Determination of the melting curve of gold up to 110 GPa

The melting curve of gold has been measured up to 110 GPa using laser-heated diamond anvil cells and synchrotron x-ray diffraction techniques. Accurate pyrometry temperature measurements and a homogeneous heating of the gold sample were achieved by implementing a sample assembly consisting of two boron-doped diamond cupped disks sandwiching the gold sample. In the investigated pressure range, the fcc solid gold remains stable up to melting. A clear structural signature of bulk melting is observed. Ab initio molecular dynamics simulations within the two-phase approach give a melting curve in good agreement with the experimental one. We discuss the validity of calculations based on the Lindemann criteria of melting which have been up to now used to obtain the melting line of Au in the 100 GPa range.

Figure 1

Sample preparation and P-T metrology. (a) Drawing of a cross-sectional view of the sample cavity located between the two diamond anvils of the DAC. Two cupped C:B disks are filled with gold and placed each in a pit (diameter: $45\mu \mathrm{m}$; depth: $6\mu \mathrm{m})$ realized by FIB at the center of the diamond anvil culet and coated with LiF or ${\mathrm{Al}}_2{\mathrm{O}}_3$. The two disks form a capsule heated from both sides by YLF laser beams. The laser focus is adjusted in order to fully illuminate the C:B plates and reduce the radial temperature gradient. The x-ray beam probes the gold sample confined between the two C:B disks. Bottom: Determination of the thermodynamic conditions. (b) Difference between the pressures measured with the gold and diamond calibrants using the Dorogokupets semiempirical state equation [22]. (c) Thermal emission of a C:B disk at 104 GPa and its analysis in the gray-body approximation. (d) The intensity vs wavelength spectrum fitted between 550 nm and 920 nm with a Planck distribution $(T_{\mathrm{Planck}}=4277\pm 3$ K).

Figure 2

X-ray diffraction patterns collected at 36.5 GPa, between 2600 and 1600 K. The spectrum in red, collected at 2600 K (above melting), shows the first three diffuse rings of the liquid gold structure factor. Below melting, the TDS from the hot solid is composed of a background signal added to the Compton contribution from the anvils, and a broad, temperature-dependent footprint around each Bragg peak. The spectrum in black was obtained after quenching the sample at 300 K. The sample pressure dropped at 27 GPa. Gold, diamond, and ${\mathrm{Al}}_2{\mathrm{O}}_3$ peaks are labeled. The saturated Au single-crystal peaks which formed under heating have been masked before integrating the image plate, which explains why the Au diffraction peaks appear relatively weak on the spectra. Inset: X-ray diffraction images collected at three different temperatures for a C:B-gold assembly in argon at $P=36.5$ GPa. At 2600 K, gold is fully melted and the first two liquid diffuse scattering rings are observed. At 2560 K and 1780 K, gold is solid and the temperature diffuse scattering around the gold XRD spots is observed.

Figure 3

X-ray diffraction patterns collected at 78 GPa during a heating cycle. Each spectrum is plotted with a different color and labeled with the temperature. A reference spectrum collected after quench is plotted in black showing the ambient temperature sample diffraction peaks and the diamond anvil Compton scattering. The TDS contribution from the hot gold solid appears as a smooth signal added to the Compton contribution from the anvils. The liquid signal appears at 3580 K as a weak broad diffuse ring centered at $10.5^{\circ }$. The sample pressure dropped at 67 GPa after quench. Gold, diamond, and ${\mathrm{Al}}_2{\mathrm{O}}_3$ peak positions are indicated by vertical tick marks.

Figure 4

Gold melting curve measured in this study by XRD. The pressure and temperature conditions at which XRD patterns have been collected are shown. The empty (plain) circles represent XRD patterns with liquid (solid only) gold signal. Each color represents a different sample. Pressure and temperature error bars are shown for the melting points only (represented by empty squares). The black line is a fit of the Simon-Glatzel equation to the melting points: $T_m=T_0{(1+P_m/a)}^b$ with $T_0=1337$ K, $a=22.265\pm 1.83$ GPa, and $b=0.662\pm 0.03$.

Figure 5

Isothermal equation of state of gold calculated by ab initio DFT methods in the present work. Green lozenge: 0 K EOS; blue square: 300 K EOS calculated with a supercell of 256 atoms and a $2\times 2\times 2$ k-point grid, and (red square) with the supercell used in the TPA, 216 atoms and the $\mathrm{\Gamma }$ point. The black line is the semiempirical Vinet EOS proposed by Dorogokupets and Oganov [22], and the black triangle the XRD data obtained by Takemura and Dewaele at 300 K [2].

Figure 6

Ab initio melting curve of Au obtained with the TPA. The blue square represents $\left(P,T\right)$ points for which the liquid part crystallizes while the red circle is $\left(P,T\right)$ points for which the solid part melts. The melting temperatures for each isochore (black diamonds) are between the solid with the highest temperature and the liquid with the lowest one. The black line is a fit of the Simon-Glatzel equation to the melting points $\mathrm{[}{T}_m=T_0{(1+P_m/a)}^b$ with $T_0=1181$ K, $a=17.94$ GPa, and $b=0.09]$.

Figure 7

Melting curve of gold obtained in this work from XRD measurements. Previous determinations from experiments (labeled Zha [7], Weir [6], Pippinger [8], Mitra [45], Errandonea [44]) are displayed in the figure inset. The plain green line shows the Hugoniot of gold calculated with the SESAME 2008 table [5].

Figure 8

Melting curves of gold obtained in this work from XRD measurements and ab initio simulations. Previous determinations from ab initio simulations (labeled Greeff [18]) and classical molecular dynamics simulations (labeled Liu [52]) are shown for comparison. The green and red dashed lines correspond to the melting curves determined using the Lindemann criterion calculated respectively from the atomic mean-squared displacements $\left(T_{m{\langle u\rangle }^2}\right)$ obtained by ab initio simulations [20] or from the bulk modulus $\left(T_{\mathrm{mB}}\right)$ [19] determined by XRD [39].