Ferroelectricity and antiferroelectricity in the BaS-PbS system with the rocksalt structure

Alexander I. Lebedev

REVIEW 3 major objections 6 minor 36 references

Ferroelectricity and antiferroelectricity in the BaS-PbS system with the rocksalt structure

T0 review · 3 major / 6 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read Barium-induced stretching of Pb–S chains in rock-salt BaS–PbS produces ferroelectric, antiferroelectric, and mixed phases at nearly equal energies, according to first-principles calculations.

desk verdict Credible first-principles discovery of a new ferroelectric mechanism in rocksalt BaS–PbS, but the infinite-minima and nonergodicity claims outrun the evidence. read the letter →

arxiv 2607.25591 v1 pith:TH777I63 submitted 2026-07-28 cond-mat.mtrl-sci

Alexander I. Lebedev This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords ferroelectricityantiferroelectricityrocksaltstructurechain-structureinstabilityBaS-PbSsoftphononmodefirst-principlescalculationsnonergodicity

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

The paper aims to establish that the BaS–PbS system in the simple rock-salt structure is ferroelectric, even though neither BaS nor PbS is ferroelectric on its own. Using first-principles calculations, it shows that barium's larger ionic radius stretches the lattice and destabilizes transverse optical phonons in infinite –Pb–S–Pb–S– chains, so the chains polarize collectively. The same calculations reveal stable antiferroelectric and mixed ferroelectric–antiferroelectric phases whose energies are nearly identical to the ferroelectric phases, so the ground state is often not purely ferroelectric. A sympathetic reader would care because this would expand ferroelectricity to a common, simple crystal structure and imply a glass-like, multi-well energy landscape with many switchable polarization configurations.

What carries the argument

The load-bearing mechanism is the chain-structure instability of the transverse-optical phonon in infinite –Pb–S–Pb–S– chains running along the fourfold axes of the NaCl lattice. An optical phonon is a vibration in which different atoms move in opposite directions; here the unstable eigenvector consists of out-of-phase Pb and S displacements along a chain, so each chain develops a one-dimensional electric polarization. Adjacent chains interact weakly and with a sign that favors antiparallel alignment in BaS–PbS. This single mechanism explains the soft mode at the zone center, the instabilities at zone-boundary points, the existence of FE, AFE, and mixed phases, and the absence of the effect

What would settle it

Synthesize an ordered Ba3PbS4 sample and measure its low-temperature structure and dielectric response; if no polar or antipolar distortion appears near the estimated ~300 K transition and no polarization develops, the central claim fails. A simpler check is computational: recompute the phonon spectrum at the experimental lattice constant; if the zone-center TO mode is stable there, the predicted ferroelectricity is an artifact of the lattice underestimate.

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Extended reading notes

Core claim

The central claim is that ordered superstructures, [001] superlattices, a PbS quantum wire in a BaS matrix, and disordered Ba1−xPbxS solid solutions all show a soft transverse-optical phonon whose eigenvector displaces Pb and S atoms out of phase along linear –Pb–S–Pb–S– chains. The soft mode appears only when the structure is stretched by substituting larger Ba atoms; it is not caused by Pb off-centering, since the on-site force constant on Pb is positive. Condensing this mode yields ferroelectric phases with polarization up to roughly 0.15 C/m2, alongside antiferroelectric and mixed phases. The paper concludes that the near-degeneracy of these phases produces a multi-minimum potential with

Load-bearing premise

The prediction rests on the approximate density-functional phonon description being accurate at the true lattice constant: calculated lattice parameters are about 0.6% smaller than experiment, and the soft-mode frequency depends strongly on strain, so a modest error could erase the instability.

Editorial extensions

If this is right

Rock-salt chalcogenides can host ferroelectricity, expanding the known structural families of ferroelectrics beyond perovskites and IV–VI compounds.
In BaS–PbS, the ground state is frequently antiferroelectric or mixed FE+AFE; an applied electric field may switch between these near-degenerate states, producing behavior like the irreversible AFE-to-FE transition seen in NaNbO3.
The roughly 29 meV per molecule ferroelectric ordering energy in Ba3PbS4 suggests a Curie temperature on the order of 300 K, making room-temperature realizations plausible.
The same chain mechanism carries over to BaX–PbX with X = Se, Te and to quantum wires, but not to SrS–PbS or CaS–PbS, so the effect is tied to the larger Ba cation's tensile strain.
The near-degenerate infinite set of polarization patterns implies a multi-minimum potential, experimentally observable as nonergodic, history-dependent dielectric response at low temperatures.

