Test of a simple and flexible molecule model for α-, β-, and γ-S8 crystals

Abstract

Libertador 8250, (1429) Buenos Aires, Argentina. e-mails: clopasto@cnea.gov.ar and gamba@cnea.gov.ar S 8 is the most stable compound of elemental sulfur in solid and liquid phases, at ambient pressure and below 400K. Three crystalline phases of S 8 have been clearly identified in this range of thermodynamic parameters, although no calculation of its phase diagram has been performed yet. α-and γ-S 8 are orientationally ordered crystals while β-S 8 is measured as orientationally disordered. In this paper we analyze the phase diagram of S 8 crystals, as given by a simple and flexible molecule model, via a series of molecular dynamics (MD) simulations. The calculations are performed in the constant pressure-constant temperature ensemble, using an algorithm that is able to reproduce structural phase transitions. Introduction:Elemental sulfur shows a rich variety of molecular forms and therefore of chemical and physical properties in the crystalline and liquid phases 1,2 . Recently, a high pressure superconductor transition has been found, with T c =17K (at 162GPa), the highest known for any elemental solid 3 . Natural sulfur is of relevance in geophysics, astrophysics, material sciences and also of massive industrial use 1 . Nevertheless, the complex phase diagram and properties of its condensed phases are far from well known 1,2 .The most stable sulfur allotrope at ambient temperature and pressure (STP) is S 8 , a crown-shaped cyclic S 8 molecule, stable in solid, liquid and gas phases. 1Orthorhombic α-S 8 is the crystalline form stable at STP. Figs 1a shows its "crankshaft" structure with four molecules in the primitive unit cell. The space group is D 24 2h (Fddd), with 16 molecules in this non-primitive orthorhombic cell. If α-S 8 is slowly heated, it shows a phase transition to monoclinic β-S 8 at 369K (Fig. 1b), which melts at 393K 1 . Nevertheless, most α-S 8 crystals do no easily convert to β-S 8 , they melt, instead, at 385.8K 1,2 . β-S 8 is a monoclinic crystal, with six molecules in the primitive unit cell, two of them orientationally disordered 4,5 . A third crystalline allotrope has been observed: γ-S 8 (Fig. 1c), that can be obtained from solutions of S 8 or from its melt 1,2 . The space group is C 4 2h (P2/c), with four molecules in the pseudo-hexagonal closed-packed unit cell 6 . The density of this allotrope, at STP, is 5.8 % higher than that of α-S 8 .In spite of its relevance, calculations on the crystalline phase diagram of elemental sulfur molecules are scarce. Previous molecular dynamics (MD) simulations of crystalline S 8 were limited to constant-volume simulations at normal pressure and temperatures of α-S 8 7 , with the only aim to study the intramolecular frequencies obtained by Raman and ir. measurements. The same scope was followed by numerous works that measured crystalline frequencies and performed calculations based on lattice dynamics sums in different aproximations 8 .No attempt to reproduce the phase diagram of this molecule, including determination of crystalline structures, lat...

Toward an anisotropic atom–atom model for the crystalline phases of the molecular S8 compound

“…Our calculations showed that the simple and flexible molecule model succesfully reproduced most experimental data available on the three crystals [10,11], including structural and dynamical data of α-and γ-S 8 at STP, the high temperature orientationally disordered phase of β-S 8 at 375K and its low temperature ordered phase. Nevertheless, below 200 K this simple isotropic LJ model did not reproduce the 100 K structure of α-S 8 , as determined by a neutron and X-ray measurements [13].…”

“…Using the anisotropic LJ model ANI-S 4 , with distances d ani =0.1 and 0.6Å, the orthorhombic α-S 8 sample does not spontaneously show the structural phase transition to the monoclinic α'-S 8 , as was calculated with the isotropic LJ model when the temperature of the orthorhombic sample was decreased below 200 K [10,11]. Nevertheless, if a new series of simulations are performed on a sample that initially has the structure of the monoclinic α'-S 8 , this phase is calculated stable, in the time scale of our simulations (about 200 ps.…”

“…Nevertheless, below 200 K this simple isotropic LJ model did not reproduce the 100 K structure of α-S 8 , as determined by a neutron and X-ray measurements [13]. Although no structural phase transition was measured for α-S 8 crystals [13], when decreasing the temperature of the sample below 200 K, our orthorhombic sample turned out to be unstable using this isotropic atom-atom potential, and transformed to a monoclinic structure that we labeled α'-S 8 [10,11] (Fig. 1).…”

“…These LJ parameters (ε iso = 1.70 kJ/mol and σ iso =3.39Å) were afterwards used throughout the calculations of all samples of α−, β− and γ − S 8 crystals at different temperatures and zero kbar pressure [10,11]. The intramolecular potential included a harmonic well term for the SSS angle and a torsional potential of the double well type for the sulfur chain, different from hydrocarbon chains that show a triple well torsional potential.…”

Density functional and Monte Carlo studies of sulfur. II. Equilibrium polymerization of the liquid phase

“…37 The DF data set and the accumulated experience of fitting molecular potential functional forms would allow an improved description of sulfur structure and dynamical properties. However, we need to perform millions of Monte Carlo ͑MC͒ moves per atom on systems with more than ϳ1000 atoms, so that our model describes satisfactorily TABLE I. Parameters of the potential energy model.…”