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Fermi Surface of Disordered Cu3Au as Determined
by Angle-resolved Photoemission
J. A. Con Foo,* S. Tkatchenko and A. P. J. Stampfl
School of Physics, La Trobe University, Victoria 3083, Australia
A. Ziegler, B. Mattern, M. Hollering, R. Denecke and L. Ley
Universitat Erlangen-Niirnberg. 91058 Erlangen, Germany
J. D. Riley and R. C. G. Leckey
School of Physics, La Trobe University, Victoria 3083, Australia
The bulk Fermi surface of the disordered phase of Cu,Au has been experimentally mapped using angle-resolved
constant initial-state photoemission spectroscopy. The shape of the Fermi cross-section so determined has been
found to be well described by a rigid band model. Comparison with previously reported de Haas-van Alphen results
of the ordered phase has shown that the neck radius is unaltered within experimental error. We find, however, that
the Fermi surface belly radius of the disordered phase is -20-30% larger than the corresponding distance as
determined by an LMTO calculation for the ordered material.
The compound Cu,Au is an interesting material which
has been extensively studied for its alloying properties,'-3 its structural
and for the bulk and
surface order-disorder transition which it display^.^
Generally for metals, the electronic states at and in the
vicinity of the Fermi level intimately determine their
physical and chemical properties." To date, little work
has been reported on the bulk Fermi surfaces of the
ordered or disordered phases of Cu,Au. de Haas-van
Alphen (dHvA) measurements have been reported on
the ordered phase,"^" and some early positron annihilation measurement^'^"^ have been reported for both
phases. The results of these reports are, however, very
incomplete: only the neck radius of the ordered
has been given. We have shown
p r e v i ~ u s l y ' ~ ,that
' ~ it is indeed possible to map the
Fermi surface of Cu using photoemission spectroscopy
with reasonable accuracy. Our technique has the advantage over the more established dHvA and positron spectroscopies for alloy materials such as Cu,Au in that it is
easy to perform on less-than-perfect crystals and the
results are readily interpreted. The presence of different
scattering centres and the need for long-range periodic
order complicate the results of dHvA measurements,'','' whereas previous positron measurements of
Cu3Au suffered from a high signal-to-noise ratio which
resulted in poor statistics.14
In this paper we report the results of our measurements on the bulk Fermi surface of the disordered
phase of Cu,Au.
Angle-resolved photoemission spectra were acquired
using an electron energy dispersing analyser of toroidal
geometry" on the TGM4 synchrotron beam line'* in
Berlin. The combined energy resolution of the monochromator and analyser (which was determined by the
width of the Fermi edge) varied from AE = f O . l to
AE = f 0.2 eV for photon energies between 10 and 100
eV. The polar angle resolution of the analyser was
determined to be f 2 " (see Refs 16 and 17 for details)
and the azimuthal resolution was f l " as determined
from the geometric dimensions of the analyser. The
Cu,Au{lll} surface was cleaned by repeated cycles of
Ar' ion sputtering (1000 eV beam energy) for 15-30
min followed by annealing to 550°C until the (1 x 1)
LEED pattern of the disordered phase was obtained.lg
The surface was deemed clean only when the characteristic surface states8*" at -0.4 eV below the Fermi edge
were clearly observed.
To determine the Fermi linear dimensions and crosssection, constant initial state (CIS) spectra at the Fermi
level were acquired between 25 < ho < 110 eV in steps
of 1 eV for angles between f90" in steps of
1" for
the (111)[1iO] plane. The background signal from the
analyser and the monochromator has been subtracted
from each of the spectra shown in this paper, the appropriate background levels being obtained by using CIS
measurements taken a few electron-volts above the
Fermi level (in the noise region) for the full range of
angles and photon energies used. After background normalization the angle spectra were further normalized so
that the intensity of the highest peak observed for each
photon energy was the same. Finally, individual spectra
taken at equivalent negative and positive polar angles
* Author to whom correspondence should be addressed.
CCC 0142-2421/96/090535-04
0 1996 by John Wiley & Sons, Ltd.
Received 14 November 1995
Accepted 17 May 1996
were summed to give averaged spectra. All spectra were
acquired with p-polarized light at normal incidence to
the surface: as a result, spectra measured at equivalent
negative and positive polar angles had nearly the same
intensity distributions.
The CIS spectra shown in Fig. 1 were obtained using a
previously reported photoemission technique' 5,16 which
restricts measurements to a high symmetry plane of the
three-dimensional bulk Brillouin zone such that only
photoemission transitions from the Fermi surface in
that plane are in general measureable. Most transitions
can be identified as being associated with primary cone
free electron final-state bands, thus allowing the crosssection of the Fermi surface in that plane to be readily
The fcc Brillouin zone slice and Fermi cross-section
probed by the measure-ments are shown in Fig. 2 for
the { 111}[ 1101 plane. Many of the major peaks in Fig. 1
4w [eV]
k" [A-']
Figure 1. Stack plot of the Cu3Au{l11}[1~0] constant initialstate spectra. Open circles indicate transitions that fall onto free
electron primary cone final states; circles enclosing crosses indicate transitions from surface-related features.
can be identified as free electron primary cone transitions from that part of the Fermi cross-section shown
in Fig. 2. Spectra were acquired over a large range of
polar angles: the x-axis in Fig. 1 has been converted to
the arallel component of the k vector, given by k" =
(2m/h)E,, where E , is the electron kinetic energy with
respect to the vacuum level. (The perpendicular component of the k vector is not conserved across the solid/
vacuum interface.) Transitions are expected to generally
obey the energy conservation law, E(k)-E,(k) = ho,
where E is the final-state energy with respect to the
Fermi level.21 Thus by acquiring constant initial-state
spectra Z(k11) such as those shown in Fig. 1, with the
initial state chosen at the Fermi energy E , as a function
of photon energy, transitions located at different k-space
points on the Fermi cross-section were observed as
peaks at the appropriate values of k " .
