Ray-tracing simulations for the coral morphology. The light absorption of various macro-scale stony-coral morphologies was simulated with TracePro, a Monte Carlo ray-tracing software. Monochromatic light was modelled with a uniform grid of source points on the rectangular upper boundary. Rays with normal incidence against the root mean square plane of the coral topography were emitted from each of the 40,000 source points. Before importing the scan of the coral morphology (Fig. 1c), a segment of the three-dimensional structure with a relatively small background curvature was selected (Fig. S1d–f). The surface of the coral morphology was defined as an opaque and diffuse surface (Fig. 1c, vertical axis), with a constant absorptance on each surface element (same value as the flat surface; Fig. 1c, horizontal axis). To model the effect of the macro-scale morphology for highly absorbing surfaces, the flux threshold was set up to 0.0005 times the incident flux. The process of ray-tracing simulation was as follows: first, rays with equal power were emitted from the source. Then, each ray interacted with the coral surface and the total reflective power was computed. Parts of the secondary reflected rays intersected with the coral surface resulting in a re-absorption/re-reflection. This process continued until the ray energy reached the flux threshold. The overall absorptance asim value with macro-scale shown in Fig. 1c was calculated by
where Eref and Ein are the reflected and incident emissive powers, respectively. Ray-tracing simulations are a powerful tool to better understand light-trapping in animals, such as black birds35 and corals (this study).
Ray-tracing simulations for the coral-structured coating. Monte Carlo ray-tracing simulations were conducted using two measurements as simulation inputs: (1) the macro-scale topography of the coating (inset of Fig. 3a), and (2) absorptance without the macro-scale morphology (Fig. 2c green solid line). A confocal microscope (SensoFar S Neox) was used to measure the coral-structured topography, which was then imported into the ray-tracing model to calculate the absorptance with macro-scale features (Fig. 2c, green dashed line) but still without nano-scale morphology. The absorptance without macro-scale features corresponded to the measured absorptance values of the base layer (Fig. 2c, green solid line) because it has a similar micro-scale morphology (Fig. 1f). The simulation was conducted for wavelength intervals of Δλ = 100 nm.
Effectiveness of morphological features. The effectiveness e of a morphological feature in improving absorptance is defined as the percentage reduction of reflection loss with a surface having that morphological feature in comparison to the reflection loss by the flat surface. The effectiveness of a coral morphology is then written as
where acoral and aplanar are the absorptance values of the macro-scale coral surface (Fig. 1c, vertical axis) and planar surface (Fig. 1c, horizontal axis), respectively. The effectiveness of each analysed coral morphology in Fig. 1c was found to be independent of the planar surface absorptance.
Materials preparation for the coral-structured coating. The proposed coating has three layers: base, absorption, and top layers, which required base, absorption, and top solutions, respectively. To prepare the base solution, an aluminium complex (aluminum ethylaceto acetate di iso-propirate) and isopropyl di glycol were mixed by screw stirring for 3 h. Black spinel pigments were then added and mixed by screw stirring for 12 h, at a weight ratio of ca. 1.15:1 of liquid to pigment ratio. To improve the adhesion with the metal substrate, a catalyst (N-2- (aminoethyl) -3-aminopropyltrimethoxysilane) was then added and mixed with a screw stirrer for 3 h. The absorptance of twelve kinds of black spinels was measured before and after heat treatment (analysis for four promising pigments shown in Figs. S19, S20), resulting in the down selection of copper chromite manganese spinel, Cu0.64Cr1.51Mn0.85O4 (pigment size distribution in Fig. S21). To prepare the absorption solution, a titanium precursor (titanium(IV) isopropoxide; TTIP) was first reacted with acetylacetone at room temperature, then heated at 80°C for 6 h, and then diluted with 2-propanol (isopropyl alcohol, or IPA); the black pigments and N-methyl-2-pirrolidone were added and dispersed by ultra-sonication for 30 min. A large liquid solution to pigment ratio of ca. 40:1 is needed to produce the coral-structured morphology. To prepare the top solution, a tetraethyl orthosilicate mixture (mixture A) was added to a mixture with silica nanospheres reacted with a tetraethyl orthosilicate (mixture B) and then diluted with ethanol (Supplementary Note 5). In an attempt to improve the coating durability on a stainless steel 316L substrate, whose oxide layer peels off more easily than nickel-based alloys, an improved coating that had an additional primer layer (between substrate and base layer) was tested. The primer layer solution consisted of an aluminium complex diluted with IPA. The article reports improvement when using the substrate Inconel 625 and Haynes 230 (Fig. 3b, e), while the Supplementary Information provides durability results for stainless steels 316L (Figs. S12b, S13b and Supplementary Note 4). In an initial durability assessment36, we reported that the coral-structured coating with preliminary morphology was significantly durable on stainless steel 253MA for ageing conditions at which Pyromark failed due to delamination.
