New methods in quantitative metamorphic petrology: 1. In situ determination of iron valence in minerals; 2. The application of 3-D textural analysis to the study of crystallization kinetics

X-ray photoelectron spectroscopy (XPS) and X-ray emission spectroscopy (XES) were investigated for in situ measurement of Fe(II)/Fe(III) in biotite. XPS was calibrated using single crystals with Fe(II)/Fe(III) determined by microprobe/wet chemistry. Peak separation and shape parameters for Fe(II) and Fe(III) 3p photoelectron peaks were estimated from single crystal spectra by constrained optimization. Biotite with low Fe/Mg, {dollar}Sigma{dollar}Fe and Fe(III)/{dollar}Sigma{dollar}Fe oxidized under the beam. Factor analysis of time series data for a beam-oxidized sample gave component peak shapes and separation similar to constrained optimization values. Fe(II)/Fe(III) obtained from XPS analyses of biotites in metapelites, using the calibration, were mostly consistent with published Mossbauer values.; Iron L{dollar}sb{lcub}alpha{rcub}{dollar} and L{dollar}sb{lcub}beta{rcub}{dollar} XES spectra were acquired with an electron probe, and a self absorption spectrum was estimated from the intensity ratio of 4 kV and 10 kV spectra. A systematic variation in L{dollar}sb{lcub}alpha{rcub}{dollar} absorption edge position and L{dollar}sb{lcub}beta{rcub}{dollar}/L{dollar}sb{lcub}alpha{rcub}{dollar} intensity ratio at 15 kV was found for ilmenite-hematite but not for biotite, as a function of Fe(III)/{dollar}Sigma{dollar}Fe. L{dollar}sb{lcub}beta{rcub}{dollar}/L{dollar}sb{lcub}alpha{rcub}{dollar} intensity ratios varied systematically for pyroxene but not amphibole. Coordination of Fe{dollar}sp{lcub}3+{rcub}{dollar} by OH{dollar}sp-{dollar} may eliminate the absorption of L{dollar}sb{lcub}beta{rcub}{dollar} intensity which occurs for Fe{dollar}sp{lcub}3+{rcub}{dollar} coordinated solely by oxygen. Beam-induced oxidation restricted to hydrous silicates is an alternative explanation.; Garnet crystallization kinetics was investigated using textural analysis. The ability of spatial statistics functions to detect clustering and/or ordering of occupied nucleation sites at different length scales was evaluated by computer simulation of nucleation and growth. The pair correlation, mark covariance and third order functions distinguish between ordered and unordered distributions resulting from growth controlled by diffusion and surface reaction respectively. The size and spatial distributions of 5000 garnet crystals in a pelitic hornfels were determined using serial sectioning. The size distribution indicates that nucleation rate initially increased and then remained constant. Spatial statistics and compositional zoning indicate surface reaction-controlled growth. A published growth rate constant suggests crystallization lasted about 600 years, and a conduction thermal model suggests a 0.25{dollar}spcirc{dollar}C temperature increase.