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Cellular growth during the transient directional solidification of Zn-rich Zn–Cu monophasic and peritectic alloys
Journal of Physics and Chemistry of Solids 73 (2012) 1173–1181
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Cellular growth during the transient directional solidification of Zn-rich Zn–Cu monophasic and peritectic alloys Crystopher Brito a, Claudio A. Siqueira b, Jose´ E. Spinelli c, Amauri Garcia a,n a
Department of Materials Engineering, University of Campinas, UNICAMP, P.O. Box 6122, 13083-970 Campinas, SP, Brazil Department of Materials Engineering, Federal University of Paraı´ba, UFPB, 58051-900 Joa~ o Pessoa, Paraı´ba, Brazil c ~ Paulo, Brazil Department of Materials Engineering, Federal University of Sa~ o Carlos, UFSCar, 13565-905 Sa~ o Carlos, Sao b
a r t i c l e i n f o
abstract
Article history: Received 6 January 2012 Received in revised form 11 April 2012 Accepted 17 May 2012 Available online 30 May 2012
Zn–Cu alloys located in the monophasic and hypoperitectic ranges of compositions of Zn-rich Zn–Cu alloys were directionally solidified under unsteady-state heat flow conditions. The experimental cooling curves allow solidification thermal parameters: tip cooling rate (T_ ), tip growth rate (VL) and temperature gradient (GL) to be experimentally determined. The observed microstructural evolution of both alloys has shown that a regular cellular morphology prevails along the whole castings lengths. Only the regions very close to the cooled casting surface showed the presence of plate-like cells due to very high cooling rates (higher than 25 K/s). The cell spacing (lc) was measured along the castings lengths, and experimental correlations between lc and experimental solidification thermal parameters have been established. Power laws with 0.55 and 1.1 exponents expressing lc as a function of T_ and VL, respectively, were found to better represent the growth of cells under transient heat flow conditions for both alloys experimentally examined. The predictions furnished by the Hunt–Lu model underestimate the experimental cell spacings found for both alloys examined. It was shown that the proposed equations relating lc as a function of T_ are able to represent both the steady-state and unsteady-state cellular growth of monophasic and peritectic Zn-rich Zn–Cu alloys. & 2012 Elsevier Ltd. All rights reserved.
Keywords: A. Alloys A. Metals B. Crystal growth D. Microstructure
1. Introduction Peritectic solidification is one of the most commonly observed phenomena in many practical alloy systems. Many technological important materials are peritectics, such as high temperature superalloys TiAl and NiAl, superconducting materials Fe–Nd–B and structural materials Fe–Ni [1,2]. The study of Zn-rich Zn–Cu peritectic alloys has recently attracted much attention due to the typical cellular/banded structure found in such alloys [3] as well as the possibility of replacing cast iron and copper alloys in many structural applications with cost, processing and performance advantages. Firstly, zinc is less costly than copper. Secondly, zinc exhibits superior machinability and corrosion resistance if compared with cast iron. The copper-hardened rolled commercial Zn-1.0 wt%Cu alloy is typically used in weather stripping, nameplates, ferrules, and drawn, formed, or spun articles requiring stiffness. These hot-rolled components have tensile properties varying from 170 to 210 MPa for tensile strength and from 50 to 35% for elongation. Moreover, the characteristic hardness values are 52 HB for hot rolled and 60 HB for cold rolled specimens [4].
n
Corresponding author. Tel.: þ55 19 35213320; fax: þ55 19 32893722. E-mail address: [email protected] (A. Garcia).
0022-3697/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jpcs.2012.05.014
Ma et al. [5] reported that complex mechanisms and structures are associated with the peritectic reaction and transformation. This is due to the extremely slow reaction kinetics and further difficulties in distinguishing the direct products of peritectic reaction from those of subsequent transformation. The peritectic process is considered to proceed in two stages. The first stage in the case of Zn–Cu peritectic alloys is ‘‘peritectic reaction’’ in which all three phases, liquid (L), primary solid (e) and secondary solid (Z) are in contact with each other and the Z phase grows along the e–L interfacial boundary, finally leaving a layer of Z phase between L and e phases. The dissolution process of the phase e can be inhibited especially under non-equilibrium solidification conditions. The second stage is ‘‘peritectic transformation’’ in which the transformations of e to Z and L to Z take place by the motions of Z–e and Z–L interfaces [1]. Some studies performed laser surface remelting (LSR) on Zn– Cu peritectic alloys [2,6]. The results emphasize the formation of a lamellar structure. The observation of coupled growth structures with two-phase island banding structures was also reported during steady-state directional solidification of the hypoperitectic Zn-2.0 wt%Cu alloy obtained at a solidification velocity range from 1.6 to 6.4 mm/s [7]. The similarity between such phase structure and that of the eutectic structure was observed. Moreover, the formation of the eutectic-like lamellar structure is
C. Brito et al. / Journal of Physics and Chemistry of Solids 73 (2012) 1173–1181
possibly ascribed to the conversion of the equilibrium peritectic reaction into a metastable eutectic reaction under sufficiently rapid solidification conditions. According to Su et al. [6] the lamellar structure (l, lamellar spacing) in a laser surface remelted Zn-2.7 wt%Cu peritectic alloy can be properly related to the growth rate by the Jackson–Hunt relationship (l2V ¼constant).The same relation was used by Xu et al. [8] to represent the structure development of a Zn-10 wt%Ag alloy rapidly solidified by a melt-spinning technique. The fully plate-like cellular structure resembles a eutecticlamellar structure in morphology. However, differences during growth are well known between them [5]. Eutectic growth implies coupling at the growth front between the constituent phases. Cellular front, in contrast, is governed by the major phase with any intercellular product phase resulting from solute segregation towards the intercellular regions. The presence of few lamellar faults and considerably low volume fraction of the minor phase are some features generally associated with the cellular growth. The effective constancy of the product lV0.5 as well as its better adjust to the experimental values characterizing the cellular growth of Zn-rich Zn–Cu peritectic alloys are reported by Ma et al. [2,9]. The entire range of solidification velocities varied from 0.02 to 19.1 mm/s considering results obtained by both Bridgman-type furnace and laser surface remelting. Their results did not agree well quantitatively with the predictions of the Hunt–Lu model [10], which was developed to predict steadystate and unsteady-state growth of cells. Ma et al. [5,9] have carried out the unidirectional solidification of Zn-rich Zn–Cu peritectic alloys (containing 1.53–7.37 wt%Cu) that span a peritectic reaction of e þL-Z under stationary conditions. A microstructure of fully cellular Z for a Zn-1.53 wt%Cu alloy grown at velocities between 0.2 and 4.82 mm/s was observed. Moreover, a microstructure transition from fully cellular Z to a complex microstructure containing nonaligned e dendrites for a Zn-2.17 wt%Cu alloy was reported. The effects of peritectic reaction and transformation on microstructures under unsteady-state solidification conditions are less well known. Most of the available studies have used Bridgmantype resistance heated furnaces to produce steady-state directionally solidified peritectic samples. There is a lack of systematic studies on the microstructural development of peritectic Zn–Cu alloys during transient heat flow conditions, which are of prime
importance since this class of heat flow encompasses the majority of solidification industrial processes. The aim of the present study is to establish correlations between the microstructure evolution and the thermal parameters during unsteady-state solidification of the Zn-1.0 wt%Cu (monophasic) and Zn-2.2 wt%Cu (hypoperitectic) alloys. The characteristic solidification length of both alloys is correlated with solidification thermal parameters such as the cooling rate (T_ ), the tip growth rate (VL) and the temperature gradient (GL), with a view to determining experimental growth laws. The main growth models existing in the literature for steady-state and unsteadystate conditions are validated against the experimental data.
