Hybrid fibers containing metallic micro- and nanowires are an emerging class of optical devices thanks to their electro-optic functionality and applicability in plasmonics. However, pure metals suffer from poor mechanical and chemical properties, which is why alloys displaying synergistic properties of their metallic constituents are becoming popular. Here, we use pressure assisted melt filling to produce micron sized gold-nickel alloy wires with aspect ratios of 105 and diameters of 1.3 μm in silica optical fibers. We show that the alloy remains stable within the highly confined wire state despite exhibiting a miscibility gap in the bulk state at room temperature. Measurements show that the loss of the alloy in the confined state is comparable to that predicted by the bulk alloy permittivity. The presented fabrication and characterization procedure represent a first step towards integration of high aspect ratio micron sized gold-nickel alloy wires in optical fibers and may be extended to a wide range of other alloys.
© 2016 Optical Society of America
The last decade has witnessed a rapid emergence of hybrid optical fibers with device oriented functionalities  for reducing costs and complexity involved in interfacing planar waveguides [1–3]. One straightforward approach to design hybrid fibers using different materials such as metals , semiconductors  and soft glasses  is to use the pressure assisted melt filling (PAMF) technique. Of particular interest are metallic micro- and nanowires integrated into microstructured optical fibers to generate new class of metal-dielectric photonic devices such as integrated near field optical nanoprobes  and structures for excitation of spiraling surface plasmons [8, 9].
However, pure metals often suffer from poor mechanical or chemical properties [10–13] which prove to be detrimental for material processing and long-term stability. Moreover, popular noble metals (e.g., gold) offer a limited spectral operation range due to interband absorptions [14, 15]. Alloys and intermetallic compounds provide an alternative to pure metals by offering improved physical or chemical properties [16, 17] while retaining a free-electron character similar to single-compound metals. An additional advantage of alloys is the possibility to tailor their dielectric response through their composition, since an addition of selected metals in the host metal alters its electronic band structure and thus the optical response . For instance, substitutional alloying of gold with aluminum, copper, magnesium and zinc improves its plasmonic response in the visible spectral domain .
Unfortunately, the use of alloy micro- and nanowires for designing hybrid fiber optics has been limited till date due to two problems: first, a limited availability of cost-effective fabrication techniques for achieving small diameters and high aspect ratio wires and second, the absence of direct permittivity measurement techniques for micron sized wires. The latter is noteworthy since an alloy in its bulk form can show different dielectric properties than in the form of micro- and nanowires, since thermal treatments common to alloy wire fabrication processes can modify alloy composition  while lateral confinement can impose strong internal stresses in the alloy due to difference in thermal expansion coefficients of glass and alloy, leading to the formation of structural imperfections in the wire .
Here, we analyze the properties of gold-nickel micron sized wires with diameters of approx. 1.3 µm fabricated using the PAMF and encapsulated in a directional mode coupling fiber, which we refer as modified graded index silica fiber (MGIF, geometry shown schematically in Fig. 1(a). The isomorphous gold-nickel alloy is particularly attractive for PAMF, due to its well-known resistance to oxidation and corrosion, good capillary flow characteristics, and single metal-like behavior during solidification . Moreover, gold-nickel is shown to exhibit composition dependent magnetostriction . We therefore choose gold-nickel near the melting point minimum composition (obtained as 30 μm bulk alloy wires from Goodfellow) as an example alloy which can be straightforwardly integrated into the small holes of silica fibers using PAMF.
The advantages of PAMF over various previously reported alloy-Pyrex glass drawing methods [24–26] are manifold: first, only a single filling step is required – in contrast to the multiple drawing or stacking procedures. Second, only trace quantities of the alloy are necessary, reducing the amount of material required for producing a single device. Third, the chemical reactivity between the glass and alloy is suppressed since the filling temperature, i.e., the melting temperature of the gold-nickel alloy (~950° C) is considerably below the softening temperature of silica (~1200°C). Therefore, we propose PAMF as a key method to fabricate a wide variety of alloy micron sized wires with extremely small diameters as long as their melting temperature is below the softening temperature of the glass.