Reading between the lines

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

As an extension of the chain mechanism, other rocksalt systems pairing a polarizable heavy cation with a larger cation that stretches the lattice could show the same instability; strontium or calcium would not, as the paper itself notes.
If the near-degenerate FE/AFE energies are real, compressive or tensile epitaxial strain should be able to flip the ground state from ferroelectric to antiferroelectric; this is a tunability lever the paper does not explicitly develop.
The predicted multi-minimum potential implies a distinctive experimental signature: frequency-dependent dielectric response and slow, history-dependent polarization relaxation at low temperatures, behavior typical of relaxor or dipole-glass states.
The quantum-wire result suggests one-dimensional ferroelectric elements can be embedded in a non-ferroelectric rock-salt matrix, which, if grown, would provide a direct nanoscale test of the chain mechanism.

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Signed reviews

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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

The bottom line: this is a credible first-principles discovery of a new ferroelectric mechanism in rocksalt chalcogenides, but the paper stretches the evidence when it talks about infinite minima and nonergodicity.

The genuinely new result is the prediction that BaS–PbS rocksalt superstructures and superlattices have soft TO phonons in linear –Pb–S–Pb–S– chains, leading to ferroelectric, antiferroelectric, and mixed chain orders. That is a real extension of the perovskite chain-instability idea to a different structural family, and the paper supports it with thoughtful checks: phonon spectra of the relaxed low-symmetry phases are positive, elastic constants are positive-definite, the instability tracks strained bulk PbS, the CuPt structure (which cannot host infinite Pb–S chains) is stable, and an isolated quantum wire also shows the instability. The link to Ba-induced tensile strain is well argued, and the on-site Pb force constant calculation reasonably rules out simple lone-pair off-centering. The methodology is standard and the numbers are internally consistent.

Where I would push back: the energy landscape is not as solid as the qualitative mechanism. The paper lists several phases with energy differences below 0.5 meV, and one superlattice, (BaS)1/(PbS)5, with a stabilization of 0.004 meV per molecule. Those numbers are below the likely accuracy of PBEsol, especially given the reported 0.6% underestimate of the lattice parameters. The authors themselves note that the task of finding the ground states in all studied structures is practically unsolvable, and that a dense mesh of wavevectors implies an infinite number of minima—that is an extrapolation, not a calculation. Zero-point motion and thermal fluctuations could easily wash out the shallowest minima. The claim of nonergodicity is suggestive but not demonstrated. I also miss input files or detailed convergence data; for a prediction of a new ferroelectric family, a functional-sensitivity test (e.g., SCAN or HSE on the key superstructures) would go a long way.

Overall: the central qualitative claim holds up well; the quantitative ground-state hierarchy and the speculative physics do not. A serious referee should engage with it, and the paper is worth publishing if the authors temper the overclaim and provide additional validation.

Referee Report

3 major / 6 minor

Summary. The paper reports first-principles DFT/DFPT calculations predicting ferroelectric (FE), antiferroelectric (AFE), and mixed FE-AFE instabilities in ordered superstructures, superlattices, quantum wires, and disordered solid solutions of the BaS-PbS system with the rocksalt structure. The instability is attributed to softening of transverse-optical phonons in linear -Pb-S-Pb-S- chains, driven by tensile strain from Ba substitution. The authors identify numerous low-energy phases with near-degenerate energies, propose a multi-minimum potential landscape, and suggest possible low-temperature nonergodicity. They also extend the prediction to selenide and telluride analogs.

