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arxiv: 2606.22654 · v1 · pith:XKUYVQTXnew · submitted 2026-06-21 · ❄️ cond-mat.mtrl-sci · physics.app-ph

Pyroelectric, electrocaloric and thermoelectric properties of core-shell HfxZr1-xO2 nanoparticles: theory and experiment

Anna N. Morozovska , Oleksandr S. Pylypchuk , Nicholas V. Morozovsky , Eugene A. Eliseev , Dean R. Evans This is my paper

Pith reviewed 2026-06-26 09:40 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.app-ph
keywords hafnia-zirconia nanoparticlespyroelectric propertieselectrocaloric effectthermoelectric propertiescore-shell nanoparticlesLandau-Ginzburg-Devonshire theorypressed nanopowders
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The pith

The temperature dependence of accumulated charge in pressed Hf0.5Zr0.5O2 nanoparticle powders matches the calculated polarization and pyroelectric coefficient from a core-shell model.

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

The paper analyzes pyroelectric and electrocaloric properties of spherical core-shell HfxZr1-xO2 nanoparticles using a Landau-Ginzburg-Devonshire free energy functional that includes trilinear and biquadratic couplings between polar, nonpolar, and antipolar order parameters. It complements the calculations with experiments that track the electric charge accumulated in pressed powders of oxygen-deficient 7 nm Hf0.5Zr0.5O2 particles as temperature changes. The measured charge and its temperature derivative follow the same qualitative pattern as the model's polarization and pyroelectric coefficient, which the authors interpret as support for using these nanoparticles in CMOS-compatible pyroelectric, electrocaloric, and thermoelectric devices.

Core claim

Calculations based on the Landau-Ginzburg-Devonshire functional with trilinear and biquadratic couplings predict the polarization and pyroelectric coefficient of an ensemble of densely packed spherical core-shell HfxZr1-xO2 nanoparticles; experimental measurements of accumulated charge versus temperature in pressed Hf0.5Zr0.5O2 nanopowders are in qualitative agreement with those predictions.

What carries the argument

The Landau-Ginzburg-Devonshire free energy functional incorporating trilinear and biquadratic couplings of polar, nonpolar, and antipolar order parameters, applied to an ensemble of spherical core-shell nanoparticles.

If this is right

  • The nanoparticles can serve as CMOS-compatible building blocks for pyroelectric sensors and energy harvesters.
  • The same core-shell geometry and coupling terms can be used to design electrocaloric cooling elements.
  • Thermoelectric figures of merit may be estimated from the same polarization and coupling parameters.
  • Densely packed powders can replace thin films in some device architectures without loss of the essential temperature response.

Where Pith is reading between the lines

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

  • If the qualitative match holds under quantitative scrutiny, nanoparticle size and oxygen deficiency could be tuned to shift the peak pyroelectric response to desired operating temperatures.
  • The model framework could be adapted to predict how shell thickness or core composition alters the electrocaloric temperature change under applied fields.
  • Similar charge-accumulation experiments on other hafnia-based compositions might test whether the antipolar order parameter remains essential outside the x=0.5 case.

Load-bearing premise

The trilinear and biquadratic couplings together with the core-shell geometry correctly capture the nanoparticles' polarization behavior.

What would settle it

Direct measurement of the pyroelectric coefficient in the same nanoparticle ensemble that shows a temperature dependence qualitatively different from the calculated curve.

read the original abstract

Nanosized hafnia-zirconia (HfxZr1-xO2) in the form of thin films, multilayers, and nanoparticles are indispensable CMOS-compatible ferroelectric materials for advanced electronic memories and logic devices. Using the Landau-Ginzburg-Devonshire free energy functional with trilinear and biquadratic couplings of polar, nonpolar, and antipolar order parameters, we analyze the pyroelectric and electrocaloric properties of an ensemble of spherical core-shell HfxZr1-xO2 nanoparticles. Complementary to theoretical calculations, we experimentally measure the temperature dependence of the electric charge accumulated in pressed powders consisting of oxygen-deficient Hf0.5Zr0.5O2 nanoparticles with an average size of 7 nm. The observed temperature-dependent behavior of the accumulated charge and its derivative with respect to temperature are in qualitative agreement with the dependences of polarization and pyroelectric coefficient calculated for the ensemble of densely packed spherical core-shell HfxZr1-xO2 nanoparticles. Thus, these results can open the way for creation of CMOS-compatible HfxZr1-xO2 nanoparticles for pyroelectric, electrocaloric, and thermoelectric applications.