Open circles mark the position of peaks in Fig. 1
which have been identified as transitions to free electron
final-state primary cone bands. These points have been
mapped back into k-space in Fig. 2: a best fit to the
calculated Fermi cross-section was obtained using an
inner potential, V, , of 4.0 eV. Circles with crosses mark
the position of points which were identified as surfacerelated features : such states are not generally expected
to coincide in k-space with bulk states and so do not fall
onto the calculated Fermi contour in Fig. 2 when they
are mapped back into k-space. Surface states/resonances
for photon energies 35 6 hw 6 40 and 100 6 ho 6 110
eV were identified by their characteristic' E(kI1) dispersion. We believe that the features within the energy
range 45 6 hw 6 50 and 90 6 hw 6 95 eV are due to
emission from previously unreported surface resonance
states: their E(kI1) dispersion is very similar to the
surface predicted for C U . ' ~
The results of mapping the primary cone transitions
into k-space for the full set of data acquired are given in
Fig. 3 for the reduced Brillouin zone. These points fall
onto the Fermi surface cross-section within the intrinsic
photoemission k-space error of Ak k0.1-l
This value is the lower limit in the error which occurs
for hw 10 eV. Larger errors up to -0.2 A-' are
expected for the photon energy range measured. The
Fermi cross-section was determined using the Fourier
k 1 . 1 6 9 2 3
k" [A-']
Figure 2. The Fermi cross-sections (thick solid lines) for the
{ 11 1}[110] plane plotted in the extended Brillouin zone. Experimental positions are shown by circles.
Figure 3. The experimental Fermi surface cross-section of Cu,Au
for the { 11 1}[1 l o ] plane as determined by photoemission. Experimental points (open circles) are mapped back onto the irreducible
Brillouin zone. Thick lines indicate the calculated position of the
Fermi surface.
series formula given by Halsez4 to fit the dHvA measurements of Cu and Au. The seven Fourier coefficients
reported by Coleridge and Templeton for Cu and Au
were used to generate the Cu,Au Fermi surface crosssection, assuming that the bands were shifted in k-space
by an amount dictated by the percentage of Cu and Au
in the alloy (i.e. each new coefficient was determined
using CY3*" = 0.75Cp 0.25Cp for i = 1, 7). Deimel
and co-workers",'' used the rigid band model to interpret their dHvA data taken from ordered (simple cubic)
Cu,Au. They found that the neck radius was well
approximated by their model: this value is included in
Table 1. Our results agree with the values generated
using this model to within experimental error. The
largest discrepancy occurs for the neck radius, which is
probably due to a number of effects: it is known for
Cu23,25that the widths of the surface and bulk bands
near the L point (neck region) are strongly temperature
dependent; furthermo;e, the mean free path is only
expected to be -4-5 A for the photoelectrons that were
acquired around the L-point region (i.e. 70 < ho < 75
eV), thereby smearing out the electron k vector to
f0.2 A-'. Our previous reported Fermi surface
results on Cu also show a similar effect.16
The LMTO calculation along the high symmetry
directions for the ordered structure is given also in
Table 1: this calculation matches previously reported
LMTO results well.4 It is expected that there should be
little change in the Fermi surface dimensions between
the ordered and disordered phase^.^.^.'^ There appears,
however, to be a large difference in the belly radius
along the TKX direction compared with the other corresponding values in Table 1. To compare the results
between the two structures directly, the two LMTO
values given were obtained by folding the bands in the
simple cubic (ordered) zone out into the face centred
(disordered) zone. (The neck radii in both the ordered
Table 1. The Cu,Au Fermi surface linear dimensions [in units
of (2x141
Rigid band model
0.142 386
0.935 485, 1.043 09
0.140 538
'Value derived using free electron final states. Second L-W value
taken from Ref. 12.
and disordered unit cells have by symmetry, however, a
one-to-one correspondence and so are directly comparable.) The ordering splits the bands in this direction
due to the addition of extra Bragg plane^.^ Our results
show that the belly radius is expanded by 20-30% upon
disordering, which is quite surprising. We are unaware
of a reason why this should happen, as the sp bands of
Cu and Au are very similar and are not expected to be
sensitive to the change in s t r ~ c t u r e . ~Deimel
. ~ . ~ ~and
Higgins12 have also reported that the belly radius may
be reduced by 30-40% upon ordering, but no numerical
distances were reported in this work. Wang et aLZ7have
reported photoemission measurements of the ordered
band structure along the T-A-X direction: they found
that the sp band did not match the calculation but corresponded to a belly radius whch was 20-30% larger
than that predicted by a linear augmented Slater-type
orbital calculation. This result would seem to indicate
that the rigid band model may be valid not only for the
disordered phase but also for the ordered phase, contrary to what is expected from the LMTO calculation;
it is, however, more likely that partial disorder in the
samples used in their study may explain this discrepancy.
The Fermi surface of the disordered phase of Cu,Au
has been mapped. A rigid band model was used to successfully describe the measured Fermi surface crosssection. The Fermi surface of the disordered phase has
been found to have the same neck radius as the ordered
phase, but our results indicate that the belly radius of
the disordered phase may be as much as 30% larger
than that predicted for the ordered phase. Measurements are under way to determine the corresponding
Fermi surface cross-section of the ordered phase using
the same methodology.
We would like to thank Professor N. E. Christensen for allowing us to
use his LMTO program. This work is supported by the Australian
Research Council and by the German Ministry of Education and
Research under contract no. 05 5WEADAB3.
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