First-principles calculation and experimental study on the influence mechanism of diffusion activation energy of Cu atoms in current-assisted sintering
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摘要: 电流辅助烧结的快速致密化是电致效应的基础之一，将这种机制表征为电场强度对烧结的表观（或扩散）激活能的影响进行了大量实验研究，并且取得显著的进展。本文从第一性原理计算与电流辅助烧结实验两个方面，对晶体Cu在外加电场对扩散激活能的影响规律进行了研究，两者的研究结果揭示扩散激活能在电场或电流作用下呈现出明显规律性的下降趋势。另外，通过改变石墨模具内径来调整电流密度的方式开展电流辅助烧结实验，来验证第一性原理计算与电流辅助烧结实验扩散激活能的下降规律的正相关性。Abstract: The mechanism of rapid densification is one of the bases of the electro-induced effect in current-assisted sintering. This mechanism has been characterized as the effect of electric field intensity on the apparent (or diffusion) activation energy of sintering, and significant progress has been made. In this paper, the effects of applied electric field on the diffusion activation energy of crystal Cu are studied from two aspects of first-principles calculation and current-assisted sintering experiment. The results of the two studies reveal that the diffusion activation energy shows an obvious trend of regular decreasing trend under the action of electric field or current. In addition, to verify the positive correlation of the decreasing rule of two methods, current-assisted sintering experiment was conducted in which the inner diameter of the graphite die was varied to adjust the current density.
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图 3 （a）无空位的Cu超晶胞；（b）存在一个空位的Cu超晶胞
Figure 3. (a) Cu supercell without vacancies; (b) Cu supercell with one vacancy
图 4 （a）迁移初始状态；（b）迁移最终状态
Figure 4. (a) Initial state of migration; (b) final state of migration
图 5 Cu原子在Cu超晶胞中迁移的能量分布和最小能量路径
Figure 5. Energy distribution and MEP diagram of Cu atom migration in Cu supercell
图 6 （a）Cu界面的晶体结构；（b）无电场Cu原子界面扩散能量路径；（c）、（d）、（e）分别为第1阶段、第2阶段、第3阶段的最小能量分布
Figure 6. (a) Crystal structure of Cu interface; (b) interfacial diffusion energy path of Cu atoms without electric field; the minimum energy distribution of (c) stage 1, (d) stage 2 and (e) stage 3
图 7 （a）计算和（b）修正后的递增场强下Cu原子各层的空位形成能
Figure 7. (a) Calculated and (b) corrected vacancy formation energy at each layer of Cu atom under increasing field strength
图 8 电场强度是（a）1 V·Å−1和（b）4 V·Å−1时Cu原子界面扩散能量路径第1、2、3阶段的最小能量分布
Figure 8. The minimum energy distribution of the Cu atomic interface diffusion energy paths in stage 1, stage 2 and stage 3 of the electric field strength of 1 V·Å−1 (a) and 4 V·Å−1 (b)
图 9 0～6 V·Å−1电场强度下Cu界面扩散系统各阶段的原子迁移能
Figure 9. Atomic migration energy of Cu interfacial diffusion system in each stage of the electric field strength of 0～6 V·Å−1
图 10 0～6 V·Å−1电场强度下Cu界面扩散系统体扩散激活能
Figure 10. Bulk diffusion activation energy of Cu interfacial diffusion system of the electric field strength of 0～6 V·Å−1
图 11 不同直径的电流密度和时间关系
Figure 11. Relationship between current density and time of different diameters
图 12 （a）不同内径的石墨模具；（b）电流辅助烧结制备的不同直径的Cu块
Figure 12. (a) Graphite dies with different inner diameters; (b) Cu blocks of different diameters prepared by current-assisted sintering
图 13 烧结温度为500 °C时不同石墨内径的烧结致密化曲线
Figure 13. Sintering densification curves with graphite different inner diameters at 500 °C
图 14 不同模具内径的
$ \ln ({\raise0.7ex\hbox{${{\text{d}}\dot \rho }$} \mathord{\left/ {\vphantom {{{\text{d}}\dot \rho } {{\text{d}}T}}}\right.} \lower0.7ex\hbox{${{\text{d}}T}$}} \times T) $ 与1/T的关系曲线：（a）8 mm；（b）10 mm；（c）25 mm；（d）30 mmFigure 14. Relationship curves of
$ \ln ({\raise0.7ex\hbox{${{\text{d}}\dot \rho }$} \mathord{\left/ {\vphantom {{{\text{d}}\dot \rho } {{\text{d}}T}}}\right.} \lower0.7ex\hbox{${{\text{d}}T}$}} \times T) $ and 1/T of different die inner diameters: (a) 8 mm; (b) 10 mm; (c) 25 mm; (d) 30 mm
图 15 扩散激活能随（a）电场强度和（b）电流密度下降趋势图
Figure 15. Decreasing trend of diffusion activation energy with current density (a) and electric field strength (b)
表 2 Cu的扩散激活能
Table 2. Diffusion activation energy of Cu eV
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表 3 无电场Cu界面扩散系统各层的空位形成能
Table 3. Vacancy formation energy of each layer of interfacial diffusion system without electric field eV
层数 EVa EPer EVF 第1层 −195.02 −199.32 0.74 第2层 −194.61 1.15 第3层 −194.44 1.32 第4层 −194.44 1.32
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