Table 1 Thermophysical properties of the Zn–Cu alloys examined [5,9]. Property
Symbol/Unit
Zn-1.0 wt%Cu
Zn-2.2 wt%Cu
Solute diffusivity Gibbs–Thomson coefficient Liquidus temperature Liquidus slope Partition coefficient
D [m2 s 1] G [m K] TLiq[1C] mL[K/wt%Zn] k0 [-]
2.04 10 9 1.10 10 7 423 3.17 1.62
2.04 10 9 1.10 10 7 433 21.57 5.68
500 Zn-1.0wt%Cu
400 Temperature (°C)
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Positions from metal/mold interface: 3mm 5mm 8mm 14mm 28mm 50mm 70mm
300
200
100 0
100
200
300 Time (s)
400
500
600 Zn-2.2wt%Cu
Temperature (°C)
500 400
Positions from metal/mold interface: 3mm 8mm 14mm 28mm 50mm 70mm
300 200 100 0
Fig. 1. Partial phase diagram of Zn–Cu system (redrawn from Ref. [5]).
100
200 300 Time (s)
400
500
Fig. 2. Experimental cooling curves obtained for (a) Zn-1.0 wt%Cu and (b) Zn-2.2 wt%Cu alloys during upward unsteady-state directional solidification.
C. Brito et al. / Journal of Physics and Chemistry of Solids 73 (2012) 1173–1181
2. Theoretical steady and unsteady-state models for cellular growth A numerical model for steady-state and nonsteady-state growth of cells and dendrites has been proposed by Hunt and Lu [10] that can predict cellular and dendritic spacings. The model was originally set up to describe cells but extended when it appeared to be making relevant predictions for dendritic structures. The numerical results provided by the model have been fitted by approximate analytical expressions, which can be used to compare experiment with theory without carrying out numerical calculations. According to the model, the following hold for cell spacings:
lc ¼
0:335 4:09k0
G
0:41
D VL
DTk0
0:59 ð1Þ
where lc is the cellular spacing, k0 is the solute partition coefficient, G is the Gibbs–Thomson coefficient, DTis the equilibrium solidification range, D is the liquid solute diffusivity and VL is the cell tip growth rate. Hunt and Lu evaluated the lower and upper limits of the spacings within which an array can be stable, and proposed that the upper limit should be twice the lower one. Since the spacing considered by the Hunt–Lu model refers to the cell radius rather than to the more commonly measured diameter, the values need to be multiplied by 2–4 for comparison with measured spacings, and
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the lower limit of stable cells, is given by 0:41 G lc ¼ 8:18k0:745 D0:59 V 0:59 0 L DT
ð2Þ
This model has been validated recently against experimental results of cellular and dendritic growth for a number of metallic alloys under nonsteady-state growth conditions [11]. Bouchard–Kirkaldy [12] have proposed the following equation for cell spacing assuming unsteady-state solidification
lc ¼ a1
16C0 1=2 G0 eGD ð1k0 ÞmL GL V L
!1=2 ð3Þ
where lc is the cell spacing, C0 is the nominal composition, G0e is a characteristic parameter E600 6 K cm 1 [12], mL is the liquidus line slope and a1 is the calibrating factor. This calibrating factor incorporates some uncertainties as the unaccounted diffusion relaxations, the contribution from solid diffusion, and the coring reduction. Hunt [13] and Kurz and Fisher [14,15] have proposed detailed theoretical models to characterize cells and primary dendrite spacings during steady-state growth conditions, which are based only on diffusive transport. Hunt has based his model on two major assumptions: a dendrite or cell profile approximated by a smooth steady-state shape even when dendrite arms have been formed and constant temperature and liquid composition in
35 1.8
-0.4
VL = 2.4 P
1.6
30
2
- R = 0.99
Zn-2.2wt%Cu
1.4
Tip cooling rate (K/s)
Tip growth rate (mm/s)
Zn-1.0wt%Cu T = 90 (P)-1.14 - R2 = 0.97 Zn-2.2wt%Cu T = 150 (P)-1.14 - R2 = 0.96
Zn-1.0wt%Cu
VL = 3.4 P -0.6 - R2 = 0.99
1.2 1.0 0.8 0.6 0.4
25 20 15 10 5
0.2 0
10
20
30
40 50 60 Position (mm)
70
80
90 100
0 0
10
20
30
40 50 60 70 Position (mm)
80
90 100
Temperature gradient (K/mm)
35 30
Zn-1.0wt%Cu GL = 35 (P) -0.7 - R2 = 0.96
25
Zn-2.2wt%Cu GL = 46 (P) -0.5 - R2 = 0.98
20 15 10 5 0 0
10
20
30
40 50 60 70 Position (mm)
80
90 100
Fig. 3. Experimental values of (a) tip growth rate, (b) cooling rate and (c) temperature gradient as a function of position from the metal/mold interface for Zn–Cu alloys during upward vertical transient solidification. R2 is the correlation coefficient.
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the direction normal to the primary dendritic growth direction. Kurz and Fisher have assumed that the overall morphology of the dendrite (tip and trunk) can be approximated by an ellipsoid. The equations representing these two theories can be expressed, respectively by
lc ¼ 2:83½GmL C0 ð1k0 ÞD1=4 GL 1=2 V L 1=4
lc ¼ 4:3
1=4
GDTD k0
GL 1=2 V L 1=4
ð4Þ
ð5Þ
Trivedi [16] proposed a model, which apply for steady-state heat flow conditions
lc ¼ 2:83½LGmL C0 ð1k0 ÞD1=4 GL 1=2 V L 1=4
ð6Þ
The model is a result of a modification in Hunt’s model, where L¼1/2(lþ 1)(lþ2) for the spherical approximation of the cellular/ dendritic front, and l is the harmonic of perturbation. For Zn–Cu alloys L¼10 has been recently adopted in calculations performed with the Trivedi model [17]. The afore mentioned cellular and dendritic growth models can also be applied to estimate the Brody–Flemings back diffusion parameter, a, [18] which is used for theoretical calculations of solute redistribution during solidification. This parameter is
generally evaluated by experimental/theoretical correlations between the cellular/dendritic spacing and the local solidification time. Wolczynski et al. proposed a model for solute redistribution during cellular and dendritic growth, which encompasses the amount of nonequilibrium precipitates and describes the limiting cases of solidification given by the lever rule and the Scheil equation [19]. These authors proposed a new approach for the determination of a, which is based on experimental measurements of solute redistribution. The authors claim that the solute profile measured by analytical electron microscopy provides more accurate values for the back diffusion parameter. The proposed model has been validated against 3D experimental solidification of a Zn 25 wt%Al alloy [20]. Fig. 1 shows the partial Zn–Cu phase diagram as well as the location of the chemistries examined in the present study in the phase diagram. The thermophysical properties necessary to perform calculations with the cell growth models are summarized in Table 1. The liquidus slope and the partition coefficient of the Zn-2.2 wt%Cu alloy have been derived from the Zn–Cu phase diagram in Fig. 1. The solute diffusivities and the Gibbs–Thomson coefficients are those reported by Ma et al. for Zn-rich Zn–Cu alloys [5,9]. The liquidus slope and the partition coefficient used for predictions of the Zn-1.0 wt%Cu alloy were those given by Ma et al. [5,9]. Assuming that the liquidus lines are straight, for an alloy of composition C0, the
Fig. 4. Directionally solidified macrostructures of (a) Zn-1.0 wt%Cu and (b) Zn-2.2 wt%Cu alloys.
