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Directional Solidification
Directional Solidification The term ‘‘directional solidification’’ (DS) was coined during the development of superalloys when conventional investment casting of turbine blades was substituted with more sophisticated techniques. By DS columnar grain structures could be produced showing anisotropic properties with a dramatically improved creep resistance in the highly stressed longitudinal direction of the blades. DS has several aspects related to microstructural and chemical control of technical castings, but is also part of the fundamentals of solidification processing. 1. Experimental Techniques DS will occur when the latent heat generated at the solid\liquid interface during freezing is extracted through the solid (or parts with a high solid fraction) in only one spatial direction, and nucleation of additional crystals in front of the solidification front is suppressed. Several principal techniques, shown in Fig. 1, with a number of variations are employed for DS (Flemings 1974, Kurz and Sahm 1975, Piwonka 1988, Biloni and Boettinger 1996, Kurz and Fisher 1998). 1.1 Normal Freezing The Bridgman method (vertical normal freezing, Fig.
1(a)) uses a crucible containing the melt. It is moved in a vertical temperature gradient toward cooler regions of the furnace. For the production of single crystals, solidification generally begins at the bottom of the crucible where a seed is located. The Chalmers method (horizontal normal freezing, Fig. 1(b)) uses a boat that is drawn through a horizontal furnace. Crystal growth occurs from a seed at one side of the boat. Compared to vertical freezing, convection and the related disturbances of the solidification front are more difficult to control, but, if appropriate, the liquid can be decanted by electromagnetic devices. A slight variation on these types of normal freezing techniques uses an arrangement where neither the furnace nor the crucible is moving. A seed is placed at the cold end of a temperature gradient furnace whose overall temperature is lowered at a controlled rate. 1.2 Crystal Pulling This method is also termed the Czochralski method (Fig. 1(c)). It is the most important technique for practical applications. The supply of liquid is large compared to the growing crystal. A seed crystal is lowered from above into the melt and then slowly withdrawn, often with simultaneous rotation in order to maintain axial symmetry of the crystal. The large volume of the bulk liquid and the thermal convection that is always present allow for the growth of crystals with a constant and uniform composition. Significant (b)
(d)
(c)
(e)
(a)
Figure 1 Directional solidification facilities: (a) Bridgman (vertical normal freezing); (b) Chalmers (horizontal normal freezing); (c) Czochralski (crystal pulling); (d) zone refining; (e) chill casting. , direction of heat flow; , direction of movement.
1
Directional Solidification advantages of this technique are that the crystal has no contact with the crucible (avoiding contamination), and that convection needs to be controlled, but not suppressed.
1.3 Zone Melting In zone melting (Fig. 1(d)) or zone-freezing, only a part of the solid is molten. Local heating using resistance or induction furnaces, electron or laser beams, among others, can be applied. The heat source is moved relative to the axis of the cylindrical solid. The technique of containerless zone melting, also termed the floating-zone method, can be used advantageously if the liquid zone is short enough to be held by surface tension, sometimes in combination with a magnetic field. In other cases a crucible is used.
1.4 Chill Casting In this method, the liquid is cast on a chill plate (Fig. 1(e)). All surfaces of the cast part except the chill plate are thermally insulated. Chill casting is used to produce columnar structures. As compared to the aforementioned methods there is less control concerning temperature gradient and solidification front velocity.
2. Morphology of the Solidification Front and Microsegregation During DS a variety of solidification morphologies can be generated. A pure metal will generally solidify with a planar front. If alloying elements are added, the morphology of the solidification front is determined by the temperature gradient, G, and the growth velocity, , on the one hand, and the physical and thermodynamic properties of the material on the other hand. In order to simplify the following considerations, a binary alloy represented by a simple equilibrium phase diagram (shown schematically in Fig. 2(c)) is considered. If a melt of uniform composition, c , is moved in the furnace toward cooler temperatures, it! begins to solidify when the temperature drops just below the liquidus temperature, TL (provided a seed crystal is used or nucleation occurs readily). The composition of the first-forming solid, cs, , differs from c by a factor k, the partition coefficient. !The partition ! coefficient, k, is defined by the ratio of equilibrium concentrations in the liquid and solid at a given temperature, k l cs\cl. A considerable amount of work (Flemings 1974, Sahm and Schubert 1979, Biloni and Boettinger 1996, Kurz and Fisher 1998, Rappaz and Rettenmayr 1998) has been, and is still being, carried out into the understanding of the quantitative relationships be2
tween the main processing variables (alloy composition, c , G, and ) and the intermediate and final states of! the cast structure (morphology of the solidification front, type and amount of the resulting phases, microstructural geometry, and micro- and macrosegregation, i.e., local variations of chemical composition). For the type of phase diagram shown in Fig. 2(c), the solid is purer (lower in solute concentration) than the liquid (i.e., k 1) and the solute element will be rejected into the liquid and enriched at the solidification front. At typical diffusivities and cooling rates, a concentration gradient develops in front of the interface ((2) in Fig. 2(b)) causing a local distribution of liquidus temperatures ((4) in Fig. 2(d)). If the actual temperature gradient is steep ((1) in Figs. 2(b) and (e)), the local temperature in front of the interface is higher than the local liquidus temperature, and irregularities will melt back, stabilizing a planar interface. However, a flat temperature gradient ((5) in Fig. 2(e)) gives rise to the so-called constitutional undercooling: the actual temperature at positions in front of the interface is lower than the local liquidus temperature (hatched area in Fig. 2(e)). In the region of constitutional undercooling, irregularities in the interface amplify, and cells or dendrites form (Fig. 2(f)). The concept of constitutional undercooling is a simplified semiquantitative criterion for the stability of a growing interface. Obviously, there are more stabilizing and destabilizing terms as, for example, the