Processing and optical behavior of dense (Hf,Zr)B 2 solid solutions for solar energy receivers

. Optical properties of (Hf 0.5 Zr 0.5 )B 2 are evaluated for the first time with focus on the possible use as novel high-temperature solar thermal absorber, by hemispherical reflectance measurements and calculation of solar absorptance, temperature-dependent spectral selectivity and absorber opto-thermal efficiency at various solar concentration ratios. To optimize the material, a chemically etched surface texture was realized to modify the optical properties. The etched sample showed a higher solar absorptance (0.71) and a lower spectral selectivity than the unetched one, with consequent higher opto-thermal efficiency at all temperatures for solar concentration ratios 1000 ÷ 3000, while at lower concentration ratios and temperatures > 1400 ÷ 1600 K, the unetched sample shows the highest efficiency. These results show the promising properties of binary diborides for solar thermal applications.


Introduction
Due to their highly refractory nature, with melting points exceeding 3200 • C, and other attractive physico-chemical properties (high hardness, thermal stability, resistance to corrosion, chemical inertness, good electrical conductivity, intrinsic spectral selectivity, etc.), zirconium and hafnium diborides are the most representative and investigated members of Ultra High Temperature Ceramics (UHTCs) [1,2].Such characteristics make them suitable for use under harsh conditions, such as in the aerospace industry (thermal protection systems) [2], but also in other emerging application fields, like solar energy [3,4].
In this work, the fabrication of highly dense and single phase (Hf 0.5 Zr 0.5 )B 2 solid solution is accomplished for the first time according to SHS-SPS technique.To date, such two steps route, consisting in the fast preparation of diboride powders by Self-propagating High temperature Synthesis (SHS) followed by their consolidation via SPS, allowed for the obtainment of various standard metal diborides, such as HfB 2 [17], ZrB 2 [18], TaB 2 [18], and TiB 2 [19].More recently, the same approach was successfully used also for the production of three bulk high entropy diborides (HEBs), namely (Hf 0.2 Mo 0⋅2 Ta 0⋅2 Nb 0⋅2 Ti 0.2 )B 2 [20][21][22], (Hf 0.2 Mo 0⋅2 Ta 0⋅2 Zr 0⋅2 Ti 0.2 )B 2 [21,22], and (Hf 0.2 Zr 0⋅2 Nb 0⋅2 Mo 0⋅2 Ti 0.2 )B 2 [22].It should be noted that, when considering standard metal borides, the desired phase can be readily obtained after the first (SHS) step [17][18][19].In contrast, when the synthesis of quinary diborides was accomplished with the same technique, multiphasic products were formed, with the desired HEB obtained only after the SPS process [20][21][22].Therefore, the latter should be then regarded as a reactive sintering route rather than merely a powder consolidation process.The beneficial role played by graphite when added to SHS powders to improve their densification and promote the formation of a single-phase product, was also evidenced [21,23].The optimized samples were found to show similar, in some cases superior, mechanical properties, with respect to ceramics with the same nominal composition prepared using alternative methods [22].
In spite of their potential applications, (Hf x Zr 1-x )B 2 bulk products have been characterized only from the corrosion [12,13], electrocatalytic [13], thermal conductivity [11], and thermal oxidation [7] points of view.On the other hand, a more complete evaluation of their properties is essential to define their potential utilization in different fields, for instance as solar energy absorbers.Indeed, in this context, ZrB 2 -and HfB 2 -based ceramics have been already widely investigated [3,4,24] as they are well known to display spectral selectivity.
A recent paper also reports on the optical properties of (Hf 0.2 Zr 0⋅2 Ta 0⋅2 Mo 0⋅2 Ti 0.2 )B 2 and (Hf 0.2 Nb 0⋅2 Ta 0⋅2 Mo 0⋅2 Ti 0.2 )B 2 to assess the possible utilization of this novel class of solid solutions in the thermal solar energy field [25].
The scope of the present work is twofold.The first one is related to the fabrication of highly dense (Hf 0.5 Zr 0.5 )B 2 samples by the SHS-SPS route, which has not been addressed in the literature so far.Moreover, the optical properties of the resulting ceramics are measured for the first time, and the influence of surface texture modification was also evaluated.The comparison of the optical behavior of the binary system here obtained with those of monolithic HfB 2 and ZrB 2 is also discussed.

