Free-energy landscape of nucleation with an intermediate metastable phase studied using capillarity approximation

Capillarity approximation is used to study the free-energy landscape of nucleation when an intermediate metastable phase exists. The critical nucleus that corresponds to the saddle point of the free-energy landscape as well as the whole free-energy landscape can be studied using this capillarity approximation, and various scenarios of nucleation and growth can be elucidated. In this study we consider a model in which a stable solid phase nucleates within a metastable vapor phase when an intermediate metastable liquid phase exists. We predict that a composite critical nucleus that consists of a solid core and a liquid wetting layer as well as pure liquid and pure solid critical nuclei can exist depending not only on the supersaturation of the liquid phase relative to that of the vapor phase but also on the wetting behavior of the liquid surrounding the solid. The existence of liquid critical nucleus indicates that the phase transformation from metastable vapor to stable solid occurs via the intermediate metastable liquid phase, which is quite similar to the scenario of nucleation observed in proteins and colloidal systems. By studying the minimum-free-energy path on the free-energy landscape, we can study the evolution of the composition of solid and liquid within nuclei not limited to the critical nucleus.Comment: 9 pages, 8 figures, Journal of chemical physics to be publishe

Minimum free-energy path of homogenous nucleation from the phase-field equation

The minimum free-energy path (MFEP) is the most probable route of the nucleation process on the multidimensional free-energy surface. In this study, the phase-field equation is used as a mathematical tool to deduce the minimum free-energy path (MFEP) of homogeneous nucleation. We use a simple square-gradient free-energy functional with a quartic local free-energy function as an example and study the time evolution of a single nucleus placed within a metastable environment. The time integration of the phase-field equation is performed using the numerically efficient cell-dynamics method. By monitoring the evolution of the size of the nucleus and the free energy of the system simultaneously, we can easily deduce the free-energy barrier as a function of the size of the sub- and the super-critical nucleus along the MFEP.Comment: 8 pages, 5 figures, Journal of Chemical Physics accepted for publicatio

Origin of the Heavy Fermion Behavior in Ca_{2-x}Sr_{x}RuO_{4}: Roles of Coulomb Interaction and the Rotation of RuO_{6} octahedra

We study the electronic states for Ca_{2-x}Sr_{x}RuO_{4} in $0.5\leq x \leq 2$ within the Gutzwiller approximation (GA) on the basis of the three-orbital Hubbard model for the Ru t_{2g} orbitals. The main effects of the Ca substitution are taken account as the changes of the $dp$ hybridizations between the Ru 4d and O 2p orbitals. Using the numerical minimization of the energy obtained in the GA, we obtain the renormalization factor (RF) of the kinetic energy and total RF, which estimates the inverse of the mass enhancement, for three cases with the effective models of x=2 and 0.5 and a special model. We find that the inverse of the total RF becomes the largest for the case of x=0.5, and that the van Hove singularity, which is located on (below) the Fermi level for the special model (the effective model of x=0.5), plays a secondary role in enhancing the effective mass. Our calculation suggests that the heavy fermion behavior around x=0.5 comes from the cooperative effects between moderately strong Coulomb interaction compared to the total bandwidth and the modification of the electronic structures due to the rotation of RuO_{6} octahedra (i.e., the variation of the $dp\pi$ hybridizations and the downward shift for the $d_{xy}$ orbital). We propose that moderately strong electron correlation and the orbital-dependent modifications of the electronic structures due to the lattice distortions play important roles in the electronic states for Ca_{2-x}Sr_{x}RuO_{4}.Comment: 16 pages, 13 figures, 1 table, accepted for publication in Physical Review B; added the discussions both about the validity of the present treatment and about Hund's metal in this allo

Scaling properties of critical bubble of homogeneous nucleation in stretched fluid of square-gradient density-functional model with triple-parabolic free energy

The square-gradient density-functional model with triple-parabolic free energy is used to study homogeneous bubble nucleation in a stretched liquid to check the scaling rule for the work of formation of the critical bubble as a function of scaled undersaturation $\Delta\mu/\Delta\mu_{\rm spin}$, the difference in chemical potential $\Delta\mu$ between the bulk undersaturated and saturated liquid divided by $\Delta\mu_{\rm spin}$ between the liquid spinodal and saturated liquid. In contrast to our study, a similar density-functional study for a Lennard-Jones liquid by Shen and Debenedetti [J. Chem. Phys. {\bf 114}, 4149 (2001)] found that not only the work of formation but other various quantities related to the critical bubble show the scaling rule, however, we found virtually no scaling relationships in our model near the coexistence. Although some quantities show almost perfect scaling relations near the spinodal, the work of formation divided by the value deduced from the classical nucleation theory shows no scaling in this model even though it correctly vanishes at the spinodal. Furthermore, the critical bubble does not show any anomaly near the spinodal as predicted many years ago. In particular, our model does not show diverging interfacial width at the spinodal, which is due to the fact that compressibility remains finite until the spinodal is reached in our parabolic models.Comment: 10 pages, 10 figures, Journal of Chemical Physics accepted for publicatio

