Theory Of Transformation Kinetics Research Articles

Neutron Bragg Edge Tomography for Phase Mapping

This paper describes non-destructive three-dimensional (3D) mapping of crystallographic phase distributions within the bulk (centimeter range) of samples with micrometer-scale resolution. The technique leverages diffraction contrast due to Bragg scattering and the large penetration power of neutrons through high-atomic-number-element-based structural materials. Our tomographic approach overcomes critical limitations of existing techniques by allowing spatially resolved phase mapping in bulk samples and offers a wide range of potential applications. The technique is demonstrated for (metastable 304L stainless) steel samples that exhibit strain-induced martensitic phase transformation after being subjected to tensile and torsional deformation. The distribution of phase fractions within the 3D reconstructed volumes was verified at select locations using neutron diffraction as well as EBSD, and results agree with transformation kinetics theory.

Transformation kinetics for surface and bulk nucleation

A rigorous mathematical approach based on the causal cone and stochastic geometry concepts is used to derive new exact expressions for transformation kinetics theory. General expressions for the mean volume density and the volume fraction are derived for both surface and bulk nucleation in a general Borel subset of R 3 . In practice, probably any specimen shape of engineering interest is going to be a Borel set. An expression is also derived for the important case of polyhedral shape, in which surface nucleation may take place on the faces, edges and vertices of the polyhedron as well as within the bulk. Moreover, explicit expressions are given for surface and bulk nucleation for three specific shapes of engineering relevance: two parallel planes, an infinitely long cylinder and a sphere. Superposition is explained in detail and it permits the treatment of situations in which surface and bulk nucleation take place simultaneously. The new exact expressions presented here result in a significant increase in the number of exactly solvable cases available to formal kinetics.

Effect of discretization and finite nuclei radius on Kolmogorov-Johnson-Mehl-Avrami isothermal kinetics: A 2-dimensional study

The Kolmogorov-Johnson-Mehl-Avrami (KJMA) isothermal phase transformation kinetics theory assumes negligible volume of the nucleus. For systems with nano-sized grain formation, the initial introduction of finite radius of the product phase nuclei has special relevance. The value of time exponent deviates from the ideal KJMA prediction for such cases. Discrete models may be advanced for explaining such deviation. The main limitation of such an approach is the discrete time step used. We have recently studied these aspects of isothermal transformation kinetics in a systematic way with the help of discrete adaptation of KJMA model. The transformation is assumed to be polymorphic and interface controlled. In this paper we present studies on 2-dimensional (2D) systems.

Evaluation of Displacive Models for Bainite Transformation Kinetics in Steels

Several kinetic models for bainite transformation have been widely applied in industry and research. The majority of these models, that do not consider the effect of cementite precipitation during bainite transformation, were validated in high silicon bainitic steels in order to avoid the interference of cementite precipitation during bainite formation. In this work, displacive models for bainite transformation have been validated in bainitic steels with different silicon content with the aim of evaluating their applicability on steels where cementite precipitation may play an important role on bainite formation. It has been found that these models fail in the calculus of the maximum volume fraction of bainite of lean silicon steels, but lead to a reasonable accuracy in high silicon steels. This is not surprising since cementite formation reduces the carbon content in the residual austenite, stimulating the formation of a further quantity of ferrite. Likewise, an imprecise estimation of the nucleation rate of bainite must be the reason for the poor correlation in the predictions of the bainite transformation kinetics in high silicon steels. This entails a better treatment of autocatalytic nucleation, still unresolved issue in the bainite transformation kinetics theory. [doi:10.2320/matertrans.47.1492]

Avrami theory for transformations from non-uniform austenite grain structures

Classical overall transformation kinetics theory for grain boundary nucleated transformations relies on the assumption that the parent phase grain size is uniform. In the present work the theory is adapted to deal with the case where there is a distribution in the size of the parent grains, as is often found in practice. It is demonstrated that the overall transformation rate is fastest when the starting grain structure is uniform. The method has been applied to the formation of allotriomorphic ferrite in austenite and the results have been compared against published experimental data.

