Como a temperatura utilizada nas simula¸c˜oes foi escolhida de acordo com a tem- peratura de fus˜ao reportada para o funcional PBE no caso do gelo Ih, uma an´alise para
temperaturas mais baixas deve ser realizada, a fim de definir a partir de qual temperatura ocorre o premelting. A fim de obter uma conclus˜ao quantitativa quanto ao processo de difus˜ao do contorno de gr˜ao no gelo, no nosso grupo j´a foram realizadas an´alises utilizando modelos emp´ıricos com c´elulas contendo milhares de ´atomos, de forma que os resultados obtidos a partir de DFT s˜ao consistentes com os resultados de MD, indicando tamb´em uma difus˜ao anˆomala de car´ater subdifusivo. Tendo isto em vista, o pr´oximo desafio ´e en- contrar qual modelo de subdifus˜ao melhor descreve a dinˆamica das mol´eculas no contorno de gr˜ao. Al´em disso, a anisotropia de migra¸c˜ao mencionada no trabalho experimental realizado por Hondoh e Higashi tamb´em pode ser analisada futuramente.
Bibliografia
[1] The world’s water. https://water.usgs.gov/edu/earthwherewater.html. Aces- sado em 25 de Abril de 2017.
[2] It’s about time: A power line that sheds heavy ice. http://www.popsci.com/ science/article/2009-10/ice-breaker. Acessado em 26 de Abril de 2017. [3] Winter weather flying. http://amablog.modelaircraft.org/amaeducation/2013/
03/25/winter-weather-flying/. Acessado em 20 de Maio de 2017.
[4] Winter microphysics topics. http://www.meted.ucar.edu/norlat/snow/micro_ ice/1.1.crystal_growth.htm. Acessado em 9 de Maio de 2017.
[5] Sosso, G. C. et al. Crystal nucleation in liquids: Open questions and future challenges in molecular dynamics simulations. Chemical reviews 116, 7078–7116 (2016). [6] Vallentyne, J. R. Principles of modern limnology. American Scientist 45, 218–244
(1957).
[7] A look under the ice: Winter lake ecology. https://www.ausableriver.org/blog/ look-under-ice-winter-lake-ecology. Acessado em 9 de Maio de 2017.
[8] Bartels-Rausch, T. et al. Ice structures, patterns, and processes: A view across the icefields. Reviews of Modern Physics 84, 885 (2012).
[9] Sohl, F., Spohn, T., Breuer, D. & Nagel, K. Implications from galileo observations on the interior structure and chemistry of the galilean satellites. Icarus 157, 104–119 (2002).
[10] Libbrecht, K. G. The physics of snow crystals. Reports on Progress in Physics 68, 855 (2005).
Bibliografia 87 [11] Thorsteinsson, T., Kipfstuhl, J. & Miller, H. Textures and fabrics in the grip ice
core. Journal of Geophysical Research: Oceans 102, 26583–26599 (1997).
[12] Understanding grain boundary migration - theory meets experiment. http://www. mpie.de/3104106/GB2015. Acessado em 8 de maio de 2017.
[13] Atlantic canada online weather watchers. http://z7.invisionfree.com/ACOWW/ index.php?showtopic=6082. Acessado em 8 de maio de 2017.
[14] Wong, C. K., Brown, T. G. & Robertson, J. S. Assessment of flexure failure models using loads measured on the conical piers of the confederation bridge during 1998– 2008. Journal of Offshore Mechanics and Arctic Engineering 139, 011502 (2017). [15] Benedict, W., Gailar, N. & Plyler, E. K. Rotation-vibration spectra of deuterated
water vapor. The Journal of Chemical Physics 24, 1139–1165 (1956).
[16] Buckingham, A., Del Bene, J. & McDowell, S. The hydrogen bond. Chemical Physics Letters 463, 1–10 (2008).
[17] Anomalous properties of water. http://www1.lsbu.ac.uk/water/water_ anomalies.html. Acessado em 30 de Maio de 2017.
