formation of Na20.2CaO.3SiO2 glass investigated by. Zanotto and Galhardi (1988) can be ... tion (Ira,x) and growth (Ym,x) rates. % = ( y~axlmax )- 1t4. (5).
Contrib Mineral Petrol (1993) 113 : 126-142
Contributions to Mineralogy and
Petrology
9 Springer-Verlag 1993
Relationship between plagioclase crystallization and cooling rate in basaltic melts Katharine V. Cashman* Department of Geological and Geophysical Sciences, Princeton University, Princeton, NJ 08544-1003, USA Received August 19, 1991/Accepted June 11, 1992
Abstract. Rock textures commonly preserve a record of
the near-surface crystallization history of volcanic rocks. Under conditions of simple cooling without convection or mixing, textures will reflect sample cooling rate, the temperature at which crystallization was initiated, and the distribution of mineral phase precipitation across the crystallization interval. Compilation of plagioclase size and number density data on natural (dike, sill and lava lake) and experimental samples suggests that (1) growth and nucleation rates of plagioclase in natural basaltic samples are a predictable function of cooling rate, and (2) the observed crystallization rate dependence on cooling rate is similar to that observed in experiments initiated at subliquidus temperatures. Comparison of natural and experimental samples thus suggests that most basalts crystallize under conditions of heterogeneous nucleation, with the number density of preexisting nucleii partially controlling textural responses to cooling rate changes. Time scales of crystallization and cooling in magmatic systems are intimately linked through a balance between heat removal from the system and heat evolved through crystallization. Evaluation of textural data in the context of recent numerical models of crystallization in simple (one- and two-component systems) provides new insight into regularities in the crystallization behavior of basaltic magmas. For example, the rate of change in crystal size (and number density, as dictated by mass balance) has been used as a measure of the relative importance of time scales of crystallization and cooling in numerical models of crystallizing systems. In natural samples, plagioclase size scales with the length scale of _cooling such that a logarithmic plot of grain size as a function of normalized distance across the dike has a slope that appears approximately independent of dike width (solidification time). Comparison with available textural data for other phenocryst phases suggests that the same may be true for pyroxene and magnetite crystallization, with each phase having a characteristic slope probably controlled by the thermodynamic properties of the crystallizing phase. *Currently at: Department of Geological Sciences, University of Oregon, Eugene, OR 97403, USA
Measured crystal size distributions are unimodal and show maximum frequencies in the smaller size classes; distributions broaden and the grain size at peak frequency increases with increasing crystallization times (decreasing cooling rates). In contrast, partially crystallized Makaopuhi lava lake samples have crystal size distributions that decrease exponentially with increasing crystal size. Measured size distributions in dikes can be explained by late stage modification of Makaopuhi-type distributions through loss of small crystals, possibly the consequence of growth without nucleation. Finally, this compilation of the textural response of basaltic magmas to changes in cooling rate suggests that empirical calibrations of crystallization rate dependence on cooling rate from natural samples provide a reasonable model for plagioclase crystallization in near-surface basaltic systems. Predicted growth rates will be slow and relatively constant (10-~~ - ~1 cm/s) for crystallization times expected in most shallow volcanic systems ( < 1000 years).
