MgO is an abundant mineral in the rocky mantle of terrestrial planets, but its melting behaviors remain enigmatic. Here we introduce a simple theoretical model to investigate the B1-liquid transition of MgO up to 370 GPa. Vibrational free energies of B1-MgO are fully computed by the moment recurrence technique in quantum statistical physics. On that basis, we associate the melting temperature with the isothermal bulk modulus via the work-heat equivalence principle. This strategy allows us to quantitatively explain recent experimental data. Our numerical analyses would yield insights into planetary dynamics and evolution.
Using first-principles only, we calculate the melting point of MgO, also called periclase or magnesia. The random phase approximation (RPA) is used to include the exact exchange as well as local and non-local many-body correlation terms, in order to provide high accuracy. Using the free energy method, we obtain the melting temperature directly from the internal energies calculated with DFT. The free energy differences between the ensembles generated by the molecular dynamics simulations are calulated with thermodynamic integration or thermodynamic perturbation theory. The predicted melting tem…
Studies of the behaviour of solids at ultra-high pressures, those beyond 200 GPa, contribute to our fundamental understanding of materials properties and allow an insight into the processes happening at such extreme conditions relevant for terrestrial and extra-terrestrial bodies. The behaviour of magnesium oxide, MgO, is of a particular importance, as it is believed to be a major phase in the Earth lower mantle and the interior of super-Earth planets. Here we report the results of studies of MgO at ultra-high static pressures up to ca. 660 GPa using the double-stage diamond anvil cell techniq…
The electronic structure and optical absorption spectrum of V^{0} and V^{-} center in MgO are investigated using first-principles calculations based on density functional theory. It is demonstrated that the configuration with distortion is energetically favorable in PBE0 functional. The six O atoms around Mg vacancy are non-equivalent due to the distortion. The defect states localized in the band gap are obtained by applying hybrid functional calculations, which is very important for optical properties. At ambient condition, the absorption peak at ~2.5 and ~2.6 eV is assigned to V^{0} and V^{-…
Melting and Pressure-Induced Amorphization of Quartz
最近的研究表明，冰的非晶化和融化是密切相关的。在这封信中，我们推断，从分子动力学模拟的SiO2系统的石英熔化线的亚稳态压力-温度域的延伸是压力诱导的非晶化线。因此，熔化似乎是压力诱导非晶化的物理现象。此外，我们表明，“压力玻璃”的结构类似于非常迅速（1 e +13至1 e +14开尔文每秒）淬火的热玻璃。
Melting of boron subphosphide (B12P2) to 26 GPa has been studied by in situ synchrotron X-ray powder diffraction in a laser-heated diamond anvil cell, and by quenching and electrical resistance measurements in a toroid-type high-pressure apparatus. B12P2 melts congruently, and the melting curve has a positive slope of 23(6) K/GPa. No solid-state phase transition was observed up to the melting in the whole pressure range under study.
Melting of rhombohedral boron subnitride B13N2 has been studied in situ at pressures to 8 GPa using synchrotron X-ray diffraction and electrical resistivity measurements. It has been found that above 2.6 GPa B13N2 melts incongruently, and the melting curve exhibits positive slope of 31(3) K/GPa that points to a lower density of the melt as compared to the solid phase.
Iron represents the principal constituent of the Earth's core, but its high-pressure melting diagram remains ambiguous. Here we present a simple analytical approach to predict the melting properties of iron under deep-Earth conditions. In our model, anharmonic free energies of the solid phase are directly determined by the moment expansion technique in quantum statistical mechanics. This basis associated with the Lindemann criterion for a vibrational instability can deduce the melting temperature. Moreover, we correlate the thermal expansion process with the shear response to explain a discont…
Melting of orthorhombic boron silicide B6Si has been studied at pressures up to 8 GPa using in situ electrical resistivity measurements and quenching. It has been found that in the 2.6-7.7 GPa range B6Si melts congruently, and the melting curve exhibits negative slope of -31(2) K/GPa that points to a higher density of the melt as compared to the solid phase. At very high temperatures B6Si melt appears to be unstable and undergoes disproportionation into silicon and boron-rich silicides. The onset temperature of disproportionation strongly depends on pressure, and the corresponding low-temperat…
Melting behaviors of defective crystals under extreme conditions are theoretically investigated using the statistical moment method. In our theoretical model, heating processes cause missing atoms or vacancies in crystal structures via dislocating them from their equilibrium positions. The coordination number of some atoms is assumed to be removed by one unit and the defect depends on temperature and external pressure. We formulate analytical expressions to directly connect the equilibrium vacancy concentration, the elastic modulus, and the melting temperature. Numerical calculations are carri…
Re-entrant melting (in which a substance's melting point starts to decrease beyond a certain pressure) is believed to be an unusual phenomenon. Among the elements, it has so far only been observed in a very limited number of species, e.g., the alkali metals. Our density functional theory calculations reveal that this behavior actually extends beyond alkali metals to include magnesium, which also undergoes re-entrant melting, though at the much higher pressure of ~300 GPa. We find that the origin of re-entrant melting is the faster softening of interatomic interactions in the liquid phase than …
