Cellular growth of single-phase Zn–Ag alloys unidirectionally solidified

Cellular growth of single-phase Zn–Ag alloys unidirectionally solidified

Materials Chemistry and Physics 143 (2014) 895e899 Contents lists available at ScienceDirect Materials Chemistry and Physics journal homepage: www.e...

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Materials Chemistry and Physics 143 (2014) 895e899

Contents lists available at ScienceDirect

Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys

Materials science communication

Cellular growth of single-phase ZneAg alloys unidirectionally solidified Marcelino Dias, Crystopher Brito, Felipe Bertelli, Amauri Garcia* Department of Materials Engineering, University of Campinas, UNICAMP, 13083-970 Campinas, SP, Brazil

h i g h l i g h t s  The scale of cellular microstructures is fundamental for properties of castings.  Cellular spacing is correlated with the cooling rate by an experimental growth law.  The proposed law encompasses steady-state and transient solidification regimes.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 25 March 2013 Received in revised form 10 September 2013 Accepted 15 November 2013

Transient unidirectional solidification experiments have been carried out with a single-phase ZneAg alloy under cooling rates in the range of 0.1e40 K s1. The resulting macrostructure is shown to be typified by columnar grains aligned along the heat flow direction and the microstructure is characterized by a cellular morphology along the entire casting length with no evidence of cellular/dendritic transition. A regular to plate-like cells transition is shown to occur for cooling rates higher than 10K s1. Experimental results from the literature on the cellular growth of single-phase ZneAg alloys in steady-state solidification conditions are compared with the results of the present investigation. An experimental growth law relating the cell spacing with the cooling rate is proposed, which is shown to be able to represent both the steady-state and transient growth regimes of single-phase ZneAg alloys. The BouchardeKirkaldy model is shown to be the only theoretical growth model that matches the cellular experimental scatters in both solidification regimes. Ó 2013 Elsevier B.V. All rights reserved.

Keywords: Alloys Solidification Optical metallography Microstructure

1. Introduction The growth of the solid/liquid interface during solidification gives rise to distinct microstructural morphologies, in which cellular and dendritic patterns are the most prevalent forms of crystallization [1,2]. The cellular and dendritic spacings are important parameters permitting the scale of the as-solidified microstructure to be characterized. These spacings have a fundamental role on the properties of castings, affecting the microscopic segregation existing between cellular/dendritic branches, and as consequence on the mechanical behavior and the corrosion resistance [2e5]. The experimental determination of solidification thermal parameters, i.e., the temperature gradient (GL), growth rate (VL) and _ is very important since the growth morphologies cooling rate ðTÞ, of alloys are strongly dependent on the kinetics of solidification. With the increase of VL, the morphology of the solid/liquid interface

changes from plane front > cells > dendrites (transitions caused by the constitutional supercooling), and cells > plane front associated with the absolute stability [1,6e8]. The main theoretical models existing in the literature, characterizing the growth of cells and primary dendrite branches during steady-state growth of binary alloys, can be synthesized by: Hunt model [9]: 1=4 lc ¼ 2:83½GmL C0 ð1  k0 ÞD1=4 G1=2 VL L

KurzeFisher model [10]:

lc ¼ 4:3







0254-0584/$ e see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matchemphys.2013.11.030


Trivedi model [11]: 1=4 lc ¼ 2:83½LGmL C0 ð1  k0 ÞD1=4 G1=2 VL L

* Corresponding author. Tel.: þ55 19 3521 3320; fax: þ55 19 3289 3722. E-mail address: [email protected] (A. Garcia).



where lc is the cellular spacing, k0 is the solute partition coefficient, G is the GibbseThomson coefficient, C0 is the alloy composition, DT


M. Dias et al. / Materials Chemistry and Physics 143 (2014) 895e899

Fig. 1. (a) Schematic representation of the experimental setup: 1) rotameter; 2) heat-extracting bottom; 3) thermocouples; 4) computer and data acquisition software; 5) data logger; 6) casting; 7) mold; 8) temperature controller; 9) electric heaters; 10) insulating ceramic shielding; (b) Split mold and bottom part of the mold.

