{"id":"71558530-35c8-4bbc-a5ba-7a3f45ad4e80","arxiv_id":"2608.03903","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Sound velocities from DFPT phonons, processed through a continuum elasticity model, recover TaAs's six elastic constants in agreement with prior DFT calculations.","lead":"This paper derives all six elastic constants of the Weyl semimetal TaAs from sound velocities read off quantum-mechanical phonon calculations, instead of the usual strain-stress method. The resulting values match earlier calculations, and the authors argue the phonon route is cheaper and links better to light-scattering experiments.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Untested convergence of acoustic fits: symmetry-equivalent C44 velocities differ by ~25%, so the averaging in Eq. (4) may conceal a window-dependent bias that propagates into C12 and C13.","rationale":"Both the reader and I identify the same load-bearing concern: the sound velocities are extracted without a stated q-window and without evidence that the fitted slopes are converged in the q→0 limit. The strongest evidence is internal: the three symmetry-equivalent velocities that should give the same C44 differ by roughly 25%, which contradicts the expectation that DFPT acoustic slopes at small q are already in the elastic regime. If this spread reflects numerical dispersion rather than random noise, Eq. (4)'s average is not a valid estimator. The paper even acknowledges this in the conclusion ('can be affected by numerical dispersion') and in Appendix B ('resultant expressions are not unique'). The separate typo in Eq. (3) (extra C44) is real but fixable and does not change the physics; it is a transcription error, not a structural flaw. The central claim—that the full stiffness tensor can be obtained accurately from phonon velocities—therefore rests on an untested convergence premise. A q-window convergence test would settle it. I do not see a reason to depart from the reader's CONDITIONAL verdict; the concern is precisely what makes acceptance conditional. The paper has supporting merits: the phonon spectra, the SOC-inclusive DFPT, and agreement for several moduli are positive; but the unresolved velocity bias affects the most method-critical outputs (C12, C13).","tokens_in":16330,"tokens_out":7103,"duration_ms":65136,"concrete_test":"Perform a q-window convergence study for the PBE phonon calculation: recompute the acoustic branches along [001], [100], [110], and [101] at q-points |q| = 0.01, 0.02, 0.04, 0.08, 0.12, 0.16 (fractional units) and fit each branch linearly over nested windows q ≤ q_max for each q_max. If the three C44-equivalent velocities (v_z,t1, v_x,t1, v_xy,t2) do not converge to a common value within, say, 2% as q_max→0, the averaging in Eq. (4) is unjustified and the derived Cij, especially C12 and C13, are not reliable. As a cross-check, compare the phonon-derived C11, C33, C12, C13 against finite-strain stress-strain values obtained at several strain amplitudes (e.g., ±0.5%, ±1%, ±2%) with error bars; the central claim fails if the phonon values fall outside the strain-derived uncertainty.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim depends on treating the linear fits in Fig. 5 as true q→0 sound velocities. The fitting window is never given, and the three velocities that should all equal sqrt(C44/ρ) disagree far beyond noise: from Table III (PBE), v_z,t1=2.57, v_x,t1=2.95, v_xy,t2=2.86 km/s, implying C44 values of roughly 80, 106, and 99 GPa respectively. Eq. (4) averages these to 95 GPa, but averaging removes scatter, not a systematic bias. If the q-window is not deep in the linear region (or is contaminated by optical branches), each extracted velocity is biased; the differences of squared velocities in Eqs. (2)-(3) then amplify that bias, which naturally explains why C12 and C13 deviate ~20% from literature. Agreement for C11, C33, and C66 does not validate the converged q→0 limit, since those constants come from single velocities that are less sensitive to the same bias. The paper's own conclusion admits 'numerical dispersion in the extracted sound velocities,' so this is an acknowledged, untested premise.