Lecture 6: Solidification of Single Phase Alloys 1
Zone Melting Process of zone melting: Start with a solid alloy bar with uniform cross-section. Place the bar horizontally. Only melt the bar within a short zone with a small heater. Move the heater along the bar from one end to the other end. Repeat the process for many times. 2 Lecture 6: Solidification of Single Phase Alloys
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Zone melting is a widely used technique for purifying metals. We can derive the equation used to calculate the solute concentration distribution in the solid after the first pass. Assumptions: No solute diffusion in the solid Complete solute diffusion and mixing in the liquid zone. 4
From the mass balance, we have: (C L * - C S *)Adx + (Co C L *) Adx = AldC L *(1) l is the length of the liquid zone, A is the crosssection area of the bar. Equation (1) can be simplified to get: (Co C S *) dx = ldc L *(2) We know C S *=kc L *, so we can change equation (2) into: 5 k(co C S *) dx = ldc S *(3)
By integrating equation (3) and using boundary condition C S *=kco when x=0, we have: C S *= Co (1 - (1-k)e -kx/l )(4) 6
Equation (3) shows that C S * increases with x, so the starting end is purer than the finishing end. After many passes, C S * 0 in a portion of the bar near the starting end. This means that the metal in this portion is significantly purified. 7
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Morphological Instability of Solid/Liquid Interface We consider the solidification of a single phase alloy liquid in Situation 3. In the steady state, the solute concentration distribution in the liquid in front of the S/L interface is given by: (5) 9
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According to the binary phase diagram of the alloy, when C L changes with x, the liquidus temperature also changes. Since normally the liquidus line of the phase diagram can be taken as a straight line, we have the following relationship between T L and C L : T L = T m + m L C L (6) T m = the melting point of the pure base metal m L = the slope of the liquidus line. 11 Lecture 6: Solidification of Single Phase Alloys
By combining equations (5) and (6), we can get the equation used to determine how T L changes with x : (7) From equation (7), we can determine the slope of the T L -x curve at the S/L interface: (8) 12
To see whether the planar S/L interface is stable, we need to compare with the actual temperature gradient at the interface, G L. When G L, T T L at all points in front of the S/L interface. In this case, any accidental protrusion of the solid into the liquid ahead of the S/L interface will be melted back the planar S/L interface is stable. 13
When G L <, T<T L within a small region in front of the S/L interface. In this region, the liquid is undercooled. This undercooling is called constitutional undercooling, because it is caused by the distribution of the solute concentration in the liquid in front of the S/L interface. 14
Supercooled = undercooled 15
If accidental solid protrusion into the liquid occurs at some point, the protruded solid will meet the undercooled liquid, T i will become higher. Higher T i faster growth of the solid. The protruded solid grows faster than the base metal at the S/L interface the rough morphology of the S/L interface will be magnified rather than suppressed. This causes the planar S/L interface to become unstable. 16 Lecture 6: Solidification of Single Phase Alloys
Therefore, the criterion for the planar S/L interface to be stable is: From equation (6), this criterion can be rewritten as: (9) 17
When than is slightly smaller, cells will form. When <<, the undercooled liquid region in front of the S/L interface will be very large. In this case, solid dendrites will form. 18
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Dendritic Growth The general condition for dendritic growth: For directional solidification in situation 3, the condition can be expressed as: 22
The initiation of dendritic growth: Breakdown of unstable planar S/L interface perturbations. The tips of perturbations grow faster than their depressions due to constitutional undercooling the perturbations change from sinusoidal to cellular. The cell growth direction deviates towards the preferred crystallographic direction. For metals with a cubic crystal structure, this direction is <100>. 23
The figure is from 徐洲, Solute rich region 姚寿山主编, 材料加工原理 科技出版社, 2003..p69 Solute rich region 24
With further growth, the cells evolve into dendrite trunks. The liquid between the dendrite trunks is also undercooled perturbations form on the side surface of the dendrite. formation of secondary dendritic arms. The secondary arms also grow along the preferred crystallographic directions. Secondary arms are perpendicular to the primary dendrites for alloy phases with cubic crystal structures. 25