C. Brito et al. / Journal of Physics and Chemistry of Solids 73 (2012) 1173–1181
equilibrium solidification range is given by m C ðk 1Þ DT ¼ L 0 0 k0
ð7Þ
3. Experimental procedure Details describing the used directional solidification assembly may be found in previous articles [21,22]. Heat is directionally extracted only through a water-cooled low carbon steel bottom, promoting vertical upward directional solidification. A stainless steel split mold was used having an internal diameter of 45 mm, a height of 115 mm and wall thickness of 5 mm. The lateral inner mold surface was covered with a layer of insulating alumina to minimize radial heat losses. The bottom part of the mold was closed with a thin (3 mm thick) steel sheet. Continuous temperature measurements in the casting were monitored during solidification via the output of a bank of fine type J thermocouples sheathed in 1.6 mm outside diameter (O.D) stainless steel tubes, and positioned at 3, 5, 8, 14, 28, 50 and
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70 mm from the heat-extracting surface at the bottom of the casting. All thermocouples were connected by coaxial cables to a data logger interfaced with a computer and the temperature data were acquired automatically. The cooling water was started when the melt temperature was about 5% and 10% above the liquidus temperature for the Zn-1.0 wt%Cu and Zn-2.2 wt%Cu alloys, respectively. The casting was sectioned along the longitudinal direction to perform the macrostructure analysis. Palmerton’s reagent (40 g CrO3; 1.5 g Na2SO4 and 200 ml of distilled water) was applied to reveal both macro and microstructure. The triangle method was employed to measure the cell spacing, lc, on transverse sections of the directionally solidified castings [23]. Image processing systems Neophot 32 (Carl Zeiss, Esslingen, Germany) and Leica Quantimet 500 MC (Leica Imaging systems Ltd., Cambridge, England) were used to measure the cell spacings and their distribution range. At least 40 measurements were performed for each selected position along the casting length, with the average taken to be the local spacing.
Fig. 5. Typical (a) transversal and (b) longitudinal as-cast microstructures of both Zn–Cu alloys. P is the position from the metal/mold interface.
C. Brito et al. / Journal of Physics and Chemistry of Solids 73 (2012) 1173–1181
Zn-2.2wt%Cu λC = 55 (T)-0.55 - R2 = 0.99
102 Cell spacing, λC (μm)
Fig. 2 depicts the resulting experimental cooling curves for the thermocouples inserted in the Zn–Cu alloys castings. These experimental thermal data were used to determine the thermal solidification parameters such as the tip cooling rate, cell tip growth rate and temperature gradient. Firstly, the thermocouples readings have been used to generate a plot of position from the metal/mold interface as a function of time corresponding to the liquidus isotherm passing by each thermocouple. A curve fitting technique on these experimental points yielded a power function of position as a function of time. The derivative of this function with respect to time gave values for the tip growth rate. Fig. 3a shows the experimental values of VL for both examined alloys together with the fitted evolutions. The experimental cooling rates (Fig. 3b) were then determined by considering the thermal data recorded immediately after the passing of liquidus isotherm by each thermocouple. The temperature gradient was determined for each position along the casting length from the corresponding experimental values of the cooling rate and the growth rate, i.e.: GL ¼ T_ =V L (Fig. 3c). Columnar grains have prevailed along the directionally solidified casting length for both alloys examined, as can be observed in Fig. 4. Optical microstructures from cross and longitudinal sections along the casting length can be seen in Fig. 5. Regular cells can be observed for both alloys examined along most of the castings lengths, with fine cell spacings close to the cooled bottom of the casting, increasing gradually toward the top of the casting. Ma et al. [9] found that the lower limit of growth velocity, VL, for the formation of the plate-like cells was about 2.64 mm/s for samples with composition ranging from 2.17 to 4.94 wt%Cu. According to these authors the operative temperature gradient, GL, measured during the Bridgman experiment was 15 K/mm. Hence, the platelike cells were found for cooling rates, T_ ðT_ ¼ GL V L Þ higher than 40 K/s. In the present investigation, plate-like cells have only been observed for cooling rates higher than 24 K/s, with temperature gradients varying from 25 to 17 K/mm, i.e. for positions in the Zn 2.2 wt%Cu alloy casting close to the cooled casting surface (in the range 0–5 mm). Moreover, the coexistence of plate-like and regular cells was not observed. The final microstructures along the whole Zn 1 wt%Cu alloy casting, as shown in Fig. 5, were identified as regular cells of the single phase Z. No evidences of dendritic growth of the phase Z have been detected. According to the study developed by Ma et al. for the steadystate growth of a 2.17 wt%Cu alloy [5], for growth rates higher than 0.22 mm/s or cooling rates higher than 3.3 K/s the peritectic reaction ceased and no peritectic product was observed in the final microstructures. In the case of the directionally solidified Zn2.2 wt%Cu examined in the present study, an appreciable portion of the casting length refers to cooling rates higher than 3.3 K/s (Fig. 3b), and no evidence that the peritectic reaction occurred could be found. The final microstructure was identified as regular cells of the Z phase with the intercellular region constituted by the primary e phase, as shown in Fig. 5. Fig. 6a–c present the experimental scatter of cell spacings as a function of tip cooling rate, tip growth rate, and temperature gradient, respectively, measured from the afore mentioned microstructures. Points are experimental results and lines represent empirical fits to the experimental points, with the cell spacing being expressed as a power function either of tip cooling rate, tip growth rate or temperature gradient. The overall quality of the fit has been parameterized in terms of least squares correlation coefficients R2. As shown in Fig. 6a–c, due to the data scatter caused by different process variables, the R2values are below but
quite closer to unity. In these figures it can be seen that the same power-function exponents used for the growth of the singlephase alloy can also be applied to the growth law of a directionally solidified peritectic Zn–Cu alloy under unsteady-state heat flow conditions. These exponents are 1.1, 0.55 and 1.0 for the growth rate, the cooling rate, and the temperature gradient,
Zn-1.0wt%Cu λC = 34 (T)-0.55 - R2 = 0.89
101
100
101
102
Tip cooling rate T (K/s) 102
Cell spacing, λC (μm)
4. Results and discussion
101
Zn-1.0wt%Cu Zn-2.2wt%Cu λC = 14 (VL)-1.1 - R2 = 0.91
100 Tip growth rate, VL (mm/s)
Cell spacing, λC (μm)
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102
2x100
Zn-1.0wt%Cu λC = 87 (GL)-1.0 - R2 = 0.91 Zn-2.2wt%Cu λC = 270 (GL)-1.0 - R2 = 0.91
101
100
101 Temperature Gradient, GL (K/mm)
Fig. 6. Cell spacing as a function of (a) cooling rate, (b) tip growth rate and (c) temperature gradient. R2 is the correlation coefficient.
C. Brito et al. / Journal of Physics and Chemistry of Solids 73 (2012) 1173–1181
respectively, and are in agreement with previous studies concerning the cellular growth of binary hypoperitectic alloys during transient directional solidification [11,24,25]. It can be seen that, higher cell spacings are associated with the Zn-2.2 wt%Cu alloy when compared with that of the Zn-1.0 wt%Cu alloy, for both the cooling rate and the temperature gradient (Figs. 6a and 6c, respectively). On the other hand, a single experimental fit can represent the variation of the cell spacing with the tip growth rate for both alloys experimentally examined (Fig. 6b). Fig. 7 shows the comparisons between the experimental values of lc obtained for the Zn–Cu alloys and the theoretical predictions by Hunt–Lu’s model. It can be seen that the experimental scatter of both alloys lie above the maximum range of theoretical values predicted by the Hunt–Lu model. It can also be seen that the slopes of the theoretical curves are significantly lower than those experimentally observed. Kaya et al. [17] reported that the Hunt–Lu model did not match their experimental lc results obtained for the steady-state growth of a monophasic Zn-0.7 wt%Cu alloy. Ma et al. [9] also reported that the Hunt–Lu model, despite showing reasonable parametric agreement, did not agree well quantitatively with the experimental evolution of cell spacing during the steady-state growth of a hypoperitectic Zn-2.17 wt%Cu alloy.