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper combines DFPT phonon calculations (PBE and PBEsol, with SOC) with a continuum elasticity model to extract the six independent elastic constants of body-centered tetragonal TaAs from acoustic sound velocities near the Γ point. The authors report C11=272.26, C33=250.53, C12=122.08, C13=102.76, C44=95.00, C66=184.60 GPa at the PBE level, compare these with earlier DFT values, and derive polycrystalline bulk, shear, and Young moduli and Poisson's ratio. The intended contribution is a shear-free, phonon-based route to the full stiffness tensor.","tokens_in":16469,"tokens_out":8605,"duration_ms":80763,"significance":"The methodological core is standard and potentially useful: DFPT acoustic branches in the long-wavelength limit are connected to elastic coefficients through the Christoffel equations, and the paper avoids explicit shear strains. The use of two functionals (PBE, PBEsol) and the comparison with an experimental sound velocity for v_xy,t2 are positives. The extraction is not circular: no parameter is fitted to the target elastic constants, and the underlying relations are textbook elasticity. However, the current manuscript contains a wrong printed formula for C13, an internally inconsistent Poisson ratio in Table V, and no convergence or uncertainty analysis for the linear fits that feed all extracted constants. These issues are load-bearing for the central claim, so the paper cannot be accepted in its present form.","major_comments":[{"comment":"Eq. (3) is not the expression for C13 as written. Combining the diagonalization results in Eq. (B16), ρ(v_xz,l^2 − v_xz,t1^2) = Δ2/2, and the square root in Eq. (3) reduces to (C13 + C44)/ρ, not C13/ρ. A numerical check with the PBE velocities in Table III gives a value of approximately 198 GPa for the square-root term; subtracting C44 = 95 GPa gives about 103 GPa, matching the reported C13. The printed formula is therefore missing a '− C44' term and must be corrected, or the derivation in Appendix B must be revised to justify the expression actually used.","section":"§II.B, Eq. (3) and Appendix B"},{"comment":"The reported Poisson ratio ν = 0.497 is inconsistent with the same table's B and E values. Using Eq. (13) with the PBE rows, B = 160.75 GPa and E = 250.33 GPa gives ν = (3B−E)/(6B) ≈ 0.240, not 0.497. The literature-average values in Table V give ν ≈ 0.277, not 0.4975. This is not a small typo: the cited B/G ratios around 1.6–1.9 correspond to ν ≈ 0.24–0.28, so the brittle/malleable and Poisson-ratio discussion built on ν ≈ 0.497 is invalid. The entire set of derived quantities in Table V must be recomputed and cross-checked.","section":"§III.C, Table V"},{"comment":"The linear-fit window for extracting sound velocities is never specified. This is a substantive issue, not just a presentation gap. The three transverse velocities that should all equal sqrt(C44/ρ) differ by about 25%: v_z,t1 = 2.57, v_x,t1 = 2.95, v_xy,t2 = 2.86 km/s imply C44 values of roughly 80, 106, and 99 GPa. Eq. (4) averages these, but averaging removes scatter only if the deviations are random; if the deviations are a window-dependent numerical dispersion, the bias propagates into C12 and C13, which already deviate about 20% from literature. The conclusion acknowledges 'numerical dispersion in the extracted sound velocities.' A convergence test over the fitting window and q-point sampling is required to support the quantitative claim.","section":"§II.B and §III.B"},{"comment":"None of the present results carry error bars or uncertainty estimates. Given the 25% spread among symmetry-equivalent velocities, reporting Cij to five significant figures without uncertainties prevents a meaningful quantitative comparison with the literature. The authors should propagate uncertainties from the linear fits and, ideally, from the finite q-grid, at least for the constants that rely on differences or averages (C12, C13, C44).","section":"Tables III–V"}],"minor_comments":[{"comment":"The eigenvalue equation writes (M(q) − ρω) Δx(q,ω) = 0, but the preceding text uses ρω². The dispersion relation below then refers to ρω_α(q), which should be ρω_α²(q). This appears to be a typographical slip, but it is confusing in a derivation-heavy appendix.","section":"Appendix B, Eq. (B11)"},{"comment":"The last term is printed as '+ C^2_33 ∂^2_z'; it should be '+ C33 ∂^2_z' (no square), consistent with the dynamical matrix in Eq. (B12).","section":"Appendix B, Eq. (B10)"},{"comment":"The text says 'we compute the sound velocities from DFTP'; this should read 'DFPT'. In the same paragraph, 'our comparison relays only' should be 'relies only.'","section":"§III.C"},{"comment":"The phrase 'elastic propertied' should be 'elastic