Articles | Volume 17, issue 3
https://doi.org/10.5194/se-17-601-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/se-17-601-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
High-pressure behaviour and elastic constants of 1M and 2M1 polytypes of phlogopite KMg3Si3AlO10(OH)2
Gianfranco Ulian
Dipartimento di Scienze Biologiche, Geologiche e Ambientali, Università di Bologna “Alma Mater Studiorum”, Plesso di Mineralogia, Piazza di Porta San Donato 1, 40126 Bologna, Italy
Francesca Ranellucci
Dipartimento di Scienze Biologiche, Geologiche e Ambientali, Università di Bologna “Alma Mater Studiorum”, Plesso di Mineralogia, Piazza di Porta San Donato 1, 40126 Bologna, Italy
Giovanni Valdrè
CORRESPONDING AUTHOR
Dipartimento di Scienze Biologiche, Geologiche e Ambientali, Università di Bologna “Alma Mater Studiorum”, Plesso di Mineralogia, Piazza di Porta San Donato 1, 40126 Bologna, Italy
Cited articles
Alexandrov, K. S. and Ryzhova, T. V.: Elastic properties of rock-forming minerals. II. Layered silicates, Bulletin of the Academy of Sciences of the U.S.S.R, Geophysics Series, 9, 1165–1168, 1961.
Aleksandrov, K. S., Alchikov, U. V., Belikov, B. P., Zaslavskii, B. I., and Krupnyi, A. I.: Velocities of elastic waves in minerals at atmospheric pressure and increasing precision of elastic constants by means of EVM, in: Izv. Acad. Sci. USSR, Geol. Ser., 10, 15–24, 1974 (in Russian).
Angel, R. J., Gonzalez-Platas, J., and Alvaro, M.: EosFit7c and a Fortran module (library) for equation of state calculations, Zeitschrift Fur Kristallographie, 229, 405–419, https://doi.org/10.1515/zkri-2013-1711, 2014.
Ariane, K., Tamayo, A., Chorfa, A., Rubio, F., and Rubio, J.: Optimization of the nucleating agent content for the obtaining of transparent fluormica glass-ceramics, Ceramics International, 49, 9826–9838, https://doi.org/10.1016/j.ceramint.2022.11.156, 2023.
Becke, A. D.: Density-Functional Thermochemistry .3. The Role of Exact Exchange, Journal of Chemical Physics, 98, 5648–5652, https://doi.org/10.1063/1.464913, 1993.
Belmonte, D.: First Principles Thermodynamics of Minerals at HP-HT Conditions: MgO as a Prototypical Material, Minerals, 7, 183, https://doi.org/10.3390/Min7100183, 2017.
Birch, F.: Finite elastic strain of cubic crystal, Phys. Rev., 71, 809–824, 1947.
Brandenburg, J. G., Alessio, M., Civalleri, B., Peintinger, M. F., Bredow, T., and Grimme, S.: Geometrical correction for the inter- and intramolecular basis set superposition error in periodic density functional theory calculations, Journal of Physical Chemistry A, 117, 9282–9292, https://doi.org/10.1021/jp406658y, 2013.
Broyden, C. G.: The convergence of a class of double-rank minimization algorithms: 1. General considerations, IMA Journal of Applied Mathematics, 6, 76–90, https://doi.org/10.1093/imamat/6.1.76, 1970a.
Broyden, C. G.: The convergence of a class of double-rank minimization algorithms: 2. The new algorithm, IMA Journal of Applied Mathematics, 6, 222–231, https://doi.org/10.1093/imamat/6.3.222, 1970b.
Cadore, A. R., De Oliveira, R., Longuinhos, R., Teixeira, V. D. C., Nagaoka, D. A., Alvarenga, V. T., Ribeiro-Soares, J., Watanabe, K., Taniguchi, T., Paniago, R. M., Malachias, A., Krambrock, K., Barcelos, I. D., and De Matos, C. J. S.: Exploring the structural and optoelectronic properties of natural insulating phlogopite in van der Waals heterostructures, 2D Materials, 9, 035007, https://doi.org/10.1088/2053-1583/ac6cf4, 2022.
