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The solidification of undercooled melts via twinned dendritic growth
Materials Science and Engineering A 375–377 (2004) 547–551
The solidification of undercooled melts via twinned dendritic growth A.M. Mullis∗ , K.I. Dragnevski, R.F. Cochrane Institute for Materials Research, University of Leeds, Leeds LS2 9JT, UK
Abstract The solidification of undercooled Cu–x wt.% Sn (x = 1, 2, 3, 4) alloys has been studied by a melt encasement (fluxing) technique. It was found that below undercoolings of T ≈ 90 K the preferred dendrite growth orientation in each of these alloys was along the 1 1 1 direction. Moreover the 2 and 3 wt.% Sn alloys also displayed evidence of twinned growth. Above T ≈ 90 K the preferred growth direction returned to the more usual 1 0 0 orientation. © 2003 Elsevier B.V. All rights reserved. Keywords: Twinned dendrites; Feather grains; Undercooling
1. Introduction In a previous study we found that Cu–3 wt.% Sn alloy, undercooled by 43–73 K, solidified by the growth of twinned dendrites with a preferred 1 1 1 growth direction [1]. Here, a melt encasement (fluxing) technique has been used to systematically study the velocity-undercooling relationship in samples of Cu–x wt.% Sn (x = 1, 2, 3, 4) up to undercoolings of T = 320 K. The resultant as-solidified samples have been subject to microstructural investigation and X-ray texture analysis in order to determine the preferred growth direction. The growth of twinned 1 1 1 dendrites has been observed [2] in DC cast aluminium, where these highly undesirable structures are commonly referred to as ‘feather grains’. However, relatively few systematic studies have been made into the twinned 1 1 1 dendrite morphology. Morris and Ryvola [3] found that a minimum solute concentration is required for feather grain growth, although the reasons for this are not firmly established. A number of authors have also found that high imposed thermal gradients tend to favour feather grain growth while Eady and Hogan [4] found that the frequency of feather grains peaks at intermediate velocities. 2. Experimental method Undercooling experiments were performed within a stainless steel vacuum chamber evacuated to a pressure of ∗
Corresponding author. Fax: +44-113-343-2384. E-mail address: [email protected] (A.M. Mullis).
0921-5093/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2003.10.135
5 × 10−6 mbar and backfilled to 500 mbar with N2 gas. Samples were heated, in fused quartz crucibles, by induction heating of a graphite susceptor contained within an alumina shell. Viewing slots were cut in the susceptor and alumina to allow sample observation. Melt encasement, within a soda lime glass flux, was employed allowing the attainment of high undercoolings. Temperature determination was by means of a k-type thermocouple positioned beneath the crucible, which had been thinned at the base so reducing the thermal lag. Temperatures were reproducible to within ±5 K. Solidification of the sample is triggered by means of a thin alumina needle that can be pushed through the flux, touching the surface of the sample in a well-defined position. A schematic diagram of the experimental apparatus is shown in Fig. 1. The experimental procedure is discussed in more detail in reference [1]. The measurement of growth velocities was performed using a 16 element linear photo-diode array, allowing the time taken for the bright recalescence front to move across the relatively dark sample to be measured. Light from the sample was passed through a beam splitter which distributed the light between a CCD camera and the photo-diode array. The CCD camera allows accurate sample positioning and focusing. It was also possible via this arrangement to measure directly the dimension of the sample along the photo-diode axis. A current proportional to the light intensity falling on each photo-diode is produced which was then amplified and recorded. Each of the 16 photo-diodes has an independent fast settling, low noise, DIFET amplifier with a current to voltage gain of 106 V A−1 . The signals are then passed, via switching circuitry, to a pair of voltage adders for output.
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A.M. Mullis et al. / Materials Science and Engineering A 375–377 (2004) 547–551
Fig. 1. Schematic diagram of the melt fluxing apparatus used.
The output signal is displayed as light intensity versus time trace on a digital storage oscilloscope from which the time taken for the solidification front to move through the sample could be measured. The accuracy of this technique was verified using high speed digital imaging (up to 40 500 fps) to track the progress of the recalescence front directly [5]. Alloys were prepared from elemental Cu and Sn with a purity of 99.9999% (metals basis). Cu–Sn alloys were formed by arc melting under an inert atmosphere to ensure complete mixing of the components. Optical microscopy was performed on polished sections using a Nikon Optiphot microscope in differential interference contrast (DIC) and bright field (BF) modes, samples having been etched in ammonium persulphate (100 g l−1 ) to reveal dendritic substructure.