[18] Onodera, A. & Takesada, M. Electronic ferroelectricity in II-VI semiconductor ZnO. In Advances in Ferroelectrics (InTech, 2012).
[19] Kuhs, W. & Lehmann, M. The structure of the ice Ih by neutron diffraction. The
Journal of Physical Chemistry 87, 4312–4313 (1983).
[20] Pauling, L. The structure and entropy of ice and of other crystals with some ran- domness of atomic arrangement. Journal of the American Chemical Society 57, 2680–2684 (1935).
[21] Bernal, J. & Fowler, R. A theory of water and ionic solution, with particular reference to hydrogen and hydroxyl ions. The Journal of Chemical Physics 1, 515–548 (1933). [22] Nagle, J. F. Lattice statistics of hydrogen bonded crystals. I. the residual entropy of
ice. Journal of Mathematical Physics 7, 1484–1491 (1966).
[23] Haida, O., Matsuo, T., Suga, H. & Seki, S. Calorimetric study of the glassy state X. enthalpy relaxation at the glass-transition temperature of hexagonal ice. The Journal of Chemical Thermodynamics 6, 815–825 (1974).
262 (1989).
[26] Lejcek, P. Grain boundary segregation in metals, vol. 136 (Springer Science & Busi- ness Media, 2010).
[27] Glicksman, M. & Vold, C. Heterophase dislocations - an approach towards interpre- ting high temperature grain boundary behavior. Surface science 31, 50–67 (1972). [28] Winning, M., Gottstein, G. & Shvindlerman, L. On the mechanisms of grain boun-
dary migration. Acta Materialia 50, 353–363 (2002).
[29] Hondoh, T. & Higashi, A. Anisotopy of migration and faceting of large-angle grain boundaries in ice bicrystals. Philosophical Magazine A 39, 137–149 (1979).
[30] Bruggeman, G., Bishop, G. & Hartt, W. Coincidence and near-coincidence grain boundaries in hcp metals. In The Nature and Behavior of Grain Boundaries, 83–122 (Springer, 1972).
[31] Warrington, D. The coincidence site lattice (csl) and grain boundary (dsc) disloca- tions for the hexagonal lattice. Le Journal de Physique Colloques 36, C4–87 (1975). [32] Kobayashi, T. & Furukawa, Y. On twelve-branched snow crystals. Journal of Crystal
Growth 28, 21–28 (1975).
[33] Kobayashi, T., Furukawa, Y., Kikuchi, K. & Uyeda, H. On twinned structures in snow crystals. Journal of Crystal Growth 32, 233–249 (1976).
[34] Higashi, A. Structure and behaviour of grain boundaries in polycrystalline ice. Jour- nal of Glaciology 21, 589–605 (1978).
[35] Nasello, O., Di Prinzio, C. & Guzm´an, P. Temperature dependence of “pure” ice grain boundary mobility. Acta Materialia 53, 4863–4869 (2005).
[36] Petrenko, V. F. & Whitworth, R. W. Physics of ice (Oxford University Press, 1999). [37] Furukawa, Y. Faszination der Schneekristalle-wie ihre bezaubernden Formen ents-
Bibliografia 89 [38] Furukawa, Y., Yamamoto, M. & Kuroda, T. Ellipsometric study of the transition layer on the surface of an ice crystal. Journal of Crystal Growth 82, 665–677 (1987). [39] Van Oss, C., Giese, R., Wentzek, R., Norris, J. & Chuvilin, E. Surface tension para- meters of ice obtained from contact angle data and from positive and negative particle adhesion to advancing freezing fronts. Journal of adhesion science and technology 6, 503–516 (1992).
[40] Dash, J., Fu, H. & Wettlaufer, J. The premelting of ice and its environmental consequences. Reports on Progress in Physics 58, 115 (1995).
[41] Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Physical Review 136, B864 (1964).
[42] Sham, L. & Kohn, W. One-particle properties of an inhomogeneous interacting electron gas. Physical Review 145, 561 (1966).
[43] Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Physical Review 140, A1133 (1965).
[44] Perdew, J. P. et al. Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. Physical Review B 46, 6671 (1992).
