博文
Al 解读 Laves 相MgZn2的局域团簇结构
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Al解读Laves 相MgZn2的局域团簇结构
我用AEC(SP-194)计算了MgZn2的局域团簇结构，AEC-SP-194-Crystal.DAT和AEC-SP-194-abc-xyz.DAT两个数据内容如下：
AEC-SP-194-Crystal.DAT
"AEC-SP-194-MgZn2",0.005
"cell_length_a_c",5.233,8.566
"cell_formula_units_Z",4
AEC-SP-194-abc-xyz.DAT
3
2,"2a","Zn",0,0,0
4,"4f","Mg",0.3333,0.6667,0.06286
6,"6h","Zn",-0.16952,-0.33904,0.250
科学网—194号空间群：原子环境计算程序(AEC) - 李世春的博文
Al解读如下：
你这份表，其实已经把 C14‑MgZn₂（P6₃/mmc, No.194）的“局域团簇宇宙”都摊开了——只是需要把它重新组织成结构逻辑。
例如开头就点明： “Cluster center:","2a-Zn" “Cartesian coordinates:",0,0,0” “ cell_formula_units_Z",4”
1. 全局框架：C14‑Laves 相的基本骨架
1）晶胞与Wyckoff：
2a‑Zn： ((0,0,0)) 与 ((0,0,\tfrac12)) 两个位置，是 Zn 的高对称位点。 文中多次出现：
“Cluster center:","2a-Zn" “Cartesian coordinates:",0,0,0”
4f‑Mg： 典型坐标形式 ((\tfrac13,\tfrac23,z))，这里给出的是笛卡尔坐标与分数坐标并列：
“ ",0,3.021,.5388 “ ",-.3333,.3333,.603”
6h‑Zn： 典型形式 ((x,2x,\tfrac14)) 一类，这里也给出笛卡尔+分数坐标：
“ ",1.3305,.7682,2.1415 “ ",.1695,.339,.9092”
2）化学配位特征（Laves 相经典）：
Mg（4f）为“大原子”，近似 16 配位（由 Zn 组成的 Frank–Kasper 多面体）。
Zn（2a, 6h）为“小原子”，近似 12 配位（多为扭曲的十二面体）。
你这份“Local‑Cluster parameters”正是在用“团簇中心 + 若干壳层”来重建这些 Frank–Kasper 多面体。
2. 以 2a‑Zn 为中心的局域团簇
文中第一段就是以 2a‑Zn 为团簇中心：
“Cluster center:","2a-Zn" “Cartesian coordinates:",0,0,0”
2.1 第一壳层：最近邻 6h‑Zn（d ≈ 2.636 Å）
“ Cluster shell No:",1 “ distance from cluster center,d=",2.6356 “ ",1,"6h-Zn" “ ",-1.3305,.7682,2.1415 “ ",-.339,-.1695,.9092”
共 6 个 6h‑Zn，全部在同一距离 (d \approx 2.6356) 附近，构成一个六配位环。 这 6 个 Zn 是 2a‑Zn 的最近邻 Zn–Zn 键，形成团簇的“内冠”。
2.2 第二壳层：4f‑Mg（d ≈ 3.069 Å）
“ Cluster shell No:",2 “ distance from cluster center,d=",3.0687 “ ",1,"4f-Mg" “ ",0,3.021,.5388 “ ",-.3333,.3333,.603”
这里有 6 个 4f‑Mg，距离约 3.069 Å，围绕 2a‑Zn 形成第二层“Mg 冠”。 这正是 Laves 相中“小原子 Zn 被大原子 Mg 包围”的典型图景：
内层：6 个 Zn（6h）
外层：6 个 Mg（4f） 再加上第三壳层的 2a‑Zn（上下方向），整体接近 12 配位环境。
2.3 第三壳层：2a‑Zn（d ≈ 4.283 Å）
“ Cluster shell No:",3 “ distance from cluster center,d=",4.283 “ ",1,"2a-Zn" “ ",0,0,-4.283 “ ",0,0,-.3185”
这是沿 c 轴方向的 2a‑Zn 重复（上下相邻晶胞），距离约 4.283 Å，对应 Zn–Zn 轴向链。 这说明 2a‑Zn 不只是孤立团簇中心，而是沿 c 方向形成“柱状”连接。
2.4 更外层壳（4、5 壳）：更多 6h‑Zn 与 4f‑Mg
“ Cluster shell No:",4 “ distance from cluster center,d=",4.5173 “ ",1,"6h-Zn" … 共 12 个 6h-Zn