3. Results Velocity-undercooling curves for the four alloys studied, plotted on log–log axes, are shown in Fig. 2. In each case two distinct power law trends of the form V ∝ (T)β are apparent. At low undercoolings, typically less than ≈90 K, the growth velocity increases quite slowly with undercooling, the exponent β increasing systematically with Sn concentration from 0.50 for Cu–1 wt.% Sn to 1.53 for Cu–4 wt.% Sn. Above T ≈ 90 K a much more rapid increase in growth velocity occurs. For x = 1, 2, 3 wt.%, β shows remarkable consistency, being (3.54 ± 0.02) while for x = 4 wt.% a smaller exponent of β = 2.32 is found. We will denote the undercooling at which the two curves intersect as T . Velocity-undercooling curves of this type have previously been reported for other systems. In Ni–Cu, Eckler and Herlach [6] have proposed that the effect may be produced by fluid flow effects in the melt. However, Ni–Cu undergoes spontaneous grain refinement at low undercooling, whereby the original structure formed during the recalescence phase is subject to remelting. Although grain refinement is likely to be an unrelated effect, remelting renders microstructural investigation of the as-solidified samples of little value. In contrast, Cu–Sn does not exhibit grain refinement at low undercooling.
Fig. 2. Velocity-undercooling curve for Cu–1, 2, 3, 4 wt.% Sn alloy, showing two distinct growth regimes.
A.M. Mullis et al. / Materials Science and Engineering A 375–377 (2004) 547–551
Fig. 3. Optical micrograph of Cu–3 wt.% Sn alloy undercooled by T = 43 K prior to nucleation with 1 1 1 pole-figure (inset) showing twin assisted growth along the 1 1 1 direction.
Of the four alloy systems investigated, Cu–3 wt.% Sn has been studied in the greatest detail. The microstructure of this alloy, undercooled by T = 43 K prior to nucleation is shown in Fig. 3. The coarse dendritic substructure is clearly seen and appears to be highly irregular. The X-ray pole-figure for this sample, taken about the 1 1 1 direction, is shown as an inset in the top right hand corner of the micrograph. Two points are notable, firstly there is a strong reflection at the centre of the pole-figure, indicating that the preferred growth direction is 1 1 1, not 1 0 0. Secondly, seven poles are evident on the plot rather than four, each having a common angle of either 72◦ 53 or 109◦ 47 with the centre pole. The poles can be grouped into two groups of four by using the centre pole twice. The implication is that solidification in this sample has proceeded by a twin growth mechanism. Similar results were obtained at T = 83 K, indicating that at this undercooling solidification was still proceeding via growth twins. However, at T = 91 K both the microstructure and texture map changes completely. Fig. 4 shows an optical micrograph of the sample, with strong orthogonality at the junctions of the dendrite arms now apparent. The 1 1 1 pole-figure (shown as an inset in Fig. 4) now shows only four poles, indicating that twinning is no longer present. Moreover, none of the poles are located at the centre of the plot and we would conclude that the preferred growth direction is 1 0 0. Generally, similar results were obtained for this alloy composition, up to the highest undercooling achieved (T = 320 K). This is illustrated in Fig. 5 which shows the microstructure of this alloy at an undercooling of T = 266 K. Under DIC mode optical microscopy the orthogonal dendritic structure is still apparent although much finer than at lower undercoolings, as would be expected from dendrite growth theory. The sample is not however grain refined. As can be seen from the bright field image of the same sample only two grain occupy the whole field of view. Consequently, we might suggest that in the
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Fig. 4. Optical micrograph of Cu–3 wt.% Sn alloy undercooled by T = 91 K prior to nucleation with 1 1 1 pole-figure (inset) showing untwinned growth along the 1 0 0 direction.
Fig. 5. Optical micrograph of Cu–3 wt.% Sn alloy undercooled by T = 266 K prior to nucleation showing fine dendritic structure under DIC mode (upper image) and coarse grain structure under BF mode (lower image).