increase of total interface energy when the interface becomes nonplanar. As in the course of solidification the temperature is decreasing, the melt is enriched in the solute element, leading in turn to an increasing solute concentration of the solidifying crystal (see phase diagram in Fig. 2(c)). As a consequence, the development of the dendritic or cellular growth morphology can be seen in the distribution of the solute concentration in which the isoconcentration lines also assume dendritic (Fig. 3) or cellular patterns. This effect is termed microsegregation or crystal segregation. It is of importance for the properties of the material, and numerical procedures have become available which describe the morphology of the solid\ liquid interface, the resulting microstructure, and the local variations of solute composition. Calculated patterns have been shown to be in close agreement to experimental findings. In these simulations, most if not all of the physical processes and parameters of influence as, for example, back diffusion in the solid, various undercooling terms, and dendrite arm coarsening, among others, are considered (Rappaz and Rettenmayr 1998). The influence of and G on the solidification morphology is shown in Fig. 4. High temperature gradient and slow interface velocity (i.e., high values of G\) favor plane front growth. Reducing the G\ ratio leads first to cellular, then to columnar dendritic, and finally to equiaxed dendritic growth. When both
Directional Solidification
(c)
(e)
(d)
(f )
(a)
(b)
Figure 2 Morphological stability of a solid\liquid interface (principle of constitutional undercooling). A sample (a) is moved in a temperature gradient (b,1). Under steady state conditions, the interface moves at a constant temperature T* (b,c). Due to the higher solubility of solute in the liquid (cLM,(c)) as compared to the solid (cSM l c ), solute atoms pile up in front of the moving interface, leading to a concentration profile as shown in (b,2). The liquidus! temperatures corresponding to the concentrations in profile (2) are given by liquidus curve (c,3) in the phase diagram. In front of the moving interface, the profile of liquidus temperatures (d,4) applicable for the concentrations in (b,2) can be compared with actual (experimental) temperature profiles (e). For a high temperature gradient (e,1), the liquidus temperature is lower than the actual temperature at all locations. The liquid is the stable phase, and the alloy solidifies with a plane front. In the case of a low temperature gradient (e,5), there is a region (hatched in (e)) where the actual temperature is lower than the liquidus temperature (‘‘constitutional undercooling’’), i.e., there is a driving force for solidification. In the undercooled region, a perturbation (i.e., a small deviation from planarity at the interface) will grow faster than the rest of the solidification front, leading to a cellular or dendritic microstructure (f).
and G at a given ratio G\ are increased (equivalent to increasing the cooling rate, TI , since TI l G), the same morphology solidifies at a finer length scale.
3. Technological Applications of DS DS is used in a number of technical applications. Examples are the production of highly elongated polycrystals or single crystals in multicomponent alloys, and ultrapure and uniformly alloyed crystals.
3.1 DS of Turbine Blades The development of the high-temperature strength of nickel-based superalloys has seen several important steps related to improvements of casting technology (Kurz and Sahm 1975, Gell et al. 1980, Higginbotham 1986, Piwonka 1988, Svoboda 1988, Goldschmidt 1994). The first two of these steps concerned the increase of volume fraction and the optimization of the morphology of the strengthening γh-phase in polycrystalline blades (Fig. 5(CC)). The third step, the introduction of DS (using the mould translation process that is still the major technique in this
application) considered the fact that grain boundaries are the weakening defects for both creep and crack propagation at high temperatures. From the grain boundaries, those oriented perpendicular to the major stress component (which, owing to centrifugal loading, is parallel to the longitudinal direction of turbine blades) are the most dangerous ones for early failure. By DS, essentially all transverse grain boundaries are eliminated, and a fiber texture with all grains oriented in f100g direction (the preferred growth direction for cubic metals and, hence, nickel alloys) was obtained (Fig. 5(DS)). The fourth step was to eliminate the remaining longitudinal grain boundaries by applying a grain selector to produce a single crystal (Fig. 5(SC)). Grain-boundary strengthening by carbides is then superfluous, the alloy can be solution treated at higher temperatures, and higher percentages of γh-phase can be precipitated yielding higher strength. In addition to applying the fundamental knowledge about the relationship between basic processing parameters, solidification morphology, and microsegregation as discussed above, defects need to be controlled. The governing factors for the required low amounts of residual porosity are a low gas content, a low velocity of mould translation, a high temperature gradient in the furnace, and an alloy composition 3
Directional Solidification
Figure 3 SEM micrograph of the microstructure in a directionally solidified Al–6.8 wt. %Cu alloy. The contrast of backscattered electrons reveals the microsegregation (light centers of dendrites, low Cu content; gray regime, higher Cu content; dark, eutectic).
away completely), they act as nuclei for new grains, either forming chains in interdendritic channels (‘‘freckles’’) or single grains at arbitrary locations of the turbine blade (‘‘spurious crystals’’). Avoiding freckles and spurious crystals requires the optimization of all processing parameters for each individual alloy. Slight variations of initial concentration, solidification velocity, or temperature gradient can lead to failure rates exceeding 50%. The success of these developments can best be demonstrated by the fact that, with the introduction of DS, the temperature at which test samples endure a stress level of 140 MPa for 100 hours could be increased by more than 100 K (from about 1000 mC to 1100 mC). This resulted in larger safety margins with respect to fatigue fracture, creep, and overloading or, if the alloys are used to their limits, in a dramatic increase of the specific efficiency (energy output per unit weight) of turbine engines. The higher corrosion resistance is an additional advantage of DS cast single crystal blades. There may be a further step of improvement in the near future as the state of the art of numerical modeling has reached a level of sophistication which seems to permit a thorough optimization of the microstructural parameters as well as a quantitative understanding of defect formation.
