Exotic colony formation in Sn-Te eutectic system

Journal Pre-proof

Exotic colony formation in Sn-Te eutectic system

Aramanda Shanmukha Kiran, Salapaka Sai Kiran, Sumeet Khanna,

Kamanio Chattopadhyay, Abhik Choudhury

PII: S1359-6454(20)30542-5
DOI: https://doi.org/10.1016/j.actamat.2020.07.036
Reference: AM 16176

To appear in: Acta Materialia

Received date: 2 March 2020

Revised date: 2 July 2020
Accepted date: 12 July 2020

Please cite this article as: Aramanda Shanmukha Kiran, Salapaka Sai Kiran, Sumeet Khanna,
Kamanio Chattopadhyay, Abhik Choudhury, Exotic colony formation in Sn-Te eutectic system, Acta
Materialia (2020), doi: https://doi.org/10.1016/j.actamat.2020.07.036

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition
of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of
record. This version will undergo additional copyediting, typesetting and review before it is published
in its final form, but we are providing this version to give early visibility of the article. Please note that,
during the production process, errors may be discovered which could affect the content, and all legal
disclaimers that apply to the journal pertain.

© 2020 Published by Elsevier Ltd on behalf of Acta Materialia Inc.

 Crystallographic orientation relations :
(000𝟏)Te // (𝟏𝟏𝟏)SnTe & (11𝟐𝟎)Te // (10𝟏)SnTe

Binary SnTe-Te (V=0.5µm/s) Binary SnTe-Te (V=32µm/s)

Ag addition to SnTe-Te Sb addition to SnTe-Te Microstructure of exotic colonies in Sn-Te eutectic

 Exotic colony formation in Sn-Te eutectic system

Aramanda Shanmukha Kiran∗, Salapaka Sai Kiran, Sumeet Khanna, Kamanio

Chattopadhyay, Abhik Choudhury
Department of Materials Engineering, Indian Institute of Science, 560012 Bangalore, India

Abstract
Eutectics are self-organized composite materials that exhibit a wide variety of
microstructural features. Besides intrinsic materials properties like interfacial
energies or diffusivities as well as the nature of the phase diagrams, the process
parameters such as magnitude and orientation of the temperature gradient as
well as the velocity of the growth interface influence the evolution of the mi-
crostructure. Recently, we have observed the evolution of complex patterns due
to addition of ternary impurities in the binary Sn-Te system that contains, in
addition to (Te), an intermetallic SnTe phase with a cubic crystal structure.
This paper examines in detail the origin of such a microstructure that arises
due to a two-phase growth instability induced by impurity addition. The bi-
nary eutectics (Sn-Te) and ternary eutectics (Sn-Te with an impurity addition)
are directionally solidified at different interfacial velocities in order to study the
morphological evolution. The binary alloy exhibits a rod-like or an intercon-
nected string of rods morphology while the addition of a third component leads
to a diffusive instability (similar to a Mullins-Sekerka instability) that results in
the formation of two-phase colonies. The onset of instability depends on both
the growth velocity and impurity concentration while the growth direction of the
cells is normal to the {0001} planes of (Te) and {111} planes of SnTe. Through
the extensive use of multiple characterization techniques, we have explored the
morphological characteristics and crystallography of these colonies. The colonies
have a complex internal structure that bears a three-fold symmetry reminiscent
of the trigonal symmetry of the (Te) crystal, arising possibly because of strong
anisotropy in the solid-liquid interfacial energy or in the kinetics of growth. For
the different impurity additions (Ag or Sb), the internal eutectic morphology
of the colony, due to the addition of Ag is different from that observed for the
addition of Sb. The latter leads to the formation of lamellae while a rod-like
feature could be observed for impurities like Ag. The complex patterns exhibit
a structural hierarchy that provides opportunities for designing novel materials.

∗ Corresponding author.
Email addresses: shanmukhaa@iisc.ac.in (Aramanda Shanmukha Kiran ),
ssaikiran@iisc.ac.in (Salapaka Sai Kiran), sumeet92k@gmail.com (Sumeet Khanna),
kamanio@iisc.ac.in (Kamanio Chattopadhyay), abhiknc@iisc.ac.in (Abhik Choudhury)

Preprint submitted to Acta Materialia July 15, 2020

 Keywords: Directional solidification; Eutectic structure; Interfacial energy
(anisotropy); Presence of impurities; Thermoelectric materials.

1 1. Introduction

2 Pattern-formation giving rise to self-organized structures are ubiquitous [1,

3 2]. Eutectic growth is one such example wherein, two or more phases so-
4 lidify from the liquid, self-organizing themselves into a wide variety of pat-
5 terns (microstructural features). Morphological evolution of eutectics is there-
6 fore an exciting subject both in terms of investigation of fundamental aspects
7 [3, 4, 5, 6] as well as technologically important for designing new materials
8 [7, 8, 9, 10, 11, 12, 13, 14].
9 Two-phase eutectic growth in a binary system has been extensively studied
10 [15, 16, 17, 18, 19, 20, 21, 22]. Typical patterns for cases where the solids are
11 non-faceted may broadly be classified as rod/lamellar/labyrinth that organize
12 themselves within a length scale range around the minimum undercooling spac-
13 ing λm (spacing corresponding to the minimum of the undercooling vs. spacing
14 curve[23]), that follows an approximate scaling relation λ2m V = constant as per
15 Jackson–Hunt theory [23]. Morphological instabilities in these two-phase growth
16 structures arise at large spacings that have been studied both experimentally
17 and using phase-field simulation for thin-film [24, 25, 26] and bulk solidification
18 [27] conditions. While the case of isotropic interfacial energies is, therefore, well-
19 investigated, complicated structures arise with the introduction of anisotropy
20 in the interfacial free energy of both the solid-solid and solid-liquid interfaces.
21 Interesting examples of the influence of anisotropy in the solid-solid interface
22 can be found in [15, 28], where locked eutectic grains grow with the direction
23 of growth being different from that imposed by the thermal gradient. This is
24 apparently because the solid-solid interface is oriented along a low energy di-
25 rection in the γ− plot of the solid-solid interface. Additionally, the solid-solid
26 interfaces themselves can assume interesting structures [29, 30, 31, 32] as a con-
27 sequence of the interface being anisotropic. Further, the presence of solid-solid
28 interfacial energy anisotropy can also lead to the formation of broken-lamellar
29 structures in contrast to rod microstructures even in eutectic systems with a
30 very low minority phase fraction [19, 33, 34, 35]. Similarly, two-phase growth
31 in which the solid-liquid interface of one or more of the phases is faceted, leads
32 to the formation of irregular growth structures such as those found in the Al-Si
33 and Al-Ge systems [18, 36, 37, 38].
34 While for the case of invariant two-phase growth we observe the formation
35 of a stable/uniform solidification front, the introduction of an impurity leads to
36 the destabilization of the eutectic front resulting in the formation of colonies.
37 This phenomenon is similar to the Mullins-Sekerka instability [39] that results
38 in the destabilization of a planar growth interface leading to the formation
39 of cells and dendrites, wherein the instability occurs via the perturbation of
40 the boundary layer formed by the partitioning of the impurity into the melt.
41 Such observations of colony formation can be found in Ref.[15, 40, 41] that

