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 (Ca_4.83Mn²⁺_0.15Sr_0.02)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 K_α). 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.

We examined the stability of amphibole in ultrahigh–pressure (UHP) conditions of about 620–750 °C, 2.9–3.7 GPa based on the mineralogy of UHP eclogites collected from the Qinglongshan and Jianchang areas in Donghai County of the Sulu region. The samples studied are mainly composed of garnet, omphacite, amphibole, rutile, kyanite, quartz, epidote, and phengite. Amphibole can be classified into three types based on its mode of occurrence; Amp I, inclusions in garnet and epidote; Amp II, the matrix phase; Amp III, small (~ 10–30 µm) grains developed along grain boundaries. Amp I from Qinglongshan, mainly barroisite–taramite, is slightly poorer in NaB (Na contents in B site <1.2 a.p.f.u.) than Amp II. Amp II is barroisite with a mostly homogeneous composition in each grain except for the margins of some grains (NaB = 1.1–1.4 a.p.f.u; Si = 7.0–7.5 a.p.f.u.) and shows the highest NaB values among the types. Amp III, mainly pargasite–taramite, shows clearly lower NaB (= 0.3–1.15 a.p.f.u.) than that of Amp II. On the other hand, Amp II and Amp III from Jianchang are nyböite and taramite, respectively, and the sum of the (NaA + NaB) values from the Jianchang amphibole is distinctly greater than that of the Qinglongshan amphibole. Polycrystalline quartz pseudomorphs after coesite and Amp I with barroisite compositions were found within a large epidote grain of the Qinglongshan samples. These petrological data suggest the following evolutionary history. Amp I with relatively low NaB values crystalized and was involved with other mineral grains during the compression of the eclogite, and then barroisitic Amp II occurred as a stable phase during the peak–P stage. Finally, Amp III with much lower NaB values was formed during the decompression stage. Thus, we concluded that a Ca–Na amphibole (Amp II) can be stably present in an eclogite even in the UHP conditions. In addition, significant amounts of F (up to 1 wt%) were detected from the barroisitic amphibole in the Qinglongshan samples. At the least, some eclogites from the studied areas may have undergone metasomatic infiltration of an F–bearing fluid in the UHP conditions.

Prosopite is an alumino–fluoride of calcium mineral. The chemical compositions of prosopite samples obtained from Zacatecas (Mexico), Ivigtut (Greenland), and Katugin deposit (Eastern Siberia, Russia) were determined using scanning electron microscopy and energy–dispersive X–ray spectroscopy. The fluorine content (in apfu) was between 4 and 5, and those less than 4 were not observed. The empirical formula derived as a mean of chemical compositions of multiple grains from Ivigtut is (Ca_0.96Sr_0.04)Al_2.00F₄[(OH)_3.72F_0.28]. The crystal structure of prosopite [monoclinic; a = 6.7103(3) Å, b = 11.1619(5) Å, c = 7.3741(3) Å, β = 94.919(2)°; space group C2/c; Z = 4] was analyzed using single–crystal X–ray diffraction and was refined to the R value of 0.0185 (wR2 = 0.0554) using 791 unique reflections with |F_o| > 4σ(|F_o|). The positions of hydrogen atoms were determined at the position where residual electron density peaks appeared using the difference Fourier method. F⁻ and O²⁻ ions are distributed at each F and O site in order. The chemical structural formula, Ca_0.964(2)Sr_0.036Al₂F₄(OH)₄, obtained from the refinement of Ivgtut sample is approximately consistent with the result of chemical analysis. During the chemical analysis (Zacatecas, Ivigtut, and Katugin deposit samples) and refinement (Ivigtut sample), we assume that (OH)⁻ dissolution into F sites does not occur (but substitution of F⁻ in (OH) sites slightly occurs) and propose that the chemical structural formula of prosopite is expressed as CaAl₂F₄[(OH)_4−xF_x] (x = 0.0–1.0). The crystal structure of prosopite consists of two types of AlF₂(OH)₄ octahedra and one kind of CaF₆(OH)₂ dodecahedra. The size difference between F sites and (OH) sites can be observed in Ca dodecahedra and Al2 octahedra; however, evident differences in Al–F and Al–O distances are not observed in Al1 octahedral sites. Two hydrogen bonds (O1–H1…O2 and O2–H2…F2) are confirmed using bond valence sum calculations.

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.