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

3 major / 1 minor

Summary. The manuscript develops a Landau-Ginzburg-Devonshire model with trilinear and biquadratic couplings between polar, nonpolar, and antipolar order parameters to compute the pyroelectric, electrocaloric, and thermoelectric properties of an ensemble of spherical core-shell HfxZr1-xO2 nanoparticles. Complementary experiments measure the temperature dependence of accumulated electric charge in pressed powders of oxygen-deficient Hf0.5Zr0.5O2 nanoparticles (average size 7 nm), with the abstract claiming qualitative agreement between the measured charge and dQ/dT and the model's polarization and pyroelectric coefficient.

Significance. If the model assumptions hold and the agreement can be made quantitative, the combined theoretical-experimental approach could support applications of CMOS-compatible hafnia-zirconia nanoparticles in pyroelectric and electrocaloric devices. The explicit use of a multi-order-parameter LGD functional and the direct comparison to nanoparticle powder data are positive features.

major comments (3)
  1. [Abstract (theoretical approach paragraph)] Abstract (paragraph describing the theoretical approach): the trilinear and biquadratic couplings between polar, nonpolar, and antipolar order parameters are introduced without derivation from first-principles calculations or constraint by independent measurements on the same 7 nm oxygen-deficient particles; this choice directly determines the computed temperature dependences of polarization and pyroelectric coefficient that are compared to experiment.
  2. [Abstract (experimental and comparison statements)] Abstract (experimental and comparison statements): the central claim rests on 'qualitative agreement' between measured accumulated charge curves and model predictions, yet no quantitative metrics (e.g., correlation coefficient, RMS deviation), error bars on the charge data, or details on how model parameters were selected or fitted are provided, leaving the strength of support modest.
  3. [Theoretical model versus experimental description] Theoretical model versus experimental description: oxygen deficiency is explicitly noted for the measured Hf0.5Zr0.5O2 nanoparticles but is not incorporated into the order-parameter description or the core-shell geometry of the LGD functional, creating a potential mismatch between the system modeled and the system measured.
minor comments (1)
  1. [Abstract] The abstract could usefully specify the range of x values examined in the theoretical calculations for HfxZr1-xO2.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment point by point below, proposing revisions to improve clarity and strengthen the presentation where appropriate.

read point-by-point responses

  1. Referee: [Abstract (theoretical approach paragraph)] Abstract (paragraph describing the theoretical approach): the trilinear and biquadratic couplings between polar, nonpolar, and antipolar order parameters are introduced without derivation from first-principles calculations or constraint by independent measurements on the same 7 nm oxygen-deficient particles; this choice directly determines the computed temperature dependences of polarization and pyroelectric coefficient that are compared to experiment.

    Authors: The trilinear and biquadratic coupling terms are standard in multi-order-parameter LGD models for HfO2-based ferroelectrics and originate from first-principles-derived functionals reported in the literature for bulk and thin-film systems. Direct first-principles calculations on 7 nm particles remain computationally prohibitive. In the revised manuscript we will add explicit citations to the source literature for these couplings in both the abstract and the methods section, along with a brief statement on their transferability to the nanoparticle geometry. revision: partial

  2. Referee: [Abstract (experimental and comparison statements)] Abstract (experimental and comparison statements): the central claim rests on 'qualitative agreement' between measured accumulated charge curves and model predictions, yet no quantitative metrics (e.g., correlation coefficient, RMS deviation), error bars on the charge data, or details on how model parameters were selected or fitted are provided, leaving the strength of support modest.

    Authors: We agree that additional quantitative detail would strengthen the comparison. The experimental charge data were obtained without reported uncertainties in the original measurements, and model parameters were chosen from literature values for Hf0.5Zr0.5O2 to reproduce the observed temperature trends rather than fitted to the specific dataset. In revision we will (i) add a dedicated paragraph in the main text describing the parameter selection rationale and (ii) include any available experimental uncertainty estimates together with a simple correlation metric between the measured dQ/dT and the calculated pyroelectric coefficient. revision: yes

  3. Referee: [Theoretical model versus experimental description] Theoretical model versus experimental description: oxygen deficiency is explicitly noted for the measured Hf0.5Zr0.5O2 nanoparticles but is not incorporated into the order-parameter description or the core-shell geometry of the LGD functional, creating a potential mismatch between the system modeled and the system measured.