3
42 have also been studied theoretically using phase-field simulations [22, 42, 43].
43 While, such colonies typically have cellular shapes with the lamellae, locally
44 growing perpendicular to the solidification envelope, exotic structures with the
45 two phases spiralling during growth as a colony have also been observed in
46 both experiments and simulations [41, 44, 45]. Similar to stable two-phase
47 eutectic growth, the presence of anisotropy in the solid-solid and the solid-liquid
48 interfaces leads to exciting examples of pattern formation. In the case when both
49 the faceted and non-faceted phases are present, the presence of strong anisotropy
50 can lead to the formation of complex irregular structures even in binary alloys as
51 reported in Ref.[46, 47]. The authors propose in Ref.[47] that the origin of this
52 instability can be linked to the generation of a solute boundary layer ahead of
53 the non-faceted interface. However, in contrast to the impurity boundary layer,
54 the segregated layer in the binary case forms because of the growth restriction of
55 the faceted phase. This leads to a build-up of solute rejected by the non-faceting
56 interface, ahead of the solid-liquid interface. The solute build up provides the
57 necessary constitutional undercooling required for destabilising the solid-liquid
58 interface leading to the formation of cellular growth of non-faceted structures
59 coupled with the phase having faceted interfaces. This yields a complex irregular
60 structure [47]. Although the mechanism of destabilisation of a two-phase growth
61 front through impurity additions has been supported by dynamical phase-field
62 simulations [42, 43], the same is not true for the destabilisation of faceted/non-
63 faceted binary eutectic interface. The formation of a boundary layer because of
64 growth restriction imposed by faceting, proposed in Ref.[47] therefore needs to
65 be explored further.
66 In the spirit of investigating such complex pattern formation, we study one
67 such eutectic system exhibiting exotic colony structures, i.e. the Sn-Te eutectic
68 system. In this system, the minority phase volume percentage is around 28
69 and typically gives rise to a microstructure that is mostly connected rod-like
70 at low velocities and rod-like at higher velocities. Unusual pattern formation,
71 however, occurs when the stable two-phase front is destabilized upon addition of
72 an impurity giving rise to colony formation that has an underlining signature of
73 the presence of solid-liquid anisotropy. Therefore, in this paper, we investigate
74 the formation of such exotic patterns, both morphologically and crystallograph-
75 ically. Moreover, we elaborate upon the influence of different impurity additions
76 on the colony structure. While such a study is interesting purely from a stand-
77 point of pattern formation, it is also of technological relevance as this material
78 is being viewed as a possible candidate for thermoelectric applications [48, 49].
79 The structure of the paper is as follows. We begin with the description of
80 the directional solidification setup in Section 2. Thereafter, we elaborate on the
81 microstructure evolution of binary SnTe and (Te) eutectic phases which involves
82 morphological and crystallographic examination in Section 3.1. Following this,
83 we explain the formation of colonies which are formed as a consequence of
84 impurity addition in Section 3.2. Using FIB (Focused Ion Beam) and EBSD
85 (Electron Backscatter Diffraction) results, we analyze the reasons behind the
86 biasing towards such structure formation. Subsequently, we elaborate on the
87 structure formation and the influence of impurities and process conditions and

4
88 finally conclude in Section 4.

89 2. Experimental details

90 2.1. Directional solidification apparatus

Thermocouple
Quartz window
Alumina tube
Silica-aerogel insulation

Nickel plated hollow copper rod

Hot zone

Alumina pipe

Heating coil (Kanthal)

Quartz tube
Gradient zone

Zirconia based ceramic insulation

Solid-liquid interface

Hollow copper
Chill zone

Sample holder having

water circulation

Silica-aerogel insulation

Water circulation

(a) (b)

Figure 1: Schematic of the modified Bridgman apparatus is shown in (a), while plot in (b) is
the axial temperature distribution from center of the hot zone to the chill zone.

91 In order to control the temperature gradient and solidification velocity inde-

92 pendently, directional solidification is employed, where we have used a modified
93 Bridgman-type apparatus (see Figure 1a). The apparatus is made up of isother-
94 mal hot zone (resistance heating) and chill zone (continuous water-glycol mix-
95 ture flow, maintained at a temperature of 4 °C) separated by an adiabatic zone
96 (made of ceramic insulation) to reduce heat transfer between hot/chill zones and
97 to create a temperature gradient. For obtaining a uniform temperature in the
98 hot zone, hollow Ni-electroplated copper rods are placed concentrically with re-
99 spect to the heating coil. In order to enhance the cooling conditions, the sample
100 is placed in a holder which has water circulation that is maintained at the same
101 temperature as in the chill zone. The furnace assembly translates along a linear
102 drive, relative to the stationary sample that is initially positioned in the hot
103 zone, thereby leading to directional solidification. The speed of traverse, that
104 directly controls the solidification velocity is controlled using a stepper motor
105 connected with a gearbox.
106 We obtained the axial temperature profile from the center of hot zone to chill
107 zone using a stationary thermocouple while the apparatus is made to traverse
108 a given distance. The axial temperature in apparatus when the hot zone tem-
109 perature is set at 650 °C, is shown in the Figure 1b and all the experiments are
110 carried out under these conditions. Using the axial temperature, one can obtain
111 the temperature gradient in the apparatus, that is around 27.4 °C/mm at the
112 eutectic temperature of the binary SnTe-Te system. The eutectic samples are

5
113 directionally solidified at different growth velocities (velocities used for binary
114 samples are V= 0.5, 1.0, 2.0, 4.0, 8.0, 32.0 µm/s and for ternary samples are se-
115 lected based on critical velocities beyond which instabilities are observed) under
116 constant temperature gradient to investigate the microstructure formation.

117 2.2. Sample preparation and material characterization

118 Samples of eutectic composition were synthesized using 99.999% purity level
119 elements and sealed in 4 mm inner diameter quartz tubes with 10−5 mbar level
120 vacuum. The quartz tube is then placed in the hot zone of the modified Bridg-
121 man furnace for around 20 mins such that there is complete melting of the
122 sample and the liquid composition is homogeneous. Thereafter, the water cir-
123 culation to the sample holder is initiated that leads to a quench of the initial
124 part of the sample, and consequently, the solidification front rises, decelerates
125 and stabilizes at the melting temperature of the alloy, i.e. the solidification front
126 velocity reaches zero. The system is allowed to equilibrate at this stage until
127 the thermocouple placed at the bottom of the sample reads a constant value.
128 Thereafter, the stepper motor translating the furnace assembly is switched on,
129 that leads to directional solidification with the imposed velocity, where the sam-
130 ples are directionally solidified up to a length of 80 mm. Conventional polishing
131 methods are used for metallographic examination of longitudinal and transverse
132 sections. For etching the SnTe phase, an etchant solution is prepared by mixing
133 methanol to 33% aqueous KOH and then after cooling it to room temperature,
134 30% H2 O2 is added (methanol:33% aq. KOH:30% H2 O2 = 1:4.5:1). Samples are
135 characterized around the middle of the sample, i.e. 40 mm from the initial seed
136 which is representative of actual growth according to the imposed conditions
137 as both in the early/final part of the sample the thermal and solutal condi-
138 tions are transient. Scanning Electron Microscope (FEI Quanta 400) is used
139 for imaging the morphology, field-emission microscope equipped with electron
140 probe microanalyzer (JEOL, JXA-8530F) has been used for obtaining composi-
141 tion distribution maps which are based on wavelength-dispersive spectroscopy
142 (WDS), dual beam microscope (FEI Helios G4) is used for electron backscat-
143 ter diffraction (EBSD) and also for milling the samples at appropriate sections
144 using gallium ions to capture the internal structures.

145 3. Results and discussion

146 3.1. Microstructure evolution in binary Sn-Te eutectic

147 Te-15 at.%Sn undergoes an invariant eutectic reaction at 401 °C during which
148 the liquid transforms into SnTe (intermetallic compound) and tellurium (solid-
149 solution) [50, 51, 52]. In the following subsections, we discuss aspects of the
150 morphology, length scales and the crystallographic orientations of the eutectic
151 phases in detail.

