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arxiv: 2606.25930 · v1 · pith:24MONYZEnew · submitted 2026-06-24 · ❄️ cond-mat.mtrl-sci · physics.app-ph

Impact of sintering conditions on the dielectric properties of TiO2 ceramics for metamaterialsapplications at terahertz frequencies

Djihad Amina Djemmah , Delphine Gourdonnaud , Faycal Bouamrane , Jean-Francois Roux , Pierre-Marie Geffroy , Eric Akmansoy This is my paper

Pith reviewed 2026-06-25 20:09 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.app-ph
keywords TiO2sinteringdielectric propertiesterahertzmetamaterialsloss tangentpermittivityspark plasma sintering
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The pith

Optimized spark plasma sintering of TiO2 produces bulk pellets with permittivity 103 and loss tangent 0.006 at THz frequencies.

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

The paper establishes that the choice of sintering method and post-annealing step controls the dielectric response of TiO2 ceramics enough to meet the thresholds needed for all-dielectric metamaterials in the terahertz band. A reader would care because conventional high-permittivity ceramics usually carry losses too high for negative or near-zero effective index designs at these frequencies. The work compares conventional sintering against spark plasma sintering, adds an annealing step, and uses THz time-domain spectroscopy to show that one process route reaches epsilon approximately 100 while keeping the loss tangent below 0.02. These measured values are then fed into numerical designs of two-dimensional all-dielectric metamaterials that are predicted to exhibit the desired index behavior.

Core claim

By switching from conventional sintering to spark plasma sintering and adding a post-sintering anneal, the authors obtain TiO2 pellets whose relative permittivity reaches 103 and whose loss tangent falls to 0.006 when measured by THz time-domain spectroscopy. These values satisfy the criteria previously identified in simulations for realizing two-dimensional all-dielectric metamaterials that display negative or near-zero effective refractive index in the terahertz range.

What carries the argument

Comparison of conventional sintering versus spark plasma sintering, with and without post-annealing, followed by direct THz-TDS measurement of permittivity and loss tangent on the resulting bulk pellets.

If this is right

  • TiO2 processed by spark plasma sintering plus annealing meets the electromagnetic requirements for negative-index or near-zero-index all-dielectric metamaterials at terahertz frequencies.
  • The electromagnetic performance of bulk TiO2 is shown to be strongly process-dependent rather than fixed by the chemistry alone.
  • Numerical designs of 2D metamaterials become feasible once the measured loss tangent drops below 0.02 and permittivity sits near 100.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the same process window works for other high-permittivity oxides, a wider palette of low-loss THz dielectrics could become available without new chemistry.
  • The result suggests that any future metamaterial design using TiO2 should specify the exact sintering route rather than quoting literature values for the material.
  • Direct measurement of the metamaterial effective index on a test structure would be the next logical step to confirm the bulk-to-device mapping.

Load-bearing premise

The dielectric constants measured on millimeter-thick bulk pellets will be representative of the local material response inside the much smaller features of a fabricated two-dimensional metamaterial.

What would settle it

Fabricate one of the simulated 2D all-dielectric metamaterial geometries from the best TiO2 pellet material and measure its effective index; if the index remains positive and greater than 1 across the target band, the bulk-to-device translation does not hold.

Figures

Figures reproduced from arXiv: 2606.25930 by Delphine Gourdonnaud, Djihad Amina Djemmah, Eric Akmansoy, Faycal Bouamrane, Jean-Francois Roux, Pierre-Marie Geffroy.

Figure 1
Figure 1. Figure 1: Sketch of a 2D All Dielectric Metamaterial (ADM). It is a periodical structure, whose [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: SEM microphotographies of TiO2 samples sintered (a) by spark plasma sintering (SPS) at 1100 °C and (b) by conventional sintering at 1550 °C. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: XRD spectra of two TiO2 ceramics samples: (a) Conventionally sintered at TCS =1350 °C (CS sample), (b) Sintered by SPS at TS PS =1100 °C (SPS sample) compared to the rutile spectrum: the Miller indexes of the TiO2 rutile form are the blue marks [21]. 22 [PITH_FULL_IMAGE:figures/full_fig_p022_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Permittivity ε ′ of all the samples in function of their density: SPS samples in violet and CS samples in green. The vertical dotted line indicates the density of 0.9. 23 [PITH_FULL_IMAGE:figures/full_fig_p023_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Loss tangent (tan δ = ϵ ′′/ϵ′ ) in function of the permittivity ε ′ of all the samples at 0.3 THz: SPS samples in violet and CS samples in green. The horizontal dotted line indicates the threshold of loss tangent tan δ = 0.02. 24 [PITH_FULL_IMAGE:figures/full_fig_p024_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Dielectric function ε ∗ = ε ′ + ıε′′ of TiO2 sample 1.3 (see [PITH_FULL_IMAGE:figures/full_fig_p025_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Effective parameters (real and imaginary parts): permeability µe f f , permittivity εe f f and index ne f f from sample 1.3 (see [PITH_FULL_IMAGE:figures/full_fig_p026_7.png] view at source ↗
read the original abstract

