Calculation Of Nucleation Rate Research Articles

First insights into the new particle formation and growth at a north-eastern Romanian urban site, Iasi. Potential health risks from ultrafine particles

New particle formation (NPF) process brings significant contribution to the global atmospheric particle number concentrations. Evidence on the formation and growth of NPF is reported for the first time at a Romanian urban site, i.e., Iasi, north-eastern Romania. Size-dependent aerosol number concentrations were obtained during two short-term campaigns undertaken in 2017 by using a scanning mobility particle sizer. The existence of two categories of events can be highlighted by investigating the net maximum increase in the nucleation mode particle number concentration and the maximum size of the geometric median diameter of new particles. The variability of meteorological parameters showed that the solar radiation peak was usually associated with NPF events, while relative humidity was anti-correlated with those events. Calculated nucleation rate values for events in May, median of 4.5 cm−3 s−1, was lower than the corresponding median values of 8.6 cm−3 s−1 for December. The particle growth rates showed a similar trend with a median of 4.0 nm h−1 and 7.7 nm h−1, in May and December, respectively. The obtained results suggest that regional emission sources might bring some contributions on the particle nucleation and growth processes, particularly over the cold season. Regarding the deposition of particles in the respiratory system, it appears that ultrafine particles are among the most significant contributors to the alveolar deposits. Moreover, evidences were obtained that the impact on the particle deposition at the alveolar region is not mandatory in direct relation to the intensity of the NPF event, the pollution burden of the particles most probably playing an important role.

Effect of gradient temperature rolling process on precipitation behavior in Q690D steel

In this paper, the second phase precipitation model is incorporated into the finite element simulation system of hot rolling process through the secondary development subprogram VUSDFLD of ABAQUS, and the simulation analysis and calculation of nucleation rate, volume fraction and size of precipitates under different temperature fields and strain fields are realized. The size, morphology and distribution of the microalloyed carbonitride precipitates in Q690D steel under gradient temperature rolling (GTR) and uniform temperature rolling (UTR) were studied by laboratory rolling experiments. The results show that the nucleation sites of the microalloyed carbonitride precipitates in the matrix increase under GTR, which is conducive to the nucleation of new precipitates and promotes the re dissolution of large precipitates. Finally, after tempering, the precipitate particles are distributed randomly on the ferrite matrix, and the size is refined by 20 ∼ 35 nm, resulting in obvious precipitation strengthening and microstructure refining effects.

A New Technique for Calculating Kinetic and Thermodynamic Barriers for Nucleation Rates and Interfacial Energy of CaCO3 Prenucleation Nanoclusters at High Temperature Using TGA Models and In Situ Crystallization

AbstractNucleation at different temperature levels can provide quantitative insights into the energy barrier associated with sub‐molecular nuclei. The accurate calculation of nucleation rates, thermodynamics, and interfacial energy for extremely small nanoclusters (1−2 nm) remains a challenge at high temperatures. Here, , are computed to estimate the nucleation rate of ultra‐small CaCO3 pre‐nucleation clusters (0.85 nm) from thermogravimetric analysis (TGA) experimental values in the temperature range from 555 to 795 K, by adopting the most accurate iterative iso‐conversional method and random nucleation dependent differential function , respectively. On the basis of these analyses, four mathematical models are presented for computing nucleation rates and interfacial energy (mJ m−2 variation with temperature and conversion for CaCO3 prenucleation clusters. Furthermore, experimental validation is also carried out in order to assess the existence of nucleation in CaCO3 pre‐nucleation clusters at high temperatures (500 °C) using X‐ray diffraction and experimental z(α) master plots. The TGA can be used to predict and understand nucleation rates for various nano systems.

A comprehensive modeling approach for polymorph selection in Lennard-Jones crystallization.

