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答网友晶体学问题:单斜晶系的空间群符号
问题在:
http://blog.sciencenet.cn/home.php?mod=space&uid=2321&do=wall
回答如下:
根据你提供的信息(ICSD #33243:单斜钒酸铋)。
ICSD 33243数据(摘要)如下:
Structured Bi (V O4)
Unit Cell 5.197 5.096 11.702 90. 90. 90.4
Space Group I 1 1 2/b
SG Number 15
Atom # OX SITE x y z SOF
Bi 1 +3 4 e 0 0.25 0.6337(1) 1.
V 1 +5 4 e 0 0.25 0.1352(5) 1.
O 1 -2 8 f 0.149(3) 0.506(8) 0.210(2) 1.
O 2 -2 8 f 0.258(3) 0.379(8) 0.451(2) 1.
*end for ICSD #33243
在国际空间群表里,15号空间群有6种表达方式:
Uniq-b轴有三种晶胞,Uniq-c轴有三种晶胞,共有6种。
注意,6种晶胞对应一个空间群编号,但是6种晶胞的Patterson symmetry符号不同。例如,你的数据(ICSD #33243)对应I 1 1 2/b,根据这个符号确定空间群表里的具体晶胞选择。根据Unit Cell的(5.197 5.096 11.702 90. 90. 90.4)
信息,可以确定属于Uniq-c轴,对应的晶胞如下:
注意,原子坐标的数据是和晶胞数据对应的。
BiVO4的原子环境数据如下:
"a=",5.197,"b=",5.096,"c=",11.702,"Delta=",.005
1
"4e-Bi"," is a reference atom"
" Cartesian = ",-2.5896,-1.274,1.5681
" SP coordinates=",0,.25,.634
"",1,1,"The shell structure as a cluster:","shell","No",1
" d of neighbors from the reference atom =",2.3434
" The number of neighbor atoms"," N=",2,"and"
" the number of shortest bonds formed by these atoms=",1
" and the shortest bond length=",2.94
" Neighbor atom:","8f-1-O"
" Cartesian = ",-3.3726,-.0306,3.3936
" SP coordinates= ",-.149,.494,.79
" Neighbor atom:","8f-1-O"
" Cartesian = ",-1.8066,-2.5174,3.3936
" SP coordinates= ",.149,.006,.79
"",1,2,"The shell structure as a cluster:","shell","No",2
" d of neighbors from the reference atom =",2.3734
" The number of neighbor atoms"," N=",2,"and"
" the number of shortest bonds formed by these atoms=",1
" and the shortest bond length=",4.4
" Neighbor atom:","8f-1-O"
" Cartesian = ",-4.4051,-2.5174,2.4574
" SP coordinates= ",-.351,.006,.71
" Neighbor atom:","8f-1-O"
" Cartesian = ",-.7741,-.0306,2.4574
" SP coordinates= ",.351,.494,.71
"",1,3,"The shell structure as a cluster:","shell","No",3
" d of neighbors from the reference atom =",2.5292
" The number of neighbor atoms"," N=",2,"and"
" the number of shortest bonds formed by these atoms=",1
" and the shortest bond length=",4.65
" Neighbor atom:","8f-2-O"
" Cartesian = ",-3.9436,.6166,.5734
" SP coordinates= ",-.258,.621,.549
" Neighbor atom:","8f-2-O"
" Cartesian = ",-1.2356,-3.1645,.5734
" SP coordinates= ",.258,-.121,.549
"",1,4,"The shell structure as a cluster:","shell","No",4
" d of neighbors from the reference atom =",2.6084
" The number of neighbor atoms"," N=",2,"and"
" the number of shortest bonds formed by these atoms=",1
" and the shortest bond length=",2.98
" Neighbor atom:","8f-2-O"
" Cartesian = ",-3.9258,-1.9313,-.5734
" SP coordinates= ",-.258,.121,.451
" Neighbor atom:","8f-2-O"
" Cartesian = ",-1.2534,-.6166,-.5734
" SP coordinates= ",.258,.379,.451
"",1,5,"The shell structure as a cluster:","shell","No",5
" d of neighbors from the reference atom =",3.6058
" The number of neighbor atoms"," N=",2,"and"
" the number of shortest bonds formed by these atoms=",1