    Authors: Oxygen deficiency is expected to renormalize the effective coefficients of the LGD functional. Our model employs literature parameters for Hf0.5Zr0.5O2 that implicitly incorporate average defect effects observed in similar oxygen-deficient samples. We will add a short discussion paragraph clarifying this approximation, noting that an explicit defect model lies outside the present scope, and indicating that the qualitative trend agreement still holds under this effective-parameter approach. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained against external benchmarks

full rationale

The paper assumes the LGD functional with trilinear/biquadratic couplings and core-shell geometry (drawn from prior ferroelectric literature) to compute polarization and pyroelectric coefficient for an ensemble of nanoparticles, then reports qualitative agreement with an independent experimental data set of temperature-dependent accumulated charge in oxygen-deficient Hf0.5Zr0.5O2 pressed powders. No equation reduces to its inputs by construction, no parameter is fitted to the target data and then relabeled a prediction, and no load-bearing premise rests solely on overlapping-author self-citation. The experimental measurement is external to the model equations, satisfying the criterion for a non-circular comparison.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The model rests on the standard assumptions of Landau-Ginzburg-Devonshire theory plus the specific choice of trilinear and biquadratic coupling terms; no new free parameters or invented entities are introduced beyond the core-shell geometry already stated in the title and abstract.

axioms (1)
  • domain assumption Landau-Ginzburg-Devonshire free energy functional with trilinear and biquadratic couplings of polar, nonpolar, and antipolar order parameters is an appropriate description for the nanoparticles
    Invoked in the abstract as the basis for all theoretical calculations

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discussion (0)

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Works this paper leans on

59 extracted references · 56 canonical work pages · 2 internal anchors

  1. [1]

    Next generation ferroelectric materials for semiconductor process integration and their applications,

    T. Mikolajick, S. Slesazeck, H. Mulaosmanovic, M. H. Park, S. Fichtner, P. D. Lomenzo, M. Hoffmann, U. Schroeder. Next generation ferroelectric materials for semiconductor process integration and their applications, J. Appl. Phys. 129, 100901 (2021); https://doi.org/10.1063/5.0037617

    work page doi:10.1063/5.0037617 2021

  2. [2]

    Mandal, A.-M

    B. Mandal, A.-M. Philippe, N. Valle, E. Defay, T. Granzow, and S. Glinsek. Ferroelectric HfO2–ZrO2 Multilayers with Reduced Wake-Up. ACS Omega, 10 (13), 13141 (2025); https://doi.org/10.1021/acsomega.4c10603

    work page doi:10.1021/acsomega.4c10603 2025

  3. [3]

    Ma et al

    J.Li, S.Deng, L. Ma et al. Enhancing ferroelectric stability: wide-range of adaptive control in epitaxial HfO2/ZrO2 superlattices. Nat. Commun. 16, 6417 (2025); https://doi.org/10.1038/s41467-025-61758-2

    work page doi:10.1038/s41467-025-61758-2 2025

  4. [4]

    K.-H. Kim, I. Karpov, R. H. Olsson III, D. Jariwala. Wurtzite and fluorite ferroelectric materials for electronic memory, Nature Nanotechnology 18, 422 (2023); https://doi.org/10.1038/s41565-023-01361-y

    work page doi:10.1038/s41565-023-01361-y 2023

  5. [5]

    Silva et al

    J.P.B. Silva et al. Roadmap on ferroelectric hafnia and zirconia-based materials and devices, APL Mater. 11, 089201 (2023); https://doi.org/10.1063/5.0148068

    work page doi:10.1063/5.0148068 2023

  6. [6]

    X. Tao, L. Liu, L. Yang and J.-P. Xu, Impacts of HfZrO thickness and anneal temperature on performance of MoS2 negative-capacitance field-effect transistors. Nanotechnology, 32, 445201 (2021); https://doi.org/10.1088/1361-6528/ac197a

    work page doi:10.1088/1361-6528/ac197a 2021

  7. [7]

    A. Paul, G. Kumar, A. Das, G. Larrieu, and S. De. Hafnium oxide-based ferroelectric field effect transistors: From materials and reliability to applications in storage-class memory and in-memory computing. J. Appl. Phys. 138, 010701 (2025); https://doi.org/10.1063/5.0278057

    work page doi:10.1063/5.0278057 2025

  8. [8]

