Cómo citar
Descargas
Métricas Alternativas
Dimensions
Resumen
En sólidos, la aproximación cuasi-armónica tiende a ser válida en un amplio rango de temperaturas, que aumenta conforme se aplica mayor presión al sistema y su máximo puede exceder ampliamente la temperatura de fusión. Cobra entonces relevancia desarrollar criterios que restrinjan la temperatura bajo la cual es razonable realizar comparaciones teóricas de estabilidad entre fases sólidas, sin incurrir en los altos costos computacionales necesarios para el cálculo preciso de la línea de fusión de cada una de ellas. Aquí reportamos que para cristales presurizados donde la aproximación cuasiarmónica es bastante confiable, el criterio fenomenológico de Lindemann es idóneo para estimar eficientemente las condiciones de presión y temperatura donde es probable que ocurra la transición desde las fases sólidas hacia el líquido. Cuantificando la desviación promedio de los átomos desde sus posiciones de equilibrio conforme aumenta la temperatura, en carbono a muy alta presión, fue posible determinar que la región de estabilidad de la fase sólida se circunscribe a una región del espacio de presión y temperatura ubicada bajo la curva que representa el 11% de desviación promedio de los átomos con respecto a las distancias interatómicas del material. Lo anterior proporciona un criterio aproximado pero confiable para sugerir el valor máximo de estabilidad de sólidos presurizados, el cual es relativamente simple de calcular representando al mismo tiempo una opción atractiva si no existen datos experimentales ni cálculos teóricos de fusión, o si estos no son concluyentes, situación que se aprovechó aplicando el criterio a los sistemas de oxígeno y flúor.
Palabras clave
Citas
Akahama, Y., Kawamura, H., Haüsermann, D., Hanfland, M., Shimomura, O. (1995). New high-pressure structural transition of oxygen at 96 gpa associated with metallization in a molecular solid. Physical Review Letters, 74(23), 4690-4693.
Alder, B. J., Christian, R. H. (1961). Behavior of strongly shocked carbon. Physical Review Letters, 7, 367-369.
Anderson, O. (1995). Equations of state of solids for geophysics and ceramic science. New York:Oxford University Press. Angel, R. J., Miozzi, F., Alvaro, M. (2019). Limits to the validity of thermal-pressure equations of state. Minerals, 9(9), 562.
Baroni, S., de Gironcoli, S., Dal Corso, A., Giannozzi, P. (2001). Phonons and related crystal properties from density-functional perturbation theory. Reviews of Modern Physics, 73, 515.
Baroni, S., Giannozzi, P., Isaev, E. (2010). Density-functional perturbation theory for quasiharmonic calculations. Solid State Physics - Advances in Research and Applications, 71, 39-57.
Benedict, L. X., Driver, K. P., Hamel, S., Militzer, B., Qi, T., Correa, A. A., Saul, A., Schwegler, E. (2014). Multiphase equation of state for carbon addressing high pressures and temperatures. Physical Review B, 89, 224109.
Bilgram, J. H. (1987). Dynamics at the solid-liquid transition: Experiments at the freezing point. Physics Reports, 153(1), 1-89.
Blöchl, P. E. (1994). Projector augmented-wave method. Physical Review B, 50, 17953-17979.
Bundy, F. P. (1980). The p, t phase and reaction diagram for elemental carbon, 1979. Journal of Geophysical Research: Solid Earth, 85(B12), 6930-6936.
Chakravarty, C., Debenedetti, P. G., Stillinger, F. H. (2007). Lindemann measures for the solidliquid phase transition. The Journal of Chemical Physics, 126(20), 204508.
Cogollo-Olivo, B. H. (2020). Phase stability of carbon, oxygen and carbon dioxide under extreme p-t conditions, beyond the harmonic approximation (Ph. D. Thesis). Universidad de Cartagena.
Cogollo-Olivo, B. H., Biswas, S., Scandolo, S., Montoya, J. A. (2018). Phase diagram of oxygen at extreme pressure and temperature conditions: An ab initio study. Physical Review B, 98(9), 094103.
Cogollo-Olivo, B. H., Biswas, S., Scandolo, S., Montoya, J. A. (2020). Ab initio determination of the phase diagram of co2 at high pressures and temperatures. Physical Review Letters, 124(9), 095701.
Correa, A. A., Benedict, L. X., Young, D. A., Schwegler, E., Bonev, S. A. (2008). First-principles multiphase equation of state of carbon under extreme conditions. Physical Review B, 78, 024101.
Correa, A. A., Bonev, S. A., Galli, G. (2006). Carbon under extreme conditions: Phase boundaries and electronic properties from first-principles theory. Proceedings of the National Academy of Sciences, 103(5), 1204-1208.
