博文
The First Table of Atomic Site Coordinates of the Ih QC (2)
||
The First Table of Atomic Site Coordinates of the Ih QC (2)
https://doi.org/10.5281/zenodo.23426598
The First Table of Atomic Site Coordinates of the Ih Quasicrystal | Zenodo
The First Table of Atomic Site Coordinates of the QC (n=1 to 6)
In the International Tables for Space Groups, set a=b=c=1. Similarly in the first table, R=0.951056516295154d; set d=1. A regular icosahedron (QC with n=1) located in Cartesian coordinate frame of reference: origin is at the center of QC, i.e., |P000|=0. Z axis coincides with one five-fold axis (C5); Y axis coincides with one two-fold axis (C2), X axis passes through the triangle but does not coincide with any three-fold axis (C3). Any atom-site position vector at nth shell of QC cell can be expressed as Puvw=uRa + vRb + wRc, where u, v, w are positive integers, can be called site index of QC (Ih), and must satisfy a restriction condition as u + v + w = n, where n being integers and ≥1, it denotes the number of shells of QC (Ih). Ra, Rb and Rc are the three basis vectors for QC (n=1) [4]. In the table, all sites with a degeneracy of 2 are marked with the symmetry code "m".
对整个点阵，层内(同一个n)最近邻点位距离为 1， 层间(不同的n之间)最近邻点位距离为0.951056516295154。这是判定一个点阵是不是Ih点群点阵的一个基本条件。
原子点位的笛卡尔坐标如下：
"n+v+w=n"," u v w","Degeneracy"
"u+v+w=",2,":",2,0,0,"Deg=",10
"u+v+w=",2,":",1,1,0,"Deg=",4
"u+v+w=",2,":",1,0,1,"Deg=",4
"u+v+w=",2,":",0,2,0,"Deg=",10
"u+v+w=",2,":",0,1,1,"Deg=",4
"u+v+w=",2,":",0,0,2,"Deg=",10
"Number of the Sites on the Shell =",6
"Site: u,v,w=",2,0,0
"dist of the site from the center of QC,|Puvw|=",1.90211303259031
" x=",0
" y=",0
" z=",1.90211303259031
"Site: u,v,w=",1,1,0
"dist of the site from the center of QC,|Puvw|=",1.6180339887499
" x=",.850650808352039
" y=",0
" z=",1.37638192047117
"Site: u,v,w=",1,0,1
"dist of the site from the center of QC,|Puvw|=",1.61803398961639
" x=",.262865557989286
" y=",.809016992972924
" z=",1.37638192194535
"Site: u,v,w=",0,2,0
"dist of the site from the center of QC,|Puvw|=",1.90211303259031
" x=",1.70130161670408
" y=",0
" z=",.850650808352042
"Site: u,v,w=",0,1,1
"dist of the site from the center of QC,|Puvw|=",1.61803399015192
" x=",1.11351636634133
" y=",.809016992972924
" z=",.850650809826216
"Site: u,v,w=",0,0,2
"dist of the site from the center of QC,|Puvw|=",1.90211303259031
" x=",.525731115978572
" y=",1.61803398594585
" z=",.85065081130039
"n+v+w=n"," u v w","Degeneracy"
"u+v+w=",3,":",3,0,0,"Deg=",10
"u+v+w=",3,":",2,1,0,"Deg=",2
"u+v+w=",3,":",2,0,1,"Deg=",2
"u+v+w=",3,":",1,2,0,"Deg=",2
"u+v+w=",3,":",1,1,1,"Deg=",6
"u+v+w=",3,":",1,0,2,"Deg=",2
"u+v+w=",3,":",0,3,0,"Deg=",10
"u+v+w=",3,":",0,2,1,"Deg=",2
"u+v+w=",3,":",0,1,2,"Deg=",2
"u+v+w=",3,":",0,0,3,"Deg=",10
"Number of the Sites on the Shell =",10
"Site: u,v,w=",3,0,0
"dist of the site from the center of QC,|Puvw|=",2.85316954888546
" x=",0
" y=",0
" z=",2.85316954888546
"Site: u,v,w=",2,1,0
"dist of the site from the center of QC,|Puvw|=",2.47801865906762
" x=",.850650808352039
" y=",0
" z=",2.32743843676633
"Site: u,v,w=",2,0,1
"dist of the site from the center of QC,|Puvw|=",2.47801866019918
" x=",.262865557989286
" y=",.809016992972924
" z=",2.3274384382405
"Site: u,v,w=",1,2,0
"dist of the site from the center of QC,|Puvw|=",2.47801865906762
" x=",1.70130161670408
" y=",0
" z=",1.8017073246472
"Site: u,v,w=",1,1,1
"dist of the site from the center of QC,|Puvw|=",2.26728394384743
" x=",1.11351636634133
" y=",.809016992972924
" z=",1.80170732612137
"Site: u,v,w=",1,0,2
"dist of the site from the center of QC,|Puvw|=",2.47801866019918
" x=",.525731115978572
" y=",1.61803398594585
" z=",1.80170732759554