    Cheema, N

    S.S. Cheema, N. Shanker, L.-C. Wang, C.-H. Hsu, S.-L. Hsu, Y.-H. Liao, M. San Jose, J. Gomez, W. Chakraborty, W. Li et al. Ultrathin ferroic HfO2–ZrO2 superlattice gate stack for advanced transistors. Nature 604, 65 (2022); https://doi.org/10.1038/s41586-022-04425-6

    work page doi:10.1038/s41586-022-04425-6 2022

  9. [9]

    Cheema, N

    S.S. Cheema, N. Shanker, S.-L. Hsu, J. Schaadt, N. M. Ellis, M. Cook, R. Rastogi, R. C.N. Pilawa- Podgurski, J. Ciston, M. Mohamed, S. Salahuddin. Giant energy storage and power density negative capacitance superlattices. Nature 629, 803 (2024); https://doi.org/10.1038/s41586-024-07365-5

    work page doi:10.1038/s41586-024-07365-5 2024

  10. [10]

    W. Yang, C. Yu, H. Li, M. Fan, X. Song, H. Ma, Z. Zhou, P. Chang, P. Huang, F. Liu, X. Liu, J. Kang. Ferroelectricity of hafnium oxide-based materials: Current statuses and future prospects from physical mechanisms to device applications. Journal of Semiconductors 44, 053101 (2023); https://doi.org/10.1088/1674- 4926/44/5/053101

    work page doi:10.1088/1674- 2023

  11. [11]

    K. P. Kelley, A. N. Morozovska, E. A. Eliseev, Y. Liu, S. S. Fields, S. T. Jaszewski, T. Mimura, J. F. Ihlefeld, S. V. Kalinin. Ferroelectricity in Hafnia Controlled via Surface Electrochemical State. Nature Materials 22, 1144 (2023); https://doi.org/10.1038/s41563-023-01619-9

    work page doi:10.1038/s41563-023-01619-9 2023

  12. [12]

    Afroze, H

    N. Afroze, H. Fahrvandi, G. Ren, P. Kumar, C. Nelson, S. Lombardo, M. Tian, et al. Atomic-scale confinement of strongly charged 180° domain wall pairs in ZrO2. arXiv.2507.18920 (2025); https://doi.org/10.48550/arXiv.2507.18920 18

    work page doi:10.48550/arxiv.2507.18920 2025

  13. [13]

    Mukherjee, N

    B. Mukherjee, N. S. Fedorova, Jorge Íñiguez -González. Extrinsic nature of the polarization in hafnia ferroelectrics, arXiv.2508.00372 (2025); https://doi.org/10.48550/arXiv.2508.00372

    work page doi:10.48550/arxiv.2508.00372 2025

  14. [14]

    A. N. Morozovska, E. A. Eliseev, R. (Yu) Liu, S. V. Kalinin, and D. R. Evans. Stress-Induced Ferroelectricity in Hafnium Oxide Core-Shell Nanoparticles (2026); https://doi.org/10.48550/arXiv.2602.09262

    work page doi:10.48550/arxiv.2602.09262 2026

  15. [15]

    Delodovici, P

    F. Delodovici, P. Barone, and S. Picozzi. Finite-size effects on ferroelectricity in rhombohedral HfO2. Phys. Rev. B 106, 115438 (2022); https://doi.org/10.1103/PhysRevB.106.115438

    work page doi:10.1103/physrevb.106.115438 2022

  16. [16]

    A. N. Morozovska, E. A. Eliseev, S. V. Kalinin, and M. V. Strikha. Critical sample sizes for appearance and disappearance of ferroelectricity in nanosized hafnia-zirconia: Landau-type theory. Physical Review B, 113, 174102 (2026); https://doi.org/10.1103/hcm2-x9nj

    work page doi:10.1103/hcm2-x9nj 2026

  17. [17]

    M. H. Park, Y. H. Lee, H. J. Kim, T. Schenk, W. Lee, K. Do Kim, F. P. G. Fengler, T. Mikolajick, U. Schroeder, and C. S. Hwang. Surface and grain boundary energy as the key enabler of ferroelectricity in nanoscale hafnia-zirconia: a comparison of model and experiment. Nanoscale 9, 9973 (2017); https://doi.org/10.1039/C7NR02121F

    work page doi:10.1039/c7nr02121f 2017

  18. [18]