6
 (a) Longitudinal section, growth direction
is from bottom to top

(b) Transverse section, growth direction is

out of the plane of paper

(c) Morphology of the quenched solid-liquid

interface of binary Sn-Te eutectic showing
a planar growth front.

Figure 2: Scanning electron micrographs of binary Sn-Te eutectic ( Te-15at%Sn) solidified at

0.5µm/s.
7
152 3.1.1. Morphology and length scale selection
153 The steady-state microstructure of the eutectic system solidified at an im-
154 posed velocity of 0.5 µm/s is shown in Figure 2a and 2b. For the same velocity
155 an additional experiment is performed with an abrupt velocity change to derive
156 the quenched interface that is shown in Figure 2c, which gives the picture of the
157 solid-liquid interface during solidification. From the quenched interface, we can
158 say that the solid-liquid interface during solidification is planar without having
159 an irregular or faceted morphology. The longitudinal section in Figure 2a shows
160 the growth of eutectic phases along the imposed thermal gradient whereas the
161 transverse section in Figure 2b reveals a microstructure that resembles strings of
162 rods, where the strings may be perceived by joining the centroids of the nearest
163 neighbor rods. An individual string can be thought to be continuous until there
164 is a change in the nearest neighbor distance between the rods, this results in the
165 termination of the string and instead a new string may get initiated. The strings
166 of rods in Figure 2b are not arranged in definite straight lines in contrast to the
167 broken-lamellar structures that have well-defined orientations of the solid-solid
168 interfaces as observed in other eutectic systems [19, 33, 34]. The lack of such
169 strong alignment between the strings of connected rods indicates the absence of
170 strong anisotropy in both the solid-solid and the solid-liquid interfaces, but the
171 possibility of presence of weak anisotropy in the solid-solid interface exists.
172 Microstructures possess short and long-range spatial relationships in the
173 distribution of phases, which becomes explicitly visible when we map the mi-
174 crostructure to a reduced vector space. A way to perform this data reduction
175 is using 2-point spatial correlations [53, 54, 55] between the phases in the mi-
176 crostructure. The resulting map with all possible vectors and their probabilities
177 of occurrence becomes the basis for understanding the different microstructures
178 in this paper. Figure 3 shows the transverse section images of the eutectic
179 samples solidified at different imposed velocities and their corresponding self-
180 correlation images of the SnTe phases (appearing dark in the microstructures).
181 2-point correlations reveal that rods are arranged in a distorted hexagonal-
182 lattice (as depicted by the pattern of the high-intensity spots near the centre
183 of the spatial correlation image), while also highlighting that the trace of the
184 rod centroids form strings that exhibit alignment at lower solidification veloci-
185 ties (V=0.5, 1.0, 2.0µm/s). Such morphologies in a distorted hexagonal lattice
186 have been previously simulated using phase-field simulations by Plapp et al.
187 [56] where such structures arise beyond a critical eutectic spacing, for isotropic
188 eutectic systems whose minority phase fraction, fall in-between 0.2-0.3. For
189 V=4.0µm/s, two of the spots on either side of the central spot in the spatial
190 correlation plot merge leading to blurring. This leads to the development of a
191 diffuse circular ring in the spatial correlation plot instead of sharper spots in
192 the correlation plots near the center at lower velocities. This indicates that the
193 structure is transitioning towards a random distribution of rods and rod-strings.
194 With increase in solidification velocities, the spatial distribution of the rods be-
195 comes increasingly random where the alignment between the strings of rods
196 breaks down as well as the individual strings become shorter, that is revealed

8
197 both in the microstructure as well as in the spatial correlations.

(a) Velocity = 0.5 µm/s (b) Velocity = 1.0 µm/s

(c) Velocity = 2.0 µm/s

198 We have used transverse section images captured in the SEM for determin-
199 ing the average eutectic spacing by performing FFT (Fast Fourier Transform).
200 The spacing is averaged from several images captured around the middle of the
201 sample. For this eutectic, two different length scales are observed at lower solid-
202 ification velocities where the transverse section resembles strings formed by the
203 connection of the nearest neighbor rods. The first principal length scale in the
204 FFT corresponds to the inter-rod spacing along the rod-strings, and the second
205 is the uniform length scale in between the strings. We have utilized the latter for
206 deriving the spacings at the lower velocities. At higher velocities(greater than
207 8µm/s), the morphology tends towards a random distribution of rods. Here,
208 the strongest FFT peaks become diffuse and closely resemble a circular ring.
209 Therefore, for this situation, we have derived the spacing from the radius of the

9
 (d) Velocity = 4.0 µm/s (e) Velocity = 8.0 µm/s

(f) Velocity = 32.0 µm/s

Figure 3: Transverse section SEM images of directionally solidified binary Sn-Te eutectic at
different velocities along with their 2-point spatial self-correlations of the SnTe phase, shows
that the morphology of the Sn-Te eutectic is predominantly rod. However, the trace of the rod-
centroids give an impression of several strings of rods with weak alignment between them, in
samples solidified with V=0.5, 1.0, 2.0, 4.0 µm/s. With increasing velocities, rod distribution
becomes random. The colorbar depicts the probability of occurrence of self-correlation vectors.

10
210 first diffuse circular intensity spot in the FFT. Figure 4a shows the variation of
211 the average eutectic spacing with velocity. Although the morphologies vary with
212 velocity, the plot of the spacing against the V −0.5 shows a good linear fit, which
213 is most likely because the differences in morphology are due to slight rearrange-
214 ment of the rods. We have obtained the scaling constant λ2 V as 40.32 µm3 /sec
215 from the linear fit of the observed spacing. Using the value of the scaling re-
216 lation λ2 V obtained from the experiments combined with the thermodynamic
217 data corresponding to the phase diagram and the liquid diffusivities one can
218 derive the undercooling vs spacing relationships (refer Appendix A) for the rod
219 and lamellar morphologies. Figure 4b gives the variation of undercooling with
220 spacing for both the morphologies (under different imposed velocities 0.5 µm/s
221 and 32.0 µm/s velocities). At higher velocity (i.e. 32.0 µm/s), the minimum
222 undercooling for the rod is lower than that of the lamellae and hence by the
223 arguments in the Jackson-Hunt theory [23] the rod microstructure would be
224 the preferred morphology and we observed the same at that velocity. At lower
225 velocity (i.e. 0.5 µm/s), the minimum undercooling for the rod morphology
226 is comparable to that of the lamellae. The curves corresponding to both the
227 morphologies at lower velocities are so flat, it implies that both morphologies
228 can possibly co-exist (and even give rise to mixed growth forms). We find some
229 evidence of this in our experiments where microstructures for V=0.5 µm/s share
230 characteristics of both lamella (because of the formation of weakly aligned string
231 of rods) and rods. The essential point from this analysis is that with decreasing
232 velocity, the difference between the minimum undercooling of the two morpholo-
233 gies reduces. Additionally, the minimum undercooling spacing is similar for the
234 different morphologies (rod and lamellae), which is possibly the reason we do
235 not see much variation in the λ2 V values that we derive at the higher and lower
velocities for seemingly different experimental microstructures.

