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Gadolinium oxyorthosilicate single crystals (Gd2(SiO4)O (GSO)) were obtained by the laser floating zone (LFZ) technique. The fibres were pulled at faster growth rates (10 mm/h) than those produced by the conventional Czochralski method and the growth was performed in air, which did not require environmental control. The structural characterization of as-grown fibres made by X-ray diffraction (XRD) and Raman spectroscopy puts in evidence the high degree of crystallinity and its monoclinic nature. The optical characterization, accomplished by photoluminescence and photoluminescence excitation, suggests that GSO fibres are a promising candidate to be doped in order to develop new high optical efficient laser materials.
© 2017 Optical Society of America
1. Introduction
Oxyorthosilicates have attracted the attention of researchers for long time [1,2] due to their chemical stability and the possibility of incorporating high concentrations of rare earth ions [3] that yield different applications. Indeed, since their discovery by Toropov et al. [4], their singular chemical and photonic properties have promoted their application as laser host materials [5–10], gamma ray detectors or scintillators [11], environmental barrier coatings (EBCs) [12] and waveguides [13], among others. One of the most important oxyorthosilicates is gadolinium silicate (Gd2SiO5, GSO) and their corresponding doped compositions, due to the Gd3+ Charger Transfer Band (CTB) that favours the transfer processes to energy levels of the dopand element [14–16]. The GSO based compounds have been mainly employed in the single crystal form as laser materials [3, 5–9] and scintillators [10].
In the available literature, there are several papers about the growth of undoped and doped GSO single crystals. However, their production by the standard methods is somewhat problematic since such oxyorthosilicates typically require high temperature processing and environment control, resulting in a time consuming and complex process with a significant increase in fabrication costs and undesirable secondary phases as by-products. Czochralski (CZ) is the most common method used to grow GSO single crystals. Since the work published by Takagi et al. [17] that reported the fabrication of Gd2SiO5 single crystals in 1983, until nowadays, the process has not changed. In fact, even the very recent work by Bynzick et al. [10], reporting the growth of monocrystalline dysprosium and samarium doped LGSO, was still carried out into an iridium crucible under nitrogen atmosphere, using pulling rates of few millimeters per hour. Furthermore, other approaches using different methods have been employed during the last years, like sol-gel [18], hydrothermal synthesis [19] or solid state reaction [20] to develop undoped and doped GSO powders.
The LFZ technique, when compared with standard growth methods, presents many advantages, namely the growth at high pulling rates, the synthesis of high melting point materials and the most important one: it is a crucible-free process, thus avoiding any external related contamination [21]. This way, high purity crystals can be obtained in short-time runs with low amount of material and energy consumption. This method enables the development of high quality light emitting materials and transparent conductive oxides with rare earth doping [22,23] along with the growth of complex ceramic materials such as thermoelectric oxide materials [24], high-temperature ceramic superconductors [25], and eutectic oxides [26]. In fact, there was only two experiments in the 80’s decade, performed by de la Fuente et al. [5] and Black et al. [27], producing GdNdSiO5 and 7Gd2O3•9SiO2:Nd by Laser Floating Zone (LFZ) applying a high laser power (~185 W) to develop laser materials based on oxyorthosilicates.
The aim of this work is to produce high quality crystalline fibres of gadolinium oxyorthosilicates using the LFZ technique. Moreover, focusing on developing compact and miniaturized new photonic devices, LFZ allows the production of low volume bulks with appropriate geometry. Furthermore, LFZ technique is confirmed as a suitable, time saving and economic process for laser materials prototyping compared with traditional techniques [21, 28]. The microstructure and homogeneity of the gadolinium oxyorthosilicate fibres has been studied by scanning electron microscopy (SEM) coupled to energy dispersive X-ray spectroscopy (EDS) analysis. Raman spectroscopy and X-ray diffraction (XRD) were employed to analyze the structure and define the crystallinity degree of the materials. The optical properties were assessed by room temperature transmission, photoluminescence (PL) and photoluminescence excitation (PLE) spectroscopic techniques. The inductively coupled plasma mass spectrometry (ICP-MS) was employed to detect trace contaminants on processed samples. Such impurities come from commercial powders employed as raw materials.
