TAILIEUCHUNG - ASM Metals HandBook P6

Fig. 30 Alternative systems for showing phase relationships in multiphase regions of ternary diagram isothermal sections. (a) Tie lines. (b) Phase-fraction lines. Source: 84Mor 12 Solidification. Tie lines and the lever rule can be used to understand the freezing of a solid-solution alloy. | Fig. 30 Alternative systems for showing phase relationships in multiphase regions of ternary diagram isothermal sections. a Tie lines. b Phase-fraction lines. Source 84Mor 12 Solidification. Tie lines and the lever rule can be used to understand the freezing of a solid-solution alloy. Consider the series of tie lines at different temperatures shown in Fig. 29 b all of which intersect the bulk composition X. The first crystals to freeze have the composition ab As the temperature is reduced to T2 and the solid crystals grow more A atoms are removed from the liquid than B atoms thus shifting the composition of the remaining liquid to L2. Therefore during freezing the compositions of both the layer of solid freezing out on the crystals and the remaining liquid continuously shift to higher B contents and become leaner in A. Therefore for equilibrium to be maintained the solid crystals must absorb B atoms from the liquid and B atoms must migrate diffuse from the previously frozen material into subsequently deposited layers. When this happens the average composition of the solid material follows the solidus line to temperature T4 where it equals the bulk composition of the alloy. Coring. If cooling takes place too rapidly for maintenance of equilibrium the successive layers deposited on the crystals will have a range of local compositions from their centers to their edges a condition known as coring . The development of this condition is illustrated in Fig. 29 c . Without diffusion of B atoms from the material that solidified at temperature T1 into the material freezing at T2 the average composition of the solid formed up to that point will not follow the solidus line. Instead it will remain to the left of the solidus following compositions a 1 through a 5. Note that final freezing does not occur until temperature T5 which means that nonequilibrium solidification takes place over a greater temperature range than equilibrium freezing. Because most metals freeze by the .

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