NaCl crystal nucleation from metastable solutions has long been considered to occur according to a single-step mechanism. Recent experimental observations suggest that NaCl crystals emerge from disordered intermediates which is seemingly at odds with this established view. Here, we performed biased and unbiased molecular dynamics simulations to analyse and characterise the pathways to crystalline phases from solutions far into the metastable region. We find that large liquid-like NaCl clusters emerge as the solution concentration is increased and two-step nucleation pathways are more dominant than one-step pathways to phase separation. Analyses of cluster size populations and the ion pair association constant show that these clusters are transient, unlike the thermodynamically stable prenulceation cluster solute species that were suggested in other mineralising systems. A Markov State Model was developed to analyse the mechanisms and timescales for nucleation from unbiased molecular dynamics trajectories in a reaction coordinate space characterising the dense regions in clusters and crystalline order. This allowed calculation of the committor probabilities for the system to relax to the solution or crystal states, and to estimate the rate of nucleation, which shows excellent agreement with literature values. From a fundamental nucleation perspective, our work highlights the need to extend the attribute 'critical' to an ensemble of clusters which can display a broad range of structures and include sizeable disordered domains depending upon the reaction conditions.Moreover, our recent simulation studies demonstrated that carbon surfaces catalyse the formation of liquid-like NaCl networks which, combined with the observations here, suggests that alternative pathways beyond the single-step mechanism can be exploited to control the crystallisation of NaCl.
Nucleation, the birth of a stable cluster from disorder, is inherently stochastic. Yet up to date, there are no quantitative studies on NaCl nucleation that accounts for its stochastic nature. Here, we report the first stochastic treatment of NaCl-water nucleation kinetics. Using a recently developed microfluidic system and evaporation model, our measured interfacial energies extracted from a modified Poisson distribution of nucleation time show an excellent agreement with theoretical predictions. Furthermore, analysis of nucleation parameters in 0.5 pL, 1.5pL and 5.5 pL microdroplets reveals …
Here we propose an NPT metadynamics simulation scheme for pressure-induced structural phase transitions, using coordination number and volume as collective variables, and apply it to the reconstructive structural transformation $B1$-$B2$ in NaCl. By studying systems with size up to 64 000 atoms we reach a regime beyond collective mechanism and observe transformations proceeding via nucleation and growth. We also reveal the crossover of the transition mechanism from Buerger-like for smaller systems to Watanabe-Tolédano for larger ones. The scheme is likely to be applicable to a broader class of…
In this Letter we report a simulation study in which we compare the solid-liquid interfacial free energy of NaCl at coexistence, with the value that follows from the height of the homogeneous nucleation barrier. We find that the two estimates differ by more than 100%. Similar, although smaller discrepancies are found for crystals of hard-sphere colloids and of Lennard-Jones ("argon") particles. We consider a variety of possible causes for this discrepancy and are forced to conclude that it is due to a finite-size effect that cannot be corrected for by any simple thermodynamic procedure. Import…
Colloidal systems offer the ideal conditions to study the nucleation process, both from an experimental viewpoint, due to their relative large size and long time-scales, and from a modeling point of view, due to the tunability of their interactions. Here we review some recent works that study the process of colloidal crystallization from a microscopic perspective. We focus in particular on non-classical pathways to nucleation where the appearance of the solid crystals involves fluctuations of two (or more) order parameters. We interpret the non-classical behavior as a decoupling of positional …
Nucleation is generally viewed as a structural fluctuation that passes a critical size to eventually become a stable emerging new phase. However, this concept leaves out many details, such as changes in cluster composition and competing pathways to the new phase. In this work, both experimental and computer modeling studies are used to understand the cluster composition and pathways. Monte Carlo and molecular dynamics approaches are used to analyze the thermodynamic and kinetic contributions to the nucleation landscape in barium silicate glasses. Experimental techniques examine the resulting p…
Electric field induced nucleation is introduced as a possible mechanism to realize a metallic phase of hydrogen. Analytical expressions are derived for the nucleation probabilities of both thermal and quantum nucleation in terms of material parameters, temperature, and the applied field. Our results show that the insulator-metal transition can be driven by an electric field within a reasonable temperature range and at much lower pressures than the current paradigm of P > 400 GPa. Both static and oscillating fields are considered and practical implementations are discussed.