3.2 DS of Semiconductor Crystals
Figure 4 Growth morphologies during directional solidification.
which leads to a small interval between solidus and liquidus temperatures and a high amount of residual eutectic. Microporosity in single crystals is generally smaller than in polycrystalline parts owing to the fact that gas bubbles can escape through the melt during slow solidification, and shrinkage is compensated for by the melt flow back through the short region in which solid and liquid phase are co-existing (‘‘mushy zone,’’ see Fig. 2(c)). Freckles and spurious crystals are a consequence of convection through the mushy zone. Due to local concentration and\or temperature changes, secondary dendrite arms can melt off at their root. If not carried away by the melt flow into hot liquid regions (melting 4
The preparation of ultrapure or uniformly alloyed semiconductor crystals (e.g., silicon and gallium arsenide) is an essential process in the production of electronic devices. For use in the electronic industry, extremely high requirements in terms of defect density, purity, and\or homogeneity must be met. Large crystals of very high lattice perfection with very low or controlled and uniformly distributed amounts of dopants can at present only be produced by directional growth from the melt. Two routes are used to manufacture silicon single crystals (Wilkes 1996). The first of these, free-floating zone refining, was introduced in the early 1950s. Polycrystalline rods of 2–3 m in length are used to prepare essentially dislocation-free crystals of up to 300 mm diameter and a purity level close to that of the input material. Defect densities are lower and resistivities are higher than those of Czochralski-grown crystals. Doping of floating-zoned silicon can be achieved during DS by adding gaseous species (PH , $ B H ) to the argon gas flowing through the furnace. In # ' this way, close specifications in a wide range of n- and p-type materials are obtained. Supply of semiconductor silicon (several million kilograms per year) is, however, dominated by the second manufacturing route, that of crystal pulling, which has seen a dramatic increase of charge weights from a few hundred grams in the early 1960s to 100 kg in the late 1990s, with
Directional Solidification
Figure 5 Turbine blades manufactured under different processing conditions: left, conventionally cast (CC); middle, directionally solidified polycrystal (DS); right, directionally solidified single crystal (SC).
dislocation densities dropping from about 10' cmV# to close to zero density. Magnetic fields are used to dampen out convection and to achieve higher growth rates. A further refinement is the push–pull process in which a solid of required composition is pushed into the melt at a controlled velocity while, at the same time, the crystal is pulled from the melt. Semiconductor compounds can be purified by zonerefining, as the conditions for high efficiency (low solubility of impurity elements and easy crystallization) are met by such strongly bonded materials. However, each compound carries its own difficulties (Mullin 1996): the varying effective k value of tellurium and the high volatility of zinc cause problems
in purifying InSb and GaSb, the high reactivity of gallium–arsenic melts attacks the container, or the very high vapor pressures of all the elements in II–IV compounds as well as of the compounds themselves lead to changes in the overall composition. Crystals of semiconductor compounds are grown by all available DS techniques. Horizontal growth of GaAs yields dislocation densities of 10# cmV# which is about two orders of magnitude less than that of vertically pulled conventional crystals, but contamination from the boat walls is a problem here. Special techniques (like low- and high-pressure liquid encapsulated Czochralski pulling) have been developed to high sophistication in order to avoid defects like faceting, 5
Directional Solidification anisotropic segregation, twinning, dislocations, and small-angle grain boundaries. Microgravity experiments were conducted to reduce or completely avoid effects like regular or irregular changes of composition (striations), but appropriate means are as effective in a normal gravity environment. The potential of zone-melting for purification and homogeneous solute distribution, described in detail by Pfann (1966), was recognized first at Bell Laboratories in 1952. The floating zone is enriched by the impurities if the partition coefficient is smaller than unity. This is the case in the majority of metal alloys. Part of the impurities can be removed when the floating zone, after moving through the sample, reaches its end. By passing the floating zone several times through the sample, more and more of the impurities can be cut off. The main limitation to the purification of most metals is then impurities from the container (crucible). The solute or impurity distribution after a certain number of passes depends on the thermal field in the sample which, in turn, sets the amount of back diffusion in the solid, convection in the liquid, and the width of the liquid zone. A high solubility of impurities in the matrix, i.e., a partition coefficient close to unity, requires a high number of passes for a complete purification with the abovementioned limitation. To remove the impurities to the required degree in an alloy with a partition coefficient k l 0.95 will take several thousand passes, and more than half of the sample will have to be cut away. Controlled uniform alloying can be achieved by using a pure solid and feeding the alloying element into the floating zone so that the composition of the melt is constant throughout the pass from one end to the other. A technically less demanding method is single pass zone leveling. An appropriate amount of alloying element is added to the molten zone at one end of the sample. After an initial transient, a steady state is reached and a uniform distribution is achieved over a considerable part of the sample. The transient zones can be shortened by passing the floating zone back and forth several times.
