332
17 Blouin Zones, Effective Mass, Muffin-tin Potential…
are sufficient to represent the full azimuth of the surface. The features of the measured
VLEED profiles in Fig. 17.1 can be summarized as follows [3]:
(1) Two sharp, solitary troughs or violent peaks (denoted by dotted lines) appear
on each curve. These two troughs move away from each other as the azimuth
moves away from the 11 direction. The angular-resolved sharp features divide
the VLEED energies (6.0–16.0 eV) into three regions with variation in boundary energies. Calibration of these critical positions gave the reduction in work
function of ~1.1 eV [2, 3].
(2) The fine-structure feature (denoted by the dashed lines) splits into its separate
components as the azimuth moves away from the symmetric point 45.0°. The
first component vanishes outside the region of 33.5°–58.5°. The second one
becomes narrower while moving away from the symmetric point. Further, the
intensity of the second peak tends to be weaker when the azimuth is greater than
45.0°.
(3) The peak positions and intensities of the curves show a reduction in symmetry relative to the symmetric center. The reduction of the intensities at higher
azimuth angles may come from the development of the reaction, as the longterm aging leads to a general attenuation of the spectral intensity. The deviation
of the symmetry means that the reaction breaks the original C 4v group symmetry
of the surface lattice.
17.2 Sharp Features: Brilliouin Zones and Energy Bands
17.2.1 Brillouin Zones and Effective Electron Masses
The Cu 3 O 2 formation results in the primary unit cell of Cu(001)–(
√
2 × 2
√
2)R45°–
2O
−2 . The presence of defects and impurities, such as the missing-row vacancy and
the oxygen adsorbates, has no effect on constructing either the real or the reciprocal
lattice [5, 6]. Displacements of lattice atoms, such as the DCu x for the atoms closing
to the missing-row, or at the 11 direction, however, deform both the real and the
reciprocal lattice.
As the emergence of new diffraction beam is independent of the inner potential
and the barrier shapes but depends on the incident and diffraction conditions, and
the two-dimensional geometry of the surface lattice [7]. Emergence happens when
the lateral components of the diffracted wave, with vector k
// , and the incident wave
k // satisfy the Bragg diffraction condition,
k
// − k // = g,
where g is the vector of a reciprocal lattice. This Bragg diffraction happens at
the band-gap or at the boundary of a Brillouin zone. Therefore, the sharp features
closing to the emergence of new beam on the VLEED spectra arise from the band-gap
reflections at the boundaries of the first two Brillouin zones.
17 Blouin Zones, Effective Mass, Muffin-tin Potential…
are sufficient to represent the full azimuth of the surface. The features of the measured
VLEED profiles in Fig. 17.1 can be summarized as follows [3]:
(1) Two sharp, solitary troughs or violent peaks (denoted by dotted lines) appear
on each curve. These two troughs move away from each other as the azimuth
moves away from the 11 direction. The angular-resolved sharp features divide
the VLEED energies (6.0–16.0 eV) into three regions with variation in boundary energies. Calibration of these critical positions gave the reduction in work
function of ~1.1 eV [2, 3].
(2) The fine-structure feature (denoted by the dashed lines) splits into its separate
components as the azimuth moves away from the symmetric point 45.0°. The
first component vanishes outside the region of 33.5°–58.5°. The second one
becomes narrower while moving away from the symmetric point. Further, the
intensity of the second peak tends to be weaker when the azimuth is greater than
45.0°.
(3) The peak positions and intensities of the curves show a reduction in symmetry relative to the symmetric center. The reduction of the intensities at higher
azimuth angles may come from the development of the reaction, as the longterm aging leads to a general attenuation of the spectral intensity. The deviation
of the symmetry means that the reaction breaks the original C 4v group symmetry
of the surface lattice.
17.2 Sharp Features: Brilliouin Zones and Energy Bands
17.2.1 Brillouin Zones and Effective Electron Masses
The Cu 3 O 2 formation results in the primary unit cell of Cu(001)–(
√
2 × 2
√
2)R45°–
2O
−2 . The presence of defects and impurities, such as the missing-row vacancy and
the oxygen adsorbates, has no effect on constructing either the real or the reciprocal
lattice [5, 6]. Displacements of lattice atoms, such as the DCu x for the atoms closing
to the missing-row, or at the 11 direction, however, deform both the real and the
reciprocal lattice.
As the emergence of new diffraction beam is independent of the inner potential
and the barrier shapes but depends on the incident and diffraction conditions, and
the two-dimensional geometry of the surface lattice [7]. Emergence happens when
the lateral components of the diffracted wave, with vector k
// , and the incident wave
k // satisfy the Bragg diffraction condition,
k
// − k // = g,
where g is the vector of a reciprocal lattice. This Bragg diffraction happens at
the band-gap or at the boundary of a Brillouin zone. Therefore, the sharp features
closing to the emergence of new beam on the VLEED spectra arise from the band-gap
reflections at the boundaries of the first two Brillouin zones.