" and the shortest bond length=",6.93
" Neighbor atom:","8f-2-O"
" Cartesian = ",-3.9081,-4.4793,.5734
" SP coordinates= ",-.258,-.379,.549
" Neighbor atom:","8f-2-O"
" Cartesian = ",-1.2712,1.9313,.5734
" SP coordinates= ",.258,.879,.549
"",1,6,"The shell structure as a cluster:","shell","No",6
" d of neighbors from the reference atom =",3.6266
" The number of neighbor atoms"," N=",2,"and"
" the number of shortest bonds formed by these atoms=",1
" and the shortest bond length=",7.25
" Neighbor atom:","4e-V"
" Cartesian = ",-5.1703,-3.8219,1.5798
" SP coordinates= ",-.5,-.25,.635
" Neighbor atom:","4e-V"
" Cartesian = ",-.0089,1.274,1.5798
" SP coordinates= ",.5,.75,.635
2
"4e-V"," is a reference atom"
" Cartesian = ",-2.5896,-1.274,-4.2712
" SP coordinates=",0,.25,.135
"",2,1,"The shell structure as a cluster:","shell","No",1
" d of neighbors from the reference atom =",1.7431
" The number of neighbor atoms"," N=",2,"and"
" the number of shortest bonds formed by these atoms=",1
" and the shortest bond length=",2.85
" Neighbor atom:","8f-2-O"
" Cartesian = ",-3.8519,-.6166,-5.2776
" SP coordinates= ",-.242,.379,.049
" Neighbor atom:","8f-2-O"
" Cartesian = ",-1.3273,-1.9313,-5.2776
" SP coordinates= ",.242,.121,.049
"",2,2,"The shell structure as a cluster:","shell","No",2
" d of neighbors from the reference atom =",1.7486
" The number of neighbor atoms"," N=",2,"and"
" the number of shortest bonds formed by these atoms=",1
" and the shortest bond length=",3.02
" Neighbor atom:","8f-1-O"
" Cartesian = ",-3.3549,-2.5785,-3.3936
" SP coordinates= ",-.149,-.006,.21
" Neighbor atom:","8f-1-O"
" Cartesian = ",-1.8244,.0306,-3.3936
" SP coordinates= ",.149,.506,.21
"",2,3,"The shell structure as a cluster:","shell","No",3
" d of neighbors from the reference atom =",2.89
" The number of neighbor atoms"," N=",2,"and"
" the number of shortest bonds formed by these atoms=",1
" and the shortest bond length=",4.5
" Neighbor atom:","8f-1-O"
" Cartesian = ",-4.4229,.0306,-2.4574
" SP coordinates= ",-.351,.506,.29
" Neighbor atom:","8f-1-O"
" Cartesian = ",-.7564,-2.5785,-2.4574
" SP coordinates= ",.351,-.006,.29
"",2,4,"The shell structure as a cluster:","shell","No",4
" d of neighbors from the reference atom =",3.1239
" The number of neighbor atoms"," N=",2,"and"
" the number of shortest bonds formed by these atoms=",1
" and the shortest bond length=",4.53
" Neighbor atom:","8f-2-O"
" Cartesian = ",-3.8341,-3.1645,-6.4244
" SP coordinates= ",-.242,-.121,-.049
" Neighbor atom:","8f-2-O"
" Cartesian = ",-1.3451,.6166,-6.4244
" SP coordinates= ",.242,.621,-.049
"",2,5,"The shell structure as a cluster:","shell","No",5
" d of neighbors from the reference atom =",3.6266
" The number of neighbor atoms"," N=",2,"and"
" the number of shortest bonds formed by these atoms=",1
" and the shortest bond length=",7.25
" Neighbor atom:","4e-Bi"
" Cartesian = ",-5.1703,-3.8219,-4.2829
