Reflectance spectral studies of spark plasma sintered tungsten carbide pellet

Hisashi Tokutomi; Kazuma Nakamura; Koji Miyazaki; Toshiharu Chono

REVIEW 3 major objections 5 minor 16 references

Reflectance spectral studies of spark plasma sintered tungsten carbide pellet

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Measured reflectance of tungsten carbide shows a solar-matched plasma edge at 0.6 eV.

desk verdict A credible first measurement of WC reflectance in the solar range with a clear ~0.6 eV plasma edge; the main weakness is an unquantified porosity-scattering explanation, but the central result holds. read the letter →

arxiv 2411.15754 v1 pith:U5LWNSGD submitted 2024-11-24 cond-mat.mtrl-sci

Toshiharu Chono , Hisashi Tokutomi , Kazuma Nakamura , Koji Miyazaki This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords tungstencarbidesolarselectiveabsorberreflectancespectroscopyplasmaedgesparksinteringabinitiocalculationmid-infraredphotothermalconversion

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper reports the first measured spectral reflectance of tungsten carbide (WC) over the visible to mid-infrared range (0.1 to 2.5 eV), obtained from a polycrystalline pellet made by spark plasma sintering. The key result is a clear low-energy plasma edge near 0.6 eV, which coincides with the energy cutoff of sunlight and matches ab initio calculations of WC's optical response. Because a solar selective absorber should absorb sunlight (0.6–4.0 eV) but emit little thermal radiation (0.12–0.6 eV), this edge position is exactly what makes WC attractive for solar thermal applications. The paper also shows that the spark-plasma-sintered sample, with fewer pores than a hot-pressed one, gives a reflectance spectrum closer to the theoretical prediction, though residual porosity still lowers the measured reflectance in the low-energy range.

What carries the argument

The key mechanism is a low-energy plasma excitation in WC at about 0.6 eV, seen as a step-like rise in reflectance (the 'plasma edge') that aligns with the wavelength cutoff of sunlight. The argument works by combining a purpose-built visible-to-mid-infrared reflectance spectrometer (covering 0.1–2.5 eV) with ab initio density-functional calculations of the dielectric function, from which reflectance is obtained as $R(\omega)=|(1-\sqrt{\epsilon(\omega)})/(1+\sqrt{\epsilon(\omega)})|^2$. The plasma edge position is the load-bearing observable: it is compared between measured and calculated spectra, and a smearing parameter (0.01 eV vs 0.1 eV) is used to model the effect of scattering on the spectral shape.

What would settle it

A reflectance measurement on a single crystal of WC, or on a series of WC pellets with deliberately varied porosity, would settle the claim: if the apparent plasma edge shifts or disappears as porosity changes, the polycrystalline measurement cannot be taken as the intrinsic optical response. The authors themselves note that single-crystal WC measurements remain to be done.

Watch

Extended reading notes

Core claim

The central claim is that the measured spectral reflectance of a polycrystalline tungsten carbide pellet exhibits a sharp low-energy plasma edge around 0.6 eV (2.0 µm), in good quantitative agreement with first-principles calculations, and that this edge corresponds to the cutoff energy of sunlight. The authors argue this makes WC a promising ingredient for solar selective absorbers: it absorbs sunlight but suppresses thermal re-radiation because reflectance remains low below the edge and rises above it. They support the assignment by comparing their measurement with ab initio reflectance spectra computed from the dielectric function in the random phase approximation, and by benchmarking their custom measurement system against known metals (Al, Au, Cu). They further show that the SPS method yields denser samples than hot pressing, reducing pore-induced scattering and bringing the measured spectrum closer to the ideal crystal prediction.

Load-bearing premise

The weakest assumption is that the residual pores and grain boundaries in the sintered polycrystalline pellet only lower the reflectance intensity without shifting the position of the observed 0.6 eV plasma edge, so that the edge can be attributed to an intrinsic electronic property of WC rather than to scattering or surface effects.