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A.M. Mullis et al. / Materials Science and Engineering A 375–377 (2004) 547–551
Fig. 6. 1 1 1 pole-figure for Cu–1 wt.% Sn alloy undercooled by T = 75 K prior to nucleation showing untwinned growth along the 1 1 1 direction.
Cu–3 wt.% Sn alloy below T solidification proceeds by twinned growth along the 1 1 1 direction while above T untwinned 1 0 0 growth occurs. In Cu–2 wt.% Sn alloy essentially identical results are obtained. However, for x = 1 and 4 wt.% a somewhat different pattern emerges. In both cases the microstructural and X-ray texture analysis indicate that above T solidification proceeds along the 1 0 0 direction by ‘normal’ untwinned dendrites. However, at lower undercoolings although the preferred growth direction remains 1 1 1, twinning now appears to be absent. Fig. 6 shows the 1 1 1 pole-figure for a Cu–1 wt.% Sn alloy undercooled by 75 K prior to nucleation (no micrograph is presented for this composition as the low solute content leads to very low contrast between the dendrites and the interdendritic regions in the sample). As before a pole at the centre of the figure indicates the preferred 1 1 1 growth direction, although now only four poles are present denoting the presence of just one grain. Consequently, at these two compositions we might conclude that below T solidification proceeds by untwinned 1 1 1 growth.
4. Discussion The experimental evidence presented above indicates that during the solidification of Cu–x wt.% Sn (x = 1, 2, 3, 4) alloy from its undercooled melt, the preferred growth direction below T is 1 1 1, while above T the preferred grow direction is 1 0 0. Moreover, for x = 2 and 3 wt.%, growth along the 1 1 1 direction proceeds via the formation of twins. We have not studied the near equilibrium solidification of these system (T < 10 K) directly using
the fluxing method due to difficulty in nucleating solidification. However, we believe from normal casting practice that as equilibrium is approached solidification will proceed by the growth of dendrites along the 1 0 0 direction. Consequently, the growth of dendrites along the 1 1 1 direction is likely to be restricted to a narrow window of undercoolings, in the region 10–90 K. In a similar study of pure Cu we found that the 1 0 0 growth direction was maintained at all undercoolings [1] and we might thus deduce that a minimum solute concentration is required in order to initiate the switch to 1 1 1 growth. In all four cases the change in the growth direction has a clear signature in the velocity-undercooling curve when this is plotted on log–log axes. For all compositions the fastest growing mode dominates. The reasons behind this behaviour are far from clear. The crystallographic growth direction is determined by the slowest growing planes, which in fcc metals would normally be expected to give rise to growth along the 1 0 0 direction. A number of cubic systems have been shown to undergo a change in growth direction from 1 0 0 to 1 1 1 as the growth velocity is increased and, in particular, this has been observed in situ in the transparent NH4 Cl–H2 O system [7]. It has been suggested that this type of behaviour is due to a competition between the surface energy anisotropy which favours 1 0 0 growth at low velocity and the kinetic anisotropy which favours 1 1 1 growth at high velocity [8]. However, in the case of Cu–Sn this cannot offer a full explanation of the observations as neither the requirement for some solute to be present nor the switch back to the 1 0 0 direction as the growth velocity is increased further are explained. Interestingly, a number of strongly faceting systems show behaviour analogous to that observed here in Cu–Sn alloys. Battersby et al. [9] showed that in dilute Ge–Fe alloys, undercooled by the fluxing technique, twinned 1 1 1 growth at low undercooling (T < 150 K) was replaced by untwinned 1 0 0 growth at higher undercoolings. Moreover, this switch in the growth direction was coincident with a transition from faceted to continuous growth. Similarly, Kuribayashi and Aoyama [10] have observed 1 1 1 growth in electromagnetically levitated Si below undercoolings of 100 K, although they do not report if there was a change in the growth direction at higher undercoolings where continuous growth was observed. It is not clear whether the transition will be observed in pure semiconductors or, as with metals, whether some solute is required. Kuribayashi and Aoyama claim to have used pure Si, although the presence of visible dendrites within their samples would strongly suggest that some solute was present. The analogous behaviour of the semiconductors Ge and Si and the Cu–Sn systems studied here might be taken as evidence that growth in Cu–Sn does not take place at a truly continuous interface, but rather that there are some characteristics of faceted growth present. This is despite the fact that none of the microstructures presented for the Cu–Sn alloys display any features which would normally be associated
A.M. Mullis et al. / Materials Science and Engineering A 375–377 (2004) 547–551
with faceted growth. However, it would be consistent with the observation of twinned growth in the 2 and 3 wt.% Sn alloys, the concept of twin assisted growth being somewhat at odds with the conventional view of a continuous dendrite. In deed, despite the importance of dendritic twins in industrial casting practice, there is no general consensus as to the morphology of a twinned dendrite. Henry et al. [11] have suggested that a twin dendrite would display a split or grooved tip with the twin plane running down the trunk from the grove. Conversely, Wood et al. [12] have argued that a more stable morphology would be for the dendrite to display a sharper than normal tip with the twin plane emanating from the point. In light of the results presented here we would suggest that future models of twinned dendritic growth consider the possibility of growth structures which are intermediate between the classical faceted crystal and the fully continuous dendrite.
