Silicon (111)

The fragmentation of Silicon (111) is carried out using a unit 
cell defined by the lattice vectors ():

a (xyz) = -5.4  0.   0.
b (xyz) =  5.4  5.4  0.
c (xyz) =  5.4  0.  -5.4

There are eight atoms in the unit cell with coordinates 
(fractional coordinates, followed by 
Cartesian coordinates in ):

1 Si
   1.000        1.000        1.000     
   5.420       -5.420       -5.420     
2 Si
   1.000       0.5000       0.5000     
  0.0000       -2.710       -2.710     
3 Si
   1.000       0.5000        1.000     
   2.710       -2.710       -5.420     
4 Si
   1.000        1.000       0.5000     
   2.710       -5.420       -2.710     
5 Si
  0.7500       0.7500       0.7500     
   4.065       -4.065       -4.065     
6 Si
  0.7500       0.2500       0.2500     
  -1.355       -1.355       -1.355     
7 Si
  0.7500       0.2500       0.7500     
   1.355       -1.355       -4.065     
8 Si
  0.7500       0.7500       0.2500     
   1.355       -4.065       -1.355  

These atoms are depicted in Figure 2(b).

LEVEL 2

The bulk crystal structure fragments at Level 2 into 24 
fragments. The F(k1,k2,k3) fragments of Eq.(2.10) contain the 
atoms shown below, where "Atom" designates the number of the 
atom in the unit cell defined above; the lattice unit cell is 
defined by adding (k1,k2,k3) to the indicated values below. For 
the cleaved crystal, (k1,k2,k3) are integers with 
-_ < k1 < -1,
-_ < k2 < _
-_ < k3 < _

Bulk fragments

  Fragment Number     fn    Atom    k1   k2   k3
________________________________________________

         1            1
                             1     -1    0    0
                             5     -1    0    0
                             8     -1    0    1
                             7     -1    1    0
                             6      0    1    1
 
         2            1
                             2     -1    0    0
                             6     -1    0    0
                             7     -1    0    0
                             8     -1    0    0
                             5      0    0    0
 
         3            1
                             1     -1    0    0
                             3     -2    0    0
                             2     -1    0    1
                             4     -1    0    1
                             8     -1    0    1
 
         4            1
                             3     -1    0    0
                             5     -1    0    0
                             7     -1    0    0
                             6     -1    0    1
                             8      0    0    1
 
         5            1
                             2     -1    0    0
                             3     -1    0    0
                             7     -1    0    0
                             4     -2   -1    0
                             1     -1   -1    0
 
         6            1
                             4     -1    0    0
                             5     -1    0    0
                             8     -1    0    0
                             6     -1    1    0
                             7      0    1    0
 
         7            1
                             1     -1    0    0
                             3     -1    0    0
                             4     -1    0    0
                             5     -1    0    0
                             2     -2    0    0
 
         8            1
                             2     -1    0    0
                             6     -1    0    0
                             1     -2   -1   -1
                             4     -1   -1    0
                             3     -1    0   -1
 
         9           -1
                             1     -1    0    0
                             8     -1    0    1
 
        10           -1
                             3     -1    0    0
                             7     -1    0    0
 
        11           -1
                             2     -1    0    0
                             7     -1    0    0
 
        12           -1
                             1     -1    0    0
                             5     -1    0    0
 
        13           -1
                             4     -1    0    0
                             8     -1    0    0
 
        14           -1
                             2     -1    0    0
                             6     -1    0    0
 
        15           -1
                             6      0    0    0
                             1     -1   -1   -1
 
        16           -1
                             7     -1    0    0
                             1     -1   -1    0
 
        17           -1
                             7      0    0    0
                             4     -1   -1    0
 
        18           -1
                             8      0    0    0
                             3     -1    0   -1
 
        19           -1
                             5      0    0    0
                             2     -1    0    0
 
        20           -1
                             6     -1    0    0
                             3     -1    0   -1
 
        21           -1
                             6     -1    0    0
                             4     -1   -1    0
 
        22           -1
                             2     -1    0    0
                             8     -1    0    0
 