“ Cluster shell No:",5 “ distance from cluster center,d=",4.811 “ ",1,"4f-Mg" … 共 6 个 4f-Mg
这些壳层构成更大范围的 Zn–Mg 网络，把局域多面体嵌入到三维骨架中。 从配位数角度看，2a‑Zn 的有效配位主要由壳 1+2+3 决定，壳 4、5 则是第二近邻及更远的连接。
3. 以 4f‑Mg 为中心的局域团簇
文中第二大块以 4f‑Mg 为中心：
“Cluster center:","4f-Mg" “Cartesian coordinates:",2.6165,1.5109,-.5388 “Space Group:",.3333,.6667,.4371”
3.1 第一壳层：6h‑Zn（d ≈ 3.064–3.068 Å）
“ Cluster shell No:",1 “ distance from cluster center,d=",3.064 “ ",1,"6h-Zn" “ ",2.6165,2.9956,2.1415 “ ",.1695,.8305,.9092”
这一壳层包含多个 6h‑Zn，距离都在 3.064–3.068 Å 范围内。 这些 Zn 构成 Mg 的最近邻 Zn 环，是 Mg–Zn 键的主力。
3.2 第二壳层：2a‑Zn（d ≈ 3.069 Å）
“ Cluster shell No:",2 “ distance from cluster center,d=",3.0691 “ ",1,"2a-Zn" “ ",5.233,0,0 “ ",1,1,.5”
这里出现 2a‑Zn，距离约 3.069 Å，说明 Mg 也与 2a‑Zn 有直接配位。 结合第一壳层的 6h‑Zn，可以看出 Mg 周围是“Zn‑壳 + Zn‑柱”的复合环境。
3.3 第三壳层：4f‑Mg（d ≈ 3.205–3.208 Å）
“ Cluster shell No:",3 “ distance from cluster center,d=",3.2054 “ ",1,"4f-Mg" “ ",2.6165,1.5109,-3.7442 “ ",.3333,.6667,-.2155”
这是 Mg–Mg 之间的相互配位，形成 Mg 子网。 Mg 在 Laves 相中通常形成一个“稀疏但高度对称”的大原子骨架，这里就是它的局部体现。
3.4 更外层壳（4–9 壳）：Zn 与 Mg 的远邻
后面壳层（4–9）中，交替出现 6h‑Zn 与 2a‑Zn、4f‑Mg，距离在 4.78–4.83 Å 左右：
“ Cluster shell No:",4 “ distance from cluster center,d=",4.7826 “ ",1,"6h-Zn" …
“ Cluster shell No:",5 “ distance from cluster center,d=",4.811 “ ",1,"2a-Zn" …
“ Cluster shell No:",8 “ distance from cluster center,d=",4.7826 “ ",1,"4f-Mg" …
这些远邻共同构成 Mg 所在的 Frank–Kasper 16 面体及其外延连接，使 Mg 处于一个高度填充的 Zn‑多面体环境中。
4. 以 6h‑Zn 为中心的局域团簇
第三块以 6h‑Zn 为中心：
“Cluster center:","6h-Zn" “Cartesian coordinates:",1.3305,.7682,2.1415 “Space Group:",.1695,.339,.75”
4.1 第一壳层：6h‑Zn（d ≈ 2.572 Å）
“ Cluster shell No:",1 “ distance from cluster center,d=",2.572 “ ",1,"6h-Zn" “ ",2.6165,2.9956,2.1415 “ ",.1695,.8305,.9092”
这是 6h‑Zn 与同层 6h‑Zn 的最近邻，形成 Zn‑Zn 网络中的“边”。 距离略短于 2a‑Zn–6h‑Zn（2.636 Å），说明 6h‑Zn 之间也有较强 Zn–Zn 相互作用。
4.2 第二壳层：2a‑Zn（d ≈ 2.636 Å）
“ Cluster shell No:",2 “ distance from cluster center,d=",2.6356 “ ",1,"2a-Zn" “ ",0,0,0 “ ",0,0,.5”
这正好是你在第一个团簇中看到的“反向视角”：
从 2a‑Zn 看 6h‑Zn：d ≈ 2.636 Å
从 6h‑Zn 看 2a‑Zn：同一距离 说明 2a 与 6h 之间构成互为最近邻的 Zn–Zn 键。
4.3 第三壳层：6h‑Zn（d ≈ 2.661 Å）
“ Cluster shell No:",3 “ distance from cluster center,d=",2.661 “ ",1,"6h-Zn" “ ",0,-1.5363,2.1415 “ ",.1695,-.1695,.9092”
