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--- a/TODO.md
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  * [ ] method
    * [ ] 无缺陷和缺陷的模型大小、缺陷结构
    * [ ] 第一性原理计算和声子计算的工具
+      * [ ] 中文
+      * [ ] 英文
 * [ ] 实验
  * [ ] 实验
    * [ ] 测试不同片子的背面 LOPC，确认它们的掺杂是否相同
--- a/paper/method/default.typ
+++ b/paper/method/default.typ
@@ -43,8 +43,31 @@ During normal incidence, a 100 μm confocal pinhole was used to improve the z-di

 == Simulation details

-无缺陷的声子在多大的模型中计算。
-带缺陷的情况下，模型大小，每个模型的代号和缺陷结构。
+我们建立了三类模型：无缺陷、点缺陷和面缺陷。
+
+Three types of models were established: defect-free models, point defect models, and surface defect models.
+
+不同模型使用不同的大小。
+
+不同大小被使用来建立不同的模型。
+无缺陷的声子使用 xxA x xxA x xxA 和 xxA x xxA x xxA 的模型计算。
+我们发现它们的结果没有显著差异，因此我们认为，对于无缺陷和点缺陷的模型，xxA x xxA x xxA 的模型大小是足够的，
+因此对于无缺陷和点缺陷的模型，我们使用 xxA x xxA x xxA 的模型大小。
+对于面缺陷，一个更大的 xxA x xxA x xxA 的模型被使用。
+
+对于点缺陷模型，我们考虑了以下这些
+
+计算工具和参数

 第一性原理计算使用 VASP，使用 PBE PAW，平面波截断能，K 点网格，涂抹，自洽和弛豫的 threshold。
 声子计算使用 phonopy phono3py ufo，BEC 修正的算法。
+
+First-principles calculations were performed using Vienna Ab-initio Simulation Package (VASP) @kresse_efficiency_1996.
+The Perdew–Burke–Ernzerhof (PBE) exchange energy @ernzerhof_assessment_1999
+  and projector-augmented wave (PAW) representation @kresse_ultrasoft_1999
+  were used along with a cutoff energy of 400 eV,
+  a Gamma-centered k-point mesh of 3 #sym.times 3 #sym.times 1,
+  and a self-consistent convergence criterion of $1 times 10^(-3)$ eV.
+The ionic relaxation was performed until the energies converged to $1 times 10^(-2)$ eV.
+
+
--- a/paper/ref.bib
+++ b/paper/ref.bib
@@ -1,4 +1,22 @@

+@article{kresse_efficiency_1996,
+	title = {Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set},
+	volume = {6},
+	issn = {09270256},
+	url = {https://linkinghub.elsevier.com/retrieve/pii/0927025696000080},
+	doi = {10.1016/0927-0256(96)00008-0},
+	abstract = {We present a detailed description and comparison of algorithms for performing ab-initio quantum-mechanical calculations using pseudopotentials and a plane-wave basis set. We will discuss: (a) partial occupancies within the framework of the linear tetrahedron method and the finite temperature density-functional theory, (b) iterative methods for the diagonalization of the Kohn-Sham Hamiltonian and a discussion of an efficient iterative method based on the ideas of Pulay’s residual minimization, which is close to an order N\&m scaling even for relatively large systems, (c) efficient Broyden-like and Pulay-like mixing methods for the charge density including a new special ‘preconditioning’ optimized for a plane-wave basis set, (d) conjugate gradient methods for minimizing the electronic free energy with respect to all degrees of freedom simultaneously. We have implemented these algorithms within a powerful package called VAMP (Vienna ab-initio molecular-dynamicspackage).The program and the techniqueshave been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semi-conducting surfaces, phonons in simple metals, transition metals and semiconductors) and turned out to be very reliable.},
+	language = {en},
+	number = {1},
+	urldate = {2022-01-13},
+	journal = {Computational Materials Science},
+	author = {Kresse, G. and Furthmüller, J.},
+	month = jul,
+	year = {1996},
+	pages = {15--50},
+	file = {Kresse 和 Furthmüller - 1996 - Efficiency of ab-initio total energy calculations .pdf:/home/chn/Zotero/storage/BDME6UG3/Kresse 和 Furthmüller - 1996 - Efficiency of ab-initio total energy calculations .pdf:application/pdf},
+}
+
@article{demenet_tem_2005,
 	title = {{TEM} observations of the coexistence of perfect and dissociated dislocations in {SiC} under high stress},
 	volume = {2},
@@ -217,6 +235,78 @@
 	file = {Harada et al. - 2022 - Suppression of stacking fault expansion in a 4H-Si.pdf:/home/chn/Zotero/storage/VJ7H4G59/Harada et al. - 2022 - Suppression of stacking fault expansion in a 4H-Si.pdf:application/pdf},
 }