Catti, M., Ferraris, G., Hull, S., and Pavese, A.: Powder Neutron-Diffraction Study of 2M1 Muscovite at Room Pressure and at 2 Gpa, European Journal of Mineralogy, 6, 171–178, 1994.
Chheda, T. D., Mookherjee, M., Mainprice, D., dos Santos, A. M., Molaison, J. J., Chantel, J., Manthilake, G., and Bassett, W. A.: Structure and elasticity of phlogopite under compression: Geophysical implications, Physics of the Earth and Planetary Interiors, 233, 1–12, https://doi.org/10.1016/j.pepi.2014.05.004, 2014.
Civalleri, B., Zicovich-Wilson, C. M., Valenzano, L., and Ugliengo, P.: B3LYP augmented with an empirical dispersion term (B3LYP-D*) as applied to molecular crystals, CrystEngComm, 10, 405–410, https://doi.org/10.1039/b715018k, 2008.
Comodi, P. and Zanazzi, P. F.: High-Pressure Structural Study of Muscovite, Physics and Chemistry of Minerals, 22, 170–177, 1995.
Comodi, P., Fumagalli, P., Montagnoli, M., and Zanazzi, P. F.: A single-crystal study on the pressure behavior of phlogopite and petrological implications, American Mineralogist, 89, 647–653, https://doi.org/10.2138/am-2004-0420, 2004.
Dion, M., Rydberg, H., Schröder, E., Langreth, D. C., and Lundqvist, B. I.: Van der Waals Density Functional for General Geometries, Physical Review Letters, 92, 246401, https://doi.org/10.1103/PhysRevLett.92.246401, 2004.
Donnay, G., Morimoto, N., and Takeda, H.: Trioctahedral one-layer micas. II. Prediction of the structure from composition and cell dimensions, Acta Cryst., 17, 1374–1381, https://doi.org/10.1107/S0365110X64003462, 1964a.
Donnay, G., Morimoto, N., and Takeda, H.: Trioctahedral one-layer micas. I. Crystal structure of a synthetic iron mica, Acta Cryst., 17, 1369–1373, https://doi.org/10.1107/S0365110X64003450, 1964b.
Dovesi, R., Roetti, C., Freyria Fava, C., Prencipe, M., and Saunders, V. R.: On the elastic properties of lithium, sodium an potassium oxide. An ab initio study, Chemical Physics, 156, 11–19, 1991.
Dovesi, R., Erba, A., Orlando, R., Zicovich-Wilson, C. M., Civalleri, B., Maschio, L., Rerat, M., Casassa, S., Baima, J., Salustro, S., and Kirtman, B.: Quantum-mechanical condensed matter simulations with CRYSTAL, Wiley Interdisciplinary Reviews-Computational Molecular Science, 8, E1360, https://doi.org/10.1002/Wcms.1360, 2018.
Fletcher, R.: A new approach to variable metric algorithms, The Computer Journal, 13, 317–322, https://doi.org/10.1093/comjnl/13.3.317, 1970.
Gaillac, R., Pullumbi, P., and Coudert, F. X.: ELATE: an open-source online application for analysis and visualization of elastic tensors, Journal of Physics-Condensed Matter, 28, 275201, https://doi.org/10.1088/0953-8984/28/27/275201, 2016.
Gatta, G. D., Merlini, M., Rotiroti, N., Curetti, N., and Pavese, A.: On the crystal chemistry and elastic behavior of a phlogopite 3T, Physics and Chemistry of Minerals, 38, 655–664, https://doi.org/10.1007/s00269-011-0438-z, 2011.
Gatta, G. D., Lotti, P., Merlini, M., Liermann, H.-P., Lausi, A., Valdrè, G., and Pavese, A.: Elastic behaviour and phase stability of pyrophyllite and talc at high pressure and temperature, Physics and Chemistry of Minerals, 42, 309–318, https://doi.org/10.1007/s00269-014-0721-x, 2015.
