Phase boundaries and phase diagrams

We are developing and applying simulation techniques to study phase boundaries in molecular systems, such as methane and water, and in tetrahedrally bonded materials.

  • Phase diagram of methane under pressure
  • Melting of ice under pressure
  • Nucleation of Si and Ge from the melt

Melting of Methane
Classical simulations of methane melting line using different techniques (circles, squares and triangles), including direct simulations of phase coexistence and integration of Clapeyron equation. Theoretical results are compared to those of several experiments (crosses).

We carried out classical simulations of liquid and solid phases of condensed methane at pressures below 25 GPa, between 150 and 300 K, where no appreciable molecular dissociation occurs [1]. We used molecular dynamics (MD) and metadynamics techniques.Our results for the melting line are in satisfactory agreement with existing measurements. We find that the fcc crystal transforms into a hcp structure with 4 molecules per unit cell (B phase) at about 10 GPa and 150 K, and that the B phase transforms into a monoclinic high pressure phase above 20 GPa. Our results for solid/solid phase transitions are consistent with those of Raman studies but the phase boundaries estimated in our calculations are at higher pressure than those inferred from spectroscopic data [1].


Melting of IceMelting of Ice

The melting curve of ice at high pressure (black circles) as predicted by our two-phase simulations (left panel). Representative snapshots of 2-phase simulations are given on the upper panel. Dashed diamonds correspond to the onset of significant proton diffusion in our single-phase simulations. The blue dashed curve is the melting curve determined from laser-heated diamond anvil cell experiments. The filled black square indicates the onset of dynamical translation proton disorder in ab-initio simulations of ice-VII and the black dashed curve indicates the same transition as identified in Raman experiments.

We investigated the melting of ice under pressure with a series of first-principles molecular dynamics simulations [2]. In particular, a two-phase approach was used to determine the melting temperature of the ice-VII phase in the range of 10–50 GPa. Our computed melting temperatures are consistent with existing diamond anvil cell experiments. We find that for pressures between 10 and 40 GPa, ice melts as a molecular solid. For pressures above ≈45 Gpa, there is a sharp increase in the slope of the melting curve because of the presence of molecular dissociation and proton diffusion in the solid before melting. The onset of significant proton diffusion in ice-VII as a function of increasing temperature is found to be gradual and bears many similarities to that of a type-II superionic solid [2].


Surface plays an intricate role in solid liquid phase transition, and only a few systems have been reported to exhibit signatures of surface-induced crystallization. By employing atomistic simulations, we have discovered that in tetrahedral liquids exhibiting a negative slope of their melting lines (dT/dP<0), e.g., Si and Ge, the presence of free surfaces may enhance the nucleation rates by several orders of magnitude with respect to those in the bulk [3,4].

Nucleation of a Si Cluster
Nucleation of a cluster of Si (red) from the melt.

References

  1. "Theoretical investigation of methane under pressure", L. Spanu, D. Donadio, D. Hohl and and G. Galli, J.Chem.Phys.130, 164520 (2009).
  2. “Melting of ice under pressure”, E. Schwegler, M. Sharma, F. Gygi and G. Galli, Proceedings of the National Academy of Sciences 105, 14779 (2008)
  3. "Surface Induced Crystallization in Supercooled Tetrahedral Liquids", T. Li, D. Donadio, L.Ghiringhelli and G.Galli Nat. Mat. 8, 726 (2009).
  4. "Nucleation of tetrahedral solids: A molecular dynamics study of supercooled liquid silicon", T. Li, D.Donadio and G.Galli, J. Chem. Phys. (in press)