551
References [1] S.E. Battersby, R.F. Cochrane, A.M. Mullis, J. Mater. Sci. 35 (2000) 1365. [2] S. Henry, T. Minghetti, M. Rappaz, Acta Mater. 46 (1998) 6431. [3] L.R. Morris, M. Ryvola, Microstr. Sci. 9 (1981) 141. [4] J.A. Eady, L.M. Hogan, J. Cryst. Growth 23 (1974) 129. [5] K.I. Dragnevski, Ph.D. Thesis, University of Leeds, 2002. [6] K. Eckler, D.M. Herlach, Mater. Sci. Eng. A 178 (1994) 159. [7] K.A. Jackson, K.A. Gudge, J. Cryst. Growth 225 (2001) 264. [8] S.K. Chan, H.H. Reimer, M. Kahlweit, J. Cryst. Growth 32 (1976) 303. [9] S.E. Battersby, R.F. Cochrane, A.M. Mullis, J. Mater. Sci. 34 (1999) 2049. [10] K. Kuribayashi, T. Aoyama, J. Cryst. Growth 237–239 (2002) 1840– 1843. [11] S. Henry, P. Jarry, M. Rappaz, Metall. Mater. Trans. 29A (1998) 2807. [12] H.J. Wood, J.D. Hunt, P.V. Evans, Acta Mater. 45 (1997) 569.
The solidification of undercooled melts via twinned dendritic growth A.M. Mullis∗ , K.I. Dragnevski, R.F. Cochrane Institute for Materials Research, University of Leeds, Leeds LS2 9JT, UK
Abstract The solidification of undercooled Cu–x wt.% Sn (x = 1, 2, 3, 4) alloys has been studied by a melt encasement (fluxing) technique. It was found that below undercoolings of T ≈ 90 K the preferred dendrite growth orientation in each of these alloys was along the 1 1 1 direction. Moreover the 2 and 3 wt.% Sn alloys also displayed evidence of twinned growth. Above T ≈ 90 K the preferred growth direction returned to the more usual 1 0 0 orientation. © 2003 Elsevier B.V. All rights reserved. Keywords: Twinned dendrites; Feather grains; Undercooling
1. Introduction In a previous study we found that Cu–3 wt.% Sn alloy, undercooled by 43–73 K, solidified by the growth of twinned dendrites with a preferred 1 1 1 growth direction [1]. Here, a melt encasement (fluxing) technique has been used to systematically study the velocity-undercooling relationship in samples of Cu–x wt.% Sn (x = 1, 2, 3, 4) up to undercoolings of T = 320 K. The resultant as-solidified samples have been subject to microstructural investigation and X-ray texture analysis in order to determine the preferred growth direction. The growth of twinned 1 1 1 dendrites has been observed [2] in DC cast aluminium, where these highly undesirable structures are commonly referred to as ‘feather grains’. However, relatively few systematic studies have been made into the twinned 1 1 1 dendrite morphology. Morris and Ryvola [3] found that a minimum solute concentration is required for feather grain growth, although the reasons for this are not firmly established. A number of authors have also found that high imposed thermal gradients tend to favour feather grain growth while Eady and Hogan [4] found that the frequency of feather grains peaks at intermediate velocities. 2. Experimental method Undercooling experiments were performed within a stainless steel vacuum chamber evacuated to a pressure of ∗
Corresponding author. Fax: +44-113-343-2384. E-mail address: [email protected] (A.M. Mullis).