        23           -1
                             3     -1    0    0
                             5     -1    0    0
 
        24           -1
                             4     -1    0    0
                             5     -1    0    0
 
Surface fragments

There are 20 surface fragments {G(k2,k3)} of Eq. (2.10) which 
contain the atoms shown below, where "Atom" designates the 
number of the atom in the unit cell defined above; the lattice 
unit cell is defined by adding (k2,k3) to the indicated values 
below. For the cleaved crystal, (k1,k2,k3) are integers with 
-_ < k2 < _
-_ < k3 < _

  Fragment Number     gn    Atom    k1   k2   k3
________________________________________________


         1            1
                             1     -1    0    0
                             5     -1    0    0
                             8     -1    0    1
                             7     -1    1    0
 
         2            1
                             2     -1    0    0
                             6     -1    0    0
                             7     -1    0    0
                             8     -1    0    0
 
         3            1
                             1     -1    0    0
                             3     -2    0    0
                             2     -1    0    1
                             4     -1    0    1
                             8     -1    0    1
 
         4            1
                             3     -1    0    0
                             5     -1    0    0
                             7     -1    0    0
                             6     -1    0    1
 
         5            1
                             2     -1    0    0
                             3     -1    0    0
                             7     -1    0    0
                             4     -2   -1    0
                             1     -1   -1    0
 
         6            1
                             4     -1    0    0
                             5     -1    0    0
                             8     -1    0    0
                             6     -1    1    0
 
         7            1
                             1     -1    0    0
                             3     -1    0    0
                             4     -1    0    0
                             5     -1    0    0
                             2     -2    0    0
 
         8            1
                             2     -1    0    0
                             6     -1    0    0
                             1     -2   -1   -1
                             4     -1   -1    0
                             3     -1    0   -1
 
         9           -1
                             1     -1    0    0
                             8     -1    0    1
 
        10           -1
                             3     -1    0    0
                             7     -1    0    0
 
        11           -1
                             2     -1    0    0
                             7     -1    0    0
 
        12           -1
                             1     -1    0    0
                             5     -1    0    0
 
        13           -1
                             4     -1    0    0
                             8     -1    0    0
 
        14           -1
                             2     -1    0    0
                             6     -1    0    0
 
        15           -1
                             7     -1    0    0
                             1     -1   -1    0
 
        16           -1
                             6     -1    0    0
                             3     -1    0   -1
 
        17           -1
                             6     -1    0    0
                             4     -1   -1    0
 
        18           -1
                             2     -1    0    0
                             8     -1    0    0
 
        19           -1
                             3     -1    0    0
                             5     -1    0    0
 
        20           -1
                             4     -1    0    0
                             5     -1    0    0

LEVEL 1

Similarly, at Level 1, we have:

Bulk fragments

  Fragment Number     fn      Atom    k1   k2   k3
________________________________________________


         1            1
                             1     -1    0    0
                             5     -1    0    0
 
         2            1
                             2     -1    0    0
                             6     -1    0    0
 
         3            1
                             3     -1    0    0
                             5     -1    0    0
 
         4            1
                             4     -1    0    0
                             5     -1    0    0
 
         5            1
                             2     -1    0    0
                             7     -1    0    0
 
         6            1
                             2     -1    0    0
                             8     -1    0    0
 
         7            1
                             6      0    0    0
                             1     -1   -1   -1
 
         8            1
                             7      0    0    0
                             4     -1   -1    0
 
         9            1
                             8      0    0    0
                             3     -1    0   -1
 
        10            1
                             5      0    0    0
                             2     -1    0    0
 
        11            1
                             7     -1    0    0
                             1     -1   -1    0
 
        12            1
                             6     -1    0    0
                             4     -1   -1    0
 
        13            1
                             8     -1    0    0
                             1     -1    0   -1
 
        14            1
                             6     -1    0    0
                             3     -1    0   -1
 
        15            1
                             3     -1    0    0
                             7     -1    0    0
 
        16            1
                             4     -1    0    0
                             8     -1    0    0
 