properties.'","section":"Appendix A"},{"comment":"The statement that all sound-velocity deviations are 'below 10^{-1}' is vague; the maximum relative deviation should be stated explicitly, and the individual deviations are better shown in a table or figure.","section":"§III.B"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses a topic appropriate for a condensed-matter/materials journal, and the underlying DFPT-based approach is plausible. However, the combination of a wrong printed formula for C13 and an internally inconsistent Table V suggests the manuscript has not been carefully checked. The acoustic-fit convergence issue is the main scientific concern and should be addressed by a sensitivity analysis before acceptance. If the authors supply corrected formulas, recomputed derived quantities, and convergence tests with uncertainties, the paper could be acceptable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"I've read the TaAs phonon-elastic paper. The short version: it's a competent application of the classic method—extract sound velocities from acoustic branches, plug into continuum-model formulas—to TaAs with SOC-inclusive DFPT phonons. The linear-response phonon spectrum is the main new calculation, and it matches earlier phonon data and the one measured sound velocity (2.8 km/s for v_xy,t2) nicely. The method does avoid shear strains and Pulay stress, which is a real practical advantage for this material class. The paper is clearly written and honest about its own weaknesses, which I appreciate.\n\nBut there are three soft spots, in increasing order of importance. First, Eq. (3) as printed gives C13 + C44, not C13. The table values only make sense if the authors actually subtracted C44, so it's a transcription error, but it has to be fixed—a referee would catch it immediately. Second, the fitting window for the acoustic modes is never specified. That's not a minor detail; the whole extraction rests on these slopes. Third, and this is the load-bearing concern: the three velocities that should all yield C44 disagree by more than 10% (PBE: v_z,t1=2.57, v_x,t1=2.95, v_xy,t2=2.86 km/s, giving C44 estimates of ~80, 106, and 99 GPa). Eq. (4) averages them to 95 GPa, but averaging removes scatter, not systematic bias. If the q-window is not deep in the linear regime, every derived Cij is biased, and the differences of squares in Eqs. (2)-(3) amplify that bias. That naturally explains why C12 and C13 deviate ~20% from the literature while the single-velocity constants look fine. No error bars are given, so the percent-level claims are unverifiable. The paper's own conclusion admits the method can be affected by numerical dispersion—that's candid, but it doesn't quantify the effect.\n\nThe physics is plausible and the numbers do land near prior work, so I wouldn't reject the paper. But it needs revision: fix Eq. (3), specify the fit window, show error bars on the velocities, and discuss the scatter among symmetry-equivalent modes. The derived B/G ratio flipping from brittle to malleable compared to literature is a symptom of the C12/C13 sensitivity and should be addressed.\n\nThis is a methods demonstration paper, not a new discovery—the elastic constants of TaAs are already in the cited literature. It's useful for people who want SOC-inclusive phonon data for TaAs and a concrete example of this inversion, but it doesn't change the field. The citation pattern is fine; I don't see a self-citation problem.\n\nI'd send it to peer review with a request for major revision on the points above. It deserves referee time, but not as is.","headline":"A solid, clearly-written methods paper that reproduces known elastic constants for TaAs via a standard phonon-to-elastic inversion; the main issues are an equation typo, an unspecified fitting window, and scatter among symmetry-equivalent velocities that is averaged over without error bars.","tokens_in":17119,"tokens_out":4508,"would_cite":false,"duration_ms":38563,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Sound speeds yield all six elastic constants of the Weyl semimetal TaAs","keywords":["Weyl semimetal","TaAs","elastic constants","phonon dispersion","sound velocity","density functional perturbation theory","spin-orbit coupling","continuum elasticity"],"falsifier":"Recompute the acoustic branches with a much denser q-mesh and shrink the fitting window toward the Γ point; if the three velocities that should all give C44 (from v_z,t1, v_x,t1, and v_xy,t2) do