Title Analysis of an Equiaxed Dendrite Growth Model with Comparisons to In-Situ Results of Equiaxed Dendritic Growth in

The Lipton Glicksman Kurz (LGK) growth model is commonly used to predict growth rates for equiaxed dendrites in solidifying mushy zones. However, the original LGK method treats an isolated dendrite growing in an infinite volume of liquid. In an equiaxed mushy zone, with multiple nucleation events, thermal and solutal interactions take place between the equiaxed dendrites. A modified version of the LGK model was developed that allows for measurement of the solute build-up ahead of the dendrites. To investigate the validity of the model, comparisons are made with results obtained from in-situ synchrotron X-ray videomicroscopy of solidification in a Bridgman furnace of an Al-12wt.%Ge alloy inoculated with Al-Ti-B grain refiner. Comparisons between the original LGK and modified LGK models are presented for discussion. The modified LGK model shows realistic tip temperature trends. Introduction The LGK growth model [1] describes tip growth for an isolated equiaxed dendrite growing in an infinite volume of liquid. The LGK model uses the Ivantsov solution [2] to treat both the thermal and solutal diffusion fields around the parabolic solid-liquid interface. The LGK model also uses the marginal stability criterion [3] to determine the operating conditions at the dendrite tip. Ultimately the LGK model gives the total undercooling at the tip as the sum of solutal undercooling, thermal undercooling, and curvature undercooling. The solutal undercooling is calculated based on the nominal composition, which is assumed to exist in the liquid at an infinite distance ahead of the tip. The thermal undercooling is calculated based on the bath temperature at an infinite distance ahead of the tip. The curvature undercooling is calculated using the dendrite tip radius and the GibbsThomson effect at the curved surface. Trivedi and Kurz [4] show that if the temperature profile is assumed a priori then the Ivantsov solution is applied to the solutal problem only. In this case, only the solutal and curvature undercoolings are calculated. This approach is adopted in this research; hence, there is no requirement to calculate the thermal undercooling. Modified LGK Model. A modified version of the LGK model has been proposed [5] whereby the growth conditions at the tip are determined by measuring the solute level at a finite distance ahead of the dendrite. Since the solutal undercooling is calculated using the measured solutal level, solute build up in the liquid is accounted for. A modified Ivantsov solution is Iv(P,R,Z) = P e P {E1(P)-E1(P(1+2Z/R))}. (1) 2 R is the tip radius. Z is known as the look-ahead distance and it is the measured length ahead of the tip where the solute level is measured. P is the solutal peclet number and it is given as