is the equilibrium solidification range, D is the liquid solute diffusivity, GL and VL are the temperature gradient and the cell tip growth rate, respectively, and mL is the liquidus slope. L ¼ 10 has been recently adopted in calculations performed with the Trivedi model for Zn-based alloys [12]. Most of the solidification studies reported in the literature have been carried out with a view to characterizing the cellular and dendritic growth in steady state heat flow conditions, despite the fact that transient solidification conditions are associated with the majority of industrial solidification processes. From the theoretical growth models, only those proposed by Hunt and Lu [13] and BouchardeKirkaldy [14] are supposed to include the growth of cells and dendrites in transient solidification conditions: HunteLu (HL) model, lower limit (upper limit: 2X):

lc ¼ 8:18k0:745 0



D0:59 VL0:59

out with a view to providing a wide range of solidification cooling rates permitting a broad range of microstructures to be examined and compared with steady-state results from the literature. 2. Experimental procedure A schematic representation of the experimental unidirectional solidification apparatus [16] is shown in Fig. 1a. It can be seen that heat is extracted only through a water-cooled bottom, promoting vertical upward unidirectional solidification. A stainless


BouchardeKirkaldy (BK): 1=2

lc ¼ a1

16C0 G0 εGD ð1  k0 ÞmL GL VL

!1=2 (5)

G0ε is a characteristic parameter z 600  6 K cm1 and a1 is a calibrating factor, given by 75 for Zn-based alloys [14]. The only experimental studies existing in the literature concerning the microstructural evolution of ZneAg alloys are those carried out by Xu et al. [6,15] for rapid solidification conditions and steady-state Bridgman growth. These authors demonstrated that the predictions furnished by Hunt, KurzeFisher and HunteLu models are quite far from the experimental scatter of lc for alloys representative of the monophasic range of ZneAg compositions, grown in steady-state conditions. However, despite the extensive experimental analysis conducted by Xu et al. on single-phase Zne Ag alloys [6], there are no studies in the literature assessing the important range of cooling rates typical of transient solidification in industrial processes. The present study aims to contribute to a better understanding of the effect of transient heat flow conditions on the microstructure evolution of single-phase ZneAg alloys. Transient directional solidification experiments have been carried

Fig. 2. Unidirectionally solidified macrostructure of the Zn-0.8%Ag alloy casting.

M. Dias et al. / Materials Chemistry and Physics 143 (2014) 895e899

steel split mold was used having an internal diameter of 50 mm, a height 110 mm and a wall thickness of 3 mm (Fig. 1b). 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) carbon steel sheet, which physically separates the alloy from the cooling fluid. Electric heaters were used to promote in situ melting, and to start solidification, the electric heaters were disconnected and at the same time the controlled water flow was initiated. The solidification experiment has been carried out with a single-phase Zn 0.8 wt%Ag alloy. With a view to determining the thermal parameters during solidification, the temperature evolution at different positions along the casting length (10; 15; 20; 27; 50 and 70 mm from the cooled bottom of the casting) were monitored via the output of fine type J thermocouples (0.2 mm diameter wire). All thermocouples were connected by coaxial cables to a data logger interfaced with a computer and the temperature data were collected at a frequency of 100 Hz. Transverse specimens were taken from the unidirectionally solidified casting at different positions along the casting length, polished and etched with the Palmerton’s reagent (40 g CrO3; 1.5 g Na2SO4 and 200 mL of distilled water) to reveal the microstructure. Image processing systems Neophot 32 (Carl Zeiss, Esslingen, Germany) and Leica Quantimet 500 MC (Leica

(a) 10

Cell Spacing,λ C (μm)

Zn-0.8wt.% Ag


Imaging systems Ltd, Cambridge, England) were used to obtain the optical micrographs and to acquire the experimental values of cellular spacing (lc), which was measured by the triangle method [12]. At least 40 measurements were performed for each selected position. 3. Results and discussion Fig. 2 depicts the macrostructure of the unidirectionally solidified Zn-0.8 wt%Ag alloy casting. It can be seen that this macrostructure is characterized by fine columnar grains aligned with the heat flow direction (vertical). The data collected by the thermocouples have been used to determine the thermal solidification parameters. Initially, they have been used to generate a plot of position from the cooled bottom of the casting as a function of time corresponding to the liquidus isotherm passing by each thermocouple. A curve fitting technique to these points yielded a power function of position vs. time. The derivative of this function with respect to time gave values for VL. The experimental T_ was determined by considering the thermal data recorded immediately after the passage of the liquidus isotherm by each thermocouple. GL was calculated from the cor_ L . Fig. 3a responding experimental values of T_ and VL, i.e., GL ¼ T=V and b shows the experimental cellular spacing as a function of VL and GL, respectively. In steady-state growth experiments, solidification is highly controlled and the significant controllable thermal variables, GL and VL, are maintained constant and are practically independent of each other. In transient solidification experiments (present study), these variables are interdependent, cannot be controlled and vary freely with time. The tip cooling rate synthesizes these two variables, since T_ ¼ ðGL $VL Þ. The evolution of lc with T_ is shown in Fig. 4, where cellular microstructures are associated with a wide range of