Gatti, C., Saunders, V. R., and Roetti, C.: Crystal-field effects on the topological properties of the electron-density in molecular-crystals – the case of urea, Journal of Chemical Physics, 101, 10686–10696, https://doi.org/10.1063/1.467882, 1994.
Geng, X., Tian, S., Xu, W., Chen, L., Lu, N., Liang, Z., Hu, W., and Liu, J.: A Two-Stage Geodynamic Model for Post-Collisional Potassic-Ultrapotassic Magmatism in Southeast Tibet, Journal of Geophysical Research: Solid Earth, 129, https://doi.org/10.1029/2024JB028887, 2024.
Goldfarb, D.: A family of variable-metric methods derived by variational means, Mathematics of Computation, 24, 23–26, https://doi.org/10.1090/S0025-5718-1970-0258249-6 1970.
Grimme, S.: Semiempirical GGA-type density functional constructed with a long-range dispersion correction, Journal of Computational Chemistry, 27, 1787–1799, https://doi.org/10.1002/jcc.20495, 2006.
Guidotti, C. V. and Sassi, F. P.: Muscovite as a petrogenetic indicator mineral in pelitic schists, Neues Jahrbuch fuer Mineralogie, Abhandlungen, 123, 97–142, 1976.
Hebbache, M. and Zemzemi, M.: Ab initio study of high-pressure behavior of a low compressibility metal and a hard material: Osmium and diamond, Physical Review B, 70, https://doi.org/10.1103/Physrevb.70.224107, 2004.
Hill, R.: The elastic behaviour of a crystalline aggregate, Proceedings of the Physical Society, London, Section A, 65, 349–354, 1952.
Icenhower, J. and London, D.: An experimental study of element partitioning among biotite, muscovite, and coexisting peraluminous silicic melt at 200 MPa (H2O), American Mineralogist, 80, 1229–1251, https://doi.org/10.2138/am-1995-11-1213, 1995.
Jaeken, J. W. and Cottenier, S.: Solving the Christoffel equation: Phase and group velocities, Computer Physics Communications, 207, 445–451, https://doi.org/10.1016/j.cpc.2016.06.014, 2016.
King, T. T., Grayeski, W., and Cooper, R. F.: Thermochemical reactions and equilibria between fluoromicas and silicate matrices: A petromimetic perspective on structural ceramic composites, Journal of the American Ceramic Society, 83, 2287–2296, https://doi.org/10.1111/j.1151-2916.2000.tb01549.x, 2000.
Kruse, H. and Grimme, S.: A geometrical correction for the inter- and intra-molecular basis set superposition error in Hartree-Fock and density functional theory calculations for large systems, Journal of Chemical Physics, 136, https://doi.org/10.1063/1.3700154, 2012.
Lacalamita, M., Mesto, E., Scordari, F., and Schingaro, E.: Chemical and structural study of 1M- and 2M (1)-phlogopites coexisting in the same Kasenyi kamafugitic rock (SW Uganda), Physics and Chemistry of Minerals, 39, 601–611, https://doi.org/10.1007/s00269-012-0515-y, 2012.
Laurora, A., Brigatti, M. F., Mottana, A., Malferrari, D., and Caprilli, E.: Crystal chemistry of trioctahedral micas alkaline and subalkaline volcanic rocks: A case study from Mt. Sassetto (Tolfa district, central Italy), American Mineralogist, 92, 468–480, https://doi.org/10.2138/am.2007.2339, 2007.
Lee, C. T., Yang, W. T., and Parr, R. G.: Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron-Density, Physical Review B, 37, 785–789, https://doi.org/10.1103/PhysRevB.37.785, 1988.
Long, M. D. and Silver, P. G.: The subduction zone flow field from seismic anisotropy: a global view, Science, 319, 315–318, https://doi.org/10.1126/science.1150809, 2008.
Mainprice, D., Le Page, Y., Rodgers, J., and Jouanna, P.: Ab initio elastic properties of talc from 0 to 12 GPa: Interpretation of seismic velocities at mantle pressures and prediction of auxetic behaviour at low pressure, Earth and Planetary Science Letters, 274, 327–338, https://doi.org/10.1016/j.epsl.2008.07.047, 2008.
