AN APPROXIMATE CRITERION FOR LOSS OF COHERENCY IN MODULATED STRUCTURES

An analytical expression is given for predicting the maximum average wavelength λ0 that can be attained by a coherent periodic composition modulation in binary solid solutions. It is assumed in the derivation that the modulated structure is eventually replaced by noncoherent or semicoherent major and minor precipitating phases. The value of λ0 is shown to be inversely proportional to the first power of the quantity η, the fractional change in lattice parameter per unit change in composition, in agreement with available experimental data. The proposed criterion correctly predicts that solid solutions of average composition located near the center of the miscibility gap should yield a smaller value of λ0 than those located near the spinodal compositions. It is also suggested that, in systems for which the parameter η is large, greater than 10 per cent, say, loss of coherency could occur before the spinodal morphology can fully develop. © 1969.