Titanium dioxyde (TiO2) is a promising dielectric material for the realization of metamaterials operating in the terahertz (THz) range. Indeed, these necessitate a high permittivity and low loss material. In this paper, we compare the processes of fabrication and the results of characterisation of bulk TiO2 pellets. From the results of this characterization, we have numerically designed 2D all dielectric metamaterials (ADM) showing that they may exhibit negative or near-zero effective index. Our previous simulations show that the relative permittivity epsilon has to be around 100, while the loss tangent has to be lower than 0.02. We have thus compared conventional sintering (CS) vs spark plasma sintering (SPS), and investigated the effect of post-sintering annealing on the loss to satisfy these two criteria. The samples were characterized by THz Time Domain Spectroscopy (THz-TDS). One of the samples exhibits a loss tangent as low as 0.006, with a permittivity epsilon = 103. These results highlight the importance of the fabrication process on the EM properties of bulk TiO2, and demonstrate that it is a promising material for the development of metamaterial in the THz band.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper compares conventional sintering (CS) versus spark plasma sintering (SPS) of TiO2, with and without post-sintering annealing, and reports THz-TDS measurements on the resulting bulk pellets. One sample reaches ε = 103 and tanδ = 0.006. The authors state that these values satisfy thresholds from their prior simulations (ε ≈ 100, tanδ < 0.02) and that numerical designs of 2D all-dielectric metamaterials performed from the characterization results can exhibit negative or near-zero effective index.

Significance. If the bulk dielectric values translate directly to the metamaterial unit-cell performance, the work supplies a concrete fabrication route for high-permittivity, low-loss TiO2 ceramics and quantifies how sintering conditions control the electromagnetic response at THz frequencies.

major comments (2)
  1. [Abstract] Abstract: the statement that numerical designs were performed “from the results of this characterization” does not indicate whether the full frequency-dependent ε(ω) and tanδ(ω) spectra measured by THz-TDS were inserted into the 2D ADM unit-cell simulations or whether single-frequency constants were used; without this information the claim that the designs exhibit negative or near-zero index cannot be evaluated.
  2. [Numerical design section (inferred from abstract)] The manuscript provides no sensitivity study or geometry-specific validation showing that the homogeneous bulk pellet values remain valid when placed inside the 2D metamaterial lattice; possible additional scattering, grain-boundary losses, or effective anisotropy introduced by the metamaterial geometry are not addressed, yet these directly affect whether the effective index reaches the claimed regime.
minor comments (2)
  1. [Abstract] Abstract contains the spelling “dioxyde” instead of “dioxide”.
  2. [Results] The abstract reports specific numerical results (ε = 103, tanδ = 0.006) but the provided text contains no accompanying figures, error bars, or reproducibility details; these should be supplied in the results section for the central experimental claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive comments. We address each major point below and indicate the revisions we will make to improve clarity and address the concerns raised.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the statement that numerical designs were performed “from the results of this characterization” does not indicate whether the full frequency-dependent ε(ω) and tanδ(ω) spectra measured by THz-TDS were inserted into the 2D ADM unit-cell simulations or whether single-frequency constants were used; without this information the claim that the designs exhibit negative or near-zero index cannot be evaluated.

    Authors: We agree the abstract is ambiguous on this point. The numerical designs used the measured permittivity (ε ≈ 103) and loss tangent (tanδ = 0.006) values at the target THz frequencies of interest, taken directly from the THz-TDS data at those frequencies rather than the full broadband spectra. These single-frequency constants were inserted into the 2D unit-cell simulations to demonstrate that the material properties satisfy the thresholds from our prior work and can yield negative or near-zero effective index. We will revise the abstract and add an explicit statement in the numerical design section clarifying the use of frequency-specific constants from the characterization. revision: yes

  2. Referee: [Numerical design section (inferred from abstract)] The manuscript provides no sensitivity study or geometry-specific validation showing that the homogeneous bulk pellet values remain valid when placed inside the 2D metamaterial lattice; possible additional scattering, grain-boundary losses, or effective anisotropy introduced by the metamaterial geometry are not addressed, yet these directly affect whether the effective index reaches the claimed regime.

    Authors: The referee is correct that the manuscript does not include a sensitivity study or explicit validation of how bulk properties translate to the metamaterial lattice. The numerical designs are illustrative, using the measured bulk values as homogeneous inputs to show the potential for negative or near-zero index under the assumptions of our prior simulations. The focus of the present work is the fabrication process and bulk characterization; geometry-specific effects such as scattering or anisotropy are outside the current scope. We will add a brief discussion paragraph acknowledging these assumptions and noting that future work will address lattice-specific validation. revision: partial

Circularity Check

0 steps flagged

No circularity: experimental characterization with independent measurements

full rationale

The paper reports fabrication processes (CS vs SPS, annealing), THz-TDS measurements on bulk pellets, and resulting values (ε=103, tanδ=0.006). It references prior simulations only to motivate target thresholds (ε≈100, tanδ<0.02) before stating that the measured samples meet them. No equations, fitted parameters, predictions, or derivations appear in the provided text; the central claims are direct experimental outcomes. The link to metamaterial performance is an application claim resting on external benchmarks, not a self-referential reduction within this work. This is a standard experimental materials study with no load-bearing circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The work relies on standard experimental methods in materials science and electromagnetic characterization; no free parameters, ad hoc axioms, or new entities are introduced.

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Reference graph

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