8615 2012 3
Si SiO 2. Si 1 VASP Si 1,, Si-Si 0.28Å Si 160 1 2 Si-Si 0.19Å Si 166 Si 4 0.85Å Si 118 2 4
1 3 1.1 SiO 2... 3 1.2 Si... 3 1.3 Cz... 4 1.4 SiO 2... 4 1.5... 5 2 6 2.1... 6 2.2 VASP(Vienna Ab-initio Simulation Package)... 7 2.3 PAW(Projector Augmented Wave)... 7 2.4 MedeA... 7 2.5 Maple... 8 2.6 Pauling File... 8 3 9 3.1 SiO 2... 9 3.1.1... 9 3.2 Si 1... 11 3.2.1... 11 3.2.2... 13 3.2.3... 17 3.3 Si 2... 21 3.3.1... 21 3.3.2... 22 3.3.3... 24 3.4 Si 4... 24 3.4.1... 25 3.4.2 3 1 26 3.4.3 2 2 28 3.4.4... 29 3.5... 31 1
3.6... 31 4 33 2
1 1.1 SiO 2 Si Cz 1500 Si SiO 2 (O) Si SiO 2 SiO Si O 2 SiO 2 Si [1, 4] Si ( ) 1.2 Si Si 1/4 1.1 Si Si 1.1: Si 3
1.3 Cz Cz Si (feed) Si (seed) Si (SiO 2 ) 1500 ( 1.2(a)) Si Si Si ( 1.2(b)) Si [1, 3, 4] 1.2: Si [1] (a) (b) 1.4 SiO 2 SiO 2 1.3 SiO 2, 4
Stishovite SiO 4 2 18 SiO 2 [1] Cristobalite Tridymite 2, [8] 1.3: SiO 2 1.5 SiO 2 Cz SiO 2 Si 1 Si 5
2 Schrödinger (First principles calculatons) VASP maple MedeA 2.1, ( adiabatic approximation) Schrödinger Hψ = ɛψ (2.1) ( d2 + V )ψ = ɛψ (2.2) dx2 [6] (Hamiltonian:H) (wave function:φ) (energy Eigen value:ɛ) (Kinetic Energy) (d 2 ψ/d 2 x) (Vψ) (potential:v) (nuclear potential) ( exchange-correlation interaction) 2.2 self consistent loop 6
[6] 2.2 VASP(Vienna Ab-initio Simulation Package) VASP ( PAW ) VASP [7] 2.3 PAW(Projector Augmented Wave) VASP PAW ( ) PAW ( ) PAW Blochl [11] GGA(Generalized Gradient Approximation) PAW(Projector Augmented Wave) 2.1 2.1: [4] PAW ( ) 2.4 MedeA MedeA 7
Windows VASP [6] VASP MedeA 2.5 Maple Maple 1980 [4] Maple 2.6 Pauling File Pauling File 1990 550 21,000 X 4 4 [10] 2.2 Pauling File SiO 2 SiO 2 O-Si-O Pauling File 2.2: [11] Si-O [Å] Si-O-Si [deg] stishovite 1.76 130 coesite 1.57 1.62 140,180 low-quartz 1.70 110 low-cristobalite 1.6 146 high-quartz 1.56,1.64 140 low-tridymite 1.58 1.61 140,150,180 high-tridymite 1.54,1.56 160,170,180 8
3 Cz Si SiO 2 SiO 2 Si SiO 2 Si 1 SiO Si-O Si-O-Si SiO 2 3.1 SiO 2 3.1 SiO 2 8 E-V [ev/sio 2 ] [Å 3 /SiO 2 ] (Stishovite) (Stishovite) (Coesite) (Low Quartz) E-V VASP 3.1.1 de δq δw de = δq δw (3.1) δq =0 δw rev = P dv de = P dv (3.2) P P = de dv 9 (3.3)
3.1: SiO 2 E-V (a) 8 E-V (b)stishovite coesite,coesite low quartz. (3.3) E-V 2 E-V [6] 3.1(b) VASP stishovite coesite low quartz E-V stishovite coesite coesite low quartz E-V ev/å 3 GPa 1[GPa] = 0.00624150948[eV/Å 3 ] (3.4) (3.4) stishovite coesite coesite low quartz E-V -0.047-0.025 3.1 3.1: 2 [9] [GPa] [GPa] stishovite coesite 7.5 10.0 coesite low-quartz 4.5 3.5 25 2 10 10
3.2 Si 1 Si 1 Si 3.2(a) Si8 2 3.2(b) Si64 3.2: Si (a)si8 (b)si64 Si 3.3(a) 3.3(b) 3.3(c) Si 3.3(d) Si-Si 3.2.1 1 Si 3.4 1 Si Si cut-off 600eV k 0.3/Å,. 11
3.3: (a)si (b)puresi (c) (d) 12
3.4: Si 3.2 Si 2 Si-Si Si-O Si 3.2: Si 63+O1 [deg] [Å] [Å] [Å 3 ] [ev] Si-O-Si Si-O Si-Si 10.9374 1308.4-351.95 109.5 2.167 2.387 3.2.2 SiO 2 Si-Si Si Si-Si 13
3.5 Si-Si 9 1 Si cut-off 600eV k 0.3/Å, Si 3.5: (a)si (b)si 3.6 site1 2 4 5 site1 2 4 5 5 5 25 3.7(b) (c) site1 site2 site4 site2 site4 5 5 25 7 7 49 3.8 3.8(c) site1 site2 site4 14
