Kinetics of Phase Change. I General Theory
01 Dec 1939-Journal of Chemical Physics (American Institute of Physics)-Vol. 7, Iss: 12, pp 1103-1112
TL;DR: In this paper, the theory of phase change is developed with the experimentally supported assumptions that the new phase is nucleated by germ nuclei which already exist in the old phase, and whose number can be altered by previous treatment.
Abstract: The theory of the kinetics of phase change is developed with the experimentally supported assumptions that the new phase is nucleated by germ nuclei which already exist in the old phase, and whose number can be altered by previous treatment. The density of germ nuclei diminishes through activation of some of them to become growth nuclei for grains of the new phase, and ingestion of others by these growing grains. The quantitative relations between the density of germ nuclei, growth nuclei, and transformed volume are derived and expressed in terms of a characteristic time scale for any given substance and process. The geometry and kinetics of a crystal aggregate are studied from this point of view, and it is shown that there is strong evidence of the existence, for any given substance, of an isokinetic range of temperatures and concentrations in which the characteristic kinetics of phase change remains the same. The determination of phase reaction kinetics is shown to depend upon the solution of a functional equation of a certain type. Some of the general properties of temperature‐time and transformation‐time curves, respectively, are described and explained.
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TL;DR: In this article, a relation between the actual transformed volume V and a related extended volume V1 ex is derived upon statistical considerations, and a rough approximation to this relation is shown to lead, under the proper conditions, to the empirical formula of Austin and Rickett.
Abstract: Following upon the general theory in Part I, a considerable simplification is here introduced in the treatment of the case where the grain centers of the new phase are randomly distributed. Also, the kinetics of the main types of crystalline growth, such as result in polyhedral, plate‐like and lineal grains, are studied. A relation between the actual transformed volume V and a related extended volume V1 ex is derived upon statistical considerations. A rough approximation to this relation is shown to lead, under the proper conditions, to the empirical formula of Austin and Rickett. The exact relation is used to reduce the entire problem to the determination of V1 ex, in terms of which all other quantities are expressed. The approximate treatment of the beginning of transformation in the isokinetic range is shown to lead to the empirical formula of Krainer and to account quantitatively for certain relations observed in recrystallization phenomena. It is shown that the predicted shapes for isothermal transfo...
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TL;DR: In this paper, a comprehensive description of the phenomena of phase change may be summarized in Phase Change, Grain Number and Microstructure Formulas or Diagrams, giving, respectively, the transformed volume, grain, and microstructure densities as a function of time, temperature, and other variables.
Abstract: The theory of the preceding papers is generalized and the notation simplified. A cluster of molecules in a stable phase surrounded by an unstable phase is itself unstable until a critical size is reached, though for statistical reasons a distribution of such clusters may exist. Beyond the critical size, the cluster tends to grow steadily. The designation ``nuclei'' or ``grains'' is used according as the clusters are below or above the critical size. It is shown that a comprehensive description of the phenomena of phase change may be summarized in Phase Change, Grain Number and Microstructure Formulas or Diagrams, giving, respectively, the transformed volume, grain, and microstructure densities as a function of time, temperature, and other variables. To facilitate the deduction of formulas for these densities the related densities of the ``extended'' grain population are introduced. The extended population is that system of interpenetrating volumes that would obtain if the grains granulated and grew through each other without mutual interference. The extended densities are much more readily derivable from an analysis of the fundamental processes of granulation and growth. It is shown that, under very general circumstances, the densities of the actual grain population may be expressed simply in terms of the extended population.
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TL;DR: In this article, non-isothermal kinetics of nucleation and its growth are derived by extending Avrami's equation and applied to DSC curves of crystallization obtained by cooling poly(ethylene terephthalate) at constant rates.
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TL;DR: The theory of the potentiostatic current transient for three-dimensional multiple nucleation with diffusion controlled growth is discussed in this paper, where the termination of the nucleation process by the expansion of diffusion fields is considered, as well as deviations from randomness observed in the distribution of nuclei on the electrode surface.
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References
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TL;DR: In this article, ausscheidung in einem ubersattigten binaren Mischkristall is considered, das die Energie eines Misch-kristalls durch einfache Addition of Nachbarbindungen berechnet werden darf.
Abstract: Unter der Annahme, das die Energie eines Mischkristalls durch einfache Addition von Nachbarbindungen berechnet werden darf, wird die Keimbildungsarbeit fur die Ausscheidung in einem ubersattigten binaren Mischkristall berechnet. Daraus last sich die Haufigkeit der Keimbildung bestimmen. Aus der Durchrechnung eines Zahlenbeispiels ergibt sich fur diejenige Unterkuhlung, bei welcher die Keimbildungshaufigkeit ihr Maximum erreicht, eine befriedigende Ubereinstimmung mit vorliegenden Messungen uber die Geschwindigkeit der Ausscheidung.
329 citations
TL;DR: Englemann et al. as mentioned in this paper showed that the properties of gases and surface tension can be explained in terms of the idea of molecule deduced in ways such as these physical properties are explained.
Abstract: THE conception of molecule is essential in explaining the phenomena of both chemistry and physics. Porosity and compressibility point to the conclusion that matter does not entirely fill space, to account for the dispersion of light requires that matter should have a grained structure; these and countless other physical facts find an explanation in the conception of molecule. Moreover, from various observations, more especially on the properties of gases and the phenomena of surface tension, the size of molecules can be approximately calculated, and in terms of the idea of molecule deduced in ways such as these physical properties are explained. Lehrbuch der Allgemeinen Chemie. Von Dr. Wilhelm Ostwald. Band 1. 1891, Band II. Theil 1. 1893. Zweite Auflage. (Leipzig: Wilhelm Englemann.)
327 citations
TL;DR: Ableitung einer Gleichung fur die Kinetik eines durch Keimbildung und Kristallwachstum bestimmten Kristallisationsvorgangs as mentioned in this paper.
Abstract: Ableitung einer Gleichung fur die Kinetik eines durch Keimbildung und Kristallwachstum bestimmten Kristallisationsvorgangs. — Korngrosenverteilung. — Vergleich mit Erfahrung.
69 citations
TL;DR: It is remarkable how little we know with any certainty about the chemical properties of solids, although the idea of a solid is so fundamental as mentioned in this paper, and it must be remembered that this simplicity is the result of long study and of many discoveries.
Abstract: IT is remarkable how little we know with any certainty -L about the chemical properties of solids, although the idea of a solid is so fundamental. At the present time we always begin the study of chemistry with the gases on account of the simplicity of their mathematical treatment, but it must be remembered that this simplicity is the result of long study and of many discoveries. To the unscientific mind the solid is simpler, because more tangible. When men have tried to understand gases, they have expressed themselves in terms of solids. The atom, however attenuated it may have become in recent years, was in the first instance essentially a solid sphere, and the elasticity of gases has been explained in terms of the collision of elastic solid particles in motion.
63 citations