e article analyses the relationship established between the executive
and legislative powers in the Cape Verdean government system
where researchers seek to understand it, taking into account their theoretical
and constitutional setting practice. It should be noted the prominence
of the debate and studies undertaken to understand how the scienti c
academy seeks to eradicate this problem. Two issues are relevant in this
debate: the  rst reporting to the theoretical and constitutional con guration
of Cape Verdean government system and the other to its policy and
legislative practice.
Keywords: Cape Verde. Semi-presidential System. Systems of Government.
Legislative and Executive Powers.O artigo procura analisar a relação que se estabelece entre o poder
executivo e legislativo no sistema de governo cabo-verdiano, onde Investigadores
buscam compreendê-lo, tendo em conta a sua con guração
prática, teórica e constitucional. Há que realçar a proeminência do debate
e dos estudos realizados no sentido de compreender como é que a academia
cientí ca procura debelar esta problemática. Duas questões são
pertinentes neste debate: a primeira refere-se à con guração teórico-constitucional
do sistema de governo cabo-verdiano e a outra à prática política
e legislativa.
Palavras-chave: Cabo Verde. Sistema Semi-presidencialista. Sistemas de Governo.
Poder legislativo e Poder Executivo

A. Schreyer

D. Lott

J.-F. Moulin

M. Haese-Seiller

M. Störmer

R. Kampmann

W. Kreuzpaintner

Madeira, João Paulo

Portal do Conhecimento

The semi-presidential system of Cape Verde: the relationship between the executive and the legislative powers = O sistema semi-presidencialista caboverdiano: a relação entre os poderes executivo e legislativo