Application of thermal analysis methods to nucleation and growth transformation kinetics, Part II

The general theory of transformation kinetics is largely confined to isothermal reactions. Several attempts have however been made to apply that theory to non-isothermal nucleation and growth transformations as well. Unfortunately, this has lead to some confusion and misunderstandings when thermal analysis experiments, such as DSC and DTA, associated with Kissinger- or Ozawa-like relationships, are used for the extraction of the kinetic parameters of the non-isothermal transformations. The present Part II of this paper widens the scope of the discussed issues, assesses the correct way of applying the theory of isothermal kinetics to non-isothermal transformations, stresses the sources of confusion and points to the mathematical and physical errors that commonly appear in the literature. It is shown that only `site saturated' transformations, i.e. those where the nucleation rate is zero, can be properly analyzed. The general non-isothermal equation for the fraction transformed is proven to be the sound and sole foundation for the correct deduction of the transformation kinetic parameters.

KINETICS OF THE SIMULTANEOUS DECOMPOSITION OF AUSTENITE INTO SEVERAL TRANSFORMATION PRODUCTS

Transformations in steels rarely occur in isolation. This paper describes a modification of the Avrami overall transformation kinetics theory as adapted by Cahn, for grain boundary nucleated phases. The modification deals with the simultaneous occurrence of two or more transformations. The method is demonstrated to faithfully reproduce published data on the volume fractions of allotriomorphic, Widmanstätten ferrite and pearlite as a function of chemical composition, austenite grain size and heat treatment (isothermal or continuous cooling transformation). © 1997 Acta Metallurgica Inc.

Yttrium sialon glasses: Nucleation and crystallization of Y 35Si 45Al 20O 83N 17

The crystallization of a glass with a composition Y 35Si 45Al 20O 83N 17 expressed in equivalent %, which corresponds to a normalized composition Y 0.28Si 0.27Al 0.16ON 0.13, has been studied using an ultrasonic technique. The results were compared with those obtained by more classical techniques such as high temperature X-ray diffraction or differential thermal analysis. The analysis of the data was made within the frame of the general theory of transformation kinetics classically used for the interpretation of differential thermal analysis and differential scanning calorimetry experiments. The structure was studied by transmission electron microscopy at different stages of the glass to glass-ceramic transformation. The devitrification was shown to develop by homogeneous nucleation in the bulk and crystal growth was controlled by diffusion. The optimum nucleation temperature was determined to be 960°C and an activation energy for crystal growth rate found equal to 1025 ± 20 kJ mol −1.

Carbide transformations in low-alloy steels during long-term ageing and service

TTT-diagrams have been obtained for several commercial low-alloy Cr-Mo-V steels over temperatures ranging from 450 to 700°C. Carbide compositions and structures have been investigated and precipitation kinetics of alloying elements during long-term ageing of a metal with the original martensite structure found. The formal theory of transformation kinetics is shown to be useful and values of the ‘n’ coefficient in Johnson-Mehl equation are determined. Cooling rate from the austenite region has a significant effect on the character of a carbide phase diagram. Data relating to the molybdenum content in the carbide phases have been obtained after long-term service of the metal for 150–200 thousand years.

Isothermal crystallization study of Se70Te28Cd2 chalcogenide glass

Bulk glass of composition Se70Te28Cd2 was prepared by the melt quenching technique. Differential Scanning Calorimetry were performed under isothermal conditions and the results have been analysed using the transformation kinetics theory developed by Johnson-Mehl and Avrami. The results indicate that the crystallization process is a three dimensional growth process. The calculated value of the effective activation energy, EG, for crystal growth, was 173 ± 0.5 kJ/mol for this glass.

Growth kinetics of the crystalline phase in Se70Te30 glass

The kinetics of the amorphous-to-crystalline transition in Se70Te30 glass has been studied using electrical conductivity as a sensitive parameter characterizing the transformation process. The experimental data were fitted to the well-known Avrami theory of transformation kinetics. A mean value for the growth parameter n=1.51+or-0.03 and effective activation energy of crystal growth E=104.2 KJ mol-1 have been obtained in the temperature range 360-375 K for the present system.