Introduction
Crystallization is a fundamental consequence of magmatic cooling. The rate at which crystallization of a magma body proceeds links the thermal history of a magmatic system to the chemical evolution of that body, and thus relates the time scales of magmatic cooling and differentiation. The rate at which crystallization occurs, and the distribution of phases across the solidification interval, may influence the presence or absence of magmatic convection (e.g., Marsh 1988a, 1989a, b; Brandeis and Marsh 1989, 1990; Tait and Jaupart 1990; Worster et al. 1990; Oldenburg and Spera 1990), rates and efficiency of crystal settling (e.g., Marsh 1988a; Martin and Nokes 1989), and the rate and form of growing mush (melt + crystal) zones at chamber margins, with their implied controls on the history of melt chemistry (e.g., Morse 1986; Martin et al. 1987; Langmuir 1989; Tait and Jaupart 1989). Additionally, crystallization during and after volcanic eruptions
127 may significantly affect eruption styles and lava flow morphology through resulting rheological changes (e.g., Sparks and Pinkerton 1978; Lipman and Banks 1987; Tait et al. 1989; Fink and Zimbelman 1990; Kilburn 1990). Recent numerical models (e.g., Brandeis et al. 1984; Brandeis and Jaupart 1987) combine conductive cooling histories with crystallization kinetics in simple (one-component) melts to provide dimensional relationships linking cooling and crystallization times. Numerical models involving ideal binary eutectics (e.g., Spohn et al. 1988; Hort and Spohn 1991a, b; Toramaru 1991) predict crystallization times and crystal size distributions of precipitating phases under conditions of different cooling rates and crystallization parameters. Important results from these studies include the recognition that crystallization may buffer magmatic temperatures close to the liquidus, and that final crystal size distributions are controlled, to a large extent, by crystal nucleation. While the parameterized relationships between nucleation rate, growth rate, crystal size and growth times are general, these models are limited in application to natural systems by the simple liquids assumed, and by inadequate experimental controls on crystallization (particularly nucleation) in complex silicates. Quantitative textural studies by Marsh (1988b), Cashman and Marsh (1988), Cashman (1988, 1990, 1992), Maatoe et al. (1989), and Peterson (1990) have illustrated the use of textural measurements to estimate in situ crystallization rates in active volcanic systems. These studies indicate that crystal growth rates of silicates vary only an order of magnitude (10 - 1 ° to 10 -11 cm/s) over a broad range of magma compositions and conditions of crystallization. This result suggests that most crystallization in natural systems proceeds under conditions of very small undercoolings (deviations from equilibrium) and predicts that the size distribution of crystals in a volcanic rock may be a direct reflection of magmatic residence time in a subliquidus (crystallizing) reservoir (e.g., Mangan 1990). A question remains, however, as to the relationship of these near-surface, short-time scale studies to more generalized models of the cooling and crystallization of magmatic systems. Accurate time controls on magmatic evolution are few, and past efforts to constrain rates of magmatic crystallization have included both crystal size measurements on natural samples with known cooling histories (e.g., Kirkpatrick 1977) and laboratory cooling rate experiments (summarized by Lofgren 1980). Of the former, dikes have long provided the most attractive target for linking the textural development of cooling magmas to their thermal evolution because of their relatively simple thermal histories (e.g., Lane 1903; Winkler 1949; Gray 1970, 1978; Ikeda 1977). Conversely, rock textures have also been used to constrain cooling histories of basalt flows (Long and Wood 1986; Degraff et al. 1989). No general model has resulted from this work. Likewise, abundant coolingrate experiments on lunar basalts furnish vast qualitative documentation of the effect of cooling rate on rock textures, but very little of this data has been quantified (exceptions include Walker et al. 1976a, 1978; Grove 1978, 1990; Lofgren et al. 1979). Here I attempt to compile all reported textural data on natural and laboratory cooling-
rate experiments with the goal of developing an empirical relationship among growth rate, nucleation rate and cooling that is consistent with the parameterizations developed in numerical models. Important conclusions from this work include (1) documentation of a consistency in growth rate versus cooling rate estimates for different natural systems, as predicted by parameterizations of numerical models, and (2) a demonstration that for cooling times appropriate to most shallow magmatic cooling, plagioclase growth rates (in units of cm s- 1) vary only one order of magnitude, and thus that crystal sizes may provide a direct determination of magma residence time in shallow storage chambers. The implications of this work for numerical models of magmatic processes are many, as crystallization provides a fundamental control on processes of thermal and chemical evolution of magmatic systems. The crystallization interval in magmatic systems tends to be large (about 200 °C), with precipitation of individual phases commonly restricted to specific portions of this interval. Because magma chambers cool from the outside inward, a transect from the margin to the interior must encounter temperatures from subsolidus to the original magma intrusion temperature. A consequence of this geometry is that a magma body will also be zoned in crystallinity from the margin to the interior, with accompanying changes in rheology and, if there has been any differential movement of crystals and liquid, changes in bulk composition. Crystallization is exothermic. The evolution of heat resulting from crystallization therefore must help control the development of the zone of thermal transition. The form of this heat release across the crystallization interval is strongly controlled by cooling rate and its resultant effect on crystallization kinetics. Because the differentiated melt fraction may have a density that is greater or less than the original melt, the rate of crystallization will also determine the likelihood of compositional convection and time scales of magmatic differentiation.
Crystallization models Crystallization of a silicate melt involves both nucleation and growth of crystals, and together these processes define the rate of liquid-to-solid transformation (where the word transformation is used here as a general expression to denote the complete phase change in a one-component system) required to model the cooling history of a simple melt. The mathematical description of this transformation was developed by Johnson and Mehl (1939) and Avrami (1939, 1940, 1941), and will be referred to here as the Avrami equation (derived in Kirkpatrick 1981). A general form of the Avrami equation is:
