{"id":183292,"date":"2025-06-14T08:24:11","date_gmt":"2025-06-14T08:24:11","guid":{"rendered":"https:\/\/www.europesays.com\/uk\/183292\/"},"modified":"2025-06-14T08:24:11","modified_gmt":"2025-06-14T08:24:11","slug":"quasicrystal-stability-and-nucleation-kinetics-from-density-functional-theory","status":"publish","type":"post","link":"https:\/\/www.europesays.com\/uk\/183292\/","title":{"rendered":"Quasicrystal stability and nucleation kinetics from density functional theory"},"content":{"rendered":"
  • \n

    Shechtman, D., Blech, I., Gratias, D. & Cahn, J. W. Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53<\/b>, 1951\u20131953 (1984).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Kelton, K. F. Quasicrystals: structure and stability. Int. Mater. Rev. 38<\/b>, 105\u2013137 (1993).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Steurer, W. Quasicrystals: what do we know? What do we want to know? What can we know? Acta Crystallogr. Sect. A: Found. Adv. 74<\/b>, 1\u201311 (2018).<\/p>\n

    Article<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Shimasaki, T. et al. Anomalous localization in a kicked quasicrystal. Nat. Phys. 20<\/b>, 409\u2013414 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Jeon, S. Y., Kwon, H. & Hur, K. Intrinsic photonic wave localization in a three-dimensional icosahedral quasicrystal. Nat. Phys. 13<\/b>, 363\u2013368 (2017).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Nagai, Y. et al. High-Temperature atomic diffusion and specific heat in quasicrystals. Phys. Rev. Lett. 132<\/b>, 196301 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Ghadimi, R., Sugimoto, T., Tanaka, K. & Tohyama, T. Topological superconductivity in quasicrystals. Phys. Rev. B: Condens. Matter Mater. Phys. 104<\/b>, 144511 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Uri, A. et al. Superconductivity and strong interactions in a tunable moir\u00e9 quasicrystal. Nature 620<\/b>, 762\u2013767 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Han, I. et al. Formation of a single quasicrystal upon collision of multiple grains. Nat. Commun. 12<\/b>, 5790 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Dyson, F. Birds and frogs. Not. AMS 56<\/b>, 212\u2013223 (2009).<\/p>\n

    MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Torquato, S., Zhang, G. & De Courcy-Ireland, M. Hidden multiscale order in the primes. J. Phys. A: Math. Theor. 52<\/b>, 135002 (2019).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Steurer, W. Twenty years of structure research on quasicrystals. Part I. Pentagonal, octagonal, decagonal, and dodecagonal quasicrystals. Z. Krist. Cryst. Mater. 219<\/b>, 391\u2013446 (2004).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Mukhopadhyay, N. K. & Yadav, T. P. Quasicrystals: a new class of structurally complex intermetallics. J. Indian Inst. Sci. 102<\/b>, 59\u201390 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Sun, W. et al. The thermodynamic scale of inorganic crystalline metastability. Sci. Adv. 2<\/b>, e1600225 (2016).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Kalugin, P. Growth of entropy stabilized quasicrystals. Eur. Phys. J. B 18<\/b>, 77\u201384 (2000).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Je, K., Lee, S., Teich, E. G., Engel, M. & Glotzer, S. C. Entropic formation of a thermodynamically stable colloidal quasicrystal with negligible phason strain. Proc. Natl Acad. Sci. USA 118<\/b>, e2011799118 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Widom, M. & Mihalkovi\u010d, M. Quasicrystal structure prediction: a review. Isr. J. Chem. https:\/\/doi.org\/10.1002\/ijch.202300122<\/a> (2023).<\/p>\n<\/li>\n