1 0
Lamellar (Velocity = 0.5 µm/sec)
9 L in e a r fit
Rod (Velocity = 0.5 µm/sec)
A v e r a g e e u t e c t i c s p a c i n g ( µm )

Lamellar (Velocity = 32.0 µm/sec)

8
Rod (Velocity = 32.0 µm/sec)
7

6
T (K)

0 .2 0 .4 0 .6 0 .8 1 .0 1 .2 1 .4
 (µm)
[ V e l o c i t y ( µm / s e c ) ] - 0 .5

(a) (b)

Figure 4: Plot depicting the variation of average eutectic spacing with velocity in (a), while
(b) is the variation of average undercooling with eutectic spacing computed at higher (32.0
µm/s) and lower velocity (0.5 µm/s) for both rod and lamellar morphology.
236

11
237 3.1.2. Crystallographic orientation relations in binary Sn-Te eutectic
238 The eutectic system consists of the SnTe and (Te) solid phases. Tellurium
239 crystallizes into a trigonal structure (space group is P31 21) whereas SnTe com-
240 pound crystallizes into a NaCl-type cubic structure (space group is Fm3̄m)
241 [50, 51]. Electron backscatter diffraction (EBSD) has been utilized to determine
242 the existence of crystallographic orientation relationships between the eutectic
243 phases. We conducted EBSD on the transverse section of the sample solidified
244 at 0.5 µm/s and the corresponding pole figures of SnTe and (Te) phases are
245 shown in the Figure 5. Orientation relations are determined by matching the
pole locations of each phase in the same reference frame.

(a) (b) (c) (d) (e)

{111}
{011}

{001}

SnTe {001} SnTe {111} SnTe {011} SnTe crystal schematic

{2201}

{0111}

(Te) {0111} (Te) {0001} (Te) {1120} (Te) {1120} (Te) crystal schematic

Figure 5: Pole figures of SnTe and (Te) obtained from EBSD data of binary eutectic solidified
at 0.5 µm/s exhibiting orientation relationships i.e. (111)SnT e // (0001)(T e) and (101̄)SnT e
// (112̄0)(T e) as highlighted in (b) and (c). Schematic of sample orientation in EBSD setup
is shown in (d). Corresponding planes are highlighted in SnTe and (Te) crystals of (e) using
VESTA [57].
246

247 Combining the EBSD pole plots we find that the (111) plane of the SnTe
248 crystal is parallel to the (0001) plane of (Te) crystal, while the (101̄) plane of
249 SnTe is parallel to (112̄0) plane of (Te), that are highlighted in Figure 5(b),(c).
250 Note that the second set of planes are also directions in the respective planes
251 in the first set. We find that the same orientation relations are observed in all
252 samples that remain invariant upon change in solidification velocity. Further,
253 we notice that the crystallographic planes forming the solid-liquid interface are
254 approximately {001} of SnTe and {01̄11} of (Te) in all binary eutectic growth
255 experiments and is shown in the Figure 5(a). Note that the planes (001) of SnTe
256 and (01̄11) are not parallel (refer Figure S1 in supplementary information file)
257 and therefore the growth relation is only approximate.

258 3.2. Microstructure evolution of Sn-Te eutectic in the presence of impurities

259 In the previous sections, we have established the morphologies that arise
260 during stable invariant two-phase growth in the SnTe-Te eutectic system. In

12
261 this section, we further investigate the formation of colonies and their inherent
262 microstructures. In order to destabilize the stable two-phase eutectic front; we
263 add impurities to the eutectic system, that generally partition into the liquid,
264 causing a boundary layer formation in front of the solid-liquid interface that
265 becomes unstable to perturbations beyond a particular velocity similar to a
266 Mullins-Sekerka instability for single-phase growth. For this study, we have
267 conducted experiments with Ag, Cu, Ge, In, Sb as impurity additions. The
268 microstructural features observed due to the addition of Ag, Cu, Ge and In are
269 similar (refer Figures S2-S6 in supplementary material), so we have restricted
270 our discussion in this section to Ag and Sb addition, that show diversity in
271 microstructural characteristics.

272 3.2.1. Ag addition to Sn-Te eutectic

273 We begin with the morphological characterization of the samples with Ag-
274 impurity addition that lead to colony formation. A typical colony microstruc-
275 ture is depicted in Figures 6a and 6b, that shows the transverse and longitudinal
276 sections respectively of a directionally solidified sample for an imposed solidifi-
277 cation velocity of 21µm/s with an impurity addition of 0.5% Ag following the
278 mono-variant line in the Ag-Sn-Te ternary phase diagram [62]. We observed a
279 colony structure with an inherent three-fold symmetry in the internal morphol-
280 ogy, while the intrinsic eutectic structure remains rod-like or connected rod-like
281 (strings of rods). The longitudinal sections reveal that the individual eutectics
282 grow in a branched fashion assuming an angle of approximately 54° to the central
283 colony axes. Our colony structures are very similar to those observed in other
284 eutectic systems such as Al2 O3 - ZrO2 (Y2 O3 ) [58, 59, 60], MnSb-(Sb,Bi) and
285 MnSb-(Sb,Sn) [61] where the two-phase eutectic front is destabilized because of
286 the addition of a third component.

287 Composition distribution of elements.

288 The composition distribution maps (refer Figure S2 in supplementary mate-
289 rial) reveal the occurrence of segregation of Ag in the inter-colony regions, owing
290 to higher compositions in the SnTe-phase in the inter-colony regions. The other
291 observation is that Ag has solubility only in the SnTe phase but not in (Te)
292 phase, which could be due to the presence of inherent Sn vacancies in SnTe
293 phase and almost no solubility of Ag in (Te) as depicted in the phase diagram
294 [62].

295 Critical velocity for colony formation.

296 In order to determine the critical velocities beyond which instabilities occur,
297 we have conducted experiments at different velocities for a given Ag compo-
298 sition. In addition, we have also performed experiments for varying impurity
299 compositions and determined the critical velocities for each system. Figure 8
300 shows the critical velocity for different percentages of Ag, while the microstruc-
301 tures are plotted in Figure 7. We see that with the addition of Ag, the critical
302 velocity decreases, that is also in agreement with the Mullins-Sekerka type mech-
303 anism for the destabilization of the interface, where the thermal length scales

13
 (i) Low magnification (ii) High magnification

(a) Transverse sections of the colonies where (i) is low magnification image and (ii) is
high magnification image

(b) Longitudinal section of the colonies,

growth direction is from bottom to top

Figure 6: Typical colony microstructure observed due to addition of Ag as an impurity,

where transverse section shows inherent three-fold symmetry in the internal morphology and
longitudinal section shows tilted growth of eutectic in a, b directions as highlighted in the
image where tilt angle is close to 54° from the central axis.

14
304 with the solute content and thereby with the increase in Ag, the interface would
305 become increasingly unstable to perturbations. In other words, formation of in-
306 stability occurs when G/V ≤ m∆c/D. For constant temperature gradient (G),
307 liquid diffusivity (D), and slope of liquidus curve (m); critical velocity for the
308 formation of an instability formation is inversely proportional to the amount
309 of impurity added. Hence, the critical velocity beyond which instabilities oc-
310 curs decrease with increase in impurity content. While from the relation one
311 expects the variation of the critical velocity with impurity composition to be
312 linear, however this also depends on the variation of the liquidus slope m with
313 composition in the liquid. Comparing the microstructures before the interface
314 becomes unstable; we see that as the critical velocity increases, the microstruc-
315 ture of the stable eutectic front that destabilizes becomes finer following the λ2 V
316 scaling for eutectics, where the scaling constant also shows variation with the
317 amount of impurity content. Whereas the eutectic spacing becomes finer as the
318 critical speed increases, the colony spacing, on the other hand, is approximately
319 the same just around the critical point, that is expected from a Mullins-Sekerka
320 type of instability. This offers an interesting paradigm of microstructural engi-
321 neering, wherein, multiple scales that are representative of the microstructure
322 may be modified upon addition of an impurity. Further, we also see that the
323 internal structure of the colonies has a three-fold symmetry for the Ag additions
324 of 1 at% and 0.5 at%, whereas it is absent for the case of 2 at%. This is most
325 likely caused by the nucleation of a separate eutectic grain having a different
326 growth orientation where the colony axis is tilted with respect to the growth
327 direction. This will be revealed in the following section.