Springer - Publisher Connector

Eur. Phys. J. Special Topics 167, 73–79 (2009)
c© EDP Sciences, Springer-Verlag 2009
DOI: 10.1140/epjst/e2009-00939-2
THE EUROPEAN
PHYSICAL JOURNAL
SPECIAL TOPICS
Regular Article
Time-of-flight grazing incidence small angle neutron
scattering on Gd nanowires
W. Kreuzpaintnera, J.-F. Moulin, D. Lott, R. Kampmann, M. Haese-Seiller, M. Sto¨rmer,
and A. Schreyer
GKSS Forschungszentrum GmbH, Max-Planck-Straße 1, 21502 Geesthacht, Germany
Abstract. A Gd nanowire grating with a periodicity of approximately 225 nm pre-
pared on a faceted α-Al2O3 substrate was investigated by Time-Of-Flight Grazing
Incidence Small Angle Neutron Scattering. These measurements allowed to obtain
information on the critical wavelength, the reﬂected and transmitted intensities
and also allowed a reconstruction of large portions of the grating truncation rods
in reciprocal space. Results were obtained for various orientations around the
sample normal and compared with a theoretical model, showing good agreement.
1 Introduction
With the evolution of nanostructuring processes, Grazing Incidence Small Angle X-ray and
Neutron Scattering (GISAXS and GISANS) have established as methods for the analysis of
laterally structured surfaces with feature sizes and periodicities of only a few to several hundreds
of nanometers [1,2]. In general such experiments are performed with quasi monochromatic
beams (typically ∆λ/λ < 10%) [1,3]. In the case of x-rays, due to high absorption, one is
limited to the scattered intensities above the sample horizon, while for neutrons the full pattern,
including the transmitted region can be recorded. In GISANS, however, transmitted intensities
are nevertheless often not evaluated due to highly complicated transmission functions and
absorption eﬀects [3]. In this paper we will show the advantages of faster data acquisition by use
of a continuous neutron wavelength spectrum over a single wavelength setup in investigating
a periodically laterally structured sample by GISANS and also show that for neutrons the
transmitted scattered intensities can be considered for sample analysis.
2 Experimental results and discusssion
2.1 Sample preparation
A nanostructered surface grating was prepared by Ultra-High-Vacuum (UHV) electron-beam
evaporation of Gd onto a pre-structured faceted Al2O3 substrate under a shallow angle of inci-
dence. In our particular case the miscut of the Al2O3 (101¯0) (m-plane) substrate was 0.1
◦ as
determined by x-ray rocking scans. The substrate was annealed in air in a three step process:
starting with the furnace and the sample at room temperature the temperature was ramped to
750 ◦C at 5 ◦C/min, followed by a dwell time of 30min after which the temperature was increased
to 1500 ◦C at a rate of 10 ◦C/min. The temperature of 1500 ◦C was then held for 24 h before it
was reduced to 750 ◦C at 10 ◦C/min. After another 30min the temperature was ramped to room
temperature at 5 ◦C/min. This process was found to give a surface pattern with the least defects.
a e-mail: Wolfgang.Kreuzpaintner@gkss.de
74 The European Physical Journal Special Topics
Fig. 1. SEM image of the nanowires, grown by geometrical self shading of a faceted substrate. During
the deposition process, a dust particle shaded oﬀ a larger area of the substrate such that no deposition
occurred in its shade. This sample defect allows to directly see the diﬀerence between the substrate
without nanowires and the area where nanowires were grown. The inset graph shows the schematic
deposition geometry with the periodic selfshading of the substrate by its surface features.
Details on the thermodynamics of the sapphire structuring process and on the sample prepara-
tion method are described in [4,5] and references therein. Deposition of 50 nm Gd occurred at a
base pressure of 2×10−10mbar and a working pressure of 3×10−8mbar at a deposition rate of
1 A˚/s under an angle of 5◦. The self-shading eﬀect of neighboring facets allows deposition of Gd
only on the upper edges of each facet, resulting in the growth of nanowires with a periodicity
of approximately 225 nm and a cross-section of approximately 50 nm×50 nm. A Scanning Elec-
tron Microscopy (SEM) image of the sample surface and the deposition geometry are shown in
Fig. 1. In order to prevent oxidization of Gd a 25 nm thick Al layer was additionally sputter
deposited at a rate of 2.5 A˚/s as capping layer. This Al capping layer does not signiﬁcantly
inﬂuence the observed intensity distribution and is therefore neglected in the sample analysis.
2.2 Sample analysis
GISANS was performed at the combined horizontal REFlectometer and Small Angle Neutron
Scattering setup REFSANS at the FRM II neutron source in Garching with a point collimated
primary neutron beam of 4mm in diameter and a primary integral beam intensity of 400
counts per second. The sample to detector distance was 11710mm with the approximately
500mm × 500mm large detector positioned at such a height that the primary neutron beam
was just below the lower edge of the detector. The detector resolution is deﬁned by the detector
channel size of 2.7mm × 2.7mm. The incidence white neutron beam was pulsed by a chopper
at a repetition rate of 10Hz and the bandwidth was limited to 4.5 A˚ to 18 A˚. Typical exposure
times for the presented results were in the range of approximately 3 h with detector count rates
in the range of 180 counts per second. The Time-Of-Flight (TOF) detection scheme allows the
reconstruction of the diﬀerent 2D intensity maps as a function of the wavelength λ by software.