    M. H. Park, C.‐C. Chung, T. Schenk, C. Richter, K. Opsomer, C. Detavernier, C. Adelmann, J.L. Jones, T. Mikolajick, U. Schroeder. Effect of Annealing Ferroelectric HfO2 Thin Films: In Situ, High Temperature X‐Ray Diffraction. Advanced Electronic Materials 4, 1800091 (2018); https://doi.org/10.1002/aelm.201800091

    work page doi:10.1002/aelm.201800091 2018

  19. [19]

    Hyun Lee, Y

    D. Hyun Lee, Y. Lee, K. Yang, J.Y. Park, S.H. Kim, P.R.S. Reddy, M. Materano, H. Mulaosmanovic, T. Mikolajick, J.L. Jones, U. Schroeder, M.H. Park, Domains and domain dynamics in fluorite-structured ferroelectrics. Appl. Phys. Reviews 8, 021312 (2021), https://doi.org/10.1063/5.0047977

    work page doi:10.1063/5.0047977 2021

  20. [20]

    Delodovici, P

    F. Delodovici, P. Barone, and S. Picozzi, Trilinear-coupling-driven ferroelectricity in HfO2, Physical Review Materials 5, 064405 (2021); https://doi.org/10.1103/PhysRevMaterials.5.064405

    work page doi:10.1103/physrevmaterials.5.064405 2021

  21. [21]

    Jung and T

    S. Jung and T. Birol, Triggered ferroelectricity in HfO2 from hybrid phonons, arXiv:2502.08633 (2025); https://doi.org/10.48550/arXiv.2502.08633

    work page doi:10.48550/arxiv.2502.08633 2025

  22. [22]

    Ferroic Polarization from Nonpolar Phonons

    S. Jung and T. Birol, Electric Polarization from Nonpolar Phonons, arXiv: 2512.00628 (2025); https://doi.org/10.48550/arXiv.2512.00628

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2512.00628 2025

  23. [23]

    E. A. Eliseev, S. V. Kalinin, A. N. Morozovska. Ferro-ionic States and Domains Morphology in HfxZr1- xO2 Nanoparticles. Journal of Applied Physics, 137 (3), 034103 (2025); https://doi.org/10.1063/5.0243067

    work page doi:10.1063/5.0243067 2025

  24. [24]

    Fujimoto, Y

    K. Fujimoto, Y. Sato, Y. Fuchikami, R. Teranishi, and Kenji Kaneko. Orthorhombic‐like atomic arrangement in hafnium‐oxide‐based nanoparticles. Journal of the American Ceramic Society 105, 2823 (2022); https://doi.org/10.1111/jace.18242

    work page doi:10.1111/jace.18242 2022

  25. [25]

    E. A. Eliseev, Y. O. Zagorodniy, V. N. Pavlikov, O. V. Leshchenko, H. V. Shevilakova, M. V. Karpec, A. D. Yaremkevych, O. M. Fesenko, S. V. Kalinin, and A. N. Morozovska. Phase diagrams and polarization reversal in nanosized HfxZr1-xO2-y, AIP Advances, 14, 055224 (2024); https://doi.org/10.1063/5.0209123

    work page doi:10.1063/5.0209123 2024

  26. [26]

    E. A. Eliseev, I. V. Kondakova, Y. O. Zagorodniy, H. V. Shevliakova, O. V. Leshchenko, V. N. Pavlikov, M. V. Karpets, L. P. Yurchenko, and A. N. Morozovska, The origin of the ferroelectric -like orthorhombic phase in oxygen-deficient HfO2-y nanoparticles. Semiconductor Physics, Optoelectronics and Quantum Electronics, 28, 134 (2025); https://doi.org/10.15...

    work page doi:10.15407/spqeo28.02.134 2025

  27. [27]

    Y. O. Zagorodniy, E . A. Eliseev, V . V. Laguta, P . Jiricek, J . Houdkova, L . D. Demchenko, O . V. Leshchenko, V. N. Pavlikov, L. P. Yurchenko, A. O. Diachenko, M. D. Volnyanskii, O. S. Pylypchuk, M. V. Karpets, M. P. Trubitsyn, D . R. Evans, and A . N. Morozovska. Stabilization of the Orthorhombic Phases in Hf 0.5Zr0.5O2 Nanoparticles by Oxygen Vacanci...

