Phase relations in the K₂CO₃-MgCO₃ system have been studied in high-pressure high-temperature (HPHT) multi-anvil experiments using graphite capsules at 6.0 ± 0.5 GPa pressures and 900–1450 °C temperatures. Subsolidus assemblies comprise the fields K₂CO₃+K₂Mg(CO₃)₂ and K₂Mg(CO₃)₂+MgCO₃ with the transition boundary near 50 mol% MgCO₃ in the system. The K₂CO₃-K₂Mg(CO₃)₂ eutectic is established at 1200 °C and 25 mol% MgCO₃. Melting of K₂CO₃ occurs between 1400 and 1450 °C. We propose that K₂Mg(CO₃)₂ disappears between 1200 and 1300 °C via congruent melting. Magnesite is observed as a subliquidus phase to temperatures in excess of 1300 °C. At 6 GPa, melting of the K₂Mg(CO₃)₂+MgCO₃ assemblage can be initiated either by heating to 1300 °C under “dry” conditions or by adding a certain amount of water at 900–1000 °C. Thus, the K₂Mg(CO₃)₂ could control the solidus temperature of the carbonated mantle under “dry” conditions and cause formation of the K- and Mg-rich carbonatite melts similar to those found as microinclusions in “fibrous” diamonds. The K₂Mg(CO₃)₂ compound was studied using in situ X-ray coupled with a DIA-type multi-anvil apparatus. At 6.5 GPa and 1000 °C, the structure of K₂Mg(CO₃)₂ was found to be orthorhombic with lattice parameters a = 8.8898(7), b = 7.8673(7), and c = 5.0528(5), V = 353.39(4). No structure change was observed during pressure decrease down to 1 GPa. However, recovered K₂Mg(CO₃)₂ exhibited a trigonal R3̄m structure previously established at ambient conditions.

A comprehensive P-V-T dataset for bcc-Mo was obtained at pressures up to 31 GPa and temperatures from 300 to 1673 K using MgO and Au pressure calibrants. The thermodynamic analysis of these data was performed using high-temperature Birch-Murnaghan (HTBM) equations of state (EOS), Mie-Grüneisen-Debye (MGD) relation combined with the room-temperature Vinet EOS, and newly proposed Kunc-Einstein (KE) approach. The analysis of room-temperature compression data with the Vinet EOS yields V0 = 31.14 ± 0.02 Å3, KT = 260 ± 1 GPa, and KT′ = 4.21 ± 0.05. The derived thermoelastic parameters for the HTBM include (∂KT/∂T)P = −0.019 ± 0.001 GPa/K and thermal expansion α = a0 + a1T with a0 = 1.55 ( ± 0.05) × 10−5 K−1 and a1 = 0.68 ( ± 0.07) × 10−8 K−2. Fitting to the MGD relation yields γ0 = 2.03 ± 0.02 and q = 0.24 ± 0.02 with the Debye temperature (θ0) fixed at 455-470 K. Two models are proposed for the KE EOS. The model 1 (Mo-1) is the best fit to our P-V-T data, whereas the second model (Mo-2) is derived by including the shock compression and other experimental measurements. Nevertheless, both models provide similar thermoelastic parameters. Parameters used on Mo-1 include two Einstein temperatures ΘE10 = 366 K and ΘE20 = 208 K; Grüneisen parameter at ambient condition γ0 = 1.64 and infinite compression γ∞ = 0.358 with β = 0.323; and additional fitting parameters m = 0.195, e0 = 0.9 × 10−6 K−1, and g = 5.6. Fixed parameters include k = 2 in Kunc EOS, mE1 = mE2 = 1.5 in expression for Einstein temperature, and a0 = 0 (an intrinsic anharmonicity parameter). These parameters are the best representation of the experimental data for Mo and can be used for variety of thermodynamic calculations for Mo and Mo-containing systems including phase diagrams, chemical reactions, and electronic structure.