Fig. 2 shows the scattering geometry and the deﬁnition of the relevant goniometer head angles.
Measurements were performed for various orientations in φ around the sample normal at a ﬁxed
angle of incidence αi = 0.67
◦.
2.3 Measurement results
2.3.1 Aligned sample
The critical wavelength at which the chosen angle of incidence corresponds to the critical
angle [6] is 9.2 A˚ as can be seen in Fig. 3 for a nominal sample orientation of φ = 0◦. The
SXNS 10 75
Fig. 2. The applied GISANS scattering geometry: a neutron beam with the shown wavelength distrib-
ution in the range from 4.5 A˚ to 18 A˚ is shined under a ﬁxed angle of incidence αi. The detector image
in real space is an integral image over all the wavelengths used and must be investigated in reciprocal
space for single wavelength or multiple wavelength evaluation. The sample orientation is deﬁned by φ
around the sample normal with the angles of deﬂection αf parallel and 2θ (not sketched) perpendicular
to the plane of incidence.
corresponding detector images at wavelengths of 6.9 A˚, 9.2 A˚ and 10.7 A˚ are given in Fig. 4
showing intensities at the intersection of the Grating Truncation Rods (GTRs) with the corre-
sponding Ewald sphere. By applying a continuous wavelength spectrum the size of the Ewald
sphere is varied in reciprocal space. Hence it is not only possible to reconstruct intersection
points but also larger portions of the GTRs by obtaining the integral image over all wave-
lengths. For this, however, one has to correct each wavelength slice by the background, weight
its intensity by the primary beam intensity, correct ballistic eﬀects and add the intensities in
reciprocal space. The such reconstructed image of the GTRs is shown in Fig. 5. It is well known,
that from the location of the GTRs of a well aligned sample one can directly obtain the periodic-
ity b = 2π
∆Qy
of the lateral structure, which in this case results in a periodicity of approximately
220 (±20) nm and hence is in agreement with the periodicity of 225 nm as obtained from the
SEM image.
2.3.2 Rotated sample
GISANS on lateral gratings is very sensitive to a rotation of the sample around its normal.
The strong inﬂuence of the rotation on the scattered detector image is shown in Fig. 6 for a
single wavelength slice, showing the scattered intensity distribution at the critical wavelength
for transmitted and reﬂected intensities. The orientations are φ = +0.5◦ and φ = −0.75◦
in mathematical direction. The corresponding integral reciprocal space images of the rotated
samples are shown in Fig. 7 and Fig. 8 and will be discussed together with the theoretical
expectations (2.3.2).
76 The European Physical Journal Special Topics
Fig. 3. Qz versus the wavelength λ as extracted by integration over −0.01 A˚−1 ≤ Qy ≤ +0.01 A˚−1.
With increasing wavelength the transition from refracted intensities to reﬂected intensities occurs with
the transition at the critical wavelength of λ ≈ 9.2 A˚.
Fig. 4. Detector images for a single wavelength slice which are extractable by the Time-Of-Flight infor-
mation collected for each neutron. Shown are the detector images for wavelengths of λ = 6.9 A˚ (below
the critical wavelength), 9.2 A˚ (at the critical wavelength) and 10.7 A˚ (above the critical wavelength).
2.4 Discussion
Yan and Gibaud [7] recently published theoretical and experimental results on the intersection
of GTRs in reciprocal space with the Ewald sphere using GISAXS. Following their theoretical
approach and by also taking the neglected solutions for transmission into account, intensities
in reciprocal space are to be expected at
Qy =
2π n cos(φ)
b
− 2π sin
2(αi) cos(φ) sin(∓φ)
λ
×
(
1±
√
1− λ
2 n2
b2 sin2(αi) cos2(φ)
(
1− 2b sin(∓φ)
nλ
))
(1)
Qz=
2π sin(αi) cos(αi) cos(φ)
λ
(
1±
√
1− λ
2 n2
b2 sin2(αi)cos2(φ)
(
1− 2b sin(∓φ)
nλ
))
· (2)
where λ denotes the neutron (or x-ray) wavelength, αi the angle of incidence, φ the angle of the
sample orientation around its normal with φ = 0 being the case in which the nanowires on the
sample are aligned parallel to the plane of incidence of the primary beam, b is the period of
the nanowire grating and n is the order of the scattered intensities. In both formulas, the positive
SXNS 10 77
Fig. 5. The reconstructed integral reciprocal space image for a nominal sample orientation of φ = 0◦
with the intensities obtained for all applied wavelengths plotted together with theoretically expected
locations of the intensities for reﬂected (green) and transmitted (white) neutrons. A large portion of
the grating truncation rods can be reconstructed allowing for a fast assessment of the lateral structure.
Fig. 6. The detector images at the critical wavelength of λ = 9.2 A˚ obtained for orientations around
the sample normal of φ = +0.50◦ (left) and φ = −0.75◦ (right) showing the drastic inﬂuence of only a
small sample rotation onto the location of the intersection of the GTR with the Ewald sphere.
sign before the root accounts for reﬂected intensities, whilst the negative sign accounts for the
transmitted intensities with the opposite relationship for the sign in sin(∓φ). As neutrons also
penetrate the sample after scattering on the nanowires both solutions should be considered. As
will be seen, however, these formulas only describe parts of the scattered intensity distribution.
Especially the transmitted intensities in the vicinity of the sample horizon lie outside the value
range of these formulas.
2.4.1 Aligned sample
In order to compare the positions of the experimentally collected portions of the GTRs to