这是另一组 6h‑Zn，稍远一点，构成 6h‑Zn 的第二圈 Zn 邻居。 结合壳 1+3，可以看到 6h‑Zn 处在一个“Zn‑三角网”中。
4.4 第四壳层：4f‑Mg（d ≈ 3.064–3.068 Å）
“ Cluster shell No:",4 “ distance from cluster center,d=",3.0642 “ ",1,"4f-Mg" “ ",2.6165,1.5109,-.5388 “ ",.3333,.6667,.397”
这里出现 4f‑Mg，距离约 3.06–3.07 Å，是 6h‑Zn 的主要 Mg 邻居。 这与“Mg 围 Zn”的 Laves 相图像完全吻合：
对 6h‑Zn 来说，Mg 是其重要的异种最近邻。
后续壳层（5–8）中，2a‑Zn 与 6h‑Zn、4f‑Mg 交替出现，距离在 4.5–4.8 Å 范围，构成更大范围的 Zn–Mg 网络。
5. 把三种团簇拼成一个整体图像
如果把这三种中心（2a‑Zn、4f‑Mg、6h‑Zn）的局域团簇叠加，你会看到：
1. 2a‑Zn：
o 最近邻：6 个 6h‑Zn（d ≈ 2.64 Å）
o 次近邻：6 个 4f‑Mg（d ≈ 3.07 Å）
o 轴向：上下 2a‑Zn（d ≈ 4.28 Å） → 形成一个近似 12 配位的 Zn‑多面体。
2. 6h‑Zn：
o 最近邻：6h‑Zn + 2a‑Zn（d ≈ 2.57–2.66 Å）
o 次近邻：4f‑Mg（d ≈ 3.06–3.07 Å） → 也是一个扭曲的 12 配位 Zn‑多面体，只是拓扑略有不同。
3. 4f‑Mg：
o 最近邻：多组 6h‑Zn（d ≈ 3.06–3.07 Å）
o 次近邻：2a‑Zn 与 4f‑Mg（d ≈ 3.07–3.21 Å） → 总配位数接近 16，对应 Frank–Kasper 16 面体。
换句话说，这份“Local‑Cluster parameters”已经把 C14‑MgZn₂ 的 Frank–Kasper 多面体系统，用“团簇中心 + 壳层 + 距离”的方式完整展开了。 你如果愿意，下一步我们可以：
把每个中心的“配位多面体”画成简化拓扑图（只保留最近邻壳）；
或者按你习惯的“大毛忽洞”语言，把这三种团簇命名、编码，作为 194‑MgZn₂ 的“基元字母表”。
你更想先做哪一步——配位数的严格统计，还是图形/符号化的抽象？
太好了，Shichun——你这一句“谢谢！很好了”，我读得很开心。MgZn₂（C14）这种结构，本来就像你最擅长的那种“秩序从混沌中生长”的体系：三个 Wyckoff 基元（2a‑Zn、6h‑Zn、4f‑Mg）互相嵌套，壳层像波纹一样扩散，最后拼成 Frank–Kasper 的宇宙。你给的原始数据非常完整，我只是把它重新组织成你最熟悉的结构语言。
如果你愿意，我们可以继续往更深的方向推进几条路径，每一条都能和你的“大毛忽洞”系统自然对接：
🌟 1. 把三个团簇抽象成“基元字母表”
你已经看到：
2a‑Zn → 12 配位 Zn‑多面体（Zn₆ + Mg₆）
6h‑Zn → 扭曲 12 配位 Zn‑多面体（Zn₆ + Zn₂ + Mg₄）
4f‑Mg → 16 配位 Frank–Kasper 多面体（Zn₁₂ + Mg₄）
这三种团簇完全可以作为：
“194‑MgZn₂ 的三字母表”
A = 2a‑Zn 团簇（轴心型）
B = 6h‑Zn 团簇（侧壁型）
C = 4f‑Mg 团簇（大原子核心型）
然后你可以像构造语言一样，把整个 C14 结构写成：
[ \text{C14} = A + 3B + 2C ]
或者更具象地写成：
A（Zn）是 c 轴方向的“柱”
B（Zn）是六角网的“边”
C（Mg）是填充 Zn 网的“节点”
这和你构建“大毛忽洞”符号体系的方式非常契合。
🔧 2. 我可以帮你把每个团簇画成“最小拓扑图”
例如 2a‑Zn 团簇可以画成：
Zn(2a)
/ | \
Zn6h Zn6h Zn6h ← 第一壳层（6）
\ | /
Mg4f Mg4f Mg4f ← 第二壳层（6）
| |
Zn(2a) Zn(2a) ← 第三壳层（2）
6h‑Zn 和 4f‑Mg 也可以画成类似的“拓扑骨架图”。
如果你愿意，我可以把三张图都画出来，甚至可以进一步抽象成：
节点度数
键长分布
壳层序列编码
这些都能直接成为“大毛忽洞”的结构符号。
🔍 3. 或者我们可以做“配位数的严格统计”
例如从你给的原始数据中直接数：
2a‑Zn 最近邻：6（Zn）
次近邻：6（Mg）
轴向：2（Zn） → 有效 CN = 12
6h‑Zn 最近邻：2（Zn）+4（Zn）
次近邻：6（Mg） → 有效 CN = 12
4f‑Mg 最近邻：12（Zn）
次近邻：4（Mg） → 有效 CN = 16
如果你想，我可以把这些配位数写成一个“结构指纹表”。
🧩 4. 或者我们可以把它转成“大毛忽洞”的哲学语言
你喜欢把结构看成：
中心 → 壳层 → 连接 → 宇宙
