Solubility Products for Precipitate Phases in Steels from First-principles Calculations
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Solubility Products for Precipitate Phases in Steels from First-principles Calculations Tetyana Klymko1,2, Chaitanya Krishna Ande1,2 and Marcel Sluiter2 1 Materials innovation institute, Mekelweg 2, 2628 CD, Delft, the Netherlands. 2 Department of Materials Science and Engineering, Delft University of Technology, Mekelweg 2, 2628 CD, Delft, the Netherlands. ABSTRACT The work presented gives an insight into using formation enthalpies determined from ab initio calculations for computing solubility products in steels. The role of enthalpy and entropy contributions to the solubility product is discussed. As an illustration of the method, we present solubility products for observed stoichiometric precipitate phases in ferrite from first-principles calculations and in austenite as obtained from the combined approach based on ab initio and experimental phase diagram analysis. The results are compared with experimental data where available. INTRODUCTION Microalloyed high strength low alloy (HSLA) steels are technologically important structural materials. Microstructure and mechanical properties of steel such as high temperature strength, ductility and creep resistance are to a great extent influenced by various microalloying elements and precipitate phases [1-26]. Although these elements are present in small concentrations compared to the amount of iron, nevertheless they determine to a high extent the mechanical properties and therefore their effectiveness is an important subject both for fundamental and applied research. Much experimental [1-26,43-56] and theoretical [27-41] research has been performed on this subject. Among theoretical studies, first principles, or ab initio, calculations are of growing interest. They are frequently used for computing formation enthalpies [27-33], elastic [34-36] or diffusion [37-41] properties. However, to our knowledge, they are not used much yet for finite temperature solubility products calculations involving multiple alloying elements simultaneously. The current investigation gives a fundamental understanding of solubility products of precipitate phases and provides an insight into using formation enthalpies determined from ab initio calculations for computing solubility products of precipitate phases in steels. THEORY Solubility product definition For a reaction of precipitation of the form pM + qX U M p X q ++G for elements M and
X, a solubility product K of the precipitate phase M p X q is commonly defined as K = [ M ] p [ X ]q [ M p X q ] . Here +G is Gibbs free energies of M p X q compound formation,
quantities in [ ] generally denote the activities of the respective phases in solution at equilibrium with the precipitate and p and q are indices defining a stoichiometry [42]. As a first approximation, we will consider formation of stoichiometric precipitates with p = q = 1 . Since
microalloying elements in steels are usually present in very small amounts compared to major iron component, we can restrict ourselves to the dilute solution limit where activities are equal to the
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