Melzer, S. and Wunder, B.: K-Rb-Cs partitioning between phlogopite and fluid: Experiments and consequences for the LILE signatures of island arc basalts, Lithos, 59, 69–90, https://doi.org/10.1016/S0024-4937(01)00061-5, 2001.
Momma, K. and Izumi, F.: VESTA: a three-dimensional visualization system for electronic and structural analysis, J. Appl. Crystallogr., 41, 653–658, 2008.
Mookherjee, M. and Capitani, G. C.: Trench parallel anisotropy and large delay times: Elasticity and anisotropy of antigorite at high pressures, Geophys. Res. Lett., 38, L09315, https://doi.org/10.1029/2011gl047160, 2011.
Mookherjee, M., Tsuchiya, J., and Hariharan, A.: Crystal structure, equation of state, and elasticity of hydrous aluminosilicate phase, topaz-OH (Al2SiO4(OH)(2)) at high pressures, Physics of the Earth and Planetary Interiors, 251, 24–35, https://doi.org/10.1016/j.pepi.2015.11.006, 2016.
Musgrave, M. J. P.: Crystal Acoustics: introduction to the study of elastic waves and vibrations in crystals, Holden-Day, San Francisco, CA, USA, ISBN 9780816262021, 1970.
Nada, R., Nicholas, J. B., McCarthy, M. I., and Hess, A. C.: Basis sets for ab initio periodic Hartree-Fock studies of zeolite/adsorbate interactions: He, Ne, and Ar in silica sodalite, International Journal of Quantum Chemistry, 60, 809-820, https://doi.org/10.1002/(SICI)1097-461X(1996)60:4<809::AID-QUA3>3.0.CO;2-0, 1996.
Nye, J. F.: Physical properties of crystals, Oxford University Press, Oxford, ISBN 9780198511656., 1957.
Ottonello, G., Civalleri, B., Ganguly, J., Perger, W. F., Belmonte, D., and Zuccolini, M. V.: Thermo-chemical and thermo-physical properties of the high-pressure phase anhydrous B (Mg14Si5O24): An ab-initio all-electron investigation, American Mineralogist, 95, 563–573, https://doi.org/10.2138/am.2010.3368, 2010.
Pavese, A., Ferraris, G., Pischedda, V., and Mezouar, M.: Synchrotron powder diffraction study of phengite 3T from the Dora-Maira massif: P-V-T equation of state and petrological consequences, Physics and Chemistry of Minerals, 26, 460–467, https://doi.org/10.1007/s002690050208, 1999.
Pavese, A., Levy, D., Curetti, N., Diella, V., Fumagalli, P., and Sani, A.: Equation of state and compressibility of phlogopite by in-situ high-pressure X-ray powder diffraction, European Journal of Mineralogy, 15, 455–463, https://doi.org/10.1127/0935-1221/2003/0015-0455, 2003.
Pawley, A. R., Clark, S. M., and Chinnery, N. J.: Equation of state measurements of chlorite, pyrophyllite, and talc, American Mineralogist, 87, 1172–1182, 2002.
Perger, W. F., Criswell, J., Civalleri, B., and Dovesi, R.: Ab-initio calculation of elastic constants of crystalline systems with the CRYSTAL code, Computer Physics Communications, 180, 1753–1759, https://doi.org/10.1016/j.cpc.2009.04.022, 2009.
Pfrommer, B. G., Côté, M., Louie, S. G., and Cohen, M. L.: Relaxation of Crystals with the Quasi-Newton Method, Journal of Computational Physics, 131, 233–240, https://doi.org/10.1006/jcph.1996.5612, 1997.
Prencipe, M., Noel, Y., Bruno, M., and Dovesi, R.: The vibrational spectrum of lizardite-1T [Mg(3)Si(2)O(5)(OH)(4)] at the Gamma point: A contribution from an ab initio periodic B3LYP calculation, American Mineralogist, 94, 986–994, 2009.
Ranganathan, S. I. and Ostoja-Starzewski, M.: Universal elastic anisotropy index, Physical Review Letters, 101, 055504, https://doi.org/10.1103/PhysRevLett.101.055504, 2008.
