Cu-Ru
...7 1.1....7 1.2....7 1.3....8...9 2.1....9 2.1.1....9 2.1.2....10 2.2.... 11 2.2.1.... 11 2.2.2. ()...12 2.2.3. ()...13 2.2....15...18 3.1. Cu z <111>...18 3.1.1....18 3.1.2....19 3.1.3....29 3.2. misfit...33 3.2.1....33 3.2.2....34 3.2.3....39 3.2.4 misfit...42 3.3. Cu z <011>...48 3.3.1....48 3.3.2....48 3.3.3....53 3.4. Cu <001>...57 3.4.1....57 3.4.2....57 3.4.3....62 3.4.4. Cu...66 - - 2
...69.70 - - 3
Fig.2.1... 11 Fig.2.2... 12 Fig.2.3... 13 Fig.2.4... 14 Fig.2.5... 14 Fig.2.6 step... 15 Fig.2.7 fcchcp... 16 Fig.2.8 z <111> Cu... 16 Fig.2.9 z <011> Cu z <001> Cu... 17 Fig.3.1.1 Cu z <111>... 18 Fig.3.1.2 Cu z <111>... 19 Fig.3.1.3 step... 20 Fig3.1.4 zeffective strain rate... 20 Fig.3.1.5 Cu z <111>... 23 Fig.3.1.6 Cu z <111> 24 Fig.3.1.7 Cu z <111> σ step... 25 Fig.3.1.8 Cu z <111>... 26 Fig.3.1.9 Cu z <111> step... 26 Fig.3.1.10 Cu z <111>... 27 Fig.3.1.11 Custrain rate... 28 Fig.3.1.12 Cu z <111>... 29 Fig.3.1.13 Cu z <111>... 31 Fig.3.1.14 Cu z <111> τ step... 32 Fig.3.2.1 misfit... 36 Fig.3.2.2 misfit... 37 Fig.3.2.3 misfit σ step... 38 Fig.3.2.4 misfit step... 39 z z - - 4
Fig.3.2.5 misfit... 40 Fig.3.2.6 misfit τ step... 41 Fig.3.2.7 Cu z <111> misfit step... 43 Fig.3.2.8 Cu z <111> misfit... 44 Fig.3.2.9 Cu z <111> misfit step... 45 Fig.3.2.10 Cu <111>... 46 Fig.3.3.1 Cu z <011>... 50 Fig.3.3.2 Cu z <011> 52 Fig.3.3.3 Cu z <011> σ step... 53 Fig.3.3.4 Cu z <011> 55 Fig.3.3.5 Cu z <011> τ step... 56 Fig.3.4.1 Cu z <001>... 59 Fig.3.4.2 Cu z <001>. 61 Fig.3.4.3 Cu z <111> σ step... 62 Fig.3.4.4 Cu z <001>. 64 Fig.3.4.5 Cu z <001> τ step... 65 Fig.3.4.6 Cu z <111> <011> <001> σ step... 67 Fig.3.4.7 Cu z <111> <011> <001> z z z τ σ τ z step... 68 - - 5
Table.2.1 GEAM Cu Ru 10 Table.3.1 Cu z <111> misfit..42 Table.3.2 Cu Ru γ sf γ us...46 Table.3.3 GEAM..47 Table.3.4 Cu z <111> <011> <001>...66 - - 6
Cu-Ru 1.1. Cu-Ru Ru Cu [1] [2] Ru GEAM GEAM 2 1.2. FEM BEM [3] - - 7
Cu-Ru 1.3. - - 8
2.1. 2.1.1. N N N 2~5 Book-keeping Verlet GEAM johnson FS - - 9
GeneralizedEAM GEAM [4] GEAM fcc bcc hcp Cu/Ru Table.2.1 GEAM 0 Cu Ru misfit Ru misfit a0 3.615 2.685 2.686 c - 4.353 4.348 0 E ev/atom -3.54-6.74-6.74 B [GPa] 116.4 309.2 309.2 [GPa] 54.0 128.9 117.1 Table.2.1 GEAM Cu Ru 2.1.2. AtomEye AtomEye JPEG PNG EPS - - 10