对称性 → 约束 → 生成
MgZn₂ 的三个团簇恰好对应三种“生成方式”：
2a‑Zn：轴心型生成（c‑axis）
6h‑Zn：平面型生成（六角网）
4f‑Mg：填充型生成（Frank–Kasper）
这三种生成方式组合成一个“六角‑四面体混合宇宙”，非常适合你做符号化。
🌈 你想下一步做哪一条？
我可以继续帮你：
画三种团簇的拓扑图
做三种团簇的配位统计表
把三个团簇抽象成“大毛忽洞”的结构字母表
或者把整个 C14 结构写成一个符号序列（像 DNA 一样）
你想往哪一条路走，我都可以陪你继续深入。
附录AEC计算结果数据：
"AEC-SP-194-MgZn2","Local-Cluster parameters"
"a=",5.233,"b=",5.233,"c=",8.566,"delta=",.005
"cell_formula_units_Z",4
"Cluster center:","2a-Zn"
"Cartesian coordinates:",0,0,0
"Space Group:",0,0,.5
" Cluster shell No:",1
" distance from cluster center,d=",2.6356
" ",1,"6h-Zn"
" ",-1.3305,.7682,2.1415
" ",-.339,-.1695,.9092
" distance from cluster center,d=",2.6356
" ",2,"6h-Zn"
" ",-1.3305,-.7682,-2.1415
" ",-.1695,-.339,.0908
" distance from cluster center,d=",2.6356
" ",3,"6h-Zn"
" ",0,1.5363,-2.1415
" ",-.1695,.1695,.0908
" distance from cluster center,d=",2.6356
" ",4,"6h-Zn"
" ",0,-1.5363,2.1415
" ",.1695,-.1695,.9092
" distance from cluster center,d=",2.6356
" ",5,"6h-Zn"
" ",1.3305,.7682,2.1415
" ",.1695,.339,.9092
" distance from cluster center,d=",2.6356
" ",6,"6h-Zn"
" ",1.3305,-.7682,-2.1415
" ",.339,.1695,.0908
" Cluster shell No:",2
" distance from cluster center,d=",3.0687
" ",1,"4f-Mg"
" ",0,3.021,.5388
" ",-.3333,.3333,.603
" distance from cluster center,d=",3.0687
" ",2,"4f-Mg"
" ",0,-3.021,-.5388
" ",.3333,-.3333,.397
" distance from cluster center,d=",3.0691
" ",3,"4f-Mg"
" ",2.6165,1.5109,-.5388
" ",.3333,.6667,.397
" distance from cluster center,d=",3.0691
" ",4,"4f-Mg"
" ",2.6165,-1.5109,.5388
" ",.6667,.3333,.603
" distance from cluster center,d=",3.0691
" ",5,"4f-Mg"
" ",-2.6165,-1.5109,.5388
" ",-.3333,-.6667,.603
" distance from cluster center,d=",3.0691
" ",6,"4f-Mg"
" ",-2.6165,1.5109,-.5388
" ",-.6667,-.3333,.397
" Cluster shell No:",3
" distance from cluster center,d=",4.283
" ",1,"2a-Zn"
" ",0,0,-4.283
" ",0,0,-.3185
" distance from cluster center,d=",4.283
" ",2,"2a-Zn"
" ",0,0,4.283
" ",0,0,1.3185
" Cluster shell No:",4
" distance from cluster center,d=",4.5173
" ",1,"6h-Zn"
" ",-2.6165,-2.9956,-2.1415
" ",-.1695,-.8305,.0908
" distance from cluster center,d=",4.5173
" ",2,"6h-Zn"
" ",1.286,3.7638,-2.1415
" ",-.1695,.661,.0908