Editorial extensions

If this is right

WC can be used as a solar selective absorber: its reflectance edge at 0.6 eV suppresses thermal radiation while absorbing sunlight, improving photothermal conversion efficiency.
First-principles calculations of optical reflectance are quantitatively reliable for refractory carbides like WC, providing a predictive route for screening absorber materials.
Spark plasma sintering produces denser WC samples than hot pressing, and the resulting reflectance is closer to the ideal crystal spectrum, confirming SPS as the preferred preparation route for optical characterization.
The figure-of-merit estimates (0.51–0.56 for ideal WC, 0.37–0.40 for the SPS sample) indicate that reducing porosity further will bring real WC close to the theoretical absorber performance.
The developed reflectance measurement system covering 0.1–2.5 eV can be used to quantitatively assess solar selectivity of other materials.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the plasma edge is intrinsic, alloying or nanostructuring WC (e.g., in TiCN cermets, where WC is a component) could tune the edge energy across the solar spectrum, extending the design space for selective absorbers.
The same measurement-plus-ab-initio approach could test other refractory carbides and nitrides whose plasma edges fall in the infrared, providing a rapid screening pipeline without fabricating single crystals.
Single-crystal WC reflectance would likely show a sharper edge and higher reflectance below 0.6 eV than the SPS pellet, which would directly validate the porosity-scattering interpretation.
The pore-scattering lowering of reflectance at low energies could be corrected for in process design; the effective-medium (Bruggeman/Maxwell-Garnett) analysis presented for TiC and TiN could be applied quantitatively to WC to separate intrinsic and extrinsic contributions.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

You should know this paper does what it says: it reports the first measured reflectance spectrum of WC in the 0.1–2.5 eV range and shows a clear low-energy plasma edge near 0.6 eV, consistent with the prior ab initio prediction from the same group. The edge is visible in the raw spectrum, not hidden in a fit, and it survives an FT-IR cross-check. The instrument is validated against Au, Al, and Cu, and the sample characterization is solid: 99.996% purity, density 15.51 vs. 15.63 g/cm3, XRD matching ICSD. The SPS vs. HP comparison for TiC/TiN with effective-medium models in the SI is a reasonable extra and strengthens the overall story.

The soft spots are real but not fatal. There are no error bars on reflectance or on the FOM. The assignment of the low-energy reflectance deficit to pore scattering is tested only by comparing 0.01 eV and 0.1 eV smearing widths in the ab initio calculation. That is a proxy, not a demonstration that pores merely reduce reflectance without shifting or obscuring the edge. The authors themselves note that single-crystal WC measurements would be needed to confirm the intrinsic assignment, which is an honest limitation but also exactly the unvalidated assumption under the headline claim. The SPS FOM (0.37–0.40) is below the ideal ab initio value and below some TiC values; they report it honestly, but the phrase "preferable for solar selective absorber" is stronger than the measured SPS data alone support.

I largely agree with the stress-test note, with one qualification: this is not a circular paper. The central claim rests on direct measurement, with the theory comparison as independent supporting evidence despite shared authorship with Ref. [4]. The porosity explanation is weak, but the plasma edge itself is not manufactured by that explanation.

Who is this for? People working on solar selective absorbers, refractory carbides, or optical characterization of sintered ceramics. It deserves a serious referee. I would send it to peer review and ask for uncertainty analysis, a more constrained discussion of scattering, and a tempering of the FOM claim. Single-crystal data should not be a precondition for acceptance, but the authors need to state more carefully that the intrinsic assignment is plausible rather than proven.