not converge to a single value, then the Eq. (4) average is hiding a systematic error that propagates into every derived elastic modulus.","tokens_in":16090,"feed_emoji":"🌊","tokens_out":5716,"duration_ms":56769,"temperature":0.7,"pith_summary":"This paper tries to establish that the complete set of six independent elastic coefficients of TaAs can be obtained from the low-frequency acoustic phonon branches, without applying any shear stress. Using DFPT phonon spectra that include spin-orbit coupling, the authors extract sound velocities along high-symmetry directions and invert the elastic dynamical matrix for a body-centered tetragonal crystal. The resulting moduli agree with prior DFT calculations to within about 10% for most coefficients, with larger deviations of roughly 20% for the off-diagonal couplings C12 and C13. From these coefficients they derive bulk, shear, and Young's moduli, plus a Poisson ratio near 0.497. This matters because direct experimental elastic constants for TaAs are still missing, and the phonon route offers a check against Raman and Brillouin scattering experiments.","feed_headline":"Sound speeds yield all six elastic constants of TaAs","feed_subtitle":"No shear strain needed: acoustic-phonon fits match prior DFT values and anchor future experiments.","key_machinery":"The central object is the C4v elastic dynamical matrix M(q) for the body-centered tetragonal lattice, built from the six Voigt stiffness coefficients. Diagonalizing this matrix along [001], [100], [110], and [101] yields relations (B13)–(B16) between sound velocities and elastic moduli, an overdetermined system that the paper inverts to express each Cij in terms of measured phonon slopes. The non-obvious piece is the definition of C44 as an average of three transverse velocities (z,t1; x,t1; xy,t2) that should be equal by symmetry but differ in the computed spectrum; the average is introduced to suppress numerical dispersion.","core_discovery":"On its own terms, the paper claims that sound velocities fitted from the acoustic branches near the Γ point are sufficient data to fix all six independent elastic stiffness coefficients of body-centered tetragonal TaAs. The PBE phonon-derived set is C11 = 272.26 GPa, C33 = 250.53 GPa, C12 = 122.08 GPa, C13 = 102.76 GPa, C44 = 95.00 GPa, C66 = 184.60 GPa, with PBEsol values somewhat higher; all satisfy the mechanical stability criteria. The claim is not that these values are exact, but that they reproduce prior first-principles elastic constants within about 10% for most coefficients, that the derived bulk, shear, Young's moduli, and Poisson ratio follow consistently, and that the method work","pith_inferences":["If the phonon-slope inversion is as transferable as the paper suggests, it should apply to the isostructural Weyl semimetals TaP, NbAs, and NbP, whose elastic constants are also experimentally unmeasured; a multi-material test would sharpen the comparison.","The near-10% agreement with prior DFT values does not by itself validate the method, because prior DFT shear calculations share the same exchange-correlation functional and similar pseudopotential errors; the decisive test is experimental sound-velocity input.","The very high Poisson ratio near 0.497 is extremely sensitive to C12 and C13, the two coefficients with the largest deviations; it should be read as a derived quantity whose accuracy is contingent on pinning down those off-diagonal couplings."],"forward_implications":["The full stiffness tensor of TaAs is obtained without applying shear strain, avoiding large supercells and Pulay stress corrections tied to shear deformations.","The six derived moduli satisfy the tetragonal mechanical stability criteria, confirming linear-elastic stability of TaAs.","The derived polycrystalline descriptors place TaAs near the brittle–malleable boundary on the B/G criterion and give a Poisson ratio close to the central-force upper bound of 0.5.","The same phonon-based inversion provides a direct comparison point for Raman, Brillouin–Mandelstam, and ultrafast X-ray measurements of acoustic modes in Weyl semimetals.","Because the velocity–modulus system is overdetermined, the method carries internal consistency checks: discrepancies among symmetry-equivalent velocities flag which acoustic branches are least reliable."],"supporting_citations":[{"why":"Supplies prior DFT bulk elastic, structural, and dielectric properties of TaAs used as the main comparison target for