原子雕刻技术：Al和Mg晶体，相同的团簇

   Al是立方晶体（a=4.049），Mg是六方晶体(a=3.209,c=5.211)，前者的空间群是225，原子占位4a；后者的空间群是194，原子占位2c。

但是，从局域看，Al和Mg具有相同原子环境。

在原子空间中，参考原子Al的周围有12个其他的Al原子；参考原子Mg的周围也有12个其他的Mg原子。

对于Al来说，参考原子周围12个Al原子距离参考原子的距离都是2.8631。这12个Al原子（Vertices）在空间的分布形成1个14【＝8（3）＋6（4）】面体，8个面是正三边形，6个面是正四边形。在14面体上，12个Al原子可以连接成24条键，键长为2.86埃。

对于Mg来说，参考原子周围12个Mg原子距离参考原子的距离都是3.1959。这12个Mg原子（Vertices）在空间的分布形成1个14【＝8（3）＋6（4）】面体，8个面是正三边形，6个面是正四边形。在14面体上，12个Mg原子可以连接成24条键，键长为3.2埃。

从Al和Mg晶体中雕刻出的13个原子的团簇，其结构是完全相同的。

从第二层开始，Al和Mg的团簇结构就开始分道扬镳了。

Al的团簇结构数据：

"4a-Al"," is a reference atom"

"      Cartesian =  ",-2.0245,-2.0245,-2.0245

"      SP coordinates=",0,0,0

"      d of neighbors from the reference atom =",2.8631

"      The number of neighbor atoms"," N=",12,"P=",24

"      Neighbor atom:","4a-Al"

"     Cartesian =  ",-4.049,-4.049,-2.0245

"      SP coordinates=  ",-.5,-.5,0

"      Neighbor atom:","4a-Al"

"      Cartesian =  ",-4.049,-2.0245,-4.049

"      SP coordinates=  ",-.5,0,-.5

"      Neighbor atom:","4a-Al"

"      Cartesian =  ",-4.049,-2.0245,0

"      SP coordinates=  ",-.5,0,.5

"      Neighbor atom:","4a-Al"

"      Cartesian =  ",-4.049,0,-2.0245

"      SP coordinates=  ",-.5,.5,0

"      Neighbor atom:","4a-Al"

"      Cartesian =  ",-2.0245,-4.049,-4.049

"      SP coordinates=  ",0,-.5,-.5

"     Neighbor atom:","4a-Al"

"      Cartesian =  ",-2.0245,-4.049,0

"      SP coordinates=  ",0,-.5,.5

"      Neighbor atom:","4a-Al"

"      Cartesian =  ",-2.0245,0,-4.049

"      SP coordinates=  ",0,.5,-.5

"      Neighbor atom:","4a-Al"

"      Cartesian =  ",-2.0245,0,0

"      SP coordinates=  ",0,.5,.5

"      Neighbor atom:","4a-Al"

"      Cartesian =  ",0,-4.049,-2.0245

"      SP coordinates=  ",.5,-.5,0

"      Neighbor atom:","4a-Al"

"      Cartesian =  ",0,-2.0245,-4.049

"      SP coordinates=  ",.5,0,-.5

"      Neighbor atom:","4a-Al"

"      Cartesian =  ",0,-2.0245,0

"      SP coordinates=  ",.5,0,.5

"      Neighbor atom:","4a-Al"

"      Cartesian =  ",0,0,-2.0245

"      SP coordinates=  ",.5,.5,0

Al团簇14面体结构数据：

1,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",-4.049,-4.049,-2.024,"---",-4.049,-2.024,-4.049

"       SP coordinates=",-.5,-.5,0,"---",-.5,0,-.5

2,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",-4.049,-4.049,-2.024,"---",-4.049,-2.024,0

"       SP coordinates=",-.5,-.5,0,"---",-.5,0,.5

3,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",-4.049,-4.049,-2.024,"---",-2.024,-4.049,-4.049

"       SP coordinates=",-.5,-.5,0,"---",0,-.5,-.5

4,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",-4.049,-4.049,-2.024,"---",-2.024,-4.049,0

"       SP coordinates=",-.5,-.5,0,"---",0,-.5,.5

5,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",-4.049,-2.024,-4.049,"---",-4.049,0,-2.024