0921-5093/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2003.10.135
5 × 10−6 mbar and backfilled to 500 mbar with N2 gas. Samples were heated, in fused quartz crucibles, by induction heating of a graphite susceptor contained within an alumina shell. Viewing slots were cut in the susceptor and alumina to allow sample observation. Melt encasement, within a soda lime glass flux, was employed allowing the attainment of high undercoolings. Temperature determination was by means of a k-type thermocouple positioned beneath the crucible, which had been thinned at the base so reducing the thermal lag. Temperatures were reproducible to within ±5 K. Solidification of the sample is triggered by means of a thin alumina needle that can be pushed through the flux, touching the surface of the sample in a well-defined position. A schematic diagram of the experimental apparatus is shown in Fig. 1. The experimental procedure is discussed in more detail in reference [1]. The measurement of growth velocities was performed using a 16 element linear photo-diode array, allowing the time taken for the bright recalescence front to move across the relatively dark sample to be measured. Light from the sample was passed through a beam splitter which distributed the light between a CCD camera and the photo-diode array. The CCD camera allows accurate sample positioning and focusing. It was also possible via this arrangement to measure directly the dimension of the sample along the photo-diode axis. A current proportional to the light intensity falling on each photo-diode is produced which was then amplified and recorded. Each of the 16 photo-diodes has an independent fast settling, low noise, DIFET amplifier with a current to voltage gain of 106 V A−1 . The signals are then passed, via switching circuitry, to a pair of voltage adders for output.
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A.M. Mullis et al. / Materials Science and Engineering A 375–377 (2004) 547–551
Fig. 1. Schematic diagram of the melt fluxing apparatus used.
The output signal is displayed as light intensity versus time trace on a digital storage oscilloscope from which the time taken for the solidification front to move through the sample could be measured. The accuracy of this technique was verified using high speed digital imaging (up to 40 500 fps) to track the progress of the recalescence front directly [5]. Alloys were prepared from elemental Cu and Sn with a purity of 99.9999% (metals basis). Cu–Sn alloys were formed by arc melting under an inert atmosphere to ensure complete mixing of the components. Optical microscopy was performed on polished sections using a Nikon Optiphot microscope in differential interference contrast (DIC) and bright field (BF) modes, samples having been etched in ammonium persulphate (100 g l−1 ) to reveal dendritic substructure.
3. Results Velocity-undercooling curves for the four alloys studied, plotted on log–log axes, are shown in Fig. 2. In each case two distinct power law trends of the form V ∝ (T)β are apparent. At low undercoolings, typically less than ≈90 K, the growth velocity increases quite slowly with undercooling, the exponent β increasing systematically with Sn concentration from 0.50 for Cu–1 wt.% Sn to 1.53 for Cu–4 wt.% Sn. Above T ≈ 90 K a much more rapid increase in growth velocity occurs. For x = 1, 2, 3 wt.%, β shows remarkable consistency, being (3.54 ± 0.02) while for x = 4 wt.% a smaller exponent of β = 2.32 is found. We will denote the undercooling at which the two curves intersect as T . Velocity-undercooling curves of this type have previously been reported for other systems. In Ni–Cu, Eckler and Herlach [6] have proposed that the effect may be produced by fluid flow effects in the melt. However, Ni–Cu undergoes spontaneous grain refinement at low undercooling, whereby the original structure formed during the recalescence phase is subject to remelting. Although grain refinement is likely to be an unrelated effect, remelting renders microstructural investigation of the as-solidified samples of little value. In contrast, Cu–Sn does not exhibit grain refinement at low undercooling.
Fig. 2. Velocity-undercooling curve for Cu–1, 2, 3, 4 wt.% Sn alloy, showing two distinct growth regimes.
A.M. Mullis et al. / Materials Science and Engineering A 375–377 (2004) 547–551
Fig. 3. Optical micrograph of Cu–3 wt.% Sn alloy undercooled by T = 43 K prior to nucleation with 1 1 1 pole-figure (inset) showing twin assisted growth along the 1 1 1 direction.