Iron under Earth's core conditions: Liquid-state thermodynamics and high-pressure melting curve
基于密度泛函理论的{ \em Ab initio}方法在投影增广波的实现下被用来计算与地核相关的高压高温下液态铁的自由能和一系列其他热力学性质。{ \em ab initio}自由能通过使用热力学积分计算从简单参考系到{ \em ab initio}系统的自由能变化而获得，热平均值通过{ \em ab initio}分子动力学模拟计算。参考系由以前工作中使用的反幂对势模型组成。将液态自由能与先前使用相同的{ \em ab initio}技术计算的六方密堆积Fe的自由能相结合，以获得熔化曲线和熔化的体积和熵。计算的熔化性能与实验测量和其他最近的{ \em从头计算}预测的比较。实验理论的比较，也提出了固体和液体Hugoniot曲线交叉的熔化线的压力，以及声速和Grüneisen参数沿Hugoniot。根据实验数据，与常用的高压/高温Fe的状态方程进行了额外的比较。
Based on ab initio molecular dynamics simulations, we determined the melting curve of magnesium (Mg) up to ~460 GPa using the solid-liquid coexistence method. Between ~30 and 100 GPa, our melting curve is noticeably lower than those from static experiments, but is in good agreement with recent shock experiments. Up to ~450 GPa, our melting curve is generally consistent with the melting points from first-principles calculations using the small-cell coexistence method. We found that, at high pressures of a few hundred GPa, due to the strong softening of interatomic interactions in the liquid pha…
The high-pressure melting properties of the ternary alloy AlCuSi with face-centred cubic structure is theoretically investigated using the statistical moment method. We calculate the melting temperature for the alloy under pressure up to 80 GPa. The dependence of the melting temperature on the content of alloying elements is also studied. Our results agree well with previous experiments, simulations, and other theoretical calculations.
The prediction of the melting curve of metals by extrapolation to high pressures and temperatures based on the Lindemann-Gilvarry criterion (LG) assuming harmonic Debye solid is presented. The LG formulation uses the bulk modulus B and its pressure derivative B' as fit parameters deduced directly from the equation of state, however, the results are not unique and strongly depends on the chosen equation of state (EOS). By introducing a constraint that the bulk moduli parameters B and B' must simultaneously obey the Lindemann-Gilvarry criterion (LG) and the EOS, consistent bulk moduli are derive…
The p-V-T equation of state of magnesium metal has been measured up to 20 GPa and 1500 K using both multianvil and opposite anvil techniques combined with synchrotron X-ray diffraction. To fit the experimental data, the model of Anderson-Grüneisen has been used with fixed parameter δT. The 300-K bulk modulus of B0 = 32.5(1) GPa and its first pressure derivative, B0' = 3.73(2), have been obtained by fitting available data up to 20 GPa to Murnaghan equation of state. Thermal expansion at ambient pressure has been described using second order polynomial with coefficients a = 25(2)x10-6 K-1 and b …
It is claimed that all of the pressure scales of the reported melting curves derived by diamond anvil cell experiments require a correction which takes into account the pressure thermal shift, where vanadium is an illustrative example. The linear behavior of the thermal pressure (Pth) vs. the temperature, as predicted by first principles theoretical assumptions is then experimentally confirmed. This allows extrapolation to determine of the actual pressure and thermal temperature at the melt. Accounting for the role of the pressure transmitting media in diamond anvil cell experiments, the analy…
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 for the first time. Further, we use the technique to measure the melting curve of platinum to the highest pressure measured to date. Melting temperature increases from $\…
Low-temperature epitaxial growth of refractory transition-metal nitride thin films by means of physical vapor deposition has been a recurring theme in advanced thin-film technology for several years. In the present study, 150-nm-thick epitaxial HfN layers are grown on MgO(001) by reactive high-impulse magnetron sputtering (HiPIMS) with no external substrate heating. Maximum film growth temperatures Ts due to plasma heating range from 70-150 °C, corresponding to Ts/Tm = 0.10-0.12 (in which Tm is the HfN melting point in K). During HiPIMS, gas and sputtered-metal ion fluxes incident at the growi…
The phase diagram of Zn has been explored up to 140 GPa and 6000 K, by combining optical observations, x-ray diffraction, and ab-initio calculations. In the pressure range covered by this study, Zn is found to retain a hexagonal close-packed crystal symmetry up to the melting temperature. The known decrease of the axial ratio of the hcp phase of Zn under compression is observed in x-ray diffraction experiments from 300 K up to the melting temperature. The pressure at which the axial ratio reaches the square root of 3 value, around 10 GPa, is slightly affected by temperature. When this axial ra…
We use first principles molecular dynamics simulations coupled to the thermodynamic integration method to study the hcp-bcc transition and melting of beryllium up to a pressure of 1600~GPa. We derive the melting line by equating solid and liquid Gibbs free energies, and represent it by a Simon Glatzel fit $T_m= 1564~\text{K} (1 + P/(15.6032 ~\text{GPa}))^{0.383}$, which is in good agreement with previous two-phase simulations below 6000~K. We also derive the hcp-bcc solid-solid phase boundary and show the quasiharmonic approximation underestimates the stability of the hcp structure, predicting…
