Theoretical analysis of strain-induced shape changes in cubic precipitates during coarsening

• Published in: Acta metallurgica 1988-06, Vol.36 (6), p.1563-1572
• Main Authors: Khachaturyan, A.G., Semenovskaya, S.V., Morris, J.W.
• Format: Article
• Language: English
• ISSN: 0001-6160
• DOI: 10.1016/0001-6160(88)90224-6

The work reported here concerns the evolution of the shape of a coherent, cubic precipitate as it grows by coarsening. The work was motivated by the need to explain recent experimental observations that show that cuboidal γ' Ni 3Al precipitates in Ni-Al alloys resist coarsening and decompose into doublets of parallel rectangular plates and octets of small cubes. The theoretical model assumes a precipitate of cubic phase with negative elastic anisotropy, and neglects any difference between the elastic constants of the precipitate and the matrix. The elastic energy of the precipitate is then calculated as a function of its morphology, including the possibility of decomposition into doublets or octets of discrete particles. The results show that a cuboidal precipitate with (100) faces and edge length, 2 a, is metastable with respect to transition to a doublet of discrete plates, with dimensions a ×. 2 a × 2 a, that are separated by the distance u ~ a, when the edge length exceeds a characteristic distance, r 0, that depends on the interfacial tension of the precipitate, its elastic constants, and its misfit with the parent lattice. When the edge length of the doublet exceeds a critical value, it becomes metastable with respect to transformation into an octet of cubic particles that have edge length, a, {100} interfaces and an interparticle separation of 0.4 a. The octet of particles becomes metastable with respect to coagulation into a thin plate on the (100) plane on further coarsening. If the interfacial tension is isotropic, the same analysis can be used to predict the transition from sphere to cube. The equilibrium transformation sizes are specifically computed for the case of γ' Ni 3Al, and are consistent with the experimental data. The possible influence of the strain energy on coarsening is also discussed. Le travail que nous présentons concerne l'évolution de la forme d'un précipité cubique cohérent lorsqu'il grossit. Il était en effet nécessaire d'expliquer les observations expérimentales récentes montrant que les précipités de Ni 3Alγ' cuboïdaux, dans les alliages Ni-Al, résistent au grossissement et se décomposent en paires de plaquettes rectangulaires parallèles et en groupes de huit petits cubes. Le modèle théorique suppose que la phase cubique précipite avec une anisotropie élastique négative, et il néglige toute différence entre les constantes élastiques du précipité et de la matrice. On calcule alors l'énergie élastique du précipité en fonctio