Latent heat method to detect melting and freezing of metals at megabar pressures

The high-pressure melting curves of metals provide simple and useful tests for theories of melting, as well as important constraints for the modeling of planetary interiors. Here, we present an experimental technique that reveals the latent heat of fusion of a metal sample compressed inside a diamond anvil cell. The technique combines microsecond-timescale pulsed electrical heating with an internally heated diamond anvil cell. Further, we use the technique to measure the melting curve of platinum to the highest pressure measured to date. Melting temperature increases from $\approx 3000$ K at 34 GPa to $\approx 4500$ K at 107 GPa, thermodynamic conditions that are between the steep and shallow experimental melting curves reported previously. The melting curve is a linear function of compression over the 0–20 % range of compression studied here, allowing a good fit to the Kraut-Kennedy empirical model with fit parameter $C=6.0$.

Figure 1

Schematic of electrical path (black), optical paths (red), and diamond anvils (blue) at the Carnegie Institution for Science. A regulated dc power supply charges a capacitor bank ($C_{\text{bank}}$: 470 $\mu \mathrm{F}$, 70 V electrolytic). When triggered by the Delay generator (SRS DG645), the MOSFET (FQP30N06L) allows current to flow through a reference resistor ($R_{\text{ref}}=0.29\mathrm{\Omega }$), and the platinum sample that is compressed between diamond anvils. The snubber capacitor ($C_{\text{snub}}$: 16 $\mu \mathrm{F}$, 100 V electrolytic) limits current oscillations. The circuitry for measuring current and four-point-probe voltage are shown in thin black lines. The voltage dividers, Vdiv, reduce input voltage to within the 15 V range of the in-amp (AD842). Each divider is made of two resistors with typical values of 1 $\mathrm{k}\mathrm{\Omega }$ and 10 $\mathrm{k}\mathrm{\Omega }$. The in-amp is operated with no gain, referenced to ground, and connected through output resistors ($R_{\text{out}}$: 105 $\mathrm{\Omega }$) to the oscilloscope (Tektronix DPO 3034). A simplified optical path is shown here; see McWilliams et al. [37] for elaboration. During each heating pulse, one flipper mirror (FM) diverts light from the left or right side of the diamond cell to a CCD camera (Point Grey Grasshopper3 Color) for two-dimensional imaging of thermal emissions. The other flipper mirror (FM) does not divert the light, allowing it to pass into a confocal filtering system, then into a spectrometer (Princeton Instruments Acton SP2300) and streak camera (Sydor ROSS 1000) for time-resolved measurements of thermal emissions. Solid red lines show the path of light in one configuration; dashed lines show the alternative configuration. Ovals represent lenses, line segments at ${45}^{\circ }$ represent mirrors, and broken line segments represent pinholes.

Figure 2

Streak camera image of platinum heated from $T=300$ K at $P=60\pm 3$ GPa to $T>5000$ K. (a) Raw data. (b) Intensity averaged over the wavelength dimension. Annotations mark regions interpreted to be melting, freezing, and heating and cooling of solid and liquid platinum.

Figure 3

Time-resolved thermal emissions of the left side of the platinum sample heated from 300 K at $60\pm 3$ GPa to past its melting point at $4060\pm 140$ K at $68\pm 5$ GPa. Each warm color (yellow to red to black) represents a set of $n$ heating pulses driven by the voltage that is listed in the legend ($V_{\text{bank}}$). Blue and cyan markings indicate melting and freezing. (a) Average counts on the streak camera CCD. (b) Fourth root of average counts per microsecond, a proxy for temperature. Noisy gray curves show unsmoothed data, $I^{1/4}$, while colored curves show smoothed data, $I_s^{1/4}$. (c) Time-derivatives, $\frac{d{I}_s^{1/4}}{dt}$ (grey), and smoothed time derivatives, ${\frac{d{I}_s^{1/4}}{dt}}_s$ (colors). The smoothing function is a second-order Savitzky-Golay filter with timescale $\tau =0.4\mu \mathrm{s}$ for both $I_s^{1/4}$ and ${\frac{d{I}_s^{1/4}}{dt}}_s$. The minima during heating (blue circles) and maxima during cooling (cyan circles), are interpreted as melting and freezing. The corresponding times, $t_{\text{melt}}\pm \tau /2$ and $t_{\text{freeze}}\pm \tau /2$, are marked in blue and cyan in (a), and used for the temperature fits in (d) and (e). (d), (e) Planck fits (blue and cyan) to thermal emissions spectra during melting and freezing. Planck fit parameters listed in the legend are melting temperature and emissivity ($T_m$ and ${\epsilon }_m$), and freezing temperature and emissivity ($T_f$ and ${\epsilon }_f$). Spectra have been filtered to improve the clarity of the figures using a second-order Savitzky-Golay filter with wavelength scale $d\lambda =20$ nm. Planck fits are performed without filtering the spectra.

Figure 4

Melting temperature of platinum as a function of (a) pressure and (b) compression. Experimental data from this study (red circles) are compared to experimental and computational data from Anzellini et al. [12], Mitra et al. [41], and Arblaster et al. [44]. X-ray diffraction-based identification of solid platinum and of liquid platinum from Anzellini et al. (small gray triangles and large black triangles, respectively) are consistent with our melting data, within the uncertainties. Observations of plateaus in temperature versus laser power (green diamonds) and calculations by the $\mathrm{Z}$ method (blue squares) from Anzellini et al. are consistent with our melting temperatures at pressures up to 40 GPa, but inconsistent at pressures above 60 GPa. Solid curves are Simon fits to the data of this study (red) and to the $\mathrm{Z}$-method calculations of Anzellini et al. (blue). Kraut-Kennedy and Lindemann fits to the data of this study are shown by dotted red and dash-dotted red curves, respectively.

Figure 5

High-pressure melting curve of platinum. Melting data of this study (red crosses), the Simon fit to the data (solid red), and an error envelope of $\pm 300$ K at pressures above 30 GPa (red shading). Past experimental studies are summarized by error envelopes: Anzellini et al. [12] (green), Errandonea [14] (magenta), Kavner and Jeanloz [15] (gray), Patel and Sunder [16] (cyan). Theoretical results are shown in solid curves: Belonoshko and Rosengren [3] (magenta), Anzellini et al. [12] (blue), Jeong and Chang [53] (gray), and Liu et al. [54] (cyan).

Figure 6

Temperature evolution of platinum heated from room temperature at $60\pm 3$ GPa during the same nine sets of heating runs shown in Fig. 3. Emissivity is fitted to emissions spectra from a narrow region of each curve. (a) Temperature, $T$, versus time, $t$. (b) Heating and cooling rates, $dT/dt$, versus $T$.

Figure 7

Signature of latent heat absorption during all melting runs documented in this study. The rate of temperature change, $dT/dt$, is plotted against temperature, $T$ (gray curves). The dip in each curve is caused by the latent heat of melting. Values of $dT/dt$ are scaled and offset so that each cluster of curves reflects all the melting data generated by heating from a single starting pressure.

Figure 8

Temperature evolution of platinum heated from room temperature at $60\pm 3$ GPa, assuming a fixed emissivity of 0.58. The data are from the same nine sets of heating runs shown in Figs. 3, 6. (a) Temperature, $T$, versus time, $t$. (b) Heating and cooling rates, $dT/dt$, versus $T$.