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In this chapter, the details of atmospheric phase transitions, nucleation, and cloud droplet formation are discussed. Some phase transitions require a nucleation process, for example, the freezing of liquids, for example ice nucleation. Other phase transitions, such as those involved in cloud droplet formation, do not require a nucleation process because cloud droplets form on water-soluble aerosol particles such as salts. Such aerosol particles often exist in the atmosphere as aqueous solution droplets because they take up water and develop a liquid phase through hygroscopic growth at much lower relative humidity than is required for nucleation of pure liquid water droplets from water vapor. Therefore, no nucleation process is involved in real-world cloud droplet formation. In this chapter, we first discuss the concept of hygroscopic growth and then introduce cloud condensation nuclei (CCN) and Köhler theory, that can be used to mathematically describe cloud droplet activation. To understand the Köhler theory, we introduce the Kelvin law and the Raoult’s law as well as the principles of the so-called 𝜅-Köhler theory.
Prior to the mid-1980s, it was thought that gas-phase reactions were the primary mechanism responsible for ozone depletion in the Earth’s stratosphere. Initial attempts to explain the observed ozone measurements in Antarctica entailed the use of gas-phase chemistry models. As scientists continued to study this phenomenon, they found that gas-phase chemistry alone could not fully account for the dramatic seasonal ozone losses observed, particularly during the Antarctic spring. This resulted in the recognition that heterogeneous chemistry occurring on polar stratospheric clouds can provide insight into the underlying Antarctic ozone hole chemistry. Including heterogeneous reactions in atmospheric models has improved our understanding of the underlying chemistry driving ozone depletion in Antarctica. Our current knowledge of heterogeneous chemistry has unearthed breakthroughs that have revolutionized our understanding of how the atmosphere operates. There remains much to learn in this field, with many important reactions and processes to be discovered.
In this chapter, we focus on the time dynamics encountered during a symmetry-breaking phase transition. After introducing the central concept of a relaxation time, the Kibble–Zurek mechanism arising in continuous phase transitions and the nucleation dynamics of discontinuous transitions are discussed.
The micromagnetic structure of ferromagnets and ferrimagnets is a consequence of minimizing their free energy, which includes a self-energy term due to the dipole field Hd(r). Free energy in micromagnetic theory is expressed in the continuum approximation, where atomic structure is averaged away and M(r) is a smoothly varying function of constant magnitude. The result of the energy minimization is domain formation in most cases. The Stoner–Wohlfarth model is an exactly soluble model for coercivity based on the simplification of coherent reversal in single-domain particles. The concepts of domain-wall pinning and nucleation of reverse domains are central to the explanation of hysteresis and coercivity in real materials. The magnetization processes of a ferromagnet are related to the modification, and eventual elimination of the domain structure with increasing applied magnetic field.
This chapter essentially faces the following question: If at equilibrium a system has a phase transition between a disordered phase and an ordered phase, how does it relax to equilibrium if it is quenched from the former to the latter phase? Quenching means that an external parameter, typically the temperature, is suddenly changed. The answer depends on some relevant factors: if dynamics conserves or not the order parameter; if the order parameter is a scalar or a vector; if long-range interactions are present or not. We devote special attention to the short-range Ising model, but we also consider nonscalar systems. If the order parameter is conserved, its value before quenching is also an important parameter, allowing to distinguish between two different trigger mechanisms of the relaxation process: spinodal decomposition and thermally activated nucleation.
The chapter starts by introducing the basic concepts of metastable and unstable states as well as time scales that control the occurrence of phase transitions. The limits for phase transitions taking place in equilibrium and out-of-equilibrium conditions are then established. In the latter case, thermally activated and athermal limits are distinguished associated with those situations where the transition is either driven or not driven by thermal fluctuations, respectively. Then the formal theory of the decay of metastable and unstable states in systems with conserved and non-conserved order parameters is developed. This general theory is in turn applied to the study of homogeneous and heterogeneous nucleation, spinodal decomposition and late stages of coarsening and domain growth.