+@article{ernzerhof_assessment_1999,
+	title = {Assessment of the {Perdew}-{Burke}-{Ernzerhof} exchange-correlation functional},
+	volume = {110},
+	issn = {0021-9606, 1089-7690},
+	url = {http://aip.scitation.org/doi/10.1063/1.478401},
+	doi = {10.1063/1.478401},
+	language = {en},
+	number = {11},
+	urldate = {2022-10-20},
+	journal = {Journal of Chemical Physics},
+	author = {Ernzerhof, Matthias and Scuseria, Gustavo E.},
+	month = mar,
+	year = {1999},
+	pages = {5029--5036},
+	file = {Ernzerhof and Scuseria - 1999 - Assessment of the Perdew–Burke–Ernzerhof exchange-.pdf:/home/chn/Zotero/storage/PXY6QH49/Ernzerhof and Scuseria - 1999 - Assessment of the Perdew–Burke–Ernzerhof exchange-.pdf:application/pdf},
+}
+
+@article{kresse_ultrasoft_1999,
+	title = {From ultrasoft pseudopotentials to the projector augmented-wave method},
+	volume = {59},
+	issn = {0163-1829, 1095-3795},
+	url = {https://link.aps.org/doi/10.1103/PhysRevB.59.1758},
+	doi = {10.1103/PhysRevB.59.1758},
+	language = {en},
+	number = {3},
+	urldate = {2022-10-20},
+	journal = {Physical Review B},
+	author = {Kresse, G. and Joubert, D.},
+	month = jan,
+	year = {1999},
+	pages = {1758--1775},
+	file = {Kresse and Joubert - 1999 - From ultrasoft pseudopotentials to the projector a.pdf:/home/chn/Zotero/storage/WEYU9JZ6/Kresse and Joubert - 1999 - From ultrasoft pseudopotentials to the projector a.pdf:application/pdf},
+}
+
+@article{momma_vesta_2011,
+	title = {\textit{{VESTA} 3} for three-dimensional visualization of crystal, volumetric and morphology data},
+	volume = {44},
+	issn = {0021-8898},
+	url = {http://scripts.iucr.org/cgi-bin/paper?S0021889811038970},
+	doi = {10.1107/S0021889811038970},
+	abstract = {VESTA
+              is a three-dimensional visualization system for crystallographic studies and electronic state calculations. It has been upgraded to the latest version,
+              VESTA 3
+              , implementing new features including drawing the external morphology of crystals; superimposing multiple structural models, volumetric data and crystal faces; calculation of electron and nuclear densities from structure parameters; calculation of Patterson functions from structure parameters or volumetric data; integration of electron and nuclear densities by Voronoi tessellation; visualization of isosurfaces with multiple levels; determination of the best plane for selected atoms; an extended bond-search algorithm to enable more sophisticated searches in complex molecules and cage-like structures; undo and redo in graphical user interface operations; and significant performance improvements in rendering isosurfaces and calculating slices.},
+	language = {en},
+	number = {6},
+	urldate = {2022-10-20},
+	journal = {Journal of Applied Crystallography},
+	author = {Momma, Koichi and Izumi, Fujio},
+	month = dec,
+	year = {2011},
+	pages = {1272--1276},
+	file = {Momma and Izumi - 2011 - VESTA 3 for three-dimensional visualization.pdf:/home/chn/Zotero/storage/JLPVVXY5/Momma and Izumi - 2011 - VESTA 3 for three-dimensional visualization.pdf:application/pdf},
+}
+
+@article{stukowski_visualization_2010,
+	title = {Visualization and analysis of atomistic simulation data with {OVITO}-the {Open} {Visualization} {Tool}},
+	volume = {18},
+	issn = {0965-0393, 1361-651X},
+	url = {https://iopscience.iop.org/article/10.1088/0965-0393/18/1/015012},
+	doi = {10.1088/0965-0393/18/1/015012},
+	abstract = {The Open Visualization Tool (OVITO) is a new 3D visualization software designed for post-processing atomistic data obtained from molecular dynamics or Monte Carlo simulations. Unique analysis, editing and animations functions are integrated into its easy-to-use graphical user interface. The software is written in object-oriented C++, controllable via Python scripts and easily extendable through a plug-in interface. It is distributed as open-source software and can be downloaded from the website http://ovito.sourceforge.net/.},
+	language = {en},
+	number = {1},
+	urldate = {2022-10-20},
+	journal = {Modelling and Simulation in Materials Science and Engineering},
+	author = {Stukowski, Alexander},
+	year = {2010},
+	pages = {015012},
+	file = {Stukowski - 2010 - Visualization and analysis of atomistic simulation.pdf:/home/chn/Zotero/storage/C27XTF39/Stukowski - 2010 - Visualization and analysis of atomistic simulation.pdf:application/pdf},
+}
+
@article{harada_observation_2022,
 	title = {Observation of in-plane shear stress fields in off-axis {SiC} wafers by birefringence imaging},
 	volume = {55},
@@ -557,3 +647,21 @@ CNKICite: 6},
 	pages = {1034},
 	file = {PDF:/home/chn/Zotero/storage/YJD5HYLD/Shaffer - 1971 - Refractive Index, Dispersion, and Birefringence of Silicon Carbide Polytypes.pdf:application/pdf},
 }
+
+@article{togo_implementation_2023,
+	title = {Implementation strategies in phonopy and phono3py},
+	volume = {35},
+	issn = {0953-8984, 1361-648X},
+	url = {https://iopscience.iop.org/article/10.1088/1361-648X/acd831},
+	doi = {10.1088/1361-648X/acd831},
+	abstract = {Scientific simulation codes are public property sustained by the community. Modern technology allows anyone to join scientific software projects, from anywhere, remotely via the internet. The phonopy and phono3py codes are widely used open-source phonon calculation codes. This review describes a collection of computational methods and techniques implemented in these codes and shows their implementation strategies as a whole, aiming to be useful for the community. Some of the techniques presented here are not limited to phonon calculations and may therefore be useful in other areas of condensed matter physics.},
+	language = {en},
+	number = {35},
+	urldate = {2025-06-27},
+	journal = {Journal of Physics: Condensed Matter},
+	author = {Togo, Atsushi and Chaput, Laurent and Tadano, Terumasa and Tanaka, Isao},
+	month = sep,
+	year = {2023},
+	pages = {353001},
+	file = {PDF:/home/chn/Zotero/storage/BQNQVQBX/Togo et al. - 2023 - Implementation strategies in phonopy and phono3py.pdf:application/pdf},
+}