On primary dendritic spacing during unidirectional solidification

In-situ observations of directionally solidifying interface of typical transparent model alloys, succinonitrile-ethanol and succinonitrile-acetone, have been performed on a Hunt-Jackson type temperature gradient stage and a Bridgman apparatus, respectively. Experimental results show that there exists a wide allowable range of primary spacings for both the two-dimensional and the three-dimensional dendritic arrays under a given growth condition. The upper and lower limits of the allowable range are very sharp at the same current growth condition, while the average primary spacing is remarkably related to the history of variation of both temperature gradient and growth velocity. The upper limit, λ_max, and the lower one, λ_max, of the allowable range as a function of growth velocity, V, obtained from the experiments of step-increment and step-decrement in growth velocity, can be generally expressed as λ_max = AV^-b, λ_max = cV^-d, where a, b, c and d are constants for given alloy and temperature gradient. The lower limit obtained experimentally by us is compared with that calculated theoretically with the Hunt-Lu model and the Warren-Langer model; it shows an excellent fit between experimental results and the Hunt-Lu model, and good agreement between experimental results and the Warren-Langer model at the high growth velocity.