        17           -3
                             5      0    0    0
 
        18           -3
                             6      0    0    0
 
        19           -3
                             2     -1    0    0
 
        20           -3
                             3     -1    0    0
 
        21           -3
                             7      0    0    0
 
        22           -3
                             4     -1    0    0
 
        23           -3
                             8      0    0    0
 
        24           -3
                             1     -1    0    0

Surface fragments

There are 16 surface fragments at Level 1:

  Fragment Number     gn    Atom    k1   k2   k3
________________________________________________

         1           -2
                             1     -1   -1   -1
 
         2           -2
                             4     -1   -1    0
 
         3           -2
                             3     -1    0   -1
 
         4           -2
                             2     -1    0    0
 
         5            1
                             1     -1    0    0
                             5     -1    0    0
 
         6            1
                             2     -1    0    0
                             6     -1    0    0
 
         7            1
                             3     -1    0    0
                             5     -1    0    0
 
         8            1
                             4     -1    0    0
                             5     -1    0    0
 
         9            1
                             2     -1    0    0
                             7     -1    0    0
 
        10            1
                             2     -1    0    0
                             8     -1    0    0
 
        11            1
                             7     -1    0    0
                             1     -1   -1    0
 
        12            1
                             6     -1    0    0
                             4     -1   -1    0
 
        13            1
                             8     -1    0    0
                             1     -1    0   -1
 
        14            1
                             6     -1    0    0
                             3     -1    0   -1
 
        15            1
                             3     -1    0    0
                             7     -1    0    0
 
        16            1
                             4     -1    0    0
                             8     -1    0    0

Silicon (100)

The fragmentation of Silicon (111) is carried out using a unit 
cell defined by the lattice vectors ():

a (xyz) = -5.4  0.   0.
b (xyz) =  0.   5.4  0.
c (xyz) =  0.   0.   5.4

There are eight atoms in the unit cell with coordinates 
(fractional coordinates, followed by Cartesian coordinates):

1 Si
   1.000        1.000        1.000     
  -5.420        5.420        5.420     
2 Si
   1.000       0.5000       0.5000     
  -5.420        2.710        2.710     
3 Si
  0.5000       0.5000        1.000     
  -2.710        2.710        5.420     
4 Si
  0.5000        1.000       0.5000     
  -2.710        5.420        2.710     
5 Si
  0.2500       0.2500       0.2500     
  -1.355        1.355        1.355     
6 Si
  0.2500       0.7500       0.7500     
  -1.355        4.065        4.065     
7 Si
  0.7500       0.7500       0.2500     
  -4.065        4.065        1.355     
8 Si
  0.7500       0.2500       0.7500     
  -4.065        1.355        4.065 

These atoms are depicted in Figure 2(a).

LEVEL 2


Bulk fragments

  Fragment Number     fn    Atom    k1   k2   k3
________________________________________________

         1            1
                             1     -1    0    0
                             7     -1    0    1
                             8     -1    1    0
                             6      0    0    0
                             5      0    1    1
 
         2            1
                             2     -1    0    0
                             7     -1    0    0
                             8     -1    0    0
                             5      0    0    0
                             6      0    0    0
 
         3            1
                             1     -1    0    0
                             4     -1    0    0
                             2     -1    1    0
                             3     -1    1    0
                             8     -1    1    0
 
         4            1
                             3      0    0    0
                             6      0    0    0
                             8      0    0    0
                             5      0    0    1
                             7      0    0    1
 
         5            1
                             4      0    0    0
                             6      0    0    0
                             7      0    0    0
                             5      0    1    0
                             8      0    1    0
 
         6            1
                             5      0    0    0
                             1     -1   -1   -1
                             2     -1    0    0
                             4      0   -1    0
                             3      0    0   -1
 
         7            1
                             3      0    0    0
                             4      0    0    0
                             6      0    0    0
                             1     -1    0    0
                             2     -1    0    0
 
         8            1
                             2     -1    0    0
                             4     -1    0    0
                             7     -1    0    0
                             1     -1    0   -1
                             3     -1    0   -1
 
         9           -1
                             1     -1    0    0
                             8     -1    1    0
 
        10           -1
                             3      0    0    0
                             8      0    0    0
 