Of the four alloy systems investigated, Cu–3 wt.% Sn has been studied in the greatest detail. The microstructure of this alloy, undercooled by T = 43 K prior to nucleation is shown in Fig. 3. The coarse dendritic substructure is clearly seen and appears to be highly irregular. The X-ray pole-figure for this sample, taken about the 1 1 1 direction, is shown as an inset in the top right hand corner of the micrograph. Two points are notable, firstly there is a strong reflection at the centre of the pole-figure, indicating that the preferred growth direction is 1 1 1, not 1 0 0. Secondly, seven poles are evident on the plot rather than four, each having a common angle of either 72◦ 53 or 109◦ 47 with the centre pole. The poles can be grouped into two groups of four by using the centre pole twice. The implication is that solidification in this sample has proceeded by a twin growth mechanism. Similar results were obtained at T = 83 K, indicating that at this undercooling solidification was still proceeding via growth twins. However, at T = 91 K both the microstructure and texture map changes completely. Fig. 4 shows an optical micrograph of the sample, with strong orthogonality at the junctions of the dendrite arms now apparent. The 1 1 1 pole-figure (shown as an inset in Fig. 4) now shows only four poles, indicating that twinning is no longer present. Moreover, none of the poles are located at the centre of the plot and we would conclude that the preferred growth direction is 1 0 0. Generally, similar results were obtained for this alloy composition, up to the highest undercooling achieved (T = 320 K). This is illustrated in Fig. 5 which shows the microstructure of this alloy at an undercooling of T = 266 K. Under DIC mode optical microscopy the orthogonal dendritic structure is still apparent although much finer than at lower undercoolings, as would be expected from dendrite growth theory. The sample is not however grain refined. As can be seen from the bright field image of the same sample only two grain occupy the whole field of view. Consequently, we might suggest that in the
549
Fig. 4. Optical micrograph of Cu–3 wt.% Sn alloy undercooled by T = 91 K prior to nucleation with 1 1 1 pole-figure (inset) showing untwinned growth along the 1 0 0 direction.
Fig. 5. Optical micrograph of Cu–3 wt.% Sn alloy undercooled by T = 266 K prior to nucleation showing fine dendritic structure under DIC mode (upper image) and coarse grain structure under BF mode (lower image).
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A.M. Mullis et al. / Materials Science and Engineering A 375–377 (2004) 547–551
Fig. 6. 1 1 1 pole-figure for Cu–1 wt.% Sn alloy undercooled by T = 75 K prior to nucleation showing untwinned growth along the 1 1 1 direction.
Cu–3 wt.% Sn alloy below T solidification proceeds by twinned growth along the 1 1 1 direction while above T untwinned 1 0 0 growth occurs. In Cu–2 wt.% Sn alloy essentially identical results are obtained. However, for x = 1 and 4 wt.% a somewhat different pattern emerges. In both cases the microstructural and X-ray texture analysis indicate that above T solidification proceeds along the 1 0 0 direction by ‘normal’ untwinned dendrites. However, at lower undercoolings although the preferred growth direction remains 1 1 1, twinning now appears to be absent. Fig. 6 shows the 1 1 1 pole-figure for a Cu–1 wt.% Sn alloy undercooled by 75 K prior to nucleation (no micrograph is presented for this composition as the low solute content leads to very low contrast between the dendrites and the interdendritic regions in the sample). As before a pole at the centre of the figure indicates the preferred 1 1 1 growth direction, although now only four poles are present denoting the presence of just one grain. Consequently, at these two compositions we might conclude that below T solidification proceeds by untwinned 1 1 1 growth.
