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Phase transition and negative thermal expansion in copper pyrophosphate Cu2P2O7 studied by neutron total scattering and the reverse Monte Carlo method

Martin T. Dove1,2,3,4,5,*, Naike Shi6,†, Shaojie Wang4, Jiaxin Song4, Juping Xu2,7, Wen Yin2,7, Jun Chen6,8, Yang Hai3,‡, and Guanqun Cai4,§

  • *Contact author: martin.dove@qmul.ac.uk
  • †Contact author: kenaishi@163.com
  • ‡Contact author: haiyang@dgut.edu.cn
  • §Contact author: guanqun_cai@scu.edu.cn
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Phys. Rev. B 114, 024309 – Published 13 July, 2026

DOI: https://doi.org/10.1103/t6fk-c61v

Abstract

The phase transition in copper pyrophosphate, Cu2P2O7, has been studied using neutron total scattering and the reverse Monte Carlo method. The results show the growth of disorder of the orientations of the PO4 tetrahedra and of the positions of the copper atoms along the long O–Cu–O linkage in the CuO6 octahedra distorted by the Jahn–Teller effect. These two types of disorder are coupled, and neither show the preference for distinct sites of partial atomic occupancy in the high-temperature phase. The origin of the negative thermal expansion identified in Cu2P2O7 can be understood as arising from the ordering of the copper atoms leading to one Cu–O bond expanding more than the other contracts.

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References (61)

