Acta Materialia 50 (2002) 4061–4073 www.actamat-journals.com Coarsening of ordered intermetallic precipitates with coherency stress V. Vaithyanathan * , L.Q. Chen Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA Received 20 November 2001; received in revised form 21 May 2002; accepted 23 May 2002 Abstract The morphological evolution and coarsening kinetics of ordered intermetallic precipitates with coherency stress were studied using a diffuse-interface phase-field model in two dimensions (2D). The emphasis is on the effects of precipitate volume fraction. The average aspect ratio of the precipitates in the microstructure is found to increase with time and decrease with volume fraction. Contrary to all the existing coarsening theories but consistent with a number of experi- mental measurements on the coarsening kinetics of ordered g' precipitates in Ni-base superalloys, we found that the coarsening rate constant from the cubic growth law decreases as a function of volume fraction for small volume fractions (20%) and is constant for intermediate volume fractions (20–50%). From the simulation results, we infer that the two length scales in a stress-dominated coherent two-phase microstructure, the average precipitate size and average spacing between arrays of aligned precipitates, follow different growth exponents. It is demonstrated that as the volume fraction increases, the precipitate size distributions become broader and their skewness become increasingly positive.  2002 Published by Elsevier Science Ltd on behalf of Acta Materialia Inc. Keywords: Phase-field; Coarsening; Ni–Al; Coherent precipitates; Effect of volume fraction 1. Introduction One of the most efficient ways to strengthen alloys is by introducing coherent precipitates through a controlled heat treatment process. This process, used commonly in metallic alloys, is referred to as the age hardening or aging or precipi- tation strengthening. The degree of strengthening depends on the volume fraction, size, morphology and spatial distribution of the second-phase pre- * Corresponding author. Fax: +1 814 234 8869. E-mail address: vxv115@psu.edu (V. Vaithyanathan). 1359-6454/02/$22.00  2002 Published by Elsevier Science Ltd on behalf of Acta Materialia Inc. PII:S1359-6454(02)00204-5 cipitates. At high temperatures, the coherent pre- cipitates undergo coarsening driven by a reduction in the total interfacial and elastic energy, resulting in an increase in their average size and an eventual loss of coherency, and thus causing a degradation of the mechanical properties of the alloy. Coarsen- ing under the influence of coherency stress (stress arising from the difference in lattice parameters across the coherent interface) is significantly more complicated than the stress-free coarsening. First, the equilibrium compositions of the coherent two- phase mixture are usually different from those determined by the incoherent phase diagrams [1]. Secondly, the elastic properties are usually aniso-