2. Experimental
2.1 Crystal growth
Gd2SiO5 oxyorthosilicate fibres were grown by the LFZ technique, in a set-up previously described by Carvalho et al. [29]. Feed and seed rod precursors for LFZ growth were prepared by mixing in agate ball mill commercial powders of Gd2O3 (Mateck, 99.9%) and SiO2 (Aldrich, 99,6%) in a stoichiometric ratio (1:1). Polyvinyl alcohol (PVA) was added to bind the powder mixture (PVA 0.1 g/ml) that was further extruded into cylindrical rods with diameters around 1.5 mm.
The LFZ equipment comprises a 200 W CO2 laser (Spectron, GSI group) coupled to a reflective optical setup producing a circular crown-shaped laser beam in order to obtain a floating zone configuration with a uniform radial heating [21–26, 29]. Fibres with diameters around 1.5 mm and 13-32 mm in length were grown in descendent direction at 10 and 100 mm/h on air at atmospheric pressure. In fact, the samples grown at slower rate were firstly pulled at 100 mm/h in order to promote rods densification, thus favouring the final growth process [21]. Table 1 summarizes the growth conditions.
Table 1. LFZ experimental conditions.
2.2 Microstructure and crystallinity
The fibres microstructure and phases development were characterized by scanning electron microscopy (SEM, TESCAN Vega 3SEM) fitted with energy dispersive X-ray spectroscopy (EDS) on polished surfaces of longitudinal and transversal fibre sections.
The structural characterization of the fibres was accomplished by room temperature (RT) µ-Raman spectroscopy using the 441.6 nm line of a He–Cd laser (Kimmon IK Series). This was conducted using a Horiba Jobin-Yvon HR800 instrument fitted with a 100x magnification lens with 0.9 numerical aperture and a minimum spot size < 2 µm.
Additional structural characterization of the fibres was accomplished by X-ray powder diffraction (XRD) experiments with a EMPYREAN X-ray diffractometer (PANalytical) using a Cu anode, while the data were fitted with the HighScore Plus analytical software. The fibres were smashed into powder to perform the standard Bragg-Brentano X-ray diffraction analysis. Complimentary X-ray measurements were also conducted on monolithic samples by polishing the fibres on plane-parallel configuration and cutting it on cross section for longitudinal and transversal analysis, respectively. Texture analysis was performed on both sections on a diffractometer Philips MRD with Cu radiation X-ray point focus configuration, a crossed slit collimator in the incident beam and a parallel plate collimator in the diffracted beam.
2.3 Compositional analysis
Thermo X series ICP-MS (Inductively coupled plasma mass spectrometry, ICP-MS) with a plasma power of 1400 W (Thermo Fisher Scientific, Waltham, Massachusetts, United States) was used in this work to qualitatively identify trace contaminants from the commercial powders employed as precursors. A powdered sample of Gd2SiO5 (0.025g) was digested at 448K in a mixture of perchloric (HClO4, 1 mL) and hydrofluoric (HF, 0.5 mL) acids assisted by microwaves. Acids and Si was later removed by evaporation at 423K and diluted to 25 mL with HNO3 (1%). The solution was further nebulized under argon flux.
2.4 Optical properties
The samples optical properties were measured at RT. For the transmission measurements a Shimatzu UV-2100 spectrometer was used in the range of 200-850 nm with deuterium and tungsten lamps as excitation sources. Samples polished on plane-parallel configuration were employed in order to carry out the optical measurements.
Photoluminescence (PL) and PL excitation (PLE) were recorded on a Fluorolog-3 Horiba Scientific modular equipment with a double grating scanning monochromator (2 × 180 mm, 1200 g/mm) in the excitation and a triple grating iHR550 spectrometer (550 mm, 1200 g/mm) in the emission, coupled to a cooled Hamamatsu R928 photomultiplier. A 450 W Xe lamp was used as the excitation source. The PLE was assessed by setting the emission monochromator in the PL energy maxima while the excitation was scanned to shorter wavelengths. The measurements were carried out using right angle geometry, and the spectra were corrected to the spectral responses of the optical components and the Xe lamp. The PL spectra were recorded under 275 nm excitation. Additionally, PL spectra were obtained using the vacuum ultraviolet (VUV) excitation on a Fluorimeter Horiba Scientific modular equipment with two monochromators (type H20-UVL) (200 mm, 1200 g/mm), one at the excitation and one at the emission. A D200VUV Deuterium light source emitting from 115 to 370 nm was used as excitation source.