3.3 Other Applications of DS Convection in the melt has been investigated thoroughly in connection with investigating the possibilities of producing functionally graded materials by DS (Siber et al. 1999). The main effect of convection is a reduction of the gradients of temperature and concentration, leading to generally less pronounced microsegregation. However, strong (forced or gravity driven) convection together with a steep temperature gradient has been shown to aid in establishing a longrange compositional gradient (usually termed macrosegregation). This is tied to significant differences in local mechanical properties of the solidified sample. In Fig. 6, gradients of mechanical properties owing 6
Figure 6 Change of hardness and crack propagation rate in a directionally solidified Al–Mg–Zn alloy. Strong convectional mixing of the melt leads to macroscopic gradients of concentration and properties.
to macroscopic concentration gradients in a ternary Al–Zn–Mg alloy are shown. Enhanced by precipitation hardening, the hardness varies systematically from 30 to 130 HV in the binary and from 40 to 200 HV in the ternary alloy, with even stronger effects on the crack propagation rates which vary by factors of up to two orders of magnitude. DS is also of interest for alloys in the composition range of eutectic, monotectic, and peritectic reactions (Kurz and Sahm 1975, Biloni and Boettinger 1996). As during eutectic solidification two (or more) phases tend to solidify simultaneously (coupled or cooperative), eutectics have been investigated extensively in connection with attempts to produce in situ composite materials with plate or fiber morphology. The spacing of eutectic structures decreases with increasing undercooling, cooling rate, or growth velocity. Thus, DS was considered an interesting route for producing composite materials with optimized fiber dimensions. An example is the (Co,Cr)-(Co,Cr) C eutectic which ( $ has a higher creep resistance than conventionally cast superalloys. However, due to difficulties in controlling directional growth with continuous needles or plates, this route has not been successful on an industrial scale and therefore has been abandoned. Very little information is available on directionally solidified peritectic alloys, and technical exploitation of DS does not seem obvious for two-phase or multiphase alloys. 4. Conclusions The possibility of varying the processing parameters independently ensures that DS will remain one of the widely used experimental methods in fundamental research on growth kinetics of the majority of solidification morphologies. In addition, the large number of highly interacting parameters makes crystal growth by directional solidification a complex but versatile technology to meet the stringent product
Directional Solidification requirements for high-technology applications. As in the past, new applications of DS as well as new techniques and devices for DS will emerge from the increasing demands for high-purity, low-defect single crystals and for cast parts with precisely adjusted microstructural geometry and carefully controlled solute distributions. See also: Solidification of Superalloys Bibliography Biloni H, Boettinger W J 1996 Solidification. In: Cahn R W, Haasen P (eds.) Physical Metallurgy, Part I, 4th edn. North Holland, Amsterdam, Chap. 8, pp. 669–842 Flemings M C 1974 Solidification Processing. McGraw-Hill, New York Gell M, Duhl D N, Giamei A F 1980 The development of single crystal superalloys. In: Superalloys 1980. American Society for Metals, Metals Park, OH, pp. 205–24 Goldschmidt D 1994 Einkristalline Gasturbinenschaufeln aus Nickelbasislegierungen, Teil I: Herstellung und Mikrogefu$ ge (Single-crystal blades for gas turbines: I. Casting processes and microstructure). Materialwiss. Werkstofftech. 25, 311–20 Higginbotham G J S 1986 From research to cost effective directional solidification and single crystal production—an integrated approach. Mater. Sci. Technol. 2, 442–60 Kurz W, Fisher D J 1998 Fundamentals of Solidification, 4th edn. Trans Tech, Uetikon-Zu$ rich, Switzerland
Kurz W, Sahm P R 1975 Gerichtet erstarrte eutektische Werkstoffe (Directionally Solidified Eutectic Materials). Springer, Berlin Mullin J B 1996 Compound semiconductor processing. In: Cahn R W, Haasen P, Kramer E J (eds.) Processing of Semiconductors. VCH, Weinheim, Germany, pp. 63–105 Pfann W G 1966 Zone Melting. Wiley, New York Piwonka T S 1988 Directional and monocrystal solidification In: Metals Handbook, 9th edn. American Society for Metals. Metals Park, OH, Vol. 15, pp. 319–23 Rappaz M, Rettenmayr M 1998 Simulation of solidification. Curr. Opin. Solid State Mater. Sci. 3, 275–82 Sahm P R, Schubert F 1979 Solidification phenomena and properties of cast and welded microstructures. In: Solidification and Casting of Metals. Metals Society, London , pp. 389–400 Siber B, Rettenmayr M, Mu$ ller C, Exner H E 1999 Concentration gradients in aluminium alloys generated by directional solidification and their effects on fatigue crack propagation In: Kaysser W (ed.) Functionally Graded Materials. Trans Tech, Uetikon-Zu$ rich, Switzerland, pp. 211–16 Svoboda J M 1988 Nickel and nickel alloys. In: Metals Handbook, 9th edn. American Society for Metals. Metals Park, OH , Vol. 15, pp. 815–23 Wilkes J G 1996 Silicon processing. In: Cahn R W, Haasen P, Kramer E J (eds.) Processing of Semiconductors. VCH, Weinheim, Germany, pp. 1–62
M. Rettenmayr and H. E. Exner
Copyright ' 2001 Elsevier Science Ltd. All rights reserved. No part of this publication may be reproduced, stored in any retrieval system or transmitted in any form or by any means : electronic, electrostatic, magnetic tape, mechanical, photocopying, recording or otherwise, without permission in writing from the publishers. Encyclopedia of Materials : Science and Technology ISBN: 0-08-0431526 pp. 2183–2189 7