Referee Report

3 major / 5 minor

Summary. The manuscript reports what the authors describe as the first spectral reflectance measurement of polycrystalline tungsten carbide (WC) over the range 0.1 to 2.5 eV, using a home-built visible-to-mid-infrared reflectometer. The sample is prepared by spark plasma sintering and characterized by density (15.51 g/cm3 versus 15.63 g/cm3 theoretical) and XRD. The measured reflectance shows a plasma-edge-like feature near 0.6 eV, which the authors compare with ab initio RPA calculations and interpret as an intrinsic low-energy plasma excitation consistent with their earlier prediction. The paper also derives a photothermal figure of merit for WC, compares SPS and hot-pressed TiC and TiN samples, and discusses the effect of porosity on reflectance. The central claim is that the measured plasma edge makes WC a promising solar selective absorber.

Significance. If the central claim is accepted, the paper provides the first direct experimental evidence for a ~0.6 eV plasma edge in WC, which is relevant for solar selective absorber design and gives independent support to the authors' earlier ab initio prediction. The instrument is benchmarked against Au, Al, and Cu reflectance spectra, and the WC sample is well characterized by density and XRD. The paper is honest about the residual porosity and about the need for single-crystal measurements. However, the quantitative anchoring of the central claim is weakened by the absence of error bars and by the ad hoc treatment of porosity scattering, so the intrinsic assignment of the measured edge remains an assumption rather than a demonstrated result.

major comments (3)

[Fig. 2(c) and the sample-properties discussion] The attribution of the low-energy (0.1-0.5 eV) reflectance deficit to multiple scattering by pores is supported only by comparing two ab initio spectra computed with different smearing widths (0.01 eV and 0.1 eV). A broader Lorentzian smearing is a rough proxy for scattering, not a quantitative model of how a specific pore distribution modifies the reflectance; it does not establish that pores only reduce the reflectance without frequency-dependent redistribution that could shift or obscure the plasma edge. Since the abstract assigns the observed ~0.6 eV edge to an intrinsic plasma excitation, this is a load-bearing assumption that needs independent validation, for example by effective-medium modeling using the measured porosity or by a measurement on a single crystal. The paper's own statement that single-crystal measurements would be needed confirms that the intrinsic assignment is not yet established.
[SI Sec. 2, Eq. (6) and Table S1] The figure of merit for WC(SPS) is computed by integrating the measured reflectance after fitting it with a five-oscillator Drude-Lorenz model. No uncertainties are reported for the reflectance data, the fit parameters, or the resulting eta_FOM values. The reported difference between WC(SPS) (0.37-0.40) and the ab initio values (0.47-0.56) is therefore not quantitatively meaningful; the difference could be comparable to the combined uncertainty. Because the practical claim that WC is preferable as a solar selective absorber rests on these numbers, an uncertainty estimate is required.
[Fig. 2(c) and SI Fig. S3] The measured reflectance spectrum is presented as a single curve with no reproducibility data, repeated measurements, or systematic uncertainty estimate from the calibration procedure (e.g., the Ag reference and the 20-degree incidence angle). Without this information, the statement that the measured spectrum is in 'good quantitative agreement' with ab initio calculations is not testable. At minimum, the authors should report the measurement-to-measurement spread and an estimate of systematic error, especially near the plasma edge where the central claim is made.

minor comments (5)

[Abstract and Introduction] The phrase 'first spectral reflectance' should be qualified, since Ref. [11] reports FT-IR reflectance measurements of WC, albeit over a narrower energy range; the authors should state explicitly that this is the first broadband measurement covering the 0.6 eV plasma edge.
[Throughout] There are several typographical errors, including 'sinterd', 'wevelength', 'absorvers', 'Acknowlegements', 'Monkhorst-Packk', 'pseudopotentioals', and 'anab initio'; these should be corrected.
[Fig. 2 caption] The notation E||x and E||z used later for the ab initio FOM values is not defined in the main text or in the caption; the polarization directions relative to the hcp crystal axes should be specified.
[SI Sec. 2] The Drude-Lorenz fitting is shown graphically for WC, but the fitted parameter values are not provided in a table; listing them would improve reproducibility and allow readers to assess the quality of the fit quantitatively.
[References] Reference [11] is cited without author names in the text; for consistency with other references, the full citation should be given.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the measured reflectance edge is an independent experimental observable and the ab initio comparison is a parameter-free calculation rather than a fit to the data.

