Novel stable crystalline phase for the Stillinger-Weber potential

Abstract

Tetrahedral liquids such as silicon, germanium, carbon, water, and silica are an important class of materials not only for industrial applications but also for our understanding of nature. The Stillinger-Weber potential is one of the most popular models for computer simulations of these systems with tetrahedral coordination, with the directionality of the interactions introduced via a three-body repulsive term which promotes locally tetrahedral arrangements. This approach has been extended to various tetrahedral liquids, providing valuable insight into the physics of group XIV elements and more recently water. Perhaps surprisingly, a consistent thermodynamic picture of this class of models is still lacking despite their widespread usage. Here we fill this gap by computing equilibrium phase diagrams for the silicon and water parametrizations and report a novel crystal structure which dominates the models' phase diagram at intermediate and high pressure, and thus warrants further theoretical and numerical investigation. Our results redefine the phase behavior of an important class of tetrahedrally coordinated systems, and also suggest that a more stringent test for simulation models is the ability to select the experimentally relevant crystalline phases, as opposed to just reproducing their mechanical stability.

Formation of inclusion type silicon phases induced by inert gases

“…This coincides with the hydration number 20 for methane within the dodecahedral water cage 5 12 , which is composed of 12 five-membered rings of water. Since the 5 12 cage is one of the major building blocks of clathrate frameworks, the formation of methane hydrate can be promoted if there exist enough building blocks in liquid. This may be facilitated through increasing pressure or lowering temperature which allows water to dissolve more methane molecules.…”

“…Given the intrinsic similarity among tetrahedral materials, the SW model has also been successfully extended to the water/ice system through representing water molecules as monoatomic particles with a tetrahedral strength intermediate between those of silicon and carbon 39 . Very recently, the phase diagram of silicon has been calculated over a wide temperature and pressure range 12 . Silicon-gas interaction, which is mediated through van der Waals (vdW) force, is modeled by a simple Morse…”

“…Structural analysis based on the local order parameter q 6 26 indeed shows that the silicon framework corresponds to DH silicon, albeit exhibiting lattice distortions. At first glance, this is rather surprising given that the thermodynamic condition at which the spontaneous crystallization occurs falls well within the phase region of liquid Si for the SW potential 12 . In fact, the nucleation of DC silicon at the same temperature, but a much lower pressure (zero) was found to be already slow enough that it requires advanced sampling methods like FFS 27 to obtain the crystallization trajectory in simulation.…”

“…A natural way of obtaining intrinsic clathrate would be the direct synthesis of empty clathrate without inclusion of guest. This certainly represents a major experimental challenge because empty clathrate was predicted to be thermodynamically stable only under negative pressure [10][11][12] . Another possibility is to use electrically inert guests that fit geometrically within cavities and weakly interact with the host atoms, for example, noble gas elements.…”

Time-optimal control of independent spin-1/2 systems under simultaneous control

“…The problem is to steer the identity 1 4 ∈ SU(4) to any desired matrix U f,1 ⊗ U f,2 ∈ SU(2)⊗SU(2) under a constraint of the form | u| ≤ D, D = 0. We assume γ 1 = γ 2 (heteronuclear spins) [18] which implies controllability [19] in SU(2) ⊗ SU (2), that is, every operator in SU(2) ⊗ SU(2) can be reached with an appropriate (arbitrarily bounded) control. Let B be the subspace in su(2) ⊕ su(2) defined as B := span{iσ x ⊗ 1 2 +γ1 2 ⊗iσ x , −iσ y ⊗1 2 −γ1 2 ⊗iσ y , iσ z ⊗1 2 +γ1 2 ⊗iσ z } with γ := γ 2 /γ 1 .…”