Synthesis and sintering of (Hf,Zr)B 2 solid solutions
The synthesis of (Hf 0.5 Zr 0.5 )B 2 was performed by SHS using hafnium (Alfa Aesar, cod.00337, 99.6% pure, <44 μm), zirconium (Alfa Aesar, cod 00847, APS 2-3 μm), and amorphous boron (Sigma-Aldrich, cod 15,580, ≥99 % pure) powders, according to the reaction stoichiometry: An excess of boron (10 mol.%), with respect to the stoichiometry value, was used to balance the loss of this reactant by volatilization during the synthesis process and the amount of it consumed for the borothermal reduction of oxides present in metal powders surface.The mixture of SHS precursors was uniaxially cold-pressed and the obtained cylindrical pellets reacted inside a stainless-steel chamber filled with Argon.Once locally initiated by an electrically heated W filament, the synthesis process proceeded in few seconds to provide a porous reacted sample.The latter is then treated for 60 min by ball milling (SPEX CertiPrep, USA, ball to powder weight ratio of 2 with hardened steel milling media) without or in presence of graphite (Sigma-Aldrich, cod 282,863, <20 μm).As explained elsewhere [21], this additive is found to play a crucial role for the elimination of residual oxide impurities present in boride powders and markedly improved their consolidation.On the other hand, residual amounts of graphite could make resistance to oxidation of the ceramic worse.According to previous findings [21], the additive content used in this work is 1 wt%.
Laser light scattering analysis (CILAS 1180, France) was used to determine particle size of the 1 h milled SHS product.
Approximately 22 g of the obtained powders were processed by SPS (515 S model equipment, Fuji Electronic Industrial Co., Ltd., Kanagawa, Japan) under vacuum conditions.Experiments were carried out under temperature-controlled mode, using an infrared pyrometer (CHINO, mod.IR-AHS2, Japan) focused on the external surface of a cylindrical graphite die (AT101, ATAL Srl, Italy; 35 mm external diameter; 18 mm internal diameter; 40 mm height).The following operating conditions were set during SPS runs: 1850 • C or 1950 • C dwell temperature (T D ), for the cases of graphite containing or additive free mixtures, respectively, 200 • C/min heating rate, 20 MPa mechanical pressure, 20 min holding time, 50 • C/min cooling rate down to 650 • C, followed by a natural cooling step.To facilitate samples' release after sintering, their surface was coated with a 0.13 mm thick graphite foil (Alfa Aesar, Karlsruhe, Germany, 99.8 % pure).The use of a graphite felt layer surrounding the die was aimed to limit heat losses by radiation.Cylindrical samples of about 18 mm diameter and about 6 mm height were obtained after SPS.

Density and thermo-gravimetric analysis
The bulk density of sintered samples was measured by the Archimedes' method using distilled water as immersion medium.Relative density was calculated using the theoretical value of 8.59 g/cm 3 , based on Rietveld analysis results.The amount of graphite (2.26 g/cm 3 density) initially added to the SHS powders was properly considered for determining the theoretical density value for the additive containing samples, as described elsewhere [21].
The oxidation resistance of the (Hf 0.5 Zr 0.5 )B 2 ceramic was evaluated by thermogravimetric analysis (NETZSCH, STA 409 PC Luxx Simultaneous DTA-TGA Instrument, Germany) under 0.1 L/min air flow.To this, non-isothermal (dynamic) tests, consisting of slowly heating (2 performed.The obtained findings are compared with literature data related to DTA-TGA experiments conducted under the same conditions on individual diborides with similar relative densities, namely ZrB 2 , prepared according to the SHS-SPS route [18], and HfB 2 , produced by reactive SPS [26].

