It is seen that the higher constitutional cooling represents higher cooling rate. The cooling rate will increase when the composition increases. The cooling rate will increase from 4.5K/s to 8K/s when the composition Al increases from 0 to 100% under the constitutional temperature to be 30K. Meanwhile the bigger constitutional cooling causes smaller dendritic secondary arm space. The dendritic secondary arm space will decreases if composition increases too. The results are that the cooling rate increases from 4.1K, 4.7K to 5K if the constitutional cooling is from 100K, 200K to 300K respectively. The arm space will decrease from 10.2?m, 10?mK, 9.5?m to 9?m when the composition is 0 and then arm sapce will decrease from 5.5?m, 5.3?m, 5?m to 4.5?m when the composition is 100% under constitutional cooling increasing from 50K, 100K, 200K to 300K respectively.

The temperature and composition with constitutional supercoiling has been important in solidification of metal in materials research. So that the modelling on relationship between them are established to study the parameters on them in detail is significant in materials research and development. For the convenience the data adopted from phase diagram and experience to ensure the correction of them. The result has been found to be consistent with the experiment and practice well so the further search is been studied to look forwards to anticipating good effectiveness to instruct practice [1-9].

As we know the constitutional cooling is the important cooling which is different to usual cooling therefore the related search will be proceeded to find its role on solidification of metal. When it attains about the solid and liquid line the constitutional super cooling will be formed to drive the nuclear crystal to form. So it is important at the solidification course in special the original solidification to new crystal. Constitutional supercoiling is formed by solute redistribution to cause solute concentration change in front of solid and liquid interface which causes to change theoretical solidification temperature for forming the super cooling in interface liquid. The final problem in constitutional super cooling is the temperature difference which can attain the effectiveness directly and clearly. Whether the result fits to practice and how it fits has been one that affects the final destination in this research.  From line equation the cooling and constitutional super rcooling has been formed through phase diagram method. The constitutional cooling is checked through chart to find the difference with its change. As we knew the constitutional supercoiling benefits to the cooling course since its high temperature so the way to choose reasonable value is necessary. In this paper the dendritic secondary arm space is searched for constitutional super cooling which is our destination. How has it affected the cooling rate and dendritic secondary arm space, which is important? Because the three parameters is important in solidificative course it needs to be further searched that is necessary and significant. 

The curve is drawn according to modelling as below. Two parts are included. One is curve between cooling rate and composition and the other is the one between dentritic secondary arm spaces. As seen in Figure 1(a~d) the cooling rate will increase from 4.5K/s to 8K/s when the composition Al increases from 0 to 100% under the constitutional temperature to be 30K. The results are as below. The cooling rate increases from 4.4K, 4.7K to 5K if the constitutional cooling is from 100K, 200K to 300K respectively. The cooling rate will increase from 8.2K to 10K with increasing constitutional cooling increases from 100K to 300K. It expresses that the higher constitutional cooling represents higher cooling rate (Figure 1).

(a)     T; ?T=30K

(a)     T; ?T=100K

(a)     T; ?T=200K

(a)     T; ?T=300K

(a)     L; ?T=50K

(a)     L; ?T=100K

(a)     L; ?T=200K

(a)     L; ?T=300K

Figure 1: The relationship between the cooling rate and dentrite secondary arm space with composition under different constitutional super cooling.

As seen in Figure 1(e~h) the secondary arm space in dentrite will decrease too from 10.2?m to 5.5?m with increasing composition from 0 to 100%. The arm space will increase from 10.2?m, 10?mK, 9.5?m to 12.2?m when the composition is 0 and then arm sapce will increase from 6?m, 6.5?m, 6.8?m to 9?m when the composition is 100% under constitutional cooling increasing from 50K, 100K, and 200K to 300K respectively. It explains the bigger constitutional cooling cause’s smaller dendritic secondary arm space. In general from Figure 1(a~h) the cooling rate and dendrite secondary arm space has not been big which is about 1K/s and 0.5?m respectively. So it is speculated that the constitutional super cooling is a certain value. Since the matrix value is 10.2K/s and 10?m which is general value to compare with difference caused by constitutional super cooling.

It is seen that the higher constitutional cooling represents the higher cooling rate. The cooling rate increases with increasing composition. Meanwhile the bigger constitutional cooling causes smaller dentritic secondary arm space. The dentritic secondary arm space will decrease too with increasing composition. The cooling rate and dentrite secondary arm space has been small which is about 1K/s and 0.5?m respectively. So it is speculated that the constitutional supercooling is a certain value. Since the matrix value is 10.2K/s and 10?m which is small too to compare with difference caused by constitutional supercooling. 

This work was supported by the Korea of Science and Engineering Fund, under the Specified Base program?96-0300-11-01-3.

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