1(a)) uses a crucible containing the melt. It is moved in a vertical temperature gradient toward cooler regions of the furnace. For the production of single crystals, solidification generally begins at the bottom of the crucible where a seed is located. The Chalmers method (horizontal normal freezing, Fig. 1(b)) uses a boat that is drawn through a horizontal furnace. Crystal growth occurs from a seed at one side of the boat. Compared to vertical freezing, convection and the related disturbances of the solidification front are more difficult to control, but, if appropriate, the liquid can be decanted by electromagnetic devices. A slight variation on these types of normal freezing techniques uses an arrangement where neither the furnace nor the crucible is moving. A seed is placed at the cold end of a temperature gradient furnace whose overall temperature is lowered at a controlled rate. 1.2 Crystal Pulling This method is also termed the Czochralski method (Fig. 1(c)). It is the most important technique for practical applications. The supply of liquid is large compared to the growing crystal. A seed crystal is lowered from above into the melt and then slowly withdrawn, often with simultaneous rotation in order to maintain axial symmetry of the crystal. The large volume of the bulk liquid and the thermal convection that is always present allow for the growth of crystals with a constant and uniform composition. Significant (b)
(d)
(c)
(e)
(a)
Figure 1 Directional solidification facilities: (a) Bridgman (vertical normal freezing); (b) Chalmers (horizontal normal freezing); (c) Czochralski (crystal pulling); (d) zone refining; (e) chill casting. , direction of heat flow; , direction of movement.
1
Directional Solidification advantages of this technique are that the crystal has no contact with the crucible (avoiding contamination), and that convection needs to be controlled, but not suppressed.
1.3 Zone Melting In zone melting (Fig. 1(d)) or zone-freezing, only a part of the solid is molten. Local heating using resistance or induction furnaces, electron or laser beams, among others, can be applied. The heat source is moved relative to the axis of the cylindrical solid. The technique of containerless zone melting, also termed the floating-zone method, can be used advantageously if the liquid zone is short enough to be held by surface tension, sometimes in combination with a magnetic field. In other cases a crucible is used.
1.4 Chill Casting In this method, the liquid is cast on a chill plate (Fig. 1(e)). All surfaces of the cast part except the chill plate are thermally insulated. Chill casting is used to produce columnar structures. As compared to the aforementioned methods there is less control concerning temperature gradient and solidification front velocity.
2. Morphology of the Solidification Front and Microsegregation During DS a variety of solidification morphologies can be generated. A pure metal will generally solidify with a planar front. If alloying elements are added, the morphology of the solidification front is determined by the temperature gradient, G, and the growth velocity, , on the one hand, and the physical and thermodynamic properties of the material on the other hand. In order to simplify the following considerations, a binary alloy represented by a simple equilibrium phase diagram (shown schematically in Fig. 2(c)) is considered. If a melt of uniform composition, c , is moved in the furnace toward cooler temperatures, it! begins to solidify when the temperature drops just below the liquidus temperature, TL (provided a seed crystal is used or nucleation occurs readily). The composition of the first-forming solid, cs, , differs from c by a factor k, the partition coefficient. !The partition ! coefficient, k, is defined by the ratio of equilibrium concentrations in the liquid and solid at a given temperature, k l cs\cl. A considerable amount of work (Flemings 1974, Sahm and Schubert 1979, Biloni and Boettinger 1996, Kurz and Fisher 1998, Rappaz and Rettenmayr 1998) has been, and is still being, carried out into the understanding of the quantitative relationships be2
tween the main processing variables (alloy composition, c , G, and ) and the intermediate and final states of! the cast structure (morphology of the solidification front, type and amount of the resulting phases, microstructural geometry, and micro- and macrosegregation, i.e., local variations of chemical composition). For the type of phase diagram shown in Fig. 2(c), the solid is purer (lower in solute concentration) than the liquid (i.e., k 1) and the solute element will be rejected into the liquid and enriched at the solidification front. At typical diffusivities and cooling rates, a concentration gradient develops in front of the interface ((2) in Fig. 2(b)) causing a local distribution of liquidus temperatures ((4) in Fig. 2(d)). If the actual temperature gradient is steep ((1) in Figs. 2(b) and (e)), the local temperature in front of the interface is higher than the local liquidus temperature, and irregularities will melt back, stabilizing a planar interface. However, a flat temperature gradient ((5) in Fig. 2(e)) gives rise to the so-called constitutional undercooling: the actual temperature at positions in front of the interface is lower than the local liquidus temperature (hatched area in Fig. 2(e)). In the region of constitutional undercooling, irregularities in the interface amplify, and cells or dendrites form (Fig. 2(f)). The concept of constitutional undercooling is a simplified semiquantitative criterion for the stability of a growing interface. Obviously, there are more stabilizing and destabilizing terms as, for example, the increase of total interface energy when the interface becomes nonplanar. As in the course of solidification the temperature is decreasing, the melt is enriched in the solute element, leading in turn to an increasing solute concentration of the solidifying crystal (see phase diagram in Fig. 2(c)). As a consequence, the development of the dendritic or cellular growth morphology can be seen in the distribution of the solute concentration in which the isoconcentration lines also assume dendritic (Fig. 3) or cellular patterns. This effect is termed microsegregation or crystal segregation. It is of importance for the properties of the material, and numerical procedures have become available which describe the morphology of the solid\ liquid interface, the resulting microstructure, and the local variations of solute composition. Calculated patterns have been shown to be in close agreement to experimental findings. In these simulations, most if not all of the physical processes and parameters of influence as, for example, back diffusion in the solid, various undercooling terms, and dendrite arm coarsening, among others, are considered (Rappaz and Rettenmayr 1998). The influence of and G on the solidification morphology is shown in Fig. 4. High temperature gradient and slow interface velocity (i.e., high values of G\) favor plane front growth. Reducing the G\ ratio leads first to cellular, then to columnar dendritic, and finally to equiaxed dendritic growth. When both