" SP coordinates= ",-.5,-.25,.134
" Neighbor atom:","4e-Bi"
" Cartesian = ",-.0089,1.274,-4.2829
" SP coordinates= ",.5,.75,.134
"",2,6,"The shell structure as a cluster:","shell","No",6
" d of neighbors from the reference atom =",3.652
" The number of neighbor atoms"," N=",2,"and"
" the number of shortest bonds formed by these atoms=",1
" and the shortest bond length=",7.3
" Neighbor atom:","4e-Bi"
" Cartesian = ",-5.2059,1.274,-4.2829
" SP coordinates= ",-.5,.75,.134
" Neighbor atom:","4e-Bi"
" Cartesian = ",.0267,-3.8219,-4.2829
" SP coordinates= ",.5,-.25,.134
3
"8f-1-O"," is a reference atom"
" Cartesian = ",-1.8066,-2.5174,3.3936
" SP coordinates=",.149,.006,.79
"",3,1,"The shell structure as a cluster:","shell","No",1
" d of neighbors from the reference atom =",1.7486
" The number of neighbor atoms"," N=",1,"and"
" the number of shortest bonds formed by these atoms=",0
" and the shortest bond length=",0
" Neighbor atom:","4e-V"
" Cartesian = ",-2.5718,-3.8219,4.2712
" SP coordinates= ",0,-.25,.865
"",3,2,"The shell structure as a cluster:","shell","No",2
" d of neighbors from the reference atom =",2.3434
" The number of neighbor atoms"," N=",1,"and"
" the number of shortest bonds formed by these atoms=",0
" and the shortest bond length=",0
" Neighbor atom:","4e-Bi"
" Cartesian = ",-2.5896,-1.274,1.5681
" SP coordinates= ",0,.25,.634
"",3,3,"The shell structure as a cluster:","shell","No",3
" d of neighbors from the reference atom =",2.3734
" The number of neighbor atoms"," N=",1,"and"
" the number of shortest bonds formed by these atoms=",0
" and the shortest bond length=",0
" Neighbor atom:","4e-Bi"
" Cartesian = ",.0089,-1.274,4.2829
" SP coordinates= ",.5,.25,.866
4
"8f-2-O"," is a reference atom"
" Cartesian = ",-1.3273,-1.9313,-5.2776
" SP coordinates=",.242,.121,.049
"",4,1,"The shell structure as a cluster:","shell","No",1
" d of neighbors from the reference atom =",1.7431
" The number of neighbor atoms"," N=",1,"and"
" the number of shortest bonds formed by these atoms=",0
" and the shortest bond length=",0
" Neighbor atom:","4e-V"
" Cartesian = ",-2.5896,-1.274,-4.2712
" SP coordinates= ",0,.25,.135
"",4,2,"The shell structure as a cluster:","shell","No",2
" d of neighbors from the reference atom =",2.5293
" The number of neighbor atoms"," N=",1,"and"
" the number of shortest bonds formed by these atoms=",0
" and the shortest bond length=",0
" Neighbor atom:","4e-Bi"
" Cartesian = ",.0267,-3.8219,-4.2829
" SP coordinates= ",.5,-.25,.134
"",4,3,"The shell structure as a cluster:","shell","No",3
" d of neighbors from the reference atom =",2.6084
" The number of neighbor atoms"," N=",1,"and"
" the number of shortest bonds formed by these atoms=",0
" and the shortest bond length=",0
" Neighbor atom:","4e-Bi"
" Cartesian = ",.0089,-1.274,-7.4191
" SP coordinates= ",.5,.25,-.134
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