Shanno, D. F.: Conditioning of quasi-Newton methods for function minimization, Mathematics of Computation, 24, 647–656, https://doi.org/10.1090/S0025-5718-1970-0274029-X 1970.
Sudo, A. and Tatsumi, Y.: Phlogopite and K-amphibole in the upper mantle: Implication for magma genesis in subduction zones, Geophys. Res. Lett., 17, 29–32, https://doi.org/10.1029/GL017i001p00029, 1990.
Sweeney, R. J., Thompson, A. B., and Ulmer, P.: Phase relations of a natural MARID composition and implications for MARID genesis, lithospheric melting and mantle metasomatism, Contributions to Mineralogy and Petrology, 115, 225–241, https://doi.org/10.1007/BF00321222, 1993.
Trønnes, R. G.: Stability range and decomposition of potassic richterite and phlogopite end members at 5-15 GPa, Mineralogy and Petrology, 74, 129–148, https://doi.org/10.1007/s007100200001, 2002.
Tutti, F., Dubrovinsky, L. S., and Nygren, M.: High-temperature study and thermal expansion of phlogopite, Physics and Chemistry of Minerals, 27, 599–603, https://doi.org/10.1007/s002690000098, 2000.
Ulian, G. and Valdrè, G.: Density functional investigation of the thermo-physical and thermo-chemical properties of 2M(1) muscovite, American Mineralogist, 100, 935–944, https://doi.org/10.2138/am-2015-5086, 2015a.
Ulian, G. and Valdrè, G.: Structural, vibrational and thermophysical properties of pyrophyllite by semi-empirical density functional modelling, Physics and Chemistry of Minerals, 42, 609–627, https://doi.org/10.1007/s00269-015-0748-7, 2015b.
Ulian, G. and Valdrè, G.: Density functional investigation of the thermophysical and thermochemical properties of talc Mg3Si4O10(OH)(2), Physics and Chemistry of Minerals, 42, 151–162, https://doi.org/10.1007/s00269-014-0708-7, 2015c.
Ulian, G. and Valdrè, G.: Second-order elastic constants of hexagonal hydroxylapatite (P63) from ab initio quantum mechanics: comparison between DFT functionals and basis sets, International Journal of Quantum Chemistry, 118, e25500, https://doi.org/10.1002/qua.25500, 2018.
Ulian, G. and Valdrè, G.: Equation of state and second-order elastic constants of portlandite Ca(OH)2 and brucite Mg(OH)2, Physics and Chemistry of Minerals, 46, 101–117, https://doi.org/10.1007/s00269-018-0989-3, 2019.
Ulian, G. and Valdrè, G.: QUANTAS, a Python software for the analysis of solids from ab initio quantum mechanical simulations and experimental data, J. Appl. Crystallogr., 55, 386–396, https://doi.org/10.1107/S1600576722000085, 2022.
Ulian, G. and Valdrè, G.: Crystal-chemical, vibrational and electronic properties of 1M-phlogopite K(Mg,Fe)3Si3AlO10(OH)2 from Density Functional Theory simulations, Applied Clay Science, 246, 107166, https://doi.org/10.1016/j.clay.2023.107166, 2023a.
Ulian, G. and Valdrè, G.: The effect of long-range interactions on the infrared and Raman spectra of aragonite (CaCO3, Pmcn) up to 25 GPa, Scientific Reports, 13, 2725, https://doi.org/10.1038/s41598-023-29783-7, 2023b.
Ulian, G. and Valdrè, G.: SEISMIC, a Python-based code of the QUANTAS package to calculate the phase and group acoustic velocities in crystals, Computers and Geosciences, 188, https://doi.org/10.1016/j.cageo.2024.105615, 2024a.
Ulian, G. and Valdrè, G.: Crystal structure and elastic and phonon properties of realgar versus pressure, J. Appl. Crystallogr., 57, 220–231, https://doi.org/10.1107/S1600576724000025, 2024b.
