Atsushi Toramaru

Model of nucleation and growth of crystals in cooling magmas

The nucleation and growth of liquidus phases in cooling magmas at constant rates are modeled taking into account homogeneous nucleation, diffusion-limited growth, and depletion of crystallizing component from melt, and the temperature-dependent diffusivity. The formulation of governing equations shows that four dimensionless parameters, whose physical meanings are the nucleation difficulty, the fusion enthalpy, the ratio of the growth rate to the cooling rate, and the activation energy of diffusion, control the crystallization phenomena. The nucleation behavior with time (or temperature) is determined primarily by the competition between increasing nucleation rate with cooling and the reduced supersaturation with depletion by progressive growth of crystals previously nucleated. The maximum nucleation rate and the number density of crystals increase with decreasing interfacial tension and diffusivity, and with increasing fusion enthalpy and cooling rate. Quantitative expressions of the time or temperature interval for which the nucleation remains appreciable, the peak nucleation rate, the number density of crystals and the mean crystal radius are derived as functions of controlling parameters, and can be used to estimate the cooling rate or other unknown parameters from the number density of crystals of a rock.

Experimental pattern transitions in a Liesegang system

We experimentally found various patterns of precipitation in a lead iodide Liesegang system: periodic precipitation, continuous tree-like crystal aggregates and periodic tree-like crystal aggregates. Gel and reactant concentrations are two major controlling factors. At high gel concentrations, Liesegang band forms, whereas at low gel concentrations, tree-like crystal aggregates similar to diffusion-limited aggregation (DLA) develop in the entire system. At an intermediate gel concentration, Liesegang band and tree-like crystal aggregates coexist. At lower reactant concentration, the periodic tree-like crystal aggregates tends to form. A simple scaling argument that the kinetics of bulk and surface nucleation plays an important role, is presented to understand the effect of gel concentration on pattern transition.

A numerical experiment of crystallization for a binary eutectic system with application to igneous textures

Numerical experiments of crystallization in a binary eutectic system were carried out to understand the origin of textural variation in igneous rocks. In this study, the number density of crystals was intensively examined as a parameter of texture. The constant cooling rate experiment (no latent heat release) yields a higher number density of crystals by 1 order of magnitude than the constant heat loss experiment (full latent heat release). Differences in growth mechanism (diffusion-limited with capillary effect versus reaction-limited without capillary effect) result in the different dependence of cooling rate on number density of crystals. For diffusion-limited growth with the capillary effect for spherical crystals the cooling rate dependence of number density of olivine, clinopyroxene, plagioclase, and opaque minerals seems to be consistent with the experimental data with superliquidus initial condition. For plagioclase, experimental data with subliquidus initial temperature and the observational data are not consistent with the present numerical results for both growth processes, suggesting that the plagioclase growth is governed by a different mechanism of nucleation and growth from homogeneous nucleation and both diffusion-limited growth with capillary effect and simple reaction-limited growth without capillary effect. Assuming the conductive cooling of a dike, it is predicted that for the diffusion-limited growth the number density of crystals is proportional to y−3, where y is distance from the cooling boundary. This is in good agreement with some of the observational data by Gray [1978] except for plagioclase. The consistency among numerical, natural, and experimental data highly suggests that at the nucleation stage with superliquidus initial condition, crystals grow by the diffusion-limited process, taking the spherical shape for olivine, pyroxene, plagioclase, and some oxides. The difference between volcanic and plutonic textures is caused by the difference of cooling rate by 2 orders of magnitude. The variation from intergranular, ophitic to poikilitic textures results from the difference in cooling rate dependence on number density between the plagioclase and the other minerals. The formation of porphyritic texture must satisfy the limited condition: the very small efficiency of latent heat production (nearly constant cooling rate), small values of interfacial energy of the first precipitating phase, and smaller value of interfacial energy of the second phase.

Igneous Layering in Basaltic Magma Chambers

Layering is a common feature in mafic and ultramafic layered intrusions and generally consists of a succession of layers characterized by contrasted mineral modes and/or mineral textures, including grain size and orientation and, locally, changing mineral compositions. The morphology of the layers is commonly planar, but more complicated shapes are observed in some layered intrusions. Layering displays various characteristics in terms of layer thickness, homogeneity, lateral continuity, stratigraphic cyclicity, and the sharpness of their contacts with surrounding layers. It also often has similarities with sedimentary structures such as cross-bedding, trough structures or layer termination. It is now accepted that basaltic magma chambers mostly crystallize in situ in slightly undercooled boundary layers formed at the margins of the chamber. As a consequence, most known existing layering cannot be ascribed to a simple crystal settling process. Based on detailed field relationships, geochemical analyses as well as theoretical and experimental studies, other potential mechanisms have been proposed in the literature to explain the formation of layered igneous rocks. In this study, we review important mechanisms for the formation of layering, which we classify into dynamic and non-dynamic layer-forming processes.

