3.1 Los ruidos sintomáticos
3.1.1 Inicio de clase
∆ρ=ρnH2O:Fe3O4(001)−ρFe3O4(001)−ρnH2O, (3.2)
where ρH2O:Fe3O4(001), ρFe3O4(001) and ρnH2O are the electron densities of the system with adsorbates, the clean Fe3O4(001) surface and water molecules, respectively. In the reference systems, the positions of the atoms correspond to the system with adsorbates.
3.4
Technical parameters and accuracy
Density functional theory calculations were performed using the FP-LAPW (full potential linear augmented plane wave) method in the WIEN2k [42] im- plementation. The generalised gradient approximation (GGA) [44] of the exchange-correlation potential is used. Since Fe3O4 is a strongly correlated material we have also considered the influence of electronic correlations within the LDA/GGA+U [43] approximation.
We have used U =5 eV and J =1 eV, similar to the values used for bulk Fe3O4 [9,10]. With these values an insulating band gap of 0.3 eV is calculated for the modified B-layer in agreement with the scanning tunneling spectroscopy (STS) [118] measurements and a previous DFT calculation [26]. In order to check the dependence of results on the chosen U value we have varied the U
from 2 eV to 8 eV . As discussed in Chapter 8, we find that for U ≥2 eV the pattern of charge order almost remains the same as shown in Fig. 9.2.
The use of two approximations for the exchange correlation potential makes our results more reliable and qualitative and therefore a substantial part of the thesis discusses the agreements/discrepancies between the two approximations and analyze them. This also brings out the limitation in the applicability of the two approximations.
We have used the following RMT’s: RM T
F e = 1.90, RM TO = 1.10 and RM T
H = 0.60 Bohr. A mixed augmented plane wave (APW+lo) and linear aug-
mented plane wave (LAPW) basis sets is used. Inside the MTs the wave func- tion are expanded in spherical harmonics up to lwf
max = 10 and non-spherical
contribution to the electron density as well as potential are considered up to
lpot
max = 6. The energy cut off for the plane wave representation and potential
areEwf
max = 25 Ry and Emaxpot = 196 Ry, respectively. For the integration in the
Brillouin zone 16 kk-points were used. The accuracy of the calculations using Wien2k for the energy is 10−4 Ryd.
The systems contain typically 100-130 atoms which results in a high numer- ical demand with matrix sizes for the diagonalisation of up to 31000×31000. To reduce the computational cost and to search more efficiently for the most favor- able adsorbate geometries we have performed for some of the systems a struc-
CHAPTER 3. Computational Details 29 tural optimisation using the Viennaab-initio Simulation Package (VASP) [76] with a default cutoff energy for the plane-wave basis and a force relaxation up to 0.01 eV/ ˚A. Using these geometries several further relaxation steps were done subsequently with the Wien2k code.
The description of the Van-der Waals interaction by DFT is not signifi- cantly correct. However in a systematic study done on water clusters [77, 78] using different exchange-correlation functionals it was found that GGA (PBE) describes the hydrogen bond well for equilibrium geometries. The error of overbinding which can be as large as 20 meV/bond will not affect our con- clusions as the hydrogen bond contribution derived from our calculations is 0.37 eV per hydrogen bond. A recent DFT investigation within GGA for water adsorption on Al2O3(0001) [79] has used the PBE description for the hydrogen bonds.
4
Monomer Adsorption
Understanding how a single water molecule interacts with a mineral surface is the starting point of the investigation. This is because water molecules tend to diffuse on the surface and form clusters which in turn masks the water substrate interaction [34, 80]. Experimentally it is hardly possible to reach the single H2O molecule limit which means very low coverages and temper- atures ¿ 100 K to limit the aggregation. Scanning tunneling microscopy (STM) is reliable in studying water monomer species and some attempts are made to visualize the same [81–83] but there are some difficulties associated with it like perturbing the water molecule by the tunneling current [34, 80]. Even with real time STM data, it is difficult to determine the orientation and the binding site in a definitive manner [34, 80]. This is where DFT calcula- tions are useful and contribute towards a better understanding. DFT calcula- tions on water monomer adsorption have been done for many transition metal (Rh(111),Pd(111)) and noble metal surfaces (Au(111),Ag(111)) [34, 80]. To our knowledge there are few metal oxides e.g. NiO(100) [84], Fe2O3(0001) [85], Fe3O4(111) [86], Al2O3(0001) [87] and MgO [88] on which similar studies were carried out. There are only few experimental studies existing on the H2O inter- action with Fe3O4(001) surface. The XPS (X-ray photoemission spectroscopy) measurements indicate a dissociative adsorption of H2O molecules while the TPD (temperature programmed desorption) measurements show three desorp- tion peaks which are assigned to water adsorption on three different iron sites. Lack of a clear picture from the existing results, motivated us to take up this problem. We have studied the adsorption of H2O molecules in various geomet- rical configurations. Section 4.1 describes the stability of each configuration in terms of Eads as calculated from Eq. 3.1. To understand the energetic trends we have analysed electronic properties in Section 4.2 with probable explana- tion for the observed results and differences between GGA and GGA+U. The structural relaxations and bond lengths upon adsorption of H2O molecule is discussed in Section 4.3.