  • \n

    Fayen, E., Filion, L., Foffi, G. & Smallenburg, F. Quasicrystal of binary hard spheres on a plane stabilized by configurational entropy. Phys. Rev. Lett. 132<\/b>, 48202 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Tsai, A. P., Guo, J. Q., Abe, E., Takakura, H. & Sato, T. J. A stable binary quasicrystal. Nature 408<\/b>, 537\u2013538 (2000).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Canfield, P. C. et al. Solution growth of a binary icosahedral quasicrystal of Sc12Zn88. Phys. Rev. B 81<\/b>, 020201 (2010).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Henley, C. L., De Boissieu, M. & Steurer, W. Discussion on clusters, phasons and quasicrystal stabilisation. Philos. Mag. 86<\/b>, 1131\u20131151 (2006).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Tsai, A. P. Icosahedral clusters, icosaheral order and stability of quasicrystals\u2014a view of metallurgy. Sci. Technol. Adv. Mater. 9<\/b>, 013008 (2008).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Tsai, A. P. A test of Hume-Rothery rules for stable quasicrystals. J. Non-Cryst. Solids 334<\/b>, 317\u2013322 (2004).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Tsai, A. P. Discovery of stable icosahedral quasicrystals: progress in understanding structure and properties. Chem. Soc. Rev. 42<\/b>, 5352\u20135365 (2013).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Tsai, A. P., Inoue, A., Bizen, Y. & Masumoto, T. Kinetics of the amorphous to icosahedral structure transition in Al-Cu-V and Al-Mn-Si alloys. Acta Metall. 37<\/b>, 1443\u20131449 (1989).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Okumura, H., Tsai, A. P., Inoue, A. & Masumoto, T. The observation of mechanical relaxation in a quasicrystalline Al75Cu15V10 alloy. Mater. Sci. Eng.: A 181<\/b>, 781\u2013784 (1994).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Weisbecker, P., Bonhomme, G., Bott, G. & Dubois, J. M. The oxidation at 500\u2009\u00b0C of AlCuFe quasicrystalline powders: a X-ray diffraction study. J. Non-Cryst. Solids 351<\/b>, 1630\u20131638 (2005).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Hennig, R. G., Carlsson, A. E., Kelton, K. F. & Henley, C. L. Ab initio Ti-Zr-Ni phase diagram predicts stability of icosahedral TiZrNi quasicrystals. Phys. Rev. B: Condens. Matter Mater. Phys. 71<\/b>, 144103 (2005).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Berns, V. M. & Fredrickson, D. C. Problem solving with pentagons: Tsai-type quasicrystal as a structural response to chemical pressure. Inorg. Chem. 52<\/b>, 12875\u201312877 (2013).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Henley, C. L., Mihalkovi\u010d, M. & Widom, M. Total-energy-based structure prediction for d(AlNiCo). J. Alloys Compd. 342<\/b>, 221\u2013227 (2002).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Engel, M., Damasceno, P. F., Phillips, C. L. & Glotzer, S. C. Computational self-assembly of a one-component icosahedral quasicrystal. Nat. Mater. 14<\/b>, 109\u2013116 (2015).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Mihalkovi\u010d, M. & Widom, M. Spontaneous formation of thermodynamically stable Al-Cu-Fe icosahedral quasicrystal from realistic atomistic simulations. Phys. Rev. Res. 2<\/b>, 013196 (2020).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Han, I. et al. Dynamic observation of dendritic quasicrystal growth upon laser-induced solid-state transformation. Phys. Rev. Lett. 125<\/b>, 195503 (2020).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Kurtuldu, G. & Bernet, M. The relation between the glass forming ability and nucleation kinetics of metastable quasicrystals in Mg\u2013Zn\u2013Yb liquid. J. Alloys Compd. 945<\/b>, 168930 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Fiorentini, V. & Methfessel, M. Extracting convergent surface energies from slab calculations. J. Phys.: Condens. Matter 8<\/b>, 6525 (1996).<\/p>\n

    ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Gavini, V., Knap, J., Bhattacharya, K. & Ortiz, M. Non-periodic finite-element formulation of orbital-free density functional theory. J. Mech. Phys. Solids 55<\/b>, 669\u2013696 (2007).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Dreyer, C. E., Janotti, A. & Van De Walle, C. G. Absolute surface energies of polar and nonpolar planes of GaN. Phys. Rev. B: Condens. Matter Mater. Phys. 89<\/b>, 081305 (2014).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Navrotsky, A. Nanoscale effects on thermodynamics and phase equilibria in oxide systems. ChemPhysChem 12<\/b>, 2207\u20132215 (2011).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Navrotsky, A. Energetics at the nanoscale: impacts for geochemistry, the environment, and materials. MRS Bull. 41<\/b>, 139\u2013145 (2016).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Takakura, H., G\u00f3mez, C. P., Yamamoto, A., De Boissieu, M. & Tsai, A. P. Atomic structure of the binary icosahedral Yb\u2013Cd quasicrystal. Nat. Mater. 6<\/b>, 58\u201363 (2007).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Yamada, T. et al. Atomic structure and phason modes of the Sc\u2013Zn icosahedral quasicrystal. IUCrJ 3<\/b>, 247\u2013258 (2016).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Motamarri, P. et al. DFT-FE\u2013A massively parallel adaptive finite-element code for large-scale density functional theory calculations. Comput. Phys. Commun. 246<\/b>, 106853 (2020).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Das, S., Motamarri, P., Subramanian, V., Rogers, D. M. & Gavini, V. DFT-FE 1.0: a massively parallel hybrid CPU-GPU density functional theory code using finite-element discretization. Comput. Phys. Commun. 280<\/b>, 108473 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Motamarri, P. & Gavini, V. Configurational forces in electronic structure calculations using Kohn-Sham density functional theory. Phys. Rev. B 97<\/b>, 165132 (2018).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Motamarri, P., Nowak, M. R., Leiter, K., Knap, J. & Gavini, V. Higher-order adaptive finite-element methods for Kohn\u2013Sham density functional theory. J. Comput. Phys. 253<\/b>, 308\u2013343 (2013).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Zhou, Y., Saad, Y., Tiago, M. L. & Chelikowsky, J. R. Self-consistent-field calculations using Chebyshev-filtered subspace iteration. J. Comput. Phys. 219<\/b>, 172\u2013184 (2006).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Das, S. et al. Fast, scalable, and accurate finite-element based ab initio calculations using mixed precision computing: 46 PFLOPS simulation of a metallic dislocation system. In Proc. International Conference for High Performance Computing, Networking, Storage and Analysis 1\u201311 (ACM, 2019).<\/p>\n<\/li>\n