Experimental test of the general theory of transformation kinetics: Homogeneous nucleation in a Na 2O·2CaO·3SiO 2 glass

Experiments were carried out to test the validity of the Johnson-Mehl-Avrami theory of transformation kinetics. The isothermal crystallization of a nearly stoichiometric Na 2O·2CaO·3SiO 2 glass was studied at 627°C and 629°C by optical microscopy, density measurements and X-ray diffraction. Both nucleation and growth rates were measured by single and double stage heat treatments up to very high volume fractions transformed and the experimental data for crystallinity were compared with the calculated values at the two temperatures. The early crystallization stages were well described by theory for the limiting case of homogeneous nucleation and interface controlled growth. For higher degrees of crystallinity, both growth and overall crystallization rate decreased due to compositional changes of the glassy matrix and the experimental kinetics could be described by theory if diffusion controlled growth was assumed. It was also demonstrated that the sole use of numerical fittings to analyze phase transformation kinetics, as very often reported in the literature, can give misleading interpretations. It was concluded that if proper precautions are taken the general theory predicts the glass-crystal transformation well.

Experimental test of the general theory of transformation kinetics: Homogeneous nucleation in a BaO · 2SiO 2 glass

The isothermal crystallization of a BaO·2SiO 2 glass at 745 and 760°C was studied by X-ray diffraction (XRD) and optical microscopy (OM). Two main observations were made. First, there is a large discrepancy between the experimental crystallinity determined by OM and XRD. The latter is initially equal to the former and gradually drops until a constant value of 64% is reached. This can be explained if one realizes that the spherulites are not entirely crystalline, some residual glassy phase remaining inside them. Second, the experimental and calculated (by the JMA equation) crystallinity versus time curves are displaced on the time axis. Explanations are given for the discrepancy.

Determination of thermal-hardening stress in steels by use of thermoplasticity theory

The problems of quenching-stress analysis are critically reviewed and an adequate simple theory is discussed. The theory accounts for both plasticity and volumetric changes due to phase transformation accompanying the thermal-hardening of a group of simple steels that are characterized by C-shaped time-temperature-transformation diagrams. The volume dilatation in the absence of stress is assumed to be a linear function of the separate specific volumes and weight fractions of the constituents (pearlite, austenite and martensite). With use of the classical relationships of a formal theory of transformation kinetics, the amounts of pearlite and martensite are expressed in terms of the temperature and the temperature-history. The specific forms of such functions are given. In order to account for the influence of phase transformation on plastic properties, the non-isothermal plastic flow-rule is generalized, and a thermal-hardening parameter is introduced which is identified with the amount of pearlite. Variational principles and bounding inequalities associated with the fundamental rate-problem are considered. As an example, the problem for a rapidly, uniformly-cooled half-space is solved. The variations of the residual stress and the final amount of martensite with distance from the outer surface are given, for several values of the rate-of-cooling. The results suggest that the residual stress vanishes on the plane containing approximately 30–35 per cent of martensite.

Crystallization statistics, thermal history and glass formation

The formal theory of transformation kinetics describes the volume fraction of a phase transformed in a given time at a given temperature. The basic concepts are extended for isotropic crystal growth in a material having a known thermal history T( r, t). A crystal distribution function ψ( r, t, R) is defined such that the number of crystallites in a volume d υ at r having radii between R and R + d R at time t is ψ( r, t, R) d υ d R. The function ψ contains essentially complete statistical information about the state of crystallinity of a material. Formal expressions for ψ are obtained. Applications are discussed, including predictions of crystallinity when T( r, t) is known; predictions of glass-forming tendencies; experimental determination of nucleation rates; and the determination of the thermal history of a sample from post mortem crystallinity measurements. As an example, ψ( r, t, R) is calculated for a lunar glass composition subjected to a typical laboratory heat treatment.

The Theory of Transformations in Metals and Alloys

Part I General introduction. Formal geometry of crystal lattices. The theory of reaction rates. The thermodynamics of irreversable processes. The structure of real metals. Solids solutions. The theory of dislocations. Polycrystalline aggregates. Diffusion in the solid state. The classical theory of nucleation. Theory of thermally activated growth. Formal theory of transformation kinetics. Part II Growth from the vapour phase. Solidification and melting. Polymorphic Changes. Precipitation from supersaturated solid solution. Eutectoidal transformations. Order-disorder transformations. Recovery recrystalisation and grain growth. Deformation twinning. Characteristics of martensic transformations. Crystallography of martensitic transformations. Kinetics of martensitic transformations. Rapid solidification. Bainite steels. Shape memory alloys.