3.6: 9,(a) (b)(a) 3.7: (a) (b)site1 2 4 5 (c) b 3 [5] 15
site5 3.8(b) site1 site2 site4 site5 Si cutoff 520eV k 0.3/Å Si 3.8: Si 64 a b a c 49 3.9 Si 1 3.9-354.32132-354.32141[eV] 3.7(b) site1 2 4 5 360 3.10 Si Si Si 6 Si-Si 3.8 6 Si-Si 3.11 Si-Si 16
3.9: Si 1 (a) (b)(a) 60 6 1,cutoff 600eV,k 0.3/Å Si -354.31532eV Si 1 3.2.3 3.3 1 Si 1 Si Si 1-5.42eV 2.4eV SiO 2 Si-O-Si 10 17
3.10: 3.9(a) 360 18
3.11: (a)[101] (b)[111] (c)(b) 19
3.3: 1 [Å] [deg] [ev] Si-O Si-Si Si-O-Si Si 63 O 1 (+Si 1 ) -351.94 2.167 2.387 109.5 Si 64 O 1-354.32 1.622 2.331 3.197 160.2 Si 64 O 1-1.62 2.33 148.7 [3] Si-Si 2 Si 20
3.3 Si 2 SiO Si 2 3.3.1 1 2 3.12(c) ( 3.12(d)) ( 3.12(e)) 3.4 3.12: 2. a si.(b)si.(c).(d).(e). 21
3.4: 2 Si62+O2 energy Si-O-Si [Å] [ev] [Å] [deg] Si-O Si-Si -359.17 2.43 118.31 1.955 2.372-357.52 0.68 119.90 1.962 2.370-357.85 0.79 140.62 1.731 2.363 2 Si-O 0.2Å Si-O-Si 20 2 2 2 Si-Si 3.3.2 3.13 2 Si 3.13 3 Si 2 Si64 2 cutoff 520eV k 0.3/Å 3.14 3.14(a) (b) (c) [110],[001] Si Si 3.6 3.14 Si Si Si 22
3.13: 2 Si-Si 3.14 a b, 3.6 Si 2 Si 3.15 3.14: 2,(a),(b)[110],(c)[001]. 23
3.15: Si. 3.5: Si 64 O 2 [Å] [deg] Si1-O1 Si3-O1 Si1-Si3 Si1-O1-Si3 1.610 1.628 3.220 166.2 3.3.3 3.0eV Si 1 Si-Si 3.4 Si 4 3.2,3.3 1 2.4eV, 2 3.0eV 4 24
3.6: Si 64 O 2 [Å] enegry a b c [Å 3 ] [ev] 11.0135 11.0097 1334.8-362.20 3.4.1 3.16 4 Si 4 5 Si 4 Si 64 4 cutoff 520eV k 0.3/Å 3.16: 25
3.17 3.17 a b [110] [001] c 3.7 3.7: Si 64 O 4 [Å] [deg] [Å] [Å 3 ] [ev] Si-O Si-Si Si-O-Si 11.1130 1372.4-375.62 1.548 2.369 180 3.17 Si Si Si Si-Si Si 3.18 4 5 Si 3 1 3.20 4 5 Si 2 2 3.4.2 3 1 3.18 5 Si 3 1 1 cutoff 520eV k 0.3/Å 26
3.17: a [110] b [001] c 3.18: 1 (a) 4.(b)[110].(c)[110]. 27
3.19 3.19 a b c [001] [110] Si -378.24eV 3.19: 1 (a) 4.(b)[001].(c)[110]. 3.4.3 2 2 3.20 5 Si 2 2 2 cutoff 520eV k 0.3/Å 3.21 3.21 a b c [001] [110] Si 2 Si-Si Si-Si 28
3.20: 2 (a) 4.(b)[011].(c)[110]. -377.99eV 1 3.21: 2 (a) 4 (b)[001].(c)[110]. 3.4.4 4 3 1 3.8 3.9 3.10 29
3.22: 3.8: 4 Si 64 O 4 [Å] enegry a b c [Å 3 ] [ev] 10.9999 10.9976 11.0774 1340.4-378.25 3.9: 4 Si Si 64 O 4 [Å] Si1-O1 Si2-O2 Si3-O3 Si4-O4 1.6706 1.6979 1.7004 1.6975 3.10: 4 Si Si 64 O 4 [deg] Si1-O1-Si5 Si2-O2-Si5 Si3-O3-Si5 Si4-O4-Si5 117.28 118.61 118.21 118.48 30
3.5 SiO 2 3.11 SiO 2 4 Si-O-Si 2 Si-O-Si 1 Si-O-Si 4 Si-O 1 3.11: BC-O Si-O Si-Si Si-O-Si [Å] [Å] [Å] [deg] Si 64 O 1 0.2745 3.1973 1.6217,1.6223 160.51 Si 64 O 2 0.1949,0.1950 3.2196 1.6102,1.6328 166.21 Si 64 O 4 0.8443-0.8523 2.7954-2.8421 1.6031-1.7004 117.27-118.61-2.6000-2.6500 1.7000 109.50 3.6 3.23 3.23(a) 3.23(b) 2 4 31
3.23: (a) b 32
4 Si (O) Si-O Si-Si 2 Si Si Si diamond Si-O Si-Si Si Si-O 1 2 Si-Si 1 Si-Si 0.27Å 2 Si-Si 0.19Å 4 Si-Si 0.85Å SiO 2 33
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[1] 2006 pp17-pp25 [2] ( 2002 [3] 1995 [4] Si SiO 2 2006 [5] Cz SiO Si SiGe 2008 [6] 2006 [7] VASP 2011 http://ist.ksc.kwansei.ac.jp/~nishitani/?recentpublications [8] 2003 pp187 [9] 1968 pp90 [10] P.Villars Pauling File User Manual (CRYSTAL IMPACT 2002) [11] VASP pp.80 http://cms.mpi.univie.ac.at/vasp/ 35