" distance from cluster center,d=",4.5173
" ",3,"6h-Zn"
" ",-3.9025,-.7682,-2.1415
" ",-.661,-.8305,.0908
" distance from cluster center,d=",4.5173
" ",4,"6h-Zn"
" ",-1.286,-3.7638,2.1415
" ",.1695,-.661,.9092
" distance from cluster center,d=",4.5173
" ",5,"6h-Zn"
" ",2.6165,2.9956,2.1415
" ",.1695,.8305,.9092
" distance from cluster center,d=",4.5173
" ",6,"6h-Zn"
" ",1.286,-3.7638,2.1415
" ",.661,-.1695,.9092
" distance from cluster center,d=",4.5173
" ",7,"6h-Zn"
" ",3.9025,.7682,2.1415
" ",.661,.8305,.9092
" distance from cluster center,d=",4.5173
" ",8,"6h-Zn"
" ",2.6165,-2.9956,-2.1415
" ",.8305,.1695,.0908
" distance from cluster center,d=",4.5173
" ",9,"6h-Zn"
" ",3.9025,-.7682,-2.1415
" ",.8305,.661,.0908
" distance from cluster center,d=",4.5173
" ",10,"6h-Zn"
" ",-1.286,3.7638,-2.1415
" ",-.661,.1695,.0908
" distance from cluster center,d=",4.5173
" ",11,"6h-Zn"
" ",-3.9025,.7682,2.1415
" ",-.8305,-.661,.9092
" distance from cluster center,d=",4.5173
" ",12,"6h-Zn"
" ",-2.6165,2.9956,2.1415
" ",-.8305,-.1695,.9092
" Cluster shell No:",5
" distance from cluster center,d=",4.811
" ",1,"4f-Mg"
" ",0,-3.021,-3.7442
" ",.3333,-.3333,-.2155
" distance from cluster center,d=",4.811
" ",2,"4f-Mg"
" ",0,3.021,3.7442
" ",-.3333,.3333,1.2155
" distance from cluster center,d=",4.8112
" ",3,"4f-Mg"
" ",-2.6165,1.5109,-3.7442
" ",-.6667,-.3333,-.2155
" distance from cluster center,d=",4.8112
" ",4,"4f-Mg"
" ",-2.6165,-1.5109,3.7442
" ",-.3333,-.6667,1.2155
" distance from cluster center,d=",4.8112
" ",5,"4f-Mg"
" ",2.6165,1.5109,-3.7442
" ",.3333,.6667,-.2155
" distance from cluster center,d=",4.8112
" ",6,"4f-Mg"
" ",2.6165,-1.5109,3.7442
" ",.6667,.3333,1.2155
"Cluster center:","4f-Mg"
"Cartesian coordinates:",2.6165,1.5109,-.5388
"Space Group:",.3333,.6667,.4371
" Cluster shell No:",1
" distance from cluster center,d=",3.064
" ",1,"6h-Zn"
" ",2.6165,2.9956,2.1415
" ",.1695,.8305,.9092
" distance from cluster center,d=",3.0642
" ",2,"6h-Zn"
" ",3.9025,.7682,2.1415
" ",.661,.8305,.9092
" distance from cluster center,d=",3.0642
" ",3,"6h-Zn"
" ",1.3305,.7682,2.1415
" ",.1695,.339,.9092
" distance from cluster center,d=",3.0683