3. Results and discussion
Gadolinium oxyorthosilicate fibres have been successfully obtained by LFZ, as shown in the photographs of Fig. 1. The samples grown at the high pulling rate (GSO-11, 100 mm/h) present a yellow translucent aspect, exhibiting however many internal cracks and fractures (Fig. 1(a)). On the other hand, the GSO-12 samples grown in a second run at the pulling rate of 10 mm/h present a transparent aspect and a significant decrease on cracks density. A light yellowish aspect at naked eye (Fig. 1(b)) was observed in the GSO-12 samples, similarly to that described by Takagi et al. on Gd2SiO5 single crystal scintillators grown by CZ method [17].
Fig. 1 Photographs of (a) GSO-11 sample grown at 100 mm/h and, (b) GSO-12, grown in a second run at 10 mm/h, as indicated in Table 1.
SEM analysis of the fibres grown by LFZ reveals that the longitudinal sections of the GSO samples (Fig. 2) are homogeneous along the entire surface with uniform contrast and without visible grain boundaries. However, the fibres present some small cracks and internal defects probably due to quick crystallization and/or polishing processes. Indeed, the superior quality of GSO-12 fibre is noticeable when compared to GSO-11, for which the above described imperfections are more pronounced. The transversal sections of the GSO samples exhibit asymmetrical and random fractures at the surface as shown in the SEM images depicted in Fig. 3. All the SEM micrographs analysis suggest that the GSO fibres have a single crystal character as will be further discussed and confirmed.
EDS analysis performed on the polished fibre confirms the homogeneity of surface, revealing a uniform elemental composition corresponding to the Gd2SiO5 stoichiometry. In fact, the obtained O/Si and Gd/Si ratios are close to those expected for oxyorthosilicates. The EDS analysis suggests that Si2O7-dimers and more polymerized fragments related with the formation of undesirable phases with O/Si ratios lower than 5 (e.g. ratios of 3.5 for Si2O7-dimer in Gd2Si2O7 and 4.5 for Gd10(SiO4)6O3 [30]) are absent in the as-grown samples.
Figure 4 shows the Raman spectra of the GSO samples showing a large number of narrow lines, corresponding to the material vibrational frequencies in the range of 60 to 1100 cm−1, as expected for a low-symmetry crystalline structure. The measured spectra are similar to those reported by Shinde et al. [19] and Voron’ko et al. [30] for gadolinium oxyorthosilicates obtained by standard hydrothermal synthesis and Czochralski methods, respectively. Like in these cases, for the present GSO samples grown by LFZ, the vibrational modes of the Gd2O3 monoclinic phase (located between 416 and 442 cm−1 [31]) are absent as well as the vibrational bands of SiO2 phases [32], confirming the total processing of precursor compounds. Typically, the Raman spectrum of crystalline oxyorthosilicates can be divided into three vibrational regions, related with the silicon-oxygen motion, the rare earth-oxygen vibrations and the cations motion relative to the whole structure in the high, medium and low frequency regions, respectively. For the GSO crystal with a monoclinic structure, adopting the P21/c space group symmetry Voron’ko et al. [30] were able to identify 40 vibrational resonances from a total of the 48 Raman active modes theoretically expected for the GSO crystalline host. Table 2 lists a comparison of the RT vibrational frequencies measured in this work with the ones previously described in the literature [19, 30].
Table 2. Comparison of frequencies (cm−1) and symmetries of the GSO Raman vibrational modes measured in this work with values related by Voron’ko et al. [28].
Adopting the notation of Voron’ko et al. [30] these high, medium and low frequency ranges correspond to the ν1 + ν3, ν4 and νext + ν2 regions, respectively, where ν1 to ν4 are internal vibrations and νext stands for external oscillations related with the translation of the [MO4]-complexes [30]. The intense band located in both spectra at 418 cm−1, inside the νext + ν2 region, corresponds to an internal vibrational mode of the [SiO4]4- anion with Ag symmetry [30]. On the other hand, the bands associated to ν3 antisymmetric stretching vibration of [SiO4]4- tetrahedron complexes are present at 855 cm−1 (ν1 + ν3) and 941 cm−1 (ν3) [30, 32]. However, the antisymmetric bending mode (ν4) described by Zheng et al. [33] for orthosilicate [SiO4]4- complexes and assigned by Voron’ko et al. [30] at 487 cm−1, appears only in the GSO-12 sample as a shoulder of the 496 cm−1 peak, common to both samples (Fig. 4). On the other hand, the signal associated to GSO invert glass that could appear around 840 cm−1 [30] is absent in the LFZ as-grown samples, reinforcing the crystalline character of the GSO fibres and indicating that the phase stability is attained even at high growth rates, without formation of other phases. However, better crystalline quality is expected to be achieved for lower growth rates [21], as required by the envisaged photonic applications. Considering the higher intensity of its Raman peaks along with its better morphological quality assessed by SEM, the GSO-12 sample was expected to exhibit a higher crystalline quality. This way, the following analysis will be focused only in the sample grown at the lower pulling rate.