328 Structure of the colonies: Crystallography and morphology.

329 In this section, we perform a combination of crystallographic and morpholog-
330 ical characterization of the colonies in order to delineate their structure during
331 growth. Electron backscatter diffraction (EBSD) has been carried out to identify
332 the orientation relationships between the phases (refer Section 3.1.2 for crystal
333 structures), during the growth of the colonies. Pole figures obtained from the
334 EBSD are shown in the Figure 9. Pole figures reveal that the entire colony is
335 a single eutectic grain. We find that the orientation relationship between the
336 phases remains the same as the orientation relationship observed in the binary
337 eutectic i.e. the (111) plane of SnTe crystal is parallel to the (0001) plane of
338 (Te) crystal and (101̄) plane of SnTe is parallel to (112̄0) plane of (Te).
339 By comparing the colony structure shown in Figure 9e and Figure 6b with
340 the corresponding pole figures shown in Figure 9a,9b, we find that the colony
341 axes is aligned with the h0001i direction of (Te) and corresponding h111i di-
342 rection of SnTe which is shown schematically in Figure 9f. In order to further
343 reveal the structure of the colony and the structure of the solid-liquid inter-
344 face, we have quenched the solidification front and is as shown in the Figure
345 10. The quenched interface shows that the solid-liquid interface is pyramidal.
346 Based on our previous EBSD results, and the quenched interface structure, we
347 can infer that the colonies grow along h0001i direction of (Te) (h111i direction
348 of SnTe) with the eutectic having the same crystallographic orientation rela-

15
 (a) 0.5at.%Ag
(b) 1.0at.%Ag
(c) 2.0at.%Ag

Velocity increase

Figure 7: Microstructures captured from transverse sections of samples solidified with different
percentage of Ag (increases from top to down) at different velocities (increases from left to
right).

16
 2 1 m m /s N o C o lo n ie s
2 0 2 0 m m /s C o lo n ie s
1 9 m m /s C o lo n ie s

1 5
V e l o c i t y ( µm / s )

1 1 m m /s
1 0 1 0 m m /s
9 m m /s

6 .0 m m /s
5 5 .5 m m /s
5 .0 m m /s

0 .0 0 .5 1 .0 1 .5 2 .0 2 .5

A t o m ic p e r c e n t o f A g

Figure 8: Plot showing the morphology observed for three different percentages of Ag at
different velocities thereby revealing the critical velocity beyond which the instability occurs.

(a) (b) (c) (d) (e) SEM image

SnTe {001} SnTe {111} SnTe {011}

(f) Crystal schematic

SnTe {001} SnTe {011}

(Te) {0111} (Te) {0001} (Te) {1120} (Te) {1120} SnTe {111}

Figure 9: Pole figures of SnTe and (Te) obtained from EBSD data of eutectic colony obtained
due to Ag addition (SEM image is shown in (e)) for the sample solidified at 21.0µm/s with
sample orientation as shown in schematic (d) are plotted in (a), (b), (c). Orientation rela-
tionships are same as the relations observed in the case of binary eutectic i.e. (111)SnT e //
(0001)(T e) and (101̄)SnT e // (112̄0)(T e) . Crystallographic planes in connection to morphology
of the colony shown in (e) are highlighted using VESTA [57] in crystal schematic (f).

17
349 tionship, while branching from central colony axes. A schematic depicting the
350 possible shape of the solid-liquid interface of the colonies is presented in Figure
10c. Further, we have utilized FEI Helios(G4) dual-beam microscope to dissect

Figure 10: Morphology of the quenched solid-liquid interface of the colony, while the schematic
shows the shape of the colonies across the solid-liquid interface.
351
352 the colony using gallium ions at appropriate locations and angles to confirm the
353 internal colony structure. Figure 11 shows the images captured using the SEM
354 after sectioning the sample as depicted in the corresponding inset schematic.
355 The images are captured at an angle with respect to the growth direction that
356 is around 52°. From Figure 11a, it is clear that the image captured is close to a
357 true transverse section, wherein the rods are growing perpendicularly outwards
358 from the plane of the paper. This is also conformant with the growth direc-
359 tions (a, b) of the eutectic that are highlighted in Figure 6b that also reveals
360 that eutectic is growing at an angle close to 54.73° which is the angle between
361 [001] and [111] of the SnTe phase. Combining with the pole figures depicted in
362 Figure 9 we derive that the growth of the (Te)-phase is approximately normal
363 to the {01̄11} planes and the SnTe crystals grow approximately normal to the
364 {001} planes that are tilted with respect to the colony axes. Surprisingly, these
365 are also the growth directions observed in stable binary eutectic growth of the
366 SnTe-Te eutectic. Similarly, Figure 11b, 11c shows how the eutectic emerges
367 from the central longitudinal section. Based on these results, we can confirm
368 that the solidification interface is probably faceted with the eutectic growing in
369 a branched manner from the central colony axes. With this discussion, it is also
370 clear that the experiments in Figure 7c correspond to tilted colonies as revealed
371 by EBSD (refer Figure S8 in supplementary material).

372 3.2.2. Sb addition to Sn-Te eutectic

373 A typical colony microstructure due to the addition of Sb as an impurity is
374 shown in Figure 12, which shows the transverse section of a directionally solid-
375 ified sample for an imposed solidification velocity of 15µm/s with an impurity
376 addition of 1.0% Sb. We observe that the structure is similar to colonies ob-
377 tained with Ag addition exhibiting a similar inherent three-fold symmetry in the

18
 52  Tilt w.r.t. electron beam 52  Tilt w.r.t. electron beam
(a) (b)

(c) 52  Tilt w.r.t. electron beam (d)

Figure 11: Internal structure of the colony captured using SEM when the sample is tilted at
an angle 52° (refer schematic (d)). Image (a) is captured when the colony was cut at an angle
54° as highlighted in inset schematic. Image (b), (c) are captured after dissecting one of the
three parts of the colony close to central longitudinal axis as highlighted in their respective
inset schematics to show eutectic emerging from the central longitudinal section with rod
morphology.

19
378 internal morphology, however, there is an important difference where a lamellar
379 morphology instead of rod-like morphology occupies the internal structure of
380 the colony. The reasons for such a phenomenon could be due to a change in
381 the volume fraction of the SnTe phase upon addition of Sb (refer phase diagram
382 [63]) but more importantly, it appears that the solid-solid interfaces are proba-
383 bly anisotropic that lead to the formation of well-aligned lamellae in the internal
384 structure of the colony. This modification to the eutectic structure for velocities
385 lesser than the critical velocity is also clear in Figure 13a where a mixture of
386 rods and broken-lamellar fragments (refer Figure 13a(ii)) form in contrast to the
387 mixture of rod and labyrinth structures for Ag-addition (refer Figure 13a(i)).
388 While the reasons for this transition in the nature of the solid-solid interface is
389 presently unclear to us, the probable reasons for the anisotropy might be due
390 to change in the nature of bonding in the SnTe phase, due to the addition of
391 Sb. However, a thorough investigation is required, which we intend to pursue
in the future.
(a) Low magnification (b) High magnification

Figure 12: Typical colony microstructure observed due to addition of Sb as an impurity, where
(a) is low magnification and (b) is high magnification transverse section images showing inher-
ent three-fold symmetry in the internal morphology, while the eutectic structure is modified
to a lamellar type.
392

393 In order to further portray the differences between the colony structures
394 we perform FIB. Under constant exposure of the sample surface consisting of
395 both phases, the milling rate of Tellurium is much higher than that of SnTe
396 that allows us to selectively mill out (Te), giving us a limited three dimensional
397 perspective of the growth microstructure. Figure 13b highlights the difference
398 between both colonies where the internal structure of the colony is rod-like for
399 the case of Ag-addition, while it is lamellar for the Sb-addition.