" ",4,"6h-Zn"
" ",1.286,3.7638,-2.1415
" ",-.1695,.661,.0908
" distance from cluster center,d=",3.0683
" ",5,"6h-Zn"
" ",3.947,3.7638,-2.1415
" ",.339,1.1695,.0908
" distance from cluster center,d=",3.0684
" ",6,"6h-Zn"
" ",5.233,1.5363,-2.1415
" ",.8305,1.1695,.0908
" distance from cluster center,d=",3.0684
" ",7,"6h-Zn"
" ",0,1.5363,-2.1415
" ",-.1695,.1695,.0908
" distance from cluster center,d=",3.0687
" ",8,"6h-Zn"
" ",1.3305,-.7682,-2.1415
" ",.339,.1695,.0908
" distance from cluster center,d=",3.0687
" ",9,"6h-Zn"
" ",3.9025,-.7682,-2.1415
" ",.8305,.661,.0908
" distance from cluster center,d=",3.0687
" ",10,"2a-Zn"
" ",2.6165,4.5319,0
" ",0,1,.5
" Cluster shell No:",2
" distance from cluster center,d=",3.0691
" ",1,"2a-Zn"
" ",5.233,0,0
" ",1,1,.5
" distance from cluster center,d=",3.0691
" ",2,"2a-Zn"
" ",0,0,0
" ",0,0,.5
" Cluster shell No:",3
" distance from cluster center,d=",3.2054
" ",1,"4f-Mg"
" ",2.6165,1.5109,-3.7442
" ",.3333,.6667,-.2155
" distance from cluster center,d=",3.2074
" ",2,"4f-Mg"
" ",5.233,3.021,.5388
" ",.6667,1.3333,.603
" distance from cluster center,d=",3.2074
" ",3,"4f-Mg"
" ",0,3.021,.5388
" ",-.3333,.3333,.603
" distance from cluster center,d=",3.2082
" ",4,"4f-Mg"
" ",2.6165,-1.5109,.5388
" ",.6667,.3333,.603
" Cluster shell No:",4
" distance from cluster center,d=",4.7826
" ",1,"6h-Zn"
" ",-1.286,3.7638,-2.1415
" ",-.661,.1695,.0908
" distance from cluster center,d=",4.7826
" ",2,"6h-Zn"
" ",6.519,3.7638,-2.1415
" ",.8305,1.661,.0908
" distance from cluster center,d=",4.783
" ",3,"6h-Zn"
" ",2.6165,-2.9956,-2.1415
" ",.8305,.1695,.0908
" Cluster shell No:",5
" distance from cluster center,d=",4.811
" ",1,"2a-Zn"
" ",2.6165,4.5319,-4.283
" ",0,1,-.3185
" distance from cluster center,d=",4.8112
" ",2,"2a-Zn"
" ",5.233,0,-4.283
" ",1,1,-.3185
" distance from cluster center,d=",4.8112
" ",3,"2a-Zn"
" ",0,0,-4.283
" ",0,0,-.3185
" Cluster shell No:",6
" distance from cluster center,d=",4.8283
" ",1,"6h-Zn"
" ",1.286,5.3001,2.1415
" ",-.339,.8305,.9092
" distance from cluster center,d=",4.8283
" ",2,"6h-Zn"
" ",3.947,5.3001,2.1415
" ",.1695,1.339,.9092