  1. C. Calvo, The crystal structure and phase transitions of β−Zn2P2O7, Can. J. Chem. 43, 1147 (1965).
  2. N. S. Rao and O. G. Palanna, Phase transition in copper(II) pyrovanadate, Bull. Mater. Sci. 16, 37 (1993).
  3. H. Wang, M. Yang, M. Chao, J. Guo, Q. Gao, Y. Jiao, X. Tang, and E. Liang, Negative thermal expansion property of β−Cu2V2O7, Solid State Ionics 343, 115086 (2019).
  4. B. H. K. Pogorzelec-Glaser, A. Pietraszko, and M. Połomska, Structure and phase transitions in Cu2P2O7, Phase Transitions 79, 535 (2006).
  5. N. Shi, A. Sanson, Q. Gao, Q. Sun, Y. Ren, Q. Huang, D. O. de Souza, X. Xing, and J. Chen, Strong negative thermal expansion in a low-cost and facile oxide of Cu2P2O7, J. Am. Chem. Soc. 142, 3088 (2020).
  6. N. Shi, A. Sanson, A. Venier, L. Fan, C. Sun, X. Xing, and J. Chen, Negative and zero thermal expansion in α-(Cu2−xZnx)V2O7 solid solutions, Chem. Commun. 56, 10666 (2020).
  7. N. Shi, A. Sanson, Q. Sun, L. Fan, A. Venier, D. Oliveira de Souza, X. Xing, and J. Chen, Strong negative thermal expansion of Cu2PVO7 in a wide temperature range, Chem. Mater. 33, 1321 (2021).
  8. N. Shi, A. Sanson, A. Venier, L. Fan, Y. Ren, D. O. de Souza, L. Olivi, Y. Song, X. Xing, and J. Chen, Tuning thermal expansion from strong negative to zero to positive in Cu2−xZnxP2O7 solid solutions, Scr. Mater. 207, 114289 (2022).
  9. K. Takenaka, M. Kano, R. Kasugai, K. Takada, K. Eto, Y. Kadowaki, Y. Yokoyama, N. Katayama, and Y. Okamoto, Structural phase transition and negative thermal expansion in Cu1.8Zn0.2V2−xPxO7 solid solutions, Appl. Phys. Express 15, 025504 (2022).
  10. Y. Xiang, X. Hao, X. Liu, M. Wang, J. Tian, C. Kang, E. Liang, W. Zhang, and Y. Jia, Tailoring thermal expansion of (LiFe)0.5xCu2−xP2O7 via codoping LiFe diatoms in Cu2P2O7 oxide, Inorg. Chem. 61, 1504 (2022).
  11. N. Shi, X. Kong, A. Sanson, N. Wang, A. Venier, D. O. de Souza, and J. Chen, Observation of near-zero thermal expansion in CrVMoO7, Scr. Mater. 235, 115597 (2023).
  12. N. Shi, L. Fan, Y. Xu, W. Yin, H. Chen, B. Yuan, C. Zhou, and J. Chen, Significant enhancement of negative thermal expansion under low pressure in Cu2P2O7, Small 20, 2312289 (2024).
  13. G. D. Barrera, J. A. O. Bruno, T. H. K. Barron, and N. L. Allan, Negative thermal expansion, J. Phys.: Condens. Matter 17, R217 (2005).
  14. J. Chen, L. Hu, J. Deng, and X. Xing, Negative thermal expansion in functional materials: Controllable thermal expansion by chemical modifications, Chem. Soc. Rev. 44, 3522 (2015).
  15. M. T. Dove and H. Fang, Negative thermal expansion and associated anomalous physical properties: Review of the lattice dynamics theoretical foundation, Rep. Prog. Phys. 79, 066503 (2016).
  16. K. Takenaka, Progress of research in negative thermal expansion materials: Paradigm shift in the control of thermal expansion, Front. Chem. 6, 267 (2018).
  17. N. Shi, Y. Song, X. Xing, and J. Chen, Negative thermal expansion in framework structure materials, Coord. Chem. Rev. 449, 214204 (2021).
  18. E. Liang, Q. Sun, H. Yuan, J. Wang, G. Zeng, and Q. Gao, Negative thermal expansion: Mechanisms and materials, Front. Phys. 16, 53302 (2021).
  19. Y. Mochizuki, K. Nagamatsu, H. Koiso, T. Isobe, and A. Nakajima, Mechanism of negative thermal expansion in monoclinic Cu2P2O7 from first principles, J. Phys. Chem. Lett. 15, 156 (2024).
  20. M. T. Dove and N. Shi, The phase transition in copper pyrophosphate, Cu2P2O7: Insights and implications for the interpretation of negative thermal expansion, Matter 8, 102149 (2025).
  21. B. E. Robertson and C. Calvo, The crystal structure and phase transformation of α−Cu2P2O7, Acta Crystallogr. 22, 665 (1967).
  22. B. E. Robertson and C. Calvo, Crystal structure of β−Cu2P2O7, Can. J. Chem. 46, 605 (1968).