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Fig. 8 shows comparisons between the present experimental results of cell spacings with theoretical predictions furnished by steady-state predictive cell growth models. The lc experimental scatter of the Zn-1.0 wt%Cu alloy lied between the predictions of the Trivedi and Hunt models. The predictions furnished by the Hunt model seem to be appropriate in the case of the Zn2.2 wt%Cu alloy, which is contradictory with the findings of Ma et al. [9] for the Zn-2.17 wt%Cu alloy solidified under stationary conditions. These authors reported that the Hunt and Kurz–Fisher models predicted large deviations from their experimental results. Fig. 9 shows comparisons between the present experimental results with the theoretical predictions furnished by Bouchard– Kirkaldy’s model, given by Eq. (3) with a calibration factor a1 of 75, as suggested by these authors for a Zn based alloy [13]. This calibration factor was shown to be inadequate for both examined alloys. If calibration factors a1 of 45 and 400 are adopted for the Zn1.0 wt%Cu and 2.2 wt%Cu alloys, respectively, the model of Bouchard–Kirkaldy fits very well the experimental scatters, since the theoretical slope is close to that of the experimental tendencies. In order to permit the results from the literature concerning the cellular steady state growth of a monophasic Zn–Cu alloy [17] and the cellular steady-state growth of a hypoperitectic Zn–Cu alloy [9] to be compared with the experimental growth laws proposed in the
102 102 Cell spacing, λC (μm)
Cell spacing λC (μm)
Zn-1.0 wt%Cu
101
101
100
Experimental Hunt-Lu Max Hunt-Lu Min
10-1
100
Zn-2.2wt%Cu
Experimental Hunt-Lu Max Hunt-Lu Min
100 Tip growth rate, VL (mm/s)
100 Tip growth rate, VL (mm/s)
Fig. 7. Experimental and theoretical (Hunt–Lu model) cell spacings as a function of tip growth rate for: (a) monophasic Zn-1.0 wt%Cu and (b) hypoperitectic Zn-2.2 wt%Cu alloys.
102
101 λC: Experimental Hunt Kurz-Fisher Trivedi
Cell spacing, λc (μm)
Cell spacing, λC (μm)
Zn-1.0wt%Cu
Zn-2.2wt%Cu
102
101
Experimental Hunt Kurz-Fisher Trivedi
100
100 100 GL-1/2 x VL-1/4
100 GL
-1/2
x VL
-1/4
Fig. 8. Experimental and theoretical (steady-state growth models) cell spacings as a function of thermal gradient and tip growth rate for: (a) the Zn-1.0 wt%Cu and (b) the Zn-2.2 wt%Cu alloys.
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C. Brito et al. / Journal of Physics and Chemistry of Solids 73 (2012) 1173–1181
102
102
Experimental Bouchard-Kirkaldy (a1 = 400) Bouchard-Kirkaldy (a1 = 75) λc = 55 (T)-0.55
Cell spacing, λc (μm)
Cell spacing, λC (μm)
Zn-1.0wt%Cu
101 λC: Experimental Bouchard-Kirkaldy (a1 = 45) Bouchard-Kirkaldy (a1 = 75)
101
Zn-2.2wt%Cu
100 100
101
102
100
Tip cooling rate, T (K/s)
101 Tip cooling rate, T (K/s)
Fig. 9. Comparison of experimental and theoretical cell spacing as a function of cooling rate for Zn–Cu alloys in unsteady-state directional solidification.
extracted from Ref. [22] -Zn-0.7wt%Cu alloy extracted from Ref. [9] -Zn-2.17wt%Cu alloy
Cell spacing, λc (μm)
102
101 Experimental laws: -0.55 λc = 55 (T) - Zn-2.2wt%Cu alloy λc = 34 (T)
10-1
-0.55
- Zn-1.0wt%Cu alloy
100
101
Tip cooling rate, T (K/s) Fig. 10. Comparison of experimental steady-state results [9,17] of cell spacing as a function of cooling rate for Zn–Cu alloys, with the experimental growth laws derived in the present study for unsteady-state directional solidification.
present study for transient growth conditions, the cell spacing has been related to the cooling rate by multiplying the constant thermal gradient adopted in these experiments [9,17] by the corresponding growth rates. It is important to remark that the range of cooling rates used by Kaya et al. [17] and Ma et al. [9] were lower and higher, respectively, than the range of cooling rates from the present study. These results have been introduced in Fig. 10 with a view to permitting a comparison with the experimental growth laws relating cell spacing to the cooling rate, proposed in the present study. It can be seen that the experimental points are generally close to the experimental tendencies derived in the present investigation. This reinforces the proper application of the exponent 0.55 in order to correlate the cell spacing evolution with the cooling rate for both steady-state and unsteady-state solidification conditions.
5. Conclusions The following major conclusions can be drawn from the present study: 1. The predictions furnished by the Hunt–Lu model, which is supposed to encompass also transient solidifications conditions,
did not match the cellular experimental scatter for both the monophasic Zn-1 wt%Cu and the hypoperitectic Zn-2.2 wt%Cu alloys. 2. The predictions of Bouchard–Kirkaldy’s model performed with the originally suggested a1 ¼75 calibration factor are, for both alloys examined, located far from the experimental points. If calibration factors a1 of 45 and 400 are adopted for the Zn1.0 wt%Cu and 2.2 wt%Cu alloys, respectively, the model of Bouchard–Kirkaldy fits very well with the experimental scatters, since the theoretical slope is close to that of the experimental tendencies. 3. The comparison between experimental cell spacings from the literature concerning the steady-state growth of a monophasic Zn0.7 wt%Cu and a hypoperitectic Zn2.17 wt%Cu alloy with the experimental equations proposed in the present study correlating the cell spacing evolution with the cooling rate, has shown that these equations are able to encompass both steady-state and unsteady-state solidification conditions of these alloys.
Acknowledgments The authors acknowledge the financial support provided by FAPESP (The Scientific Research Foundation of the State of Sa~ o Paulo, Brazil), CNPq (The Brazilian Research Council), CAPES (Coordination for the Improvement of Personnel of Superior Level) and FAEPEX–UNICAMP. References [1] M. Ohno, K. Matsuura, ISIJ Int. 50 (2010) 1879–1885. [2] D. Ma, Y. Li, F.D. Wang, Z.Y. Li, Mater. Sci. Eng. A 318 (2001) 235–243. [3] U. Boyuk, H. Kaya, E. C - adirli, N. Marasli, A. Ulgen, J. Alloys Compd. 491 (2010) 143–148. [4] R. Barnhurst, Zinc and Zinc Alloys, ASM Handbook, 2, , 1990, pp. 1619–1653. [5] D. Ma, Y. Li, S.C. Ng, H. Jones, Acta Mater. 48 (2000) 419–431. [6] Y. Su, X. Lin, M. Wang, L. Xue, W. Huang, Scripta Mater. 51 (2004) 397–403. [7] Y. Su, M. Wang, X. Lin, W. Huang, Mater. Lett. 58 (2004) 2670–2674. [8] W. Xu, D. Ma, Y.P. Feng, Y. Li, Scripta Mater. 44 (2001) 631–636. [9] D. Ma, Y. Li, S.C. Ng, H. Jones, Acta Mater. 48 (2000) 1741–1751. [10] J.D. Hunt, S.Z. Lu, Metall. Mater. Trans. 27A (1996) 611–623. [11] J.E. Spinelli, N. Cheung, A. Garcia, Philos. Mag. 91 (2011) 1705–1723. [12] D. Bouchard, J.S. Kirkaldy, Metall. Mater. Trans. 28B (1997) 651–663. [13] J.D. Hunt, in: International Conference on Solidification and Casting of Metals, The Metals Society, London 1979, pp. 3–9. [14] W. Kurz, J.D. Fisher, Acta Metall. 29 (1981) 11–20. [15] W. Kurz, J.D. Fisher, Fundamentals of Solidification, Trans Tech Publication Switzerland, 1992, pp. 85–90. [16] R. Trivedi, Metall. Mater. Trans. A 15A (1984) 977–982.
