F. Sommer

Analysis of solid state phase transformation kinetics: models and recipes

Abstract The progress of solid-state phase transformations can generally be subdivided into three overlapping mechanisms: nucleation, growth and impingement. These can be modelled separately if hard impingement prevails. On that basis, an overview has been given of recent numerical and analytical methods for determination of the kinetic parameters of a transformation. The treatment focuses on both isothermally and isochronally conducted transformations. To extend the range of transformations that can be described analytically, a number of more or less empirical submodels, which are compatible with experimental results, has been included in the discussion. It has been shown that powerful, flexible, analytical models are possible, once the concept of time or temperature dependent growth exponent and effective activation energy, in agreement with the existing experimental observations, has been adopted. An explicit (numerical) procedure to deduce the operating kinetic processes from experimental transformation-rate data, on the basis of different nucleation, growth and hard impingement mechanisms, has been demonstrated. Without recourse to any specific kinetic model, simple recipes have been given for the determination of the growth exponent and the effective activation energy from the experimental transformation-rate data.

Determination and interpretation of isothermal and non-isothermal transformation kinetics; the effective activation energies in terms of nucleation and growth

A general model for the kinetics of solid state phase transformations has been discussed. The model is valid for both isothermal as well as non-isothermal transformations. In certain specific cases, the model can be simplified such that it reduces to so-called Johnson-Mehl-Avrami (JMA) kinetics. The model kinetic parameters are independent of the time-temperature program. In addition, it has been shown that in certain cases where the presented model does not pertain to JMA exactly, the JMA description still holds within practical accuracy. This holds for example, for nucleation of mixed nature. In this case, it is possible to obtain the activation energies for growth and for nucleation, separately, from measurements, if it is possible to vary the nucleation mode, for example by pre-annealing. This determination of the separate activation energies has been tested on a virtual and a real phase transformation: crystallisation of glassy Pd40Cu30P20Ni10.

An analytical model for isothermal and isochronal transformation kinetics

An analytical model for the kinetics of phase transformations has been discussed that combines three overlapping processes: nucleation, growth, and impingement. Two kinds of nucleation have been considered in particular: a mixture of site saturation and continuous nucleation and Avrami nucleation. In combination with either interface-controlled growth or volume diffusion controlled growth, and incorporating the effect of impingement of the growing particles, a general analytical description of the transformation kinetics has been given for both isothermally and isochronally conducted transformations. The corresponding kinetic parameters are time and temperature dependent. In specific, limiting cases, the model reduces to the so-called Johnson-Mehl-Avrami description of transformation kinetics. The analytical model has been verified by exact results obtained from numerical calculations. The influences of the different nucleation and growth modes on the time and temperature dependencies of the transformation rate and the kinetic parameters have been demonstrated.

Abnormal austenite-ferrite transformation behaviour in substitutional Fe-based alloys

Abstract The γ → α phase transformation behaviours of Fe-Co and Fe-Mn alloys were systematically investigated by dilatometry and Differential Thermal Analysis (DTA). Two kinds of transformation kinetics, called normal and abnormal, were recognized for the first time and classified according to the variation of the ferrite formation rate. These transformation characteristics were observed for both isothermally and isochronally conducted annealing experiments. A transition, from abnormal to normal transformation kinetics, occurs for Fe-1.79at.%Co when successive heat treatment cycles are executed, which contrasts with Fe-2.26at.%Mn for which only normal transformation kinetics occurs after each of all successive heat treatment cycles. A possible mechanism for the appearance of abnormal transformation kinetics is given, which is based on the austenite grain size. Light microscopical analysis indicates a repeated nucleation of ferrite in front of the migrating γ / α interface.