the derived elastic moduli.","marker":"[57]"},{"why":"Supplies comparative first-principles structural, elastic, and thermodynamic data for TaAs that the present values are checked against.","marker":"[60]"},{"why":"Applies a similar elastic model but computes elastic constants via DFT and sound velocities from them, the inverse of the present procedure.","marker":"[61]"},{"why":"Provides another set of first-principles elastic constants for the Weyl MX family used in the literature comparison.","marker":"[62]"},{"why":"Provides the experimental field-angle sound-velocity measurement along [110] used to benchmark the computed v_xy,t2 value.","marker":"[29]"},{"why":"Supplies experimental Raman optical-phonon frequencies and averaged DFT values against which the Γ-point phonons are compared.","marker":"[39]"},{"why":"Supplies the density functional perturbation theory framework used to compute the phonon dispersions from which sound velocities are extracted.","marker":"[69]"},{"why":"Supplies the implementation of DFPT with spin-orbit coupling that the phonon calculations rely on.","marker":"[70]"},{"why":"Supplies Voigt notation and the point-group reduction that restricts the elasticity tensor to six independent coefficients for C4v symmetry.","marker":"[71]"}],"fun_headline_variants":["Sound waves pin all six TaAs elastic constants","No shear strain needed: phonons give TaAs elasticity","Phonon sound speeds replace strain supercells in TaAs","Acoustic phonons reveal all six elastic constants of TaAs"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The slopes of the acoustic phonon branches near zero wave vector are treated as unbiased sound speeds, so the scatter among symmetry-equivalent branches is harmless numerical dispersion that averaging removes rather than a systematic bias from the fitting window.","fun_headline_variants_meta":{"raw":{"variants":["Sound waves pin all six TaAs elastic constants","No shear strain needed: phonons give TaAs elasticity","Phonon sound speeds replace strain supercells in TaAs","Acoustic phonons reveal all six elastic constants of TaAs"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000762,"raw_usage":{"total_tokens":3209,"prompt_tokens":723,"completion_tokens":2486,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":467,"completion_tokens_details":{"reasoning_tokens":2419}},"tokens_in":467,"tokens_out":2486,"duration_ms":17832,"temperature":1.0,"reasoning_tokens":2419,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T05:57:21.618794+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the acoustic branches with a much denser q-mesh and shrink the fitting window toward the Γ point; if the three velocities that should all give C44 (from v_z,t1, v_x,t1, and v_xy,t2) do not converge to a single value, then the Eq. (4) average is hiding a systematic error that propagates into every derived elastic modulus.","supporting_citations":[{"cited_title":"Buckeridge, D","cited_arxiv_id":null,"evidence_quote":"Supplies prior DFT bulk elastic, structural, and dielectric properties of TaAs used as the main comparison target for the derived elastic moduli."},{"cited_title":"Liu, Z.-Q","cited_arxiv_id":null,"evidence_quote":"Supplies comparative first-principles structural, elastic, and thermodynamic data for TaAs that the present values are checked against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Applies a similar elastic model but computes elastic constants via DFT and sound velocities from them, the inverse of the present procedure."},{"cited_title":"Ullah, S","cited_arxiv_id":null,"evidence_quote":"Provides another set of first-principles elastic constants for the Weyl MX family used in the literature comparison."},{"cited_title":"Lalibert´ e, F","cited_arxiv_id":null,"evidence_quote":"Provides the experimental field-angle sound-velocity measurement along [110] used to benchmark the computed v_xy,t2 value."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies experimental Raman optical-phonon frequencies and averaged DFT values against which the Γ-point phonons are compared."},{"cited_title":"Urru and A","cited_arxiv_id":null,"evidence_quote":"Supplies the implementation of DFPT with spin-orbit coupling that the phonon calculations rely on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies Voigt notation and the point-group reduction that restricts the elasticity tensor to six independent coefficients for C4v symmetry."}],"review_version":1}