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2603.14642 2026

  28. [28]

    Boscke, S

    T.S. Boscke, S. Teichert, D. Brauhaus, J. Muller, U. Schroder, U. Bottger, and T. Mikolajick, Phase transitions in ferroelectric silicon doped hafnium oxide, Appl. Phys. Lett. 99, 112904 (2011); https://doi.org/10.1063/1.3636434

    work page doi:10.1063/1.3636434 2011

  29. [29]

    Buragohain, M

    Yu Yun, P. Buragohain, M. Li, Z. Ahmadi, Y. Zhang, X. Li, H. Wang, J. Li, P. Lu, L. Tao, H. Wang, Intrinsic ferroelectricity in Y-doped HfO2 thin films, Nature Materials, 21, 903 (2022); https://doi.org/10.1038/s41563-022-01282-6

    work page doi:10.1038/s41563-022-01282-6 2022

  30. [30]

    Shlyakhov, K

    I. Shlyakhov, K. Iakoubovskii, D. Lin, I. Asselberghs, A. Gaur, G. Delie, and V. Afanas' ev. Energy band alignment in MoS2/HfO2: Transfer-related artifacts and interfacial effects. J. Appl. Phys. 137, 244304 (2025); https://doi.org/10.1063/5.0279067

    work page doi:10.1063/5.0279067 2025

  31. [31]

    M. H. Park, T. Schenk, M. Hoffmann, S. Knebel, J. Gartner, T. Mikolajick, U. Schroeder, Effect of acceptor doping on phase transitions of HfO2 thin films for energy-related applications, Nano Energy 36, 381 (2017); https://doi.org/10.1016/j.nanoen.2017.04.052

    work page doi:10.1016/j.nanoen.2017.04.052 2017

  32. [32]

    M. H. Park, H. J. Kim, Y. J. Kim, T. Moon, K. D. Kim, Y. H. Lee, S. D. Hyun, C. S. Hwang, Giant negative electrocaloric effects of Hf0.5Zr0.5O2 thin films. Adv. Mater. 28, 7956 (2016); https://doi.org/10.1002/adma.201602787

    work page doi:10.1002/adma.201602787 2016

  33. [33]

    Hoffmann, U

    M. Hoffmann, U. Schroeder, C. Künneth, A. Kersch, S. Starschich, U. Böttger, and T.Mikolajick. Ferroelectric phase transitions in nanoscale HfO2 films enable giant pyroelectric energy conversion and highly efficient supercapacitors. Nano Energy 18, 154 (2015); http://dx.doi.org/10.1016/j.nanoen.2015.10.005

    work page doi:10.1016/j.nanoen.2015.10.005 2015

  34. [34]

    M. H. Park, M . Hoffmann, C . Hwang, Chapter 5.2 - Pyroelectric and Electrocaloric Effects and Their Applications, Editor(s): Uwe Schroeder, Cheol Seong Hwang, Hiroshi Funakubo, In Woodhead Publishing Series in Electronic and Optical Materials, Ferroelectricity in Doped Hafnium Oxide: Materials, Properties and Devices, Woodhead Publishing (2019), Pages 21...

    work page doi:10.1016/b978-0-08-102430- 2019

  35. [35]

    O. S. Pylypchuk, I. V. Fesych, V. V. Vainberg, Y. O. Zagorodniy, V. I. Styopkin, J. M. Gudenko, I. V. Kondakova, L. P. Yurchenko, V. N. Pavlikov, A. O. Diachenko, M. M. Koptiev, M. D. Volnyanskii, V. V. Laguta, E. A. Eliseev, M. P. Trubitsyn, and A. N. Morozovska. Resistive switching and charge accumulation in Hf0.5Zr0.5O2 nanoparticles. Journal of Physic...

    work page doi:10.1021/acs.jpcc.5c04140 2025

  36. [36]

    O. S. Pylypchuk, V. V. Vainberg, V. N. Poroshin, O. V. Leshchenko, V. N. Pavlikov, I. V. Kondakova, S. E. Ivanchenko, L. P. Yurchenko, L. Demchenko, A. O. Diachenko, M. V. Karpets, M. P. Trubitsyn, E. A. Eliseev, and A. N. Morozovska. A colossal dielectric response of HfxZr1-xO2 nanoparticles. Physical Review Materials 9, 114412 (2025); https://doi.org/10...

    work page doi:10.1103/y2pb-5g5w 2025

  37. [37]

    H. Han, C. Voisin, S. Guillemet -Fritsch, P. Dufour, C. Tenailleau, C. Turner, and J. C. Nino, Origin of colossal permittivity in BaTiO 3 via broadband dielectric spectroscopy. Journal of Applied Physics 113, 024102 (2013); https://doi.org/10.1063/1.4774099 20

    work page doi:10.1063/1.4774099 2013

  38. [38]

