allotropes.
- Step 3: We continued to perform first-principles calculations to fully optimize the structures that were successfully optimized in the previous step, with high Monkhorst-pack k-mesh. The k-mesh in high-resolution DFT calculations depends on the length of lattice of the cell. Specifically, the product of the k-mesh in each direction and lattice size was approximately 60 Å. This was equivalent to the k-mesh of for diamond with an 8-atom conventional cell, which was high enough for global structure optimization. After this step, we had 1461 carbon allotropes.
- Step 4: After global structure optimization was finished, we cross-checked the 1461 carbon structures and also compared the structures with those downloaded from the SACADA database [29]. We found that some of the finally optimized structures had been already identified or reported in previous studies. After cross-checking and screening, we had 1105 new and unique carbon allotropes.
- Step 5: We finally calculated the elastic constants with conventional unit cells for all 1105 unique structures. Again, the k-mesh in each direction was determined by the same procedure as in Step 3. After this step, we successfully obtained the elastic constants of 1105 carbon allotropes.
- Step 6: Some structures had unreasonable universal anisotropy [32] so we decided to only report the carbon allotropes with universal anisotropy between 0 and 3. Finally, 904 carbon allotropes remained from all the screening processes.
3. Results and Discussion
3.1. Ground-State Energy and Thermodynamic Stability
3.2. Pearson Correlation
4. Conclusions
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Materials | Hybridizations | Vickers’ Hardness, (GPa) | Ground-State Energy, (eV) | Average Local Potential, (eV) |
---|---|---|---|---|
(a) 135-3-40-C-r89-np-id355667 | 30.88994 | −341.2203 | −11.7709 | |
(b) 136-3-20-C-r689-np-id545421_1 | Hybrid / | 69.35087 | −175.5362 | −12.7828 |
(c) 179-3-36-C-r6789-p-id545421 | 90.11029 | −320.6033 | −12.9213 | |
(d) 165-3-28-C-r68-np-id545421 | 90.10081 | −245.7932 | −13.1631 |
Materials | Vickers’ Hardness, (GPa) | Universal Anisotropy | Bulk Modulus, (GPa) | Elastic Modulus, (GPa) | Poisson’s Ratio | Volume Per Atom | Packing Fraction | Average Local Potential, (eV) | |
---|---|---|---|---|---|---|---|---|---|
206-1-16-C-r0-np-id355667 | 104.302 | 0.00457 | 385.28 | 1060.73 | 0.04114 | 3.5534 | 5.61272 | 0.25595 | −13.467 |
181-1-6-C-r0-p-id224838_1 | 94.8507 | 0.04505 | 429.82 | 1108.01 | 0.07036 | 3.9125 | 5.71263 | 0.2515 | −13.185 |
154-1-6-C-r0-p-id224838 | 94.36159 | 0.044264 | 431.9735 | 1109.813 | 0.071805 | 3.496109 | 5.704695 | 0.251855 | −13.195 |
180-1-12-C-r0-p-id224838 | 94.16793 | 0.055942 | 428.2763 | 1102.033 | 0.071136 | 3.485896 | 5.72141 | 0.251119 | −13.169 |
182-1-12-C-r6x-p-id224838 | 94.13454 | 0.084798 | 433.4282 | 1111.486 | 0.072599 | 3.487636 | 5.718554 | 0.251244 | −13.169 |
Materials | Vickers’ Hardness, (GPa) | Universal Anisotropy | Bulk Modulus, (GPa) | Elastic Modulus, (GPa) | Poisson’s Ratio | Volume Per Atom | Packing Fraction | Average Local Potential (eV) | |
---|---|---|---|---|---|---|---|---|---|
224-3-72-C-r69-np-id355667 | 2.99986 | 1.56873 | 99.07801 | 87.23116 | 0.353262 | 1.561686 | 12.77097 | 0.112502 | −8.092 |
131-2-48-C-r68x-np-id224838 | 3.082382 | 2.944065 | 170.7716 | 125.9887 | 0.37704 | 2.074342 | 9.61473 | 0.149433 | −9.773 |
207-3-72-C-r689-np-id224838 | 1.162879 | 1.085925 | 66.67588 | 42.13926 | 0.394666 | 1.276296 | 15.62666 | 0.091943 | −6.915 |
222-3-112-C-r6x-np-id355667 | 1.541133 | 1.974846 | 118.8571 | 70.42662 | 0.401245 | 1.477887 | 13.4951 | 0.106465 | −7.750 |
155-3-54-C-r6x-p-id355667 | 3.318981 | 2.33672 | 69.3944 | 72.49172 | 0.325894 | 1.541569 | 12.93762 | 0.111052 | −8.030 |
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Al-Fahdi, M.; Rodriguez, A.; Ouyang, T.; Hu, M. High-Throughput Computation of New Carbon Allotropes with Diverse Hybridization and Ultrahigh Hardness. Crystals 2021, 11, 783. https://doi.org/10.3390/cryst11070783
Al-Fahdi M, Rodriguez A, Ouyang T, Hu M. High-Throughput Computation of New Carbon Allotropes with Diverse Hybridization and Ultrahigh Hardness. Crystals. 2021; 11(7):783. https://doi.org/10.3390/cryst11070783
Chicago/Turabian StyleAl-Fahdi, Mohammed, Alejandro Rodriguez, Tao Ouyang, and Ming Hu. 2021. "High-Throughput Computation of New Carbon Allotropes with Diverse Hybridization and Ultrahigh Hardness" Crystals 11, no. 7: 783. https://doi.org/10.3390/cryst11070783