2.2. 2.2.1. [5] Fig.2.1 Wad = + material-connected state material-separated state Wad Fig.2.1 Material-connected state material-separated state - - 11
GEAM 0[K] step 1.08[fs] Verlet x,y z 2.2.2. () 2.2.1 material-connected state z Fig.2.2 Fig.2.3 GEAM x,y z 1[K] 1step 1.08[fs] z 5000step 5.4[ps] 3 3 Fig.2.2 - - 12
Fig.2.3 2.2.3. () Fig.2.4 Fig.2.5 2.2.2 y x y z y 6.0[nm] z 0.65[nm] - - 13
Fig.2.4 Fig.2.5 2.2.2 GEAM 1[K] 1step 1.08[fs] 5000step 5.4[ps] step 25,000step 27ps step Fig.2.6 5000step100step 0.1[ps] 100step 0.1[ps] =4.5 10 [m/s] 3 - - 14
Fig.2.6 step 2.2. misfit Cu misfit Cu misfit misfit Cu z:<111>, x:<10-1>, y:<-12-1>ru z:<0001>, x:<11-20>, y:<-1100> Cu fcc Ru hcp fcc hcp Fig.2.7 Cu z <111> Cu z Fig.2.7 Ru z Fig.2.7 misfit - - 15
Fig.2.8 Cu Fig.2.7 fcc hcp Fig.2.8 z <111> Cu misfit Cu Ru Cu misfit misfit misfit - - 16
misfit Ru GEAM Cu Ru misfit Cu Cu z:<110>, x:<001>, y:<-110> z:<001>, x:<100>, y:<010> Cu Fig.2.9 Cu Fig.2.9 z <011> Cu z <001> Cu - - 17
3.1. Cu z <111> Cu z <111> misfit 3.1.1. Fig.3.1.1 material-connected state Cu-Ru x=10.5nm y=18.2nm z=10.6nm 161,700 material-separated state Cu Cu x=10.5nm y=18.2nm z=6.3nm 100,860 Ru Ru x=10.5nm y=18.2nm z=4.3nm 60,840 Fig.3.1.1 Cu z <111> Cu-Ru -760,091[eV] Cu -353,477[eV] Ru -401,200[eV] material-connected state material-separated state 5,414[eV] 4.56[J/m ] - - 18
3.1.2. Fig3.1.2 x=10.5nm y=18.2nm z=12.8nm 190,545 Fig.3.1.2 Cu z <111> step Fig.3.1.3 Fig3.1.3 real strain rate 100step(0.1[ps]) 100step(0.1[ps]) Fig3.1.3 effective strain rate effective strain rate σ effective strain rate Fig3.1.4 z - - 19
Fig.3.1.3 step 1 effective strain rate [ s ] Fig3.1.4 z effective strain rate - - 20
effective strain ratezeffective strain rate z effective strain 8 1 rate 7.5 10 s 9 1 1.5 10 s Fig.3.1.5 fcc hcp fcc hcp 12 12 σ 17,000[MPa] z -3,000[MPa] Fig.3.1.5 Cu/Ru misfit Cu Ru Cu misfit z Fig.3.1.5 σ σ σ σ z z z z - - 21
5.4[ps] 15[ps] 29[ps] -3000 17000 [Mpa] - - 22
30[ps] 31[ps] 40[ps] -3000 17000 [Mpa] Fig.3.1.5 Cu z <111> - - 23
Fig.3.1.6 Cu Cu Ru Cu-Ru 5.4[ps] 30[ps] 43[ps] 70[ps] Fig.3.1.6 Cu z <111> Fig.3.1.7 σ step z σ z = 5.2 10 3 [MPa] =1.78[%] step 27,000 40,000[step] σ z Cu - - 24