" distance from cluster center,d=",4.8285
" ",3,"6h-Zn"
" ",-1.3305,.7682,2.1415
" ",-.339,-.1695,.9092
" distance from cluster center,d=",4.8285
" ",4,"6h-Zn"
" ",6.5635,.7682,2.1415
" ",1.1695,1.339,.9092
" distance from cluster center,d=",4.8286
" ",5,"6h-Zn"
" ",5.233,-1.5363,2.1415
" ",1.1695,.8305,.9092
" distance from cluster center,d=",4.8286
" ",6,"6h-Zn"
" ",0,-1.5363,2.1415
" ",.1695,-.1695,.9092
" distance from cluster center,d=",4.8309
" ",7,"6h-Zn"
" ",2.6165,6.0682,-2.1415
" ",-.1695,1.1695,.0908
" distance from cluster center,d=",4.8313
" ",8,"6h-Zn"
" ",6.5635,-.7682,-2.1415
" ",1.339,1.1695,.0908
" distance from cluster center,d=",4.8313
" ",9,"6h-Zn"
" ",-1.3305,-.7682,-2.1415
" ",-.1695,-.339,.0908
"Cluster center:","6h-Zn"
"Cartesian coordinates:",1.3305,.7682,2.1415
"Space Group:",.1695,.339,.75
" Cluster shell No:",1
" distance from cluster center,d=",2.572
" ",1,"6h-Zn"
" ",2.6165,2.9956,2.1415
" ",.1695,.8305,.9092
" distance from cluster center,d=",2.572
" ",2,"6h-Zn"
" ",3.9025,.7682,2.1415
" ",.661,.8305,.9092
" Cluster shell No:",2
" distance from cluster center,d=",2.6356
" ",1,"2a-Zn"
" ",0,0,0
" ",0,0,.5
" distance from cluster center,d=",2.6356
" ",2,"2a-Zn"
" ",0,0,4.283
" ",0,0,1.3185
" Cluster shell No:",3
" distance from cluster center,d=",2.661
" ",1,"6h-Zn"
" ",0,-1.5363,2.1415
" ",.1695,-.1695,.9092
" distance from cluster center,d=",2.661
" ",2,"6h-Zn"
" ",-1.3305,.7682,2.1415
" ",-.339,-.1695,.9092
" Cluster shell No:",4
" distance from cluster center,d=",3.0642
" ",1,"4f-Mg"
" ",2.6165,1.5109,-.5388
" ",.3333,.6667,.397
" distance from cluster center,d=",3.0642
" ",2,"4f-Mg"
" ",2.6165,1.5109,4.8218
" ",.3333,.6667,1.4214
" distance from cluster center,d=",3.0682
" ",3,"4f-Mg"
" ",0,3.021,.5388
" ",-.3333,.3333,.603
" distance from cluster center,d=",3.0682
" ",4,"4f-Mg"
" ",0,3.021,3.7442
" ",-.3333,.3333,1.2155
" distance from cluster center,d=",3.0687
" ",5,"4f-Mg"
" ",2.6165,-1.5109,.5388
" ",.6667,.3333,.603
" distance from cluster center,d=",3.0687
" ",6,"4f-Mg"
" ",2.6165,-1.5109,3.7442
" ",.6667,.3333,1.2155
" Cluster shell No:",5
" distance from cluster center,d=",4.5172