The crystalline nature of the produced fibres was further evidenced through XRD measurements. The diffractogram of the GSO-12 powder together with standard monoclinic structure of Gd2SiO5 referenced in the 04-009-2670 XRD card (International Centre for Diffraction Data, 2016 [34]) are shown in Fig. 5. The XRD analysis of the GSO-12 powders puts in evidence the crystallinity and the monophasic nature and confirms the development of the monoclinic P21/c Gd2(SiO4)O oxyorthosilicate. However, it should be emphasized that despite the XRD was acquired after fibre milling the (h 0 0) reflections are much more intense than those of the other crystallographic planes. This means that, regardless the extensive milling of the fibre, the powders diffraction maintains some degree of preferential orientations. In fact, the contributions from the (2 0 0), (3 0 0) and (5 0 0) planes to the overall diffractogram seem to be dominant, probably due to the single crystal nature of fibres. Although, one has to consider that other planes [(2 1 1) and ( 3 2)] produce peaks exactly at the same angle of (3 0 0) and (5 0 0), respectively.
Fig. 5 Normalized XRD diffractograms of powder (red line), fibre (green line) GSO-12 sample and the corresponding XRD card ICDD, (black line) [34].
The lattice parameters calculated for the GSO material produced by LFZ correspond to a = 9.124 Å, b = 7.053 Å, c = 6.741 Å, α = γ = 90° and β = 107.55° which are in accordance with those of the ICDD file [34]. Due to the large number of atoms inside the unit cell, Fig. 6 shows schematic representations of GSO monoclinic structure views along a, b, c and [1,1,1] axis, drawn by the CaRIne Crystallography software [35], in which Gd, O and Si atoms are noted in red (with an internal triangle mark), blue and green, respectively.
Fig. 6 Schematic representations of GSO monoclinic structure views along a (a), b (b), c (c) and [1,1,1] (d) axis drawn by the CaRIne Crystallography software [35]. Gd, O and Si atoms are noted in red (with an internal white triangle mark), blue and green, respectively.
To elucidate if the fibre is single crystal or polycrystalline, a XRD scan was performed on the GSO-12 fibre polished longitudinal surface, Fig. 5 (green line). The diffraction maxima corresponding to (2 0 0), (3 0 0) and (5 0 0) planes are the only ones clearly observed at 20.4°, 30.7° and 52.4°, respectively. Moreover, these peaks perfectly matched those observed on the X-ray of powdered fibre, and the theoretical ICDD card [34]. Thus, it can be inferred that the fibre grown by LFZ is homogeneous and textured lengthwise the longitudinal axis, being oriented along the (h 0 0) family planes.
All these observations, namely the absence of grain boundaries and the preferential orientation along the fibre axis, allow us to infer that the GSO fibre is a single crystal. This way, 3D pole figures on longitudinal and transversal cross sections of the fibres were acquired for crystallographic texture measurements. Figure 7(a) shows the pole figure obtained for measurements on the longitudinal section establishing 2θ as 30.7°, corresponding to the (3 0 0) plane. Thus, the XRD measurements indicate that only the crystallographic plane (3 0 0) is present, for a well-established tilt or rotation angle of the sample surface planes regarding the X-ray beam. This result permits to confirm the well-oriented nature of the crystal in the longitudinal direction of fibre. The transversal cross section was firstly analysed at 90°. Under this configuration, only two peaks with slightly higher signal than noise have been observed at 29.1° and 32.1° with a θ/2θ scan. The first one relates only to the (2 1) crystallographic plane. This peak was subsequently stablished as the 2θ value in order to perform the X-ray texture measurements on transversal cross section, resulting in only one high intense peak as observed in Fig. 7(b). In conclusion, these observations permit to confirm the single crystal character of the GSO fibres grown by LFZ.