Significance. If correct, the paper identifies a new family of ferroelectric/antiferroelectric materials in a simple rocksalt system, expanding the known structural classes beyond perovskites and IV-VI ferroelectrics. The work is methodologically solid: it uses standard DFPT, checks phonon and elastic stability, cross-validates against strained bulk PbS and prior FP-LAPW data, and provides parameter-free predictions (no fitted parameters, machine-checked stability criteria). The qualitative mechanism—chain-structure instability from Ba-induced tensile strain—is plausible and supported by the absence of instability in the CuPt structure where chains are broken. However, the quantitative claims of near-degenerate phases and an effectively infinite number of minima rest on energy differences of tens to hundreds of micro-electronvolts, which are at the limit of DFT accuracy, particularly with PBEsol's known lattice-parameter underestimate. The paper is a significant prediction but requires additional validation of the marginal phase stabilities before the strongest conclusions can be accepted.

major comments (3)

[§III.B, Table IV] The central claim of a multi-minimum potential relies on energy differences of 0.4 meV or less among the six phases listed in Table IV (e.g., Cmc21 at -29.85 meV vs R3m at -29.45 meV). PBEsol underestimates lattice constants by ~0.6% (Sec. II), and Fig. 6 shows the TO instability is strongly strain-dependent. A functional error of this magnitude could easily reorder these phases or eliminate the marginal ones (e.g., (BaS)1/(PbS)5 with -0.004 meV in Table II). The authors should provide an estimate of the numerical and functional uncertainty on these energy differences, and ideally test a subset of phases with a more accurate functional (e.g., HSE) or with experimental lattice constants. Without this, the specific ground-state assignments and the claim of 'virtually infinite' near-degenerate minima are not quantitatively robust.
[§III.B, last paragraph] The inference from a dense set of unstable q-points to 'a virtually infinite number of minima in the configuration space, separated by potential barriers' is a logical leap. A continuum of harmonic instabilities does not guarantee that each q vector yields a distinct metastable minimum; anharmonic couplings could merge them into a single soft valley or create only a few basins. The paper demonstrates several distinct minima but does not map the energy surface along different q vectors or compute barriers. The 'infinite minima' claim is central to the nonergodicity conclusion and should either be demonstrated by explicit calculations for several q vectors or clearly reframed as a speculative extrapolation.
[§III.C, Fig. 6] The strain sensitivity of the TO mode is used to support the mechanism, but it also highlights a vulnerability. PBEsol's 0.6% lattice-parameter underestimate means the calculations are performed at a slightly compressed state compared to experiment. For strongly unstable structures (e.g., Ba3PbS4, -29.45 meV), the instability is robust because stretching would deepen it. However, for marginal cases such as (BaS)1/(PbS)5 (-0.004 meV) or the 3BaS/7PbS SL (-0.161 meV), the instability could be an artifact of the underestimated lattice constant. The paper should either test these marginal structures at experimental lattice parameters or otherwise quantify the strain error margin. This is load-bearing because the purported coexistence of FE, AFE, and mixed phases at near-zero energy cost underpins the nonergodicity prediction.

minor comments (6)

[Abstract/Introduction] The abstract and conclusion emphasize 'discovered' phenomena; it would be clearer to say 'predicted' since no experimental confirmation is provided.
[Sec. II] Typo: 'calcualated' should be 'calculated'. Also, provide more detail on the pseudopotentials (e.g., valence-electron configurations) and convergence checks for k-point density and plane-wave cutoff.
[Table II] Several rows lack polarization values for some phases (e.g., 7BaS/1PbS Amm2, 3BaS/1PbS Amm2). Either fill these in or explicitly state they were not calculated; otherwise the table appears incomplete.
[Fig. 4] The figure has many data points from different structure types; using distinct symbols or a legend would improve readability. The 'quantum wire' point is mentioned in the text but not clearly identified in the figure.
[Sec. II / III.B] The disordered solid solutions are modeled with SQS8 and SQS16, but no supercell sizes or number of atoms are given. This information is essential for reproducibility.
[Sec. III.C] The on-site force constant for Pb is reported as +0.02290 Ha/Bohr^2 for one superstructure with 12.5% PbS. Providing the corresponding values for other compositions or for the selenide/telluride analogs would strengthen the conclusion that Pb is not off-center.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: first-principles prediction is self-contained; cited analogies are background, not inputs.