10 -1.1

λ c=14 VL


- R = 0.99 10

Tip Growth Rate, VL (mm/s)




Cell Spacing, λ C (μm)

Zn-0.8wt.% Ag



λ c=149 GL



- R = 0.98 10


Temperature Gradient, G L (K/mm) Fig. 3. lc as a function of: (a) VL and (b) GL$R2 is the coefficient of determination.

_ The arrows correlate each microstructure with the corFig. 4. lc as a function of T. responding lc.


M. Dias et al. / Materials Chemistry and Physics 143 (2014) 895e899

Fig. 5. Experimental lc as a function of: (a) GL and VL compared with the steady-state growth models; (b) VL compared with the HunteLu model and (c) T_ for transient solidification (present study: range between 101e40 K s1 and steady-state solidification [6]: range between 10 and 103 K s1) compared with the experimental growth law and the Boucharde Kirkaldy model.

experimental T_ values. Regular cells of the h single phase (solid solution of Ag in Zn) can be observed along most of the casting length, except for positions close to the cooled bottom of the casting, i.e., for T_ > 10 K=s, where a transition from regular to platelike cells has been detected. This indicates that the morphology of the cellular structure is dependent on the cooling rate during transient solidification. Xu et al. [6] reported the presence of platelike cells for T_ > 15 K=s and > 36 K=s for Zn-1 wt%Ag and Zn2.9 wt%Ag single-phase alloys, respectively, for steady-state solidification in a Bridgman apparatus. Brito et al. [17] examined the transient solidification of ZneCu alloys and reported the occurrence of plate-like cells for T_ > 16 K=s for a Zn 2.2 wt%Cu alloy. Fig. 5a shows comparisons between the present experimental scatter of lc values and the theoretical predictions furnished by the steady-state growth models. The thermophysical properties used in the calculations are shown in Table 1. Despite the agreement observed between the experimental points and the Trivedi model 1=2 1=4 along a small range of GL  VL values, the slopes are very different and the discrepancy increases significantly outside the mentioned range. The predictions by the Hunt and KurzeFisher models also do not match the experimental scatter. Fig. 5b shows a similar comparison between the experimental values of lc vs. the tip growth rate and the predictions by the HunteLu model. It can be seen that the experimental scatter lies above the maximum range of values predicted by the HunteLu model, and that the slopes of the theoretical curves are significantly lower than that of the

experimental one. Xu et al. [6] also reported that the aforementioned models did not match quantitatively their experimental lc results obtained for the steady-state growth of single-phase ZneAg alloys. Fig. 5c synthesizes the present experimental lc values (transient solidification e Zn-0.8 wt%Ag alloy) and those from the experimental study by Xu et al. [6] (steady-state solidification of Zn-1.0 wt _ It can be seen that %Ag and Zn-2.9 wt%Ag alloys) as a function of T. the experimental growth law, derived in the present study, fits adequately the experimental scatters of both solidification regimes. Moreover, the BouchardeKirkaldy model also provides a good fit to the experimental results, if the calibrating factor a1 ¼ 75, suggested by these authors for Zn-based binary alloys, is adopted. However, it is important to remark that the use of such parametric factor for ZneCu alloys did not allow the BouchardeKirkaldy model to represent the cellular growth during the transient solidification of

Table 1 Thermophysical properties [6]. Property


Zn-0.8 wt%Ag

Solute diffusivity GibbseThomson coefficient Liquidusesolidus range Liquidus slope Partition coefficient

D [m2 s1] G [m K] DT [K] mL [K/wt%Zn] k0 [e]