Computational predictions of the polymorphic outcomes of a crystallization process, referred to as polymorph selection, can accelerate the process development for manufacturing solid products with targeted properties. Polymorph selection requires understanding the interplay between the thermodynamic and kinetic factors that drive nucleation. Moreover, post-nucleation events, such as crystal growth and polymorphic transformation, can affect the resulting crystal structures. Here, the nucleation kinetics of the Lennard-Jones (LJ) fluid from the melt is investigated with a focus on the competition between FCC and HCP crystal structures. Both molecular dynamics (MD) simulations and 2D free energy calculations reveal that polymorph selection occurs not during nucleation but when the cluster sizes exceed the critical cluster size. This result contrasts with the classical nucleation mechanism, where each polymorph is assumed to nucleate independently as an ideal bulk-like cluster, comprised only of its given structure. Using the 2D free energy surface and the MD simulation-derived diffusion coefficients, a structure-dependent nucleation rate is estimated, which agrees with the rate obtained from brute force MD simulations. Furthermore, a comprehensive population balance modeling (PBM) approach for polymorph selection is proposed. The PBM combines the calculated nucleation rate with post-nucleation kinetics while accounting for the structural changes of the clusters after nucleation. When applied to the LJ system, the PBM predicts with high accuracy the polymorphic distribution found in a population of crystals generated from MD simulations. Due to the non-classical nucleation mechanism of the LJ system, post-nucleation kinetic events are crucial in determining the structures of the grown crystals.

A novel approach for determination of nucleation rates and interfacial energy of metallic magnesium nanoclusters at high temperature using non-isothermal TGA models

The exploration of temperature-dependent nucleation is required to appraise the extent of kinetic and thermodynamic barriers associated with the origin of subatomic size nuclei, which controls the nucleation rate. The precise computation of nucleation rate, thermodynamic parameters, and interfacial surface energy for ultra-small nanoclusters (0.5–2 nm) is still absent in the high-temperature range. Here, apparent activation energy (Ea), thermodynamic parameters (ΔG, ΔH, and ΔS), and pre-exponential kinetic factor were estimated by utmost accurate Vyazovkin advanced, and KAS isoconversional techniques for calculation of nucleation rate and interfacial energy for ultra-small magnesium nanoclusters (∼0.8 ± 0.24 nm), in the temperature range from 555 to 780 K. The master plots propounded the existence of third order random nucleation in magnesium metal matrix over a specified conversion. Based on the above findings, four mathematical models are proposed to compute nucleation rate and interfacial energy in magnesium clusters over respective temperatures and conversions. These models are beneficial for predicting the nucleation rate and interfacial energy over a high range of temperature and specific conversion.

Assessment of the classical nucleation theory in supercooled nickel by molecular dynamics

In this work, we performed a thorough study of crystal nucleation rates in supercooled liquid (SCL) nickel by comparing molecular dynamics (MD) simulation results, theoretical calculations, and experimental data. Our aim was to assess the validity of the most used theoretical framework, the Classical Nucleation Theory (CNT), in describing homogeneous nucleation in a deeply supercooled liquid. To this end, we carried out MD simulations using an embedded atom interaction potential, which describes quite well the melting point, Tm, the enthalpy of fusion, Δh, and the liquid density, ρl, of our model material. We then determined the critical nucleus size and the diffusion coefficient in the temperature range from 0.68 to 0.80Tm. By combining the physical properties obtained from our MD simulations and the calculated crystal-liquid free energy difference, we compared the CNT predictions with the nucleation rates obtained directly via brute force MD simulations on a system with 4 million atoms. We found an excellent agreement between the theoretically calculated nucleation rates and the values obtained by MD simulations. Moreover, the CNT prediction for the nucleation rate agrees with experimental data at 1350 K. Our results confirm that the CNT is indeed a powerful tool to describe the nucleation kinetics in supercooled liquids.

Metastable–solid phase diagrams derived from polymorphic solidification kinetics

Nonequilibrium processes during solidification can lead to kinetic stabilization of metastable crystal phases. A general framework for predicting the solidification conditions that lead to metastable-phase growth is developed and applied to a model face-centered cubic (fcc) metal that undergoes phase transitions to the body-centered cubic (bcc) as well as the hexagonal close-packed phases at high temperatures and pressures. Large-scale molecular dynamics simulations of ultrarapid freezing show that bcc nucleates and grows well outside of the region of its thermodynamic stability. An extensive study of crystal-liquid equilibria confirms that at any given pressure, there is a multitude of metastable solid phases that can coexist with the liquid phase. We define for every crystal phase, a solid cluster in liquid (SCL) basin, which contains all solid clusters of that phase coexisting with the liquid. A rigorous methodology is developed that allows for practical calculations of nucleation rates into arbitrary SCL basins from the undercooled melt. It is demonstrated that at large undercoolings, phase selections made during the nucleation stage can be undone by kinetic instabilities amid the growth stage. On these bases, a solidification-kinetic phase diagram is drawn for the model fcc system that delimits the conditions for macroscopic grains of metastable bcc phase to grow from the melt. We conclude with a study of unconventional interfacial kinetics at special interfaces, which can bring about heterogeneous multiphase crystal growth. A first-order interfacial phase transformation accompanied by a growth-mode transition is examined.

