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基于第一性原理计算, 深入研究了(H2dabco)[K(ClO4)3](DAP-2)晶体在0—50 GPa压力作用下的晶体结构、分子结构、电子结构和力学性质变化, 并评估了压力对其撞击感度和稳定性的影响. 通过分析晶体内部特征键长和键角发现, 在25 GPa处, 有机阳离子H2dabco2+的笼状结构发生了扭曲. 对H2dabco2+和KO12多面体的质心平均分数坐标和欧拉角的计算结果显示, 整个压力范围内晶体可能保持Pa-3空间群对称性不变. 根据第一性原理带隙判据和不同压力下的带隙变化, 发现在低于20 GPa时, DAP-2的撞击感度随着压力增加而逐渐减小; 而当压力高于20 GPa时, 撞击感度则呈现出随压力增加而缓慢增大的趋势. 此外, 弹性常数Cij、杨氏模量(E)、体积模量(B)、剪切模量(G)以及柯西压(C12–C44)均随着压力的增大而增大, 表明在压力作用下晶体的刚性和延展性得到了显著增强. 根据力学稳定性准则, 该晶体在整个压力范围内保持力学稳定性.The crystal structure, molecular structure, electronic structure and mechanical properties of molecular perovskite high-energetic material (H2dabco)[K(ClO4)3] (DAP-2) under hydrostatic pressure ranging from 0 to 50 GPa are calculated and studied based on density functional theory. And the influences of pressure on its stability and impact sensitivity of DAP-2 are investigated. As the external pressure gradually increases, both the lattice parameters and the volume of DAP-2 crystal exhibit a monotonic decreasing trend. In the entire pressure range, the unit cell volume shrinks by up to 40.20%. By using the Birch Munnaghan equation of state to fit P-V relation, the bulk modulus B0 and its first-order derivative B0’ with respect to pressure are obtained to be 23.4 GPa and 4.9 GPa, respectively. The observations of the characteristic bond length and bond angle within the crystal indicate that the cage-like structure of organic cation H2dabco2+ undergoes distortion at 25 GPa. Further analysis of the average fractional coordinates of the center-of-mass and Euler angles for H2dabco2+ and KO12 polyhedron shows that within a pressure range from 0 to 50 GPa, both the average fractional coordinates of the center-of-mass and the Euler angles exhibit fluctuations at 25 GPa, but the overall amplitude of these fluctuations is very small. Based on this finding, it is speculated that the space group symmetry of the crystal may remain unchanged in the entire pressure range. In terms of electronic structure, with the increase of pressure, the band gap value increases rapidly and reaches a maximum value at about 20 GPa, followed by a slow decreasing trend. Based on the first-principles band gap criterion and the variation of the band gap under different pressures, it is demonstrated that below 20 GPa, the impact sensitivity of DAP-2 gradually decreases with pressure increasing; however, when the pressure exceeds 20 GPa, the impact sensitivity exhibits a slow increasing trend. In addition, the elastic constants Cij, Young’s modulus (E), bulk modulus (B), shear modulus (G), and Cauchy pressure (C12–C44) all increase with pressure rising, indicating that the rigidity and ductility of the crystal under pressure are significantly strengthened. According to the mechanical stability criterion, the crystal maintains the mechanical stability throughout the pressure range.
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Keywords:
- density functional theory /
- crystal structure /
- electronic structure /
- mechanical properties
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图 1 (a) DAP-2单胞的多面体模型示意图; (b) DAP-2单胞的球棍模型示意图; (c) 有机阳离子H2dabco2+结构, K, O, Cl, C, N和H原子分别用蓝紫色、粉色、绿色、深灰色、蓝色和浅灰色表示, 而N-H…O键用青色虚线表示, 对称性代码: A: -z+1, -x+1, -y+1; B: -y+1/2, z–1/2, x; C: x–1/2, y, -z+3/2; D: z–1/2, -x+1/2, -y+1; E: x, y, z; F: -y+1/2, -z+1, x+1/2
Fig. 1. (a) Schematic diagram of the polyhedral model for the unit cell of DAP-2; (b) schematic diagram of the ball-and-stick model for the unit cell of DAP-2; (c) structure of the organic cation H2dabco2+. The atoms of K, O, Cl, C, N and H are represented by blue purple, pink, green, dark gray, blue, and light gray, respectively, while N—H···O bonds are represented by cyan dashed lines. Symmetry code: A: -z+1, -x+1, -y+1; B: -y+1/2, z–1/2, x; C: x–1/2, y, -z+3/2; D: z-1/2, -x+1/2, -y+1; E: x, y, z; F: -y+1/2, -z+1, x+1/2.
图 2 不同压力下DAP-2的晶格常数a(a)和晶胞体积V(b)
Fig. 2. Lattice constant a (a) and cell volume V (b) of DAP-2 crystal under different pressures.
图 3 不同压力下DAP-2晶体中部分键长
Fig. 3. Partial bond lengths in DAP-2 crystal under different pressures.
图 4 不同压力下DAP-2晶体中部分键角
Fig. 4. Partial bond angles in DAP-2 crystal under different pressures.
图 6 不同压力下H2dabco2+阳离子的质心平均分数坐标(a)与欧拉角(b)
Fig. 6. The average fractional coordinates of the centers-of-mass (a) and Euler angle (b) of H2dabco2+cation under different pressures.
图 7 不同压力下K1O12多面体(a)与K2O12多面体(b)的欧拉角
Fig. 7. Euler angles of K1O12 polyhedron (a) and K2O12 polyhedron (b) under different pressures.
图 8 不同压力下DAP-2晶体的带隙值
Fig. 8. Band gap values of DAP-2 crystal under different pressures
图 9 0 GPa时DAP-2晶体的总态密度和分态密度图
Fig. 9. Total density of states and partial density of states of DAP-2 crystal at 0 GPa.
图 10 不同压力下DAP-2晶体的态密度图
Fig. 10. Density of States of DAP-2 Crystals under different pressures.
图 11 不同压力下DAP-2晶体的弹性常数及其模量 (a)弹性常数; (b)力学稳定性(c)B, G, E; (d)C11-C22
Fig. 11. Elastic constants and moduli of DAP-2 crystal under different pressures: (a) Elastic constants; (b) Mechanical stability (c) B, G, E; (d) C11-C22.
表 1 DAP-2晶胞参数的计算值与实验值
Table 1. The calculated and experimental values of crystal cell parameters for DAP-2.
Method a/Å Δa /% α /(°) V/Å3 ΔV/% Experiment[21] 14.291 — 90 2918.689 — PBE 14.530 +1.67 90 3067.650 +5.10 PBEsol 14.288 –0.02 90 2917.954 –0.03 PBE+D3 14.282 –0.06 90 2913.178 –0.19 
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