To interpret the erratic conditions, rates, and extent of gibbsite crystallization from partially neutralized A1C13 solution, the following hypothesis is proposed: The initial OH-A1 polymers in the freshly prepared solutions were probably unstable and transformed into either gibbsite or stable OH-A1 polymers via two different reaction paths. In the presence of nuclei, the OH-A1 polymers dissociated into monomeric ions, which then deposited onto nuclei to form gibbsite. In the absence of nuclei, the unstable polymers slowly converted to stable polymers. The erratic stability of OH-Al solutions and gibbsite crystallization are therefore attributed to the relative magnitudes of these two reaction paths which, in turn, are attributed to two key factors: (1) the distribution of unstable vs. stable OH-Al polymers; and (2) the presence or absence of nuclei. The duration of aging of the parent solution governed the distribution of unstable vs. stable polymers. The rate of neutralization resulted in varying localized high alkalinity in OH-Al solution preparation and thus varying development of nuclei.
Burial-induced and hydrothermal-related illitization in bentonites and in sandstones can be modeled on the basis of isotopic studies of fundamental particles separated from mixed-layer illitesmectite. The model envisages different reaction rates and durations relative to the varied impacts of temperature, considering that the water:rock ratio also has an influence. The different pathways for illitization are suggested on the basis of the K-Ar, Rb-Sr and δ18O compositions of previously studied materials.
New information is provided on why fundamental particles separated from mixed-layer illite-smectite in shales yield K-Ar age data that are systematically greater than the ages of the fundamental particles from associated bentonites and/or sandstones, and greater than the reported stratigraphic ages. The study of pure authigenic, recent to present-day smectite from Pacific sediments shows that (1) those collected from active hydrothermal vents have 40Ar/36Ar ratios identical to that of the atmosphere, and (2) those of mud sediments have 40Ar/36Ar ratios above the atmospheric value, indicating addition of 40Ar not generated in situ by radioactive decay. A preliminary but detailed analysis of the noble-gas (Ar, Xe, Kr) contents of authigenic smectite-rich size fractions from Pacific deep-sea red clays suggests trapping of these gases by smectite. Therefore, the results point to the fact that fundamental particles can incorporate excess 40Ar into their structure when nucleating in restricted to closed systems, such as shales. This excess 40Ar, which represents radiogenic 40Ar released from nearby altered silicates, might be temporarily adsorbed at the surface of the rock pore spaces and is therefore available for incorporation in nucleating and growing particles.
The crystal growth of NH4-illite (NH4-I) from the hydrothermal system of Harghita Bãi (Eastern Carpathians) was deduced from the shapes of crystal thickness distributions (CTDs). The <2 mm and the <2-0.2 mm fractions of clay samples collected from the argillized andesite rocks consist of NH4-illite-smectite (I-S) interstratified structures (R1, R2, and R3-type ordering) with a variable smectite-layer content. The NH4-I-S (40-5% S) structures were identified underground in a hydrothermal breccia structure, whereas the K-I/NH4-I mixtures were found at the deepest level sampled (-110 m). The percentage of smectite interlayers generally decreases with increasing depth in the deposit. This decrease in smectite content is related to the increase in degree of fracturing in the breccia structure and corresponds to a general increase in mean illite crystal thickness. In order to determine the thickness distributions of NH4-I crystals (fundamental illite particles) which make up the NH4-I-S interstratified structures and the NH4-I/K-I mixtures, 27 samples were saturated with Li and aqueous solutions of PVP-10 to remove swelling and then were analyzed by X-ray diffraction. The profiles for the mean crystallite thickness (Tmean) and crystallite thickness distribution (CTD) of NH4-I crystallites were determined by the Bertaut-Warren-Averbach method using the MudMaster computer code. The Tmean of NH4-I from NH4-I-S samples ranges from 3.4 to 7.8 nm. The Tmean measured for the NH4-I/K-I mixture phase ranges from 7.8 nm to 11.7 nm (NH4-I) and from 12.1 to 24.7 nm (K-I).
The CTD shapes of NH4-I fundamental particles are asymptotic and lognormal, whereas illites from NH4-I/K-I mixtures have bimodal shapes related to the presence of two lognormal-like CTDs corresponding to NH4-I and K-I.
The crystal-growth mechanism for NH4-I samples was simulated using the Galoper code. Reaction pathways for NH4-I crystal nucleation and growth could be determined for each sample by plotting their CTD parameters on an α-ß2 diagram constructed using Galoper. This analysis shows that NH4-I crystals underwent simultaneous nucleation and growth, followed by surface-controlled growth without simultaneous nucleation.