Deposition method of the coral-structured coating. For laboratory-scale deposition, the coatings were sprayed under normal atmospheric conditions on 3-mm thick metallic coupons of 3 cm ´ 3 cm; deposition on cut tube samples was also conducted to test whether the coral-like morphology is kept when changing the substrate curvature. Inconel 625, Haynes 230, and stainless steels SS316L were used as substrate materials, as these are of interest to the CST industry. The underlying substrate was chemically cleaned and did not require grit blasting, as opposed to most reported coatings37. The Haynes 230 coupons was the only substrate type that was grit blasted (as in the Method “Preparation of benchmark Pyromark samples”). To deposit the base layer, the base solution was sprayed with a spraying nozzle twice while heating the substrate at 300°C; the rapid evaporation of the solvent (iso propyl alcohol and isopropyl di glycol) produced the open micropore morphology observed for the base layer. To deposit the coral-structured absorption layer, the absorption solution was sprayed through a nozzle multiple times onto the base layer while it was held at ca. 300°C. The thermal decomposition of titanium acetylacetonate complex, which only occurs when the substrate is held above 300°C (acetylacetone desorbs from titanium acetylacetonate complex at ca. 300°C), produced the coral-structured macro-scale morphology, while the rapid evaporation of the solvent (acetylacetone and IPA) produced the elongated micropores. Importantly, residual stresses at room temperature are expected since our coating forms at ca. 300°C, potentially mitigating the large thermal stresses that occur at typical operating (ageing) temperatures. To deposit the top layer, the coupon was removed from the hotplate so that it cooled down to room temperature, and the top solution was then sprayed onto the absorption layer with an airbrush. Curing was conducted for 30 min at 400°C after each spray pass of the top layer (two passes were conducted) to produce the ‘pristine’ samples.
In order to tune the self-assembled coral-structured morphology, several conditions need to be met. (1) Adequate amount of acetylacetone to titanium precursor for proper coordination; a large ratio of TTIP (wt%) to acetylacetone (AcAc, wt%) causes an excess of TiO2, so a denser titanium bridged network with very few open micropores is created after the desorption process. On the other hand, when there is a small ratio of TTIP : AcAc, isolated TiO2 is formed without the formation of a bridged network that can create the macro-scale protrusions, resulting in an absorption layer having only open micropores produced by the solvent evaporation (Fig. S14). (2) Stable substrate heating; a substrate that can keep a temperature above 300°C is needed to achieve the desorption of acetylacetone in the titanium acetylacetonate complex; the substrate temperature can be tuned to modify the number density of the macro-scale protrusions (Fig. S16). (3) Appropriate air and liquid pressures; when spraying on the heated substrate, if the air pressure is much larger than that of the liquid, then the flow removes the coral-like protrusions before they adhere well to the base layer (Fig. S15). (4) Well-diluted absorption solution with IPA; if the concentration of titanium is too large, then neither open micropores nor macro-scale coral-like protrusions appear. (5) Distance from nozzle to substrate; for an excessively short distance, the substrate becomes soaked preventing a quick solvent evaporation and resulting in a rather flat coating without macro-scale protrusions; for an excessively large distance, the protrusion size becomes small. These five conditions were modified to tune the micro- and macro-scale morphologies, e.g. increasing the protrusion size and number density (Fig. 3f), to improve the light absorptance of the coral-structured coating.
Preparation of benchmark Pyromark samples. Substrate coupons of stainless steel 316L, Inconel 625 (both 30 mm × 30 mm × 3 mm), and Haynes 230 (30 mm × 30 mm × 1 mm) were grit blasted using white aluminium oxide grit with mesh 60 (250 µm) at about 90 psi to remove any oxides and contaminations from the surface. Then, they were chemically cleaned by the following procedure: (1) soaking for 60 s in tetrachloroethylene, (2) scrubbing the surface for 30 s to remove any oils or contamination, (3) soaking for 60 s in methyl ethyl ketone, and (4) scrubbing them for 30 s.
