Thermodynamic estimation of liquidus, solidus, Ae3 temperatures and phase compositions for low alloy multicomponent steels
Thermodynamic estimation of liquidus, solidus, Ae3 temperatures and phase compositions for low alloy multicomponent steels, by A. A. B. Sugden and H.K.D.H. Bhadeshia
In an attempt to develop improved models for the prediction of microstructures in steel weld deposits, established thermodynamic procedures have been used to estimate the liquidus, solidus, and Ae3 transformation temperatures for multicomponent steels, together with partitioning coefficients and other parameters. The method has been tested against a large amount of published data and there is found to be good agreement between experiment and theory.
This research paper introduces a computational model designed to predict critical thermodynamic properties of low alloy multicomponent steels, specifically for use in welding applications. By utilising and expanding upon established thermodynamic procedures, the authors estimate various transformation temperatures, including the liquidus, solidus, and $Ae_3$ points.
The study focuses on how different alloying elements cause phase boundaries to deviate from the standard binary iron–carbon system. To ensure accuracy, the model’s predictions were rigorously compared against experimental data, showing strong agreement across diverse steel compositions. Ultimately, these calculations help engineers understand chemical segregation and the development of microstructures within steel weld deposits.
Answer Key
Non-Equilibrium Cooling:
The primary consequence is the chemical segregation of substitutional alloying elements. Unlike interstitials, which can diffuse and homogenise during cooling, substitutional elements persist in their segregated state as the weld reaches ambient temperature.
Transformation of Austenite:
Segregation influences reaction kinetics by accelerating the transformation of austenite into ferrite in solute-depleted regions. This causes carbon to redistribute into the remaining austenite, thereby increasing its hardenability and altering the final volume fraction of the microstructure.
Kirkaldy and Baganis Method:
The method circumvents infinite dilution issues by calculating the temperature deviation ($\Delta T$) of a specific phase boundary from the corresponding boundary in a binary iron–carbon system. The total change in carbon concentration is determined by summing the individual effects of each substitutional alloying element.
Composition Constraints:
The assumption that $\Delta T$ values are additive holds true as long as solute–solute interactions are negligible. Practically, this is valid when the total alloying element content is less than approximately 6 wt-% and the silicon content remains below 1 wt-%.
Kaufman et al. Data:
While other data sources existed, the Kaufman et al. data provided reliable values down to 0 K. This was essential for the long-term goal of accurately extrapolating $Ae_3$ temperatures to lower temperature ranges well below the eutectoid temperature.
Carbon–Carbon Interaction Parameter:
In $\delta$-ferrite, the maximum solubility of carbon is extremely low (0.09 wt-%), resulting in roughly one carbon atom for every 119 unit cells. Even at saturation, the probability of two carbon atoms occupying the same unit cell is only 0.004, making carbon–carbon interactions negligible.
Solidification Modes:
Solute segregation is much lower during ferritic solidification because the diffusion rate of substitutional elements in ferrite is two orders of magnitude greater than in austenite. If a steel solidifies as austenite, the slower diffusion leads to more pronounced chemical inhomogeneities and different inclusion distributions.
Iron–Niobium (Fe–Nb) Discrepancy:
The discrepancy arose from an error in the original source regarding the excess molar Gibbs free energy of niobium. It was corrected by recalculating the values with respect to niobium rather than pure iron, which effectively eliminated the previous deviation from experimental data.
Partition Coefficient:
The partition coefficient is a characteristic value indicating the level of microsegregation by comparing the concentration of an element in two different phases at equilibrium. Thermodynamic calculations are preferred because experimental determination is extremely time-consuming, and for dilute solutions, the contributions of element interactions are negligible.
Practical Limitations:
The program is limited by the underlying theory's inability to account for complex solute–solute interactions, as it is strictly designed for infinitely dilute solutions. Additionally, it is constrained by the availability and accuracy of experimental data for pure binary systems with iron.