"       SP coordinates=",-.5,0,-.5,"---",-.5,.5,0

6,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",-4.049,-2.024,-4.049,"---",-2.024,-4.049,-4.049

"       SP coordinates=",-.5,0,-.5,"---",0,-.5,-.5

7,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",-4.049,-2.024,-4.049,"---",-2.024,0,-4.049

"       SP coordinates=",-.5,0,-.5,"---",0,.5,-.5

8,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",-4.049,-2.024,0,"---",-4.049,0,-2.024

"       SP coordinates=",-.5,0,.5,"---",-.5,.5,0

9,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",-4.049,-2.024,0,"---",-2.024,-4.049,0

"       SP coordinates=",-.5,0,.5,"---",0,-.5,.5

10,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",-4.049,-2.024,0,"---",-2.024,0,0

"       SP coordinates=",-.5,0,.5,"---",0,.5,.5

11,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",-4.049,0,-2.024,"---",-2.024,0,-4.049

"       SP coordinates=",-.5,.5,0,"---",0,.5,-.5

12,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",-4.049,0,-2.024,"---",-2.024,0,0

"       SP coordinates=",-.5,.5,0,"---",0,.5,.5

13,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",-2.024,-4.049,-4.049,"---",0,-4.049,-2.024

"       SP coordinates=",0,-.5,-.5,"---",.5,-.5,0

14,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",-2.024,-4.049,-4.049,"---",0,-2.024,-4.049

"       SP coordinates=",0,-.5,-.5,"---",.5,0,-.5

15,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",-2.024,-4.049,0,"---",0,-4.049,-2.024

"       SP coordinates=",0,-.5,.5,"---",.5,-.5,0

16,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",-2.024,-4.049,0,"---",0,-2.024,0

"       SP coordinates=",0,-.5,.5,"---",.5,0,.5

17,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",-2.024,0,-4.049,"---",0,-2.024,-4.049

"       SP coordinates=",0,.5,-.5,"---",.5,0,-.5

18,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",-2.024,0,-4.049,"---",0,0,-2.024

"       SP coordinates=",0,.5,-.5,"---",.5,.5,0

19,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",-2.024,0,0,"---",0,-2.024,0

"       SP coordinates=",0,.5,.5,"---",.5,0,.5

20,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",-2.024,0,0,"---",0,0,-2.024

"       SP coordinates=",0,.5,.5,"---",.5,.5,0

21,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",0,-4.049,-2.024,"---",0,-2.024,-4.049

"       SP coordinates=",.5,-.5,0,"---",.5,0,-.5

22,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",0,-4.049,-2.024,"---",0,-2.024,0

"       SP coordinates=",.5,-.5,0,"---",.5,0,.5

23,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",0,-2.024,-4.049,"---",0,0,-2.024

"       SP coordinates=",.5,0,-.5,"---",.5,.5,0

24,"  The distance of","4a-Al","and","4a-Al","d==",2.86

"       Coordinates of these two atoms:"

"       Cartesian=",0,-2.024,0,"---",0,0,-2.024

"       SP coordinates=",.5,0,.5,"---",.5,.5,0

Mg团簇的结构数据：

"2c-Mg"," is a reference atom"

"      Cartesian =  ",1.6045,.9282,-1.3027

"      SP coordinates=",.333,.667,.25

"      d of neighbors from the reference atom =",3.1959

"      The number of neighbor atoms"," N=",12,"P=",24

"      Neighbor atom:","2c-Mg"

"      Cartesian =  ",-1.6045,.9282,-1.3027

"      SP coordinates=  ",-.667,-.333,.25

"      Neighbor atom:","2c-Mg"

"      Cartesian =  ",0,-1.8509,-1.3027

"      SP coordinates=  ",.333,-.333,.25

"      Neighbor atom:","2c-Mg"

"      Cartesian =  ",0,1.8509,-3.9082

"      SP coordinates=  ",-.333,.333,-.25

"      Neighbor atom:","2c-Mg"

"      Cartesian =  ",0,1.8509,1.3027

"      SP coordinates=  ",-.333,.333,.75

"      Neighbor atom:","2c-Mg"