In addition, we evaluate the effect of PAMF on the optical properties of the gold-nickel alloy micro-wire. The optical loss of the bulk alloy and confined state can be different and contain contributions from intrinsic interband absorptions  and extrinsic losses arising from grain boundaries and irregular microstructures that largely depend on the fabrication process (for example, gold-nickel films show very high optical losses compared to bulk samples ). Therefore, it is imperative to ascertain if any additional optical losses are introduced into the alloy wire by PAMF. We first compare the composition of the alloy in its bulk state and the confined wire state to evaluate if PAMF alters the composition of the alloy, e.g., due to selective interaction with the furnace atmosphere or crucible material. Following this, we measure the optical loss of the alloy confined in the MGIF by using the cut-back technique that yields a quantitative value of the optical attenuation. To compare the loss to bulk sample, we numerically calculate the loss of the filled MGIF using the alloy permittivity obtained via ellipsometry measurements on a macroscopic bulk alloy sample of the same composition. Since these simulations rely on the bulk permittivity of gold-nickel, comparing the simulated loss with the experimentally measured loss allows us to make a quantitative comparison between the optical loss of the alloy in its bulk form and confined wire state. The proposed material and optical loss comparative study thus serves as a representative of the quality of alloy micron and nano-wires inside a silica matrix obtained via PAMF.
2. Experimental section
2.1 Sample fabrication
The ellipsometric measurements demanded a bulk macroscopic gold-nickel alloy sample which was produced by casting as a 20g ingot in a vacuum levitation induction furnace using 99.99% pure nickel and 99.99% pure gold granulates with repeated re-melting to ensure ideal mixing. To obtain a sufficiently large and smooth surface, it was cold rolled repeatedly to a final thickness of 0.6 mm. As the alloy is prone to spinodal decomposition at room temperature , it was subsequently homogenized at 850°C for 4 hours and quenched in water. After this thermal treatment the sample was immediately mounted in a custom sample mount for grinding and polishing. The mechanical grinding was performed with SiC paper up to 2400 grit, followed by subsequent polishing with diamond (grain size 1 µm) and SiO2 suspension (grain size 0.05 µm). After this metallographic preparation, the sample was stored in liquid nitrogen to suppress renewed decomposition and was removed from nitrogen storage only immediately before the ellipsometry measurements. The dielectric response of the alloy in the visible (VIS) was measured using a variable-angle spectroscopic ellipsometer (SE850 SENTECH) at two angles of incidence (55° and 65°) at room temperature. Following this, EDX measurements averaging over an area of approximately 15 µm2 were conducted on both a Leica S440i and a Zeiss Auriga 60 scanning electron microscope (SEM) to measure the composition of the bulk alloy.
The MGIF used in this work (SEM shown in Fig. 1(a)) is a custom-drawn fiber and consists of a 200 μm silica cladding with a germanium oxide doped graded core (core radius: rc ~0.95 μm and peak doping level: 11 mol %). An empty channel with a radius of about rh ~0.65 μm runs parallel to the core with a center-to-center distance (pitch, Λ) of 3.9 μm. The channel was filled with the gold-nickel alloy using PAMF (schematic of an alloy- MGIF shown in Fig. 1(b) and side view in Fig. 1(c)).
The first step of the PAMF process involved fusion splicing a large diameter auxiliary capillary (inner diameter ~140 μm) with the empty MGIF, required to be filled. The gold-nickel alloy probe wire (diameter~30 μm and length~5 mm) obtained from Goodfellow Inc. was inserted manually into the larger capillary and the entire system was transferred to a vertical furnace where the temperature was raised to 1100°C to melt the alloy wire. Argon gas pressure of about 50 bars was applied to the big capillary which presses the molten alloy into the hollow channel of the MGIF. The treated sample was slightly more brittleness than the original sample, which had no impact on the future experiments. This splicing based PAMF technique can principally be extended to alloy probes in the form of granulates or micro-rods which can be inserted into the auxiliary capillary (shown in Fig. 1(d)). The viscosity of the gold-nickel alloy was estimated to be 0.57 mPa.s at a filling temperature of 1100°C using equations given in Appendix A1  and the filling pressure required to fill 10 cm of the fiber with alloy was estimated using the Lucas-Washburn equation  which determined the capillary flow dynamics. Figure 1(e) is a figure-of-merit calculation showing the minimum pressure required to fill a hole with a certain radius (shown as inverse radius along x axis) which can be filled with the alloy within 30 minutes up to a length of 10 cm.
