## 2 Materials and Methods  
Whole-rock samples of the Mudeungsan tuff were processed into powder, and SiO\({}_{2}\), Al\({}_{2}\)O\({}_{3}\), TiO\({}_{2}\), Fe\({}_{2}\)O\({}_{3}\), K\({}_{2}\)O, Na\({}_{2}\)O, CaO, MgO, MnO, and P\({}_{2}\)O\({}_{5}\) abundances were measured using X-ray fluorescence spectrometer (SHIMADZU XRF-1700) at the at the National Center for Interuniversity Research Facilities (NICIRF) at Seoul National University (SNU), Republic of Korea. Analytical error was within 0.1-1% according to rock-based standards, and loss on ignition (LOI) values were calculated by weight before and after igniting powder samples at 950 C. Measured major element compositions are shown in Table 1.  
The high-resolution synchrotron XRD analysis of the selected rock samples was measured at the 9B beamline of Pohang Accelerator Laboratory (PAL). Incident X-rays were generated by deceleration of the electron bundle as they passed through the bending magnet. Its average spectral luminous intensity is about 10,000 times higher than that of X-rays extracted from laboratory sources. The incident beam was vertically bonded by a mirror and monochromatized to a wavelength of 1.5419(1) or 1.5225(1) A using a double-crystal Si(111) monochromator. The detector arm of the vertical scan diffractometer is composed of 6 sets of seller slits, flat Ge(111) crystal analyzers, anti-scatter baffles, and scintillation detectors, with each set separated by 20 degrees. The seller slits and crystal analyzers play a role in removing noise signals such as inelasticity or air scattering. A good peak-to-background is achieved by very bright synchrotron X-ray beams and instrumental devices, which can detect very weak signals (i.e., very low quantity of phases) in diffraction patterns. Each specimen of ca. 0.2 g powder was prepared using the flat-plate side-loading method to avoid the preferred orientation, and the sample rotated normally with respect to the surface during measurement to increase sampling statistics. The step scan was performed at room temperature from 7 to 121 in 2 0 with 0.005 increments and 2 overlaps to the next detector bank. Samples were exposed for 4 s at each stage to increase the degree of normalization of the diffracted beam intensity. Qualitative and quantitative phase analysis of minerals in rock samples was derived from Rietveld refinement using the Match3 program (Crystal Impact, Bonn, Germany) [6; 7]. The background curve was manually and graphically determined. A quadratic derivative method was used to retrieve Bragg's peaks [8]. The pseudo-Voigt function proposed by [PERSON] et al. was employed for the profile shape function of the diffracted pattern [9]. 'PDF-2\({}^{\beta}\)' and 'crystal open database' were used as mineral databases. In order to determine the integrated peak intensity for quantitative phase analysis, the full width of the half maximum (FWHM) of each peak was calculated by the profile-fitting method. The weighted residual factor (R-factor) of all analyses was measured to see that fit was achieved between experimental X-ray diffraction data and crystallographic models. The R-factor can be mathematically defined by the following equation:  
\[R=\frac{\sum{kF_{\text{obs}}}/\sqrt[]{F_{\text{calc}}}{k}}{\sum{/F_{\text{obs }}}/}\]