Microstructure and topological characterization
Compositional and microstructural characteristics of SHS powders and SPS products were first assessed by X-Ray Diffraction (XRD) analysis using a SMARTLAB diffractometer with a rotating anode source of copper (λCu Kα = 1.54178Å) working at 40 kV and 100 mA over a range of scattering angles 2ϑ from 20 • to 80 • , in steps of 0.05 • with 15 s acquisition time per angle step.The instrument is equipped with a graphite monochromator and a scintillation tube in the diffracted beam.Quantitative analysis of the crystalline phases and structure determinations were performed with the MAUD software (Materials Analysis Using Diffraction), a Rietveld extended program [27].
The cylindrical sintered specimens were sectioned at half height to obtain two portions of 1.8 cm diameter and 2.5 mm thickness.The resulting surfaces were polished with abrasive papers of decreasing grain size and diamond suspensions down to 1 μm.To evaluate the effect of changes in surface texture on optical properties, chemical attack was applied to half of the polished samples.
Based on previous work [24], chemical etching was performed as follows.An etching solution containing 13 wt % of a 70 % aqueous solution of HNO 3 and 77 wt % of a 40 % aqueous solution of HF was prepared; then the polished surface of the samples was immersed in this solution for 15 s and then rinsed with deionized water.
Microstructural and surface morphology characterization was performed by a scanning electron microscope (SEM, Zeiss EVO MA15, Zeiss, Oberkochen, Germany) equipped with an energy dispersive detector (Xmax 50 Oxford Instruments).SEM micrographs were processed by using an image analysis software (Image-Pro Plus® version 6, Media Cybernetics, Silver Springs, MD, USA) to obtain a quantitative evaluation of microstructural parameters.
Surface texture analysis was performed with a noncontact optical profilometer (Taylor-Hobson CCI MP, Leicester, UK) equipped with a green light and a 20X magnification objective lens.
Four distinct areas were analysed for each sample, and the collected surface data were processed with the Talymap 6.2 software (Taylor-Hobson, Leicester, UK) to obtain 3D areal field parameters.
The 3D texture parameters were evaluated on primary surfaces after denoising (median filter 5 × 5) and form removing (S-F surface).

Optical properties
Hemispherical reflectance spectra were acquired at room temperature using a double-beam spectrophotometer (Lambda900 by Perki-nElmer) with Spectralon®-coated integration sphere for the 0.25 − 2.5 μm wavelength region and a Fourier Transform spectrophotometer (FT-IR "Excalibur" by Bio-Rad) with gold-coated integrating sphere and liquid nitrogen-cooled detector for the range 2.5 − 16.0 μm.From the experimental reflectance data R ∩ (λ), the spectral absorbance α(λ) or emittance ε(λ) of fully opaque materials, like in our case, can be obtained, as: Then, the solar absorptance α can be calculated according to the relationship: where S(λ) is the sunlight spectral distribution [28].Similarly, the total hemispherical emittance ε at the temperature T is given by: where B (λ,T) is the spectral radiance of a blackbody at the temperature T.

