Polytypism in the ground state structure of the Lennard-Jonesium

From Hard to Soft Dense Sphere Packings: The Cohesive Energy of Barlow Structures Using Exact Lattice Summations for a General Lennard-Jones Potential

There are infinitely many distinguishable dense sphere packings in dimension three (Barlow structures) with maximum packing density of ρ = π/√18. While Hales [Hales, T. C. Ann. Math. 2005, 162, 1065-1185.] proved that the packing density of the most dense cubic packing cannot be surpassed, it is currently not known how the infinite possibilities of densely packed Barlow structures with different sequences of hexagonal close packed layers are energetically related compared to the well-known face centered cubic (fcc) and hexagonal close packed (hcp) structures. We demonstrate that, for a general Lennard-Jones potential, which includes the hard-sphere model as a limiting case, Barlow packings lie energetically between fcc and hcp. Exceptions to this energy sequence only occur when fcc and hcp are energetically quasi-degenerate.

100 Years of the Lennard-Jones Potential

It is now 100 years since Lennard-Jones published his first paper introducing the now famous potential that bears his name. It is therefore timely to reflect on the many achievements, as well as the limitations, of this potential in the theory of atomic and molecular interactions, where applications range from descriptions of intermolecular forces to molecules, clusters, and condensed matter.

Surface phase diagrams from nested sampling

Studies in atomic-scale modeling of surface phase equilibria often focus on temperatures near zero Kelvin due to the challenges in calculating the free energy of surfaces at finite temperatures. The Bayesian-inference-based nested sampling (NS) algorithm allows for modeling phase equilibria at arbitrary temperatures by directly and efficiently calculating the partition function, whose relationship with free energy is well known. This work extends NS to calculate adsorbate phase diagrams, incorporating all relevant configurational contributions to the free energy. We apply NS to the adsorption of Lennard-Jones (LJ) gas particles on low-index and vicinal LJ solid surfaces and construct the canonical partition function from these recorded energies to calculate ensemble averages of thermodynamic properties, such as the constant-volume heat capacity and order parameters that characterize the structure of adsorbate phases. Key results include determining the nature of phase transitions of adsorbed LJ particles on flat and stepped LJ surfaces, which typically feature an enthalpy-driven condensation at higher temperatures and an entropy-driven reordering process at lower temperatures, and the effect of surface geometry on the presence of triple points in the phase diagrams. Overall, we demonstrate the ability and potential of NS for surface modeling.

Sensitivity of solid phase stability to the interparticle potential range: studies of a new Lennard-Jones like model

In a recent article, Wang et al. (Phys. Chem. Chem. Phys., 2020, 22, 10624) introduced a new class of interparticle potential for molecular simulations. The potential is defined by a single range parameter, eliminating the need to decide how to truncate truly long-range interactions like the Lennard-Jones (LJ) potential. The authors explored the phase diagram for a particular value of the range parameter for which their potential is similar in shape to the LJ 12-6 potential. We have reevaluated the solid phase behaviour of this model using both Lattice Switch Monte Carlo and thermodynamic integration. In addition to finding that the boundary between hexagonal close packed (hcp) and face centred cubic (fcc) phases presented by Wang et al. was calculated incorrectly, we show that owing to its finite range, the new potential exhibits several reentrant transitions between hcp and fcc phases. These phases, which do not occur in the full (untruncated) LJ system, are also found for typically adopted forms of the truncated and shifted LJ potential. However, whilst in the latter case one can systematically investigate and correct for the effects of the finite range on the calculated phase behaviour (a correction beyond the standard long-range mean field tail correction being required), this is not possible for the new potential because the choice of range parameter affects the entire potential shape. Our results highlight that potentials with finite range may fail to represent the crystalline phase behavior of systems with long-range dispersion interactions, even qualitatively.

Crystallization of FAPbI3: Polytypes and stacking faults

Molecular dynamics simulations are performed to study the crystallization of formamidinium lead iodide. From all-atom simulations of the crystal growth process and the δ-α-phase transitions, we try to reveal the formation of various stack-faulted intermediate defected structures and report various polytypes of formamidinium lead iodide that are observed from simulations.

Continuous transition of colloidal crystals through stable random orders

Randomly stacked 2D hexagonal close-packed (RHCP) layer structures are frequently observed in colloids and other material systems but are considered metastable. We report a stable RHCP phase domain of poly(butadiene-b-ethylene oxide) (PB-PEO) diblock copolymer micellar colloids in water. The stable RHCP colloidal crystals emerge in the middle of a continuously transiting phase domain of close-packed PB-PEO colloids from a face-centered cubic (FCC) polytype to a HCP polytype. We attribute the stability of RHCP structures to two competing contributions, entropic preference for FCC lattices and long PEO corona chains stabilizing HCP lattices. When these two contributions become comparable in the phase space, thermal fluctuation randomizes the stacking order of the 2D-HCP layers, and RHCP orders are stabilized. The continuously transiting close-packed structures of PB-PEO colloids with stable RHCP states suggest that similar structural transitions and equivalent RHCP states may occur in other polytypic crystal systems because polytypic crystals have the common crystal construction rule, i.e., stacking 2D-HCP lattice layer groups in different orders.