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[22] A.P. Silva, J.E. Spinelli, N. Mangelinck-Noel, A. Garcia, Mater. Des. 31 (2010) 4584–4591. [23] M. Gunduz, E. C - ardili, Mater. Sci. Eng. A 327 (2002) 167–185. [24] J.E. Spinelli, D.M. Rosa, I.L. Ferreira, A. Garcia, Meter. Sci. Eng. A 383 (2004) 271–282. [25] O.L. Rocha, C.A. Siqueira, A. Garcia, Mater. Sci. Eng. A 347 (2003) 59–69.
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Journal of Physics and Chemistry of Solids journal homepage: www.elsevier.com/locate/jpcs
Cellular growth during the transient directional solidification of Zn-rich Zn–Cu monophasic and peritectic alloys Crystopher Brito a, Claudio A. Siqueira b, Jose´ E. Spinelli c, Amauri Garcia a,n a
Department of Materials Engineering, University of Campinas, UNICAMP, P.O. Box 6122, 13083-970 Campinas, SP, Brazil Department of Materials Engineering, Federal University of Paraı´ba, UFPB, 58051-900 Joa~ o Pessoa, Paraı´ba, Brazil c ~ Paulo, Brazil Department of Materials Engineering, Federal University of Sa~ o Carlos, UFSCar, 13565-905 Sa~ o Carlos, Sao b
a r t i c l e i n f o
abstract
Article history: Received 6 January 2012 Received in revised form 11 April 2012 Accepted 17 May 2012 Available online 30 May 2012
Zn–Cu alloys located in the monophasic and hypoperitectic ranges of compositions of Zn-rich Zn–Cu alloys were directionally solidified under unsteady-state heat flow conditions. The experimental cooling curves allow solidification thermal parameters: tip cooling rate (T_ ), tip growth rate (VL) and temperature gradient (GL) to be experimentally determined. The observed microstructural evolution of both alloys has shown that a regular cellular morphology prevails along the whole castings lengths. Only the regions very close to the cooled casting surface showed the presence of plate-like cells due to very high cooling rates (higher than 25 K/s). The cell spacing (lc) was measured along the castings lengths, and experimental correlations between lc and experimental solidification thermal parameters have been established. Power laws with 0.55 and 1.1 exponents expressing lc as a function of T_ and VL, respectively, were found to better represent the growth of cells under transient heat flow conditions for both alloys experimentally examined. The predictions furnished by the Hunt–Lu model underestimate the experimental cell spacings found for both alloys examined. It was shown that the proposed equations relating lc as a function of T_ are able to represent both the steady-state and unsteady-state cellular growth of monophasic and peritectic Zn-rich Zn–Cu alloys. & 2012 Elsevier Ltd. All rights reserved.
Keywords: A. Alloys A. Metals B. Crystal growth D. Microstructure
1. Introduction Peritectic solidification is one of the most commonly observed phenomena in many practical alloy systems. Many technological important materials are peritectics, such as high temperature superalloys TiAl and NiAl, superconducting materials Fe–Nd–B and structural materials Fe–Ni [1,2]. The study of Zn-rich Zn–Cu peritectic alloys has recently attracted much attention due to the typical cellular/banded structure found in such alloys [3] as well as the possibility of replacing cast iron and copper alloys in many structural applications with cost, processing and performance advantages. Firstly, zinc is less costly than copper. Secondly, zinc exhibits superior machinability and corrosion resistance if compared with cast iron. The copper-hardened rolled commercial Zn-1.0 wt%Cu alloy is typically used in weather stripping, nameplates, ferrules, and drawn, formed, or spun articles requiring stiffness. These hot-rolled components have tensile properties varying from 170 to 210 MPa for tensile strength and from 50 to 35% for elongation. Moreover, the characteristic hardness values are 52 HB for hot rolled and 60 HB for cold rolled specimens [4].
n
Corresponding author. Tel.: þ55 19 35213320; fax: þ55 19 32893722. E-mail address: [email protected] (A. Garcia).
0022-3697/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jpcs.2012.05.014
Ma et al. [5] reported that complex mechanisms and structures are associated with the peritectic reaction and transformation. This is due to the extremely slow reaction kinetics and further difficulties in distinguishing the direct products of peritectic reaction from those of subsequent transformation. The peritectic process is considered to proceed in two stages. The first stage in the case of Zn–Cu peritectic alloys is ‘‘peritectic reaction’’ in which all three phases, liquid (L), primary solid (e) and secondary solid (Z) are in contact with each other and the Z phase grows along the e–L interfacial boundary, finally leaving a layer of Z phase between L and e phases. The dissolution process of the phase e can be inhibited especially under non-equilibrium solidification conditions. The second stage is ‘‘peritectic transformation’’ in which the transformations of e to Z and L to Z take place by the motions of Z–e and Z–L interfaces [1]. Some studies performed laser surface remelting (LSR) on Zn– Cu peritectic alloys [2,6]. The results emphasize the formation of a lamellar structure. The observation of coupled growth structures with two-phase island banding structures was also reported during steady-state directional solidification of the hypoperitectic Zn-2.0 wt%Cu alloy obtained at a solidification velocity range from 1.6 to 6.4 mm/s [7]. The similarity between such phase structure and that of the eutectic structure was observed. Moreover, the formation of the eutectic-like lamellar structure is
C. Brito et al. / Journal of Physics and Chemistry of Solids 73 (2012) 1173–1181
possibly ascribed to the conversion of the equilibrium peritectic reaction into a metastable eutectic reaction under sufficiently rapid solidification conditions. According to Su et al. [6] the lamellar structure (l, lamellar spacing) in a laser surface remelted Zn-2.7 wt%Cu peritectic alloy can be properly related to the growth rate by the Jackson–Hunt relationship (l2V ¼constant).The same relation was used by Xu et al. [8] to represent the structure development of a Zn-10 wt%Ag alloy rapidly solidified by a melt-spinning technique. The fully plate-like cellular structure resembles a eutecticlamellar structure in morphology. However, differences during growth are well known between them [5]. Eutectic growth implies coupling at the growth front between the constituent phases. Cellular front, in contrast, is governed by the major phase with any intercellular product phase resulting from solute segregation towards the intercellular regions. The presence of few lamellar faults and considerably low volume fraction of the minor phase are some features generally associated with the cellular growth. The effective constancy of the product lV0.5 as well as its better adjust to the experimental values characterizing the cellular growth of Zn-rich Zn–Cu peritectic alloys are reported by Ma et al. [2,9]. The entire range of solidification velocities varied from 0.02 to 19.1 mm/s considering results obtained by both Bridgman-type furnace and laser surface remelting. Their results did not agree well quantitatively with the predictions of the Hunt–Lu model [10], which was developed to predict steadystate and unsteady-state growth of cells. Ma et al. [5,9] have carried out the unidirectional solidification of Zn-rich Zn–Cu peritectic alloys (containing 1.53–7.37 wt%Cu) that span a peritectic reaction of e þL-Z under stationary conditions. A microstructure of fully cellular Z for a Zn-1.53 wt%Cu alloy grown at velocities between 0.2 and 4.82 mm/s was observed. Moreover, a microstructure transition from fully cellular Z to a complex microstructure containing nonaligned e dendrites for a Zn-2.17 wt%Cu alloy was reported. The effects of peritectic reaction and transformation on microstructures under unsteady-state solidification conditions are less well known. Most of the available studies have used Bridgmantype resistance heated furnaces to produce steady-state directionally solidified peritectic samples. There is a lack of systematic studies on the microstructural development of peritectic Zn–Cu alloys during transient heat flow conditions, which are of prime
importance since this class of heat flow encompasses the majority of solidification industrial processes. The aim of the present study is to establish correlations between the microstructure evolution and the thermal parameters during unsteady-state solidification of the Zn-1.0 wt%Cu (monophasic) and Zn-2.2 wt%Cu (hypoperitectic) alloys. The characteristic solidification length of both alloys is correlated with solidification thermal parameters such as the cooling rate (T_ ), the tip growth rate (VL) and the temperature gradient (GL), with a view to determining experimental growth laws. The main growth models existing in the literature for steady-state and unsteadystate conditions are validated against the experimental data.