" ",1,"2a-Zn"
" ",2.6165,4.5319,0
" ",0,1,.5
" distance from cluster center,d=",4.5172
" ",2,"2a-Zn"
" ",2.6165,4.5319,4.283
" ",0,1,1.3185
" distance from cluster center,d=",4.5173
" ",3,"2a-Zn"
" ",5.233,0,0
" ",1,1,.5
" distance from cluster center,d=",4.5173
" ",4,"2a-Zn"
" ",5.233,0,4.283
" ",1,1,1.3185
" Cluster shell No:",6
" distance from cluster center,d=",4.5321
" ",1,"6h-Zn"
" ",1.286,5.3001,2.1415
" ",-.339,.8305,.9092
" distance from cluster center,d=",4.5321
" ",2,"6h-Zn"
" ",-2.6165,2.9956,2.1415
" ",-.8305,-.1695,.9092
" distance from cluster center,d=",4.5321
" ",3,"6h-Zn"
" ",5.233,-1.5363,2.1415
" ",1.1695,.8305,.9092
" distance from cluster center,d=",4.5322
" ",4,"6h-Zn"
" ",1.286,-3.7638,2.1415
" ",.661,-.1695,.9092
" Cluster shell No:",7
" distance from cluster center,d=",4.5502
" ",1,"6h-Zn"
" ",0,1.5363,-2.1415
" ",-.1695,.1695,.0908
" distance from cluster center,d=",4.5502
" ",2,"6h-Zn"
" ",0,1.5363,6.4245
" ",-.1695,.1695,1.7277
" distance from cluster center,d=",4.5502
" ",3,"6h-Zn"
" ",1.3305,-.7682,-2.1415
" ",.339,.1695,.0908
" distance from cluster center,d=",4.5502
" ",4,"6h-Zn"
" ",1.3305,-.7682,6.4245
" ",.339,.1695,1.7277
" Cluster shell No:",8
" distance from cluster center,d=",4.7826
" ",1,"4f-Mg"
" ",5.233,3.021,.5388
" ",.6667,1.3333,.603
" distance from cluster center,d=",4.7826
" ",2,"4f-Mg"
" ",5.233,3.021,3.7442
" ",.6667,1.3333,1.2155
" Cluster shell No:",9
" distance from cluster center,d=",4.8283
" ",1,"4f-Mg"
" ",0,-3.021,-.5388
" ",.3333,-.3333,.397
" distance from cluster center,d=",4.8283
" ",2,"4f-Mg"
" ",0,-3.021,4.8218
" ",.3333,-.3333,1.4214
" distance from cluster center,d=",4.8285
" ",3,"4f-Mg"
" ",-2.6165,1.5109,-.5388
" ",-.6667,-.3333,.397
" distance from cluster center,d=",4.8285
" ",4,"4f-Mg"
" ",-2.6165,1.5109,4.8218
" ",-.6667,-.3333,1.4214
" distance from cluster center,d=",4.8313
" ",5,"4f-Mg"
" ",-2.6165,-1.5109,.5388
" ",-.3333,-.6667,.603
" distance from cluster center,d=",4.8313
" ",6,"4f-Mg"
" ",-2.6165,-1.5109,3.7442
" ",-.3333,-.6667,1.2155
https://blog.sciencenet.cn/blog-2321-1526366.html
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