        11           -1
                             2     -1    0    0
                             8     -1    0    0
 
        12           -1
                             4      0    0    0
                             8      0    1    0
 
        13           -1
                             3      0    0    0
                             6      0    0    0
 
        14           -1
                             5      0    0    0
                             2     -1    0    0
 
        15           -1
                             2     -1    0    0
                             7     -1    0    0
 
        16           -1
                             5      0    0    0
                             1     -1   -1   -1
 
        17           -1
                             6      0    0    0
                             1     -1    0    0
 
        18           -1
                             5      0    0    0
                             4      0   -1    0
 
        19           -1
                             7     -1    0    0
                             1     -1    0   -1
 
        20           -1
                             5      0    0    0
                             3      0    0   -1
 
        21           -1
                             3      0    0    0
                             7      0    0    1
 
        22           -1
                             2     -1    0    0
                             6      0    0    0
 
        23           -1
                             4      0    0    0
                             6      0    0    0
 
        24           -1
                             4      0    0    0
                             7      0    0    0

There are 8 surface fragments:

Surface fragments

  Fragment Number     gn    Atom    k1   k2   k3
________________________________________________

         1            1
                             1     -1    0    0
                             7     -1    0    1
                             8     -1    1    0
 
         2            1
                             2     -1    0    0
                             7     -1    0    0
                             8     -1    0    0
 
         3            1
                             1     -1    0    0
                             4     -1    0    0
                             2     -1    1    0
                             3     -1    1    0
                             8     -1    1    0
 
         4            1
                             2     -1    0    0
                             4     -1    0    0
                             7     -1    0    0
                             1     -1    0   -1
                             3     -1    0   -1
 
         5           -1
                             1     -1    0    0
                             8     -1    1    0
 
         6           -1
                             2     -1    0    0
                             8     -1    0    0
 
         7           -1
                             2     -1    0    0
                             7     -1    0    0
 
         8           -1
                             7     -1    0    0
                             1     -1    0   -1


LEVEL 1


Bulk fragments

  Fragment Number     fn    Atom    k1    k2   k3
________________________________________________

         1            1
                             1     -1    0    0
                             7     -1    0    1
 
         2            1
                             2     -1    0    0
                             7     -1    0    0
 
         3            1
                             3      0    0    0
                             7      0    0    1
 
         4            1
                             4      0    0    0
                             7      0    0    0
 
         5            1
                             5      0    0    0
                             1     -1   -1   -1
 
         6            1
                             3      0    0    0
                             6      0    0    0
 
         7            1
                             3      0    0    0
                             8      0    0    0
 
         8            1
                             6      0    0    0
                             1     -1    0    0
 
         9            1
                             6      0    0    0
                             2     -1    0    0
 
        10            1
                             8     -1    0    0
                             1     -1   -1    0
 
        11            1
                             8      0    0    0
                             4      0   -1    0
 
        12            1
                             3      0    0    0
                             5      0    0    1
 
        13            1
                             2     -1    0    0
                             8     -1    0    0
 
        14            1
                             4      0    0    0
                             6      0    0    0
 
        15            1
                             5      0    0    0
                             2     -1    0    0
 
        16            1
                             5      0    0    0
                             4      0   -1    0
 
        17           -3
                             7      0    0    0
 
        18           -3
                             3      0    0    0
 
        19           -3
                             8      0    0    0
 
        20           -3
                             6      0    0    0
 
        21           -3
                             5      0    0    0
 
        22           -3
                             4      0    0    0
 
        23           -3
                             1     -1    0    0
 
        24           -3
                             2     -1    0    0


There are 6 surface fragments:

Surface fragments

  Fragment Number     gn    Atom    k1    k2   k3
________________________________________________

         1           -1
                             1     -1   -1   -1
 
         2           -1
                             2     -1    0    0
 
         3            1
                             1     -1    0    0
                             7     -1    0    1
 
         4            1
                             2     -1    0    0
                             7     -1    0    0
 
         5            1
                             8     -1    0    0
                             1     -1   -1    0
 
         6            1
                             2     -1    0    0
                             8     -1    0    0