When a system undergoes a transition from a liquid to a solid phase, it passes through multiple intermediate structures before reaching the final state. However, our knowledge on the exact pathways of this process is limited, mainly due to the difficulty of realizing direct observations. Here, we experimentally study the evolution of symmetry and density for various colloidal systems during liquid-to-solid phase transitions, and visualize kinetic pathways with single-particle resolution. We observe the formation of relatively-ordered precursor structures with different symmetries, which then c…
The fundamental understanding of crystallization, in terms of microscopic kinetic and thermodynamic details, remains a key challenge in the physical sciences. Here, by using in situ graphene liquid cell transmission electron microscopy, we reveal the atomistic mechanism of NaCl crystallization from solutions confined within graphene cells. We find that rock salt NaCl forms with a peculiar hexagonal morphology. We also see the emergence of a transitory graphite-like phase, which may act as an intermediate in a two-step pathway. With the aid of density functional theory calculations, we propose …
The kinetics of nucleation of a core-shell composite nucleus that consists of a core of stable final phase surrounded by a wetting layer of intermediate metastable phase is studied using the kinetic theory of binary nucleation not only in the size and composition space but also in the component space. The steady-state solution of the Fokker-Planck equation is considered. Various formulas for the critical nucleus at the saddle point as well as for the post-critical nucleus are derived. The kinetics of nucleation at the saddle point is more appropriately characterized in the size and composition…
Motivated by unexpected morphologies of the emerging liquid phase (channels, bulges, droplets) at the edge of thin, melting alkane terraces, we propose a new heterogeneous nucleation pathway. The competition between bulk and interfacial energies and the boundary conditions determine the growth and shape of the liquid phase at the edge of the solid alkane terraces. Calculations and experiments reveal a "pre-critical" shape transition (channel-to-bulges) of the liquid before reaching its critical volume along a putative shape-conserving path. Bulk liquid emerges from the new shape, and depending…
Crystallization often proceeds through successive stages that lead to a gradual increase in organization. Using molecular simulation, we determine the nucleation pathway for solid solutions of copper and gold. We identify a new nucleation mechanism (liquid$\to$$L1_2$~precursor$\to$solid solution), involving a chemically ordered intermediate that is more organized than the end product. This nucleation pathway arises from the low formation energy of $L1_2$ clusters which, in turn, promote crystal nucleation. We also show that this mechanism is composition-dependent since the high formation energ…
Crystallization represents a fundamental process engendering solidification of a material and determines its microstructure. Driven by complex phenomena at the atomic scale, its understanding for alloys still remains elusive. The present work proposes a large scale molecular dynamics simulation study of the homogeneous crystal nucleation pathways of prototypical undercooled Al-Ni binary alloys. An unsupervised topological learning analysis shows that the nucleation sets in first from a chemical ordering, followed by a bond-orientational ordering of the underlying crystal phase. Our results ind…
DNA-coated colloids can self-assemble into an incredible diversity of crystal structures, but applications of this technology are limited by poor understanding and control over the dynamical crystallization pathways. To address this challenge, we use microfluidics to quantify the self-assembly dynamics of DNA-programmed colloidal crystals, from thermally-activated nucleation through reaction-limited and diffusion-limited phases of crystal growth. Our detailed measurements of the temperature and concentration dependence of the kinetics at all stages along the crystallization pathway provide a s…
The transformation of monolayer islands into bilayer islands as a first step of the overall two-dimensional to three-dimensional (2D-3D) transformation in the coherent Stranski-Krastanov mode of growth is studied for the cases of expanded and compressed overlayers. Compressed overlayers display a nucleation-like behavior: the energy accompanying the transformation process displays a maximum at some critical number of atoms, which is small for large enough values of the misfit, and then decreases gradually down to the completion of the transformation, non-monotonically due to the atomistics of …