"      Cartesian =  ",0,3.7073,-1.3027

"      SP coordinates=  ",-.667,.667,.25

"      Neighbor atom:","2c-Mg"

"      Cartesian =  ",1.6045,-.9282,-3.9082

"      SP coordinates=  ",.667,.333,-.25

"      Neighbor atom:","2c-Mg"

"      Cartesian =  ",1.6045,-.9282,1.3027

"      SP coordinates=  ",.667,.333,.75

"      Neighbor atom:","2c-Mg"

"      Cartesian =  ",3.209,-1.8509,-1.3027

"      SP coordinates=  ",1.333,.667,.25

"      Neighbor atom:","2c-Mg"

"      Cartesian =  ",3.209,1.8509,-3.9082

"      SP coordinates=  ",.667,1.333,-.25

"      Neighbor atom:","2c-Mg"

"      Cartesian =  ",3.209,1.8509,1.3027

"      SP coordinates=  ",.667,1.333,.75

"      Neighbor atom:","2c-Mg"

"      Cartesian =  ",3.209,3.7073,-1.3027

"      SP coordinates=  ",.333,1.667,.25

"      Neighbor atom:","2c-Mg"

"      Cartesian =  ",4.8135,.9282,-1.3027

"      SP coordinates=  ",1.333,1.667,.25

Mg团簇14面体结构数据：

1,"  The distance of","2c-Mg","and","2c-Mg","d==",3.2

"       Coordinates of these two atoms:"

"       Cartesian=",-1.605,.928,-1.303,"---",0,1.851,-3.908

"       SP coordinates=",-.667,-.333,.25,"---",-.333,.333,-.25

2,"  The distance of","2c-Mg","and","2c-Mg","d==",3.2

"       Coordinates of these two atoms:"

"       Cartesian=",-1.605,.928,-1.303,"---",0,1.851,1.303

"       SP coordinates=",-.667,-.333,.25,"---",-.333,.333,.75

3,"  The distance of","2c-Mg","and","2c-Mg","d==",3.2

"       Coordinates of these two atoms:"

"       Cartesian=",0,-1.851,-1.303,"---",1.605,-.928,-3.908

"       SP coordinates=",.333,-.333,.25,"---",.667,.333,-.25

4,"  The distance of","2c-Mg","and","2c-Mg","d==",3.2

"       Coordinates of these two atoms:"

"       Cartesian=",0,-1.851,-1.303,"---",1.605,-.928,1.303

"       SP coordinates=",.333,-.333,.25,"---",.667,.333,.75

5,"  The distance of","2c-Mg","and","2c-Mg","d==",3.2

"       Coordinates of these two atoms:"

"       Cartesian=",0,1.851,-3.908,"---",0,3.707,-1.303

"       SP coordinates=",-.333,.333,-.25,"---",-.667,.667,.25

6,"  The distance of","2c-Mg","and","2c-Mg","d==",3.2

"       Coordinates of these two atoms:"

"       Cartesian=",0,1.851,1.303,"---",0,3.707,-1.303

"       SP coordinates=",-.333,.333,.75,"---",-.667,.667,.25

7,"  The distance of","2c-Mg","and","2c-Mg","d==",3.2

"       Coordinates of these two atoms:"

"       Cartesian=",1.605,-.928,-3.908,"---",3.209,-1.851,-1.303

"       SP coordinates=",.667,.333,-.25,"---",1.333,.667,.25

8,"  The distance of","2c-Mg","and","2c-Mg","d==",3.2

"       Coordinates of these two atoms:"

"       Cartesian=",1.605,-.928,1.303,"---",3.209,-1.851,-1.303

"       SP coordinates=",.667,.333,.75,"---",1.333,.667,.25

9,"  The distance of","2c-Mg","and","2c-Mg","d==",3.2

"       Coordinates of these two atoms:"

"       Cartesian=",3.209,1.851,-3.908,"---",3.209,3.707,-1.303

"       SP coordinates=",.667,1.333,-.25,"---",.333,1.667,.25

10,"  The distance of","2c-Mg","and","2c-Mg","d==",3.2

"       Coordinates of these two atoms:"