32 4.1. Adsorption models and energetic stability
4.1
Adsorption models and energetic stability
In this Section we will discuss the different configurations1 that were considered for an isolated water molecule adsorbed on the Fe3O4(001) surface. Among all studied geometries we concentrate on some important ones. In Fig. 4.1, we define the tilt angle α between the H2O molecule and the surface. We define all our molecular adsorption models based on this angle. In an upright configuration α=90◦ while in the flat/tilted configuration α=0◦. We have
optimized the tilt angle as well.
α
θ
c2
Figure 4.1: Right panel: Tilt angle α between the H2O molecule and the surface. Left panel: Angle θ is between H-Ow-H of the H
2O molecule. Positions of oxygen, FeB, FeA and H are marked by cyan, purple, orange and white circles. The oxygens of the adsorbate are marked by smaller circles.
Besides the molecular adsorption we have studied dissociated configura- tions, where the hydroxyl group binds to the surface cation (surface FeB) and the hydrogen binds to a nearby surface oxygen atom (O(S)) forming O(S)-H. The possibility that the H atom diffuses on the surface is also taken into ac- count by adsorbing the hydrogen atom on more distant O(S) namely T2 and T3, as shown in Fig. 4.2. The three O(S) sites T1, T2, T3 give rise to three distinct dissociated configurations 1D-1, 1D-2 and 1D-3 respectively. The top view of 1D-1, 1D-2 and 1D-3 are shown in Fig. 4.2.
GGA:Fig. 4.2 shows adsorption of a water molecule in 1F configuration is most favorable with an adsorption energy of -0.70 eV. It is followed in stability by the dissociated configuration 1D-1 with an Eads of -0.66 eV, 0.04 eV less favorable than 1F. The upright adsorption of water (1U) is less favorable by 0.08 eV than 1F. The diffusion of hydrogen to a distant surface oxygen site was found to be 0.44 eV less favorable. For a water molecule two types of dissociation are possible namely heterolytic and homolytic. In the heterolytic mode (1D-1) water splits as H2O⇒OH−+H+. In the homolytic mode (1D-OH) water splits as H2O⇒H ˙O+1/2H2. The H ˙O in homolytic fission signifies the
1Naming scheme: (No. of H
2O molecules)(Mode of adsorption like M/F/D)-(Model
CHAPTER 4. Monomer Adsorption 33
1F
1D-2
1D-1
1U
1D-3
T1
T2
T3
Figure 4.2: Top view of different adsorbate geometries of a single water molecule per(√2×√2)R45◦-unit cell. The diagram shows the corresponding adsorption ener- gies (in eV per molecule). GGA (GGA+U) results are given by a solid black (grey) line. Different hydrogen adsorption sites are marked as T1, T2 and T3. Positions of oxygen, FeB, FeA and H are marked by cyan, purple, orange and white circles. The oxygens of the adsorbate are marked by smaller circles.
bond cleavage is isoelectronic i.e. the hydrogen atom retains its electron and finally desorbs as 1/2H2. Our calculation shows that the homolytic mode of dissociation is endothermic with Eads of 0.56 eV. The side view of 1D-OH is shown in the right panel of Fig. 4.10.
GGA+U: The influence of correlation effects is explored with the inclu- sion of an onsite Coulomb repulsion term within the GGA+U approach. A change in the mode of adsorption from that of GGA is observed as shown in the Fig. 4.2. The dissociative adsorption(1D-1) is now most favorable with anEads of -0.73 eV, while the 1F configuration is now less favorable by 0.34 eV. In- terestingly we find that 1U configuration which was competing with 1F within GGA is now highly unfavorable with a vanishing Eads. Another prominent feature is the binding position of the H atom which now has equal probability to adsorb at a distant O(S) sites (1D-2 and 1D-3). We observe that the total energies of all the dissociated configurations are nearly degenerate. The ho- molytic dissociation is not considered within GGA+U as it was already found to be unfavorable within GGA.