  23. See Supplemental Material at http://link.aps.org/supplemental/10.1103/t6fk-c61v for figures showing the fitting of the RMC to the experimental data for each temperature, the figures showing the fitting of the Rietveld refinement to the neutron powder diffraction for each bank of detectors, the tables presenting the refined crystal structure of each temperature, and a discussion of why the strains are expected to be proportional to the square of the order parameter.
  24. D. C. Palmer, Visualization and analysis of crystal structures using crystalmaker software, Zeitschrift für Kristallographie-Crystalline Materials 230, 559 (2015).
  25. R. Bianchi, T. Pilati, V. Diella, C. M. Gamaccioli, and G. Mannucci, A re-examination of thortveitite, Am. Mineral. 73, 601 (1988).
  26. W. W. Schmahl, I. P. Swainson, M. T. Dove, and A. Graeme-Barber, Landau free energy and order parameter behaviour of the α/β phase transition in cristobalite, Zeitschrift für Kristallographie 201, 125 (1992).
  27. M. G. Tucker, M. P. Squires, M. T. Dove, and D. A. Keen, Dynamic structural disorder in cristobalite: Neutron total scattering measurement and reverse Monte Carlo modelling, J. Phys.: Condens. Matter 13, 403 (2001).
  28. H. Effenberger, Structural refinement of low-temperature copper(II) pyrophosphate, Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 46, 691 (1990).
  29. R. Cowley, Structural phase transitions I. Landau theory, Adv. Phys. 29, 1 (1980).
  30. E. Salje, Application of Landau theory for the analysis of phase transitions in minerals, Phys. Rep. 215, 49 (1992).
  31. M. T. Dove, Theory of displacive phase transitions in minerals, Am. Mineral. 82, 213 (1997).
  32. M. A. Carpenter, E. K. Salje, and A. Graeme-Barber, Spontaneous strain as a determinant of thermodynamic properties for phase transitions in minerals, Eur. J. Mineral. 10, 621 (1998).
  33. B. Sheng, J. Xie, Q. Shao, K. Zhao, S. Zhao, J. Guo, E. Liang, Y. Qiao, B. Wei, and Q. Gao, Structure and abnormal thermal expansion in Cu2−xMgxP2O7, Phys. Lett. A 525, 129843 (2024).
  34. Y. Liang, G. Zeng, X. Hao, J. Guo, X. Liu, Q. Gao, Y. Jia, and E. Liang, Distinct Jahn-Teller–induced negative thermal expansion behaviors in Cr2P2O7, Phys. Rev. B 112, 104307 (2025).
  35. M. Khalid, Y. Liang, C. Wang, X. Hao, J. Guo, X. Ren, Q. Gao, Y. Jia, and E. Liang, Giant negative thermal expansion in Zn2P2O7 driven by pseudo Jahn-Teller effect, Phys. Rev. B 113, 094309 (2026).
  36. M. G. Tucker, D. A. Keen, M. T. Dove, A. L. Goodwin, and Q. Hui, RMCProfile: Reverse Monte Carlo for polycrystalline materials, J. Phys.: Condens. Matter 19, 335218 (2007).
  37. W. A. Sławiński, C. J. Kerr, Y. Zhang, H. Y. Playford, M. T. Dove, A. E. Phillips, and M. G. Tucker, RMCProfile7: Reverse Monte Carlo for multiphase systems, J. Appl. Crystallogr. 57, 1251 (2024).
  38. M. G. Tucker, A. L. Goodwin, M. T. Dove, D. A. Keen, S. A. Wells, and J. S. O. Evans, Negative thermal expansion in ZrW2O8: Mechanisms, rigid unit modes, and neutron total scattering, Phys. Rev. Lett. 95, 255501 (2005).
  39. A. L. Goodwin, S. A. T. Redfern, M. T. Dove, D. A. Keen, and M. G. Tucker, Ferroelectric nanoscale domains and the 905 K phase transition in SrSnO3: A neutron total-scattering study, Phys. Rev. B 76, 174114 (2007).
  40. J. Du, A. E. Phillips, D. C. Arnold, D. A. Keen, M. G. Tucker, and M. T. Dove, Structural study of bismuth ferrite BiFeO3 by neutron total scattering and the reverse Monte Carlo method, Phys. Rev. B 100, 104111 (2019).
  41. M. T. Dove, J. Du, Z. Wei, D. A. Keen, M. G. Tucker, and A. E. Phillips, Quantitative understanding of negative thermal expansion in scandium trifluoride from neutron total scattering measurements, Phys. Rev. B 102, 094105 (2020).