400 Composition distribution of elements.

401 The composition distribution maps (refer Figure S6 in supplementary mate-
402 rial) reveal that segregation of Sb in the inter-colony regions is very similar to
403 segregation observed in Ag added colonies. Due to segregation of Sb, the com-
404 position of the liquid in the segregated part shifts to an invariant three-phase

20
(a) Morphology of eutectic structure in the presence of Ag/Sb as an impurity below
critical velocity. Ag addition results in mixture of rod and labyrinth structures while
Sb addition results in mixture of rod and well-aligned lamellar structures.

(b) Morphology of colony structure in presence of Ag/Sb as an impurity, where the

(Te) phase is removed. Images show lamellar structure for Sb-addition whereas rod-
structure for Ag-addition.

Figure 13: Variation in morphology of eutectic obtained due to Ag-addition as well Sb-addition
where (a) is a comparison in the stable eutectic while (b) is a comparison in the eutectic colony.

21
405 eutectic composition leading to the formation of a third phase in the segregated
406 regions. The solubility of Sb is also observed only in the SnTe phase.

407 Structure of the colonies: Crystallography and morphology.

408 As we have seen in the previous sections, the orientation relationships be-
409 tween the phases in the binary SnTe-Te eutectic system are not affected due to
410 the formation of colonies. However, the internal structure of the colony obtained
411 due to Ag and Sb additions are different, so it is important to determine and
412 compare the orientation relationship between the phases. We performed EBSD
413 of the colony structures in order to obtain the pole figures as depicted in Figure
414 14. We find that the orientation relationships between the phases remain the
415 same as that observed in the binary eutectic and colonies observed due to Ag
416 addition, i.e. (111) plane of the SnTe crystal is parallel to the (0001) plane of
417 (Te) crystal and (101̄) plane of SnTe is parallel to (112̄0) plane of (Te).

(a) (b) (c) (d) (e) SEM image

SnTe {001} SnTe {111} SnTe {011}

(f) Crystal schematic

SnTe {001} SnTe {011}

(Te) {0111} (Te) {0001} (Te) {1120} (Te) {1120} SnTe {111}

Figure 14: Pole figures of SnTe and (Te) obtained from EBSD data of eutectic colony ob-
tained due to Sb addition (SEM image is shown in (e)) for the sample solidified at 15.0µm/s
with sample orientation as shown in schematic (d) are plotted in (a), (b), (c). Orientation
relationships are same as the relations observed in the case of binary eutectic and Ag added
colonies i.e. (111)SnT e // (0001)(T e) and (101̄)SnT e // (112̄0)(T e) . Crystallographic planes
in connection to morphology of the colony shown in (e) are highlighted using VESTA [57] in
crystal schematic (f).

418 Here again, we dissect the colony using gallium ions at appropriate loca-
419 tions and angles to confirm the internal colony structure. From Figure 15a, it is
420 clear that the image captured is close to a true transverse section, wherein the
421 lamellae are growing perpendicularly outwards from the plane of the paper. By
422 comparing the colony structure shown in Figures 14e and 15, with the corre-
423 sponding pole figures shown in Figure 14a, 14b and schematic shown in Figure
424 14f, we find that this colony growth is very similar to those observed with Ag
425 addition except that morphology of the eutectic is modified. Similarly, Figure
426 15b, 15c shows how the lamellar eutectic emerges from the central longitudinal

22
 52  Tilt w.r.t. electron beam 52  Tilt w.r.t. electron beam
(a) (b)

52  Tilt w.r.t. electron beam

(c) (d)

Figure 15: Internal structure of the colony captured using SEM when the sample is tilted at
an angle 52° (refer schematic (d)). Image (a) is captured when the colony was cut at an angle
54° as highlighted in inset schematic. Image (b), (c) are captured after dissecting one of the
three parts of the colony close to central longitudinal axis as highlighted in their respective
inset schematics to show eutectic emerging from the central longitudinal section with lamellar
morphology.

23
427 section. Based on these results, we can confirm that the solidification interface
428 is probably faceted with lamellar eutectic growing from the central colony axes.

429 4. Conclusions

430 In this paper, we have experimentally investigated microstructural forma-

431 tion both during stable invariant two-phase growth and during colony forma-
432 tion upon addition of impurities, in the SnTe-(Te)based alloy system. For stable
433 two-phase growth in the binary SnTe-(Te) we observe microstructures with mor-
434 phologies distributed between connected rod-like (weakly aligned strings of rods)
435 and rod-like (random distribution of rods or rod-strings). We have obtained the
436 eutectic scaling constant λ2 V as 40.32 µm3 /sec for the binary SnTe-(Te) eutec-
437 tic system where the solid phases also share an orientation relationship between
438 the (Te) and SnTe phases i.e. (111) plane of the SnTe crystal is parallel to
439 the (0001) plane of (Te) crystal and (101̄) plane of SnTe is parallel to (112̄0)
440 plane of (Te). Upon addition of a third component to the eutectic leads to
441 a diffusive instability (similar to a Mullins-Sekerka instability) leading to the
442 formation of two-phase colonies which arise beyond a critical velocity depend-
443 ing on the impurity composition. In our experiments, we find that the colony
444 exhibits an internal structure that appears to arise because of the solid-liquid
445 interface being strongly anisotropic. Critical velocities beyond which these in-
446 stabilities form are determined for each of the impurity levels, from which we
447 confirm that the instability is similar to a Mullins-Sekerka like instability as the
448 critical velocity reduces with an increase in the impurity content, that is further
449 substantiated by the composition maps which show that the impurity additions
450 are segregated in the inter-colony regions. Here, while the colonies obtained by
451 adding either Ag or Sb as an impurity show inherent three-fold symmetry in the
452 morphology, but the eutectic is rod-like for Ag-addition, while for Sb-addition,
453 the morphology of the eutectic is lamellar. We expect this change to be due to
454 the modifications of the volume fraction of the SnTe- phase as well as the na-
455 ture of the solid-solid interface where we suspect that the interfacial free-energy
456 becomes a function of the orientation. While, we presently are unsure about
457 the origin of this anisotropy, we expect the underlying reason to be a change in
458 the nature of bonding in the SnTe-phase upon addition of Sb. Additionally, we
459 observe that the orientation relations observed between SnTe and (Te) remains
460 the same even after the formation of colonies, for both the impurity additions.
461 We find that the colony axis is aligned with the h0001i direction of (Te) and
462 h111i direction of SnTe, while the eutectic phases grow in a branched manner
463 from the central colony axes, with a three-fold symmetry. Here, we find that
464 the (Te) crystals grow approximately normal to the {01̄11} planes and the SnTe
465 crystals grow approximately normal to the {001} planes which is the same set
466 of directions as in the binary eutectic.

24
467 5. Acknowledgment

468 The authors would like to thank DST-SERB for funding the current project
469 (DSTO1679). The authors would also like to thank Prof. Michel Rappaz, Prof.
470 Silvère Akamatsu, Prof. Mathis Plapp and Prof. Sabine Bottin-Rousseau for
471 insightful discussions during the work. ASK would like to thank Advanced
472 Facility for Microscopy and Microanalysis (AFMM), IISc for characterization
473 facilities.

474 Appendices
475 Calculation of the thermal gradient at the solid-liquid interface and phase dia-
476 grams are removed in order to focus only on the core contributions.