The figure is from 徐洲, 姚寿山主编, 材料加工原理 科技出版社, 2003. p70 The process of dendrite growth 26
The figure is from 徐洲, 姚寿山主编, 材料加工原理 科技出版社, 2003. p71 27 The growth of crystals with a cubic structure: (a) faceted growth, (b) non-faceted growth
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Similarly, tertiary and even higher order arms can form as well. 29
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Dendritic solidification of Cu-15wt%Sn alloy (bronze), which occurs when the solidification front becomes unstable with respect to small perturbations. This results in the growth of the perturbations, producing dendrites of the primary phase. Subsequently the secondary phase forms in the solute enriched melt between the dendrites. (http://www.doitpoms.ac.uk/miclib/micrograph_record.php?id=485, contributed by Dr R F Cochrane, Department of Materials, University of Leeds, UK) 31
After directional solidification of the Co-10at%Sm (samarium)-10at%cu alloy, the sample has been deeply etched with 10% nitric acid in ethyl alcohol (10%Nital) to remove the Sm and Cu enriched phases between the primary dendrites, revealing the dendritic morphology of the Co rich primary phase. (R. Glardon, W. Kurz, "Solidification path and phase diagram of directionally solidified Co-Sm-Cu alloys", J. Cryst. Growth, 51 (1981) 283-291) 32
Summary of the solidification conditions for different morphologies of the solid phase formed. 33
Secondary Dendrite Arm Spacing The average spacing between secondary dendrite arms, λ 2, is largely determined by the contact time between the arms and the liquid. This contact time is equal to the local solidification time, t S. The following relationship between λ 2 and t s, has been established through experimental study: λ 2 = Kt S 1/3 (10) 34 K is a constant.
Normally t S is defined as the time taken for a thermocouple tip placed at a fixed point to be passed by a growing dendrite from its tip to its root. For directional solidification, we have: (11) T S is the temperature range of the solidification T S can be measured from phase diagram 35
General points to be noted on secondary dendrite arm spacing: Measurement of the secondary dendrite arm spacing, λ 2, in casting can generally tell local solidification conditions, especially t S. Secondary dendrite arm spacing also has a significant effect on the mechanical properties of cast alloys. Reducing the secondary dendrite arm spacing higher strength, higher ductility and higher fracture toughness. 36
Formation of Equiaxed Grains When the magnitude of constitutional undercooling is sufficiently large, new crystals can nucleate in front of the dendrite trunks. Since the new crystals are in the middle of an undercooled liquid, dendrites can grow in all possible preferred crystallographic directions. This causes formation of equiaxed grains. 37
The figure is from 徐洲, 姚寿山主编, 材料加工原理 科技出版社, 2003. p70 38 Transition from dendritic columnar growth to dendritic growth of equiaxed grains
Under certain conditions (e.g. liquid convection), some growing dendrite arms are broken off to become crystal fragments. These crystal fragments can grow into equiaxed grains in the liquid as well. 39
Cast Microstructure of Ingots and Castings A typical cast microstructure normally consists of three distinguished zones: chill zone; columnar zone; equiaxed zone. Sometime one or two of the zones may be absent in the microstructure. 40
Schematic diagrams showing the typical cast microstructure of an ingot. 41
Chill zone Chill zone consists of a large number of small and equiaxed grains. It forms on the wall of mould at the beginning of solidification, due to the low temperature of the mould. Due to the high undercooling of the melt chilled by the cold mould surface, the nucleation rate is very high, so the grain size is very small. 42 With undercooled melt, it is likely to form equiaxed grains, since crystal growth is not limited by direction of heat flow.
Columnar zone Columnar zone consists of many coarse cells or dendrites aligned in one direction. It forms when only a limited number of grains in the chill zone can grow out of the chill zone and along the opposite direction of the heat flow. These columnar grains have preferred growth crystal orientations lying close to the opposite of the heat flow. 43
Heat flow Chill or wall of mould Only grains with favourable growth directions can grow away from the cold surface to form columnar zone 44
Equiaxed zone Equiaxed zone consists of a large number of equiaxed grains. It forms when nucleation can occur in front of S/L interface or solid crystal fragments can survive and grow in the liquid. 45 The condition for this is that: the liquid in front of S/L interface is undercooled because of constitutional undercooling; or the liquid is thermally undercooled.