In addition to the alloy-MGIF samples, two 200 µm silica capillaries with a central hole diameter of 1.3 and 1.6 µm were filled with the alloy using the same PAMF process parameters as above. The 1.3 µm capillary was prepared for SEM and EDX investigations by mounting it in a transparent resin with a slight inclination towards the resin surface and preparing it by the same metallographic procedure as outlined above. The composition of the MGIF sample using EDX was determined by averaging 15 point measurements, spaced 1 µm along the capillary axis. Each point and area measurement encompassed at least 250,000 photon counts, ensuring a precision of ± 0.5 at%. The composition was compared with EDX measurements performed on the 30 μm purchased gold-nickel wires to assess if any significant changes occurred during re-melting and solidification of the wire upon PAMF. In addition, the resistivity of the 1.6 μm filled capillaries was determined by placing the ends of the alloy filled capillary in liquid gallium and measuring the resistance using a multimeter.
2.2 Optical characterization of alloy-MGIF
The optical characterization of the alloy-MGIF samples was performed using a broadband transmission setup, schematically shown in Fig. 2(a). As light source we used a NKT superK supercontinuum laser source (450 nm-2.4 μm). The broadband light was coupled into the core of 8.1 cm long alloy-MGIF sample using a 20x microscope objective. For this purpose, an initial 6 mm unfilled part of the fiber was used for in-coupling to avoid scattering losses from the alloy at the input end face. The polarization of the in-coupled laser light was controlled using a combination of a thin film linear polarizer and a half-waveplate. The transmitted light from samples was coupled out using another 20x objective and characterized using an optical spectrum analyzer (OSA, YOKOGAWA (AQ-6315A)). An iris diaphragm in front of the OSA was used to block light propagating in the cladding of the samples.
Using this setup, the modal optical attenuation of the alloy-MGIF samples was experimentally measured via the cut-back method for wavelengths between 550 nm and 750 nm. In this technique, the input coupling conditions of the fiber were kept constant while the transmission as a function of sample length was measured by cutting back the fiber from the output end in a series of seven cut-back steps. The multi-step cut-back ensures that the losses arising from the transmission setup (e.g., Fresnel reflections) are excluded since these losses remain constant during each measurement and only the fiber loss is measured. The optical loss was calculated for two different light polarization states; in the ‘x’ state, light electric field was parallel to the symmetry axis of the MGIF while in ‘y’ state it was perpendicular to the symmetry axis (symmetry axis shown in Fig. 1(a)). As example, the transmission of the filled MGIF for different sample lengths measured during a cut-back measurement are shown in Fig. 2(b) (x-polarization state, wavelength 650 nm).
The optical attenuation of the fundamental core mode of the fiber was calculated for wavelengths between 550 and 750 nm using a commercial finite element solver (COMSOL). For these simulations, alloy permittivity obtained from ellipsometry together with permittivity of pure and GeO2 doped silica obtained from literature were used . Details of fiber geometry such as pitch and hole radius were obtained from the SEM image of an unfilled fiber (Fig. 1(a)). To account for the influence of errors in determining the precise fiber geometry on the loss calculations, a combination of all the uncertainties in the fiber geometry were included during the loss calculations. This included calculating the loss for the following parameters, fiber pitch (3.8 – 4 μm), hole diameter (1.25-1.35 μm) and core-clad refractive index difference (14.3 - 14.6 ∙10−3). Since gold-nickel has a much higher thermal expansion coefficient (14∙10−6 K−1) than silica (0.5∙10−6 K−1), the alloy may contract during re-solidification after the filling process. This can induce air gaps of the order of ~18 nm between the alloy and the glass surfaces, which alters the modal losses. The influence of the gap is presumably strongest when it faces the dielectric core since then it has a largest possible overlap with the modal field of the core than when compared to a gap located further away from the core. Therefore, the modal attenuation for an alloy filled fiber containing an air gap with a maximum extension of 18 nm facing the core was also calculated for the above mentioned three parameter ranges.
3. Results and discussions
The dielectric response of the Au-Ni alloy measured via ellipsometry is shown in Fig. 3 and is compared with the pure single compound metals gold and nickel (dielectric properties obtained from ). The resulting data of the measurement was fitted with a Lorentz-Drude function, to account for both the free-electron and the interband contributions [15, 27] (details of the mathematical model and fitting parameters can be found in the Appendix A2).