Table 1 Thermophysical properties of the Zn–Cu alloys examined [5,9]. Property
Symbol/Unit
Zn-1.0 wt%Cu
Zn-2.2 wt%Cu
Solute diffusivity Gibbs–Thomson coefficient Liquidus temperature Liquidus slope Partition coefficient
D [m2 s 1] G [m K] TLiq[1C] mL[K/wt%Zn] k0 [-]
2.04 10 9 1.10 10 7 423 3.17 1.62
2.04 10 9 1.10 10 7 433 21.57 5.68
500 Zn-1.0wt%Cu
400 Temperature (°C)
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Positions from metal/mold interface: 3mm 5mm 8mm 14mm 28mm 50mm 70mm
300
200
100 0
100
200
300 Time (s)
400
500
600 Zn-2.2wt%Cu
Temperature (°C)
500 400
Positions from metal/mold interface: 3mm 8mm 14mm 28mm 50mm 70mm
300 200 100 0
Fig. 1. Partial phase diagram of Zn–Cu system (redrawn from Ref. [5]).
100
200 300 Time (s)
400
500
Fig. 2. Experimental cooling curves obtained for (a) Zn-1.0 wt%Cu and (b) Zn-2.2 wt%Cu alloys during upward unsteady-state directional solidification.
C. Brito et al. / Journal of Physics and Chemistry of Solids 73 (2012) 1173–1181
2. Theoretical steady and unsteady-state models for cellular growth A numerical model for steady-state and nonsteady-state growth of cells and dendrites has been proposed by Hunt and Lu [10] that can predict cellular and dendritic spacings. The model was originally set up to describe cells but extended when it appeared to be making relevant predictions for dendritic structures. The numerical results provided by the model have been fitted by approximate analytical expressions, which can be used to compare experiment with theory without carrying out numerical calculations. According to the model, the following hold for cell spacings:
lc ¼
0:335 4:09k0
G
0:41
D VL
DTk0
0:59 ð1Þ
where lc is the cellular spacing, k0 is the solute partition coefficient, G is the Gibbs–Thomson coefficient, DTis the equilibrium solidification range, D is the liquid solute diffusivity and VL is the cell tip growth rate. Hunt and Lu evaluated the lower and upper limits of the spacings within which an array can be stable, and proposed that the upper limit should be twice the lower one. Since the spacing considered by the Hunt–Lu model refers to the cell radius rather than to the more commonly measured diameter, the values need to be multiplied by 2–4 for comparison with measured spacings, and
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the lower limit of stable cells, is given by 0:41 G lc ¼ 8:18k0:745 D0:59 V 0:59 0 L DT
ð2Þ
This model has been validated recently against experimental results of cellular and dendritic growth for a number of metallic alloys under nonsteady-state growth conditions [11]. Bouchard–Kirkaldy [12] have proposed the following equation for cell spacing assuming unsteady-state solidification
lc ¼ a1
16C0 1=2 G0 eGD ð1k0 ÞmL GL V L
!1=2 ð3Þ
where lc is the cell spacing, C0 is the nominal composition, G0e is a characteristic parameter E600 6 K cm 1 [12], mL is the liquidus line slope and a1 is the calibrating factor. This calibrating factor incorporates some uncertainties as the unaccounted diffusion relaxations, the contribution from solid diffusion, and the coring reduction. Hunt [13] and Kurz and Fisher [14,15] have proposed detailed theoretical models to characterize cells and primary dendrite spacings during steady-state growth conditions, which are based only on diffusive transport. Hunt has based his model on two major assumptions: a dendrite or cell profile approximated by a smooth steady-state shape even when dendrite arms have been formed and constant temperature and liquid composition in
35 1.8
-0.4
VL = 2.4 P
1.6
30
2
- R = 0.99
Zn-2.2wt%Cu
1.4
Tip cooling rate (K/s)
Tip growth rate (mm/s)
Zn-1.0wt%Cu T = 90 (P)-1.14 - R2 = 0.97 Zn-2.2wt%Cu T = 150 (P)-1.14 - R2 = 0.96
Zn-1.0wt%Cu
VL = 3.4 P -0.6 - R2 = 0.99
1.2 1.0 0.8 0.6 0.4
25 20 15 10 5
0.2 0
10
20
30
40 50 60 Position (mm)
70
80
90 100
0 0
10
20
30
40 50 60 70 Position (mm)
80
90 100
Temperature gradient (K/mm)
35 30
Zn-1.0wt%Cu GL = 35 (P) -0.7 - R2 = 0.96
25
Zn-2.2wt%Cu GL = 46 (P) -0.5 - R2 = 0.98
20 15 10 5 0 0
10
20
30
40 50 60 70 Position (mm)
80
90 100
Fig. 3. Experimental values of (a) tip growth rate, (b) cooling rate and (c) temperature gradient as a function of position from the metal/mold interface for Zn–Cu alloys during upward vertical transient solidification. R2 is the correlation coefficient.
