图  1   Cu晶体结构

Figure  1.   Crystal structure of Cu

图  2   空位扩散机理示意图

Figure  2.   Schematic diagram of the vacancy diffusion mechanism

图  3   无空位的Cu超晶胞（a）和存在一个空位的Cu超晶胞（b）

Figure  3.   Cu supercell without vacancies (a) and with one vacancy (b)

图  4   迁移初始状态（a）和迁移最终状态（b）

Figure  4.   Initial state of migration (a) and the final state of migration (b)

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示意图

Figure  5.   Energy distribution and MEP diagram of Cu atom migration in Cu supercell

图  6   Cu界面晶体结构（a）、无电场Cu原子界面扩散能量路径（b）和最小能量分布（第1阶段（c）、第2阶段（d）、第3阶段（e））

Figure  6.   Crystal structure of Cu interface (a), interfacial diffusion energy path of Cu atoms (b), and the minimum energy distributions of stage 1 (c), stage 2 (d), and stage 3 (e)

图  7   0～6 V·Å^‒1电场强度下Cu界面扩散系统各层空位形成能：（a）修正前；（b）修正后

Figure  7.   Vacancy formation energy for each layer of the Cu interfacial diffusion system in the electric field strength of 0~6 V·Å^‒1: (a) before correction; (b) after correction

图  8   电场强度1 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.   Minimum energy distribution of the Cu atomic interface diffusion energy paths in stage 1, stage 2 and stage 3 in the electric field strength of 1 V·Å^‒1

图  9   电场强度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  9.   Minimum energy distribution of the Cu atomic interface diffusion energy paths in stage 1, stage 2 and stage 3 in the electric field strength of 4 V·Å^‒1

图  10   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  10.   Atomic migration energy of Cu interfacial diffusion system in each stage of the electric field strength of 0~6 V·Å^‒1

图  11   0～6 V·Å^‒1电场强度下Cu界面扩散系统体扩散激活能

Figure  11.   Bulk diffusion activation energy of Cu interfacial diffusion system in the electric field strength of 0~6 V·Å^‒1

图  12   通过不同内径模具的电流密度和时间关系

Figure  12.   Relationship between time and current density through the graphite dies with different inner diameters

图  13   不同内径石墨模具（a）和制备得到的不同直径Cu块（b）

Figure  13.   Graphite dies with different inner diameters (a) and the obtained Cu blocks in different diameters (b)

图  14   不同内径石墨模具烧结致密化曲线（500 ℃）

Figure  14.   Sintering densification curves for the graphite dies with different inner diameters at 500 ℃

图  15   不同内径石墨模具烧结的$ {\text{ln}}\left[ {\left( {{\text{d}}\dot \rho /{\text{d}}T} \right) \cdot T} \right] $与1/T关系曲线：（a）8 mm；（b）10 mm；（c）25 mm；（d）30 mm

Figure  15.   Relationship curves of $ {\text{ln}}\left[ {\left( {{\text{d}}\dot \rho /{\text{d}}T} \right) \cdot T} \right] $ and 1/T for the graphite dies with different inner diameters: (a) 8 mm; (b) 10 mm; (c) 25 mm; (d) 30 mm

图  16   扩散激活能随电场强度和电流密度下降趋势：（a）电场强度；（b）电流密度

Figure  16.   Decreasing trend of diffusion activation energy with current density and electric field strength: (a) current density; (b) electric field strength