Journal of Materials Science & Technology  2019 , 35 (7): 1309-1314 https://doi.org/10.1016/j.jmst.2019.03.004

Orginal Article

Probing the degenerate pattern growth of {100}<011> orientation in a directionally solidified Al-4.5 wt% Cu alloy

Yumin Wanga, Shuangming Lia*, Zhenpeng Liua, Hong Zhonga, Lei Xub, Hui Xingac

aState Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an, 710072, China;
bCollege of Materials Science and Engineering, Qingdao University of Science and Technology, Qingdao, 266000, China
cMOE Key Laboratory of Material Physics and Chemistry under Extraordinary, Shaanxi Key Laboratory of Condensed Matter Structure and Properties, Northwestern Polytechnical University, Xi'an, 710129, China

Corresponding authors:   *Corresponding author.E-mail address: lsm@nwpu.edu.cn (S. Li).

Received: 2019-01-4

Revised:  2019-01-18

Accepted:  2019-01-27

Online:  2019-07-20

Copyright:  2019 Editorial board of Journal of Materials Science & Technology Copyright reserved, Editorial board of Journal of Materials Science & Technology

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Abstract

Degenerate pattern is a seemingly disordered morphology but it exhibits the inherently ordered crystal connected with tip-splitting and limited stability which makes it difficult to observe in the metallic system. Here we employ (100)[011] orientated planar-front seeds using directional solidification and reveal the fundamental origins of the degenerate pattern growth in an Al-4.5 wt% Cu alloy. We find that the spacing of the tip-splitting (λ) in the degenerate of the alloys followed a power law, λV-0.5, and the frequency (f) of the splitting was related to the growth velocity (V) by f∝V1.5. The dimensionless growth direction (θ/θ0) increased monotonously and approached 0.6 with faster velocity, attributed to its anisotropy in the interface kinetics. Once growth velocity exceeded a threshold, two types of pattern transitions from degenerate to regular dendrites were proposed. One of them exhibited a random and chaotic mode and the other underwent a rotation in growth direction.

Keywords: Al-Cu alloy ; Anisotropy ; Direction solidification ; Degenerate pattern

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Yumin Wang, Shuangming Li, Zhenpeng Liu, Hong Zhong, Lei Xu, Hui Xing. Probing the degenerate pattern growth of {100}<011> orientation in a directionally solidified Al-4.5 wt% Cu alloy[J]. Journal of Materials Science & Technology, 2019, 35(7): 1309-1314 https://doi.org/10.1016/j.jmst.2019.03.004

1. Introduction

Dendrites, commonly observed in alloys solidification, have scientifically and technologically resided in the central subjects of considerable researches [[1], [2], [3]]. It is well known that the stable growth of dendrites predicted by the microscopic solvability theory depends on the anisotropy of the solid-liquid interfacial energy [4,5]. The growth magnitude relies on the crystallographic orientation with respect to the crystal lattice [[6], [7], [8]]. In a cubic crystal, the dendrites growing in the <100> direction within the {001} plane form stable tips, and the interfacial energy of this plane demonstrates relatively strong anisotropy. The interfacial energy close to the {111} plane, however, is isotropic so that an irregular seaweed pattern emerges [[9], [10], [11]]. That is, a diminishing magnitude of the anisotropy of the interfacial energy leads to a transition from the stable dendritic structures to an unstructured seaweed pattern [[12], [13], [14]].

At a small but finite anisotropy, the crystal orientation of interest is that two <100> axes are symmetrically titled at ±45° with respect to the pulling axis of solidification. For a cubic crystal, this corresponds to the (001)[110] orientation [12,15]. The crystal presents two equivalent minima of its surface stiffness plot arranged symmetrically relative to the pulling direction. The major fact concerning such observed crystal is that an unsteady, strongly disordered regime, namely, the degenerate pattern, was found in the transparent modeling systems [12,16]. The local feature of the degenerate pattern is a finger titled at about ±23° which is basically different from the dendrites and the seaweed pattern.