    H. Han, D. Ghosh, J.L. Jones, and J. C. Nino, Colossal Permittivity in Microwave‐Sintered Barium Titanate and Effect of Annealing on Dielectric Properties. J. Am. Ceram. Soc., 96, 485 (2013). https://doi.org/10.1111/jace.12051

    work page doi:10.1111/jace.12051 2013

  39. [39]

    Petzelt, D

    J. Petzelt, D. Nuzhnyy, V. Bovtun, M. Savinov, M. Kempa, I. Rychetsky, Broadband dielectric and conductivity spectroscopy of inhomogeneous and composite conductors. Phys. Stat. Sol. A 210, 2259 (2013), https://doi.org/10.1002/pssa.201329288

    work page doi:10.1002/pssa.201329288 2013

  40. [40]

    O. S. Pylypchuk, S. E. Ivanchenko, M. Y. Yelisieiev, A. S. Nikolenko, V. I. Styopkin, B. Pokhylko, V. Kushnir, D. O. Stetsenko, O. Bereznykov, O. V. Leschenko, E. A. Eliseev, V. N. Poroshin, N. V. Morozovsky , V. V. Vainberg, and A. N. Morozovska. Behavior of the Dielectric and Pyroelectric Responses of Ferroelectric Fine - Grained Ceramics. Journal of th...

    work page doi:10.1111/jace.20391 2025

  41. [41]

    Hoshina, Size effect of barium titanate: fine particles and ceramics

    T. Hoshina, Size effect of barium titanate: fine particles and ceramics. Journal of the ceramic society of Japan 121 (1410) 156 (2013); https://doi.org/10.2109/jcersj2.121.156

    work page doi:10.2109/jcersj2.121.156 2013

  42. [42]

    L. Liu, S. Ren, J. Liu, F. Han, J. Zhang, B. Peng, D. Wang, A. A. Bokov, and Z.-G. Ye, Localized polarons and conductive charge carriers: Understanding CaCu3⁢Ti4⁢O12 over a broad temperature range. Phys. Rev. B 99, 094110 (2019); https://doi.org/10.1103/PhysRevB.99.094110

    work page doi:10.1103/physrevb.99.094110 2019

  43. [43]

    Saleem, M

    M. Saleem, M. S. Butt, A. Maqbool, M. A. Umer, M. Shahid, F. Javaid, R. A. Malik, H. Jabbar, H. M. W. Khalil, L. D. Hwan, M. Kim, B. -K. Koo, S. J. Jeong, Percolation phenomena of dielectric permittivity of a microwave-sintered BaTiO3-Ag nanocomposite for high energy capacitor, Journal of Alloys and Compounds, 822, 153525 (2020), https://doi.org/10.1016/j...

    work page doi:10.1016/j.jallcom.2019.153525 2020

  44. [44]

    Lunkenheimer, S

    P. Lunkenheimer, S. Krohns, S. Riegg, S.G. Ebbinghaus, A. Reller, and A. Loidl, Colossal dielectric constants in transition -metal oxides. Eur. Phys. J. Spec. Topics, 180, 61 -89 (2009), https://doi.org/10.1140/epjst/e2010-01212-5

    work page doi:10.1140/epjst/e2010-01212-5 2009

  45. [45]

    Petzelt, D

    J. Petzelt, D. Nuzhnyy, V. Bovtun, D.A. Crandles. Origin of the colossal permittivity of (Nb+ In) co-doped rutile ceramics by wide -range dielectric spectroscopy. Phase Transitions 91, 932 (2018). https://doi.org/10.1080/01411594.2018.1501801

    work page doi:10.1080/01411594.2018.1501801 2018

  46. [46]

    Nataf, E

    I. Rychetský, D. Nuzhnyy, J. Petzelt, Giant permittivity effects from the core –shell structure modeling of the dielectric spectra. Ferroelectrics 569, 9 (2020). https://doi.org/10.1080/00150193.2020.1791659

    work page doi:10.1080/00150193.2020.1791659 2020

  47. [47]

    O. S. Pylypchuk, E. A. Eliseev, A. V. Bodnaruk, V. V. Laguta, Y. O. Zagorodniy, D. O. Stetsenko, A. D. Yaremkevich, O. V. Leshchenko, V. N. Pavlikov, L. Demchenko, V. I. Styopkin, M. V. Karpets, O. M. Fesenko, V. V. Vainberg, and A. N. Morozovska, Magnetic properties and charge transport mechanisms in oxygen-deficient HfxZr1-xO2-y nanoparticles. Ceramics ...

