2. Methods
2.3 Elasticity measurements at high pressure, HP, and high temperature, HT
2.3.2 Pressure determination
One of the major sources of uncertainty in high-pressure experiments is the pressure determination in the DAC. In fact, a direct calculation of the pressure versus the applied load as in piston-cylinder or multi-anvil devices is not possible, as the distribution of the load over the anvils is unknown and part of the load given by turning the screws is lost to internal friction and gasket deformation (Miletich et al., 2000; Boffa Ballaran et al., 2013). Therefore, internal standard materials for which the physical properties change with pressure are employed and loaded together with the sample in the pressure chamber. Different pressure standards, however, usually do not yield identical pressures at the same experimental conditions, leading to considerable uncertainty in determination of the pressure dependence of physical properties, and particularly derivative properties such as bulk modulus.
2.3.2.1 Fluorescence measurements
The most common method for determining the pressure inside the DAC is to use the laser-induced fluorescence technique applied to luminescence sensors, for instance, by measuring the fluorescence shift of optical pressure gauges such as ruby (Cr3+ doped α-Al2O3).
Fluorescence is the emission of light after irradiation of a sample. In this process, the system is transferred first to an exited state upon irradiation with a light of frequency 1. A subsequent transition to a second exited state occurs without emission of light. Finally the system decays to the ground state with the emission of light with frequency 2. The essential instrumentation suitable for fluorescence measurements is shown in Figure 2.3-4. It consists of a laser-light source, which excites the fluorescent radiation, an optics system for collection of the incident laser light and the fluorescent light, and a spectrometer for the spectral analysis of the fluorescence signal. More details can be found in Miletich et al. (2000).
Figure 2.3-4. Schematic diagram of a fluorescence pressure calibration system. Modified after Miletich et al. (2000).
The pressure determination requires the measurements of the fluorescence spectrum from a reference sample at ambient pressure (1 bar) and comparison with the spectrum of the equivalent material within the sample chamber at high pressure.
The fluorescence signal of ruby is characterized by an intense doublet with sharp bands centered at 694.2 (R1 line) and 692. 8 nm (R2 line) at 1 bar, which, exhibit a shift toward higher wavelengths as the applied pressure increases (Piermarini et al., 1975; Mao et al., 1986). Pressures inside the pressure chamber can be then calculated using the quasi-hydrostatic ruby gauge of Mao et al. (1986) according to the following formula:
1 ( / ) 1
/ 0
A B B
P (2.1) where P is pressure in megabars, λ is the wavelength of the ruby R line, A = 19.04 and B = 7.665.
Pressures may also be calculated according to a similar calibration of the scale made by Jacobsen et al. (2008). This pressure scale is adjusted for the softer helium medium and is based on the shift of the ruby R1 line, calibrated against the primary MgO scale of Zha et al.
(2000). The formula for calculating the pressure is the same as the one reported above for Mao et al. (1986), with the difference that B = 10.32(7).
Sm:YAG, whose fluorescence and density of single crystal has been calibrated against an absolute pressure determination (Trots et al., 2013), was also used as a pressure calibrant to determine the pressure in this study. Similarly to ruby, the pressure-induced shifts of the
fluorescence lines Y1 and Y2 of Sm:YAG are described as P A/B
1(/0)
B 1
with
A = 2089.91(23.04), B = −4.43(1.07) for Y1, and A = 2578.22(48.70), B = −15.38(1.62) for
Y2 bands, where Δλ = λ−λ0, λ and λ0 are wavelengths in nanometer at pressure and ambient
conditions. The pressure induced shifts of the fluorescence lines of Sm:YAG and ruby are
shown in Figure 2.3-5.
Figure 2.3-5. Sm:YAG and ruby fluorescence spectra at different pressures in helium pressure transmitting medium. The shifts of the of the Sm:YAG Y1 line and the ruby R1line are used to calculate pressure by using the Sm:YAG calibration of Trots et al. (2013) and the ruby pressure calibration of (a) Mao et al. (1986) and (b) Jacobsen et al. (2008).
Sm:YAG is also suitable for determining pressure at elevated temperatures, since its fluorescence shift is insensitive to temperature changes. In this study, we have combined the fluorescence shifts of Sm:YAG which is independent of temperature with the fluorescence shift of ruby chips which are strongly temperature dependent, to better constrain the temperature inside the pressure chamber without relying uniquely on the thermocouple. In fact, by loading chips of these two calibrants in the DAC, one can determine pressure independently from temperature using the fluorescence of YAG and determine temperature using the fluorescence of ruby (Rekhi et al., 1999) by fixing the pressure value obtained from the YAG fluorescence measurement. The temperature induced shift of ruby, from 100-600
°C, was calibrated up to 15 GPa by Rekhi et al. (1999) and can be calculated as follow:
1 ) 298 (
100
0
b
T m
R b
P a
(2.2)
Where P is the pressure in GPa, T is the temperature in Kelvin, 0 is the initial wavelength of the ruby line; a/GPa = 19.99 and b0= 6.75; R= (R1+R2/2) for high temperatures and b= b0 + b1(T – 298) + b2(T – 298)2.
Fluorescence spectra were collected at BGI using a Dilor XY spectrometer in a backscattering geometry operating with a 514 nm Ar+ ion laser equipped with a cryogenic solid-state detector. Measurements were performed with 150 mW laser power. Reference fluorescence spectra of Sm:YAG and ruby at ambient pressure where collected before and after each high-pressure measurements. For experiments at APS, the pressure was monitored using an Acton standard series spectrograph from Princeton Instruments operating with a Nd:YVO4 solid-state laser (532 nm) with 400 mV laser power.
The materials such as ruby described above are secondary standards as they are calibrated
In this study, measuring simultaneously density and sound velocities for the same sample at the same conditions provides the advantage of being able to determine accurately the absolute pressure without having to rely on a secondary pressure scale. Absolute pressure can be (where α is the thermal expansion and γ is the Grüneisen parameter), calculated from elastic constants obtained from Brillouin spectroscopy, V is the unit-cell volume determined by means of X-ray diffraction and CV is the isochoric heat capacity.