Homogeneous water nucleation: Experimental study on pressure and carrier gas effects.

Homogeneous nucleation of water is investigated in argon and in nitrogen at about 240 K and 0.1 MPa, 1 MPa, and 2 MPa by means of a pulse expansion wave tube. The surface tension reduction at high pressure qualitatively explains the observed enhancement of the nucleation rate of water in argon as well as in nitrogen. The differences in nucleation rates for the two mixtures at high pressure are consistent with the differences in adsorption behavior of the different carrier gas molecules. At low pressure, there is not enough carrier gas available to ensure the growing clusters are adequately thermalized by collisions with carrier gas molecules so that the nucleation rate is lower than under isothermal conditions. This reduction depends on the carrier gas, pressure, and temperature. A qualitative agreement between experiments and theory is found for argon and nitrogen as carrier gases. As expected, the reduction in the nucleation rates is more pronounced at higher temperatures. For helium as the carrier gas, non-isothermal effects appear to be substantially stronger than predicted by theory. The critical cluster sizes are determined experimentally and theoretically according to the Gibbs-Thomson equation, showing a reasonable agreement as documented in the literature. Finally, we propose an empirical correction of the classical nucleation theory for the nucleation rate calculation. The empirical expression is in agreement with the experimental data for the analyzed mixtures (water-helium, water-argon, and water-nitrogen) and thermodynamic conditions (0.06 MPa-2 MPa and 220 K-260 K).

Crystal Nucleation Kinetics in Supercooled Germanium: MD Simulations versus Experimental Data.

The validity of the classical nucleation theory (CNT), the most important tool to describe and predict nucleation kinetics in supercooled liquids, has been at stake for almost a century. Here, we carried out comprehensive molecular dynamics simulations of the nucleation kinetics of a fast quenched supercooled germanium using the Stillinger-Weber potential at six temperatures, covering a supercooling range of T/Tm = 0.70-0.86, where Tm is the equilibrium melting temperature. We used the seeding method to determine the number of particles in the critical crystal nuclei at each supercooling, which yielded n* = 150-1300 atoms. The transport coefficient at the liquid/nucleus interface and the melting point were also obtained from the simulations. Using the parameters resulting directly from the simulations, the CNT embraces the experimental nucleation rates, J(T), with the following fitted (average) values of the nucleus/liquid interfacial free energy: γ = 0.244 and 0.201 J/m2, for the experimental and calculated values of thermodynamic driving force, Δμ(T), respectively, which are close to the value obtained from n*(T). Without using any fit parameter, the calculated nucleation rates for the experimental and calculated values of Δμ(T) embrace the experimental J(T) curve. Therefore, this finding favors the validity of the CNT.

Theoretical Models of Decompression-Induced Plagioclase Nucleation and Growth in Hydrated Silica-Rich Melts

Microlites crystallization changes the flow properties of ascending magmas, with major implications on eruption dynamics. In order to predict microlite number density and size, we present a theoretical modelling of plagioclase nucleation and growth in rhyolitic melts, aimed at reproducing the decompression-induced isothermal crystallization experiments of Mollard et al. (2012). Thus, the modelling is valid for plagioclase crystallization in haplotonalitic/rhyolitic melts decompressed at 875 °C from 200 MPa to final pressures of 50, 75, or 100 MPa, which represents effective undercooling (Teff) of 110, 80 and 55 °C, respectively. The nucleation-rate calculation using the Classical Nucleation Theory (CNT; case of homogeneous nucleation) and values of crystal-melt interfacial tensions () either from literature or empirically calculated strongly disagree with the experimental nucleation rates. Inverting the CNT calculation by using the experimentally-determined nucleation rates suggests plagioclase-liquid from 0.041 to 0.059 J.m-2 with Teff increasing from 55 to 110 °C, which is about 2-3 times lower than  determined empirically and macroscopically. Further refining  by considering a non-smooth and non-spherical plagioclase nucleus leads to an elongated and rough morphology with a shape parameter () of 500-1350 and a rugosity parameter (ds) of 2.3. The experimental plagioclase growth rates have been modelled by atom diffusion in melt, following Fick’s second law adapted to multicomponent systems. The component with the smallest flux (i.e. limiting growth) is calcium, as determined from the analytical profiles of the experimental glasses. The crystal-growth model considers a crystal-melt interface advancing over time and a chemically-closed finite reservoir. The overall good agreement between the model and the experimental growth laws validates diffusion as the main process controlling isothermal decompression-induced plagioclase growth under moderate Teff <110 °C. The calculated CaO diffusion coefficients in silicic melt at 875 °C and water saturation pressures from 50 to 100 MPa ranges from 10-14 to 10-15 m2/s. The simulations may be relevant to predict nucleation and growth of plagioclase microlites in phenocryst-poor rhyolitic magmas that rapidly ascend from a storage zone and crystallize at shallower. This may be relevant to eruption dynamics such as dome-related blasts.