Though not prolific, our prehistoric material both significantly amplifies our knowledge of the prehistory of the study area and informs on wider debates about settlement trends prior to Etruscan urbanization.Palaeolithic finds were very sparse, but the area was occasionally visited by Mesolithic hunter-gatherers in the Early Holocene (9700-6200 BC) even though its volcanic soils were heavily wooded. The first farming communities (Earlier Neolithic, c.5500-4500 BC: 10 sites) consisted of small residential units of one or two households. The Later Neolithic (4500-3500 BC: 15 sites) data fit the regional evidence of increasing complexity and social inequality.Site numbers doubled in the Copper Age (3500-2200 BC: 30 sites) and doubled again in the Earlier Bronze Age (2200-1400 BC: 62 sites) but these societies remained small scale, living as individual households or in small clusters. The same rural structure continued into the Later Bronze Age (1400-950 BC: 53 sites) but above it Tuscania’s Colle San Pietro acropolis developed as a nucleated and probably defended hilltop community.The process of nucleation accelerated in the Iron Age (950-700 BC: 16 sites). Tuscania was probably in a subordinate relationship to Tarquinia, one of five ‘super-centres’ that developed into the major Etruscan cities of South Etruria.
Using the Flory-Huggins theory for uncharged polymer solutions, key concepts of the critical point, coexistence curve, and spinodal curve are presented. These concepts are then generalized to charged systems by explicitly considering restricted primitive model for electrolytes and new developments for polyelectrolyte solutions that include the liquid-liquid phase separation invoked in the formation of membrane-less organelles. Fibrillization in amyloids and collagen is discusses with a focus of electrostatic effects.
In this appendix, we briefly review the concept of a multi-component system exhibiting a miscibility gap, and define the concept of the binodal and spinodal lines explain phase separation process once the system moves from a single-phase field into a two-phase field.
Most solid-to-solid phase transformations are much more interesting than just the growth of a small, homogeneous particle of the new phase. For reasons of both kinetics and thermodynamics, the new particles evolve in crystal structure, chemical composition, interface structures, defects, elastic energies, and shapes. Chapter 14 gives an overview of processes that occur during the nucleation and growth of a new phase from a parent phase. It covers essential features of precipitation in a solid, with a few traditional examples from steels, such as the pearlite transformation, and examples of precipitation sequences in aluminum alloys. Much of the content is central to physical metallurgy. The Kolmogorov-Johnson-Mehl-Avrami model of the rates of nucleation and growth transformations is presented. The late-stage coarsening process is also discussed in terms of the self-similarity of the microstructure.
Phase transformations often begin by nucleation, where a small but distinct volume of material forms with a structure and composition that differ from those of the parent phase. An unfavorable surface bounds the new phase, giving rise to a barrier that must be overcome before thefluctuation in structure and composition can become a stable, growing region of new phase. Chapter 4 develops the thermodynamics of forming a nucleus, with emphasis on the characteristic size and undercooling that are required. Homogeneous and heterogeneous nucleation are explained. The temperature dependence of nucleation is explained. The time dependence of nucleation is discussed in terms of the shape of the free energy barrier that must be crossed by a growing nucleus. There is some discussion of nucleation in multicomponent alloys.
Asymptotic Giant Branch (AGB) stars contribute a major part to the global dust budget in galaxies. Owing to their refractory nature alumina (stoichiometric formula AlO) is a promising candidate to be the first condensate emerging in the atmospheres of oxygen-rich AGB stars. Strong evidence for that is supplied by the presence of alumina in pristine meteorites and a broad spectral feature observed around ∼ 13 μm. The emergence of a specific condensate depends on the thermal stability of the solid, the gas density and its composition. The evaluation of the condensates is based on macroscopic bulk properties. The growth and size distribution of dust grains is commonly described by Classical Nucleation Theory (CNT). We question the applicability of CNT in an expanding circumstellar envelope as CNT presumes thermodynamic equilibrium and requires, in practise, seed nuclei on which material can condense. However, nano-sized molecular clusters differ significantly from bulk analogues. Quantum effects of the clusters lead to non-crystalline structures, whose characteristics (energy, geometry) differ substantially, compared to the bulk material. Hence, a kinetic quantum-chemical treatment involving various transition states describes dust nucleation most accurately. However, such a treatment is prohibitive for systems with more than 10 atoms. We discuss the viability of chemical-kinetic routes towards the formation of the monomer (Al2O3) and the dimer (Al4O6) of alumina.