4. Discussion The experimental evidence presented above indicates that during the solidification of Cu–x wt.% Sn (x = 1, 2, 3, 4) alloy from its undercooled melt, the preferred growth direction below T is 1 1 1, while above T the preferred grow direction is 1 0 0. Moreover, for x = 2 and 3 wt.%, growth along the 1 1 1 direction proceeds via the formation of twins. We have not studied the near equilibrium solidification of these system (T < 10 K) directly using
the fluxing method due to difficulty in nucleating solidification. However, we believe from normal casting practice that as equilibrium is approached solidification will proceed by the growth of dendrites along the 1 0 0 direction. Consequently, the growth of dendrites along the 1 1 1 direction is likely to be restricted to a narrow window of undercoolings, in the region 10–90 K. In a similar study of pure Cu we found that the 1 0 0 growth direction was maintained at all undercoolings [1] and we might thus deduce that a minimum solute concentration is required in order to initiate the switch to 1 1 1 growth. In all four cases the change in the growth direction has a clear signature in the velocity-undercooling curve when this is plotted on log–log axes. For all compositions the fastest growing mode dominates. The reasons behind this behaviour are far from clear. The crystallographic growth direction is determined by the slowest growing planes, which in fcc metals would normally be expected to give rise to growth along the 1 0 0 direction. A number of cubic systems have been shown to undergo a change in growth direction from 1 0 0 to 1 1 1 as the growth velocity is increased and, in particular, this has been observed in situ in the transparent NH4 Cl–H2 O system [7]. It has been suggested that this type of behaviour is due to a competition between the surface energy anisotropy which favours 1 0 0 growth at low velocity and the kinetic anisotropy which favours 1 1 1 growth at high velocity [8]. However, in the case of Cu–Sn this cannot offer a full explanation of the observations as neither the requirement for some solute to be present nor the switch back to the 1 0 0 direction as the growth velocity is increased further are explained. Interestingly, a number of strongly faceting systems show behaviour analogous to that observed here in Cu–Sn alloys. Battersby et al. [9] showed that in dilute Ge–Fe alloys, undercooled by the fluxing technique, twinned 1 1 1 growth at low undercooling (T < 150 K) was replaced by untwinned 1 0 0 growth at higher undercoolings. Moreover, this switch in the growth direction was coincident with a transition from faceted to continuous growth. Similarly, Kuribayashi and Aoyama [10] have observed 1 1 1 growth in electromagnetically levitated Si below undercoolings of 100 K, although they do not report if there was a change in the growth direction at higher undercoolings where continuous growth was observed. It is not clear whether the transition will be observed in pure semiconductors or, as with metals, whether some solute is required. Kuribayashi and Aoyama claim to have used pure Si, although the presence of visible dendrites within their samples would strongly suggest that some solute was present. The analogous behaviour of the semiconductors Ge and Si and the Cu–Sn systems studied here might be taken as evidence that growth in Cu–Sn does not take place at a truly continuous interface, but rather that there are some characteristics of faceted growth present. This is despite the fact that none of the microstructures presented for the Cu–Sn alloys display any features which would normally be associated
A.M. Mullis et al. / Materials Science and Engineering A 375–377 (2004) 547–551
with faceted growth. However, it would be consistent with the observation of twinned growth in the 2 and 3 wt.% Sn alloys, the concept of twin assisted growth being somewhat at odds with the conventional view of a continuous dendrite. In deed, despite the importance of dendritic twins in industrial casting practice, there is no general consensus as to the morphology of a twinned dendrite. Henry et al. [11] have suggested that a twin dendrite would display a split or grooved tip with the twin plane running down the trunk from the grove. Conversely, Wood et al. [12] have argued that a more stable morphology would be for the dendrite to display a sharper than normal tip with the twin plane emanating from the point. In light of the results presented here we would suggest that future models of twinned dendritic growth consider the possibility of growth structures which are intermediate between the classical faceted crystal and the fully continuous dendrite.
551
References [1] S.E. Battersby, R.F. Cochrane, A.M. Mullis, J. Mater. Sci. 35 (2000) 1365. [2] S. Henry, T. Minghetti, M. Rappaz, Acta Mater. 46 (1998) 6431. [3] L.R. Morris, M. Ryvola, Microstr. Sci. 9 (1981) 141. [4] J.A. Eady, L.M. Hogan, J. Cryst. Growth 23 (1974) 129. [5] K.I. Dragnevski, Ph.D. Thesis, University of Leeds, 2002. [6] K. Eckler, D.M. Herlach, Mater. Sci. Eng. A 178 (1994) 159. [7] K.A. Jackson, K.A. Gudge, J. Cryst. Growth 225 (2001) 264. [8] S.K. Chan, H.H. Reimer, M. Kahlweit, J. Cryst. Growth 32 (1976) 303. [9] S.E. Battersby, R.F. Cochrane, A.M. Mullis, J. Mater. Sci. 34 (1999) 2049. [10] K. Kuribayashi, T. Aoyama, J. Cryst. Growth 237–239 (2002) 1840– 1843. [11] S. Henry, P. Jarry, M. Rappaz, Metall. Mater. Trans. 29A (1998) 2807. [12] H.J. Wood, J.D. Hunt, P.V. Evans, Acta Mater. 45 (1997) 569.