"Site: u,v,w=",0,3,0
"dist of the site from the center of QC,|Puvw|=",2.85316954888546
" x=",2.55195242505612
" y=",0
" z=",1.27597621252806
"Site: u,v,w=",0,2,1
"dist of the site from the center of QC,|Puvw|=",2.47801866089853
" x=",1.96416717469336
" y=",.809016992972924
" z=",1.27597621400224
"Site: u,v,w=",0,1,2
"dist of the site from the center of QC,|Puvw|=",2.47801866089853
" x=",1.37638192433061
" y=",1.61803398594585
" z=",1.27597621547641
"Site: u,v,w=",0,0,3
"dist of the site from the center of QC,|Puvw|=",2.85316954888546
" x=",.788596673967858
" y=",2.42705097891877
" z=",1.27597621695059
"n+v+w=n"," u v w","Degeneracy"
"u+v+w=",4,":",4,0,0,"Deg=",10
"u+v+w=",4,":",3,1,0,"Deg=",2
"u+v+w=",4,":",3,0,1,"Deg=",2
"u+v+w=",4,":",2,2,0,"Deg=",4
"u+v+w=",4,":",2,1,1,"Deg=",2
"u+v+w=",4,":",2,0,2,"Deg=",4
"u+v+w=",4,":",1,3,0,"Deg=",2
"u+v+w=",4,":",1,2,1,"Deg=",2
"u+v+w=",4,":",1,1,2,"Deg=",2
"u+v+w=",4,":",1,0,3,"Deg=",2
"u+v+w=",4,":",0,4,0,"Deg=",10
"u+v+w=",4,":",0,3,1,"Deg=",2
"u+v+w=",4,":",0,2,2,"Deg=",4
"u+v+w=",4,":",0,1,3,"Deg=",2
"u+v+w=",4,":",0,0,4,"Deg=",10
"Number of the Sites on the Shell =",15
"Site: u,v,w=",4,0,0
"dist of the site from the center of QC,|Puvw|=",3.80422606518062
" x=",0
" y=",0
" z=",3.80422606518062
"Site: u,v,w=",3,1,0
"dist of the site from the center of QC,|Puvw|=",3.38705417066211
" x=",.850650808352039
" y=",0
" z=",3.27849495306148
"Site: u,v,w=",3,0,1
"dist of the site from the center of QC,|Puvw|=",3.38705417190392
" x=",.262865557989286
" y=",.809016992972924
" z=",3.27849495453566
"Site: u,v,w=",2,2,0
"dist of the site from the center of QC,|Puvw|=",3.23606797749979
" x=",1.70130161670408
" y=",0
" z=",2.75276384094235
"Site: u,v,w=",2,1,1
"dist of the site from the center of QC,|Puvw|=",3.07768353882343
" x=",1.11351636634133
" y=",.809016992972924
" z=",2.75276384241652
"Site: u,v,w=",2,0,2
"dist of the site from the center of QC,|Puvw|=",3.23606797923279
" x=",.525731115978572
" y=",1.61803398594585
" z=",2.7527638438907
"Site: u,v,w=",1,3,0
"dist of the site from the center of QC,|Puvw|=",3.38705417066211
" x=",2.55195242505612
" y=",0
" z=",2.22703272882322
"Site: u,v,w=",1,2,1
"dist of the site from the center of QC,|Puvw|=",3.07768353910497
" x=",1.96416717469336
" y=",.809016992972924
" z=",2.22703273029739
"Site: u,v,w=",1,1,2
"dist of the site from the center of QC,|Puvw|=",3.07768353956052
" x=",1.37638192433061
" y=",1.61803398594585
" z=",2.22703273177157
"Site: u,v,w=",1,0,3
"dist of the site from the center of QC,|Puvw|=",3.38705417190392
" x=",.788596673967858
" y=",2.42705097891877
" z=",2.22703273324574
"Site: u,v,w=",0,4,0
"dist of the site from the center of QC,|Puvw|=",3.80422606518061
" x=",3.40260323340816
" y=",0
" z=",1.70130161670408
"Site: u,v,w=",0,3,1
"dist of the site from the center of QC,|Puvw|=",3.38705417267139
" x=",2.8148179830454
" y=",.809016992972924
" z=",1.70130161817826
"Site: u,v,w=",0,2,2
"dist of the site from the center of QC,|Puvw|=",3.23606798030384
" x=",2.22703273268265
" y=",1.61803398594585
" z=",1.70130161965243
"Site: u,v,w=",0,1,3
"dist of the site from the center of QC,|Puvw|=",3.3870541726714
" x=",1.6392474823199
" y=",2.42705097891877
" z=",1.70130162112661
"Site: u,v,w=",0,0,4
"dist of the site from the center of QC,|Puvw|=",3.80422606518061
" x=",1.05146223195714
" y=",3.2360679718917
" z=",1.70130162260078
准晶体一层(n=2)，一层(n=3)，一层(n=4)地平移向外扩展，一直到充满整个空间，始终要保持层内最近邻距离为1， 层间最近邻距离为0.951056516295154。始终保持这个条件，直到充满整个空间，这就是满足Ih点群对称性的空间点阵。
https://blog.sciencenet.cn/blog-2321-1557015.html
上一篇：The First Table of Atomic Site Coordinates of the Ih QC (1)
下一篇：The First Table of Atomic Site Coordinates of the Ih QC (3)
