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Figure 7.7 illustrates the calculated spin density distributions of the iron atoms in the first four layers of the proposed surface model. Blue and silver spin densities represent the majority and minority spin orientations, respec- tively. Feoct and Fetet sites are antiferromagnetically coupled, as is the case

for bulk magnetite. A spherical distribution indicates a half filled d-band, and hence Fe3+ _{character. Deviation from a spherical distribution indicates}

an increased occupation of the 3d6 _{orbital, and hence Fe}2+ _{character [109].}

The four surface Feoct atoms all display Fe2+ character. The two that

have an in-plane dangling bond due to an oxygen vacancy display greater Fe2+ character. This is in agreement with a previous study of Fe3O4(001),

which demonstrated a progressive reduction of surface iron to Fe2+ as the surface Fe/O ratio was increased [109]. The remaining Feoct atoms all display

close to spherical character, this can be interpreted as Fe2.5+ _{character, as is}

the case with bulk Feoct. Fetet atoms which have a bond removed due to the

Figure 7.7: Side view illustration of the B-terminated O2 vacancy model.

Overlayed onto the iron atoms is their respective spin density distributions obtained from DFT calculations. Blue and silver distributions represent the majority and minority spin channels. A spherical spin distribution indicates a half filled d-band , and hence Fe3+ _{character. Any deviation from spherical}

shape indicates increased 3d6 occupation, and hence Fe2+ character. Surface Feoct atoms and Fetetatoms, with a dangling bond due to presence of surface

144 Chapter 7. Oxygen vacancy induced surface stabilisation

existence of surface oxygen vacancies exhibit Fe2+ _{character. The remaining}

Fetet atoms display Fe3+ character, as is the case for bulk magnetite.

A polar surface can compensate for its polarity by reducing its surface charge to half that of the bulk value [6, 120], this is detailed further in section 4.1.2. One must take care when defining the surface region; When considering polarity compensation we define the surface region as the area which deviates from the bulk. For the considered model the surface region is defined as the termination plane and first sub-surface layer. The sub-surface layer is included as the Fetet atoms, which are missing a bond due to the

presence of the surface oxygen vacancies, exhibits Fe2+ _{character opposed}

to Fe3+ _{character of bulk-like Fe}

tet. Considering that we are dealing with a

(1×2) model and a bulk-like B-plane (a B-plane is immediately below the surface region) with (1×2) size has a net charge of -6 electrons, the surface region must have a charge deficit of 3 electrons to be polar compensated.

In order to examine how the existence of oxygen vacancies and predicted Feoct charge ordering influences the stability of this surface, the surface re-

gion charge has been calculated for the following ions charges: the octa- hedrally coordinated surface iron are designated Fe2+_{, while the remaining}

Feoct are designated Fe2.5+, as they are in the bulk. The tetrahedrally co-

ordinated iron, which has a dangling bond due to the existence of the oxy- gen surface vacancies, are designated Fe2+_{, while the other Fe}

tet atoms are

Fe3+_{, as they are in the bulk. Starting with the terminating layer, two sur-}

face oxygens are bonded to two sub-surface Fe2_oct.5+(6-fold) and one surface Fe_oct2+(4-fold), resulting in a charge of 2₆.5+2₆.5+2₄=4₃e− each. A further two surface oxygens are bonded to two sub-surface Fe2_oct.5+(6-fold) and one surface Fe2+_oct(3-fold), resulting in a charge of 2.5

6 + 2.5 6 + 2 3= 3 2e

− _{each. Lastly, two}

surface oxygens are bonded to one sub-surface Fe3+_tet(4-fold) and one surface Fe2+_oct(4-fold), resulting in a charge of 3₄+2₄=5₄e− each. Therefore, consider- ing there are four Fe2+_oct within the terminating layers unit cell, the charge ex- cess per unit cell is 2(4₃) + 2(3₂) + 2(5₄) - 4(2) =1₆e−. Turning to the sub-surface layer, four oxygens are bonded to one surface Fe2+_oct(3-fold), two Fe2_oct.5+(6-fold) and one Fe3+_tet(4-fold), resulting in a charge of 2₃+2₆.5+2₆.5+3₄ =9₄e−. A fur- ther four oxygens are bonded to one surface Fe2+_oct(4-fold), two Fe2_oct.5+(6-fold)

7.2. Density functional theory calculations 145

and one Fe2+_tet(3-fold), resulting in a charge of 2₄+2₆.5+2₆.5+2₃= 2e−. There- fore, considering there are four Fe2_oct.5+, two Fe3+_tet and two Fe2+_tet within the (1×2) area of the sub-surface layer, the charge deficit per (1×2) area is 4(2.5) + 2(3) + 2(2) - 4(2) - 4(9₄) = 3e−. Finally, considering the terminating and sub-surface layers exhibit charge excess and deficits of 1₆e− and 3e−, respectively, the surface region charge deficit is equal to 2.83e−. As was dis- cussed above, to achieve polar compensation this surface region is required to have a charge deficit of 3e−. Increased surface covalent character, out of plane charge transfer or a combination of both can lead to polar compen- sated and stable surface. It is noted that spin density distributions do not provide quantitative analysis of the cation charges. However, the analysis provided here demonstrates that the combination of oxygen surface vacan- cies and charge ordering can contribute towards a polar compensated and stable termination.

The largest and brightest features in figure 7.2 form rows separated by 17 ˚A along the [001] direction, the orientation of these features differ from row to row. This indicates that the surface exhibits longer range order than the (1×2) model in figure 7.5. It is possible minor relaxations along the [¯110] direction to give rise to these asymmetries. A (1×4) model, which corresponds to the (1×2) model depicted in figure 7.5 doubled in the [001] direction, has been allowed to relax. No additional distortions along the [¯110] direction were observed. In the present work, the nature of these subtle fea- tures or the size of the unit cell are not determined. However, the good agree- ment between experimental and simulated STM images of the B-terminated model containing twofold oxygen vacancies - which have been predicted by DFT calculations to be the most energetically stable surface vacancy of those considered - leads to the strong suggestion that the investigated surface is B-terminated and contains an ordered array of twofold oxygen vacancies.

Due to the fact that this termination occupies the minority of the surface, further experiments to verify the proposed model are limited. IV-LEED and angular resolved XPS would clearly be ideal experiments. In theory, this model could be tested by dosing the surface with small amounts of H2O. The

146 Chapter 7. Oxygen vacancy induced surface stabilisation

site for the water molecule. This could lead to the presence of a surface hydroxide, which should be identifiable by the combination of STM and DFT.