Al2O3晶体的壳层结构：Hexa vs Rhom
电子在原子中，是一层一层的，这叫原子的壳层结构。
实际上，如果站在晶体的某个原子上看，周围原子也是一层一层的，这就是所谓的局域团簇结构。
下面左边的AEC数据，用的晶体结构实验数据(CIF)对应空间群的六方晶胞，下面右边的AEC数据，用的晶体结构实验数据(CIF)对应空间群的三方晶胞。如果让观察者H站在原子12c-Al上，让观察者R站在原子4c-Al上，H和R观察的原子环境是完全相同的，因为Hexa数据和Rhom数据描述的是同一个晶体Al2O3。原始的CIF实验数据，Hexa数据中的原子坐标有4位有效数字，Rhom数据中的原子坐标只有3位有效数字。因为两套晶体结构数据的实验误差，导致在AEC的计算中，距离参考原子越远，左边和右边原子环境的差别也越大。
文件头部 + Shell 1–4 完整排版
Hexa 数据（左） | Rhom 数据（右） |
"AEC-SP-167-Hexa-Al2O3","Local-Cluster" | "AEC-SP-167-Rhom-Al2O3","Local-Cluster" |
"AEC-SP-167-Hexa-Al2O3","delta=",.005 | "AEC-SP-167-Rhom-Al2O3",0.005 |
"a=b=",4.7352,"c=",12.9176 | "a=b=c=”, 5.128 |
"alpha=beta=",90, "gamma=",120 | "alpha=beta=gamma=",55.27 |
"cell_formula_units_Z",6 | "cell_formula_units_Z",2 |
"Cluster center:","12c-Al" | "Cluster center:","4c-Al" |
"Cartesian coordinates:",0,0,-1.9092 | "Cartesian coordinates:",0,0,-1.8838 |
"Space Group:",0,0,.3522 | "Space Group:",.355,.355,.355 |
Shell 1
Hexa | Rhom |
" Cluster shell No:",1 | " Cluster shell No:",1 |
" distance from cluster center,d=",1.8443 | " distance from cluster center,d=",1.8455 |
" ",1,"18e-O" | " ",1,"6e-O" |
" ",-.7257,-1.4767,-1.076 | " ",.7207,-1.4982,-1.0826 |
" ",.0268,-.3333,.2728 | " ",.75,.053,.447 |
" distance from cluster center,d=",1.8445 | " distance from cluster center,d=",1.8456 |
" ",2,"18e-O" | " ",2,"6e-O" |
" ",1.6419,.1103,-1.076 | " ",-1.6579,.125,-1.0826 |
" ",.3333,.3602,.2728 | " ",.053,.447,.75 |
" distance from cluster center,d=",1.8447 | " distance from cluster center,d=",1.8456 |
" ",3,"18e-O" | " ",3,"6e-O" |
" ",-.9163,1.3672,-1.076 | " ",.9372,1.3733,-1.0826 |
" ",-.3602,-.0268,.2728 | " ",.447,.75,.053 |
Shell 2
Hexa | Rhom |
" Cluster shell No:",2 | " Cluster shell No:",2 |
" distance from cluster center,d=",1.9619 | " distance from cluster center,d=",1.9845 |
" ",1,"18e-O" | " ",1,"6e-O" |
" ",-1.4513,0,-3.2294 | " ",-.7207,1.2483,-3.2479 |
" ",-.3065,-.3065,-.182 | " ",-.053,.553,.25 |
" distance from cluster center,d=",1.962 | " distance from cluster center,d=",1.9845 |
" ",2,"18e-O" | " ",2,"6e-O" |
" ",.7257,1.2569,-3.2294 | " ",-.7207,-1.2483,-3.2479 |
" ",0,.3065,-.182 | " ",.25,-.053,.553 |
" distance from cluster center,d=",1.962 | " distance from cluster center,d=",1.9845 |
" ",3,"18e-O" | " ",3,"6e-O" |
" ",.7257,-1.2569,-3.2294 | " ",1.4414,0,-3.2479 |
" ",.3065,0,-.182 | " ",.553,.25,-.053 |
Shell 3
Hexa | Rhom |
" Cluster shell No:",3 | " Cluster shell No:",3 |
" distance from cluster center,d=",2.6404 | " distance from cluster center,d=",2.7282 |
" ",1,"12c-Al" | " ",1,"4c-Al" |
" ",0,0,-4.5496 | " ",0,0,-4.612 |
" ",0,0,-.4608 | " ",.145,.145,.145 |
Shell 4
Hexa | Rhom |
" Cluster shell No:",4 | " Cluster shell No:",4 |
" distance from cluster center,d=",2.7766 | " distance from cluster center,d=",2.8036 |
" ",1,"12c-Al" | " ",1,"4c-Al" |
" ",0,-2.7336,-2.3962 | " ",0,-2.7465,-2.4467 |
" ",.3333,-.3333,-.006 | " ",.645,-.355,.645 |
" distance from cluster center,d=",2.777 | " distance from cluster center,d=",2.8037 |
" ",2,"12c-Al" | " ",2,"4c-Al" |
" ",2.3676,1.3672,-2.3962 | " ",-2.3786,1.3733,-2.4467 |
" ",.3333,.6667,-.006 | " ",-.355,.645,.645 |
" distance from cluster center,d=",2.777 | " distance from cluster center,d=",2.8037 |
" ",3,"12c-Al" | " ",3,"4c-Al" |
" ",-2.3676,1.3672,-2.3962 | " ",2.3786,1.3733,-2.4467 |
" ",-.6667,-.3333,-.006 | " ",.645,.645,-.355 |
科学网—167号空间群的AEC：Hexagonal axes & Rhombohedral axes - 李世春的博文
科学网—Al解读Hexa axes 和 Rhom axes 的实验数据：Al2O3局域团簇结构 - 李世春的博文
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