EDX measurements on the 30 μm wire sample (purchased wire) and on the 1.3 μm filled capillary yielded a Ni content of 16.03 wt% and 16.61 wt%, respectively. Moreover, SEM measurements performed on the alloy capillaries showed that the alloy was single phase gold with dissolved nickel. We thus infer that the PAMF process results in a homogenous filling of the alloy even down to diameters of 1.3 μm, with no significant composition changes or phase separation during re-melting and filling of the alloy wires into the SiO2 capillaries. Even though the nickel content is in the miscibility gap at room temperature, no spinodal decomposition of the alloy filled capillaries was observed during the SEM investigations. Measurements on the separately cast bulk sample yielded a nickel content of 16.10 wt%, which slightly deviates from the weighted constituents, but also within the error range of uncalibrated EDX measurements. As a result, we may directly compare the bulk optical properties of the gold-nickel alloy with those of the wires contained in the MGIF samples. In addition, the resistivity of 3.5 cm long filled 1.6 μm diameter capillaries was found to be 21.72 μOhm.cm which is slightly higher than the bulk resistivity of the alloy of about 15.5 μOhm.cm (provided from Goodfellow) and which may originate from the resistance measurement method (i.e. unremoved gallium-alloy transition resistance).
The MGIF geometry is ideally suited for measuring the optical losses of an alloy wire running parallel to the fiber core, since the optical mode propagating in the core overlaps with the alloy in the channel (saturated Poynting vector field distribution shown in the insets of Fig. 4. The empty MGIF fiber exhibits low loss and single mode operation over the visible region (fiber V-parameter at 550 nm ~2.37). In the presence of an alloy wire to the vicinity of the core, the fundamental core mode becomes a lossy mode which is attenuated as it propagates through the fiber as a result of absorption and scattering by the alloy wire, and thus contains information on the alloy losses. The modal attenuation was simulated for two cases (illustrated by the right-handed images of Fig. 4): (i) for a MGIF containing perfectly filled alloy in the hole (green shaded region between dashed green curves of Fig. 4), and (ii) the MGIF including an additional air gap between alloy wire surface and glass wall facing towards the fiber core (blue shaded region between dashed blue curves of Fig. 4). Both the blue and green regions contain all possible loss values that can arise due to the uncertainties in fiber geometry (hole diameter, pitch and core-clad refractive index difference) as described in Sec. 2.4. In the above mentioned case (ii), where an air gap is present (blue shaded region in Fig. 4), the overall loss is higher compared to case (i) where the hole is entirely filled (green shaded region in Fig. 4), originating from an increased fraction of electromagnetic field inside the few nanometers sized gap, i.e. the light is confined in a sub-wavelength environment. The gap enhances the interaction of the core mode with metal and leads to increase in optical losses. This nanoscale concentration effect can be compared with subwavelength modal confinement in air gaps or air slots which are deliberately introduced in metal-dielectric-metal (MDM) waveguides since nanoscale air slots are able concentrate a large amount of energy density .
The simulated loss was compared with the experimentally measured modal attenuation (red curves of Fig. 4) of the alloy-MGIF for both the x and y polarization states. The loss in x-polarization is generally higher than in the y-polarization due to greater modal field overlap with the alloy wire [34, 35] which can also be seen in the insets of Fig. 4 where the saturated Poynting vector fields are shown. It is important to note that the experimentally measured attenuation falls within the range of simulated loss for case where no air gap is present, thus implying that the alloy is located into the channel without any air gaps between wire and silica wall. Since the experimentally measured loss is comparable to the simulated loss, we can conclude that no significant changes to the imaginary part of the dielectric function of the alloy occurred during PAMF.