Synthesis and sintering
The high standard reaction enthalpies for the formation of individual hafnium and zirconium diborides from their elements, i.e. (-Δ H o r ) = 335.975and 322.586 kJ/mol [29], respectively, are responsible for the self-propagating character displayed by their synthesis processes [18,26].The same behavior was also experimentally observed in this work during the preparation of the (Hf 0.5 Zr 0.5 )B 2 solid solution according to Eq. ( 1), with the synthesis reaction which propagated spontaneously and rapidly across the mixture, after local ignition.This is also consistent with the correspondingly high adiabatic temperature (T ad = 3203 K) [10], i.e., the maximum temperature achievable in case the SHS process evolves in an isolated system, which is well above of the empirical threshold limit of 1800 K [30].For the same system, the combustion synthesis event was also observed to occur when Zr, Hf, and B powders (1:1:4 at.ratio) were mechanically treated for 24 min in a planetary ball milled using a ball to powder weight ratio equal to 17.35 [10].
The conversion of raw reactants into the desired phase was checked by XRD analysis.Results are shown in Fig. 1a with the corresponding amounts of the detected phases reported in Supplementary Table S1 along with the microstructural parameters obtained by the Rietveld method.
While the SHS process of individual metal diborides led to ZrB 2 [18], and HfB 2 [26] powders with neither residual reactants nor secondary phases, a multiphasic product is obtained when considering the binary system.Quantitative analysis reveals that the content (in percentage by weight) of the (Hf 0.5 Zr 0.5 )B 2 phase is 21%, with HfB 2 , ZrB 2 , and Zr also found in the powders, i.e. 31.2, 43.0, and 4.5 %, respectively.Minor amounts of other secondary phases, in particular metal oxides (ZrO 2 and HfO 2 ), are also likely present, even though they were not clearly detectable by this analysis.The low conversion degree of initial reactants into the desired phase could be attributed to the extreme conditions involved during SHS, with Zr and Hf elements not allowed to uniformly diffuse across the sample during the very rapid occurrence of the synthesis process.
These powders were sintered by SPS either additive-free or in presence of graphite.The consolidation process of powders with no graphite was conducted at T D = 1950 • C, as for the case of high entropy borides [20], and resulted in 94.2% dense samples (8.09 g/cm 3 absolute density).The corresponding XRD pattern is shown in Fig. 1b, while the related phases' amount and microstructure parameters are listed in Table S2.It is apparent that the yield in the desired binary phase is highly improved, from 21 to 85.5 wt%, after SPS.However, the sintered ceramic is rich of oxides, namely ZrO 2 (tetragonal and cubic), and HfO 2 , 8.1 and 6.4 wt%, respectively.In the latter regard, Fig. 1c and Table S2 evidence the unequivocal beneficial effect produced by the introduction 1 wt% graphite for the removal of such impurities, which were reduced to 2.1 wt% (ZrO 2 ), from SHS powders.This fact concurrently determined a further raise of sample consolidation, with the obtainment of relative densities of about 98.3 % (8.21 g/cm 3 absolute density) at lower dwell temperatures with respect to the case of additive-free powders, 1850 instead of 1950 • C, respectively.
As observed elsewhere for the case of high-entropy systems [23], the obtainment of highly pure boride ceramics at relatively milder processing conditions is a direct consequence of the removal of surface oxides from powder particles, which makes them more reactive, so that the synthesis of single-phase products is promoted.Almost fully dense samples consisting of 96.6 wt% of (Hf 0.5 Zr 0.5 )B 2 , with traces of ZrC (0.6 wt%) and residual graphite (0.7 wt%), other than minor amounts of oxides, are finally obtained.The latter ceramic is subjected to further characterization, as discussed in what follows.

TGA test
The oxidation behavior of the dense binary diboride sample produced at 1850 • C with 1 wt%C was examined by conducting dynamic TGA experiments in air flow.Fig. 2 shows the corresponding curve, expressed as normalized weight gain.For the sake of comparison, results relative to monophasic ZrB 2 (98.5% relative density) [18], and HfB 2 (97.6% relative density) [26] samples prepared according the SHS-SPS and R-SPS routes, respectively, are also shown.
Negligeable weight changes were observed up to about 800 • C for the three systems.Above such temperature level, TGA curves increase in an exponential way, although with different rates, being the ZrB 2 sample more sensitive to the high-temperature oxidizing environment and HfB 2 the system which gain less weight, while an intermediate behavior is displayed by the solid solution.
The outcomes obtained in this work are consistent with thermal oxidation resistance data reported in the literature for flash sintered 95% dense (Hf 0.5 Zr 0.5 )B 2 samples tested by TGA-DSC in flowing air [7].In particular, it was found that no noteworthy weight gain was recorded up to 800 • C.However, as a difference, a weight loss was observed to occur from about 800 to 1000 • C, which was ascribed by the authors to the evaporation of some amorphous phases present in flash-sintered samples [7].
Based on the results above, it is possible to state that the (Hf 0.5 Zr 0.5 ) B 2 system shows a good resistance to oxidation up to 800 • C, whereas, as for the case of standard Zr-and Hf-diborides, suitable additives such as Si-containing compounds (SiC, MoSi 2 , HfSi 2 , etc.), should be introduced if the ceramic has to be exposed to more severe temperature and oxidizing environments [17,26,31,32].

