On the applicability of the Ivantsov growth equation

Abstract

The steady state growth equation for a paraboloid of revolution and a parabolic cylinder, taking the interfacial energy into account, is revisited. Although the consideration of the interfacial energy was necessary, the growth equation was much more complicated than the original equation with a zero interfacial energy, since both the thermodynamics and kinetics of the growth are considered in one equation. In the present work, we take advantage of the development in computational thermodynamics and consider the thermodynamics and kinetics of the process in separate equations, but solve them simultaneously. A consistent framework to describe the phenomena and compare it with previous treatment of the interfacial energy will be presented.

Why solidification has an S-shaped history

“…Refs. 17,18,19,20,21). The instantaneous length of the needle is x, and the length of the volume is L (Fig.…”

The Kinetics of Primary Alpha Plate Growth in Titanium Alloys

“…However, for isothermal transformation, the interfacial curvature and kinetics must be taken into account. Bosze and Trivedi,[30,29] and Liu and Chang [31] developed the approach, using the Ivantsov equation with the Trivedi modification and applying this to carbon composition close to an interface with curvature. In the present work, the growing alpha plate is treated as a paraboloid with tip growth velocity V, Figure 1.…”

Optimization of Low-Cost Ti-35421 Titanium Alloy: Phase Transformation, Bimodal Microstructure, and Combinatorial Mechanical Properties

“…(1) The local equilibrium condition at each time/temperature step was approximately satisfied at the interface; (2) the Gibbs-Thomson effect played a part in lengthening/dissolution of the α lamellar tip because of the tip curvature, but did not work in thickening/dissolution of the broad face. The details of the modeling can be found in Appendix A and in [24,25,26]. By selecting the appropriate diffusion coefficients from the handbook [27], the interface migration distances in calculations were compared with the experiments.…”

“…In the last parenthesis of Equation (A1), the second term was introduced by Trivedi [33,34] to calibrate the effect of interfacial curvature on the local composition. ρ c is the critical radius for growth and was set to 9.0 × 10 −10 m. S ( P ) was approximated as 2/πP in accord with [24]. Ω is the non-dimensional supersaturation of each partitioned element and expressed as sans-serifΩ=x0β−xβ/α(xα/β−x0β)(xα/β−xβ/α).x0β is the mole fraction of alloying element in β phase before α lamellar precipitation.…”