Fig.3.1.7 Cu z <111> σ step z Ru Cu Cu 6 Fig.3.1.8 Fig.3.1.8 5,330 Fig.3.1.9 step 200[step] 26,800[step] 1.30 10 3 [MPa] 27,000[step] 40,000[step] Fig.3.1.10 3,000[MPa] 0[MPa] - - 25
Fig.3.1.8 Cu z <111> Fig.3.1.9 Cu z <111> step - - 26
25,400[step] 26,200[step] 27,000[step] 27,800[step] 28,600[step] 29,400[step] 0 3,000[MPa] Fig.3.1.10 Cu z <111> - - 27
Fig.3.1.10 Fig.3.1.5 σ 27,000[step] z Cu Cu <111> Fig.3.1.11 Fig.3.1.11 Cu 3 2.89 10 [MPa] Fig.3.1.9 1.30 10 3 [MPa] Fig.3.1.9 Fig.3.1.11 Fig.3.1.9 3 3 2.5 10 4.0 10 [MPa] Fig.3.1.11 Cu strain rate - - 28
3.1.3. Fig.3.1.12 x=10.5nm y=18.2nm z=12.8nm 188,196 A B Fig.3.1.12 Cu z <111> Fig.3.1.13 Fig.3.1.12 AB fcc hcp y τ 6,000[MPa] -3000[MPa] misfit misfit τ τ 5.4 16[ps] misfit Fig.3.1.13 misfit 16[ps] τ 19[ps] misfit - - 29
τ 0[ps] 5.4[ps] 12[ps] -3000 6000 [Mpa] - - 30
16[ps] 19[ps] 27[ps] -3000 6000 [Mpa] Fig.3.1.13 Cu z <111> - - 31
misfit misfit τ misfit 3.1.2 Fig.3.1.14 τ step τ τ Fig.3.1.13 misfit 4.86[%] misfit Fig.3.1.14 Cu z <111> τ step - - 32
3.2. misfit misfit misfit Ru Cu GEAM 3.2.1. Ru material-connected state Cu/Ru x=10.5nm y=18.2nm z=10.6nm 171,462 material-separated state Cu Cu x=10.5nm y=18.2nm z=5.6nm 90,774 Ru Ru x=10.5nm y=18.2nm z=5.0nm 80,688 Cu z <111> Cu-Ru -858,586[eV] Cu -317,773[eV] Ru -534,463[eV] material-connected state material-separated state 6,350[ev] 5.35[J/m ] - - 33
3.2.2. x=10.5nm y=18.2nm z=12.5nm 200,121 Cu z <111> Fig.3.2.1 Cu z <111> σ Cu z <111> Fig.3.2.1 Cu/Ru misfit Ru Cu 15[ps] Cu z <111> Cu z <111> z Fig.3.2.1 Cu z <111> Cu z <111> σ z Cu z <111> Cu z <111> - - 34
5.4[ps] 15[ps] 24[ps] -3000 17000 [Mpa] - - 35
25[ps] 45[ps] 52[ps] -3000 17000 [Mpa] Fig.3.2.1 misfit - - 36
Fig.3.2.2 Cu z <111> y z Cu Cu z <111> misfit Cu/Ru 5.4[ps] 30[ps] 50[ps] 70[ps] Fig.3.2.2 misfit Fig.3.2.3 σ step z σ z = 4.2 10 3 [MPa] =1.38[%] Cu z <111> 50,000[step] σ z Cu - - 37
Fig.3.2.3 misfit σ step z Ru Cu 6 Cu Cu z <111> 5,002 Fig.3.2.4 step 200step 3 21,600[step] 1.13 10 [MPa] 22,000[step] - - 38
Fig.3.2.4 misfit step 3.2.3. x=10.5nm y=18.2nm z=12.5nm 197,620 Cu z <111> misfit Cu z <111> Fig.3.2.5 τ Cu z <111> Cu z <111> 27[ps] misfit τ - - 39
0[ps] 5.4[ps] 10[ps] 15[ps] 20[ps] 27[ps] -3000 6000 [Mpa] Fig.3.2.5 misfit - - 40
Fig.3.2.6 τ step τ 5000step τ Fig.3.2.5 Cu z <111> τ 6.0 10 τ 3.1 10 [MPa] 6 misfit τ Fig.3.2.6 misfit τ step - - 41