full rationale

The paper's central claim—that BaS–PbS rocksalt superstructures, superlattices, wires, and solid solutions develop ferroelectric/antiferroelectric instabilities via chain-like TO phonon softening—is derived ab initio from DFPT phonon calculations and total-energy relaxations in ABINIT. No parameter is fitted to the predicted energies or polarizations; the soft-mode mechanism is established from the eigenvectors of the unstable phonons (Sec. III-A: 'analysis of the character of atomic displacements in the eigenvectors of unstable modes reveals that the displacements occur in infinite –Pb–S–Pb–S– chains') and checked independently by an isolated Pb–S chain in a BaS matrix and by comparison with biaxially strained bulk PbS (Fig. 6). Citations to prior perovskite chain-instability work, including the author's own papers [27,28,32], are illustrative analogy, not a load-bearing premise: the conclusion rests on the paper's own phonon spectra and the positive on-site Pb force constant (Sec. III-C). The ~0.6% PBEsol lattice-parameter deviation and strain sensitivity are correctness/falsifiability risks, not circularity, because no target property is used as input. No equation reduces to a definition, and no fitted input is renamed as a prediction; the derivation chain is therefore self-contained.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

No free parameters are fitted; the paper is a standard first-principles DFT study. The main input assumptions are the choice of exchange-correlation functional, the harmonic-instability criterion, finite-size disorder models, and the transfer of the chain-instability concept from perovskites to rocksalt chalcogenides. The 'infinite number of minima' is a conceptual extrapolation, not a new physical entity.

assumptions (5)

domain assumption PBEsol DFT and ONCV pseudopotentials yield accurate enough lattice parameters and phonons to predict ferroelectric instabilities.
Section II: computed lattice parameters are 0.6% below experiment; all subsequent phonon and phase-stability predictions rely on this accuracy. If a more accurate functional shifts the soft-mode sign, the central claim would fail.
domain assumption Harmonic phonon instabilities in the paraelectric phase correspond to real ferroelectric/antiferroelectric distortions after relaxation.
Section III.A–B: instabilities are identified from DFPT spectra and then checked by relaxing phases and verifying positive phonons and positive-definite elastic moduli. The link between harmonic instability and actual ground states is an assumed standard criterion.
domain assumption SQS8 and SQS16 models capture the essential disorder of Ba1−xPbxS solid solutions.
Section II: calculations use special quasirandom structures with 8 and 16 atoms; finite-size and specific configuration effects are addressed only via four realizations, so the representation of random disorder is an assumption.
domain assumption The chain-structure instability mechanism from oxide perovskites applies to Pb–S chains in the rocksalt matrix.
Section III.B: the interpretation of unstable eigenvectors as chain displacements and the quantum-wire result support this, but the transfer of the mechanism from perovskites to rocksalt chalcogenides is an assumption, not a derived theorem.
ad hoc to paper A dense set of unstable q-points implies a virtually infinite number of metastable minima separated by barriers.
Section III.B final paragraphs: this extrapolates from a finite mesh of calculated q-points to a continuum and underlies the nonergodicity claim; it is not established by the calculations themselves.

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Cite this review

Pith. "Pith review of Ferroelectricity and antiferroelectricity in the BaS-PbS system with the rocksalt structure." pith.science (2026). https://pith.science/paper/TH777I63

@misc{pith2026260725591,
  author       = {Pith},
  title        = {Pith review of: Ferroelectricity and antiferroelectricity in the BaS-PbS system with the rocksalt structure},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TH777I63}},
  note         = {Machine review of arXiv:2607.25591}
}

read the original abstract

The ferroelectric instability in superstructures, superlattices, quantum wires, and disordered solid solutions in the BaS--PbS system with the NaCl structure has been discovered and investigated using first-principles calculations within the density functional theory. The emergence of ferroelectricity in these structures is associated with the instability of TO phonons in linear --Pb--S--Pb--S-- chains, which arises as a result of stretching of the structures upon the introduction of large barium atoms. Additionally, it has been discovered that, alongside ferroelectric phases, the structures also exhibit stable, competing antiferroelectric phases and those with a mixed ferroelectric--antiferroelectric ordering (ferroelectrically polarized one-dimensional Pb--S chains arranged in an ordered or disordered manner in the perpendicular direction). These phases often become the ground state of the studied systems. The closeness of the energies of the ferroelectric, antiferroelectric, and mixed states indicates the emergence of a multi-minimum potential with an infinite number of wells separated by potential barriers in the configuration space. This suggests a possible emergence of nonergodicity in the structures at low temperatures.

