14.2 Oxide Tetrahedron Bond Formation
275
1 is Cu
2+ and 2 is Cu
+ . Atoms 3 are the lone pair induced Cu
p dipoles. This configuration gives rise to a unit cell of the Cu(001)−
√
2 × 2
√
2
R45
◦
−2O
−2 structure that
contains one O
−2 , one Cu vacancy, and two diploes in the top layer. For the Cu(001)
surface, the first and the second shortest atomic spacings are 2.555 and 3.614 Å,
respectively. Such a surrounding accommodates the Cu 3 O 2 pairing-tetrahedron in
the way to form the complex unit cell.
The O
−2 prefers the center of a quasi-tetrahedron. Atoms 1 and 2 are Cu
+2 and
Cu
+ . Atom 3 is Cu
p and M is the vacancy of the missing Cu arisen from the isolation
of this atom. Atom 4 is a metallic Cu atom. The oppositely coupled 3 ↔ 3 dipoles
bridge over the MR vacancy (Fig. 14.5).
14.2.5 Bond Geometry Versus Atomic Position
14.2.5.1 Parameters Required in Calculation
In the multi-atom VLEED calculation code, the geometrical variables are the layer
spacing D 12 , and the atomic positions in the complex unit cell of the topmost plane
which added to the normal lattice matrix of the Cu(001) crystal. For the O–Cu(001)
system, there are no y-directional (along the missing row) displacements for all the
atoms due to the lattice periodicity. The D 12 and the x, z-directional displacements of
oxygen (DO x , DO z ) and Cu dipoles (DCu x , DCu z ) are used as input used in calculations. Atom 1 was taken as the coordination origin. The pairing dipoles dislocate by
the same (DCu x , DCu z ) amount but in opposite direction. The MR vacancy is in the
symmetric central position. There are five independent parameters in terms atomic
dislocations if considers the symmetry and periodicity.
14.2.5.2 Bond Variables
Instead of the conventional dislocation of individual atoms, the following Cu 3 O 2
bond geometry for the Cu(001) − (
√
2 × 2
√
2) R45° − 2O
−2 phase employs:
BL1 - distance between the O
−2 and the Cu
+2 that was taken as coordination origin
BL2 - distance between the O
−2 and the Cu
+ in the second layer
BL3 - distance between the O
−2 and the Cu
p that bulked up of the surface
BAij(∠iOj) - angle between atoms i-O
−2 -j(i, j = 1, 2, 3).
BL1 and BL2 are subject to the undercoordination-induced contraction:
BLi =
R O
−2 + R Cu
+
× (1 − Q i ) (i = 1, 2)
Q i (i = 1, 2)is the CN-resolved contraction coefficient.
275
1 is Cu
2+ and 2 is Cu
+ . Atoms 3 are the lone pair induced Cu
p dipoles. This configuration gives rise to a unit cell of the Cu(001)−
√
2 × 2
√
2
R45
◦
−2O
−2 structure that
contains one O
−2 , one Cu vacancy, and two diploes in the top layer. For the Cu(001)
surface, the first and the second shortest atomic spacings are 2.555 and 3.614 Å,
respectively. Such a surrounding accommodates the Cu 3 O 2 pairing-tetrahedron in
the way to form the complex unit cell.
The O
−2 prefers the center of a quasi-tetrahedron. Atoms 1 and 2 are Cu
+2 and
Cu
+ . Atom 3 is Cu
p and M is the vacancy of the missing Cu arisen from the isolation
of this atom. Atom 4 is a metallic Cu atom. The oppositely coupled 3 ↔ 3 dipoles
bridge over the MR vacancy (Fig. 14.5).
14.2.5 Bond Geometry Versus Atomic Position
14.2.5.1 Parameters Required in Calculation
In the multi-atom VLEED calculation code, the geometrical variables are the layer
spacing D 12 , and the atomic positions in the complex unit cell of the topmost plane
which added to the normal lattice matrix of the Cu(001) crystal. For the O–Cu(001)
system, there are no y-directional (along the missing row) displacements for all the
atoms due to the lattice periodicity. The D 12 and the x, z-directional displacements of
oxygen (DO x , DO z ) and Cu dipoles (DCu x , DCu z ) are used as input used in calculations. Atom 1 was taken as the coordination origin. The pairing dipoles dislocate by
the same (DCu x , DCu z ) amount but in opposite direction. The MR vacancy is in the
symmetric central position. There are five independent parameters in terms atomic
dislocations if considers the symmetry and periodicity.
14.2.5.2 Bond Variables
Instead of the conventional dislocation of individual atoms, the following Cu 3 O 2
bond geometry for the Cu(001) − (
√
2 × 2
√
2) R45° − 2O
−2 phase employs:
BL1 - distance between the O
−2 and the Cu
+2 that was taken as coordination origin
BL2 - distance between the O
−2 and the Cu
+ in the second layer
BL3 - distance between the O
−2 and the Cu
p that bulked up of the surface
BAij(∠iOj) - angle between atoms i-O
−2 -j(i, j = 1, 2, 3).
BL1 and BL2 are subject to the undercoordination-induced contraction:
BLi =
R O
−2 + R Cu
+
× (1 − Q i ) (i = 1, 2)
Q i (i = 1, 2)is the CN-resolved contraction coefficient.