Session C17: Matter in Extreme Environments: Melting and Melts

Melting Under Extreme Conditions: Ab Initio Monte Carlo Simulations

Melting results for rare gas clusters and solids under extreme pressures and magnetic fields are presented. Phase transitions are simulated by exploring phase space with classical (parallel-tempering) Monte Carlo methods combined with a very accurate computation of the interaction energy of the sampled configurations. We employ many-body expansions where the total interaction energy of the N-atom system is obtained by decomposing the total energy into two-, three- and higher-body fragments.

For rare gases, this approach works well for melting under ambient conditions¹ and for argon for pressures up to 100 GPa, 1 Million times the atmospheric pressure². We work in the isobaric, isothermal ensemble, allowing for atom displacements as well as cell volume adjustments employing periodic boundary conditions. Excellent agreement with experimental data is found up to very high pressures.

Neon clusters in high magnetic fields show elevated melting points and also give fascinating insight in the melting process itself.
In a strong homogeneous magnetic field applied in z-direction the clusters get squeezed in the perpendicular plane as also observed for atoms. Around the melting temperature, we observe an additional squeezing parallel to the magnetic field due to perpendicular paramagnetic bonding responsible for the enhanced melting points. For these studies, dimer potential curves were computed on MP2 and coupled-cluster level depending on the magnetic field, the interatomic distance and the angle of the molecular axis with the magnetic field direction.

1 O.Smits, P.Jerabek, E.Pahl, P.Schwerdtfeger, Angew. Chem. Int. Ed. (2018) 57, 9961 and references therein.
2 J.Wiebke, E.Pahl, and P.Schwerdtfeger, Angew. Chem. Int. Ed. (2013) 52, 13202   

Fast determination of melting curves at high pressure

Determination of accurate melting curves of materials is an old problem. In the past twenty years, reliable results have been obtained with ab-initio molecular dynamics (AIMD). These simulations are usually based on molecular dynamics of the solid or the liquid (one phase approach), or the direct simulation of the solid-liquid interface (two phases approach) [1]. Unfortunately, AIMD can be very time consuming, and prevent applications on complex systems or heavy elements. Fast alternative methods are necessary, at least to give a starting point for more complex calculations.
The famous phenomelogical Lindeman [2] approach based on the comparison of the amplitude of thermal vibrations of atoms with the interatomic distance and proposed more than 100 years ago is still widely used [3]. We have tested its validity for several metals (Au, Al, Fe…) on a large pressure scale. We will also discussed applications on MgO and U in regard to our recent calculations of vibrational frequencies in temperature [4].

[1] J Bouchet, F Bottin, G Jomard, G Zérah, Phys. Rev. B 80, 094102 (2008)
[2] F. A. Lindemann, Physik. Zeitschr. 11, 609 (1910)
[3] D. V. Minakov, P. R. Levashov, Phys. Rev. B 92, 224102 (2015)
[4] J Bouchet, F Bottin, Phys. Rev. B 95 , 054113 (2017)   

Critical point, liquid-vapor coexistence, and melting of Mg2SiO4 from ab-initio simulations

We report density functional theory-based molecular dynamics calculations (DFT-MD) of Mg₂SiO₄ liquid and vapor across the liquid-vapor coexistence boundary that spanned 0.22-3.22 g/cc in density and 5000-10000 K in temperature. The critical point was estimated through a bootstrap analysis of a collection of DFT-MD isotherms above and below the critical point. Additionally, we describe the structure and composition of the liquid and vapor around the critical point. Finally, we discuss melting behavior at P=1 bar.   

Chain melting simulations in dense potassium from a machine-learned atomic potential

Compressed potassium forms a host-guest structure above 19 GPa, K-III, where the host and guest structures have incommensurate lattice constants c_h and c_g [1]. The guest structure comprises a linear set of chains with long range order at low temperature and has been observed to de-correlate or "melt" upon heating, while the host structure remains solid [2]. We studied this motion and onset of inter- and intra-chain de-correlation, which lead to the disappearance of guest structure diffraction peaks, by ab initio molecular dynamics (AIMD) using approximants of the incommensurate crystal. The system sizes that can be simulated with AIMD are limited, so a forcefield was trained on the AIMD data set. The trained potential was used to produce potassium's PT phase diagram up to 60 GPa and 1000 K, correctly predicting the stable solid phases, the chain melt and the full melting line [3].
[1] G. Woolman et al., Phys. Rev. Materials 2, 053604 (2018).
[2] E.E. McBride et al., Phys. Rev. B 91, 144111 (2015).
[3] H. Zong et al., submitted.   

