Pressure determination

Two general methods are commonly used in order to determine pressure within a DAC. One possibility is to monitor pressure using a pressure marker loaded along with the sample, such as ruby sphere or powder of a metal with well-defined equations of state (e.g. W, Ag, Cu, Pt…). Another possibility is to determine pressure using the surrounding pressure medium. Ruby pressure relies on the fluorescence method and it requires an incident laser source and a spectrometer. In the case of the metal pressure markers or the pressure medium, one needs to know their EOS and to determine unit-cell using X-ray diffraction. In this study pressure was determined using ruby fluorescence method and/or neon EOS.

Ruby is a red gemstone-quality variety of corundum (α-Al2O3) in which Cr³⁺ atoms substitute Al³⁺ at the octahedral site. As a transition metal ion, Cr³⁺ is a strong adsorption and fluorescence center.

Upon absorption of light, d-electrons of chromium are transferred from the ground ⁴A2 state to the excited ⁴T1 state, corresponding to a spin-allowed transition. This excited state then decays into an excited ²E state, which has a spin multiplicity different from that of the ⁴T1. This transition does not involve energy emission because the energy is used for the lattice vibration. From the ²E state the system returns to the ground ⁴A2 state, involving light emission due to a sharp spin-forbidden transition. The emission spectrum of ruby related to the ²E -> ⁴A2 transition is dominated by two sharp bands, R1 and R2, located at about 692.8 nm and 694.2 nm at room pressure and temperature, respectively (Nasdala et al. 2004). The difference of ~ 1.4 nm between the two bands is caused by splitting of the ²E excited state. The red fluorescence bands of ruby show significant pressure dependence and their frequency shift was calibrated to obtain a ruby pressure gauge in several studies (Dewaele et al., 2004; Mao et al., 1986; Xu et al., 1986; Zha et al., 2000). The most commonly used gauge is the one reported by Mao et al. (1986), calibrated up to ~80 GPa in argon pressure medium.

The wavelength shift of the R2 fluorescence line was in that study calibrated against the pressure derived from simultaneous X-ray diffraction measurements of the unit cell volume of copper, by referencing it to the Hugoniot equation of state obtained in an earlier shock wave experimental study (Mao et al. 1979). The pressure relation for the ruby line is given as:

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𝑃 = 𝐴 𝐵⁄ {[1 + (∆λ 𝜆₀

⁄ )^𝐵] − 1} (2)

Where P is the pressure in Mbar, 𝜆₀ is the wavelength of the ruby line in nm at ambient conditions and whose position is dependent on the initial Cr content, 𝛥𝜆 is the difference between 𝜆 at a measured pressure and the 𝜆₀, and A and B are refined parameters of the function. In quasi-hydrostatic conditions A = 19.04 Mbar and B = 7.665, but in non-quasi-hydrostatic environment B = 5. The difference between the two scales is demonstrated in Figure 2.5.

FIGURE 2.5. Ruby spectra recorded at different pressures and at room temperature during compression and decompression of cristobalite X-I (experiment Exp4, Chapter 6). Dotted lines are given equations (2) for the ruby line pressure dependence in hydrostatic (circles) and non-hydrostatic (triangles) environment. The differences between the two estimates are significant above 40 GPa. Inset of the ruby spectra shape demonstrates slightly asymmetric appearance at the highest pressure.

A more recent study by Zha et al. (2000) recalibrated the ruby pressure scale against a primary pressure scale of MgO, which is based on integrated pressure-density data obtained by Brillouin and X-ray diffraction measurements up to 55 GPa in helium pressure-transmitting medium. The accuracy of the ruby scale was reestablished within ±1 %, suggesting B = 7.715. At higher pressures, however, the upcoming studies provided increasing evidences that the Mao ruby scale underestimates pressures, particularly above 40 GPa (e.g. Chijioke et al., 2005; Dewaele et al., 2004; Fei et al., 2007).

A quasi-hydrostatic compression in helium up to 120 GPa suggests significantly higher B values of

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10.32(7), as established by studying MgO (Jacobsen et al., 2008). The effect of hydrostaticity was seen even earlier (Hemley, 1989), where ruby was calibrated against tungsten in neon pressure medium up to megabar pressures. Their data collected in neon suggest slightly higher B values than in Mao’s scale (argon) for the pressures exceeding 80 GPa, but not as high as suggested for data collected more recently in helium (Zha et al. 2000; Jacobsen et al. 2008). It should be noted that argon pressure medium provides hydrostatic conditions only up to low pressures - first signs of non-hydrostaticity are seen ~2 GPa (Angel et al., 2007; Klotz et al., 2009). A recent overview on methodology of pressure determination using ruby luminescence is given by Syassen (2008).

The ruby spheres obtained commercially for the purposes of this study are 5-10μm in diameter and contain 3600 ppm Cr³⁺. A description on synthesis is given by Chervin, Canny & Mancinelli (2001).

FIGURE 2.6. Full-rotation or a wide-scan image collected in DAC with coesite-II at 27.5 GPa. Strong diamond reflections, weak sample reflections and rings from the solidified neon are indicated. Pressure is determined based on d-spacings of neon (111) reflections (e.g. Fei et al. 2007). Further details of in situ X-ray diffraction are given in the section 2.2.3.

Neon. At pressures exceeding 50 GPa the ruby fluorescence signal becomes broad (inset in Fig. 2.5) and consequently the pressure determination becomes difficult. An alternative way to determine pressure is from the neon EOS. Based on X-ray diffraction analyses by Dewaele et al. (2008) up to 208 GPa, the crystal structure of neon remains face-centered cubic over the entire pressure domain, which covers the compression range up to V/V0 = 0.24. Mie–Grüneisen–Debye formalism reproduces very well the present P-V-T data for neon as well as low pressure–low temperature data available in the literature. This makes neon a well calibrated X-ray pressure gauge, suitable for high-pressure, high-temperature studies. Compressional behaviour of neon is best described by least-squares fit of

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the Vinet equation of state (K0 = 1.16 (±0.14) GPa and K0’=8.23 (±0.31), with an initial volume V0 = 88.967 ų (Dewaele et al., 2008; Fei et al., 2007). The pressure is determined based on the d-spacings of the (111) reflections (Fig. 2.6).