Dynamic laser heating and optical probes in the diamond anvil cell

Our time-resolved single-pulse laser heating diamond anvil cell experiments combine measurements of optical emission, transmission, and reflectance spectroscopy in the visible spectral range (480–750 nm) using a streak camera, as has been described in our previous publications6, 39 (Supplementary Fig. 1). Nitrogen was loaded in a high-pressure cavity along with a metallic (Ir) suspended foil (coupler), which has one or several cylindrical holes of 5–8 μm in diameter. The sample is conductively heated locally via the energy transport of a near IR (1064 nm) laser focused down to approximately 10 μm (normally from both sides) and absorbed by the rim of the coupler surrounding the hole (or by a flat coupler surface in a few experiments). The laser pulses of 4–10 μs duration are sufficiently long to transfer heat to the nitrogen sample in the hole of the coupler creating a localized heated state of several μm in linear dimensions and a few μs long as determined in our FE calculations (Supplementary Fig. 2). The optical spectroscopic probes, aligned to the heated spot, were used in a confocal geometry suppressing spurious probe signals. Transient transmittance and reflectivity were obtained using pulsed broadband supercontinuum (1 MHz, 150 ps, 480–720 nm) and (occasionally) continuous laser (532 nm) probes having focal spots of approximately 6 μm in diameter (Supplementary Fig. 1) that are spatially filtered with a confocal aperture of some 50% larger in diameter.

Time-resolved (with the resolution down to 0.5 μs) sample temperature was obtained from fitting thermal radiation spectra emitted by the coupler and hot sample to a Planck function (Supplementary Fig. 3). These were normally determined in a separate experiment with identical heating without probing and integrated over a number of laser heating events (5–20) to improve signal-to-noise. The measured temperature should be treated cautiously as the thermal radiation measured represent a sum of contributions from the Ir coupler and the sample. Normally one expects that coupler has higher temperature than the sample and emits more because of difference in emissivity. However, the sample emissivity changes substantially once it becomes absorptive, suggesting that the measured thermal emission in this regime characterizes the sample temperature. Additionally, FE calculations6, 39, 46 have been used to model the temperature distribution in the high-pressure cavity to estimate the necessary corrections.

At each nominal pressure, temperature was increased stepwise with an increase of the heating laser power. Pressure was measured before and after the heating cycles using Raman spectra of the nitrogen vibrons and stressed diamond edge (Supplementary Fig. 4). Pressure was found to remain essentially constant (within <3 GPa) during heating. No correction for the thermal pressure has been used.

Transient optical data reduction

To determine the transient reflectance values of conducting nitrogen at extreme P–T conditions, the following procedure has been adopted. The reflectance of the outside diamond–air interface has been a natural reflectivity standard for many experiments of such kind. However, in the majority of experiments reported here this reference reflectivity has not been measured for two reasons. First, it is normally too strong and without the unwanted attenuation can damage the streak camera detector, and second, it requires an additional correction for the absorption of diamonds and change in geometrical factors, which is normally overlooked. However, these measurements have been performed in two experiments and yielded generally consistent results.

In the majority of the experiments, we have used the reflectivity (or transmission in the associated experiments) of the diamond–sample interface at room temperature measured just before the laser heating shot as the reference (Supplementary Fig. 6). The reflectivity of the diamond–nitrogen interface is determined as R nd = (n N − n D )2/(n N + n D )2, where n N and n D are the refractive indices of nitrogen and diamond, respectively, in the high-pressure chamber. While we assumed that the refractive index of diamond is the same as at ambient pressure, we have performed a separate experiment in molecular nitrogen at 75 GPa to determine its refractive index (Supplementary Fig. 5).

Furthermore, at high temperatures due to large temperature gradients, the conducting state of nitrogen occurs only inside a small hole of the coupler (Supplementary Fig. 6) or immediately next to the coupler flat surface (if the hole is not used). Thus there is an additional interface between the reflective state and hot but untransformed (semiconducting) nitrogen. Because temperature is the continuous function of the coordinate in the experimental cavity, the conducting reflective nitrogen is in contact with the absorptive nitrogen, the transmission of which has been determined in the preceding high temperature shot with a slightly smaller laser energy but almost the same recorded temperature. It has been assumed that the reflectivity of the conducting highly reflective nitrogen was attenuated by a strong absorption of nitrogen that resides at smaller T and has not been transformed.

Drude model

Reflectivity spectra are well fitted by a Drude model having conductivity of the form σ = σ 0 (1−iωτ)−1, where ω is the angular frequency. The DC conductivity σ 0 = Ω p 2τε 0 , in which Ω p is the plasma frequency, τ the scattering time, and ε 0 the permittivity of free space. The dielectric constant is ε* = ε b + iσ(ωε 0 )−1 where ε b is the bound electron contribution to the dielectric constant. A range of ε b from 1 to n N 2 are examined when assessing uncertainty; we generally found ε b = n N 2 provided a better fit to the data. The corresponding index of refraction is \(n^ \ast = \sqrt {\varepsilon ^ \ast }\). The reflectivity of the interface between the metallic and semiconducting nitrogen is modeled as R = |(n* − n N )/(n* + n N )|2, where the refractive index of the semiconducting state is assumed to be the same as for molecular nitrogen determined in our separate experiment (Supplementary Fig. 5); use of this expression is strictly valid for a sharp interface between the two states occurring at a particular temperature in the cell cavity (Supplementary Fig. 6), as is expected for metallization based on our observations.

Data availability

All relevant numerical data are available from the authors upon request.