Proseso De Hall

160

BASIC SOLIDIFICATION CONCEPTS

Figure 6.12 Breakdown of a planar S/L interface during the solidification of pivalic acid–ethanol: (a) 0 s, (b) 120 s, (c) 210 s, (d) 270 s, (e) 294 s, (f) 338 s, (g) 378 s, (h) 456 s, (i) 576 s, and (j) 656 s. Reprinted from Liu and Kirkaldy (24). Copyright 1994 with permission from Elsevier Science.

similar to the constitutional supercooling theory arenot available for predicting the transitions from the cellular mode to the columnar dendritic mode and from the columnar dendritic mode to the equiaxed dendritic mode. Figure 6.12 is a series of photographs showing the breakdown of a planar S/L interface into a cellular one during the solidification of a pivalic acid alloyed with 0.32 mol % ethanol (24). The temperature gradient G was 15°C/mm, andthe growth rate R was suddenly raised to a higher level of 5.7 mm/s, to suddenly lower the G/R ratio and trigger the breakdown by constitutional supercooling.

6.3 6.3.1

MICROSEGREGATION AND BANDING Microsegregation

Solute redistribution during solidification results in microsegregation across cells or dendrite arms. The analysis of solute redistribution during the direc-MICROSEGREGATION AND BANDING

161

tional solidification of a liquid metal (Section 6.1) can be applied to solute redistribution during the solidification of an intercellular or interdendritic liquid during welding (or casting). The total volume of material in directional solidification (Figures 6.3–6.5) is now a volume element in a cell or a dendrite arm, as shown in Figure 6.13. Within the volume element theS/L interface is still planar even though the overall structure is cellular or dendritic. The volume element covers the region from the centerline of the cell or dendrite arm to the boundary between cells or dendrite arms. Solidification begins in the volume element when the tip of the cell or dendrite arm reaches the volume element. The case of the equilibrium partition ratio k < 1 is shown inFigure 6.14a. No segregation occurs when diffusion is complete in both the liquid and solid.
volume element L S (a) L S

(b)

Figure 6.13 Volume elements for microsegregation analysis: (a) cellular solidification; (b) dendritic solidification. complete liquid & solid diffusion complete liquid & solid diffusion

composition

composition

Co

k1

complete liquid diffusion, no soliddiffusion Co kCo Co kCo limited liquid diffusion, no solid diffusion distance

complete liquid diffusion, no solid diffusion

kCo Co

limited liquid diffusion, no solid diffusion distance

cell or dendrite arm

centerline of cell or dendrite arm

volume element (a)

boundary between cells or dendrite arms (b)

Figure 6.14 Microsegregation profiles across cells or dendrite arms: (a) k < 1;(b) k > 1.

cell or dendrite arm

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BASIC SOLIDIFICATION CONCEPTS

This requires that DLt >> l 2 and that DSt >> l 2, where l is now half the cell or dendrite arm spacing (the length of the volume element). Segregation is worst with complete diffusion in the liquid but no diffusion in the solid. This requires that DLt >> l 2 and that DSt 1 is shown in Figure 6.14b. The segregationprofiles are opposite to those of k < 1. Consider the case of a eutectic phase diagram, which is common among aluminum alloys. Assume complete liquid diffusion and no solid diffusion. As shown in Figure 6.15, the solid composition changes from kC0 to CSM, the maximum possible solute content in the solid, when the eutectic temperature TE is reached. The remaining liquid at this point has the eutecticcomposition

T

m L S

initial melt composition,Co (a) L S+L eutectic

T

Temperature, T

T T

S
E

kC

o

C

o

C SM CE

C E Concentration, C

C

Complete Liquid Diffusion (b) C L(f S)

C SM C

o

C S(f S) kC
o

fE 1

0 Fraction of Solid, f solid

s

volume element

eutectic

Figure 6.15 Solute redistribution during solidification with complete...