In this work, we report on the optical properties of high aspect ratio alloy micron sized wires in silica optical fibers, fabricated using pressure assisted melt filling. Specifically, we fabricate continuous gold-nickel wires of 1.3 μm diameter up to a length of 8.1 cm. In addition, we compared the alloy composition in its bulk and confined wire state in order to characterize the wire quality. We found that the encapsulated gold-nickel alloy can be filled homogenously (i.e., single phase) in silica fibers and that the alloy wires showed no decomposition up to a week even though the alloy exhibits a miscibility gap at room temperature. We further integrated the alloy wires into a directional-mode coupling microstructured optical fiber and measured the optical loss of the propagating mode using a cut-back technique. This measured optical loss showed good agreement with the calculated loss, where the latter assumed a bulk dielectric response of a comparable bulk sample, measured using ellipsometry. This leads to the conclusion that no significant changes of the imaginary part of the dielectric response occur when gold-nickel is filled into silica fiber using pressure-assisted melt filling. Moreover, the calculated loss of the alloy wires indicates that no air gaps along the alloy-glass interface are created which would have otherwise increased the modal loss to higher values. We therefore propose that using the PAMF technique, a wide variety of alloys can be filled in various different geometries of microsructured fibers with optical properties similar to the bulk alloy, providing new possibilities to design alloy based integrated fiber structures. For instance, alloys of gold with aluminum, copper, magnesium and zinc  may be used and integrated into microstructured silica fibers for plasmonics integrated fiber optics. Photonic applications based on multicomponent metallic glasses employing effects such as magnetostriction can be additionally envisioned.
The viscosity of a binary alloy as a function of temperature near the alloy melting temperature can be approximated by an Arrhenius relationship when the alloy composition and density are known. The viscosity η in [Pa.s] of an alloy at the filling temperature T can be estimated using the following relationships Eq. (1), A and B are constants and can be calculated from a known value of alloy density ρ (in [kg. m−3]) at room temperature and its atomic weight M (in [kg. mol−1]). The alloy melting temperature is given by Tm and the universal gas constant R used above has a value of 8.3144 J.mol−1K−1.
The dielectric functions of the gold-nickel alloy (Au16wt%Ni) was ellipsometrically determined between 200 nm and 2 µm using a variable-angle spectroscopic ellipsometer (Sentech, SE850). A Lorentz-Drude model was used to fit the measured data according to the following equation:Table 1 below.
This work was partly funded by the German Science Foundation (DFG) via grant no. SCHM 2655/2-1 and the Open Access fund of the Leibniz Association.
References and links
1. M. A. Schmidt, A. Argyros, and F. Sorin, “Hybrid optical fibers – an innovative platform for in-fiber photonic devices,” Adv. Opt. Mater. 4(1), 13–36 (2016). [CrossRef]
2. J. V. Badding, V. Gopalan, and P. J. A. Sazio, “Building semiconductor structures in optical fiber,” Photon. Spectra 40(8), 80 (2006).
3. R. R. He, P. J. A. Sazio, A. C. Peacock, N. Healy, J. R. Sparks, M. Krishnamurthi, V. Gopalan, and J. V. Badding, “Integration of gigahertz-bandwidth semiconductor devices inside microstructured optical fibres,” Nat. Photonics 6(3), 174–179 (2012). [CrossRef]
4. H. W. Lee, M. A. Schmidt, R. F. Russell, N. Y. Joly, H. K. Tyagi, P. Uebel, and P. S. J. Russell, “Pressure-assisted melt-filling and optical characterization of Au nano-wires in microstructured fibers,” Opt. Express 19(13), 12180–12189 (2011). [CrossRef] [PubMed]
5. H. K. Tyagi, M. A. Schmidt, L. Prill Sempere, and P. S. J. Russell, “Optical properties of photonic crystal fiber with integral micron-sized Ge wire,” Opt. Express 16(22), 17227–17236 (2008). [CrossRef] [PubMed]
