Title: Effect of H overlayer on the dispersion of Pt111 surface phonons
1Effect of H overlayer on the dispersion of
Pt(111) surface phonons
- Sampyo Hong, Talat S. Rahman (Department of
Physics, Kansas State University, Manhattan, KS
66506) - Rolf Heid, Klaus Peter Bohnen (Forschungszentrum
Karlsruhe, IFF, Karlsruhe, Germany)
2Outline
- Introduction
- Details of theoretical calculations
- Results
- Relaxations clean, H covered Pt surface
- Phonon dispersions bulk, clean, H covered Pt
surface - Conclusions
3Introduction
- First principles calculations of the dispersion
of surface phonons of Pt(111) and of H/Pt(111)
are still not available although there have been
theoretical studies based on force constant
parameterization method - there are several unresolved questions
- Anomaly in bulk Pt
- characteristics
- Observed anomalous surface modes of clean Pt
surface - Surface anomaly
- Longitudinal resonance
- The effect of H overlayer on the dispersion of Pt
surface - Completely negligible? mass ratio 1 195
- Additional question is how to quantify the impact
of H overlayer on the characteristics of Pt(111)
surface - Little consensus on the assignment of the modes
for H on Pt(111)
4Harten et al, PRL 55,2308(1985)
Bortolani et al, PRB 40, 3524(1989)
Pt
H
112
110
5Details of Theoretical Calculations
- DFT/LDA/Mixed basis formulation (MB)
- Wavefunction representation
- Plane waves localized functions
- Pt d-type (cutoff 2.14 a.u.)
- H s-type (cutoff 0.7 a.u.)
- Energy-cutoff for plane waves
- 16.5 Ryd
- Pseudopotential
- Norm-conserving
- Brillouin zone(BZ) summation
- Bulk 770 special points in IBZ
- Surface 42 special points in IBZ
- Periodic slab geometry
- Surface (111) 9 Pt layers 9 Pt
atoms vacuum 16 Å - H adsorption 9 Pt/ 2 H layers 9 Ni/ 2 H
atoms vacuum 14 Å - All structures are fully relaxed
- Density functional perturbation theory (DFPT) and
the harmonic approximation - Interpolation
- (6x6) q-mesh, 7 q-points
6Pseudopotential DFT Approach to calculation of
electronic structure properties
- Total energy functional Kohn-Sham equation
fictitious non-interacting electrons
exchange-correlation energy
7Pseudopotential method
- smooth (pseudo) wave functions
- norm-conserving
- identical eigenvalues
- transferable non-local pseudopotential
Supercell method
supercell slab vacuum
8Construct given atomic numbers and
positions of ions
Pick a trial density n(r)
Calculate
Solve Kohn-Sham equations by diagonalization
of
Calculate new n(r)
Is solution self-consistent?
no
yes
Compute Total Energy
Generate new density n(r)
9Linear-response Approach to calculation of
lattice dynamical properties
2n 1 theorem
Density functional perturbation theory
10Relaxations of Pt(111) and H/Pt(111)
11 Weak Kohn anomaly along ?- ? direction (TA)
couplings beyond second nearest neighbors
Bulk phonon dispersion
O Theoretical data X Experimental data
(neutron scattering)
12Pt(111)
- Softening of projected bulk phonon modes along
most of ?- ? and ?- M - Rayleigh mode(S1) to become a resonance for long
wavelengths. -
- Experiments show the existence of two sets of
modes which are assigned as Rayleigh wave and
longitudinal resonance.
Black dots theoretical surface modes (S. Hong
Heid et al, to be published), open circles HAS
data ( Bortolani et al, PRB 40, 3524(1989))
13(No Transcript)
14H/Pt(111)
circles HAS data ( Bortolani et al, PRB 40,
3524(1989).)
15(No Transcript)
16Comparison of assignment of calculated
vibrational mode of H with other studies
17Conclusions
- The weak Kohn anomaly in the transverse acoustic
mode of bulk phonon dispersion has strong effect
on the characteristics of the surface modes. For
example, the softening of the bulk phonon
spectrum causes the Rayleigh wave to immerse into
the bulk spectrum and appear only as a surface
resonance.
- The experimentally measured second surface mode
(classified as longitudinal resonance) above the
Rayleigh wave in the Pt(111) was not found in our
calculation. - The phonon dispersion curves of H/Pt(111) show
significant stiffening of the surface branches.