  • \n

    Hamann, D. R. Optimized norm-conserving Vanderbilt pseudopotentials. Phys. Rev. B: Condens. Matter Mater. Phys. 88<\/b>, 085117 (2013).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Prandini, G., Marrazzo, A., Castelli, I. E., Mounet, N. & Marzari, N. Precision and efficiency in solid-state pseudopotential calculations. npj Comput. Mater. 4<\/b>, 72 (2018).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Das, S. et al. Large-scale materials modeling at quantum accuracy: ab initio simulations of quasicrystals and interacting extended defects in metallic alloys. In Proc. International Conference for High Performance Computing, Networking, Storage and Analysis 1\u201312 (ACM, 2023).<\/p>\n<\/li>\n

  • \n

    Service, R. F. Exascale computers show off emerging science. Science 382<\/b>, 864\u2013865 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Curtarolo, S., Morgan, D. & Ceder, G. Accuracy of ab initio methods in predicting the crystal structures of metals: a review of 80 binary alloys. Calphad 29<\/b>, 163\u2013211 (2005).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Brown, I. D. Chemical and steric constraints in inorganic solids. Acta Crystallogr. Sect. B: Struct. Sci. Cryst. Eng. Mater. 48<\/b>, 553\u2013572 (1992).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Lalvani, H. Non-periodic space structures. Int. J. Space Struct. 2<\/b>, 93\u2013108 (1987).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Palenzona, A. & Manfrinetti, P. The phase diagram of the Sc-Zn system. J. Alloys Compd. 247<\/b>, 195\u2013197 (1997).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Sun, W., Jayaraman, S., Chen, W., Persson, K. A. & Ceder, G. Nucleation of metastable aragonite CaCO3 in seawater. Proc. Natl Acad. Sci. USA 112<\/b>, 3199\u20133204 (2015).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Sun, W. & Ceder, G. Efficient creation and convergence of surface slabs. Surf. Sci. 617<\/b>, 53\u201359 (2013).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Sun, W., Kitchaev, D. A., Kramer, D. & Ceder, G. Non-equilibrium crystallization pathways of manganese oxides in aqueous solution. Nat. Commun. 10<\/b>, 573 (2019).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Balluffi, R. W., Allen, S. M. & Carter, W. C. Kinetics of Materials (Wiley, 2005).<\/p>\n<\/li>\n

  • \n

    Bocklund, B. et al. ESPEI for efficient thermodynamic database development, modification, and uncertainty quantification: Application to Cu-Mg. MRS Commun. 9<\/b>, 618\u2013627 (2019).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Tang, C. et al. Thermodynamic modeling of the Sc-Zn system coupled with first-principles calculation. J. Min. Metall. Sect. B: Metall. 48<\/b>, 123\u2013130 (2012).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Palenzona, A. The ytterbium-cadmium system. J. Less Common Met. 25<\/b>, 367\u2013372 (1971).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Togo, A., Chaput, L., Tadano, T. & Tanaka, I. Implementation strategies in phonopy and phono3py. J. Phys.: Condens. Matter 35<\/b>, 353001 (2023).<\/p>\n