3.2.4 misfit misfit Cu z <111> misfit Cu Ru Cu/Ru Cu z <111> 4.56[J/m ] misfit 5.35[J/m ] Cu z <111> misfit 15% Cu z <111> misfit Table.3.1 Cu z <111> σ 24% 29% misfit z Cu z <111> misfit σ z [MPa] [%] step 3 5.2 10 1.78 27,000 3 4.2 10 1.38 22,000 Table.3.1 Cu z <111> misfit Cu z <111> misfit Fig.3.2.7 Cu z <111> misfit σ z step misfit - - 42
Fig.3.2.7 Cu z <111> misfit step σ z misfit Cu z <111> Fig.3.2.8 Cu z <111> misfit Cu z <111> 1.78[%] misfit 1.38[%] Fig.3.2.8 misfit misfit misfit misfit - - 43
Fig.3.2.8 Cu z <111> misfit Cu z <111> misfit τ step Fig.3.2.9 7000step Model A B τ Cu z <111> τ Cu z <111> misfit 1/6 misfit - - 44
Fig.3.2.9 Cu z <111> misfit τ step Ru Fig.3.2.10 GEAM fcc γ sf γ us - - 45
Fig.3.2.10 Cu <111> Table.3.2 GEAM Cu Ru [6] Cu Ru misfit Ru misfit <111> γ sf (mj/m ) 23 <111> γ us (mj/m ) 111 basal γ sf (mj/m ) 184 238 basal γ us (mj/m ) 543 606 prism prism γ sf (mj/m ) γ us (mj/m ) 1015 1059 Table.3.2 Cu Ru γ sf γ us - - 46
Ru Cu misfit Table.4.2 Ru γ us misfit Cu Ru Cu Cu Table.3.3 GEAM [7] γ sf γ us γ sf GEAM 23 111 39 158 35 45 γ us Table.3.3 GEAM GEAM γ sf γ us GEAM Cu Cu GEAM - - 47
3.3. Cu z <011> Cu Cu Cu z:<110>, x:<001>, y:<-110>cu 3.3.1. material-connected state Cu/Ru x=10.5nm y=26.1nm z=12.7nm 273,024 material-separated state Cu Cu x=10.5nm y=26.1nm z=6.1nm 141,984 Ru Ru x=10.5nm y=26.1nm z=6.5nm 131,040 Cu z <111> Cu-Ru -1,373,094[eV] Cu -496,674[eV] Ru -870,486[eV] material-connected state material-separated state 5,394[ev] 3.48[J/m ] 3.3.2. x=10.5nm y=26.1nm z=12.7nm 271,453 Cu z <111> Fig.3.3.1 Cu z <111> σ 12,000[MPa] 0[MPa] z - - 48
5.4[ps] 15[ps] 41[ps] 0 12000 [Mpa] - - 49
42[ps] 43[ps] 45[ps] 0 12000 [Mpa] Fig.3.3.1 Cu z <011> - - 50
Fig.3.3.1 misfit Cu z <111> Cu z <111> misfit misfit misfit z Cu Cu z <111> misfit 43[ps] xz Cu Ru Cu z <111> misfit Cu z <111> misfit z - - 51
Fig.3.3.2 Cu z <111> misfit Ru Cu Cu z <111> misfit y Cu 5.4[ps] 30[ps] 50[ps] 70[ps] Fig.3.3.2 Cu z <011> Fig.3.3.3 σ step z σ z 3 = 6.0 10 [MPa] =1.85[%] Cu z <111> misfit σ z z - - 52
Fig.3.3.3 Cu z <011> σ step z 3.3.3. x=10.5nm y=21.6nm z=12.7nm 269,227 Cu z <111> misfit Fig.3.3.3 Cu z <111> Fig.3.1.8 AB fcc hcp y τ Cu z <111> misfit - - 53
0[ps] 5.4[ps] 15[ps] -3000 6000 [Mpa] - - 54