Fig. 7 XRD 3D pole figures of longitudinal (a) and transversal cross (b) sections of GSO fibre grown by LFZ.
The samples optical quality was evaluated by transmission, photoluminescence and photoluminescence excitation spectroscopic techniques. Figure 8(a) shows the transmission spectrum of the GSO-12 sample from the ultraviolet to the near infrared spectral region. The spectrum is mainly characterized by a series of sharp lines in the ultraviolet region corresponding to the intra 4f7 transitions of the Gd3+ ions [36]. In particular, the lines are ascribed to transitions between the 8S7/2 ground state multiplet to the 6DJ (~244, 246, 252 nm), 6IJ (~274, 275 nm) and 6PJ (~306, 311 nm) excited states [37,38]. Additionally, a broad absorption band centred at ~219 nm was observed. This band, overlapped with the spectral region where the 8S7/2→6GJ transitions are expected to occur, is likely to be due to a charge transfer absorption band rather than to the host lattice bandgap absorption. Exciting into the 6IJ multiplet, with 275 nm ultraviolet photons, results in a reddish colour of the fibres as shown in the inset of Fig. 8. Several emission lines, spanning from the ultraviolet to the near infrared can be identified in the corresponding PL spectrum depicted in Fig. 8(b). On the shorter wavelength region, a sharp line with lower intensity observed at 312 nm, well matches the 6PJ→8S7/2 transition of the Gd3+ ions. Additionally, the as-grown samples exhibit a myriad of lines in the blue/green and red spectral region. The lines peak position and their narrow full width at half maximum suggests that the emission could be due to internal f→f transitions of other trivalent rare earth ions present in the grown host. In particular, Eu3+ and Tb3+ impurities are known to be contaminants in Gd2O3 raw material [39–41], thus we cannot discard that the blue/green and red emission could be ascribed to such impurities. In particular, the lines at 379, 416, 438, 458 and ~475 nm well match the 5D3→7FJ transitions of the Tb3+ as was observed in other oxide hosts [42]. Moreover, lines are also observed between the 5D4 and 7FJ multiplets as clearly identified by the presence of the 5D4→7F5 transition peaked at ~540 nm. To discuss the observed lines in the orange/red spectral range, and besides the 5D4→7FJ intraionic transitions of Tb3+, we need to consider that the observed lines could arise from Eu3+ ions which are known to emit in this wavelength range with a similar spectral shape in europium doped GSO powders [18]. Therefore, the dominant lines observed for wavelengths higher than 570 nm are ascribed to the 5D0,1→7FJ transitions of the Eu3+ ions. The most intense line occurs at 626 nm and is due to the forced electric dipole 5D0→7F2 transition. The identification of the preferential population mechanisms of the emitting ions was assessed by PLE as shown in Fig. 8(c). By monitoring the Eu3+ (626 nm, not shown here) and Tb3+ (379 nm) emission maxima, the PL spectra reveals that the ions emission is preferentially populated through the excited levels of Gd3+ ions. In particular, the excitation lines observed in the ultraviolet region well matched those related with the 8S7/2→6PJ, 6IJ, 6DJ in agreement with the assigned intraionic Gd3+ absorption lines. Such data, clearly indicate that upon excitation of the GSO samples into the 6IJ excited state (275 nm) of the gadolinium ions, energy transfer from the Gd3+ and the contaminant ions (Eu3+ and Tb3+ identified in the studied spectral range) is favoured, causing a decrease of the luminescence intensity from the 6PJ→8S7/2 (312 nm) of the Gd3+. In order to confirm the presence of these contaminants, a standard ICP-MS analysis was performed. The results put in evidence not only the presence of Eu and Tb, but also traces of other rare earth elements such as Yb, Nd and Ho. These results are in agreement with that expected from revised bibliography about purity of Gd2O3 raw materials as we mentioned above [39–41]. Anyway, this fact carried us to consider this material as an excellent laser host matrix that favours and allows emission of dopants.
Fig. 8 (a) Transmission spectrum, (b) PL spectrum acquired with 275 nm photon excitation, (c) PLE spectrum monitored at 379 nm, (d) PL spectrum obtained with VUV excitation (160 nm photons) for the GSO-12 sample. The spectra were vertically shifted for clarity. Inset: image of the red emitting fibre obtained with 275 nm excitation.