Resent experimental and theoretical studies suggested preferential stability of Fe₃C over Fe₇C₃at the condition of the Earth's inner core. Previous studies showed that Fe₃C remains in an orthorhombic structure with the space groupPnmato 250 GPa, but it undergoes ferromagnetic (FM) to paramagnetic (PM) and PM to nonmagnetic (NM) phase transitions at 6–8 and 55–60 GPa, respectively. These transitions cause uncertainties in the calculation of the thermoelastic and thermodynamic parameters of Fe₃C at core conditions. In this work we determinedP‐V‐Tequation of state of Fe₃C using the multianvil technique and synchrotron radiation at pressures up to 31 GPa and temperatures up to 1473 K. A fit of ourP‐V‐Tdata to a Mie‐Gruneisen‐Debye equation of state produce the following thermoelastic parameters for the PM‐phase of Fe₃C:V₀ = 154.6 (1) ų,K_T0= 192 (3) GPa,K_T′ = 4.5 (1),γ₀= 2.09 (4),θ₀ = 490 (120) К, andq = −0.1 (3). Optimization of theP‐V‐Tdata for the PM phase along with existing reference data for thermal expansion and heat capacity using a Kunc‐Einstein equation of state yielded the following parameters:V₀ = 2.327 cm³/mol (154.56 ų),K_T0 = 190.8 GPa,K_T′ = 4.68, Θ_E10 = 305 K (which corresponds toθ₀ = 407 K), γ₀ = 2.10,e₀ = 9.2 × 10⁻⁵K⁻¹,m = 4.3, andg = 0.66 with fixed parametersm_E1 = 3n = 12, γ_∞ = 0,β = 0.3, anda₀ = 0. This formulation allows for calculations of any thermodynamic functions of Fe₃C versusTandVor versusTandP. Assuming carbon as the sole light element in the inner core, extrapolation of our equation of state of the NM phase of Fe₃C suggests that 3.3 ± 0.9 wt % С at 5000 К and 2.3 ± 0.8 wt % С at 7000 К matches the density at the inner core boundary.

Phase relations in the Na 2 CO 3 -MgCO 3 system have been studied in high-pressure high-temperature (HPHT) multi-anvil experiments using graphite capsules at 6.0 ± 0.5 GPa pressures and 900-1400 °C temperatures. Sub-solidus assemblages are represented by Na 2 CO 3 +Na 2 Mg(CO 3 ) 2 and Na2Mg(CO 3 ) 2 +MgCO 3 , with the transition boundary near 50 mol% MgCO 3 in the system. The Na 2 CO 3 -Na 2 Mg(CO 3 ) 2 eutectic is established at 1200 °C and 29 mol% MgCO 3 . Melting of Na 2 CO 3 occurs between 1350 and 1400 °C. We propose that Na 2 Mg(CO 3 ) 2 disappears between 1200 and 1250 °C via congruent melting. Magnesite remains as a liquidus phase above 1300 °C. Measurable amounts of Mg in Na 2 CO 3 suggest an existence of MgCO 3 solid-solutions in Na 2 CO 3 at given experimental conditions. The maximum MgCO 3 solubility in Na-carbonate of about 9 mol% was established at 1100 and 1200 °C. The Na 2 CO 3 and Na 2 Mg(CO 3 ) 2 compounds have been studied using in situ X‑ray coupled with a DIA-type multi-anvil apparatus. The studies showed that eitelite is a stable polymorph of Na 2 Mg(CO 3 ) 2 at least up to 6.6 GPa and 1000 °C. In contrast, natrite, γ-Na 2 CO 3 , is not stable at high pressure and is replaced by β-Na 2 CO 3 . The latter was found to be stable at pressures up to 11.7 GPa at 27 °C and up to 15.2 GPa at 1200 °C and temperatures at least up to 800 °C at 2.5 GPa and up to 1000 °C at 6.4 GPa. The X‑ray and Raman study of recovered samples showed that, under ambient conditions, β-Na 2 CO 3 transforms back to γ-Na 2 CO 3 . Eitelite [Na 2 Mg(CO 3 ) 2 ] would be an important mineral controlling insipient melting in subducting slab and upwelling mantle. At 6 GPa, melting of the Na 2 Mg(CO 3 ) 2 +MgCO 3 assemblage can be initiated, either by heating to 1300 °C under “dry” conditions or at 900-1100 °C under hydrous conditions. Thus, the Na 2 Mg(CO 3 ) 2 could control the solidus temperature of the carbonated mantle under “dry” conditions and cause formation of the Na- and Mg-rich carbonatite melts similar to those found as inclusions in olivines from kimberlites and the deepest known mantle rock samples-sheared peridotite xenoliths (190-230 km depth).