Observing non-classical nucleation pathways remains challenging in simulations of complex materials with technological interests. This is because it requires very accurate force fields that can capture the whole complexity of their underlying interatomic interactions and an advanced structural analysis. Here, we first report the construction of a machine-learning force field for zinc oxide interactions using the Physical LassoLars Interaction Potentials approach which allows us to be predictive even for untrained structures. Then, we carried out freezing simulations from a liquid and observed …
Calcium sulfate minerals are found under the form of three crystalline phases: gypsum (CaSO4.2H2O), bassanite (CaSO4.0.5H2O), and anhydrite (CaSO4). Due to its relevance in natural and industrial processes, the formation pathways of these calcium sulphate phases from aqueous solution have been the subject of intensive research. There is a growing body of literature, that calcium sulfate forms essentially through a non-classical nanoparticle- or cluster-mediated crystallisation process. At the early stages of precipitation calcium sulfate crystals grow through the reorganization and coalescence…
The direct graphite-to-diamond transformation mechanism has been a subject of intense study and remains debated concerning the initial stages of the conversion, the intermediate phases, and their transformation pathways. Here, we successfully recover samples at early conversion stage by tuning high-pressure/high-temperature conditions and reveal direct evidence supporting the nucleation-growth mechanism. Atomistic observations show that intermediate orthorhombic graphite phase mediates the growth of diamond nuclei. Furthermore, we observe that quenchable orthorhombic and rhombohedra graphite a…
CaSO4 minerals (i.e. gypsum, anhydrite and bassanite) are widespread in natural and industrial environments. During the last several years, a number of studies have revealed that nucleation in the CaSO4-H2O system is non-classical, where the formation of crystalline phases involves several steps. Based on these recent insights we have formulated a tentative general model for calcium sulfate precipitation from solution. This model involves primary species that are formed through the assembly of multiple Ca2+ and SO42- ions into nanoclusters. These nanoclusters assemble into poorly ordered (i.e.…
The field of complex self-assembly is moving toward the design of multi-particle structures consisting of thousands of distinct building blocks. To exploit the potential benefits of structures with such `addressable complexity,' we need to understand the factors that optimize the yield and the kinetics of self-assembly. Here we use a simple theoretical method to explain the key features responsible for the unexpected success of DNA-brick experiments, which are currently the only demonstration of reliable self-assembly with such a large number of components. Simulations confirm that our theory …
The kinetic pathways resulting from the formation of coherent L12-ordered y'-precipitates in the g-matrix (f.c.c.) of Ni-7.5 Al-8.5 Cr at.% and Ni-5.2 Al-14.2 Cr at.% alloys, aged at 873 K, are investigated by atom-probe tomography (APT) over a range of aging times from 1/6 to 1024 hours; these alloys have approximately the same volume fraction of the y'-precipitate phase. Quantification of the phase decomposition within the framework of classical nucleation theory reveals that the y-matrix solid-solution solute supersaturations of both alloys provide the chemical driving force, which acts as …
We introduce a simple nearest-neighbor spin model with multiple metastable phases, the number and decay pathways of which are explicitly controlled by the parameters of the system. With this model we can construct, for example, a system which evolves through an arbitrarily long succession of metastable phases. We also construct systems in which different phases may nucleate competitively from a single initial phase. For such a system, we present a general method to extract from numerical simulations the individual nucleation rates of the nucleating phases. The results show that the Ostwald rul…
Crystallization of supersaturated liquids usually starts by heterogeneous nucleation. Mounting evidence shows that even homogeneous nucleation in simple liquids takes place in two steps; first a dense amorphous precursor forms, and the crystalline phase appears via heterogeneous nucleation in/on the precursor cluster. Herein, we review recent results by a simple dynamical density functional theory, the phase-field crystal model, for (precursor-mediated) homogeneous and heterogeneous nucleation of nanocrystals. It will be shown that the mismatch between the lattice constants of the nucleating c…
Viscoelastic phase separation of colloidal suspensions can be interrupted to form gels either by glass transition or by crystallization. With a new confocal microscopy protocol, we follow the entire kinetics of phase separation, from homogeneous phase to different arrested states. For the first time in experiments, our results unveil a novel crystallization pathway to sponge-like porous crystal structures. In the early stages, we show that nucleation requires a structural reorganization of the liquid phase, called stress-driven ageing. Once nucleation starts, we observe that crystallization fo…