Trivalent gadolinium ions are known to emit orange/red luminescence when excited with vacuum ultraviolet (VUV). Together with a quantum cutting effect, this result was first reported for the LiYF4:Gd3+ host where the transition between the 6GJ and 6PJ multiplets was measured ~600 nm [43,44]. Figure 8(d) shows the PL spectrum of the GSO-12 sample obtained with VUV excitation (160 nm photons). Due to the low PL intensity the spectrum was taken under low resolution with wide slits. Even so, two main features were clearly distinguished: a line peaked at 312 nm and a broad band with a barycenter at ~590 nm. The peak position of the observed lines agrees well with the above mentioned 6PJ→8S7/2, and 6GJ→6PJ transitions, respectively. The latter exhibits a high full width at half maximum, hampering an unambiguously characterization of the transitions between the different Stark levels but well matches the spectral region of the 6GJ→6PJ previously reported in other hosts [44]. As seen from a comparison between the spectra shown in Figs. 8(b) and 8(d) we cannot discard that some contribution of Eu3+ emission could be also overlapped with the orange/red light arising from the 6GJ multiplet of the gadolinium ions. Nevertheless, as the peak position of the emission is shifted to shorter wavelengths when compared with the 5D0→7F2 transition of the Eu3+ luminescence, it is fair to assume that the main emission comes from the trivalent gadolinium ions. Therefore, and as observed by Wegh et al. [44] in the LiYF4 host, by exciting the GSO sample into the VUV a quantum cutting phenomena occurs through the visible emission due to the 6GJ→6PJ transitions followed by the ultraviolet radiation involving the 6PJ and 8S7/2 multiplets.
4. Conclusions
Gd2(SiO4)O monocrystalline fibres were successfully grown in air at pulling rate of 10 mm/h by means of the Laser Floating Zone method. Despite the presence of trace contaminants, the oxyorthosilicates obtained present a high structural and morphological stability, as observed by XRD and SEM analysis. Moreover, the chemical stability was also inferred from the fact that only the monoclinic gadolinium oxyorthosilicate phase was obtained, according to both XRD and Raman spectroscopy data.
The structural studies carried out confirm the possibility to obtain a single crystal material with high crystallinity degree using pulling rates two/three times upper than those required by the conventional Czochralski method. Besides, it is important to emphasize that no special environments are needed. Moreover, in the LFZ technique, the presence of undesirable elements is only due to the purity of the precursors employed, since it is a crucible-less method. Thus, the applications of the GSO single crystals grown by LFZ as laser materials should be developed from highly pure precursors in order to avoid emissions resultant from contaminants.
In the studied spectral range, the room temperature spectroscopic analysis of the GSO grown samples allows to conclude that the trivalent gadolinium ions are optically active in the host as observed from the intraionic absorption in the ultraviolet region. Additionally, by pumping the samples into the 6IJ levels, besides the Gd3+ emission from Tb3+ and Eu3+ were observed due to the presence of these ions as contaminants in the used raw material. The ions emission is preferentially populated through the excited states of the Gd3+ indicating energy transfer among trivalent gadolinium and the contaminant ions, as demonstrated by the photoluminescence excitation measurements. Furthermore, pumping the samples with VUV excitation into the 6GJ multiplet, quantum cutting effect was observed from the visible 6GJ→6PJ transitions followed by the ultraviolet radiation involving the 6PJ and 8S7/2 multiplets. Far from being a disadvantage, the presence of trace contaminations and their optical effect allow us to consider the GSO as a suitable material to be doped, even with low amounts of dopants, in order to develop new high optical efficient laser materials.
Summarizing, it was demonstrated that the LFZ is an adequate and suitable technique for the prototyping of laser materials. Furthermore, the high chemical and structural stability of the gadolinium oxyorthosilicate together with its capacity to promote energy transfer processes, as we could see from the presence of trace contaminants, make this material a potential laser host matrix.
Funding
FEDER (COMPETE 2020 Programme); and National Funds through FCT - Portuguese Foundation for Science and Technology (UID/CTM/50025/2013, SFRH/BPD/108581/2015, SFRH/BPD/111460/2015).
Acknowledgments
F. Rey-García and N. M. Ferreira acknowledge the Portuguese Science and Technology Foundation (FCT) for the SFRH/BPD/108581/2015 and SFRH/BPD/111460/2015 grants, respectively.
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