477 A. Calculation of Jackson-Hunt parameters for lamellar and rod mor-

478 phology

The variation of undercooling with spacing for both morphologies [23] i.e.
lamellar (L) and rod morphology (R) is

∆T = K1 V λ + K2 /λ. (1)

479 The expressions of K1 and K2 are different for both morphologies and are
480 given as follows. For lamellar morphology, K1L = mCo P/fα fβ D and K2L =
481 2m(Γα sin θα /fα mα + Γβ sin θβ /fβ mβ ), where Co = (Cα − Cβ ) ( i.e Co is the
482 composition difference between of the solid phases at the eutectic temperature),
483 fα , fβ are the volume fractions of the solid-phases, 1/m = (1/mα + mβ ), mα ,
484 mβ are the liquidus slopes of the solid phases. Γα and Γβ are the Gibbs-
485 Thomson coefficients of the solid and the liquid phases while the θα and θβ
486 are angles the α−liquid and the β−liquid tangents make with the horizon-
487 tal.
P∞ P is1 a function of the volume fraction of the one of the phases that reads
2
488
n=1 nπ 3 sin (nπfα√ ). Similarly for rod morphology, K1R = mCo M/fβ D, where
P∞ J 2
( fα γn )
489 M = n=1 (γ 1 )3 1 J 2 (γn ) , where γn is the n−th zero of the first order Bessel
n 0
490 function J1 , while Jo is the zeroth order Bessel function. We calculated K1L and
491 K1R values for Sn-Te eutectic based on their thermodynamic properties and the
492 liquid diffusivities [64] as 0.000457 and 0.000144 respectively. Thereafter using
493 the value of λ2 V (= K2L /K1L ) that we find using our experiments,
√ we assessed
494 the value of K2R as 0.00581. Using the relation K2R /K2L = fα from Jackson-
495 Hunt theory, we calculated K2L value as 0.011192. This allows us to determine
496 the ∆T vs spacing λ relationship for both morphologies.

25
497 References

498 [1] P. Ball, Nature’s patterns: a tapestry in three parts, Nature’s Patterns: A
499 Tapestry in Three Parts by Philip Ball. Oxford Univerity Press, July 2009.
500 (2009).
501 [2] P. Ball, Patterns in nature: why the natural world looks the way it does,
502 University of Chicago Press, 2016.
503 [3] W. Kurz, D. J. Fisher, Fundamentals of solidification, Vol. 1, trans tech
504 publications Aedermannsdorf, Switzerland, 1986.
505 [4] R. Trivedi, W. Kurz, Microstructure selection in eutectic alloy systems,
506 Solidification processing of eutectic alloys (1988) 3–34.
507 [5] J. Hunt, Pattern formation in solidification, Science and Technology of
508 Advanced Materials 2 (1) (2001) 147–155.
509 [6] J. A. Dantzig, M. Rappaz, Solidification, EPFL press, 2009.
510 [7] F. Galasso, Unidirectionally solidified eutectics for optical, electronic, and
511 magnetic applications, JOM 19 (6) (1967) 17–21.
512 [8] F. Galasso, F. Douglas, J. Batt, Recent studies of eutectics for nonstruc-
513 tural applications, JOM 22 (6) (1970) 40–44.
514 [9] H. Weiss, Electromagnetic properties of eutectic composites (a critical re-
515 view), Metallurgical Transactions 2 (6) (1971) 1513–1521.
516 [10] J. Parsons, A. Yue, Growth of fiber optic eutectics and their applications,
517 Journal of Crystal Growth 55 (3) (1981) 470–476.
518 [11] G. Chadwick, Structure and properties of eutectic alloys, Metal Science
519 9 (1) (1975) 300–304.
520 [12] D. A. Pawlak, Metamaterials and photonic crystals–potential applications
521 for self-organized eutectic micro-and nanostructures, Scientia Plena 4 (1)
522 (2008).
523 [13] D. A. Pawlak, S. Turczynski, M. Gajc, K. Kolodziejak, R. Diduszko,
524 K. Rozniatowski, J. Smalc, I. Vendik, How far are we from making meta-
525 materials by self-organization? the microstructure of highly anisotropic
526 particles with an SRR-like geometry, Advanced Functional Materials 20 (7)
527 (2010) 1116–1124.
528 [14] A. A. Kulkarni, E. Hanson, R. Zhang, K. Thornton, P. V. Braun,
529 Archimedean lattices emerge in template-directed eutectic solidification,
530 Nature 577 (7790) (2020) 355–358.
531 [15] J. Hunt, K. Jackson, Binary eutectic solidification, Trans. Metall. Soc.
532 AIME 236 (6) (1966) 843–852.

26
533 [16] G. A. Chadwick, Eutectic alloy solidification, Progress in materials science
534 12 (1963) 99–182.
535 [17] R. Kraft, Controlled eutectics, JOM 18 (2) (1966) 192–200.
536 [18] R. Elliott, Eutectic solidification processing: crystalline and glassy alloys,
537 Elsevier, 2013.
538 [19] M. Taylor, R. Fidler, R. Smith, The classification of binary eutectics, Met-
539 allurgical Transactions 2 (7) (1971) 1793–1798.
540 [20] M. Croker, R. Fidler, R. Smith, The characterization of eutectic structures,
541 Proceedings of the Royal Society of London. A. Mathematical and Physical
542 Sciences 335 (1600) (1973) 15–37.
543 [21] V. Podolinsky, Y. N. Taran, V. Drykin, Classification of binary eutectics,
544 Journal of Crystal Growth 96 (2) (1989) 445–449.
545 [22] L. Rátkai, G. I. Tóth, L. Környei, T. Pusztai, L. Gránásy, Phase-field
546 modeling of eutectic structures on the nanoscale: the effect of anisotropy,
547 Journal of materials science 52 (10) (2017) 5544–5558.
548 [23] K. A. Jackson, J. D. Hunt, Lamellar and rod eutectic growth, Transactions
549 of The Metallurgical Society of AIME 236 (1966) 1129–1142.
550 [24] A. Karma, A. Sarkissian, Morphological instabilities of lamellar eutectics,
551 Metallurgical and Materials Transactions A 27 (3) (1996) 635–656.
552 [25] M. Ginibre, S. Akamatsu, G. Faivre, Experimental determination of the
553 stability diagram of a lamellar eutectic growth front, Physical Review E
554 56 (1) (1997) 780.

555 [26] A. Parisi, M. Plapp, Stability of lamellar eutectic growth, Acta Materialia
556 56 (6) (2008) 1348–1357.
557 [27] S. Akamatsu, S. Bottin-Rousseau, G. Faivre, Experimental evidence for a
558 zigzag bifurcation in bulk lamellar eutectic growth, Physical review letters
559 93 (17) (2004) 175701.

560 [28] S. Akamatsu, M. Plapp, Eutectic and peritectic solidification patterns, Cur-
561 rent Opinion in Solid State and Materials Science 20 (1) (2016) 46–54.
562 [29] V. Witusiewicz, L. Sturz, U. Hecht, S. Rex, Lamellar coupled growth in
563 the neopentylglycol-(d) camphor eutectic, Journal of Crystal Growth 386
564 (2014) 69–75.

565 [30] S. Akamatsu, S. Bottin-Rousseau, G. Faivre, S. Ghosh, M. Plapp, Lamellar

566 eutectic growth with anisotropic interphase boundaries, in: IOP Conference
567 Series: Materials Science and Engineering, Vol. 84, IOP Publishing, 2015,
568 p. 012083.