6. S. Xie, F. Tani, J. C. Travers, P. Uebel, C. Caillaud, J. Troles, M. A. Schmidt, and P. S. J. Russell, “As₂S₃-silica double-nanospike waveguide for mid-infrared supercontinuum generation,” Opt. Lett. 39(17), 5216–5219 (2014). [CrossRef] [PubMed]
7. P. Uebel, S. T. Bauerschmidt, M. A. Schmidt, and P. S. J. Russell, “A gold-nanotip optical fiber for plasmon-enhanced near-field detection,” Appl. Phys. Lett. 103(2), 021101 (2013). [CrossRef]
9. R. Spittel, P. Uebel, H. Bartelt, and M. A. Schmidt, “Curvature-induced geometric momenta: the origin of waveguide dispersion of surface plasmons on metallic wires,” Opt. Express 23(9), 12174–12188 (2015). [CrossRef] [PubMed]
11. G. H. Chan, J. Zhao, E. M. Hicks, G. C. Schatz, and R. P. Van Duyne, “Plasmonic properties of copper nanoparticles fabricated by nanosphere lithography,” Nano Lett. 7(7), 1947–1952 (2007). [CrossRef]
12. W. M. Moore and P. J. Codella, “Oxidation of silver films by atomic oxygen,” J. Phys. Chem. A 92(15), 4421–4426 (1988). [CrossRef]
15. A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998). [CrossRef] [PubMed]
19. V. J. Keast, R. L. Barnett, and M. B. Cortie, “First principles calculations of the optical and plasmonic response of Au alloys and intermetallic compounds,” J. Phys. Condens. Matter 26(30), 305501 (2014). [CrossRef] [PubMed]
20. V. Manov, P. Popel, E. Brook-Levinson, V. Molokanov, M. Calvo-Dahlborg, U. Dahlborg, V. Sidorov, L. Son, and Y. Tarakanov, “Influence of the treatment of melt on the properties of amorphous materials: ribbons, bulks and glass coated microwires,” Mater. Sci. Eng. A 304, 54–60 (2001). [CrossRef]
21. A. Zhukov, J. Gonzalez, M. Vazquez, V. Larin, and A. Torcunov, “Nanocrystalline and amorphous magnetic microwires,” Encyclopedia of Nanoscience and Nanotechnology 6, 365–387 (2004).
22. J. Colbus and K. F. Zimmermann, “Properties of gold-nickel alloy brazed joints in high temperature materials,” Gold Bull. 7(2), 42–49 (1974). [CrossRef]
23. C. M. Hurd, S. P. McAlister, and I. Shiozaki, “Weak ferromagnetism and the electrical properties of AuNi alloys,” J. Phys. F 11(2), 457–469 (1981). [CrossRef]
24. M. Vázquez, “Soft magnetic wires,” Physica B 299(3), 302–313 (2001). [CrossRef]
25. X. Zhang, Z. Ma, Z. Y. Yuan, and M. Su, “Mass‐productions of vertically aligned extremely long metallic micro/nanowires using fiber drawing nanomanufacturing,” Adv. Mater. 20(7), 1310–1314 (2008). [CrossRef]
26. I. W. Donald and B. L. Metcalfe, “The preparation, properties and applications of some glass-coated metal filaments prepared by the Taylor-wire process,” J. Mater. Sci. 31(5), 1139–1149 (1996). [CrossRef]
27. M. Bassett and D. Beaglehole, “Optical studies of dilute AuNi alloys,” J. Phys. F 6(6), 1211–1221 (1976). [CrossRef]
28. D. J. McPherson, S. Supansomboon, B. Zwan, V. J. Keast, D. L. Cortie, A. Gentle, A. Dowd, and M. B. Cortie, “Strategies to control the spectral properties of Au–Ni thin films,” Thin Solid Films 551, 200–204 (2014). [CrossRef]
29. J. C. Zhao and M. R. Notis, “Ordering transformation and spinodal decomposition in Au-Ni alloys,” Metall. Mater. Trans., A Phys. Metall. Mater. Sci. 30(3), 707–716 (1999). [CrossRef]
30. M. Hirai, “Estimation of viscosities of liquid alloys,” ISIJ Int. 33(2), 251–258 (1993). [CrossRef]
31. E. W. Washburn, “The dynamics of capillary flow,” Phys. Rev. 17(3), 273–283 (1921). [CrossRef]
33. C. Y. Jeong and S. Kim, “Dielectric slot embedded metal cavity waveguides,” Opt. Commun. 324, 134–140 (2014). [CrossRef]
34. A. Tuniz, C. Jain, S. Weidlich, and M. A. Schmidt, “Broadband azimuthal polarization conversion using gold nanowire enhanced step-index fiber,” Opt. Lett. 41(3), 448–451 (2016). [CrossRef] [PubMed]
35. P. Uebel, M. A. Schmidt, M. Scharrer, and P. S. J. Russell, “An azimuthally polarizing photonic crystal fibre with a central gold nanowire,” ,” New J. Phys. 13(6), 063016 (2011). [CrossRef]