Atomic Surfaces

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Atomic Surface Generator This program generates the atomic cordinates for slices through body-centered cubic (bcc) or face-centered cubic (fcc) solids. a is the lattice spacing; (hkl) define the Miller indices.

Parameters a := 4.0782 ⋅Å

Au

a := 4.0853 ⋅Å

Ag

h := 1

k := 1

Unit cell spacing (lattice spacing)

l := 1

Surface identifier (111), (210), etc.

max := 10

Cut position. (increase to obtain a larger surface)

depth := 2

Depth of slice (number of unit cells)

Bulk Samples bcc :=

i← 0 for z ∈ 0 ..2 ⋅max for y ∈ 0 ..2 ⋅max for x ∈ 0 ..2 ⋅max M

i ,0

M

i ,2

← 1 ⋅x +

0 if even( z) = 1

 0.5 otherwise  M ← 1 ⋅y + 0 if even( z) = 1 i ,1  0.5 otherwise  1

←

2

     

⋅z

i← i+1 M fcc :=

i← 0 for z ∈ 0 ..

2 ⋅max 2

for y ∈ 0 ,0.5 ..2 ⋅max for x ∈ 0 ,0.5 ..2 ⋅max M

i ,0

M

i ,1

M

i ,2

← x ← y ← z+

0.5 if int( x) = 0 ⊕ int( y) = 0 0 otherwise

i← i+1 M

Atomic_Surfaces.xmcd

-1-

© Roy Jensen, 2002

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Selected Surface bulk := fcc surface :=

Selects the bulk solid. temp ← ( 0 0 0 ) for j ∈ 0 ..rows( bulk) − 1 if max − h ⋅bulk

j ,0

− k ⋅bulk

j ,1

if max − depth − h ⋅bulk

j ,0

≥ l ⋅bulk

j ,2

− k ⋅bulk

j ,1

≤ l ⋅bulk

j ,2

temp ← stack( temp ,submatrix( bulk ,j ,j ,0 ,2 ) ) 1 1 submatrix( temp ,1 ,rows( temp) − 1 ,0 ,2 )

Unit Cell Positions for Defined Surface

file := concat( "(" ,num2str( h ) ,num2str( k) ,num2str( l ) ,") surface.dat" )

Atomic_Surfaces.xmcd

-2-

© Roy Jensen, 2002