Interfacial Energy of Strained Coherent Interfaces and a New Design Rule To Select Phase Combinations for In Situ Coherent Nanocomposites

Nanocomposites show the best performance when their reinforcing phase precipitates in situ from a matrix upon heat treatment and when coherency between the matrix and the reinforcing phase is preserved even upon coarsening the precipitated particles. In this paper, first a new equation is derived for the interfacial energy of strained coherent interfaces. From here, a new design rule is derived in a form of a new dimensionless number to select phase combinations for in situ coherent nanocomposites (ISCNCs). This is calculated from the molar volume mismatch between the two phases, their elastic constants, and the modeled interfacial energy between them. When this dimensionless number is smaller than a critical value, ISCNCs are formed. The critical value of this dimensionless number is found here using experimental data for the Ni-Al/Ni₃Al superalloy. The validity of the new design rule was confirmed on the Al-Li/Al₃Li system. An algorithm is suggested to apply the new design rule. Our new design rule can be simplified to more easily available initial parameters: if the matrix and the precipitate have the same cubic crystal structure the precipitate is expected to form ISCNCs with that matrix if their standard molar volumes differ less than by about 2%.