The kinetics of the austenite-ferrite phase transformation of Fe-Mn: differential thermal analysis during cooling

Abstract Differential thermal analysis (DTA) has been employed to study the austenite–ferrite phase transformation of Fe-1.89at% Mn upon cooling. The transformation has been shown to occur in two stages. The first stage is not thermally activated; the second stage is thermally activated. A phase transformation model, incorporating a new impingement correction, has been used for the extraction, from the DTA experiments, of data for the velocity of the austenite–ferrite interface. It follows that the interface velocity does not only depend on temperature, but also on transformed fraction. This has been interpreted as the consequence of the (non-neglectable) dissipation of energy by the volume misfit of the austenite and ferrite phases during the transformation. This misfit accommodation Gibbs energy has been assessed quantitatively; it has been shown to be of the same order of magnitude as the chemical Gibbs energy.

Investigation of the AlMgSi system by experiments and thermodynamic calculations

Abstract The enthalpies of formation and fusion as well as the heat capacity of Mg 2 Si were measured calorimetrically. The Al corner of the AlMgSi ternary system was investigated by DTA and optical micrography. A few points of the solvus of the Al(f.c.c.) solid solution were determined by dilatometry. The results of these experiments, together with literature data, were used to redetermine a complete set of analytical descriptions of the Gibbs energies of all stable phases of the AlMgSi system.

Thermodynamic properties of compound-forming liquid alloys

Abstract The experimentally determined properties of compound-forming liquid alloys show specific concentration and temperature dependences, which are caused by the existence of chemical short range order in these alloys. The concentration and temperature dependences of thermodynamic mixing functions are explained on the basis of homogeneous equilibria reactions within an association model for a simple description of chemical short range order. The ability of this model to predict thermodynamic properties of a binary liquid alloy from experimental results and to extrapolate it to ternary liquid alloys is demonstrated.

The isothermal and isochronal kinetics of the crystallisation of bulk amorphous Pd40Cu30P20Ni10

Abstract The amorphous alloy Pd 40 Cu 30 P 20 Ni 10 has been produced by water quenching the molten alloy. The kinetics of crystallisation has been measured by means of isothermal and isochronal differential scanning calorimetry. The associated microstructural changes have been analysed using scanning electron microscopy. Special interest has been devoted to the influence of isothermal pre-annealing on subsequent isochronal crystallisation kinetics. By applying appropriate isothermal pre-annealing temperatures, nucleation of the crystalline phases takes place to different extents. Accordingly, the initial state for the subsequent isochronal crystallisation could be changed gradually with respect to the number of pre-existing nuclei. This leads to a gradual change of the mode of nucleation from site saturation to continuous nucleation during the crystallisation. The corresponding change of the kinetic parameters has been used to determine the activation energies of nucleation and growth separately.

Corrosion inhibition in magnesium-aluminium-based alloys induced by rapid solidification processing

The effect of rapid solidification on the corrosion behaviour in aerated 0.001 M NaCl solution of Mg-Al alloys containing 9.6 to 23.4wt% AI has been investigated in comparison with chill-cast material. Polarization studies show that rapid solidification decreases corrosion current by up to two orders of magnitude corresponding to a corrosion rate of 6 to 11 mil y−1. Increasing the aluminium content in solid solution by rapid solidification gave rise to a steep increase in pitting potential between 10 and 23 wt% Al and resulted in development of an anodic plateau at ∼ 30μAcm−2 attributable to magnesium depletion for the alloy surface and formation of a protective film. Chemical analysis of the electrolyte as a function of dissolution time for the rapidly solidified material indicated that initially only magnesium dissolved and that this dissolution of magnesium ceased within 2 to 5 min. The results indicate the formation of an aluminium-enriched interdiffusion zone at the surface underlying a more stable surface oxide than for ingot-processed Mg-Al-based alloys.

Determination of the enthalpy of mixing of liquid alloys using a high-temperature mixing calorimeter

A high-temperature mixing calorimeter that allows the measurement of the enthalpy of mixing of liquid alloys at temperatures ranging up to 1800 K is described. The suitability of the apparatus is shown by the measurement of the enthalpy of mixing of liquid Al-Cu, Al-Ni, and Cu-Ni alloys. The results are compared with data from literature and are discussed using an association model.