Pyromark 2500 paint was applied using an Artlogic AC330 airbrush. The air pressure was adjusted at 50 psi and the airbrush gun was moved backward and forward over the coupon. This process is repeated eight times to achieve the target thickness (30–40 µm), which we found to perform well at 850°C 38. To have a uniform paint, in addition to keeping the gun about 10 cm above the samples, after each spray pass the surface was allowed to dry for ~15 s before applying the following pass. Samples are then allowed to dry for 18–24 h before being cured. The curing process follows this process: (1) 120°C for 2 h, (2) 250°C for 2 h, (3) 540°C for 1 h, (4) 750°C for 1 h, and (5) cooled to the ambient temperature. It is worth noting that the Pyromark samples in this work exhibit higher initial absorptance than in a previously reported work39 due to the presence of macro-scale cracks resulting from the modified deposition method described above37.
Absorptance measurement. To calculate the solar-weighted absorptance (SWA, or αSW) of the coatings, measurements of spectral absorptance α(λ) were carried out in the pristine state and after aging, in the wavelength range of λ = [250, 2500] nm. The SWA follows a clear consensus in the literature defined as
where G(λ) is the standard G173-03 of the American Society for Testing and Materials (ASTM) for the spectral solar irradiance, commencing at λ = 280 nm; the upper limit of 2500 nm is deemed sufficient to capture most of the solar radiation. The spectral reflectance of the sample was measured at room temperature by a spectrophotometer (Perkin Elmer UV/VIS/NIR Lambda 1050) with an angle of incidence of 8°. The spectrophotometer was set to use an integrating sphere that measures the spectral directional–hemispherical reflectance ρ from the surface of the sample. As the samples are opaque, there is no transmittance and hence ρ(λ) + α(λ) = 1, where ρ is the measured spectral hemispherical reflectance. The spectral values were measured with intervals of Δλ =10 nm. A linear interpolation scheme was conducted to approximate the values of absorptance a at the wavelengths λ that were available in the reference solar irradiance spectrum G but not for the measurement a, which occurred in the lower wavelength range (where the resolution of G is Δλ =0.5 nm). The approximated integrals in Eq. (3) were evaluated at the same discrete values of λ. We found that using the interpolation scheme with the data obtained in intervals of Δλ =10 nm yields the same results (up to three decimal places) as those obtained with the data having intervals of Δλ = 5 nm.
It was found during the execution of the long-term isothermal ageing tests that the spectrophotometer produced slightly different measurements after each calibration (e.g. see solid lines in Fig. S22a). The observed ‘shift’ in value was consistent with the accuracy of the instrument, which required a routine calibration. Importantly, we aimed at assessing optical resilience, i.e. relatively small change in absorptance relative to an initial value, by performing a highly precise measurement of the solar-weighted absorptance. Hence, the following correction for a more accurate relative measurement (dashed line in Fig. S22a) was conducted for all wavelengths:
where ρaged, corrected is the corrected reflectance (directional–hemispherical reflectance) of the aged sample, ρbenchmark, initial is the reflectance of a benchmark sample measured before ageing the sample, ρbenchmark, measured is the reflectance of a benchmark sample measured when acquiring ρaged, measured, which is the measured reflectance of the aged sample (to be compared with the ‘initial’ sample before additional heat treatment). The benchmark sample is a preliminary coral-structured coating (i.e. before modifying macro-scale protrusions to improve absorptance, as in Fig. 3f) on Inconel 625 aged at 850°C for 100 h. In addition, the repeatability of the measurement was excellent, within ±0.05% in the visible range and ±0.1% in the near infrared range (Fig. S22b). The asymmetric error bar of the solar-weighted absorptance (Fig. 3b, e) was determined by the minimum and maximum values (lower and upper error bars, respectively) from a batch of samples aged in the same condition. For the long-term ageing, four to six samples were aged in each condition. The symmetric error bar used in the spectral absorptance (Fig. 3a) was set to plus/minus one standard deviation.
The directional–hemispherical reflectance as a function of the angle of incidence (Fig. 2d, Fig. S8) was measured with an add-on kit (Fig. 23Sa), which provides manual control over the angle of incidence with an accuracy of 0.5°. The spectrophotometer is adjusted with a pinhole and lens so that the light can be narrowly focused on the centre of the sample to allow larger angles of incidence (up to ~82°). The light reflection profile (indicated in Fig. S23b) is beyond the scope of this study.