"       Cartesian=",3.209,1.851,-3.908,"---",4.813,.928,-1.303

"       SP coordinates=",.667,1.333,-.25,"---",1.333,1.667,.25

11,"  The distance of","2c-Mg","and","2c-Mg","d==",3.2

"       Coordinates of these two atoms:"

"       Cartesian=",3.209,1.851,1.303,"---",3.209,3.707,-1.303

"       SP coordinates=",.667,1.333,.75,"---",.333,1.667,.25

12,"  The distance of","2c-Mg","and","2c-Mg","d==",3.2

"       Coordinates of these two atoms:"

"      Cartesian=",3.209,1.851,1.303,"---",4.813,.928,-1.303

"       SP coordinates=",.667,1.333,.75,"---",1.333,1.667,.25

13,"  The distance of","2c-Mg","and","2c-Mg","d==",3.21

"       Coordinates of these two atoms:"

"       Cartesian=",0,1.851,1.303,"---",3.209,1.851,1.303

"       SP coordinates=",-.333,.333,.75,"---",.667,1.333,.75

14,"  The distance of","2c-Mg","and","2c-Mg","d==",3.21

"       Coordinates of these two atoms:"

"       Cartesian=",0,3.707,-1.303,"---",3.209,3.707,-1.303

"       SP coordinates=",-.667,.667,.25,"---",.333,1.667,.25

15,"  The distance of","2c-Mg","and","2c-Mg","d==",3.21

"       Coordinates of these two atoms:"

"       Cartesian=",1.605,-.928,-3.908,"---",3.209,-1.851,-1.303

"       SP coordinates=",.667,.333,-.25,"---",1.333,.667,.25

16,"  The distance of","2c-Mg","and","2c-Mg","d==",3.21

"       Coordinates of these two atoms:"

"       Cartesian=",1.605,-.928,-3.908,"---",3.209,1.851,-3.908

"       SP coordinates=",.667,.333,-.25,"---",.667,1.333,-.25

17,"  The distance of","2c-Mg","and","2c-Mg","d==",3.21

"       Coordinates of these two atoms:"

"       Cartesian=",1.605,-.928,1.303,"---",3.209,-1.851,-1.303

"       SP coordinates=",.667,.333,.75,"---",1.333,.667,.25

18,"  The distance of","2c-Mg","and","2c-Mg","d==",3.21

"       Coordinates of these two atoms:"

"       Cartesian=",1.605,-.928,1.303,"---",3.209,1.851,1.303

"       SP coordinates=",.667,.333,.75,"---",.667,1.333,.75

19,"  The distance of","2c-Mg","and","2c-Mg","d==",3.21

"       Coordinates of these two atoms:"

"       Cartesian=",3.209,-1.851,-1.303,"---",4.813,.928,-1.303

"       SP coordinates=",1.333,.667,.25,"---",1.333,1.667,.25

20,"  The distance of","2c-Mg","and","2c-Mg","d==",3.21

"       Coordinates of these two atoms:"

"       Cartesian=",3.209,1.851,-3.908,"---",3.209,3.707,-1.303

"       SP coordinates=",.667,1.333,-.25,"---",.333,1.667,.25

21,"  The distance of","2c-Mg","and","2c-Mg","d==",3.21

"       Coordinates of these two atoms:"

"       Cartesian=",3.209,1.851,-3.908,"---",4.813,.928,-1.303

"       SP coordinates=",.667,1.333,-.25,"---",1.333,1.667,.25

22,"  The distance of","2c-Mg","and","2c-Mg","d==",3.21

"       Coordinates of these two atoms:"

"       Cartesian=",3.209,1.851,1.303,"---",3.209,3.707,-1.303

"       SP coordinates=",.667,1.333,.75,"---",.333,1.667,.25

23,"  The distance of","2c-Mg","and","2c-Mg","d==",3.21

"       Coordinates of these two atoms:"

"       Cartesian=",3.209,1.851,1.303,"---",4.813,.928,-1.303

"       SP coordinates=",.667,1.333,.75,"---",1.333,1.667,.25

24,"  The distance of","2c-Mg","and","2c-Mg","d==",3.21

"       Coordinates of these two atoms:"

"       Cartesian=",3.209,3.707,-1.303,"---",4.813,.928,-1.303

"       SP coordinates=",.333,1.667,.25,"---",1.333,1.667,.25