full rationale

The central claim is that the measured WC reflectance shows a low-energy plasma edge near 0.6 eV and that this is consistent with ab initio calculations. The experimental spectrum is a direct measurement, and the ab initio reflectance is computed from first principles via Eq. (1) using RPA dielectric functions with stated DFT parameters (smearing 0.01 eV), not fitted to the WC measurement. The same-group prediction in Ref. [4] is cited, but the paper independently reproduces it with its own RESPACK calculation, so the self-citation is not load-bearing. The porosity-scattering interpretation of the low-energy deficit is an auxiliary hypothesis tested by comparing smearing widths and by TiC/TiN density analyses, not by fitting the central edge position. The Drude-Lorenz model in Eq. (S7) is used only to evaluate the figure of merit from fitted reflectance, and those FOM values are presented as estimates, not as predictions derived from the theory. No derivation step reduces by construction to its own inputs, and no fitted parameter is renamed as a prediction. The main scientific caveat—that the intrinsic assignment would be strengthened by single-crystal measurements—is a validity limitation, not circularity.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The paper introduces no new physical entities. Its central claim depends on the validity of standard DFT/RPA methods, the Fresnel reflectance model, and the assumption that the sintered sample faithfully represents intrinsic WC optical properties. Free parameters appear mainly in the secondary FOM calculation and in the ad hoc smearing adjustment.

free parameters (4)

Drude-Lorenz model parameters (epsilon_inf, Omega_p, Gamma, Omega_i, Omega_pi, Gamma_i for i=1..5) = Not listed; fitted to reproduce ab initio and experimental reflectance spectra in SI Section 2
Used in SI Eq. (7) to compute the figure of merit. These parameters are directly fitted to the spectral data and are not derived from first principles.
Ab initio smearing width (0.1 eV) = 0.1 eV
Chosen ad hoc to represent scattering by pores in the low-energy region, while 0.01 eV is used as the baseline. This choice improves the apparent agreement with experiment but is not derived from a physical model.
Cutoff wavelengths for solar absorptivity and thermal emissivity = 0.28-4 um and 0.1-10 um
These integration limits in SI Eqs. (4)-(5) affect the calculated alpha_s and epsilon_t values, and ultimately the FOM. They are standard but arbitrary choices.
FOM operating conditions (T, c, I0, B) = Condition 1: T=673 K, c=30 suns, I0=863 W/m2, B=0.91; Condition 2: T=400 K, c=1 sun, I0=1 kW/m2, B=1
Selected to represent two solar thermal scenarios. The FOM depends strongly on these assumptions, which are reasonable but not unique.

assumptions (6)

standard math DFT-PBE and RPA-Lindhard dielectric function are accurate for WC optical response
Used to compute the ab initio reflectance spectrum. Standard condensed matter methods, but their predictive accuracy for the plasma edge is part of the validation.
standard math Fresnel reflectance formula for a semi-infinite planar medium (Eq. 1)
Assumes specular reflection from a smooth surface. The sample is polished to Ra 0.001 um, and angle-dependence was checked in SI, so this is reasonable.
domain assumption Solar selective absorber model with defined spectral ranges
The definition of sunlight as 0.6-4 eV and thermal radiation as 0.12-0.6 eV underpins the interpretation of the 0.6 eV plasma edge as favorable for suppressing thermal loss.
ad hoc to paper The 0.1 eV smearing represents scattering by pores
Introduced in the discussion of Fig. 2(c) to reconcile the low-energy measured reflectance with the ab initio spectrum. This is a qualitative assumption without direct experimental validation.
ad hoc to paper The sintered pellet's surface and microstructure do not fundamentally shift the intrinsic plasma edge
The central interpretation relies on the measured spectrum reflecting intrinsic WC properties. The paper notes pore scattering lowers reflectance but assumes the edge position remains representative.
standard math Effective medium theory (Bruggeman and Maxwell-Garnett) describes pore effects on reflectance
Used in SI Section 3 to model relative density dependence. These are established approximations for composite media.