2.31  109 1.10  107 4 3.63 2.14

M. Dias et al. / Materials Chemistry and Physics 143 (2014) 895e899

ZneCu alloys [17]. This means that care should be taken when applying such parametric factor (a1) to any Zn-based binary alloy, i.e., a1 seems to be constant for alloys of a given Zn-based system, but not for any Zn-based alloy as proposed by Bouchard and Kirkaldy. Additional experimental studies on the evolution of microstructures of alloys of different Zn-based systems seem to be necessary in order to permit an appropriate range of a1 values to be determined. That would permit accurate theoretical predictions of cellular and dendritic growth by the BouchardeKirkaldy model. It is important to remark that the slopes of the theoretical models in Fig. 5a and b are significantly different from that of the experimental trend. However, this is not the case of the theoretical predictions provided by the BouchardeKirkaldy model. Brito et al. [17] has also shown that the slope of this model agreed well with the experimental evolution of cellular spacings of both single-phase and hypoperitectic ZneCu alloys during transient solidification conditions, but different calibration factors, which do not affect the slope, had been necessary to adjust the predictions to the experimental scatters of each alloy (a1 ¼ 45 and 400 respectively). A recent study dealing with the validation of cellular and dendritic growth models under transient heat flow conditions has also pointed out similar observations for Al-based and PbeSb and Sne Pb alloys [18]. The predictions by the BouchardeKirkaldy model performed with the originally suggested a1 factors have been shown, in most cases, to be located above the experimental scatters, while the slopes of the theoretical trends were in good agreement. 4. Conclusions The present study proposes an experimental cellular growth law, which was shown to represent both steady-state and transient solidification regimes of single-phase Zn-rich ZneAg alloys. From the main theoretical growth models existing in the literature, only


the BouchardeKirkaldy model was shown to furnish reliable predictions of cellular spacings for both aforementioned growth regimes. It has also been demonstrated that a transition from regular to plate-like cells occurs for T_ > 10 K=s. Acknowledgments The authors acknowledge the financial support provided by FAPESP e São Paulo Research Foundation, Brazil (grants 2012/ 16328-2; 2012/08494-0 and 2013/09267-0) and CNPq (The Brazilian Research Council). References [1] W. Kurz, D. Fisher, Fundamentals of Solidification, third ed., Trans Tech Publications, Switzerland, 1992. [2] W.R. Osório, L.R. Garcia, P.R. Goulart, A. Garcia, Mater. Chem. Phys. 106 (2007) 343e349. [3] D.M. Rosa, J.E. Spinelli, I.L. Ferreira, A. Garcia, Metall. Mater. Trans. A 39 (2008) 2161e2174. [4] P.R. Goulart, J.E. Spinelli, N. Cheung, A. Garcia, Mater. Chem. Phys. 119 (2010) 272e278. [5] W.R. Osório, C.M. Freire, A. Garcia, Mater. Sci. Eng. A 402 (2005) 22e32. [6] W. Xu, Y.P. Feng, Y. Li, Z.Y. Li, Mater. Sci. Eng. A 373 (2004) 139e145. [7] O.L. Rocha, C.A. Siqueira, A. Garcia, Mater. Sci. Eng. A 347 (2003) 59e69. [8] I.T.L. Moura, C.L.M. Silva, N. Cheung, P.R. Goulart, A. Garcia, J.E. Spinelli, Mater. Chem. Phys. 132 (2012) 203e209. [9] J.D. Hunt, in: International Conference on Solidification and Casting of Metals, The Metals Society, London (, 1979, pp. 3e9. [10] W. Kurz, D. Fisher, Acta Metall. 29 (1981) 11e20. [11] R. Trivedi, Metall. Mater. Trans. A 15 (1984) 977e982. [12] H. Kaya, S. Engin, U. Boyuk, E. Çadirli, N. Marasli, J. Mater. Res. 24 (2009) 3422e3431. [13] J.D. Hunt, S.Z. Lu, Metall. Mater. Trans. A 27 (1996) 611e623. [14] D. Bouchard, J.S. Kirkaldy, Metall. Mater. Trans. B 28 (1997) 651e663. [15] W. Xu, Y.P. Feng, Y. Li, G.D. Zhang, Z.Y. Li, Acta Mater. 50 (2002) 183e193. [16] I.L. Ferreira, J.E. Spinelli, J.C. Pires, A. Garcia, Mater. Sci. Eng. A 408 (2005) 317e 325. [17] C. Brito, C.A. Siqueira, J.E. Spinelli, A. Garcia, Mater. Lett. 80 (2012) 106e109. [18] J.E. Spinelli, N. Cheung, A. Garcia, Philos. Mag. 91 (2011) 1705e1723.