[Paper Review] Generalized estimates for the density of oxide scale in the range from 0 C to 1300 C

Emmanuil Beygelzimer, Yan Beygelzimer|arXiv (Cornell University)|Oct 19, 2021

Metallurgical Processes and Thermodynamics19 references4 citations

TL;DR

This paper proposes generalized analytical formulas to estimate the true density of oxide scale on steel surfaces across 0–1300 °C, accounting for phase transitions (wustite, magnetite, hematite, iron) and their temperature-dependent thermal expansion. The model incorporates variable Curie and polymorphic transition temperatures to reflect microstructural influences, yielding a predicted density range of 5200–5600 kg/m³, with a local minimum near 570 °C due to wustite decomposition.

ABSTRACT

Oxide scale formed on the surface of steel products during high-teperature processes is studied as a composite material, the main solid components of which, in general, are wustite, magnetite, hematite and metallic iron. To estimate the density of each of these components in the temperature range from 0 C to 1300 C, formulas are proposed that are consistent with the empirical functions of the coefficient of linear thermal expansion, which the authors obtained earlier by generaizing data from open sources. The Curie and polymorphic transformation temperatures are included in these generalized formulas as variable parameters, which allows one to take into account the movability of phase transitions due to impurities, crystal lattice defects, particle sizes, cooling rate, and other factors. When specifying the particular values of critical temperatures, the other parameters of the formulas are recalculated automatically. In a particular form, the proposed formulas correspond to the basic values of critical temperatures. According to the calculation examples given, the true (not including pores) density of oxide scale can be about 5200 to 5600 kg/m3, depending on the temperature and percentage of components, whereby a local density minimum may be observed in the region of 570 C due to eutectoid decomposition of wustite into magnetite and iron. The proposed methods are recommended for use in mathematical simulation of processing of steel products in the presence of oxide scale on its surface.

Motivation & Objective

• To develop a generalized method for estimating the true density of oxide scale on steel across a wide temperature range.
• To account for the influence of variable phase transition temperatures (Curie and polymorphic) due to impurities, defects, and processing conditions.
• To provide a computationally efficient model suitable for integration into mathematical simulations of steel processing.
• To quantify the density variation of oxide scale components (wustite, magnetite, hematite, iron) with temperature and phase composition.
• To identify conditions under which local density minima occur, such as during eutectoid decomposition of wustite.

Proposed method

• The authors derive empirical formulas for the density of each oxide scale component based on generalized temperature-dependent linear thermal expansion coefficients from open-source data.
• Phase transition temperatures (Curie and polymorphic) are treated as adjustable parameters within the model to reflect microstructural variability.
• The model recalculates other parameters automatically when specific critical temperatures are input, enabling dynamic adaptation to different material conditions.
• The approach uses known phase stabilities and thermal expansion behavior to compute component densities across 0–1300 °C.
• The method is validated through calculation examples showing consistent density trends and a local minimum at ~570 °C.
• The model is designed for direct use in mathematical simulations of high-temperature steel processing with oxide scale.

Experimental results

Research questions

• RQ1 How does the true density of oxide scale vary across 0–1300 °C, considering phase composition and thermal expansion?
• RQ2 What is the effect of variable phase transition temperatures on the predicted density of oxide scale components?
• RQ3 Where and why does a local density minimum occur in the oxide scale during heating or cooling?
• RQ4 How can the density of individual oxide phases (wustite, magnetite, hematite, iron) be estimated with sufficient accuracy for simulation purposes?
• RQ5 To what extent can the model account for microstructural factors such as impurities and cooling rate through adjustable transition temperatures?

Key findings

• The true density of oxide scale is predicted to range between 5200 and 5600 kg/m³ across the 0–1300 °C temperature range, depending on phase composition.
• A local density minimum occurs near 570 °C due to the eutectoid decomposition of wustite into magnetite and metallic iron.
• The model successfully captures the influence of variable phase transition temperatures on density estimation, reflecting real material behavior.
• The proposed formulas are consistent with empirical thermal expansion data and allow automatic recalibration when critical temperatures are specified.
• The method enables accurate, physics-based density estimation for use in high-temperature steel processing simulations.
• The model is robust across different material conditions, including variations in impurities and cooling rates, via adjustable transition parameters.