Due to structural incommensurability, the emergence of a quasicrystal from a crystalline phase represents a challenge to computational physics. Here the nucleation of quasicrystals is investigated by using an efficient computational method applied to a Landau free-energy functional. Specifically, transition pathways connecting different local minima of the Lifshitz-Petrich model are obtained by using the high-index saddle dynamics. Saddle points on these paths are identified as the critical nuclei of the 6-fold crystals and 12-fold quasicrystals. The results reveal that phase transitions betwe…
In a solid-state diffusional phase transformation involving nucleation and growth, the size of the critical nucleus for a homogeneous process (r*homo=r* ) has been assumed to be a time invariant constant of the transformation. The strain associated with the process has a positive energy contribution and leads to an increase in the value of r*, with respect to that for nucleation from a liquid. With the progress of such a transformation, the strain energy stored in the matrix increases and nuclei forming at a later stage encounter a strained matrix. Using devitrification of a bulk metallic glas…
In recent years, we have come to appreciate the astounding intricacy of the formation process of minerals from ions in aqueous solutions. In this context, a number of studies have revealed that nucleation in the calcium sulfate system is non-classical, involving the aggregation and reorganization of nanosized prenucleation particles. In a recent work we have shown that this particle-mediated nucleation pathway is actually imprinted in the resultant single micron-sized CaSO4 crystals. This property of CaSO4 minerals provides us with an unique opportunity to search for evidence of non-classical …
Understanding the gypsum (CaSO4.2H2O) formation pathway from aqueous solution has been the subject of intensive research in the past years. This interest stems from the fact that gypsum appears to fall into a broader category of crystalline materials whose formation does not follow classical nucleation and growth theories. The pathways involve transitory precursor cluster species, yet the actual structural properties of such clusters are not very well understood. Here, we show how in situ high-energy X-ray diffraction experiments and molecular dynamics (MD) simulations can be combined to deriv…
Understanding the mechanism of nucleation of the stable phase inside the metastable parent phase during a first order phase transition has been a subject of outstanding interest in natural science. The problem becomes even more challenging as the spinodal is approached. In this work, we have undertaken extensive computer simulation studies to probe the molecular mechanism for the onset of instability. We have constructed the free energy surfaces of nucleation as a function of multiple reaction coordinates, both for supercooled Lennard-Jones fluid and for 2- and 3-dimensional Ising models. Whil…
We study low-salt, binary aqueous suspensions of charged colloidal spheres of size ratio Phi = 0.57, number densities below the eutectic number density n_E, and number fractions of p = 1.00-0.40. The typical phase obtained by solidification from a homogeneous shear-melt is a substitutional alloy of body centred cubic structure. In strictly gas-tight vials, the polycrystalline solid is stable against melting and further phase transformation for extended times. For comparison, we prepare the same samples also by slow and mechanically undisturbed deionization in commercial slit cells. These cells…
The present paper investigates the influence of gluconate and hexitol additives on the precipitation mechanism and kinetics of C-S-H. To this end, wet chemistry C-S-H precipitation experiments were performed under controlled conditions of solution supersaturation, under varying silicate concentration, while the transmittance of the solution was followed. This allowed determining induction times for the formation of C-S-H precursors in the presence and absence of gluconate and three hexitol molecules. Characterization of the precipitates was performed via small angle X-ray scattering and cryo-t…
The formation of crystalline calcium sulfate (CaSO4*xH2O) polymorphs from aqueous solutions is assumed to occur via a single-step process following the classical nucleation paradigm. However, although recent research contradicts this classical picture and indicates that CaSO4*2H2O forms at room temperature through multiple steps at different length and time-scales, these steps have so far not been quantified. By using in situ and fast time-resolved small angle X-ray scattering (SAXS), we demonstrate that the nucleation and growth of CaSO4*2H2O involves at the very initial stages the formation …