Model of layering formation in a mantle peridotite (Horoman, Hokkaido, Japan)

Abstract The Horoman peridotite complex exhibits a conspicuous layered structure. It is found, from the geological and petrological survey, that the pattern of layering has three characteristics: symmetry, asymmetry (subtly collapsed symmetry) and scale invariance. Especially, symmetric and asymmetric patterns clearly recognized in the sequence of mafic layers at the Northern ridge of Apoi-dake peak, and at the Western ridge of Bozu-yama peak are noticeable. We present a simple mathematical model describing stretching (thinning) and folding during deformation that accounts for the three characteristics. The model quantitatively reproduces the slope in cumulative frequency distribution of the width of mafic layers and indicates that the frequency distribution is strongly influenced by the spatial strain contrast. Applying the model result to the observational data for mafic layers, it is found that the strain contrast approximately ranges several to 10 times between regions with the highest and the lowest strain rates.

A simple model of oscillatory zoning in magmatic plagioclase: Development of an isothermal undercooling model

Abstract According to the model of Sibley et al. (1976), the alternate switching of the crystal surface between smooth and rough states results in a drastic change in the growth velocity and the subsequent development of oscillatory zoning (OZ). In the present paper, we develop the isothermal undercooling mechanism of the Sibley et al. model and calculate the magnitudes of the amplitude and wavelength of OZ to check the validity of the Sibley et al. model. We assume that the growth velocity depends on the roughness of the crystal surface. The roughness is expressed as a function of the surface area, and it is found that the growth velocity varies twice due to the switching. We also assume that the surface states change when steady states are achieved or when the growth and diffusion velocities are balanced. Simulating the diffusion-reaction on the supposition that the thickness of the diffusion layer is fixed, we determine the concentrations at which the switching takes place. We simulate the OZ growth based on these mathematical considerations. The results show that the magnitudes of the calculated amplitude and wavelength agree with those observed in nature.

Conduit process in vulcanian eruptions at Sakurajima volcano, Japan: Inference from comparison of volcanic ash with pressure wave and seismic data

To elucidate the conduit processes controlling the amplitude of air pressure waves (Apw) from vulcanian eruptions at the Sakurajima volcano, Japan, we examine ash particles emitted by eruptions preceded by swarms of low-frequency B-type earthquakes (BL-swarms). We measure the water content of glassy ash, an indicator of shallow magma storage pressure, and vesicle textures, such as vesicle number density (VND). These data allow us to reconstruct the shallow conduit by comparing vesicularity with inferred pressure, and therefore depth, of magma storage. The results show that VND increases with depth, implying formation of a dense, outgassed magma cap underlain by more-vesicular, less-outgassed, magma. The VND and water content in the glassy ash positively correlate with the duration of BL-swarms, suggesting that such seismic signals reflect upward migration of deep gas- and vesicle-rich magma. Finally, it is determined that Apw positively correlates with VND, suggesting that the amplitude of the air pressure waves is controlled by the amount of accumulated gas- and bubble-rich magma below the dense magma cap.

Quantitative description of oscillatory zoning in basaltic to dacitic plagioclases from the Shirahama Group, Japan

New criteria related to the origin of oscillatory zoning (OZ) in plagioclase are presented. We compare the OZs in basaltic to those of dacitic plagioclases in the tholeiitic series volcanic rocks of the Shirahama Group, Izu Peninsula, Japan. Nomarski differential interference contrast (NDIC) images of the etched thin sections are used to measure zone thicknesses of the OZs. The normalized standard deviations per data series of the thicknesses are then calculated. We found that the average thicknesses are almost constant (mostly from 2 to 3 μm) through all the rock samples. This constancy corresponds to our idea that the length of oscillation, D/V (D: diffusivity in the melt; V: growth velocity of plagioclase) is almost constant for a variety of melt viscosity because strong dependences on the viscosity of D and V are canceled out in D/V. Consequently, we concluded that the growth of the OZ is basically controlled by an interface kinetics mechanism. In contrast, the plagioclases in SiO2-rich rocks have the following features: (1) larger standard deviations, (2) abundant erode-like zones, and (3) large oscillation amplitudes. These features reveal that the OZ patterns of plagioclases in more silicic magmas are disturbed due to change of the environmental parameters under the magma dynamics.