Figures

Figures reproduced from arXiv: 2607.25591 by the authors.

**Figure 2.** FIG. 2. Phonon spectrum of the Ba [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. Phonon spectrum of the (BaS) [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: FIG. 4. TO phonon frequencies in superstructures, superlat [PITH_FULL_IMAGE:figures/full_fig_p003_4.png]

**Figure 5.** Figure 5: FIG. 5. (001) section of the ground state structure for the [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]

**Figure 6.** Figure 6: FIG. 6. TO phonon frequency as a function of the lattice [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

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Reference graph

Works this paper leans on

36 extracted references

[1]

isolated

is characterized by the suppres- sion of the formation of two inﬁnite Pb–S chains along the z axis, as the Pb atoms are “isolated” from each other by BaS layers. However, two inﬁnite –Pb–S–Pb–S– chains remain in the structure in the x and y directions. The primitive cell of this superlattice, in the P 4/mmm phase, is constructed using the vectors (1/2,1/2...
[2]

E. F. Steigmeier and G. Harbeke, Soft phonon mode and ferroelectricity in GeTe, Solid State Commun. 8, 1275 (1970)

1970
[3]

Goldak, C

J. Goldak, C. S. Barrett, D. Innes, and W. Youdelis, Structure of α-GeTe, J. Chem. Phys. 44, 3323 (1966)

1966
[4]

is consistent with this explanation, as inﬁnite –Pb–S–Pb–S– chains cannot ex- ist in this structure. The conclusion about the chain- structure instability is further supported by the data ob- tained for an isolated inﬁnite chain of Pb–S atoms embed- ded in a BaS matrix, known as a quantum wire (green 4 TABLE I. Energies of distorted ferroelectric phases (...

1926
[5]

Iizumi, Y

M. Iizumi, Y. Hamaguchi, K. F. Komatsubara, and Y. Kato, Phase transition in SnTe with low carrier con- centration, J. Phys. Soc. Jap. 38, 443 (1975)

1975
[6]

K. L. I. Kobayashi, Y. Kato, Y. Katayama, and K. F. Ko- matsubara, Carrier-concentration-dependent phase tran- sition in SnTe, Phys. Rev. Lett. 37, 772 (1976)

1976
[7]

J. N. Bierly, L. Muldawer, and O. Beckman, The contin- uous rhombohedral–cubic transformation in GeTe-SnTe alloys, Acta Metall. 11, 447 (1963)

1963
[8]

Clarke, X-ray study of the structural phase transitio n in Sn xGe1−xTe, Phys

R. Clarke, X-ray study of the structural phase transitio n in Sn xGe1−xTe, Phys. Rev. B 18, 4920 (1978) . 10

1978

Show all 36 references

[9]

Jantsch, A

W. Jantsch, A. Lopez-Otero, and G. Bauer, Submillimetre spectroscopy of Pb 1−xGexTe, Infrared Phys. 18, 877 (1978)

1978
[10]

K. A. Abdullin and A. I. Lebedev, Inﬂuence of defects and impurities on the carrier scattering near the phase transition in ferroelectric semiconductor Pb 1−xGexTe, Fiz. Tverd. Tela 25, 3571 (1983)

1983
[11]

K. A. Abdullin, A. I. Lebedev, A. M. Gas’kov, V. N. Demin, and V. P. Zlomanov, Structural phase transition in the PbTe 1−xSx solid solution, JETP Lett. 40, 998 (1984)

1984
[12]

V. F. Kozlovskii, A. I. Lebedev, and Y. E. Petrov, X-ray and electrical studies of the phase transition in Pb1−xGexSe, Fiz. Tverd. Tela 28, 3610 (1986)

1986
[13]

A. I. Lebedev and I. A. Sluchinskaya, Possible appearan ce of a dipole-glass phase in solid solutions of IV-VI group semiconductors, JETP Lett. 46, 536 (1987)

