Influence of uniaxial stress on the lamellar spacing of eutectics

Directional solidification of lamellar eutectic structures submitted to uni axial stress is investigated. In the spirit of an approximation first used by Jackson and Hunt, we calculate the stress tensor for a two-dimensional c rystal with triangular surface, using a Fourier expansion of the Airy funct ion. The effect of the resulting change in chemical potential is introduced into the standard model for directional solidification. This calculation i s motivated by an observation, made recently [I. Cantat, K. Kassner, C. Mis bah, and H. Muller-Krumbhaar, Phys. Rev. E 58, 6027 (1998)], that the therm al gradient produces similar effects as a strong gravitational field in the case of dilute-alloy solidification. Therefore, the coupling between the G rinfeld and the Mullins-Sekerka instabilities becomes strong, as the critic al wavelength of the former instability gets reduced to a value close to th at of the latter. Analogously, in the case of eutectics, the characteristic length scale of the Grinfeld instability should be reduced to a size not e xtremely far from typical lamellar spacings. Following Jackson and Hunt, we assume the selected wavelength to be determined by the minimum undercoolin g criterion and compute its shift due to the external stress. In addition, we find that in general the volume fraction of the two solid phases is chan ged by uniaxial stress. Implications for experiments on eutectics are discu ssed.