27
569 [31] S. Akamatsu, S. Bottin-Rousseau, M. Şerefoğlu, G. Faivre, Lamellar eu-
570 tectic growth with anisotropic interphase boundaries: Experimental study
571 using the rotating directional solidification method, Acta Materialia 60 (6-
572 7) (2012) 3206–3214.
573 [32] S. Akamatsu, S. Bottin-Rousseau, M. Şerefoğlu, G. Faivre, A theory of
574 thin lamellar eutectic growth with anisotropic interphase boundaries, Acta
575 Materialia 60 (6-7) (2012) 3199–3205.
576 [33] H. Kaya, E. Çadırlı, M. Gündüz, Effect of growth rates and temperature
577 gradients on the spacing and undercooling in the broken-lamellar eutec-
578 tic growth (sn-zn eutectic system), Journal of materials engineering and
579 performance 12 (4) (2003) 456–469.
580 [34] H. Kerr, M. Lewis, Crystallographic relationships and morphologies of the
581 Bi-Zn and Bi-Ag eutectic alloys, Journal of Crystal Growth 15 (2) (1972)
582 117–125.
583 [35] H. Kerr, W. Winegard, The structure of some eutectics with high ratios of
584 the volume fractions, Canadian Metallurgical Quarterly 6 (1) (1967) 67–70.
585 [36] A. Hellawell, The growth and structure of eutectics with silicon and ger-
586 manium, Progress in Materials Science 15 (1) (1970) 3–78.
587 [37] P. Magnin, J. Mason, R. Trivedi, Growth of irregular eutectics and the alsi
588 system, Acta metallurgica et materialia 39 (4) (1991) 469–480.
589 [38] A. J. Shahani, X. Xiao, P. W. Voorhees, The mechanism of eutectic growth
590 in highly anisotropic materials, Nature communications 7 (2016) 12953.
591 [39] W. W. Mullins, R. Sekerka, Stability of a planar interface during solidi-
592 fication of a dilute binary alloy, Journal of applied physics 35 (2) (1964)
593 444–451.
594 [40] S. Akamatsu, G. Faivre, Traveling waves, two-phase fingers, and eutectic
595 colonies in thin-sample directional solidification of a ternary eutectic alloy,
596 Physical Review E 61 (4) (2000) 3757.

597 [41] S. Akamatsu, M. Perrut, S. Bottin-Rousseau, G. Faivre, Spiral two-phase

598 dendrites, Physical review letters 104 (5) (2010) 056101.
599 [42] M. Plapp, A. Karma, Eutectic colony formation: A phase-field study, Phys-
600 ical Review E 66 (6) (2002) 061608.
601 [43] M. Plapp, A. Karma, Eutectic colony formation: A stability analysis, Phys-
602 ical Review E 60 (6) (1999) 6865.
603 [44] T. Pusztai, L. Rátkai, A. Szállás, L. Gránásy, Spiraling eutectic dendrites,
604 Physical Review E 87 (3) (2013) 032401.

28
605 [45] A. Lahiri, C. Tiwary, K. Chattopadhyay, A. Choudhury, Eutectic colony
606 formation in systems with interfacial energy anisotropy: A phase field
607 study, Computational Materials Science 130 (2017) 109–120.
608 [46] M. Croker, R. Fidler, R. Smith, The cellular growth of Bi-Pb2Bi eutectic,
609 Journal of Crystal Growth 11 (2) (1971) 121–130.

610 [47] S. Bagheri, J. Rutter, Origin of microstructure in Bi–Pb and Bi–Sn binary
611 eutectics, Materials science and technology 13 (7) (1997) 541–550.
612 [48] P. Sireesha, Thermo-electric properties of Sn-Te eutectic and off eutectic
613 composites (phd thesis, unpublished work).

614 [49] B. Yang, S. Li, X. Li, Y. Wang, H. Zhong, S. Feng, Microstructure

615 and enhanced thermoelectric performance of Te–SnTe eutectic composites
616 with self-assembled rod and lamellar morphology, Intermetallics 112 (2019)
617 106499.
618 [50] R. Sharma, Y. Chang, The Sn- Te (tin-tellurium) system, Bulletin of Alloy
619 Phase Diagrams 7 (1) (1986) 72–80.
620 [51] B. Predel, Sn-Te (tin-tellurium), in: Pu-Re–Zn-Zr, Springer, 1998, pp. 1–5.
621 [52] Sn-Te binary phase diagram 0-100 at.% te: Datasheet from
622 “pauling file multinaries edition – 2012” in springermaterials
623 (https://materials.springer.com/isp/phase-diagram/docs/c 0903205),
624 copyright 2016 Springer-Verlag Berlin Heidelberg & Material Phases Data
625 System (MPDS), Switzerland & National Institute for Materials Science
626 (NIMS), Japan.
627 [53] D. Wheeler, D. Brough, T. Fast, S. Kalidindi, A. Reid, Pymks: materials
628 knowledge system in python (2014).

629 [54] S. R. Kalidindi, Hierarchical materials informatics: novel analytics for ma-
630 terials data, Elsevier, 2015.
631 [55] D. B. Brough, D. Wheeler, S. R. Kalidindi, Materials knowledge systems in
632 python—a data science framework for accelerated development of hierar-
633 chical materials, Integrating materials and manufacturing innovation 6 (1)
634 (2017) 36–53.
635 [56] A. Parisi, M. Plapp, Defects and multistability in eutectic solidification
636 patterns, EPL (Europhysics Letters) 90 (2) (2010) 26010.
637 [57] K. Momma, F. Izumi, Vesta 3 for three-dimensional visualization of crystal,
638 volumetric and morphology data, Journal of applied crystallography 44 (6)
639 (2011) 1272–1276.
640 [58] C. Boldt, Directional solidification of the alumina-zirconia ceramic eutectic
641 system (1994).

29
642 [59] J. Lee, A. Yoshikawa, H. Kaiden, K. Lebbou, T. Fukuda, D. Yoon, Y. Waku,
643 Microstructure of Y2O3 doped Al2O3/ZrO2 eutectic fibers grown by the
644 micro-pulling-down method, Journal of Crystal Growth 231 (1-2) (2001)
645 179–185.
646 [60] L.-s. Fu, G.-q. Chen, X.-s. Fu, W.-l. Zhou, Insights into the ternary eutec-
647 tic microstructure formed in intercolony regions in Al2O3–ZrO2 (Y2O3)
648 system, Journal of the American Ceramic Society 102 (1) (2019) 498–507.
649 [61] M. Durand-Charre, F. Durand, Effects of growth rate on the morphology
650 of monovariant eutectics: MnSb-(Sb, Bi) and MnSb-(Sb, Sn), Journal of
651 Crystal Growth 13 (1972) 747–750.

652 [62] G. Effenberg, B. Grieb, Materials Science International

653 Team, MSIT®, Ag-Sn-Te ternary phase diagram evalu-
654 ation · phase diagrams, crystallographic and thermody-
655 namic data: Datasheet from msi eureka in springermaterials
656 (https://materials.springer.com/msi/docs/sm msi r 10 017334 01), copy-
657 right 1988 MSI Materials Science International Services GmbH.

658 [63] Sb-Sn-Te isothermal section of ternary phase diagram: Datasheet

659 from “pauling file multinaries edition – 2012” in springermate-
660 rials (https://materials.springer.com/isp/phase-diagram/docs/c 0952756),
661 copyright 2016 Springer-Verlag Berlin Heidelberg & Material Phases Data
662 System (MPDS), Switzerland & National Institute for Materials Science
663 (NIMS), Japan.
664 [64] K. Kinoshita, K. Sugii, PbTe-SnTe mutual diffusion coefficient at just above
665 the pb0. 8sn0. 2te solidus temperature, Journal of crystal growth 67 (2)
666 (1984) 375–379.

667 [65] Sb-Sn-Te liquidus projection of ternary phase diagram: Datasheet

668 from “pauling file multinaries edition – 2012” in springermate-
669 rials (https://materials.springer.com/isp/phase-diagram/docs/c 0952750),
670 copyright 2016 Springer-Verlag Berlin Heidelberg & Material Phases Data
671 System (MPDS), Switzerland & National Institute for Materials Science
672 (NIMS), Japan.

30
Declaration of interests

 The authors declare that they have no known competing financial interests or personal
relationships that could have appeared to influence the work reported in this paper.
673