1987
[14]

A. I. Lebedev and I. A. Sluchinskaya, Structural disorder and phase transition in Pb 1−xSnxTe1−ySey, Sov. Phys. Solid State 32, 1780 (1990)

1990
[15]

A. I. Lebedev and I. A. Sluchinskaya, Unusual phase transitions in Pb 1−xSnxTe1−ySey and Pb1−xSnxTe1−ySy crystals induced by Sn oﬀ-center ions, Ferroelectrics 143, 91 (1993)

1993
[16]

A. I. Lebedev and I. A. Sluchinskaya, Low-temperature phase transitions in some quaternary solid solutions of IV–VI semiconductors, J. Alloys Comp. 203, 51 (1994)

1994
[17]

Chattopadhyaya and R

S. Chattopadhyaya and R. Bhattacharjee, Theo- retical study of structural, electronic and op- tical properties of Ba xPb1−xS, Ba xPb1−xSe and BaxPb1−xTe ternary alloys using FP-LAPW approach, J. Alloys Comp. 694, 1348 (2017)

2017
[18]

C. Siﬁ, F. Chouit, H. Bendjeddou, H. Meradji, and S. Ghemid, Results of optical and thermal study of lead sulﬁde (PbS), barium sulﬁde (BaS) and their ternary (Pb 1−xBaxS) (0 ≤ x ≤ 1) alloys, Comput. Condens. Matter 21, e00398 (2019)

2019
[19]

Vennila, P

R. Vennila, P. Kamaraj, K. Rajeswari, G. Karthick, V. Hariharan, and V. Aroulmoji, Novel synthesis and characterization of barium doped lead sulphide nanopar- ticles by facile chemical precipitation method, Int. J. Adv. Sci. Eng. 3, 308 (2016)

2016
[20]

S.-H. Wei, L. G. Ferreira, J. E. Bernard, and A. Zunger, Electronic properties of random alloys: Special quasiran- dom structures, Phys. Rev. B 42, 9622 (1990)

1990
[21]

Gonze, B

X. Gonze, B. Amadon, P.-M. Anglade, J.-M. Beuken, F. Bottin, P. Boulanger, F. Bruneval, D. Caliste, R. Cara- cas, M. Cˆ ot´ e, T. Deutsch, L. Genovese, P. Ghosez, M. Gi- antomassi, S. Goedecker, D. R. Hamann, P. Hermet, F. Jollet, G. Jomard, S. Leroux, M. Mancini, S. Mazevet, ...

2009
[22]

D. R. Hamann, Optimized norm-conserving Vanderbilt pseudopotentials, Phys. Rev. B 88, 085117 (2013)

2013
[23]

J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vy- drov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the density-gradient expansion for exchange in solids and surfaces, Phys. Rev. Lett. 100, 136406 (2008)

2008
[24]

Gonze, J.-C

X. Gonze, J.-C. Charlier, D. Allan, and M. Teter, Inter- atomic force constants from ﬁrst principles: The case of α-quartz, Phys. Rev. B 50, 13035 (1994)

1994
[25]

Hellwege and A

K.-H. Hellwege and A. M. Hellwege, eds., Landolt-B¨ ornstein. Numerical data and functional relationships in scienc Vol. 6 (Springer-Verlag, 1971)

1971
[26]

Wu and R

Z. Wu and R. E. Cohen, More accurate gen- eralized gradient approximation for solids, Phys. Rev. B 73, 235116 (2006)

2006
[27]

Yu and H

R. Yu and H. Krakauer, First-principles deter- mination of chain-structure instability in KNbO 3, Phys. Rev. Lett. 74, 4067 (1995)

1995
[28]

Ghosez, X

P. Ghosez, X. Gonze, and J.-P. Michenaud, Ab initio phonon dispersion curves and interatomic force constants of barium titanate, Ferroelectrics 206–207, 205 (1998)

1998
[29]

A. I. Lebedev, Ground-state structure of KNbO3/KTaO3 superlattices: Array of nearly independent ferroelectrically ordered planes, Phys. Status Solidi B 249, 789 (2012)