Directional Solidification
(c)
(e)
(d)
(f )
(a)
(b)
Figure 2 Morphological stability of a solid\liquid interface (principle of constitutional undercooling). A sample (a) is moved in a temperature gradient (b,1). Under steady state conditions, the interface moves at a constant temperature T* (b,c). Due to the higher solubility of solute in the liquid (cLM,(c)) as compared to the solid (cSM l c ), solute atoms pile up in front of the moving interface, leading to a concentration profile as shown in (b,2). The liquidus! temperatures corresponding to the concentrations in profile (2) are given by liquidus curve (c,3) in the phase diagram. In front of the moving interface, the profile of liquidus temperatures (d,4) applicable for the concentrations in (b,2) can be compared with actual (experimental) temperature profiles (e). For a high temperature gradient (e,1), the liquidus temperature is lower than the actual temperature at all locations. The liquid is the stable phase, and the alloy solidifies with a plane front. In the case of a low temperature gradient (e,5), there is a region (hatched in (e)) where the actual temperature is lower than the liquidus temperature (‘‘constitutional undercooling’’), i.e., there is a driving force for solidification. In the undercooled region, a perturbation (i.e., a small deviation from planarity at the interface) will grow faster than the rest of the solidification front, leading to a cellular or dendritic microstructure (f).
and G at a given ratio G\ are increased (equivalent to increasing the cooling rate, TI , since TI l G), the same morphology solidifies at a finer length scale.
3. Technological Applications of DS DS is used in a number of technical applications. Examples are the production of highly elongated polycrystals or single crystals in multicomponent alloys, and ultrapure and uniformly alloyed crystals.
3.1 DS of Turbine Blades The development of the high-temperature strength of nickel-based superalloys has seen several important steps related to improvements of casting technology (Kurz and Sahm 1975, Gell et al. 1980, Higginbotham 1986, Piwonka 1988, Svoboda 1988, Goldschmidt 1994). The first two of these steps concerned the increase of volume fraction and the optimization of the morphology of the strengthening γh-phase in polycrystalline blades (Fig. 5(CC)). The third step, the introduction of DS (using the mould translation process that is still the major technique in this
application) considered the fact that grain boundaries are the weakening defects for both creep and crack propagation at high temperatures. From the grain boundaries, those oriented perpendicular to the major stress component (which, owing to centrifugal loading, is parallel to the longitudinal direction of turbine blades) are the most dangerous ones for early failure. By DS, essentially all transverse grain boundaries are eliminated, and a fiber texture with all grains oriented in f100g direction (the preferred growth direction for cubic metals and, hence, nickel alloys) was obtained (Fig. 5(DS)). The fourth step was to eliminate the remaining longitudinal grain boundaries by applying a grain selector to produce a single crystal (Fig. 5(SC)). Grain-boundary strengthening by carbides is then superfluous, the alloy can be solution treated at higher temperatures, and higher percentages of γh-phase can be precipitated yielding higher strength. In addition to applying the fundamental knowledge about the relationship between basic processing parameters, solidification morphology, and microsegregation as discussed above, defects need to be controlled. The governing factors for the required low amounts of residual porosity are a low gas content, a low velocity of mould translation, a high temperature gradient in the furnace, and an alloy composition 3
Directional Solidification
Figure 3 SEM micrograph of the microstructure in a directionally solidified Al–6.8 wt. %Cu alloy. The contrast of backscattered electrons reveals the microsegregation (light centers of dendrites, low Cu content; gray regime, higher Cu content; dark, eutectic).
away completely), they act as nuclei for new grains, either forming chains in interdendritic channels (‘‘freckles’’) or single grains at arbitrary locations of the turbine blade (‘‘spurious crystals’’). Avoiding freckles and spurious crystals requires the optimization of all processing parameters for each individual alloy. Slight variations of initial concentration, solidification velocity, or temperature gradient can lead to failure rates exceeding 50%. The success of these developments can best be demonstrated by the fact that, with the introduction of DS, the temperature at which test samples endure a stress level of 140 MPa for 100 hours could be increased by more than 100 K (from about 1000 mC to 1100 mC). This resulted in larger safety margins with respect to fatigue fracture, creep, and overloading or, if the alloys are used to their limits, in a dramatic increase of the specific efficiency (energy output per unit weight) of turbine engines. The higher corrosion resistance is an additional advantage of DS cast single crystal blades. There may be a further step of improvement in the near future as the state of the art of numerical modeling has reached a level of sophistication which seems to permit a thorough optimization of the microstructural parameters as well as a quantitative understanding of defect formation.