theory, calculations were performed using above formulas (1) and (2). The applied wavelength
spectrum above and below the critical wavelength, as obtained from the plot in Fig. 3 was taken
into account and a real space grating periodicity of 225 nm was assumed for the calculations. The
such calculated intensity positions up to 3rd order GTRs for reﬂected and transmitted neutrons
are plotted into the corresponding Fig. 5 for direct comparison with experimental data. The
length and the positions of the GTRs can be well described for reﬂected neutrons. However,
the calculated positions of transmitted intensities are not obtainable with the experimentally
applied measurement parameters as they would lie below the lower edge of the detector for this
sample orientation. It is apparent that the above formulas do not describe the transmission
areas in reciprocal space in the vicinity of the sample horizon where intensities that extend the
GTRs of reﬂected neutrons into the regime below the sample horizon are visible. For explanation
of this intensity distribution refraction corrections and more sophisticated theoretical methods
must be used. Close to the sample horizon, Yoneda peaks [8] are expected (and visible) and
78 The European Physical Journal Special Topics
Fig. 7. The reconstructed integral reciprocal space image for a nominal sample orientation of φ =
+0.50◦ plotted together with theoretically expected locations of the intensities for only reﬂected (green)
and also transmitted (white) neutrons.
Fig. 8. The reconstructed integral reciprocal space image for a nominal sample rotation state of
φ = −0.75◦ plotted together with theoretically expected locations of the intensities for reﬂected (green)
and transmitted (white) neutrons.
the transmission function is also expected to be complicated for the transmitted intensities,
therefore a Distorted Wave Born Approximation (DWBA) approach as used in [9,10] would be
necessary to describe the observations but is beyond the scope of this paper.
2.4.2 Rotated sample
Due to the term 2bsin(∓φ)
nλ
in the root of equations (1) and (2) the GISANS pattern is very
sensitive to a rotation of the grating around the plane of incidence. As a consequence, the
accessible portions of the GTRs also change very asymmetrically around the scattering plane
for a given wavelength distribution. The theoretically expected GTRs that were calculated
analogous to the case of the non-rotated sample are plotted together with the experimental
results in Fig. 7 and Fig. 8. In these two investigated cases, the theoretical ﬁts are less precise
for the intensity distributions above the sample horizon, but in this scattering geometry the
ﬁrst order of transmitted intensities is accessible and their location in reciprocal space is in
good agreement with the theoretical predictions.
3 Conclusion
We have shown that TOF is a very powerful technique for extending the use of Grazing Incidence
Small Angle Neutron Scattering as it allows for the use of a basically white neutron beam. This
SXNS 10 79
makes it possible to collect in a single measurement a more complete reciprocal space image
than can be obtained by a single wavelength measurement. By our measurement method we are
further able to directly obtain the critical wavelength and can also analyze single wavelength
GISANS results. Our ﬁrst results were evaluated and found to be in good agreement with
theoretical expectations. It should be noted that a full quantitative analysis would allow to
obtain not only the position of the GTRs but information on all sample surface characteristics,
including lateral structure sizes, shapes and periodicities and variations thereof as a statistical
average from the entire illuminated sample surface convoluted with the instrumental resolution.
Additional GISANS investigations with a pulsed and nearly white neutron beam, including the
magnetic properties of the investigated Gd nanowire sample will be presented elsewhere.
References
1. M. Pannetier, F. Ott, C. Fermon, Y. Samson, Physica B 335, 54 (2004)
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B 248, 343 (1998)
3. P. Mu¨ller-Buschbaum, J.S. Gutmann, R. Cubitt, W. Petry, Physica B 350, 207 (2004)
4. M. Huth, K.A. Ritley, J. Oster, H. Dosch, H. Adrian, Adv. Funct. Mater. 12, 333 (2002)
5. A. Westphalen, H. Zabel, K. Theis-Bro¨hl, Thin Solid Films 449, 207 (2004)
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2003), pp. 3.2–8
7. M. Yan, A. Gibaud, J. Appl. Cryst. 40, 1050 (2007)
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Time-of-flight grazing incidence small angle neutron scattering on Gd nanowires

A Gd nanowire grating with a periodicity of approximately 225 nm prepared on a faceted $\alpha\hbox{-}{\rm Al}_2{\rm O}_3$ substrate was investigated by Time-Of-Flight Grazing Incidence Small Angle Neutron Scattering. These measurements allowed to obtain information on the critical wavelength, the reflected and transmitted intensities and also allowed a reconstruction of large portions of the grating truncation rods in reciprocal space. Results were obtained for various orientations around the sample normal and compared with a theoretical model, showing good agreement

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The semi-presidential system of Cape Verde: the relationship between the executive and the legislative powers = O sistema semi-presidencialista caboverdiano: a relação entre os poderes executivo e legislativo

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