A promising candidate to initiate dust formation in oxygen-rich AGB stars is alumina (Al2O3) showing an emission feature around ∼13μm attributed to Al−O stretching and bending modes (Posch+99,Sloan+03). The counterpart to alumina in carbon-rich AGB atmospheres is the highly refractory silicon carbide (SiC) showing a characteristic feature around 11.3μm (Treffers74). Alumina and SiC grains are thought to represent the first condensates to emerge in AGB stellar atmospheres. We follow a bottom-up approach, starting with the smallest stoichiometric clusters (i.e. Al4O6, Si2C2), successively building up larger-sized clusters. We present new results of quantum-mechanical structure calculations of (Al2O3)n, n = 1−10 and (SiC)n clusters with n = 1−16, including potential energies, rotational constants, and structure-specific vibrational spectra. We demonstrate the energetic viability of homogeneous nucleation scenarios where monomers (Al2O3 and SiC) or dimers (Al4O6 and Si2C2) are successively added. We find significant differences between our quantum theory based results and nanoparticle properties derived from (classical) nucleation theory.
This paper highlights new research on the biomineralization of otoliths and uses a mineralogical approach to understand mechanisms of crystal growth and metal incorporation into otoliths. Petrographic observations of the nucleation of otolith growth in the core for several fish species reveals that sagittal otoliths appear to nucleate around a few or many nucleation sites (primordia) and that these sites vary in size (ranging in diameter from 1 to 20 μm), depending on the species. Spectroscopic data show a large Mn-enrichment in the primordia within the core but the reasons for this enrichment are still unclear (e.g. organic matter or possibly another material other than CaCO3). This study also provides the first multi trace-element data for endolymph fluid and the growing otolith; we found large enrichments (Ca and Sr) and depletions (Na, K, Zn and Rb) of elements in the otolith relative to the endolymph. The last part of this paper examines the effect of crystal structure on the microchemistry ofotoliths. Our investigation helps understand how the chemical characteristics of the metal ions (i.e. ionic radii) and the crystalline structure interact to cause differential trace-metal uptake between the CaCO3 polymorphs, aragonite and vaterite.
Supersaturation-Nucleation-Time (S-N-T) diagrams are shown to be a useful tool to predict nucleation during reactive-transport processes in porous media. Such diagrams can be determined experimentally or estimated from theoretical calculations based on classical nucleation theory. With this aim, a ‘pragmatic’ understanding of the nucleation rate equation is adopted here and the meaning and magnitude of the interfacial tension and induction time discussed. Theoretical diagrams and experimental data are shown to match fairly well as long as there is an appropriate choice of the ‘relevant’ volume for induction-time calculations.
The micro-inclusions located in the genetic centre of Yakutian diamond monocrystals have been studied using optical (anomalous birefringence, photoluminescence, cathodoluminescence) and microanalytical (electron-microprobe, proton-microprobe, scanning electron microscope) methods. Most diamonds nucleated heterogeneously on mineral seeds, that lowered the energy barrier to nucleation. Nucleation of peridotitic diamonds occurred on a matrix of graphite+iron+wüstite, in an environment dominated by forsteritic olivine and Fe-Ni sulfide. Nucleation of eclogitic diamonds occurred on a matrix of sulfide ± iron in an environment dominated by Fe-sulfide and omphacite (±-K-Na-Al-Si-melt). The mineral assemblages recorded in the central inclusions of Yakutian diamonds indicate that they grew in a reduced environment, with oxygen fugacity controlled by the iron-wüstite equilibrium. Nucleation of diamond occurred in the presence of a fluid, possibly a volatile-rich silicate melt, highly enriched in LIL (K, Ba, Rb, Sr) and HFSE (Nb, Ti, Zr) elements. This fluid also carried immiscible Fe-Ni-sulfide melts, and possibly a carbonatitic component; the introduction of this fluid into a reduced refractory environment may have been accompanied by a thermal pulse, and may have created the conditions necessary for the nucleation and growth of diamond.
Strain path changes during clock rolling cause more serious interaction between adjacent grains, resulting in the occurrence of interactive regions (IRs) with random orientations. Furthermore, plenty of new grains with relatively random orientations are introduced by the subsequent annealing of these IRs. The morphology of the IR and the origin of random orientations were therefore investigated in this study, and the electron backscatter diffraction technique was used to characterize crystallographic orientations of nuclei and deformed matrices. A short-time annealing was imposed on a specimen to catch the transient nucleation behaviors. The results indicate that the orientations of nuclei are similar to their surrounding deformed matrices, especially the points with larger local-misorientation. Additionally, the shape of new grains depends on where it forms, and it is suggested that this fact mainly results from the great difference in stored energies between deformed matrices with {111} and {100} orientations.