Molecular Dynamics Simulations To Capture Nucleation and Growth of Particulates in Ethanolamine-Based Post-Combustion CO2 Capture Columns

Ethanolamines have traditionally been used for capturing CO2 in a post-combustion carbon capture column. However, the use of ethanolamines, due to their high volatility and solvent losses, is not sustainable. One of the ways in which the solvent loss occurs is in the form of aerosols from the top of the column. The mechanism, rate of nucleation, growth rate, and interaction leading to the formation of aerosols, although essential for better process design, remain obscure. Using molecular dynamics simulations, we herein, analyze the formation of aerosols in columns based on aqueous monoethanolamine (MEA), aqueous methyldiethanolamine (MDEA), and their mixtures, using reference, pilot-scale, and industrial-scale data. In particular, the nucleation rate and cluster growth analyses were performed for five different cases. The results show that CO2 concentration had a strong influence on the rate of aerosol formation, a factor that can be easily controlled for better process design. Moreover, the interactions within the formed aerosols were mainly dominated by CO2–water interactions. Taken together, our results and analysis contribute toward a better understanding of aerosol formation and present some practical value, namely, calculated nucleation rates and particulate growth rates can be used in process simulators to account for solvent losses, factors that were identified as contributing to formation of particulate matter can be controlled and adjusted in design process simulations and in real plants, providing better performance of post-combustion carbon capture columns and thus suggest ways to prevent solvent loss.

Reaction coordinates and rate constants for liquid droplet nucleation: Quantifying the interplay between driving force and memory

In this work, we revisit the classic problem of homogeneous nucleation of a liquid droplet in a supersaturated vapor phase. We consider this at different extents of the driving force, or equivalently the supersaturation, and calculate a reaction coordinate (RC) for nucleation as the driving force is varied. The RC is constructed as a linear combination of three order parameters, where one accounts for the number of liquidlike atoms and the other two for local density fluctuations. The RC is calculated from biased and unbiased molecular dynamics (MD) simulations using the spectral gap optimization approach "SGOOP" [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. U. S. A. 113, 2839 (2016)]. Our key finding is that as the supersaturation decreases, the RC ceases to simply be the number of liquidlike atoms, and instead, it becomes important to explicitly consider local density fluctuations that correlate with shape and density variations in the nucleus. All three order parameters are found to have similar barriers in their respective potentials of mean force; however, as the supersaturation decreases, the density fluctuations decorrelate slower and thus carry longer memory. Thus, at lower supersaturations, density fluctuations are non-Markovian and cannot be simply ignored from the RC by virtue of being noise. Finally, we use this optimized RC to calculate nucleation rates in the infrequent metadynamics framework and show that it leads to a more accurate estimate of the nucleation rate with four orders of magnitude acceleration relative to unbiased MD.

