(PbS)32: A baby crystal

Abstract

Theoretical calculations based on density functional theory have found (PbS)(32) to be the smallest cubic cluster for which its inner (PbS)(4) core enjoys bulk-like coordination. Cubic (PbS)(32) is thus a "baby crystal," i.e., the smallest cluster, exhibiting sixfold coordination, that can be replicated to obtain the bulk crystal. The calculated dimensions of the (PbS)(32) cluster further provide a rubric for understanding the pattern of aggregation when (PbS)(32) clusters are deposited on a suitable surface, i.e., the formation of square and rectangular, crystalline nano-blocks with predictable dimensions. Experiments in which mass-selected (PbS)(32) clusters were soft-landed onto a highly ordered pyrolytic graphite surface and the resulting aggregates imaged by scanning tunneling microscopy provide evidence in direct support of the computational results.

Size Selected Clusters on Surfaces

“…However, in experiments performed using size selected silver clusters, it was observed that silver clusters containing 50 to 250 atoms deposited onto HOPG diffuse and coalesce into larger nanoparticles with a diameter of about 14 nm, irrespective of the incident gas phase cluster size [13]. In contrast, our knowledge of the size-dependent surface behavior of metal compound clusters (e.g, metal oxides [20][21][22], sulfides [23], nitrides), is extremely limited despite their importance in catalysis and material science [24].…”

“…Here, we are interested in identifying the smallest, viable crystalline unit of the lead sulfide rock salt crystal, i.e., its "baby crystal." [23] To set the stage for the STM studies of "baby crystals," our previous work combined both experiments and theory to explore the geometric structures and electron affinities of small, gas-phase, lead sulfide clusters, (PbS) n , ranging in size from n = 2-15. [25] First, photoelectron spectroscopy was conducted on size-selected cluster anions to acquire both ground and excited state electronic structure information as well as the electron affinity values of the cluster anions' neutral counterparts.…”

Structural and electronic properties of lead sulfide quantum dots from screened hybrid density functional calculations including spin–orbit coupling effects

“…The relative stabilities and gaps of (PbS) 32 structures deserve a separated comment as Kiran et al have studied theoretically and by STM and XPS techniques (PbS) 32 clusters deposited in highly ordered porous graphite (HOPG) [11]. Many of the structures found by these authors in their STM images exhibit square or rectangular-like shapes.…”

“…For these reasons, the structures and electronic properties of PbS nanoparticles have been examined, both theoretically and experimentally. However, even the most recent density functional theory calculations have been limited by the use of either generalized gradient approximation (GGA) based functionals [11], that are known to underestimate the band gaps due to the selfinteraction error, or by the use of the hybrid B3LYP exchange-correlation functional [12,13], known to largely overestimate the band gaps and to fail in the description of metallic systems [14,15]. Moreover, the accurate description of the electronic structure of these systems requires taking into account the semicore Pb d states and the incorporation of the relativistic effects (spin-orbit coupling, SOC) for the valence Pb electrons [16].…”

Thermodynamic Parameters of Lead Sulfide Chrystals in the Cubic Phase

“…As for crystal structure, the minor deviation from the perpendicular relative position of sides was observed also in structure modelling lead selenide by authors [23], who used calculation program GAUSSIAN 03 and SBKJC base set. These results do not contradict to experimental data given in [2], and to data of structural cards given in [24], where among compounds of lead chalcogenides are on the side of PbS cubic structure near the boundary between the cubic and orthorhombic modifications.…”