27[ps] -3000 6000 [Mpa] Fig.3.3.4 Cu z <011> misfit τ Cu z <111> misfit Fig.3.3.5 τ step τ τ 9.9 10 [MPa] Cu z <111> 165[%] misfit 32[%] misfit - - 55
Fig.3.3.5 Cu z <011> τ step - - 56
3.4. Cu <001> Cu Cu z:<001>, x:<100>, y:<010> 3.4.1. material-connected state Cu/Ru x=10.5nm y=27.5nm z=12.7nm 287,932 material-separated state Cu Cu x=10.5nm y=27.5nm z=6.1nm 149,872 Ru Ru x=10.5nm y=26.1nm z=6.5nm 138,060 Cu <111> Cu-Ru -1,449,252[eV] Cu -524,924[eV] Ru -917,119[eV] material-connected state material-separated state 7,209[ev] 4.01[J/m ] 3.4.2. x=10.5nm y=27.5nm z=12.7nm 286,362 Fig.3.4.1 σ 17,000[MPa] -3,000[MPa] z - - 57
5.4[ps] 50[ps] 63[ps] -3000 17000 [Mpa] - - 58
65[ps] 66[ps] 67[ps] -3000 17000 [Mpa] Fig.3.4.1 Cu z <001> - - 59
Fig.3.4.1 misfit Cu <011> misfit misfit misfit z 65[ps] Cu <011> Cu Ru σ Cu <011> z Cu <011> z Fig.3.4.2 Ru Cu Cu y Cu <011> Cu <001> - - 60
5.4[ps] 30[ps] 50[ps] 70[ps] Fig.3.4.2 Cu z <001> Fig.3.4.3 σ step z σ z 3 = 7.0 10 [MPa] =3.81[%] 63[ps] step 60,000[step] Fig.3.4.3 60,000[step] - - 61
Fig.3.4.3 Cu z <111> σ step z 3.4.3. x=10.5nm y=21.6nm z=12.7nm 269,227 Fig.3.4.4 Cu z <111> Fig.3.1.8 AB fcc hcp y τ Cu z <111> misfit Fig.3.4.4 misfit misfit τ τ Fig.3.1.9 16[ps] misfit - - 62
0[ps] 5.4[ps] 15[ps] -3000 6000 [Mpa] - - 63
27[ps] -3000 6000 [Mpa] Fig.3.4.4 Cu z <001> Fig.3.3.5 τ step τ τ 7.1 10 [MPa] Cu z <111> 118[%] misfit 23[%] misfit - - 64
Fig.3.4.5 Cu z <001> τ step - - 65
3.4.4. Cu Cu Cu z <111> <011> <001> misfit Cu z <011> <001> 3 Cu z <111> 4.56[J/m ] Cu z <011> 3.48[J/m ] Cu z <001> 4.01[J/m ] <111><011> 24% <001> 12% <111><001><011> Table.3.3 σ z <111><011> 15% <001> 35%<111><011> 46% <001> 114% σ z [MPa] [%] step <111> 5.2 10³ 1.78 27,000 <011> 6.0 10³ 2.60 37,000 <001> 7.0 10³ 3.81 52,000 Table.3.4 Cu z <111> <011> <001> Fig.3.4.6 Cu z <111> <011> <001> σ step <111><011><001> z - - 66
Fig.3.4.6 Cu z <111> <011> <001> σ step z misfit Fig.3.1.8 Fig.3.3.3 Fig.3.4.3 <111> misfit <011><001> misfit Fig.3.4.7 Cu z <111> <011> <001> step <111> <011> <001> misfit 3,000[MPa] 20 33 23 τ τ misfit - - 67
Fig.3.4.7 Cu z <111> <011> <001> τ step misfit Cu misfit - - 68
Cu-Ru Cu-Ru Ru Cu Ru Ru 5 Cu Ru misfit Cu misfit misfit misfit misfit Cu - - 69
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