Ferromagnetic fluctuation and possible triplet superconductivity in Na_xCoO_2*yH_2O: Fluctuation-exchange study of multi-orbital Hubbard model

Spin and charge fluctuations and superconductivity in a recently discovered superconductor Na_xCoO_2*yH_2O are studied based on a multi-orbital Hubbard model. Tight-binding parameters are determined to reproduce the LDA band dispersions with the Fermi surface, which consist of a large cylindrical one around the Gamma-point and six hole pockets near the K-points. By applying the fluctuation-exchange (FLEX) approximation, we show that the Hund's-rule coupling between the Co t2g orbitals causes ferromagnetic (FM) spin fluctuation. Triplet f_{y(y^2-3x^2)}-wave and p-wave pairings are favored by this FM fluctuation on the hole-pocket band. We propose that, in Na_xCoO_2*yH_2O, the Co t2g orbitals and inter-orbital Hund's-rule coupling play important roles on the triplet pairing, and this compound can be a first example of the triplet superconductor in which the orbital degrees of freedom play substantial roles.Comment: 5 pages, 3 figure

Direct numerical simulation of homogeneous nucleation and growth in a phase-field model using cell dynamics method

Homogeneous nucleation and growth in a simplest two-dimensional phase field model is numerically studied using the cell dynamics method. Whole process from nucleation to growth is simulated and is shown to follow closely the Kolmogorov-Johnson-Mehl-Avrami (KJMA) scenario of phase transformation. Specifically the time evolution of the volume fraction of new stable phase is found to follow closely the KJMA formula. By fitting the KJMA formula directly to the simulation data, not only the Avrami exponent but the magnitude of nucleation rate and, in particular, of incubation time are quantitatively studied. The modified Avrami plot is also used to verify the derived KJMA parameters. It is found that the Avrami exponent is close to the ideal theoretical value m=3. The temperature dependence of nucleation rate follows the activation-type behavior expected from the classical nucleation theory. On the other hand, the temperature dependence of incubation time does not follow the exponential activation-type behavior. Rather the incubation time is inversely proportional to the temperature predicted from the theory of Shneidman and Weinberg [J. Non-Cryst. Solids {\bf 160}, 89 (1993)]. A need to restrict thermal noise in simulation to deduce correct Avrami exponent is also discussed.Comment: 9 pages, 8 figures, Journal of Chemical Physics to be publishe

Stability of critical bubble in stretched fluid of square-gradient density-functional model with triple-parabolic free energy

The square-gradient density-functional model with triple-parabolic free energy, that was used previously to study the homogeneous bubble nucleation [J. Chem. Phys. 129, 104508 (2008)], is used to study the stability of the critical bubble nucleated within the bulk under-saturated stretched fluid. The stability of the bubble is studied by solving the Schr\"odinger equation for the fluctuation. The negative eigenvalue corresponds to the unstable growing mode of the fluctuation. Our results show that there is only one negative eigenvalue whose eigenfunction represents the fluctuation that corresponds to the isotropically growing or shrinking nucleus. In particular, this negative eigenvalue survives up to the spinodal point. Therefore the critical bubble is not fractal or ramified near the spinodal.Comment: 9 pages, 8 figures, Journal of Chemical Physics accepted for publicatio

The Last 41.000 Years Fluctuation in Atmosperic CO2 Concentration Inferred From the Changes in Oxygen and Carbon Stable Isotopes Ratios of the Marine Sediment

The past atmospheric CO2 concentrations were reconstructed based on the results of measurements of stable oxygen and carbon isotopic ratios of fossil foraminifer and total organic carbon contained in marine sediment taken from the Okinawa Trough, East China Sea. In this study, we utilized two models of Popp et al and Rau et al. for the reconstruction. The results show that the whole trends of the changes in CO2 concentrations are very similar, even when it is compared to the atmospheric CO2 concentration of air trapped in ice core from southern pole. Changes in atmospheric CO2 concentrations are interpreted as a consequence of fluctuation in ocean surface water utilization of CO2 by marine organism and those are closely related to glacial-interglacial (cold-warm) fluctuations between maximum and minimum values through most Quaternary. Rekonstruksi terhadap Perubahan konsentrasi CO2 yang terkandung dalam udara telah dilakukan berdasarkan hasil pengukuran rasio isotop stabil oksigen dan karbon dalam fosil foraminifera dan total karbon organik yang terkandung dalam sedimen dasar laut dari Okinawa Trough, Laut Cina Timur. Dalam studi ini, dipakai model dari Popp et al. dan Rau et al. untuk rekonstruksi. Hasil studi menunjukkan bahwa kedua tren dari Perubahan kandungan CO2 udara sangat mirip, bahkan bila dibandingkan dengan kandungan CO2 udara yang terperangkap dalam inti es di Kutup Selatan sekalipun. Perubahan kandungan CO2 udara diinterpretrasikan sebagai akibat fluktuasi konsumsi CO2 di permukaan air laut oleh mikro-organisme yang juga sangat erat hubungannya dengan fluktuasi glasial-interglasial (dingin-panas) antara suhu udara bumi maksimum dan minimum sepanjang masa Kuarter