Insight into Liquid Polymorphism from the Complex Phase Behavior of a Simple Model

We systematically explored the phase behavior of the hard-core two-scale ramp model suggested by Jagla [Phys. Rev. E 63, 061501 (2001)PRESCM1539-375510.1103/PhysRevE.63.061501] using a combination of the nested sampling and free energy methods. The sampling revealed that the phase diagram of the Jagla potential is significantly richer than previously anticipated, and we identified a family of new crystalline structures, which is stable over vast regions in the phase diagram. We showed that the new melting line is located at considerably higher temperature than the boundary between the low- and high-density liquid phases, which was previously suggested to lie in a thermodynamically stable region. The newly identified crystalline phases show unexpectedly complex structural features, some of which are shared with the high-pressure ice VI phase.

Random Structure Searching with Orbital-Free Density Functional Theory

The properties of a material depend on how its atoms are arranged, and predicting these arrangements from first principles is a longstanding challenge. Orbital-free density functional theory provides a quantum-mechanical model based solely on the electron density, not individual wave functions. The resulting speedups make it attractive for random structure searching, whereby random configurations of atoms are relaxed to local minima in the energy landscape. We use this strategy to map the low-energy crystal structures of Li, Na, Mg, and Al at zero pressure. For Li and Na, our searching finds numerous close-packed polytypes of almost-equal energy, consistent with previous efforts to understand their low-temperature forms. For Mg and Al, the searching identifies the expected ground state structures unambiguously, in addition to revealing other low-energy structures. This new role for orbital-free density functional theory-particularly as continued advances make it accurate for more of the periodic table-will expedite crystal structure prediction over wide ranges of compositions and pressures.

Phase behavior of the quantum Lennard-Jones solid

The Lennard-Jones (LJ) potential is perhaps one of the most widely used models for the interaction of uncharged particles, such as noble gas solids. The phase diagram of the classical LJ solid is known to exhibit transitions between hcp and fcc phases. However, the phase behavior of the quantum LJ solid remains unknown. Thermodynamic integration based on path integral molecular dynamics (PIMD) and lattice dynamics calculations are used to study the phase stability of the hcp and fcc LJ solids. The hcp phase is shown to be stabilized by quantum effects in PIMD, while fcc is shown to be favored by lattice dynamics, which suggests a possible re-entrant low pressure fcc phase for highly quantum systems. Implications for the phase stability of noble gas solids are discussed. For parameters equating to helium, the expansion due to zero-point vibrations is associated with quantum melting: neither crystal structure is stable at zero pressure.

Pressure-Temperature Phase Diagram of Lithium, Predicted by Embedded Atom Model Potentials

In order to study the performance of interatomic potentials and their reliability at higher pressures, the phase diagrams of two different embedded-atom-type potential models (EAMs) and a modified embedded-atom model (MEAM) of lithium are compared. The calculations were performed by using the nested sampling technique in the pressure range 0.01-20 GPa, in order to determine the liquid-vapor critical point, the melting curve, and the different stable solid phases of the compared models. The low-pressure stable structure below the melting line is found to be the body-centered-cubic (bcc) structure in all cases, but the higher pressure phases and the ground-state structures show a great variation, being face-centered cubic (fcc), hexagonal close-packed (hcp), a range of different close-packed stacking variants, and highly symmetric open structures are observed as well. A notable behavior of the EAM of Nichol and Ackland (Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 93, 184101) is observed, that the model displays a maximum temperature in the melting line, similarly to experimental results.

Stacking Characteristics of Close Packed Materials

It is shown that the enthalpy of any close packed structure for a given element can be characterized as a linear expansion in a set of continuous variables α_{n}, which describe the stacking configuration. This enables us to represent the infinite, discrete set of stacking sequences within a finite, continuous space of the expansion parameters H_{n}. These H_{n} determine the stable structure and vary continuously in the thermodynamic space of pressure, temperature, or composition. The continuity of both spaces means that only transformations between stable structures adjacent in the H_{n} space are possible, giving the model predictive as well as descriptive ability. We calculate the H_{n} using density functional theory (DFT)and interatomic potentials for a range of materials. Some striking results are found: e.g., the Lennard-Jones potential model has 11 possible stable structures and over 50 phase transitions as a function of cutoff range. The very different phase diagrams of Sc, Tl, Y, and the lanthanides are understood within a single theory. We find that the widely reported 9R-fcc transition is not allowed in equilibrium thermodynamics, and in cases where it has been reported in experiments (Li, Na), we show that DFT theory is also unable to predict it.