Probing Local Pressure Environment in Anvil Cells with Nitrogen-Vacancy (N-$V^{-}$) Centers in Diamond

Important discoveries have frequently been made through studies of matter under high pressure. Conditions of the pressure environment are important for the interpretation of experimental results. Due to various restrictions inside the pressure cell, detailed information relevant to the pressure environment, such as the pressure distribution, can be hard to obtain experimentally. Here we present the study of pressure distributions inside the pressure medium under different experimental conditions with $\mathrm{N}$-$V^{-}$ centers in diamond particles as the sensor. These studies not only show a good spatial resolution, wide temperature and pressure working ranges, compatibility of the existing pressure cell design with the proposed method, but also demonstrate the usefulness to measure with these sensors as the pressure distribution is sensitive to various factors. The method and the results will benefit many disciplines such as material research and phase transitions in fluid dynamics.

Figure 1

(a) Structure of the $\mathrm{N}$-$V^{-}$ center. In a single crystal diamond, the nitrogen substitute could replace one of the four carbon atoms around the vacancy, giving four possible orientations relative to one of the four axes of the carbon bonding. (b) Simplified energy structure of the $\mathrm{N}$-$V^{-}$ center. $D=2.87\mathrm{GHz}$ at ambient pressure and room temperature and E is from negligible small to several tens of MHz depending on the diamond sample. (c) The pressure cell consists of a pair of opposing moissanite anvils. The central hole of the gasket is $400\mu \mathrm{m}$ with sample, micro coil, $\mathrm{N}$-$V^{-}$ centers, and ruby inside. In order to probe the local pressure, $\mathrm{N}$-$V^{-}$ centers are drop casted either on the top of one anvil surface or on the surface of a dummy sample. (d) Fluorescence microscopy setup. A plano-convex lens is used to focus the 520-nm laser to the pressurized region. Given that the diamond particles are very dense, so in principle, the average effects from numerous $\mathrm{N}$-$V^{-}$ centers are measured. (e) Confocal microscopy setup. The spatial scanning is achieved by using a galvo mirror. Using the confocal microscope the local pressure experienced by individual $\mathrm{N}$-$V^{-}$ centers can be measured.

Figure 2

Benchmarking ODMR method with traditional ruby method. (a),(b) Selected ODMR spectrum traces (ruby spectra) under different pressure. For the ODMR spectra, the center frequency of two resonances shifts to higher frequencies with higher pressures, while for the ruby spectra, the evolution of the $R_1$ peak is used to determine the pressure. Pressures reported in the legend are determined by ruby spectra. (c) The longitudinal ZFS D against the pressure. $dD/dP=1.49$ MHz/kbar is perfectly linear over the whole pressure range even after solidification. (d) The FWHM of ODMR (black) and ruby spectra (red) against the pressure. Both data show an increasing trend with the pressure.

Figure 3

Pressure distribution mapped via $\mathrm{N}$-$V^{-}$ centers. (a),(b) Polar plot of individual NDs with the color scale representing local pressure under average pressure 13.4 and 61.4 kbar. The origin is defined as the center of the gasket hole. In the range of $\pm 10\mathrm{\%}$, no noticeable pressure gradient is observed under 13.4 kbar, while an obvious pressure gradient is observed under 61.4 kbar. Nonetheless, no circular pressure dependence is observed. (c),(d) ZFS D and the difference of D against the distance from the origin. The data diverge at high pressures as a result of the linear gradient. It is clear that 61.4 kbar has a large pressure gradient. (e),(f) Another dataset from a similar measurement in a pair of anvils with a slight angular offset between two anvil culets. (e) Pressure distribution of individual NDs with the color scale representing local pressure at average pressure 53.6 kbar inside the gasket hole. Significantly huge pressure gradient is observed in the range of $\pm 30\mathrm{\%}$. (f) Enlarged plot of (e), showing the contour plot inside the microcoil. A noticeable pressure gradient is observed in the range of $\pm 15\mathrm{\%}$.

Figure 4

Pressure-driven solidification process. (a) FWHM of spectra measured in C-A1 and C-S (definition of these abbreviations is explained in the main text). Data of C-A1 show a gradual increase with pressure, while those of C-S have a much larger increase. (b) SD of C-A2, C-A1, and C-S. Both data show a significant increase at approximately 30 kbar. We can determine the onset of the critical pressure of Daphne oil 7373 being 28 kbar in C-A1 and 29.3 kbar in C-S, which is slightly higher than the previously reported value. (c) ZFS E of C-A1 and C-S. These behaviors are similar to (a). Data of SFM are plotted as additional information, which shows a sharp turn at 26 kbar. (d) Temperature-pressure phase diagram of Daphne oil 7373. We also include the previously reported results and the results of this work.

Figure 5

Change of pressure distribution with temperature. (a) Average pressures at room temperature and low temperature. The pressure in the $x$ axis is measured by ruby spectra in room temperature. The pressure in cryogenic temperature is overall higher than the ones measured at room temperature. (b) Pressure offsets in low temperature from room temperature. The pressure increases by nearly 5% of the average pressure. (c),(d) Spatial pressure distribution at different temperature of 50.8 and 7.0 kbar. Pressure distribution changes are observed after cooling down, even when it is already in nonhydrostatic state in room temperature as shown in (c). A photo taken from the optical axis of the confocal setup is shown in the insert of (c). The direction from the high-pressure region to the low-pressure region is nearly parallel to the line joining the two screws for applying the pressure. On the other hand, when it is hydrostatic state at room temperature, inhomogeneity rises up at low temperature as shown in (d). No spatial pattern can be found in this scenario, it may be because the solidification starts randomly inside the medium.

Figure 6

Pressure relaxation over time. (a) Average pressure of ten NDs over time. We define the starting time ($t=0$) to be the moment we use a hydraulic press to change the cell pressure. The pink shadow shows the estimated error bar. (b) Pressure distribution of ten NDs over time. The color of each point represents the pressure offset from the average pressure. The $X$-$Y$ axes indicate the position of the NDs inside the pressurized region. The dashed lines connect the same NDs over time. The measurements of the NDs are performed one by one in the same order at different time.