[45] Perdew, J. P., Ernzerhof, M. & Burke, K. Rationale for mixing exact exchange with density functional approximations. The Journal of Chemical Physics 105, 9982–9985 (1996).
[46] Payne, M. C., Teter, M. P., Allan, D. C., Arias, T. & Joannopoulos, J. Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients. Reviews of modern physics 64, 1045 (1992).
[47] Vanderbilt, D. Soft self-consistent pseudopotentials in a generalized eigenvalue for- malism. Physical Review B 41, 7892 (1990).
[48] Laasonen, K., Car, R., Lee, C. & Vanderbilt, D. Implementation of ultrasoft pseu- dopotentials in ab initio molecular dynamics. Physical Review B 43, 6796 (1991). [49] Laasonen, K., Pasquarello, A., Car, R., Lee, C. & Vanderbilt, D. Car-parrinello
molecular dynamics with vanderbilt ultrasoft pseudopotentials. Physical Review B 47, 10142 (1993).
[52] Model Box Periodic Boundary Conditions - P.B.C. http://isaacs.sourceforge. net/phys/pbc.html. Acessado em 23 de Maio de 2017.
[53] Hoy, A. & Bunker, P. R. A precise solution of the rotation bending schr¨odinger equation for a triatomic molecule with application to the water molecule. Journal of Molecular Spectroscopy 74, 1–8 (1979).
[54] Sholl, D. & Steckel, J. A. Density functional theory: a practical introduction (John Wiley & Sons, 2011).
[55] Alder, B. & Wainwright, T. Phase transition for a hard sphere system. The Journal of chemical physics 27, 1208–1209 (1957).
[56] Alder, B. J. & Wainwright, T. E. Studies in molecular dynamics. I. general method. The Journal of Chemical Physics 31, 459–466 (1959).
[57] Stillinger, F. H. & Rahman, A. Improved simulation of liquid water by molecular dynamics. The Journal of Chemical Physics 60, 1545–1557 (1974).
[58] Nos´e, S. A unified formulation of the constant temperature molecular dynamics methods. The Journal of Chemical Physics 81, 511–519 (1984).
[59] Nos´e, S. A molecular dynamics method for simulations in the canonical ensemble. Molecular Physics 52, 255–268 (1984).
[60] Hoover, W. G. Canonical dynamics: equilibrium phase-space distributions. Physical Review A 31, 1695 (1985).
[61] Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Physical Review B 47, 558 (1993).
[62] Kresse, G. & Hafner, J. Ab initio molecular-dynamics simulation of the liquid-metal- amorphous-semiconductor transition in germanium. Physical Review B 49, 14251 (1994).
[63] Kresse, G. & Furthm¨uller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Physical Review B 54, 11169 (1996).
Bibliografia 91 [64] Kresse, G. & Furthm¨uller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Computational Materials Science 6, 15–50 (1996).
[65] Pulay, P. Convergence acceleration of iterative sequences. the case of scf iteration. Chemical Physics Letters 73, 393–398 (1980).
[66] Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. Journal of Computational Physics 117, 1–19 (1995).
[67] Wu, Y., Tepper, H. L. & Voth, G. A. Flexible simple point-charge water model with improved liquid-state properties. The Journal of Chemical Physics 124, 024503 (2006).
[68] Yoo, S., Zeng, X. C. & Xantheas, S. S. On the phase diagram of water with density functional theory potentials: the melting temperature of ice Ih with the Perdew-
Burke-Ernzerhof and Becke-Lee-Yang-Parr functionals. The Journal of Chemical Physics (2009).
[69] Pamuk, B. et al. Anomalous nuclear quantum effects in ice. Physical review letters 108, 193003 (2012).
[70] Li, J.-C. et al. Inelastic incoherent neutron scattering study of ice Ih, II, IX, V and
VI in the region from 50-500 meV. Journal of Physics: Condensed Matter 4, 2109 (1992).
[71] Li, J. Inelastic neutron scattering studies of hydrogen bonding in ices. The Journal of Chemical Physics 105, 6733–6755 (1996).