Microstructure and topological characteristics
Both the polished and the etched samples were analysed by SEM/ EDS to characterize their microstructure, and to correlate surface texture features to the optical properties.
The microstructure of the polished sample obtained with the addition of 1 wt% carbon (relative density 98%) is shown in Fig. 3, where the surface is revealed by secondary and backscattered electrons.Residual porosity, closed and rounded, with an average size of 0.64 μm, is uniformly distributed and mainly incorporated into the grains of the binary phase.The densification process induced a grain growth, thus reaching an average size of about 11 μm.
Backscattered electron images show a phase contrast effect, essentially crystallographic, due to electron channelling phenomena linked to the different grains' orientations.After densification, the material reached an excellent homogeneity, with the percentage of binary phase in the ceramic above 96%.This suggests that, during the SPS process, the interdiffusion of metallic elements was rapid and allowed to minimize segregation and avoid core-shell phenomena.
Fig. 4 shows a SEM micrograph of the sample surface, together with the corresponding EDX maps.The element distribution maps confirm   [18,26].the previous observations.The sample is rather homogeneous in composition: in particular, the metallic elements, Hf and Zr, are uniformly distributed over the whole analysed surface.In accordance with the Rietveld analysis (Table S2), residual carbon and some remaining oxides are also observed locally.
To increase the absorption of solar radiation, the surface texture was modified by means of chemical etching.Figs. 5 and 6 show the surface of the sintered sample (1 wt%C) after chemical attack.
The etching solution consists of nitric acid and hydrofluoric acid.Nitric acid is a powerful oxidant and acts by oxidizing the metal cations and the boride ion forming tetravalent cations and soluble borates.However, when used alone, HNO 3 does not provide any etching effect, as it instead reinforces the passive film, naturally formed in the air, mainly consisting of mixed hafnium and zirconium oxides that protect the surface of the ceramic material.
Hydrofluoric acid has the double function of breaking the passive  S. Barbarossa et al. film, allowing substrate oxidation, and complexing the metal cations, thus preventing their precipitation as insoluble fluorides, if the concentration of fluoride ions is sufficiently high.
As suggested by XRD analysis data reported in Supplementary Fig. S1, the etching process does not generate any new phases, while it induced a rather uniform dissolution of the elements in the solid solution.Nonetheless, it significantly changed the surface morphology, which became very irregular, thus revealing different morphological characteristics.
The attack was preferentially localized on certain grains: in these areas the binary phase was strongly attacked, and an acicular morphology was obtained.On the other hand, other areas appeared only slightly attacked and retained a flat morphology.In addition, in some strongly etched areas, the attack occurred in a generalized manner, thus forming flat regions without texturing.
The evaluation of the surface extension of these areas was carried out by image analysis.It was found that the strongly textured portion covers about 62% of the entire surface, while the slightly attacked and the flat areas at the base account for 18 and 20%, respectively.
Details of the etched surface can be deduced from Fig. 7a and 7b, where two micrographs obtained from the cross-sectional observation are shown.The etched areas are characterized by the presence of variably oriented truncated pinnacles, with an average height of 2 μm, and spaced about 600 nm apart.
The EDX maps collected on the etched sample are reported in Fig. 8.The binary phase appears to be uniformly attacked, with no evidence of preferential dissolution of elements present in the solid solution.In fact, a rather homogeneous distribution of the main elemental constituents was observed over the entire surface, with the presence of residual carbon which was apparently not dissolved by the mixture of mineral acids.
Fig. 9 shows a 3D map of the etched surface (Fig. 9a) and the average values of the height parameters together with the relative uncertainties collected on both unetched (polished) and etched samples (Fig. 9b).The unetched surface shows typical values of polished surfaces, with Sa and Sq values close to 79 and 101 nm, respectively; the surface displays a slight prevalence of smooth irregularities (shallow peaks max 0.5-0.6 nm) and the height values are quite symmetrically dispersed with respect to the mean plane, following an essentially Gaussian distribution (Ssk≅ 3).The chemical treatment substantially modifies the texture, thus producing a much more irregular surface, with a slight predominance of valleys/depression (negative value of Ssk) characterized by Sq and Sa values of one order of magnitude higher than the unetched surface.The analysis of the profiles extracted from the studied surfaces shows that the chemical attack proceeded by eroding the initial sample by about 2.2 μm.