Improving new particle formation simulation by coupling a volatility-basis set (VBS) organic aerosol module in NAQPMS+APM

We developed a new modeling framework to simulate aerosol microphysics by incorporating a volatility basis-set (VBS) organic aerosol (OA) module into a three-dimensional (3-D) atmospheric transport model, namely, Nested Air Quality Prediction Modeling System with an Advanced Particle Microphysics (NAQPMS + APM). The new model calculates not only the condensation of sulfuric acid, nitrate, and ammonium and the coagulation of five types of particles (namely secondary, sea salt, dust, black carbon and organic carbon particles) but also the condensation of low-volatility organic vapors and the equilibrium partitioning of semi-volatile organic compounds. The new model was applied to simulate new particle formation (NPF) in summer in Beijing. The new model could noticeably improve the NPF simulation. On comparing the simulation with observation, the ion-mediated nucleation scheme was found to underestimate nucleation rates in summer in Beijing. By incorporating a nucleation formula involving the participation of organic compounds, NPF events could be reproduced satisfactorily. Reasonably calculating nucleation rates is essential for successfully simulating NPF. Accounting for the condensation of anthropogenic low-volatility organic vapors and the volatility of primary OA (POA) can improve the temporal variation of the number concentrations of particles in Aitken and accumulation modes. On a regional scale, anthropogenic low-volatility secondary organic gases (LV-SOGs) and the volatility of POA have large impacts on the aerosol number concentration and cloud condensation nuclei (CCN) concentration. Both anthropogenic LV-SOGs and volatility of POA must be considered to quantify the contribution of NPF to the aerosol number concentration and CCN concentration.

Моделирование нуклеации в бинарных сплавах на основе метода функционала плотности свободной энергии

In this study, the approach for nucleation rate calculation is developed on the basis of free energy density functional approach. The nucleation rate and characteristics of critical nucleus are calculated from results of composition field simulation, derived by the solution of deterministic or stochastic Cahn-Hilliard equation.

Methane hydrate nucleation on water—methane and water—decane boundaries

The nucleation of methane hydrate in water – methane and two-layer water – decane – methane systems was studied using thermal analysis under methane pressure. The nucleation processes in the systems under consideration were represented as empirical survival curves. The effect of aggregate state of guest-rich phase on the methane hydrate nucleation process was evaluated. The experiments were carried out at constant supercooling (19.7 °C). The two-step shape of experimental survival curves was observed in the both studied systems. Based on the data obtained and literature data, it was assumed that in the case of Teflon containers steady-state methane hydrate nucleation occurred at interfaces of water – methane and water – decane saturated with methane while non-isothermal nucleation with a higher rate may be caused by the presence of a small quantity of microimpurities in the initial samples or two-step mechanism of the methane hydrate nucleation process. The comparison of the observed periods of non-stationarity during which nucleation rate takes constant value and calculated nucleation rates showed that the presence of a liquid phase rich with the hydrate-forming component promotes a steadier nucleation of the methane hydrate in the quiescent reactor and facilitates the formation of clusters in the surface layer (water – decane).

Nucleation and epitaxial growth of highly textured Al2O3–ZrO2 nanoeutectic rapidly solidified from oxyacetylene flame remelting

The nucleation and epitaxial growth behavior of a novel Al2O3-ZrO2 nanoeutectic rapidly solidified from the oxyacetylene flame remelting have been investigated. The nanoeutectic ceramic consists mainly of highly textured cellular structure with an average interphase spacing of 136 nm. Especially, a singular transition mechanism associated with “one-step cellular refining” to “two-step cellular refining” is proposed in a variable region from a coarse irregular to an ultrafine lamellar structure, and the regional undercooling is estimated to be 0.57–2.86 K. The Al2O3 phase nucleates as the leading phase in the rapidly solidified structure according to a quantitative calculation of nucleation rate. The cellular eutectic exhibits with a tilted feature, where its cellular growth deviates from the heat flow direction to a preferred growth orientation.