  42. J. Xu, L. Mei, W. Yin, X. Wang, W. Cai, Z. Li, T. Bo, H. Chen, B. Wang, and Y. Chen, Physical design of multipurpose physics neutron diffractometer for the CSNS, Nucl. Instrum. Methods Phys. Res., Sect. A 927, 161 (2019).
  43. J. Xu, Y. Xia, Z. Li, H. Chen, X. Wang, Z. Sun, and W. Yin, Multi-physics instrument: Total scattering neutron time-of-flight diffractometer at China Spallation Neutron Source, Nucl. Instrum. Methods Phys. Res., Sect. A 1013, 165642 (2021).
  44. D. A. Keen, A comparison of various commonly used correlation functions for describing total scattering, J. Appl. Crystallogr. 34, 172 (2001).
  45. M. T. Dove and G. Li, Review: Pair distribution functions from neutron total scattering for the study of local structure in disordered materials, Nuclear Analysis 1, 100037 (2022).
  46. S. Wang, M. Gao, Y. Qin, S. Zhang, L. Tan, and M. T. Dove, Accounting for instrument resolution in the pair distribution functions obtained from total scattering data using Hermite functions, J. Appl. Crystallogr. 58, 1269 (2025).
  47. B. H. Toby and R. B. Von Dreele, GSAS-II: The genesis of a modern open-source all purpose crystallography software package, J. Appl. Crystallogr. 46, 544 (2013).
  48. M. T. Dove and G. Rigg, RMCgui: a new interface for the workflow associated with running Reverse Monte Carlo simulations, J. Phys.: Condens. Matter 25, 454222 (2013).
  49. M. T. Dove, Complete set of data for the RMC simulations, generation of the PDFs from the total scattering data, and the Rietveld refinements using GSAS II, Zenodo, 2026, https://doi.org/10.5281/zenodo.20263257.
  50. M. G. Tucker, M. T. Dove, and D. A. Keen, Direct measurement of the thermal expansion of the Si–O bond by neutron total scattering, J. Phys.: Condens. Matter 12, L425 (2000).
  51. https://cstr.cn/31113.02.CSNS.
  52. https://cstr.cn/31113.02.CSNS.MPI.
  53. X. Xing, J. Deng, J. Chen, and G. Liu, Novel thermal expansion of lead titanate, Rare Metals 22, 294 (2003).
  54. J. Chen, X. R. Xing, R. B. Yu, and G. R. Liu, Structure and enhancement of negative thermal expansion in the PbTiO3–CdTiO3 system, Appl. Phys. Lett. 87, 231915 (2005).
  55. J. Chen, X. R. Xing, G. R. Liu, J. H. Li, and Y. T. Liu, Structure and negative thermal expansion in the PbTiO3–BiFeO3 system, Appl. Phys. Lett. 89, 101914 (2006).
  56. P. Lloveras, E. Stern-Taulats, M. Barrio, J. Tamarit, S. Crossley, W. Li, V. Pomjakushin, A. Planes, L. Mañosa, N. D. Mathur, and X. Moya, Giant barocaloric effects at low pressure in ferrielectric ammonium sulphate, Nat. Commun. 6, 8801 (2015).
  57. G. Cai, J. Liu, H. Y. Playford, H. C. Walker, A. E. Phillips, and M. T. Dove, Hydrogen bonding order, librational entropy, and negative thermal expansion in the barocaloric material ammonium sulfate (unpublished).
  58. F. Qin, L. Hu, Y. Zhu, Y. Sakai, S. Kawaguchi, A. Machida, T. Watanuki, Y.-W. Fang, J. Sun, X. Ding, and M. Azuma, Integrating abnormal thermal expansion and ultralow thermal conductivity into (Cd,Ni)2Re2O7 via synergy of local structure distortion and soft acoustic phonons, Acta Mater. 264, 119544 (2024).
  59. M. T. Dove, Comment on “integrating abnormal thermal expansion and ultralow thermal conductivity into (Cd,Ni)2Re2O7 via synergy of local structure distortion and soft acoustic phonons”, Scripta Materialia 282, 117395 (2026).
  60. T. Claeys, B. Fahs, G. Lambert, and C. Webb, How much can the eigenvalues of a random Hermitian matrix fluctuate? Duke Math. J. 170, 2085 (2021).
  61. P. Li, P. Yao, G. Cai, T. Li, A. E. Phillips, and M. T. Dove, Dynamic structural disorder and negative thermal expansion (unpublished).

Outline

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Phys. Rev. B 114, 024309– Published 13 July, 2026
  • Received 27 February 2026
  • Revised 8 May 2026
  • Accepted 15 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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