2012
[30]

A. I. Lebedev, Properties of BaTiO 3/BaZrO3 fer- roelectric superlattices with competing instabilities, Phys. Solid State 55, 1198 (2013)

2013
[31]

H¨ uller, Displacement correlation and anomalous X-ray scattering in BaTiO 3, Solid State Commun

A. H¨ uller, Displacement correlation and anomalous X-ray scattering in BaTiO 3, Solid State Commun. 7, 589 (1969)

1969
[32]

N. L. Matsko, E. G. Maksimov, and S. V. Lep- eshkin, Peculiarities of the correlation func- tions, X-ray and neutron scattering in BaTiO 3, J. Exp. Theor. Phys. 115, 309 (2012)

2012
[33]

Zhang, L

M.-H. Zhang, L. Fulanovi´ c, S. Egert, H. Ding, P. B. Groszewicz, H.-J. Kleebe, L. Molina-Luna, and J. Ko- ruza, Electric-ﬁeld-induced antiferroelectric to ferro- electric phase transition in polycrystalline NaNbO 3, Acta Mater. 200, 127 (2020)

2020
[34]

A. I. Lebedev, Ab initio calculations of phonon spectra in atio 3 perovskite crystals (a = Ca, Sr, Ba, Ra, Cd, Zn, Mg, Ge, Sn, Pb), Phys. Solid State 51, 362 (2009)

2009
[35]

Hill, The elastic behaviour of a crystalline aggrega te, Proc

R. Hill, The elastic behaviour of a crystalline aggrega te, Proc. Phys. Soc. A 65, 349 (1952)

1952
[36]

Hao, L.-D

S. Hao, L.-D. Zhao, C.-Q. Chen, V. P. Dravid, M. G. Kanatzidis, and C. M. Wolverton, Theoretical predic- tion and experimental conﬁrmation of unusual ternary ordered semiconductor compounds in Sr–Pb–S system, J. Am. Chem. Soc. 136, 1628 (2014)

2014

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.

[1] [1]

isolated

is characterized by the suppres- sion of the formation of two inﬁnite Pb–S chains along the z axis, as the Pb atoms are “isolated” from each other by BaS layers. However, two inﬁnite –Pb–S–Pb–S– chains remain in the structure in the x and y directions. The primitive cell of this superlattice, in the P 4/mmm phase, is constructed using the vectors (1/2,1/2...

[2] [2]

E. F. Steigmeier and G. Harbeke, Soft phonon mode and ferroelectricity in GeTe, Solid State Commun. 8, 1275 (1970)

1970

[3] [3]

Goldak, C

J. Goldak, C. S. Barrett, D. Innes, and W. Youdelis, Structure of α-GeTe, J. Chem. Phys. 44, 3323 (1966)

1966

[4] [4]

is consistent with this explanation, as inﬁnite –Pb–S–Pb–S– chains cannot ex- ist in this structure. The conclusion about the chain- structure instability is further supported by the data ob- tained for an isolated inﬁnite chain of Pb–S atoms embed- ded in a BaS matrix, known as a quantum wire (green 4 TABLE I. Energies of distorted ferroelectric phases (...

1926

[5] [5]

Iizumi, Y

M. Iizumi, Y. Hamaguchi, K. F. Komatsubara, and Y. Kato, Phase transition in SnTe with low carrier con- centration, J. Phys. Soc. Jap. 38, 443 (1975)

1975

[6] [6]

K. L. I. Kobayashi, Y. Kato, Y. Katayama, and K. F. Ko- matsubara, Carrier-concentration-dependent phase tran- sition in SnTe, Phys. Rev. Lett. 37, 772 (1976)

1976

[7] [7]

J. N. Bierly, L. Muldawer, and O. Beckman, The contin- uous rhombohedral–cubic transformation in GeTe-SnTe alloys, Acta Metall. 11, 447 (1963)

1963

[8] [8]

Clarke, X-ray study of the structural phase transitio n in Sn xGe1−xTe, Phys

R. Clarke, X-ray study of the structural phase transitio n in Sn xGe1−xTe, Phys. Rev. B 18, 4920 (1978) . 10

1978