========================================= CRYSTAL STRUCTURE RELATIONSHIPS ========================================= #Exercise 3.5 (cristobalite): # Space Group ITA number (high-symmetry phase) #Origin Choice 2 227 7.147 7.147 7.147 90 90 90 1 Si 1 8a 0.125 0.125 0.125 # Space Group ITA number (high-symmetry phase) #Origin Choice 1 227 7.147 7.147 7.147 90 90 90 1 Si 1 8a 0.0 0.0 0.0 # Space Group ITA number (low-symmetry phase) 92 4.9586 4.9586 6.9074 90 90 90 1 Si 1 4a 0.3028 0.3028 0 ------------------------------------------------------ Exercise 3.6(a): Pb3(PO4)2 #lead phosphate: high-symmetry phase (ICSD: CC8095) 166 5.56 5.56 20.39 90 90 120 5 Pb 1 3a 0 0 0 Pb 2 6c 0 0 0.2126 P 1 6c 0 0 0.4021 O 1 6c 0 0 0.329 O 2 18h 0.181 -0.181 0.096 #Lead Phosphate: low-symmetry phase: Guimaraes T=25C 15 13.80 5.691 9.42 90 102.3 90 7 O 1 8f 0.643 0.030 0.392 O 2 8f 0.634 0.464 0.374 O 3 8f 0.642 0.280 0.612 O 4 8f 0.491 0.222 0.420 P 1 8f 0.599 0.241 0.447 Pb 1 4e 0 0.291 0.25 Pb 2 8f 0.317 0.309 0.352 #Exercise 3.6(b)(lead vanadate) #High symmetry structure Pb3(VO4)2 166 5.6748 5.6748 20.3784 90 90 120 5 Pb 1 3a 0.000000 0.000000 0.000000 Pb 2 6c 0.000000 0.000000 0.207100 PV 3 6c 0.000000 0.000000 0.388400 O 4 6c 0.000000 0.000000 0.324000 O 5 18i 0.842400 0.157600 0.430100 #low-symmetry exper(Kiat et al, 1993). 14 7.5075 6.0493 9.4814 90. 115.162 90. 7 Pb 1 2a 0 0 0 Pb 2 4e 0.3835 0.5815 0.2879 PV 1 4e 0.2071 0.0143 0.3999 O 1 4e 0.2872 0.2559 0.0159 O 2 4e 0.2598 0.7979 0.0216 O 3 4e 0.3194 0.9784 0.2823 O 4 4e 0.0335 0.5431 0.2091 ------------------------------------------------------------------------------- #Exercise 3.8 beta-brass hettotype #CuZn (CsCl type): P432 221 #V=25.67 2.959 2.959 2.959 90. 90. 90. 2 Cu 1 1a 0 0 0 Zn 1 1b 0.5 0.5 0.5 #CoU type:I213 199 #V=256.74 6.3557 6.3557 6.3557 90. 90. 90. 2 Co 1 8a 0.294 0.294 0.294 U 1 8a 0.0347 0.0347 0.0347 --------------------------------------------------------------------------------- #Exercise 3.11:Pb2MgWO6 # Space Group ITA number 62 # Lattice parameters 11.4059 7.9440 5.6866 90.00 90.00 90.00 # Number of independent atoms in the asymmetric unit 8 # [atom type] [number] [WP] [x] [y] [z] Pb 1 8d 0.1422 0.0032 0.7804 Mg 1 4c 0.3772 0.25 0.7519 W 1 4c 0.1161 0.25 0.2577 O 1 8d 0.1314 0.4907 0.2365 O 2 4c 0.0027 0.25 0.0133 O 3 4c 0.0103 0.25 0.4991 O 4 4c 0.237 0.25 -0.0153 O 5 4c 0.2491 0.25 0.4745 ---------------------------------------------------------------------------------- #Exercise 3.12:VirtualStructure # Space Group ITA number C2221 20 5.4435 9.4122 9.0630 90 90 90 7 A 1 4a 0.0790 0 0 A 2 4b 0 0.385 0.25 B 1 8c -0.0323 0.3562 0.6231 C 1 4a 0.5412 0 0 C 2 8c 0.7812 0.222 0.0385 C 3 4b 0 -0.1998 0.25 C 4 8c 0.2596 0.0999 0.2312 ----------------------------------------------------------------------------------- #Exercise 3.13: Ga_under pressure 20 5.976 8.576 35.758 90 90 90 14 Ga 1 4b 0.5000 0.1802 0.2500 Ga 2 8c 0.6956 0.4684 0.2716 Ga 3 8c 0.5804 0.7858 0.2861 Ga 4 8c 0.2772 0.5622 0.3081 Ga 5 8c -0.0341 0.7809 0.3292 Ga 6 8c 0.8482 0.4567 0.3430 Ga 7 8c 0.5632 0.6919 0.3666 Ga 8 8c 0.2324 0.4838 0.3851 Ga 9 8c 0.6129 0.2914 0.4003 Ga 10 8c 0.8276 0.5660 0.4250 Ga 11 8c -0.0030 0.2613 0.4435 Ga 12 4a 0.2460 0.0 0.5000 Ga 13 8c 0.1052 0.3090 0.5170 Ga 14 8c 0.3574 0.5518 0.5409 --------------------------------------------------------------------------------------- ##Exercise 3.15: ferroelectric_NaSb3F10 # Space Group ITA number 173 # Lattice parameters 8.285 8.285 7.600 90. 90. 120. # Number of independent atoms in the asymmetric unit 6 # [atom type] [number] [WP] [x] [y] [z]- Sb 1 6c 0.883700 0.224300 0.250000 Na 1 2b 0.333300 0.666700 0.167000 F 1 6c 0.204000 0.393000 0.994000 F 2 6c 0.111000 0.229000 0.340000 F 3 6c 0.035000 0.491000 0.281000 F 4 2b 0.666700 0.333300 0.245000