Dust in brown dwarfs and extra-solar planets

Context.The cloud formation process starts with the formation of seed particles, after which, surface chemical reactions grow or erode the cloud particles. If seed particles do not form, or are not available by another means, an atmosphere is unable to form a cloud complex and will remain cloud free.Aims.We aim to investigate which materials may form cloud condensation seeds in the gas temperature and pressure regimes (Tgas= 100–2000 K,pgas= 10−8–100 bar) expected to occur in planetary and brown dwarf atmospheres.Methods.We have applied modified classical nucleation theory which requires surface tensions and vapour pressure data for each solid species, which are taken from the literature. Input gas phase number densities are calculated assuming chemical equilibrium at solar metallicity.Results.We calculated the seed formation rates of TiO2[s] and SiO[s] and find that they efficiently nucleate at high temperatures ofTgas= 1000–1750 K. Cr[s], KCl[s] and NaCl[s] are found to efficiently nucleate across an intermediate temperature range ofTgas= 500–1000 K. We find CsCl[s] may serve as the seed particle for the water cloud layers in cool sub-stellar atmospheres. The nucleation rates of four low temperature ice species (Tgas= 100–250 K), H2O[s/l], NH3[s], H2S[s/l], and CH4[s], are also investigated for the coolest sub-stellar and planetary atmospheres.Conclusions.Our results suggest a possibly (Tgas,pgas) distributed hierarchy of seed particle formation regimes throughout the substellar and planetary atmospheric temperature-pressure space. With TiO2[s] providing seed particles for the most refractory cloud formation species (e.g. Al2O3[s], Fe[s], MgSiO3[s], Mg2SiO4[s]), Cr[s] providing the seed particles for MnS[s], Na2S[s], and ZnS[s] sulfides, and K/Na/Rb/Cs/NH4-Cl binding solid species providing the seed particles for H2O[s/l] and NH4-H2PO4/SH[s] clouds.A detached, high-altitude aerosol layer may form in some sub-stellar atmospheres from the nucleation process, dependent on the upper atmosphere temperature, pressure and availability of volatile elements. In order to improve the accuracy of the nucleation rate calculation, further research into the small cluster thermochemical data for each cloud species is warranted. The validity of these seed particle scenarios will be tested by applying it to more complete cloud models in the future.

Forward flux sampling calculation of homogeneous nucleation rates from aqueous NaCl solutions.

We used molecular dynamics simulations and the path sampling technique known as forward flux sampling to study homogeneous nucleation of NaCl crystals from supersaturated aqueous solutions at 298 K and 1 bar. Nucleation rates were obtained for a range of salt concentrations for the Joung-Cheatham NaCl force field combined with the Extended Simple Point Charge (SPC/E) water model. The calculated nucleation rates are significantly lower than the available experimental measurements. The estimates for the nucleation rates in this work do not rely on classical nucleation theory, but the pathways observed in the simulations suggest that the nucleation process is better described by classical nucleation theory than an alternative interpretation based on Ostwald's step rule, in contrast to some prior simulations of related models. In addition to the size of NaCl nucleus, we find that the crystallinity of a nascent cluster plays an important role in the nucleation process. Nuclei with high crystallinity were found to have higher growth probability and longer lifetimes, possibly because they are less exposed to hydration water.

Computational Fluid Dynamics Studies of a Flow Reactor: Free Energies of Clusters of Sulfuric Acid with NH3 or Dimethyl Amine.

Computational fluid dynamics simulations of a flow reactor provided 3D spatial distributions of its temperature and flow profiles and abundances of sulfuric acid, nitrogeneous base, and the acid-base clusters formed from them. Clusters were simulated via their kinetic formation and decomposition involving sulfuric acid and base molecules. Temperature and flow profiles and the base and sulfuric acid distributions are characterized and the latter is compared to mass spectrometer measurements. Concentrations of simulated clusters of sulfuric acid with either NH3 or dimethylamine were compared to experimentally measured particle concentrations. Cluster thermodynamics were adjusted to better the agreement between simulated and experimental results. Free energies of acid-base clusters derived here are also compared to recent quantum chemistry calculations. Sensitivities to the thermodynamics were explored with a 2D laminar flow simulation and the abundance of large clusters was most sensitive to the thermodynamics of the smallest cluster, consisting of 1 base and 1 acid. Comparisons of this model to the computational fluid dynamics models provide verification of the implemented cluster chemistry. A box model was used to calculate nucleation rates for the conditions of other experimental work, and to provide predictions of nucleation for typical atmospheric conditions.

Pathways to self-organization: Crystallization via nucleation and growth.

Crystallization, a prototypical self-organization process during which a disordered state spontaneously transforms into a crystal characterized by a regular arrangement of its building blocks, usually proceeds by nucleation and growth. In the initial stages of the transformation, a localized nucleus of the new phase forms in the old one due to a random fluctuation. Most of these nuclei disappear after a short time, but rarely a crystalline embryo may reach a critical size after which further growth becomes thermodynamically favorable and the entire system is converted into the new phase. In this article, we will discuss several theoretical concepts and computational methods to study crystallization. More specifically, we will address the rare event problem arising in the simulation of nucleation processes and explain how to calculate nucleation rates accurately. Particular attention is directed towards discussing statistical tools to analyze crystallization trajectories and identify the transition mechanism.