Is the 2d Information of Objects in Thin Sections Representative of the 3d- Object? – Determining the Bulk Compositions of Chondrules from Meteorite Thin Sections

Introduction: In each chondrite group, the bulk composition of all group members is the same, whereas the few bulk compositions of chondrules known so far show large variations [e.g. 1,2]. As these variations are observed even in primitive type 3 meteorites, they must be related to the formation event of chondrules or their precursors in the solar nebular, for example, the formation of the precursors due to fractional condensation [e.g. 2-5]. Second, as stated earlier by e.g. [6], chondrules and matrix of carbonaceous chondrites are chemically complementary. The reason for this is still a matter of debate. One possibility is that the components of each meteorite group formed in separate nebular reservoirs. Yet, the bulk compositions of chondrules are still poorly known [e.g. 3], although this information is essential for constraining chondrule formation models. Obtaining reliable bulk chondrule data is difficult. A fast approach is calculating the 2D “bulk composition” in a thin section from measured phase compositions and modal abundances. Taking this as the 3D bulk implicitly assumes that the 2D slice is more or less representative of the 3D object. As this assumption is questionable, these estimates are inevitably criticized. In a new approach I developed a computer model that allows simulating this problem. To compare the calculated results with real chondrules, I am grinding down meteorite thick sections in defined steps and measure the 2D composition of chondrules and other components at each step. The 3D bulk compositions can then be calculated from the 2D bulk compositions. Method: In the computer model (programmed using Mathematica) the chondrule is represented by a sphere, in which cuboids – representing minerals – are enclosed (Fig. 1). The volume of the sphere not occupied by cuboids represents mesostasis. Intersecting cuboids can be used to build specific forms; the intersecting volume is only considered once during calculations. The cuboids are allowed to protrude across the sphere, to simulate objects at the border. The volume outside the sphere is not counted during calculations. A cross-cutting plane moves vertically and perpendicular to the z-axis trough this structure (Fig. 1). At each step the sphere is cut and the 2D area fraction of the resulting circle is calculated (= circle area minus area of cut cuboids). This area fraction (“fraction of the sphere”) is plotted, with the fraction of the sphere on the yand the z-axis intercept of the plane on the xaxis (Fig. 2). The bulk 3D volume fraction of the sphere can be calculated from the 2D area fractions.