Crespo, Y., Fabrizio, M., Scandolo, S., Tosatti, E. (2014). Collective spin 1 singlet phase in highpressure oxygen. Proceedings of the National Academy of Sciences, 111(29), 10427–10432.
Duan, D., Liu, Z., Lin, Z., Song, H., Xie, H., Cui, T., Pickard, C.J., Miao, M. (2021). Multistep dissociation of fluorine molecules under extreme compression. Physical Review Letters,126, 225704.
Dubrovinskaia, N., Dubrovinsky, L., Solopova, N. A., Abakumov, A., Turner, S., Hanfland, M., Bykova, E., Bykov, M., Prescher C., Prakapenka, V.B., Petitgirard, S., Chuvashova, I., Gasharova, B., Mathis, Y.L., Ershov, P., Snigireva I., Snigirev, A. (2016). Terapascal static pressure generation with ultrahigh yield strength nanodiamond. Science Advances, 2(7), e1600341.
Dubrovinsky, L., Dubrovinskaia, N., Bykova, E., Bykov, M., Prakapenka, V., Prescher, C., K Glazyrin K., Liermann H-P., Hanfland M., Ekholm M., Feng Q., Pourovskii L.V., Katsnelson M.I., Wills J.M., Abrikosov, I. A. (2015). The most incompressible metal osmium at static pressures above 750 gigapascals. Nature, 525(7568), 226-229.
Giannozzi, P., Andreussi, O., Brumme, T., Bunau, O., Buongiorno Nardelli, M., Calandra, M., Car, R., Cavazzoni, C., Ceresoli, D., Coccoccioni, M., Colonna, N., Carnemeo, I., DalCorso, A., deGironcoli, S., Delugas, P., DiStasio, R.A., Ferretti, a., Floris, A., Fratesi, G., Fugallo, G., . . . Baroni, S. (2017). Advanced capabilities for materials modelling with quantum espresso. Journal of Physics: Condensed Matter, 29, 465901.
Giannozzi, P., Baroni, S., Bonini, N., Calandra, M., Car, R., Cavazzoni, C., Ceresoli D., Chiarotti G.L., Cococcioni M., Dabo I., Corso A.D., deGironcoli S., Fabris S., Fratesi G., Gebauer R., Gerstmann U., Gougoussis C., Kokalj A., Lazzeri M., Martin-Samos L., . . . Wentzcovitch, R. M. (2009). Quantum espresso: A modular and open-source software project for quantum simulations of materials. Journal of Physics: Condensed Matter, 21, 21832390.
Gilvarry, J. J. (1956). The lindemann and graneisen laws. Physical Review, 102, 2.
Goncharenko, I. N., Makarova, O. L., Ulivi, L. (2004). Direct determination of the magnetic structure of the delta phase of oxygen. Physical Review Letters, 93(5), 055502.
Goncharov, A. F., Montoya, J. A., Subramanian, N., Struzhkin, V. V., Kolesnikov, A., Somayazulu, M., Hemley, R. J. (2009). Laser heating in diamond anvil cells: developments in pulsed and continuous techniques. Journal of Synchrotron Radiation, 16(6), 769-772.
Goncharov, A. F., Subramanian, N., Ravindran, T. R., Somayazulu, M., Prakapenka, V. B., Hemley, R. J. (2011). Polymorphism of dense, hot oxygen. Journal of Chemical Physics, 135(8), 84512.
Gorelli, F., Santoro, M., Ulivi, L., Hanfland, M. (2002). Crystal structure of solid oxygen at high pressure and low temperature. Physical Review B, 65(17), 172106.
Grumbach, M. P., Martin, R. M. (1996). Phase diagram of carbon at high pressures and temperatures. Physical Review B, 54, 15730-15741.
Grüneisen, E. (1926). Zustand des festen ko¨rpers. In C. Drucker et al. (Eds.), Thermische eigenschaften der stoffe (pp. 1–59).
Hunter, L. (1942). The variation with temperature of the principal elastic moduli of nacl near the melting point. Physical Review, 61, 84-90.
Leibfried, G., Ludwig, W. (1961). Theory of anharmonic effects in crystals. Reviews in Mineralogy and Geochemistry, 12(C), 275-444.
Lindemann, F. A. (1910). Ueber die berechnung molekularer eigenfrequenzen. Physikalis- che Zeitschrift, 11, 609-612.
Loveday, J. (2012). High-pressure physics. Chapman Hall.
Löwen, H. (1994). Melting, freezing and colloidal suspensions. Physics Reports, 237(5), 249-324.
Ma, Y., Oganov, A. R., Glass, C. W. (2007). Structure of the metallic ζ-phase of oxygen and isosymmetric nature of the ε-ζphase transition: Ab initio simulations. Physical Review B, 76(6), 064101.
Martinez-Canales, M., Pickard, C. J., Needs, R. J. (2012). Thermodynamically stable phases of carbon at multiterapascal pressures. Physical Review Letters, 108, 045704.
Montoya, J. A., Goncharov, A. F. (2012). Finite element calculations of the time dependent thermal fluxes in the laser-heated diamond anvil cell. Journal of Applied Physics, 111(11), 112617.
Murray, C. A., Grier, D. G. (1996). Video microscoopy of monodisperse colloidal systems. Annual Review of Physical Chemistry, 47(1), 421-462.
Nicol, M., Hirsch, K. R., Holzapfel, W. B. (1979). Oxygen phase equilibria near 298 k. Chemical Physics Letters, 68(1), 49-52.
Ohnesorge, R., Löwen, H., Wagner, H. (1993). Density distribution in a hard-sphere crystal. Europhysics Letters, 22(4), 245.
Olson, M. A., Bhatia, S., Larson, P., Militzer, B. (2020). Prediction of chlorine and fluorine crystal structures at high pressure using symmetry driven structure search with geometric constraints. The Journal of Chemical Physics, 153(9), 094111.
Pack, J. D., Monkhorst, H. J. (1977). Special points for brillouin-zone integrations. Physical Review B, 16, 1748-1749.
Pal, S., Sharma, P. K. (1967). On lindemann’s melting criterion. Physica Status Solidi B, 23(1), 361-364.
Perdew, J. P., Burke, K., Ernzerhof, M. (1996). Generalized gradient approximation made simple. Physical Review Letters, 77, 3865-3868.
Robinson, D. R., Wilson, M. (2013). The liquid←→amorphous transition and the high pressure phase diagram of carbon. Journal of Physics: Condensed Matter, 25(15), 155101.
Ross, M. (1969). Generalized lindemann melting law. Physical Review, 184, 1.
Ross, M. (1981). Polymorphism of dense, hot oxygen. Nature, 292(5822), 435-436.
Santoro, M., Hajeb, A., Gorelli, F. A. (2020). Resistively heated, high pressure, membrane and screw driven diamond anvil cell. High Pressure Research, 40(3), 379-391.
Schiferl, D., Cromer, D.T., Schwalbe, L.A., Mills, R.L. (1983). Structure of ’orange’18o2 at 9.6 gpa and 297 k. Acta Crystallographica Section B, 39(39), 153-157.
Schöttler, M., French, M., Cebulla, D., Redmer, R. (2016). Free energy model for solid highpressure phases of carbon. Journal of Physics: Condensed Matter, 28(14), 145401.
Smith, R.F., Eggert, J.H., Jeanloz, R., Duffy, T.S., Braun, D.G., Patterson, J.R., Rudd, R.E., Biener, J., Lazicki, A.E., Hamza, A.V., Wang J., Braun, T., Benedict, L.X., Celliers, P.M.,Collins, G.W. (2014). Ramp compression of diamond to five terapascals. Nature, 511, 330-333.
Somayazulu, M., Ahart, M., Mishra, A.K., Geballe, Z.M., Baldini, M., Meng, Y., Struzhkin, V.V., Hemley, R.J. (2019). Evidence for superconductivity above 260 k in lanthanum superhydride at megabar pressures. Physical Review Letters, 122(2), 027001.
Stroud, D., Ashcroft, N. W. (1972). Theory of the melting of simple metals: Application to na. Physical Review B, 5, 371-383.
J., Martinez-Canales, M., Klug, D.D., Pickard, C.J., Needs, R.J. (2012). Persistence and eventual demise of oxygen molecules at terapascal pressures. Physical Review Letters, 108(4), 045503.
D.C., Heuze, O., Lazicki, A., Hamel, S., Benedict, L.X., Smith, R.F., McNaney, J.M., Ackland, G.J. (2022). Equation of state and strength of diamond in high-pressure ramp loading. Physical Review B, 105, 014109.
Vopson, M. M., Rogers, N., Hepburn, I. (2020). The generalized lindemann melting coefficient. Solid State Communications, 218, 113977.
Wang, X., Scandolo, S., Car, R. (2005). Carbon phase diagram from ab initio molecular dynamics. Physical Review Letters, 95, 185701.
Weck, G., Desgreniers, S., Loubeyre, P., Mezouar, M. (2009). Single-crystal structural characterization of the metallic phase of oxygen. Physical Review Letters, 102(25), 255503.
Weck, G., Loubeyre, P., Eggert, J. H., Mezouar, M., Hanfland, M. (2007). Melting line and fluid structure factor of oxygen up to 24 gpa. Physical Review B, 76(5), 054121.
Young, D. A., Alder, B. J. (1974). Studies in molecular dynamics. xiii. singlet and pair distribution functions for hard-disk and hard-sphere solids. The Journal of Chemical Physics, 60(4), 1254-1267.
Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-SinDerivadas 4.0.
Derechos de autor 2023 Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales