3.6.- PRUEBA DE HIPOTESIS GENERAL

Although a few different crystal structures have been proposed for CaPv, we focus mainly on resolving the differences among two cases: octahedral distortion (P 4/mmm) (Shim et al., 2002) and octahedral rotation (such as I4/mcm) (Stixrude et al., 2007). We focus particularly on splitting of the CaPv 200_C diffraction line, be-cause it shows the largest difference between the two structures. Octahedral rotation alone can result in a few different tetragonal structures, such as I4/mcm, P 4/mbm, and I4/mmm. However, because differences are subtle in powder diffraction patterns among the three structures (see Fig. 1 in Shim et al. (2002)), we use I4/mcm as a

proxy for the tetragonal crystal structure of CaPv induced by octahedral rotation.

The 200_C diffraction line of CaPv splits the most in both tetragonal diffraction patterns (Fig. 5.1). However, the intensities of tetragonal CaPv 200_C diffraction peaks differ depending on space groups. The lower angle split peak of the 200_C line has a smaller intensity in I4/mcm, while it has a higher intensity in the P 4/mmm structure. It is also important to note that the lower angle split line of 200_C exist at a similar diffraction angle as the original cubic 200 line for the octahedral rotation cases, while it is the higher angle split line for the octahedral distortion case (P 4/mmm).

The 110_C, 211_C, and 220_C lines also show splitting but with smaller degrees in both I4/mcm and P 4/mmm structures.

During laser heating of the starting material, XRD patterns show formation of CaPv. We did not observe any splitting at T between 1700 and 2300 K (Fig. 5.2), supporting the stability of the cubic structure at high T (Kurashina et al., 2004). After T -quench, we have observed clear peak splitting of the 200_C line in CaPv as shown in Fig. 5.2b at all pressures between 25 and 62 GPa at an X-ray wavelength of 0.4066 ˚A.

With smaller wavelengths of X-ray, it was difficult to observe the splitting (such as 0.3344 ˚A). Instead, we observed the selective broadening of the 200_C diffraction line.

Although we observe peak splitting for the 200_C line, unlike the previous studies (Shim et al., 2002), we found that the higher-angle diffraction line of the split 200_C line has a greater intensity throughout the pressure range at 300 K. As shown in (Figure 5.2), our new results obtained under a Ne pressure medium is more consistent the XRD patterns expected for tetragonal structures induced by octahedral rotation than octahedral distortion. In order to detect the 200C line with a higher X-ray wavelength, Shim et al. (2002) used a shaped DAC aperture. However, slot-shaped DAC aperture only allow for 10–20^◦ portion of the Debye rings. In this study, we were able to measure full Debye rings by using conical aperture of DAC. Due to

the full coverage in this study, our diffraction intensities should be less affected by preferred orientation.

We performed Rietveld refinements on diffraction patterns measured at pressures between 28 and 62 GPa at 300 K after laser heating. We only choose diffraction patterns measured under the best resolution setup (Figure 5.3). These refinements were performed with two different crystal structures for CaPv: I4/mcm (octahedral rotation Stixrude et al., 1996a) and P 4/mmm (octahedral distortion Shim et al., 2002). The atomic positions in the I 4/mcm structure are obtained from Caracas and Wentzcovitch (2006).

Through rotations of the SiO₆ octahedra in the (001) plane, the c_p axis (subscript

“p” represents pseudo-cubic unit cell) becomes longer than the a_p axis in the I4/mcm structure. However, depending on distortion in the SiO₆octahedra, the c_p/a_pratio can be smaller than 1 in the P 4/mmm space group (Shim et al., 2002). The c_p/a_p of CaPv obtained from our Rietveld refinement is 1.0054±0.0005 without significant change with pressure (Fig. 5.4). Shim et al. (2002) reported cp/ap = 0.993−0.996. Through ab initio calculations, Stixrude et al. (2007) suggested an increase in c_p/a_p from 1.013 to 1.020 with an increase in pressure from zero to 140 GPa at 0 K. Because our pressure range is much smaller, such small increase over the larger pressure interval would be difficult to resolve from our data. Because the value from ab initio calculation is performed for 0 K, thermal effect could further decrease c_p/a_p. Stixrude et al. (2007) estimated that the value would decrease to 1.0094 at 25.2 GPa 300 K. Therefore, our new results are consistent with theoretical predictions on the crystal structure of Ca-Pv with octahedral rotation.

We fit the pressure–volume data at 300 K to the Vinet equation (Vinet et al., 1989). For the Pt scales of Dewaele et al. (2004) or Holmes et al. (1989), we obtained isothermal bulk modulus (B₀) of 220(1) and 234(1) GPa, respectively (Figure 5.5). In

Table 5.1: Model Parameters for EOS of CaPv

Noguchi et al. (2013) 45.80 225 4^f BM Cub. Pt-F NaCl

Theoretical caculations

Magyari-K¨ope et al. (2002) 45.69 216 4.82 V Orth.

Jung and Oganov (2005) 46.89 219 4.08 BM Tet.

Chizmeshya et al. (1996) 45.62 227 4.29 BM Cub.

Akber-Knutson et al. (2002) 45.90 228 4.3 BM Orth.

Zhang et al. (2006) 45.58 242 4.18 BM Cub.

Caracas et al. (2005)^d 44.537 249 4.09 BM Tet.

Stixrude et al. (2007)^d 44.00 252 4.1 BM Tet.

aV and BM represent Vinet and third order Birch-Murnaghan equations, respectively

bCub., Tet., and Orth. represent cubic, tetragonal, and orthorhombic structures, respectively

cPt-D refers to Pt scale by Dewaele et al. (2004). Pt-H refers Pt scale by Holmes et al. (1989).

Au-F and Pt-F refer to Au and Pt scales by Fei et al. (2007).

dBulk modulus calculated at 0 K.

eThey used pyrolitic composition as a starting material.

fThese values were fixed during EOS fit.

the fitting, we fixed the pressure derivative of the isothermal bulk modulus (B₀⁰) to 4.0, while we didn’t fit the volume at 1 bar and 300 K (V₀), because CaPv is unstable at the conditions and therefore V₀ is unknown. Comparison with Shim et al. (2002), we found much smaller B₀ when we use the same pressure scale (Table 5.1). Considering different pressure medium in these two studies, it is likely that the improved stress conditions in this study yields a smaller B₀ (Klotz et al., 2009). The differences between this study and Wang et al. (1996) are due to the fact that they only covered 1 to 10 GPa, where CaPv is metastable.