Pre-melting hcp to bcc Transition in Beryllium by First-Principles Phonon Quasiparticle Approach

<p style="margin: 0px; text-align: justify; line-height: normal; text-justify: inter-ideograph;"><span style="color:black; font-family:times new roman,serif; font-size:12pt; margin:0px">Beryllium (Be) is an important material with wide applications ranging from aerospace components to x-ray ray equipment. Yet a precise understanding of its phase diagram under extreme conditions remains elusive. We have investigated the phase stability of Be using a recently developed hybrid free energy computation method that accounts for anharmonic effects by invoking phonon quasiparticles. We find that the hcp → bcc transition occurs near the melting curve at 0 < P < 11 GPa with a positive Clapeyron slope of 41(4) K/GPa, which is more consistent with recent experimental measurements. This work also demonstrates the validity of this theoretical framework based on the phonon quasiparticle to study the structural stability and phase transitions in strongly anharmonic materials.</span></p>   

Direct Observation of Shock-Induced Melt Kinetics in a Porous Solid Using Time-Resolved X-Ray Diffraction

Time-resolved x-ray diffraction was used to obtain direct (real time) evidence of shock-induced melting and associated kinetics in a porous solid (aluminum (Al) powder). Broadening of the Debye-Scherrer ring corresponding to the (111) peak of Al provided unambiguous evidence of melting. Our data showed that complete bulk melting of the powder could take in excess of 450 ns even when it is shocked to equilibrium pressure-temperature states above the melt boundary. Information on the melt kinetics obtained from our work provide insight into the thermal equilibration time and thermal diffusivity of the material under high-pressure dynamic loading, which are essential to developing well-constrained heat transfer and melting models for Al powder and other porous materials (LA-UR-18-30166).   

In situ X-ray diffraction of Ce melting under shock loading

With 7 observed crystalline phases below 20 GPa, cerium exhibits a complex phase diagram. In particular, the γ-α phase transition exhibits a large volume collapse (13%-16%) resulting in a low melting pressure for a metal. Sound speed measurements have shown that Hugoniot intersects the melt boundary at 10 GPa with complete melting near 18 GPa; however, the processes and timescales involved are not yet known. This work presents experiments performed at the Dynamic Compression Sector examining the phase evolution of γ-Ce under shock loading. The results indicate that γ-Ce and α-Ce coexist with liquid Ce at pressures near the onset of melt. With increasing pressure, α-Ce is no longer observed; however, γ-Ce persists after impact at pressures beyond 18 GPa. The results indicate significant kinetics, with complete melting observed 200 ns after impact. An experiment performed below the melting pressure shows that the γ-α transition occurs over a similar timescale, with visible peaks for γ-Ce and α-Ce observed over 50 ns after impact. As a result, the γ-α transition appears to exhibit occurs over a relatively long timescale, which is surprising for an isostructural phase transition, and appears to be a significant barrier to melting.
LA-UR-18-30167   

Pressure-volume-temperature equation of state and high-pressure melting of zirconium

Robust modeling of shock phenomena requires accurate and precise experimental measurements of equations of state and phase diagrams. Zirconium is of particular interest in nuclear applications because of its low neutron cross section. Here, we present the thermal equation of state and melting curve of ultra-high purity Zr in the body-centered cubic (bcc) phase measured using the laser-heated diamond-anvil cell (LHDAC) coupled with in situ synchrotron-based X-ray diffraction (XRD). From quasi-hydrostatic room-temperature compression to pressure (P) = ~70 GPa using helium as a pressure transmitting medium, we constrain the bcc-Zr bulk modulus, K₀ = 120(7) GPa and its pressure derivative, K₀’ = 3.0(1). Additionally, we have collected LHDAC XRD data over a range of P = ~10 – 40 GPa and temperature (T) = ~1400 – 2200 K to further constrain the bcc-Zr thermal equation of state parameters. Within a separate set of experiments, we have observed melting of bcc-Zr between P = ~10 – 20 GPa based on plateaus in the T versus laser-power curves coupled with diffuse X-ray scattering and visual changes in the sample before and after laser-heating. At P = ~10 GPa, initial results suggest a melting temperature, T_m = 2270(50), that implies a melting curve slope of ~14 K/GPa.   

Melting Line and Structure of Hot dense Fluids probed by X-ray diffraction

Warm dense simple molecular fluids constitute a large fraction of planetary interiors. Their current microscopic understanding is essentially based on ab-initio calculations. Novel states are predicted such as: ionic water and ammonia, metallic oxygen and hydrogen, or polymerized carbon dioxide and nitrogen with possible first-order transition. These remain to be tested by experiment. In this contribution, we will present some developments which have enabled to perform structural measurements on dense simple molecular fluids in the 100 GPa range and few thousand Kelvin. An elaborate sample environment has been implemented to homogeneously laser heat the molecular system. A multichannel collimator is used to filter the overwhelming x-ray diffraction background contribution from the diamond anvils. A careful data analysis is applied to extract the liquid structure factor and the radial distribution function. Observing the liquid diffraction is essential to unambiguously determine the occurrence of melting. Measurements on laser heated nitrogen, gold and xenon will be presented to illustrate this experimental approach.