Ulian, G. and Valdrè, G.: Elastic properties of phlogopite 1M and 2M1 polytypes, Mendeley Data, V1 [data set], https://doi.org/10.17632/r4wmxz7kcc.1, 2024c.
Ulian, G. and Valdrè, G.: Crystallographic, electronic and vibrational properties of 2D silicate monolayers, J. Appl. Crystallogr., 58, 349–362, https://doi.org/10.1107/S1600576725000731, 2025.
Ulian, G., Tosoni, S., and Valdrè, G.: Comparison between Gaussian-type orbitals and plane wave ab initio density functional theory modeling of layer silicates: Talc Mg3Si4O10(OH)(2) as model system, Journal of Chemical Physics, 139, 204101, https://doi.org/10.1063/1.4830405, 2013.
Ulian, G., Tosoni, S., and Valdrè, G.: The compressional behaviour and the mechanical properties of talc [Mg3Si4O10(OH)2]: a density functional theory investigation, Physics and Chemistry of Minerals, 41, 639–650, https://doi.org/10.1007/s00269-014-0677-x, 2014.
Ulian, G., Moro, D., and Valdrè, G.: Elastic properties of heterodesmic composite structures: The case of calcite CaCO3 (space group R-3c), Composites Part C: Open Access, 6, https://doi.org/10.1016/j.jcomc.2021.100184, 2021.
Valenzano, L., Torres, F. J., Doll, K., Pascale, F., Zicovich-Wilson, C. M., and Dovesi, R.: Ab initio study of the vibrational spectrum and related properties of crystalline compounds; the case of CaCO3 calcite, Zeitschrift Fur Physikalische Chemie-International Journal of Research in Physical Chemistry & Chemical Physics, 220, 893–912, https://doi.org/10.1524/zpch.2006.220.7.893, 2006.
Valenzano, L., Noel, Y., Orlando, R., Zicovich-Wilson, C. M., Ferrero, M., and Dovesi, R.: Ab initio vibrational spectra and dielectric properties of carbonates: magnesite, calcite and dolomite, Theoretical Chemistry Accounts, 117, 991–1000, https://doi.org/10.1007/s00214-006-0213-2, 2007.
Van Reenen, D. D., Smit, C. A., Huizenga, J. M., Tsunogae, T., and Safonov, O.: Thermo-tectonic evolution of the Neoarchaean Southern Marginal Zone of the Limpopo granulite Complex (South Africa), South African Journal of Geology, 126, 373–406, https://doi.org/10.25131/sajg.126.0027, 2023.
Vaughan, M. T. and Guggenheim, S.: Elasticity of muscovite and its relationship to crystal structure, Journal of Geophysical Research: Solid Earth, 91, 4657–4664, https://doi.org/10.1029/JB091iB05p04657, 1986.
Ventruti, G., Levy, D., Pavese, A., Scordari, F., and Suard, E.: High-temperature treatment, hydrogen behaviour and cation partitioning of a Fe-Ti bearing volcanic phlogopite by in situ neutron powder diffraction and FTIR spectroscopy, European Journal of Mineralogy, 21, 385–396, https://doi.org/10.1127/0935-1221/2009/0021-1903, 2009.
Virgo, D. and Popp, R. K.: Hydrogen deficiency in mantle-derived phlogopites, American Mineralogist, 85, 753–759, https://doi.org/10.2138/am-2000-5-614, 2000.
Wang, J., Wang, Q., Ma, L., Hu, W. L., Wang, J., Belousova, E., and Tang, G. J.: Rapid Recycling of Subducted Sediments in the Subcontinental Lithospheric Mantle, Journal of Petrology, 64, https://doi.org/10.1093/petrology/egad056, 2023.
Short summary
Layer silicates (phyllosilicates) are important minerals because of their ubiquity on the Earth’s crust and due to their ability to release water in the mantle. The present study focuses on the elastic properties of a specific phyllosilicate known as phlogopite [KMg3Si3AlO10(OH)2], which were characterised using first-principles methods. The results show the mineral's anisotropic mechanical behaviour, which also depends on how the mineral layers are stacked in the crystal structure.
Layer silicates (phyllosilicates) are important minerals because of their ubiquity on the...