METALS AND MATERIALS International, Vol. 14, No. 5 (2008), pp. 575~582

Dependency of Microstructural Parameters and Microindentation Hardnesson the Temperature Gradient in the In-Bi-Sn Ternary Alloy with

a Low Melting Point

H. Kaya1, U. Böyük

1, E. Çadlrll

2, Y. Ocak

3, S. Akbulut

4, K. Ke lio lu

3 and N. Mara ll

3,*

1Department of Science Education, Education Faculty, Erciyes University, Kayseri, Turkey 2Department of Physics, Faculty of Arts and Sciences, Ni de University, Ni de, Turkey

3Department of Physics, Faculty of Arts and Sciences, Erciyes University, Kayseri, Turkey

4Institute of Science and Technology, Department of Physics, Erciyes University, Kayseri, Turkey

The ternary alloy In-21.5 at.% Bi-17.8 at.% Sn, which has a melting point of 60oC, was directionally solidified

upward with a constant growth rate (V = 3.2 μm/s) and different temperature gradients (G = 0.91 K/mm to2.85 K/mm) by using a Bridgman-type directional solidification furnace. The lamellar spacings (λ) and micro-hardness (HV) were measured from both the transverse and longitudinal sections of the samples. The dependenceof the lamellar spacings (λ) and microhardness (HV) on the temperature gradients (G) were determined bymeans of linear regression analysis. According to these results, the value of λ decreases as the value ofG increases and the value of HV increases for a constant V. The results obtained in this work are comparedwith previous similar experimental results obtained for binary or ternary alloys.

Keywords: directional solidification, eutectic, growth from melt, alloys

s g˘ s

g˘ g˘

1. INTRODUCTION

Many commercial materials are multicomponent alloys

whose properties can be determined by the microstructure

that develops during solidification and subsequent process-

ing stages. One of the essential challenges of materials sci-

ence is to understand how multiphase microstructures form

and how they can be controlled via deliberate selection of

alloy composition and processing parameters. Multiphase

solidification in multicomponent alloys is pertinent to many

commercial materials and industrial processes, while also

raising challenging questions from a fundamental point of

view. In the past few years, there has been a surge of research

activities dedicated to multiphase solidification of ternary

and multicomponent alloys.

Multiphase solidification of multicomponent materials has

also attracted pronounced academic interest. The study of

the solidification behavior of multicomponent and mul-

tiphase systems is important for understanding the different

properties of these materials. The fundamental knowledge

on solidification has been developed mainly for pure materi-

als and for binary alloys that exhibit single-phase growth

(solid solution) or two-phase growth in eutectic and peritec-

tic class reactions. Nonetheless, the formation process of

microstructures during solidification is less understood for

cases where multiphase reactions occur along the solidifica-

tion path of these alloys. A comprehensive overview with

respect to the last topic is given by Hecht et al. [1].

The industrial and fundamental aspects of multiphase

microstructure evolution in multicomponent alloys can only

be addressed with the hope for success if close interaction is

maintained among scientists investigating the thermody-

namic, thermophysical, and microstructural properties of these

alloys. The In-Bi-Sn ternary system is technologically impor-

tant for soldering applications. Alloys of eutectic composition

may also serve as model alloys for the investigation of pattern

formation during directional solidification of eutectics [2-6].

Prior studies indicate that several invariant reactions exist in

this alloy system at temperatures below 100oC [7-9].

Thus, the purpose of this paper is to experimentally inves-

tigate the dependence of lamellar spacings (λ) and microin-

dentation hardness (HV) on the temperature gradient (G) in

the In-21.5 at.% Bi-17.8 at.% Sn ternary alloy and compare

the results with previous experimental results for binary or

ternary alloys.

2. EXPERIMENTAL PROCEDURE

2.1. Sample production and microstructure observation

In the present work, the In-Bi-Sn ternary alloy was chosen*Corresponding author: marasli@erciyes.edu.tr

doi: 10.3365/met.mat.2008.10.575 Published 23 October 2008

576 H. Kaya et al.

with a composition of In-21.5 at.% Bi-17.8 at.% Sn for the

growth of the eutectic structure from the ternary liquid.

Thus, the In-21.5 at.% Bi-17.8 at.% Sn alloy was prepared in

a vacuum furnace [10] with 99.9 % pure indium, 99.99 %

pure bismuth and 99.99 % pure tin. After sufficient time was

allowed for the melt homogenization, the molten alloy was

poured into 10 graphite crucibles (250 mm in length, 4 mm

ID, and 6.35 mm OD) held in a specially constructed casting

furnace (hot filling furnace) at approximately 30oC above

the melting point of alloy. The molten alloy was then direc-

tionally frozen from bottom to top to ensure that the crucible

was completely full.

Each sample was then positioned in a Bridgman-type fur-

nace in a graphite cylinder (300 mm in length, 10 mm ID,

and 40 mm OD). The details of the apparatus and experi-

mental procedures are given in [10-16]. In the experimental

technique, the sample was usually heated at about 50oC,

100oC, 150

oC, 200

oC, and 250

oC above the melting tem-

perature to get a different temperature gradient of the sam-

ple, and the sample was then grown by being pulled

downwards by a constant speeded synchronous motor after

the stabilization of the thermal conditions in the furnace

under an argon atmosphere. After a steady state growth of

10 cm to 12 cm, the samples were quenched by being rap-

idly pulled down into a water reservoir. The temperature of

the water in the reservoir varied from about 20oC to 25

oC.

The water cooling was sufficient to get a well-defined solid-

liquid interface at a melting temperature higher than 100oC

but, after a few experimental works, the water cooling

appeared to be insufficient to produce a well-defined solid-

liquid interface at a melting temperature lower than 100oC.

