The diffusion-controlled growth of solid solution scales on binary alloys

Abstract A detailed examination is made of the equations originally developed by Wagner (1969), and subsequently modified by other workers, which describe the growth of solid solution scales by cation diffusion on binary alloys. By reference to finite difference solutions of the relevant differential equations, it is demonstrated that an accurate limiting solution can be obtained for k, the parabolic rate constant for scale growth. Upon combining this with existing equations describing both diffusion in the alloy and mass-balances at the scale boundaries, a set of interdependent relations is extracted which provide a complete analytical description of scale growth. As a result, k can be calculated for conditions relevant to the formation of compact, solid solution scales on single phase, binary alloys, from pertinent diffusion and thermodynamic data. Representative values for the relative diffusion rates of the participating metal atoms in the alloy and ions in the scale, the individual rates of cation diffusion in the scale, the degree of selective oxidation of the appropriate alloy component and the activity of the oxidizing atmosphere are each examined quantitatively for their influence both on k and on the cation distribution in the scale. General patterns of behaviour are established and the relation between the cation distribution and the precipitation of a second phase is discussed. A quantitative assessment of the reliability of the analysis is restricted by the limited availability of the requisite data for real systems and is confined to the calculation of k for Co-Ni, Co-Fe, Fe-Mn and dilute Ni-Cr alloys. Satisfactory agreement with experimental data is obtained in each case. Further support for the analysis is obtained from a consideration of distributions of cations in scales on the same alloys.