基於貪婪演算法的系統化搜尋發現 BC2N 超晶格的結構排列。使用樹狀資料結構, 我們已經獲得先前 Sun 等人發現的七種 c-BC2N 1x1x1 晶格的原子結構 [Phys. Rev. B 64, 094108 (2001)]。 而且, 將貪婪演算法應用在樹狀資料結構上, 發現在 c-BC2x2x2 , 3x3x3, 和4x4x4的超晶格上擁有最大數目碳-碳鍵結的原子結構。這些新的結構排列仍未被之前的文獻提出。在 c-BC2N 超晶格上已經搜索到512顆原子。這些原子在超晶格上的位置皆為類鑽石結構形式。並且碳原子與硼、氮原子分別形成八面體的結構。這些碳原子構成的八面體結構被{111}面所包圍著,同時每個面和鄰近硼與氮原子所構成的八面體接觸。新發現的低能量結構的電性與力學也已被分析。

Structural motifs for the BC2N superlattices were identified from a systematic search based on a greedy algorithm. Using a tree data structure, we have retrieved seven structural models for c-BC2N 1x1x lattice which were identified previously by Sun et al. [Phys. Rev. B 64, 094108 (2001)]. Furthermore, the atomic structures with the maximum number of C-C bonds for c-BC2N 2x2x2, 3x3x3, and 4x4x4 superlattices were found by imposing the greedy algorithm in the tree data structure. This new structural motif has not been previously proposed in the literature. A total of up to 512 atoms in the c-BC2N superlattice are taken into consideration. The atoms in these superlattices are in diamond-like structural form. Furthermore, the C atoms, as well as B and N atoms, form the octahedral motif separately. The octahedral structure consisting of C is bounded with {111} facets, and each facet is interfaced to a neighboring octahedral structure consisting of B and N atoms. The electronic and mechanical properties of newly identified low energy structures were analyzed.

摘要 i
ABSTRACT ii
LIST OF FIGURES v
LIST OF TABLES vi
1 Introduction 1
2 Theory 3
2.1 Born-Oppenheimer approxmation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Density functional theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.1 Thomas-Fermi model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.2 Honhenberg-Kohn theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.3 Kohn-Sham equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.4 Exchange-correlation energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Psuedopotential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.1 Norm-Conserving pseudopotential . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.2 Project augmented plane wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 Geometry optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4.1 Hellman-Feynman theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.2 Linear search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5 Struactural searach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5.1 Tree structure and greedy algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5.2 Choice of fitness function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5.3 Structural comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.6 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 Results and discussions 19
3.1 Structural models and energetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 X-ray diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3 Ideal strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4 Conclusions 30
References 31

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