    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Carreras, A., Togo, A. & Tanaka, I. DynaPhoPy: a code for extracting phonon quasiparticles from molecular dynamics simulations. Comput. Phys. Commun. 221<\/b>, 221\u2013234 (2017).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Puchala, B. et al. CASM \u2014 a software package for first-principles based study of multicomponent crystalline solids. Comput. Mater. Sci. 217<\/b>, 111897 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Edagawa, K., Kajiyama, K., Tamura, R. & Takeuchi, S. High-temperature specific heat of quasicrystals and a crystal approximant. Mater. Sci. Eng.: A 312<\/b>, 293\u2013298 (2001).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Maintz, S., Deringer, V. L., Tchougr\u00e9eff, A. L. & Dronskowski, R. LOBSTER: a tool to extract chemical bonding from plane-wave based DFT. J. Comput. Chem. 37<\/b>, 1030\u20131035 (2016).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Fredrickson, D. C. DFT-chemical pressure analysis: visualizing the role of atomic size in shaping the structures of inorganic materials. J. Am. Chem. Soc. 134<\/b>, 5991\u20135999 (2012).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Fredrickson, R. T. & Fredrickson, D. C. Chemical pressure-derived assembly principles for dodecagonal quasicrystal approximants and other complex Frank-Kasper phases. Inorg. Chem. 61<\/b>, 17682\u201317691 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Jiang, K. & Zhang, P. Numerical methods for quasicrystals. J. Comput. Phys. 256<\/b>, 428\u2013440 (2014).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Yin, J., Jiang, K., Shi, A. C., Zhang, P. & Zhang, L. Transition pathways connecting crystals and quasicrystals. Proc. Natl Acad. Sci. USA 118<\/b>, e2106230118 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Miao, J., Ercius, P. & Billinge, S. J. L. Atomic electron tomography: 3D structures without crystals. Science 353<\/b>, aaf2157 (2016).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Fredrickson, D. C., Lee, S. & Hoffmann, R. Interpenetrating polar and nonpolar sublattices in intermetallics: the NaCd2 structure. Angew. Chem. Int. Ed. 46<\/b>, 1958\u20131976 (2007).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Dijkstra, M. & Luijten, E. From predictive modelling to machine learning and reverse engineering of colloidal self-assembly. Nat. Mater. 20<\/b>, 762\u2013773 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Zhou, W. et al. Colloidal quasicrystals engineered with DNA. Nat. Mater. 23<\/b>, 424\u2013428 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Liu, X.-Y. et al. Self-assembled soft alloy with Frank\u2013Kasper phases beyond metals. Nat. Mater. 23<\/b>, 570\u2013576 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Zuo, Y. et al. Performance and cost assessment of machine learning interatomic potentials. J. Phys. Chem. A 124<\/b>, 731\u2013745 (2020).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Giannozzi, P. et al. QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials. J. Phys.: Condens. Matter 21<\/b>, 395502 (2009).<\/p>\n


    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Giannozzi, P. et al. Advanced capabilities for materials modelling with Quantum ESPRESSO. J. Phys.: Condens. Matter 29<\/b>, 465901 (2017).<\/p>\n


    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77<\/b>, 3865 (1996).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Schlipf, M. & Gygi, F. Optimization algorithm for the generation of ONCV pseudopotentials. Comput. Phys. Commun. 196<\/b>, 36\u201344 (2015).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Jain, A. et al. A high-throughput infrastructure for density functional theory calculations. Comput. Mater. Sci. 50<\/b>, 2295\u20132310 (2011).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Tran, R. et al. Surface energies of elemental crystals. Sci. Data 3<\/b>, 160080 (2016).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Dinsdale, A. T. SGTE data for pure elements. Calphad 15<\/b>, 317\u2013425 (1991).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Redlich, O. & Kister, A. T. Algebraic representation of thermodynamic properties and the classification of solutions. Ind. Eng. Chem. 40<\/b>, 345\u2013348 (1948).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Eslami, H., Muggianu, Y. M., Gambino, M. & Bros, J. P. Enthalpies de formation des alliages liquides aluminium-germanium, gallium-germanium et aluminium-gallium-germanium entre 713 et 1230\u2009K. J. Less Common Met. 64<\/b>, 31\u201344 (1979).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Gelman, A. et al. Bayesian Data Analysis (CRC, 2013).<\/p>\n<\/li>\n","protected":false},"excerpt":{"rendered":"Shechtman, D., Blech, I., Gratias, D. & Cahn, J. W. Metallic phase with long-range orientational order and no…\n","protected":false},"author":2,"featured_media":183293,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3845],"tags":[11701,11700,11705,11704,75242,3968,11699,11702,11703,12374,74,70,75243,11698,3723,16,15],"class_list":{"0":"post-183292","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-physics","8":"tag-atomic","9":"tag-classical-and-continuum-physics","10":"tag-complex-systems","11":"tag-condensed-matter-physics","12":"tag-density-functional-theory","13":"tag-general","14":"tag-mathematical-and-computational-physics","15":"tag-molecular","16":"tag-optical-and-plasma-physics","17":"tag-phase-transitions-and-critical-phenomena","18":"tag-physics","19":"tag-science","20":"tag-structure-of-solids-and-liquids","21":"tag-theoretical","22":"tag-thermodynamics","23":"tag-uk","24":"tag-united-kingdom"},"share_on_mastodon":{"url":"https:\/\/pubeurope.com\/@uk\/114680762370961896","error":""},"_links":{"self":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts\/183292","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/comments?post=183292"}],"version-history":[{"count":0,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts\/183292\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/media\/183293"}],"wp:attachment":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/media?parent=183292"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/categories?post=183292"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/tags?post=183292"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}