Mathematical analysis of rare earth element patterns of fluorites from the Ehrenfriedersdorf tin deposit, Germany: evidence for a hydrothermal mixing process of lanthanides from two different sources

Systematic changes in REE patterns of fluorites with various colourations from the Ehrenfriedersdorf tin deposit, Germany, can be related to the evolution of the mineral forming hydrothermal fluid within the endo- and exocontact of a related Li-F granite. One possible geochemical model that may explain the fluorite REE patterns assumes that lanthanides derived from two distinct element sources. It is suggested that a mantle- or lower crust-derived fluid (LREEsn < HREEsn) participated as one source of elements in the formation of the Li-F granitic magmas and in ore deposition. The metamorphic wall rocks (LREEsn > HREEsn) were involved as a second source of elements due to assimilation and fluid-rock interaction (including admiring of crustal fluids). Minerals that crystallised in the relatively cool and/or oxidising environment of the exocontact incorporated the REEs from the ore-forming fluid and therefore exhibit REE patterns that result from simple mixing of the lanthanide distributions of the two element sources. Mineral precipitation in the exocontact vein system led to a successive decrease of the total lanthanide concentration of the migrating fluid. The fluorite REE patterns further suggest that the mineral-forming fluid in the exocontact showed a relative enrichment of Eu that can be attributed to fluid evolution within the endocontact. The large ionic radius of EU2+ hampered the incorporation of Eu into minerals crystallising from the fluid-magma system in this high temperature and/or low oxygen fugacity environment. This process lead to an enrichment of Eu in the fluid that subsequently entered the exocontact and resulted in a corresponding Eu depletion of the altered granite. The lanthanide distributions of three differently coloured fluorite samples from a single zoned fluorite aggregate out of a cassiterite-bearing quartz vein of the exocontact are suitable for mathematical modelling because of their sample location in a sequence of homogeneous wall rocks and their well-constrained relative age relationships. Mathematical modelling has been carried out to test whether the geochemical mixing model can indeed explain the entire REE patterns of the three samples. In accordance with the proposed geochemical model, it is assumed that two endmembers with distinct REE patterns were mixed and that a process such as mineral precipitation reduced the total REE content of the mixture. The incorporation of REEs from the fluid into fluorite is described by a partition coefficient. Model values that are in closest possible agreement with the measured fluorite lanthanide concentrations were derived from the mathematical model by minimising the mean squared deviation between the two data sets. It is shown that the global minimum was found by application of the Gauss-Newton method and a specially designed evolutionary strategy. Ce and Eu were not considered in a first analysis because positive anomalies in the fluorite REE patterns indicate anomalous geochemical behaviour of these elements during the ore forming processes. The differences between the model values and the measured lanthanide concentrations were found to be smaller than the analytical errors of the REE measurements. In a second analysis the Ce and Eu concentrations of the three fluorites were taken into account and deviations between the model and measured values for these two elements were observed that could not be explained by analytical errors only. These findings suggest that the geochemical mixing model is a likely explanation for the measured fluorite REE patterns, while the observed Ce and Eu contents do not simply result from mixing processes.