Optical properties
Fig. 10 shows the hemispherical reflectance spectra of polished and etched sample, together with those of pure polished ZrB 2 [3] and HfB 2 [4], for comparison.It is interesting to notice that the curve of the pristine binary boride shows a different spectral shape with respect to the individual ZrB 2 and HfB 2 , as expected from the formation of the solid solution, which is a new material rather than the simple mix of two components.We can see that the spectrum of (Hf 0.5 Zr 0.5 )B 2 from time to time coincides with that of ZrB 2 or HfB 2 (see Fig. 10a for the range 0.3-16.0μm and Fig. 10b for shorter infrared wavelengths), while it is differentiated from them in the ranges ~0.9-1.9 μm and ~3.5-5.7 μm, respectively.In these regions, the binary sample shows either a slightly higher reflectance than both ZrB 2 /HfB 2 (in the first interval), or intermediate characteristics between them (in the second one).
When the effect of the etching process on optical properties is concerned, it is possible to clearly appreciate the dramatic decrease of the reflectance in the etched surface with respect to the pristine one, across the whole investigated range.The reflectance decrease is wavelengthdependent.If we consider the ratio R e-p between the spectra of etched and pristine sample, its value is the lowest in the range ~1.3-2.0 μm  Following the approach shown in Refs.[33,34], the obtained result   on optical properties can be qualitatively explained in terms of the structures created by the etching treatment and their sizes.The involved light-material interaction phenomena are light trapping (when the radiation wavelength is similar to the size of surface features) and increase the effective surface (when the surface features are much larger than radiation wavelength).On the other hand, when the surface features are smaller than the wavelength of the involved radiation, we expect an increasingly reduced effect.In our case, the pointy pyramids created by the etching process appear not homogeneous in orientation, size and density on the specimen surface, likely because of the non-homogenous etching rate on the differently-oriented crystal grains, as noted above.Therefore, a quantitative assessment of the size distribution of etching-produced pinnacles from SEM images is difficult.However, we can make some qualitative comments: the height and spacing of the pinnacles agrees with trapping effects of radiation wavelengths shorter than about 2 μm, corresponding to the spectral range of the observed maximum reduction of the reflectance (i.e.maximum increase of absorbance or emittance), while the presence of the relatively few depressed large flat areas, whose typical sizes are smaller than 10 μm, explains the (lower) reduction of reflectance (i.e. the lower increase of absorbance or emittance) at the corresponding wavelengths and is consistent with the cutoff behavior around 7 μm observed in the reflectance ratio R e-p .In other words, the radiation with wavelengths shorter than the cutoff experiences, depending on its specific wavelength, the increase of the effective surface available for interaction and/or the trapping within surface features.Thus, both these effects contribute to the observed decrease of reflectance at these wavelengths.On the contrary, longer-wavelength radiation cannot be trapped and does not see any surface increase, so that the reflectance tends to recover the value of the original surface.
For the sake of comparison, Fig. 11 shows the spectra of the solid solutions and those of two materials commercially available and used in solar power plants: SiC [35] and Al 2 O 3 [36].SiC is characterized by the lowest reflectance in the spectral range of solar radiation, but also in the remaining of the infrared range, which entails high thermal emittance.Al 2 O 3 has very poor solar absorption properties (see the high reflectance in Fig. 11b), and a high thermal emittance as well.
Fig. 12 shows the temperature-dependent values of thermal emittance ε and spectral selectivity α/ε of the binary samples, the reference single borides and the two commercial reference materials SiC and Al 2 O 3 [38].As for emittance, the pristine binary boride shows intermediate values between the single borides, and a solar absorptance slightly lower than ZrB 2 , while the etched binary sample is characterized by significantly increased solar absorptance and thermal emittance.The emittance of both binary samples is considerably lower than that of SiC at all temperatures including the highest one here considered (ε = 0.57 and 0.25 at T = 1700 K for the etched and pristine binary pellets, respectively, to be compared to ε = 0.83 for SiC at the same temperature).If the spectral selectivity is concerned, again the pristine sample shows an intermediate behavior between the single borides, and a curve superimposed to that of HfB 2 for temperatures >1100 K. Interestingly, the etched sample keeps the spectral selectivity, even if with lower values.This favorably compares the binary samples to both SiC and Al 2 O 3 , none of which can be considered spectrally selective.Finally, if we compare the pristine binary boride with other kinds of advanced ceramics, for instance MAX phases, the values of the optical parameters appear fully comparable [39].
From the α and ε parameters, it is possible to evaluate the optothermal conversion efficiency of the solar absorber, defined as [34]: C⋅I solar (5) where σ = 5.67 × 10 − 8 W/(m 2 K 4 ) is the Stefan-Boltzmann constant, T is the absorber temperature, C the solar concentration ratio of the solar plant where the absorber is used (i.e. the ratio between the overall area of solar-collecting surfaces in the plant -mirrors or lenses-and the area of the solar absorbing surface) and I solar = 1 kW/m 2 is the standard solar radiation intensity at 1 sun.Fig. 13a compares the opto-thermal efficiency of samples as a function of temperature for four values of the solar concentration ratio C = 100 and 300 (compatible with solar tower systems), C = 1000 (solar towers or solar dishes) and C = 3000 (solar dishes) [40].It is immediate to see the significant improvement in efficiency obtained with the etching treatment, especially at high concentration ratios.For mid concentration ratios, the etched sample is better performing for T ≤ 1600 K (C = 500) and T ≤ 1400 K (C = 300), while, for higher temperatures, the choice of the untreated pristine sample should be privileged at these concentration ratios, because of its lower emittance.Fig. 13b compares the opto-thermal efficiency of the etched binary boride to the performances of the two commercial reference materials, showing that it is always much more efficient than Al 2 O 3. In addition, in the investigated space of parameters, remarkably, it is also better than SiC at high temperatures and moderate values of concentration ratio (T ≥ 1300 K or 1500 K for C = 300 or 500, respectively).At T = 1700 K and C = 1000, the binary boride has the same efficiency than SiC, and a higher one at higher temperatures (not shown in Figure ).

Conclusions
The (Hf 0.5 Zr 0.5 )B 2 solid solution was produced in highly dense form by the SHS-SPS processing route, and the optical properties of the resulting ceramic were evaluated for the first time.Based on the obtained results, it is possible to draw the following conclusions.% of the desired binary compound.On the other hand, the yield in the (Hf 0.5 Zr 0.5 )B 2 phase increased to 85 wt%, when the SHS powders were consolidated at 1950 • C by SPS, which should be then considered as a reactive sintering process.As a drawback, the resulting ceramics were rich of oxide impurities, whose presence does not permit to obtain fully dense samples.2) The introduction of 1 wt% of graphite markedly purifies the sintered product, with a decrease of the oxide content (from 14.5 to 2.1 wt%) by carbothermal reduction mechanism; in parallel, powder densification is promoted, with an increase in the relative density from about 94% to values exceeding 98%.Moreover, the removal of surface oxides by graphite made powders more reactive, so that the obtainment of a single-phase product by SPS was achieved at lower temperature, i.e. 1850 instead of 1950 • C. 3) The (Hf 0.5 Zr 0.5 )B 2 system was found to be thermally stable in air up to 800 • C, similarly to the individual diborides, therefore, with reference to the solar absorber application, no oxidation issues are expected below this temperature.At higher temperatures, again similarly to the individual borides, they can be used either in vacuum or under inert atmosphere, or, in case of planned use under oxidizing environments, the introduction of suitable silicon-containing additives (SiC, MoSi 2 , etc) in the ceramics should be considered.4) Chemical etching modified the surface of the binary boride, producing a surface with high roughness characterised by the presence of pinnacle structures of the order of 0.4-2 μm size and few large, heavily attacked, flat areas of typical size below 10 μm.
Texturisation significantly modifies the optical properties of the material due to the different interaction of the various spectral components of sunlight and thermal radiation with surface textures of different sizes.In particular, the optical parameters are modified as follows: the solar absorptance α is increased, the spectral selectivity α/ε is decreased, but still maintained (α/ε > 1).Consequently, the opto-thermal efficiency of the etched sample in significantly increased at all the investigated temperatures if the material is used in a system with solar concentration ratios C = 1000 ÷ 3000 and at temperatures T < 1400 ÷ 1600 K for C < 1000.For those concentration ratios and higher operating temperatures, the unetched sample should be privileged.The considered materials, in particular the etched one, favorably compares to the existing commercial materials used in solar absorbers.
The fabrication route proposed in this work, also employed successfully for the obtainment of bulk single-phase high-entropy borides, is intended to be valid also when considering additional multicomponent boride systems (binary, ternary, etc.).

Fig. 1 .
Fig. 1.XRD patterns of SHS (a), and SPS products with no additive at T D = 1950 • C (b) and in presence of 1 wt% graphite at T D = 1850 • C (c).Red dots are experimental data, the continuous lines are the calculated best fit.

Fig. 2 .
Fig. 2. Comparison of specific weight changes during TGA oxidation test in air of (Hf 0.5 Zr 0.2 )B 2 sample prepared by SPS (T D = 1850 • C, 1 wt%C) in this work as a function of temperature (heating rate equal to 2 • C/min).Literature data of individual diborides (HfB 2 , ZrB 2 ) are also reported for comparison[18,26].

Fig. 6 .
Fig. 6.SEM micrograph of the etched sample, details of etched morphology at higher magnification.A) Secondary and B) backscattered electron images.

Fig. 7 .
Fig. 7. SEM micrograph of the etched sample, with details of etched morphology at higher magnification.A) SE image obtained from cross-section observation; B) SE image of textured areas.

Fig. 8 .
Fig. 8. SEM micrograph and related EDX elemental maps collected on an etched sample.

Fig. 9 .
Fig. 9. (a) Areal surface maps of etched surface; (b) Height parameter values evaluated on polished and etched samples.

Fig. 13 .
Fig. 13.Opto-thermal efficiency as a function of the temperature.(a) Comparison of the two binary borides.Hollow symbols: untreated sample.Filled symbols: etched sample.(b) Comparison of the etched binary sample to two commercial reference materials (SiC and Al 2 O 3 ).Meaning of symbols: crosses: SiC; filled squares: etched binary boride; stars: Al 2 O 3 .The color code is referred to the values of the solar concentration ratio, as explained in legend.
• C/ min) the sample from room temperature to 1450 • C, have been S.Barbarossa et al.