    work page doi:10.1016/j.ceramint.2026.03.015 2026

  48. [48]

    D. A. Freedman, D. Roundy, and T. A. Arias. Elastic effects of vacancies in strontium titanate: Short- and long-range strain fields, elastic dipole tensors, and chemical strain. Phys. Rev. B 80, 064108 (2009), https://doi.org/10.1103/PhysRevB.80.064108

    work page doi:10.1103/physrevb.80.064108 2009

  49. [49]

    Y. Kim, A. S. Disa, T. E. Babakol, and J. D. Brock. Strain screening by mobile oxygen vacancies in SrTiO3. Appl. Phys. Lett. 96, 251901 (2010), https://doi.org/10.1063/1.3455157 21

    work page doi:10.1063/1.3455157 2010

  50. [50]

    A. N. Morozovska, O. V. Bereznykov, M. V. Strikha, O. S. Pylypchuk, Z. Kutnjak, E. A. Eliseev, and D. R. Evans. Domain Morphology, Electrocaloric Response, and Negative Capacitance States of Ferroelectric Nanowires Array. Composite Interfaces (2025); https://doi.org/10.1080/09276440.2025.2605389

    work page doi:10.1080/09276440.2025.2605389 2025

  51. [51]

    The Basis of Easy Controllability in Boolean Networks

    S. Dutta, P. Buragohain, S. Glinsek, C. Richter, H. Aramberri, H. Lu, U. Schroeder, E. Defay, A. Gruverman, J. Íñiguez. Piezoelectricity in hafnia. Nature Communications 12, 7301 (2021); https://doi.org/10.1038/s41467-021- 27480-5

    work page doi:10.1038/s41467-021- 2021

  52. [52]

    Lee, K .-J

    H.-J. Lee, K .-J. Go, P. Kumar, C. H. Kim, Y. Kim, K. Lee, T. Shimizu, S. C. Chae, H. Jin, M. Lee, U. Waghmare, S.-Y. Choi, J. H. Lee, Phonon -pair-driven Ferroelectricity Causes Costless Domain -walls and Bulk - boundary Duality, arXiv: 2403.01415 (2024); https://doi.org/10.48550/arXiv.2403.01415

    work page doi:10.48550/arxiv.2403.01415 2024

  53. [53]

    Glinchuk, E.A

    M.D. Glinchuk, E.A. Eliseev, A.N. Morozovska. Superparaelectric phase in the ensemble of noninteracting ferroelectric nanoparticles. Phys. Rev. B. 78 (13), 134107 (2008); https://doi.org/10.1103/PhysRevB.78.134107

    work page doi:10.1103/physrevb.78.134107 2008

  54. [54]

    R. W. Whatmore, Pyroelectric devices and materials. Reports on progress in physics 49 (12) 1335 (1986); https://doi.org/10.1088/0034-4885/49/12/002

    work page doi:10.1088/0034-4885/49/12/002 1986

  55. [55]

    Woodfield, Alexandra Navrotsky

    Wei Zhou, Quan Shi, Brian F. Woodfield, Alexandra Navrotsky. Heat capacity of hafnia at low temperature, J. Chem. Thermodynamics 43, 970–973 (2011); https://doi.org/10.1016/j.jct.2011.02.002

    work page doi:10.1016/j.jct.2011.02.002 2011

  56. [56]

    https://www.wolfram.com/mathematica

  57. [57]

    Eliseev, and M.D

    E.A. Eliseev, and M.D. Glinchuk. Size effects in thin films of order–disorder ferroelectrics allowing for the depolarization field. Phys. Stat. Sol. (b) 241, R52-R55 (2004); https://doi.org/10.1002/pssb.200402109

    work page doi:10.1002/pssb.200402109 2004

  58. [58]

    G. L. Carr, S. Perkowitz, and D. B. Tanner. Far-infrared properties of inhomogeneous materials. Infrared and millimeter waves. Volume 13, Part 4 (Orlando, Academic Press, 1985) pp. 171-263 (see page 200, equation 72)

    1985

  59. [59]

    Landau, E.M

    L.D. Landau, E.M. Lifshitz, L. P. Pitaevskii. Electrodynamics of Continuous Media, (Second Edition, Butterworth-Heinemann, Oxford, 1984)

    1984