Conventional clustering algorithms such as k–means and fuzzy c–means (FCM) cluster analysis do not fully utilize the spatial distribution information of geologic samples. In this paper, we propose GEOFCM, a new clustering method for geochemical datasets with location coordinates. A spatial FCM algorithm originally constructed for image segmentation was modified for application to a sparse and unequally–spaced dataset. The proposed algorithm evaluates the membership function of each sample using neighboring samples as a weighting function. To test the proposed algorithm, a synthetic dataset was analyzed by several hyper–parameter settings. Applying this algorithm to a geochemical dataset of granitoids in the Ina–Mikawa district of the Ryoke belt shows that samples collected from the same geological unit are likely to be classified as the same cluster. Moreover, overlapping geochemical trends are classified consistently with spatial distribution, and the result is more robust against noise addition than standard FCM analysis. The proposed method is a powerful tool to use with geological datasets with location coordinates, which are becoming increasingly available, and can help find overviews of complicated multidimensional data structure.
The local structural features around Mn in a transparent pale blue Mn–bearing fluorapatite (MnO: 2.0 wt%) from Lavra da Golconda, Brazil were investigated by a combined analysis of single crystal X–ray diffraction and XAFS. The crystal structure with the optimized formula (Ca4.83Mn2+0.15Sr0.02)P3O12F with space group P63/m, a = 9.384(2), c = 6.8842 (6) Å, Z = 2 has been refined to R = 1.92% for the unique 555 reflections (Mo Kα). The structural refinement suggests that Mn almost exclusively occupies the Ca1 site. The EXAFS analysis indicates that Mn at the Ca1 site is surrounded by nine oxygen atoms with six shorter bonds and three longer bonds. BVS calculated for the local environment around Mn shows good agreement with the expected valence state of Mn. The present EXAFS results suggest that the longer bond distances (Ca1–O3) in fluorapatite structures will not be affected by Mn due to weak bonding interactions.
The moganite–form of AlPO4 has recently been discovered from our high–pressure study. Similar to SiO2–moganite, a temperature–induced displacive phase transition is expected. In order to confirm the phase transition, high–temperature in–situ Raman spectroscopy study was conducted at ambient pressure up to 600 °C. One of the low–frequency Raman modes (74 cm−1 at room temperature) significantly softened with temperature, and disappeared at 420 °C. Its frequency versus temperature relation can be well fitted with an order parameter equation, and the mode is interpreted as a soft mode with a critical exponent of 0.232(8). According to this fitting, the transition temperature is determined as 415 °C. Some hard modes also revealed slight softening or hardening with temperature up to ~ 420 °C and reached nearly constant frequency at higher temperature. Vibrational mode calculations by the first–principles density functional theory (DFT) method showed that the soft mode corresponds to tetrahedral rotations, representing the pathway of the transformation.