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the direction normal to the primary dendritic growth direction. Kurz and Fisher have assumed that the overall morphology of the dendrite (tip and trunk) can be approximated by an ellipsoid. The equations representing these two theories can be expressed, respectively by
lc ¼ 2:83½GmL C0 ð1k0 ÞD1=4 GL 1=2 V L 1=4
lc ¼ 4:3
1=4
GDTD k0
GL 1=2 V L 1=4
ð4Þ
ð5Þ
Trivedi [16] proposed a model, which apply for steady-state heat flow conditions
lc ¼ 2:83½LGmL C0 ð1k0 ÞD1=4 GL 1=2 V L 1=4
ð6Þ
The model is a result of a modification in Hunt’s model, where L¼1/2(lþ 1)(lþ2) for the spherical approximation of the cellular/ dendritic front, and l is the harmonic of perturbation. For Zn–Cu alloys L¼10 has been recently adopted in calculations performed with the Trivedi model [17]. The afore mentioned cellular and dendritic growth models can also be applied to estimate the Brody–Flemings back diffusion parameter, a, [18] which is used for theoretical calculations of solute redistribution during solidification. This parameter is
generally evaluated by experimental/theoretical correlations between the cellular/dendritic spacing and the local solidification time. Wolczynski et al. proposed a model for solute redistribution during cellular and dendritic growth, which encompasses the amount of nonequilibrium precipitates and describes the limiting cases of solidification given by the lever rule and the Scheil equation [19]. These authors proposed a new approach for the determination of a, which is based on experimental measurements of solute redistribution. The authors claim that the solute profile measured by analytical electron microscopy provides more accurate values for the back diffusion parameter. The proposed model has been validated against 3D experimental solidification of a Zn 25 wt%Al alloy [20]. Fig. 1 shows the partial Zn–Cu phase diagram as well as the location of the chemistries examined in the present study in the phase diagram. The thermophysical properties necessary to perform calculations with the cell growth models are summarized in Table 1. The liquidus slope and the partition coefficient of the Zn-2.2 wt%Cu alloy have been derived from the Zn–Cu phase diagram in Fig. 1. The solute diffusivities and the Gibbs–Thomson coefficients are those reported by Ma et al. for Zn-rich Zn–Cu alloys [5,9]. The liquidus slope and the partition coefficient used for predictions of the Zn-1.0 wt%Cu alloy were those given by Ma et al. [5,9]. Assuming that the liquidus lines are straight, for an alloy of composition C0, the
Fig. 4. Directionally solidified macrostructures of (a) Zn-1.0 wt%Cu and (b) Zn-2.2 wt%Cu alloys.
C. Brito et al. / Journal of Physics and Chemistry of Solids 73 (2012) 1173–1181
equilibrium solidification range is given by m C ðk 1Þ DT ¼ L 0 0 k0
ð7Þ
3. Experimental procedure Details describing the used directional solidification assembly may be found in previous articles [21,22]. Heat is directionally extracted only through a water-cooled low carbon steel bottom, promoting vertical upward directional solidification. A stainless steel split mold was used having an internal diameter of 45 mm, a height of 115 mm and wall thickness of 5 mm. The lateral inner mold surface was covered with a layer of insulating alumina to minimize radial heat losses. The bottom part of the mold was closed with a thin (3 mm thick) steel sheet. Continuous temperature measurements in the casting were monitored during solidification via the output of a bank of fine type J thermocouples sheathed in 1.6 mm outside diameter (O.D) stainless steel tubes, and positioned at 3, 5, 8, 14, 28, 50 and
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70 mm from the heat-extracting surface at the bottom of the casting. All thermocouples were connected by coaxial cables to a data logger interfaced with a computer and the temperature data were acquired automatically. The cooling water was started when the melt temperature was about 5% and 10% above the liquidus temperature for the Zn-1.0 wt%Cu and Zn-2.2 wt%Cu alloys, respectively. The casting was sectioned along the longitudinal direction to perform the macrostructure analysis. Palmerton’s reagent (40 g CrO3; 1.5 g Na2SO4 and 200 ml of distilled water) was applied to reveal both macro and microstructure. The triangle method was employed to measure the cell spacing, lc, on transverse sections of the directionally solidified castings [23]. Image processing systems Neophot 32 (Carl Zeiss, Esslingen, Germany) and Leica Quantimet 500 MC (Leica Imaging systems Ltd., Cambridge, England) were used to measure the cell spacings and their distribution range. At least 40 measurements were performed for each selected position along the casting length, with the average taken to be the local spacing.
Fig. 5. Typical (a) transversal and (b) longitudinal as-cast microstructures of both Zn–Cu alloys. P is the position from the metal/mold interface.
C. Brito et al. / Journal of Physics and Chemistry of Solids 73 (2012) 1173–1181
Zn-2.2wt%Cu λC = 55 (T)-0.55 - R2 = 0.99
102 Cell spacing, λC (μm)
Fig. 2 depicts the resulting experimental cooling curves for the thermocouples inserted in the Zn–Cu alloys castings. These experimental thermal data were used to determine the thermal solidification parameters such as the tip cooling rate, cell tip growth rate and temperature gradient. Firstly, the thermocouples readings have been used to generate a plot of position from the metal/mold interface as a function of time corresponding to the liquidus isotherm passing by each thermocouple. A curve fitting technique on these experimental points yielded a power function of position as a function of time. The derivative of this function with respect to time gave values for the tip growth rate. Fig. 3a shows the experimental values of VL for both examined alloys together with the fitted evolutions. The experimental cooling rates (Fig. 3b) were then determined by considering the thermal data recorded immediately after the passing of liquidus isotherm by each thermocouple. The temperature gradient was determined for each position along the casting length from the corresponding experimental values of the cooling rate and the growth rate, i.e.: GL ¼ T_ =V L (Fig. 3c). Columnar grains have prevailed along the directionally solidified casting length for both alloys examined, as can be observed in Fig. 4. Optical microstructures from cross and longitudinal sections along the casting length can be seen in Fig. 5. Regular cells can be observed for both alloys examined along most of the castings lengths, with fine cell spacings close to the cooled bottom of the casting, increasing gradually toward the top of the casting. Ma et al. [9] found that the lower limit of growth velocity, VL, for the formation of the plate-like cells was about 2.64 mm/s for samples with composition ranging from 2.17 to 4.94 wt%Cu. According to these authors the operative temperature gradient, GL, measured during the Bridgman experiment was 15 K/mm. Hence, the platelike cells were found for cooling rates, T_ ðT_ ¼ GL V L Þ higher than 40 K/s. In the present investigation, plate-like cells have only been observed for cooling rates higher than 24 K/s, with temperature gradients varying from 25 to 17 K/mm, i.e. for positions in the Zn 2.2 wt%Cu alloy casting close to the cooled casting surface (in the range 0–5 mm). Moreover, the coexistence of plate-like and regular cells was not observed. The final microstructures along the whole Zn 1 wt%Cu alloy casting, as shown in Fig. 5, were identified as regular cells of the single phase Z. No evidences of dendritic growth of the phase Z have been detected. According to the study developed by Ma et al. for the steadystate growth of a 2.17 wt%Cu alloy [5], for growth rates higher than 0.22 mm/s or cooling rates higher than 3.3 K/s the peritectic reaction ceased and no peritectic product was observed in the final microstructures. In the case of the directionally solidified Zn2.2 wt%Cu examined in the present study, an appreciable portion of the casting length refers to cooling rates higher than 3.3 K/s (Fig. 3b), and no evidence that the peritectic reaction occurred could be found. The final microstructure was identified as regular cells of the Z phase with the intercellular region constituted by the primary e phase, as shown in Fig. 5. Fig. 6a–c present the experimental scatter of cell spacings as a function of tip cooling rate, tip growth rate, and temperature gradient, respectively, measured from the afore mentioned microstructures. Points are experimental results and lines represent empirical fits to the experimental points, with the cell spacing being expressed as a power function either of tip cooling rate, tip growth rate or temperature gradient. The overall quality of the fit has been parameterized in terms of least squares correlation coefficients R2. As shown in Fig. 6a–c, due to the data scatter caused by different process variables, the R2values are below but
quite closer to unity. In these figures it can be seen that the same power-function exponents used for the growth of the singlephase alloy can also be applied to the growth law of a directionally solidified peritectic Zn–Cu alloy under unsteady-state heat flow conditions. These exponents are 1.1, 0.55 and 1.0 for the growth rate, the cooling rate, and the temperature gradient,
Zn-1.0wt%Cu λC = 34 (T)-0.55 - R2 = 0.89
101
100
101
102
Tip cooling rate T (K/s) 102
Cell spacing, λC (μm)
4. Results and discussion
101
Zn-1.0wt%Cu Zn-2.2wt%Cu λC = 14 (VL)-1.1 - R2 = 0.91
100 Tip growth rate, VL (mm/s)
Cell spacing, λC (μm)
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102
2x100
Zn-1.0wt%Cu λC = 87 (GL)-1.0 - R2 = 0.91 Zn-2.2wt%Cu λC = 270 (GL)-1.0 - R2 = 0.91
101
100
101 Temperature Gradient, GL (K/mm)
Fig. 6. Cell spacing as a function of (a) cooling rate, (b) tip growth rate and (c) temperature gradient. R2 is the correlation coefficient.