Isothermal and thermal cycling ageing. The isothermal ageing was conducted in a programmable muffle furnace with small heating and cooling rates of 3 K min–1, minimising possible effects of ramp rates. Hence, the time to reach the target temperature and return to room temperature at the end of the process was time additional to the aging time. The thermal cycling ageing, both rapid cycling and cycle-and-hold patterns (DT = 200 K; see Figs. S9, S10), was conducted in an in-house apparatus comprising a split furnace assigned for heating at a given setpoint temperature and an airflow nozzle to cool the samples from the back of the substrate. Details of the experimental procedure can be found in our previous work17. For these measurements, additional thermocouples were inserted in the dummy sample to confirm that the temperature differences within the sample during the cooling process were small (<10 K) relative to the temperature difference within a cycle.
Emittance measurement. Based on Kirchhoff’s law, at thermal equilibrium the spectral directional emittance is equal to the spectral directional absorptance, which is equal to one minus the spectral directional–hemispherical reflectance. Here, we report spectral near-normal emittance (Fig. 3d) for an angle of incidence of 8° for wavelengths l < 2.5 mm (measured with a Perkin Elmer UV/VIS/NIR spectrophotometer, Lambda 1050) and 17° for 2.5 mm < l < 20 mm (measured with a Shimadzu Fourier transform infrared spectrophotometer, IRTracer-100). Even if the angle of incidence of both ranges was slightly different, we can consider that the angle of incidence has negligible effect since it is less than the measured acceptance angle of ~70° (Fig. S8).
Materials characterisation. SEM characterisation was performed on a Zeiss UltraPlus analytical FESEM. XRD analysis was performed on a using a Bruker system (D2 Phaser, USA) equipped with Cu Kα radiation of average wavelength 1.54059 Å. EDX elemental mappings were performed on an FEI QEMSCAN. Samples were cut and mounted in epoxy resin for polishing. Next, the polished samples were carbon-coated prior to the elemental mapping.
Computational electromagnetics simulations. The magnitude and direction of the Poynting vector were analysed by Finite-Difference Time-Domain (FDTD) method using the software ANSYS Lumerical. A plane wave was launched from normal direction and then interacted with nano-scale structures (Fig. S5c). With the diameter of 120 nm and density of 42 spheres per µm2 obtained from SEM images, SiO2 nanospheres were placed randomly with 8 nm thickness SiO2 matrix on top of the bulk material. The refractive indices of SiO2 were obtained from literature40. In order to simulate the effect of nanospheres on top of a single material with similar initial wavelength-dependent absorptance as the coral-structured coating with micro- and macro-scales, we designed a dummy material with good light-absorbing properties (Fig. S5e). Periodic boundary conditions were set in the later boundaries outside the randomly placed nanosphere distribution. A plane monitor collecting frequency-domain field profile and power was set returning the Poynting vector and power, which were then normalised against the incident power (Fig. 2b top).
Scalability demonstration. A commercial liquid sodium receiver of Vast Solar (Fig. 1d inset) was used for these tests32. The heating of the receiver was conducted by circulating high-temperature oil that achieved a good surface temperature stability. The hazardous gases were removed using a doughnut-shaped exhaust around the spray (Fig. S24a). The morphology and optical properties of the coating on the receiver agreed with those of samples prepared in a laboratory environment (Fig. S24b).
Evaluation of the coating performance on a high-temperature receiver. The performance of the coatings considered in this study were numerically evaluated in a large-scale high-temperature CST system. The modelling of large-scale CST systems was performed using an in-house multi-physics modelling code in Python language coupled with radiative heat-transfer simulations. The complex geometrical optics interactions were solved using two open-source ray-tracing codes. Ray-tracing is computationally expensive when many geometrical elements are included in single simulations. Simulating a full-scale CST power plant is generally impractical because a conventional plant is comprised of tens of thousands of individually aimed heliostats onto receiver panels with detailed geometrical structures, such as pipe gaps and panel thermal insulation. Therefore, coating performance was made computationally tractable by splitting the global simulation into two steps addressing different length scales: Step (1) simulations at the pipe length scale, an elementary volume of receiver panel containing three adjacent pipes was used to determine the effective directional absorptance of coated pipes, and Step (2) simulations at the CST power plant length scale, the geometry of the receiver panels was approximated to planar apertures, placed tangent to the pipes. The directional absorptance of the coated pipes pre-determined in Step (1) was applied to the boundary surfaces in Step (2) to accurately determine the correct directional radiation absorption in each receiver panel.
Tracer41, to which the Australian National University is main contributor, is used for the pipe-level simulations in Step (1), while Solstice42,43 from CNRS PROMES (Centre National de la Recherche Scientifique; Le Laboratoire PROcédés, Matériaux et Energie Solaire) is used for the heliostat field optics simulations in Step (2). See Supplementary Note 6 for details on Steps (1) and (2).