3.2 DS of Semiconductor Crystals
Figure 4 Growth morphologies during directional solidification.
which leads to a small interval between solidus and liquidus temperatures and a high amount of residual eutectic. Microporosity in single crystals is generally smaller than in polycrystalline parts owing to the fact that gas bubbles can escape through the melt during slow solidification, and shrinkage is compensated for by the melt flow back through the short region in which solid and liquid phase are co-existing (‘‘mushy zone,’’ see Fig. 2(c)). Freckles and spurious crystals are a consequence of convection through the mushy zone. Due to local concentration and\or temperature changes, secondary dendrite arms can melt off at their root. If not carried away by the melt flow into hot liquid regions (melting 4
The preparation of ultrapure or uniformly alloyed semiconductor crystals (e.g., silicon and gallium arsenide) is an essential process in the production of electronic devices. For use in the electronic industry, extremely high requirements in terms of defect density, purity, and\or homogeneity must be met. Large crystals of very high lattice perfection with very low or controlled and uniformly distributed amounts of dopants can at present only be produced by directional growth from the melt. Two routes are used to manufacture silicon single crystals (Wilkes 1996). The first of these, free-floating zone refining, was introduced in the early 1950s. Polycrystalline rods of 2–3 m in length are used to prepare essentially dislocation-free crystals of up to 300 mm diameter and a purity level close to that of the input material. Defect densities are lower and resistivities are higher than those of Czochralski-grown crystals. Doping of floating-zoned silicon can be achieved during DS by adding gaseous species (PH , $ B H ) to the argon gas flowing through the furnace. In # ' this way, close specifications in a wide range of n- and p-type materials are obtained. Supply of semiconductor silicon (several million kilograms per year) is, however, dominated by the second manufacturing route, that of crystal pulling, which has seen a dramatic increase of charge weights from a few hundred grams in the early 1960s to 100 kg in the late 1990s, with
Directional Solidification
Figure 5 Turbine blades manufactured under different processing conditions: left, conventionally cast (CC); middle, directionally solidified polycrystal (DS); right, directionally solidified single crystal (SC).
dislocation densities dropping from about 10' cmV# to close to zero density. Magnetic fields are used to dampen out convection and to achieve higher growth rates. A further refinement is the push–pull process in which a solid of required composition is pushed into the melt at a controlled velocity while, at the same time, the crystal is pulled from the melt. Semiconductor compounds can be purified by zonerefining, as the conditions for high efficiency (low solubility of impurity elements and easy crystallization) are met by such strongly bonded materials. However, each compound carries its own difficulties (Mullin 1996): the varying effective k value of tellurium and the high volatility of zinc cause problems
in purifying InSb and GaSb, the high reactivity of gallium–arsenic melts attacks the container, or the very high vapor pressures of all the elements in II–IV compounds as well as of the compounds themselves lead to changes in the overall composition. Crystals of semiconductor compounds are grown by all available DS techniques. Horizontal growth of GaAs yields dislocation densities of 10# cmV# which is about two orders of magnitude less than that of vertically pulled conventional crystals, but contamination from the boat walls is a problem here. Special techniques (like low- and high-pressure liquid encapsulated Czochralski pulling) have been developed to high sophistication in order to avoid defects like faceting, 5
Directional Solidification anisotropic segregation, twinning, dislocations, and small-angle grain boundaries. Microgravity experiments were conducted to reduce or completely avoid effects like regular or irregular changes of composition (striations), but appropriate means are as effective in a normal gravity environment. The potential of zone-melting for purification and homogeneous solute distribution, described in detail by Pfann (1966), was recognized first at Bell Laboratories in 1952. The floating zone is enriched by the impurities if the partition coefficient is smaller than unity. This is the case in the majority of metal alloys. Part of the impurities can be removed when the floating zone, after moving through the sample, reaches its end. By passing the floating zone several times through the sample, more and more of the impurities can be cut off. The main limitation to the purification of most metals is then impurities from the container (crucible). The solute or impurity distribution after a certain number of passes depends on the thermal field in the sample which, in turn, sets the amount of back diffusion in the solid, convection in the liquid, and the width of the liquid zone. A high solubility of impurities in the matrix, i.e., a partition coefficient close to unity, requires a high number of passes for a complete purification with the abovementioned limitation. To remove the impurities to the required degree in an alloy with a partition coefficient k l 0.95 will take several thousand passes, and more than half of the sample will have to be cut away. Controlled uniform alloying can be achieved by using a pure solid and feeding the alloying element into the floating zone so that the composition of the melt is constant throughout the pass from one end to the other. A technically less demanding method is single pass zone leveling. An appropriate amount of alloying element is added to the molten zone at one end of the sample. After an initial transient, a steady state is reached and a uniform distribution is achieved over a considerable part of the sample. The transient zones can be shortened by passing the floating zone back and forth several times.