Despite these advances, the authors are not aware of any degenerate pattern in the solidification experiments on metallic alloys. Firstly, in the solidification experiments on bulk metallic alloys, the solid is generally polycrystalline, and difficult to control the anisotropy of interfacial energy. Secondly, selection of the crystal orientation to study degenerate patterns of the alloys needs to be specifically designed on single crystal seed. Thirdly, the single crystal seed should be constrained to grow in the planar front, because the single-crystal seed with dendritic interface induces the general dendritic growth and destroys the observation of degenerate patterns. These difficulties basically explain why the degenerate pattern is not common in the solidification processing of metallic materials. Without any degenerate pattern growing in metallic system, we still remain unknown whether the anisotropy of interfacial energy ensures the stability of the degenerate patterns and determines their selection rules in real metallic system.

In this work, we present an experimental investigation of the degenerate pattern in a directionally solidified Al-4.5 wt% Cu alloy. The experimental solidification configurations were specifically designed to study the degenerate patterns of the single crystal alloy. The degenerate pattern was first observed at the (100)[011]-orientated Al-4.5 wt% Cu alloy. With a seemingly disordered morphology, the inherently ordered crystal still demonstrated pole figures in the X-ray diffraction (XRD) spectrum and electron backscattered diffraction (EBSD) that were not available in the transparent modeling systems. Morphological transitions were examined between the degenerate and the dendrites. The influences of velocity on the tilted angle and on splitting dynamics of the degenerate pattern were also discussed in this work.

2. Experimental

Al-4.5 wt% Cu was prepared with high purity Al (99.99 wt%) and Cu (99.99 wt%) bulk material under argon atmosphere using a vacuum induction furnace. At a pre-determined velocity of 1 μm s-1, the single crystal alloy with a planar-front interface morphology was obtained in a ceramic mold (the diameter of 16 mm and length of 200 mm) by employing a block starter and a spiral selector of grains in the directional solidification. The seeds were cut from the single crystal in the (100)[011] orientation and the cut procedure was described elsewhere [17]. The seed was placed in a specially designed alumina crucible. The dimensions of the seed and crucible were 0.8 mm × 4 mm × 40 mm and 0.8 mm × 4 mm × 150 mm corresponding to x-y-z axis, respectively. The [011] orientation was denoted to be along the z direction and the (100) plane is the y-z plane, similar to the configuration in Ref. [15]. After heated to about 850 °C and maintained for 1 h, the samples were pulled downwards at various growth velocities. When the pulling distance reached about 50 mm, the specimens were quenched into liquid-metal bath to “freeze” the morphology of the solid/liquid interface. The temperature gradient in the liquid ahead of the solid/liquid interface was measured as about 220 K cm-1 and described elsewhere [2]. The solidified samples were polished and etched with a diluted Keller solution (1 ml HF, 3 ml HNO3, and 46 ml H2O). Microstructural and crystallographic characteristics on the y-z section were investigated by means of the Olympus TG-3 optical microscope (OM), the Panalytical X-ray diffractometer with Cu and the EBSD on a Tescan Mira 3 field emission-scanning electron microscope (FE-SEM).

3. Results and discussion

3.1. Growth patterns in directionally solidified Al-4.5 wt% Cu alloy

Fig. 1 represents the quenched solid-liquid interface in the directionally solidified Al-4.5 wt% Cu alloy at various growth velocities. The cellular interface morphology in Fig. 1(a) indicates the onset of constitutional supercooling at a low growth velocity of 2 μm s-1. Degenerate patterns were evident in Fig. 1(b) and (c) as the growth velocities were elevated to 5 and 25 μm s-1, respectively. Each tip alternately split with time. The tip was laterally widened and locally flattened before splitting. Two new equally-sized branches produced by the splitting from the tip center spread apart and grew as the main branches. Further, new tip-splitting was generated only when it was blocked by the branch from the neighboring tip. The degenerate pattern formed after a repetitive process off the tip splitting. This degenerate pattern was not accidentally observed and could grow stably at the growth velocity ranging from 5 to 50 μm s-1. Similarly, the degenerate has been observed in the organic alloy [12] and one of the authors, Xing et al. [18] have presented phase-field simulation and reported this degenerate pattern. Rather, in this work, the degenerate pattern is first observed and characterized in the metallic alloy. Additionally, there are only two types of local structures in Fig. 1(c), a finger tilted to the right and one to the left. The tilting angle of the degenerate branch changes with the velocity, not a value of 23° previously reported by the simulation results [12].

Fig. 1.   Quenched solid-liquid interface patterns in directionally solidified Al-4.5 wt% Cu alloy at various growth velocities: (a) 2 μm s-1; (b) 5 μm s-1; (c) 25 μm s-1; (d) 50 μm s-1; (e) 100 μm s-1; (f) 200 μm s-1.

In Fig. 1(d), the similarity of the left tilted branch to a tilted dendrite suggests that a degenerate-to-dendrite transition may occur at 50 μm s-1. Both two morphologies coexisted under this velocity. The interface morphology underwent a second morphology transition, from degenerate pattern to regular dendrite at a higher velocity of 100 μm s-1, as shown in Fig. 1(e). It finally became well-developed regular dendrite pattern at 200 μm s-1 in Fig. 1(f). It can be primarily deduced the pattern transition from degenerate, through titled dendrite, to regular dendrite, with accelerated growth velocity. This pattern transition was observed first time in a metallic alloy with varied orientation.

3.2. Pattern transition from degenerates to dendrites

The pattern transition, from degenerate pattern to regular dendrite in Fig. 1e, involves the (100)[011]-degenerate and (100)[001]-dendrites. This pattern transition process was relatively complicated. Fig. 2(a) and (b) presents the evolution of longitudinal microstructures at a growth velocity of 100 μm s-1. Complete pole figures for the (100) and (110) crystal orientations obtained from the rectangle regions a1 and a2 in white shown in Fig. 2(a) are given in Fig. 2(c). The (100)[011] well-oriented degenerate microstructures in the region of a1 inherited from the orientation of the planar-front seed from the start. The degenerate became unstable after a short period. The plane (100) was not concentrated in the pole figures and the distribution of <011> poles were disorder, as indicated in the lower pole figures (a2) of Fig. 2(c). This means that the dendrites were nucleated with random orientations and the pole figures (Fig. 2(c)) obtained from XRD were chaotic.

Fig. 2.   Longitudinal microstructures and corresponding texture and EBSD analysis in directionally solidified Al-4.5 wt% Cu alloy of growth velocity of 100 μm s-1: (a, b) longitudinal microstructure; (c) (100) and (110) pole figures of texture obtained from white rectangle a1 and a2; (d) EBSD map, misorientation profiles and pole figures obtained from dotted rectangle in (a).

Further, we use the EBSD to analyze the dendritic growth. The EBSD reconstructed orientation map was obtained from the red dotted rectangle in Fig. 2(a), and their results are shown in Fig. 2(d), including EBSD map, misorientation profiles and pole figures. Along the white solid line in the EBSD map, the misorientations between grains d1-d2 and d1-d3 were measured about 23° and 35°, respectively. The (100) and (110) pole figures in Fig. 2(d) demonstrated that grain d1 was in (100)[011] orientation, while grains d2 and d3 were independent of grain d1, and remained random causing the chaotic chart of a2 in Fig. 2(c).

As the growth velocity was increased to 200 μm s-1, the pattern transition process incurred a new change. The degenerate inherited from the seed at first and then became unstable (Fig. 3(a) and (b)). Based on the pole figures in Fig. 3(c), in the region a1 high intensities are obtained in the case of [100] // x and [011] // z. In region b1, the degenerate to dendrite occurred, a severe intensity of [100] direction perpendicular to y-z plane, while the high intensities of (110) formed a diffraction ring and the ring center being the [100] direction. It indicates that the degenerate to dendrite transition though rotating with the [100] axis. In addition, the EBSD results in Fig. 3(d) indicate that the grain d1 is degenerate pattern circled in the (100) and (110) pole figures and the grain d2 being regular dendrites, taken from the blue dotted rectangular region in Fig. 3(b). The misorientation between these two grains was measured to be ∼42°, very close to 45°.

Fig. 3.   Longitudinal microstructures and corresponding texture and EBSD analysis in directionally solidified Al-4.5 wt% Cu alloy of growth velocity of 200 μm s-1: (a, b) longitudinal microstructure; (c) pole figures of texture obtained from white rectangle a1 and b1; (d) EBSD map, misorientation profiles and pole figures obtained from dotted rectangle in (b).

In this study, two types of pattern transitions were found by comparison from the degenerate to regular dendrites. One underwent a random and chaotic mode, close to a critical growth velocity. The other underwent a growth direction rotation far away from the critical growth velocity. These experimental results are distinguished from the transparent modeling systems [8,9,12] where the pattern transient was observed sharply near the threshold velocity.

3.3. Growth dynamics of degenerate pattern

The spacing of the two tips (λ) and splitting frequency (ƒ) are of importance to characterize the growth dynamics of the degenerate pattern. Fig. 4(a) presents the growth morphology extracted from Fig. 1(c). λ and ƒ cannot be directly determined because of the opacity of the metal alloys. Quenching and observing the behavior of a single branch and solidified grooves can help measuring the data. In between, the splitting frequency ƒ was determined by measuring the distance, h, along the z axis of two adjacent splitting points on the same branch and divided by the growth velocity, V. The spacing λ was obtained by measuring two advancing tips as shown in Fig. 4(a).

Fig. 4.   Spacing of two tips (λ) and splitting frequency (ƒ) vs. growth velocity for Al-4.5 wt% Cu: (a) meaning of λ and h; (b) spacing λ follows power law λV-0.5; (c) splitting frequency ƒ.

Fig. 4(b) plots λ as a function of the growth velocity in a logarithmic coordinate. The error bars correspond to the standard deviation of the distribution. These data collapsed following the power law λV-0.5. Previous experimental results of the degenerate growth in directional solidification of SCN-PEO and SCN-ACE alloys by Utter et al. [16] were also displayed on the graph. The exponent value of fitting line in this work, obviously, conformed to these experimental results, as well as the simulation results by Xing et al. [18]. The exponent of -0.5 is an expected value for the instability of a planar front based on linear analysis derived by Mullins and Sekerka [19]:

λi=2π[Γ/(mLGc-G)]-0.5 (1)

Gc=C0(k-1)V/(kDL) (2)

$Γ=\frac{γ_{sl}+\partial^{2}γ_{sl}/ \partial θ^{2}}{ΔS_{f}}=\frac{γ^{0}_{sl}(1-15ε_{4}cos4θ_{0})}{ΔS_{f}}$ (3)

where λi is the shortest wavelength of morphological instability, Γ is the Gibbs-Thomson coefficient, Gc the concentration gradient, mL the liquidus slope, G the temperature gradient, C0 the alloy composition, k the partition coefficient, DL the diffusivity of solute in the liquid, γsl the solid-liquid interface energy, $γ^{0}_{sl}$the mean value of γsl, ΔSf the entropy of melting, ε4 the normalized anisotropy parameter, and θ0 = 45° in this study.

The dotted line in Fig. 4(b) represents the shortest unstable wavelength for Al-4.5 wt% Cu as a function of the growth velocity. Once the tip radius exceeds λi, the tip becomes unstable and starts to break down [20]. The degenerates of Al-4.5 wt% Cu in this study exhibited a tip-splitting behavior, because all spacing data are greater than the shortest wavelength of morphological instability. Further, the fitting solid lines for results of Utter and this work corresponds to λ = 75V-0.5 and λ = 125V-0.5, respectively. It suggests that prefixing coefficient depends on specific material properties, e.g. the interface energy. The interface energy anisotropy of Al-4.5 wt% Cu is about twice than that in SCN.

The splitting frequency ƒ, in Fig. 4(c) is found to elevate with the increasing growth velocity. It follows a power law ƒ∝V1.5 for Al-4.5% Cu and R2 = 0.9998. The transparent modeling systems including SCN-PEO and SCN-ACE assume the same law in Fig. 4(c). Chen et al. [20], however, found the seaweed growth in Al-Cu alloy with a scaling of ƒ∝V2. Considering that the noise at solid-liquid interface drove the seaweed growth in (001)[001] orientation, the scaling of ƒ with V may be different.

In between the degenerate growth, the dimensionless growth direction, θ/θ0, as a function of dimensionless growth velocity V/Vc, is plotted in Fig. 5, where Vc is the critical velocity for the planar interface instability and about 1 μm s-1, θ and θ0 defined in the right-upper inset, are the angles between the growth direction of the degenerate and the <001> direction with the z axis, respectively. The growth direction of one branch determined in the degenerate relies on the distinction of liquid grooves irrelevant to quenching. θ0 is constant ( = 45°) in this situation. θ/θ0 monotonously climbed from zero to about 0.6 with the growth velocity. The maximum tilting angle of the branch was close to 27°, slightly larger than the numerical simulation result of Akamatsu (about 23°) [15]. Following the regular dendritic growth [[21], [22], [23]], the growth direction for the degenerate with respect to the dimensionless velocity can be expressed as follows:

$\frac{θ}{θ_{0}}=1-\frac{1}{1+a(V/V_{c})^{b}}$ (4)

where a and b are fitting parameters. The data in Fig. 5 yields a good agreement (R2 = 0.96) for a = 0.1186 and b = 0.6730.

Fig. 5.   Relationship between dimensionless growth velocity and dimensionless growth direction found in Al-4.5 wt% Cu. The inset shows the illustration for the growth direction and preferred <001> direction.

At the growth velocity of 100 μm s-1, the microstructure was observed with part of degenerate and part of dendrite as shown in Fig. 1(e). Since it cannot rule out the effect of dendrite on the dimensionless growth velocity and dimensionless growth direction for the degenerate pattern, the data of 100 μm s-1 was screened out in Fig. 5. In addition, at the growth velocity of 200 μm s-1, the quenching microstructure was observed as well-aligned array of regular dendrites (Fig. 1(f)). As a result, the dimensionless growth direction θ/θ0 is close to 0 because the growth direction is nearly parallel to the temperature gradient direction, leading to a sudden drop happening at the growth velocity of 200 μm s-1.

In addition, the degenerate grown at V/Vc = 5, 25 and 50 possesses a well-orientated (100)[110], as seen in the (100) and (110) pole figures in Fig. 5, suggesting that these degenerates are the inherently ordered crystal. The interface morphology is only cellular at V/Vc = 2 in Fig. 1(a). The change in the dimensionless growth direction for the degenerate could be attributed to the influence of the growth velocity, excluding the effect from the anisotropy of interface energy. The kinetic anisotropy caused by the variation of the growth velocity may be responsible for this dimensionless growth direction change.

4. Conclusion

A degenerate pattern possessing the (100)[011] orientation was first observed in a directionally solidified Al-4.5 wt% Cu alloy. The tip-splitting spacing of this degenerate pattern followed a power law λ∝V-0.5, agreeing with the M-S instability and the frequency of the tip splitting was related to the growth velocity as ƒ∝V1.5. In addition, the dimensionless growth direction, θ/θ0, increased monotonously with the dimensionless growth velocity and its value changed from 0 to ˜0.6. The maximum tilting angle of the branch was close to 27°. The kinetic anisotropy caused by the variation of growth velocity was responsible for this dimensionless growth direction change. At high velocity, two types of pattern transition from the degenerate to regular dendrite are proposed: One form exhibits a random and chaotic mode under a critical growth velocity and the other undergoes a growth direction rotation, far away from the critical growth velocity. These results clearly show that the degenerate pattern can survive and grow stably in metallic alloys, and the exploration of this pattern for application becomes feasible in the future.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (No. 51474174), Research Funds of the State Key Laboratory of Solidification Processing in NWPU (No. SKLSP201714). Yumin Wang thanks Ming Ma from Electronic Materials Research Laboratory of Xian Jiaotong University for his help on RO-XRD tests.

The authors have declared that no competing interests exist.


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