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Cite this review

Pith. "Pith review of Reflectance spectral studies of spark plasma sintered tungsten carbide pellet." pith.science (2026). https://pith.science/paper/U5LWNSGD

@misc{pith2026241115754,
  author       = {Pith},
  title        = {Pith review of: Reflectance spectral studies of spark plasma sintered tungsten carbide pellet},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/U5LWNSGD}},
  note         = {Machine review of arXiv:2411.15754}
}

read the original abstract

We report the first spectral reflectance of tungsten carbide (WC) as potential solar selective absorber. We developed an optical measurement system for visible to mid-infrared spectroscopy, covering the range of 0.1 to 2.5 eV, to evaluate the solar selectivity. A polycrystalline WC was prepared using spark plasma sintering method. The measured spectral reflectance of WC exhibits a low-energy plasma excitation around 0.6 eV corresponding to the cutoff energy of sunlight, consistent with ab initio calculations, thus making it preferable for the solar selective absorber. We also discuss effects of the sample quality on the spectral reflectance.

Figures

Figures reproduced from arXiv: 2411.15754 by the authors.

**Figure 2.** Results for microcrystalline WC synthesized by the SPS method. (a) [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Microscopic images of (a) TiC (SPS), (b) TiC (HP), (c) TiN (SPS) and (d) TiN [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [4]

F. Cao, K. McEnaney, G. Chen, and Z. Ren, Energy Environ. Sci. 7, 1615-1627 (2014)

work page 2014

[2] [1]

Takashiri, T

M. Takashiri, T. Shirakawa, K. Miyazaki, and H. Tsukamoto, Journal of Alloys and Compounds 441, 246 (2007)

work page 2007

[3] [2]

Pfluger and J

J. Pfluger and J. Fink, Handbook of Optical Constants of Solids, edited by E. D. Palik (Academic Press, Burlington, 1997) REFERENCES 8 Supplementary Figure S 5: Relative integral intensity of the spectral reflectance R∗ in Eq. (9) as a function of the relative density ρ∗ in Eq. (8) of (a) TiC and (b) TiN. The blue squares indicate the experimental results...

work page 1997

[4] [3]

Bermel, Peter and Lee, Jeongwon and Joannopoulos, John D and Celanovic, Ivan and Soljaˇ ci´ c, Marin, Annual Review of Heat Transfer15, 299 (2012)

work page 2012

[5] [5]

Zhang, Jing and Wang, Chengbing and Shi, Jing and Wei, Dan and Zhao, Heng and Ma, Chuang, Advanced Energy and Sustainability Research3, 2100195 (2022)

work page 2022

[6] [6]

Gueymard, Solar Energy 71, 325-346 (2001)

Christian A. Gueymard, Solar Energy 71, 325-346 (2001). REFERENCES 9 Supplementary Figure S 6: XRD patterns of samples obtained with spark-plasma- sintering (SPS) and hot-press (HP) methods. Blue lines are observed data and red lines are database (NIST: 62979 for TiC and ICSD: 64904 for TiN): (a) TiC and (b) TiN

work page 2001

[7] [7]

Planck, Max, Annalen der Physik 309, 553-563 (1901)

work page 1901

[8] [8]

and Loomis, James and Bhatia, Bikram and Bierman, David M

Weinstein, Lee A. and Loomis, James and Bhatia, Bikram and Bierman, David M. and Wang, Evelyn N. and Chen, Gang, Chemical Reviews 115, 12797-12838 (2015)

work page 2015