C. Brito et al. / Journal of Physics and Chemistry of Solids 73 (2012) 1173–1181
respectively, and are in agreement with previous studies concerning the cellular growth of binary hypoperitectic alloys during transient directional solidification [11,24,25]. It can be seen that, higher cell spacings are associated with the Zn-2.2 wt%Cu alloy when compared with that of the Zn-1.0 wt%Cu alloy, for both the cooling rate and the temperature gradient (Figs. 6a and 6c, respectively). On the other hand, a single experimental fit can represent the variation of the cell spacing with the tip growth rate for both alloys experimentally examined (Fig. 6b). Fig. 7 shows the comparisons between the experimental values of lc obtained for the Zn–Cu alloys and the theoretical predictions by Hunt–Lu’s model. It can be seen that the experimental scatter of both alloys lie above the maximum range of theoretical values predicted by the Hunt–Lu model. It can also be seen that the slopes of the theoretical curves are significantly lower than those experimentally observed. Kaya et al. [17] reported that the Hunt–Lu model did not match their experimental lc results obtained for the steady-state growth of a monophasic Zn-0.7 wt%Cu alloy. Ma et al. [9] also reported that the Hunt–Lu model, despite showing reasonable parametric agreement, did not agree well quantitatively with the experimental evolution of cell spacing during the steady-state growth of a hypoperitectic Zn-2.17 wt%Cu alloy.
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Fig. 8 shows comparisons between the present experimental results of cell spacings with theoretical predictions furnished by steady-state predictive cell growth models. The lc experimental scatter of the Zn-1.0 wt%Cu alloy lied between the predictions of the Trivedi and Hunt models. The predictions furnished by the Hunt model seem to be appropriate in the case of the Zn2.2 wt%Cu alloy, which is contradictory with the findings of Ma et al. [9] for the Zn-2.17 wt%Cu alloy solidified under stationary conditions. These authors reported that the Hunt and Kurz–Fisher models predicted large deviations from their experimental results. Fig. 9 shows comparisons between the present experimental results with the theoretical predictions furnished by Bouchard– Kirkaldy’s model, given by Eq. (3) with a calibration factor a1 of 75, as suggested by these authors for a Zn based alloy [13]. This calibration factor was shown to be inadequate for both examined alloys. If calibration factors a1 of 45 and 400 are adopted for the Zn1.0 wt%Cu and 2.2 wt%Cu alloys, respectively, the model of Bouchard–Kirkaldy fits very well the experimental scatters, since the theoretical slope is close to that of the experimental tendencies. In order to permit the results from the literature concerning the cellular steady state growth of a monophasic Zn–Cu alloy [17] and the cellular steady-state growth of a hypoperitectic Zn–Cu alloy [9] to be compared with the experimental growth laws proposed in the
102 102 Cell spacing, λC (μm)
Cell spacing λC (μm)
Zn-1.0 wt%Cu
101
101
100
Experimental Hunt-Lu Max Hunt-Lu Min
10-1
100
Zn-2.2wt%Cu
Experimental Hunt-Lu Max Hunt-Lu Min
100 Tip growth rate, VL (mm/s)
100 Tip growth rate, VL (mm/s)
Fig. 7. Experimental and theoretical (Hunt–Lu model) cell spacings as a function of tip growth rate for: (a) monophasic Zn-1.0 wt%Cu and (b) hypoperitectic Zn-2.2 wt%Cu alloys.
102
101 λC: Experimental Hunt Kurz-Fisher Trivedi
Cell spacing, λc (μm)
Cell spacing, λC (μm)
Zn-1.0wt%Cu
Zn-2.2wt%Cu
102
101
Experimental Hunt Kurz-Fisher Trivedi
100
100 100 GL-1/2 x VL-1/4
100 GL
-1/2
x VL
-1/4
Fig. 8. Experimental and theoretical (steady-state growth models) cell spacings as a function of thermal gradient and tip growth rate for: (a) the Zn-1.0 wt%Cu and (b) the Zn-2.2 wt%Cu alloys.
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C. Brito et al. / Journal of Physics and Chemistry of Solids 73 (2012) 1173–1181
102
102
Experimental Bouchard-Kirkaldy (a1 = 400) Bouchard-Kirkaldy (a1 = 75) λc = 55 (T)-0.55
Cell spacing, λc (μm)
Cell spacing, λC (μm)
Zn-1.0wt%Cu
101 λC: Experimental Bouchard-Kirkaldy (a1 = 45) Bouchard-Kirkaldy (a1 = 75)
101
Zn-2.2wt%Cu
100 100
101
102
100
Tip cooling rate, T (K/s)
101 Tip cooling rate, T (K/s)
Fig. 9. Comparison of experimental and theoretical cell spacing as a function of cooling rate for Zn–Cu alloys in unsteady-state directional solidification.
extracted from Ref. [22] -Zn-0.7wt%Cu alloy extracted from Ref. [9] -Zn-2.17wt%Cu alloy
Cell spacing, λc (μm)
102
101 Experimental laws: -0.55 λc = 55 (T) - Zn-2.2wt%Cu alloy λc = 34 (T)
10-1
-0.55
- Zn-1.0wt%Cu alloy
100
101
Tip cooling rate, T (K/s) Fig. 10. Comparison of experimental steady-state results [9,17] of cell spacing as a function of cooling rate for Zn–Cu alloys, with the experimental growth laws derived in the present study for unsteady-state directional solidification.
present study for transient growth conditions, the cell spacing has been related to the cooling rate by multiplying the constant thermal gradient adopted in these experiments [9,17] by the corresponding growth rates. It is important to remark that the range of cooling rates used by Kaya et al. [17] and Ma et al. [9] were lower and higher, respectively, than the range of cooling rates from the present study. These results have been introduced in Fig. 10 with a view to permitting a comparison with the experimental growth laws relating cell spacing to the cooling rate, proposed in the present study. It can be seen that the experimental points are generally close to the experimental tendencies derived in the present investigation. This reinforces the proper application of the exponent 0.55 in order to correlate the cell spacing evolution with the cooling rate for both steady-state and unsteady-state solidification conditions.
5. Conclusions The following major conclusions can be drawn from the present study: 1. The predictions furnished by the Hunt–Lu model, which is supposed to encompass also transient solidifications conditions,
did not match the cellular experimental scatter for both the monophasic Zn-1 wt%Cu and the hypoperitectic Zn-2.2 wt%Cu alloys. 2. The predictions of Bouchard–Kirkaldy’s model performed with the originally suggested a1 ¼75 calibration factor are, for both alloys examined, located far from the experimental points. If calibration factors a1 of 45 and 400 are adopted for the Zn1.0 wt%Cu and 2.2 wt%Cu alloys, respectively, the model of Bouchard–Kirkaldy fits very well with the experimental scatters, since the theoretical slope is close to that of the experimental tendencies. 3. The comparison between experimental cell spacings from the literature concerning the steady-state growth of a monophasic Zn0.7 wt%Cu and a hypoperitectic Zn2.17 wt%Cu alloy with the experimental equations proposed in the present study correlating the cell spacing evolution with the cooling rate, has shown that these equations are able to encompass both steady-state and unsteady-state solidification conditions of these alloys.
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