3.3 Other Applications of DS Convection in the melt has been investigated thoroughly in connection with investigating the possibilities of producing functionally graded materials by DS (Siber et al. 1999). The main effect of convection is a reduction of the gradients of temperature and concentration, leading to generally less pronounced microsegregation. However, strong (forced or gravity driven) convection together with a steep temperature gradient has been shown to aid in establishing a longrange compositional gradient (usually termed macrosegregation). This is tied to significant differences in local mechanical properties of the solidified sample. In Fig. 6, gradients of mechanical properties owing 6
Figure 6 Change of hardness and crack propagation rate in a directionally solidified Al–Mg–Zn alloy. Strong convectional mixing of the melt leads to macroscopic gradients of concentration and properties.
to macroscopic concentration gradients in a ternary Al–Zn–Mg alloy are shown. Enhanced by precipitation hardening, the hardness varies systematically from 30 to 130 HV in the binary and from 40 to 200 HV in the ternary alloy, with even stronger effects on the crack propagation rates which vary by factors of up to two orders of magnitude. DS is also of interest for alloys in the composition range of eutectic, monotectic, and peritectic reactions (Kurz and Sahm 1975, Biloni and Boettinger 1996). As during eutectic solidification two (or more) phases tend to solidify simultaneously (coupled or cooperative), eutectics have been investigated extensively in connection with attempts to produce in situ composite materials with plate or fiber morphology. The spacing of eutectic structures decreases with increasing undercooling, cooling rate, or growth velocity. Thus, DS was considered an interesting route for producing composite materials with optimized fiber dimensions. An example is the (Co,Cr)-(Co,Cr) C eutectic which ( $ has a higher creep resistance than conventionally cast superalloys. However, due to difficulties in controlling directional growth with continuous needles or plates, this route has not been successful on an industrial scale and therefore has been abandoned. Very little information is available on directionally solidified peritectic alloys, and technical exploitation of DS does not seem obvious for two-phase or multiphase alloys. 4. Conclusions The possibility of varying the processing parameters independently ensures that DS will remain one of the widely used experimental methods in fundamental research on growth kinetics of the majority of solidification morphologies. In addition, the large number of highly interacting parameters makes crystal growth by directional solidification a complex but versatile technology to meet the stringent product
Directional Solidification requirements for high-technology applications. As in the past, new applications of DS as well as new techniques and devices for DS will emerge from the increasing demands for high-purity, low-defect single crystals and for cast parts with precisely adjusted microstructural geometry and carefully controlled solute distributions. See also: Solidification of Superalloys Bibliography Biloni H, Boettinger W J 1996 Solidification. In: Cahn R W, Haasen P (eds.) Physical Metallurgy, Part I, 4th edn. North Holland, Amsterdam, Chap. 8, pp. 669–842 Flemings M C 1974 Solidification Processing. McGraw-Hill, New York Gell M, Duhl D N, Giamei A F 1980 The development of single crystal superalloys. In: Superalloys 1980. American Society for Metals, Metals Park, OH, pp. 205–24 Goldschmidt D 1994 Einkristalline Gasturbinenschaufeln aus Nickelbasislegierungen, Teil I: Herstellung und Mikrogefu$ ge (Single-crystal blades for gas turbines: I. Casting processes and microstructure). Materialwiss. Werkstofftech. 25, 311–20 Higginbotham G J S 1986 From research to cost effective directional solidification and single crystal production—an integrated approach. Mater. Sci. Technol. 2, 442–60 Kurz W, Fisher D J 1998 Fundamentals of Solidification, 4th edn. Trans Tech, Uetikon-Zu$ rich, Switzerland
Kurz W, Sahm P R 1975 Gerichtet erstarrte eutektische Werkstoffe (Directionally Solidified Eutectic Materials). Springer, Berlin Mullin J B 1996 Compound semiconductor processing. In: Cahn R W, Haasen P, Kramer E J (eds.) Processing of Semiconductors. VCH, Weinheim, Germany, pp. 63–105 Pfann W G 1966 Zone Melting. Wiley, New York Piwonka T S 1988 Directional and monocrystal solidification In: Metals Handbook, 9th edn. American Society for Metals. Metals Park, OH, Vol. 15, pp. 319–23 Rappaz M, Rettenmayr M 1998 Simulation of solidification. Curr. Opin. Solid State Mater. Sci. 3, 275–82 Sahm P R, Schubert F 1979 Solidification phenomena and properties of cast and welded microstructures. In: Solidification and Casting of Metals. Metals Society, London , pp. 389–400 Siber B, Rettenmayr M, Mu$ ller C, Exner H E 1999 Concentration gradients in aluminium alloys generated by directional solidification and their effects on fatigue crack propagation In: Kaysser W (ed.) Functionally Graded Materials. Trans Tech, Uetikon-Zu$ rich, Switzerland, pp. 211–16 Svoboda J M 1988 Nickel and nickel alloys. In: Metals Handbook, 9th edn. American Society for Metals. Metals Park, OH , Vol. 15, pp. 815–23 Wilkes J G 1996 Silicon processing. In: Cahn R W, Haasen P, Kramer E J (eds.) Processing of Semiconductors. VCH, Weinheim, Germany, pp. 1–62
M. Rettenmayr and H. E. Exner
Copyright ' 2001 Elsevier Science Ltd. All rights reserved. No part of this publication may be reproduced, stored in any retrieval system or transmitted in any form or by any means : electronic, electrostatic, magnetic tape, mechanical, photocopying, recording or otherwise, without permission in writing from the publishers. Encyclopedia of Materials : Science and Technology ISBN: 0-08-0431526 pp. 2183–2189 7