The task of investigating how the microstructure parame-

ters depend on the temperature gradient is diffucult because

the experimental conditions preclude any wide-ranging tem-

perature gradients. The task is even more difficult at a low

melting temperature. The melting point of the In-21.5 at.%

Bi-17.8 at.% Sn ternary alloy was measured to be 60oC with

a standard route. Thus, in the present work, the water tem-

perature in the reservoir was kept at minus 10oC to an accu-

racy of ± 0.01 K by means of a Poly Science digital 9102

model heating/refrigerating circulating bath containing an

aqueous ethylene glycol solution; this method ensure the

largest temperature gradients and a well-quenched solid-liq-

uid interface. The temperature on the sample was controlled

to an accuracy of ± 0.01 K with a Eurotherm 2604-type con-

troller. The solidification of the samples for five different

temperature gradients was carried out in a range of 0.91 K/

mm to 2.85 K/mm at a constant growth rate (3.2 μm/s). Fig-

ure 1 shows a block diagram of the experimental setup.

The quenched sample was removed from the graphite cru-

cible and cut into lengths of about 8 mm. The longitudinal

and transverse sections were ground flat with 180 grit SiC

paper, and the longitudinal and transverse sections of the

ground sample were cold mounted with epoxy-resin. Because

of the low melting point of this alloy, the limited amount of

epoxy hardener must be handled with care. During the set-

ting of the epoxy, any excess hardener can elevate the tem-

perature to a level that is sufficient to melt the sample during

the cold mounting. After the polishing, the samples were

etched for 3 s with 4 g of picric acid ((NO2)3C6H2OH) and

20 ml of hydrochloric acid (HCl) in 400 ml of ethanol

(C2H5OH). The microstructures of the samples, which were

Fig. 1. Block diagram of the experimental setup.

Dependency of Microstructural Parameters and Microindentation Hardness on the Temperature... 577

revealed after the metallographic process, were photo-

graphed with an Olympus DP12 digital camera placed in

conjunction with an Olympus BHX-type light optical micro-

scope. A graticule (200 × 0.01 = 2 mm) was also photo-

graphed with the same objective.

Figure 2 shows typical microstructural images for differ-

ent temperature gradients. In addition, an energy dispersive

X-ray analyzer (EDX) was used for the quantitative chemi-

cal composition analysis of the solid lamella phases in the

sample for the purpose of designating and ensuring the exist-

ence of solid phases. The results are given in Fig. 3. The

solid solubility of Bi in Sn is 1.5 at.% Bi and the solid solu-

bility of Sn in Bi is less than 0.18 at.% Sn at room tempera-

ture. Note also that the maximum solubility of Bi in solid

indium is 4 at.% Bi, though there are no data concerning the

solubility of In in solid Bi at room temperature. Furthermore,

the maximum solid solubility of In in solid Sn is about

6.7 at.% and the maximum solid solubility of Sn in solid In

is about 4 at.% Sn [17]. According to the EDX results, which

are shown in Fig. 3, and the solubility of the components in

each phase, the grey phase was found to contain mostly In

(66.63 at.% In) and Bi (29.87 at.% Bi), with a small amount

of Sn (3.5 at.% Sn); hence, the grey phrase was identified as

the In2Bi intermetallic solid solution phase (In-30.52 at.%

Fig. 2. Typical optical images of the growth morphologies of the directional solidified In-21.5 at.% Bi-17.8 at.% Sn ternary eutectic alloy with adifferent temperature gradient in a constant growth rate (V = 3.20×10

-4 cm/s) for (a) a longitudinal section with a temperature gradient of 0.91 K/

mm, (b) a transverse section with a temperature gradient of 0.91 K/mm, (c) a longitudinal section with a temperature gradient of 1.80 K/mm, (d)a transverse section with a temperature gradient of 1.80 K/mm, (e) a longitudinal section with a temperature gradient of 2.85 K/mm, and (f) atransverse section with a temperature gradient of G = 2.85 K/mm.

578 H. Kaya et al.

Bi-3 at.% Sn) and the dark phase was identified as the solid

Sn solution phase (Sn-16.11 at.% Bi-40.14 at.% Sn) [2]. As

shown in Fig. 2, the microstructure consists of a regular

lamellar γ-Sn structure in the In2Bi intermetallic solution

matrix.

2.2. The measurement of temperature gradient, growth

rate and lamellar spacing

The temperature in the specimen was measured with three

K-type 0.25 mm diameter insulated thermocouples fixed

within the sample with a spacing of 10 mm to 20 mm. In the

present work, an alumina tube with dimensions of 1.2 mm

OD × 0.8 mm ID was used to insulate the thermocouples

from the melt. All the thermocouple ends were then con-

nected to the measurement unit, which consisted of a data

logger and computer. The cooling rates during the growth

period were recorded with the data logger via the computer.

When the solid-liquid interface was at the second thermo-

couple, the temperature difference between the first and sec-

ond thermocouples (ΔT) was read from the data logger

records. The temperature gradient (G = ΔT/ΔX) for each

sample was determined on the basis of the measured value of

ΔT and the known value of ΔX.

The time taken for the solid-liquid interface to pass the

thermocouples at given distances was read from the data log-

ger records. Thus, the value of the growth rate (V= ΔX/Δt)

for each sample was determined on the basis fo the measured

value of Δt and the known value of ΔX.

The lamellar spacings were measured from the photo-

graphs of the microstructure (Fig. 2) with a linear intercept

method [18]. The value of the lamellar spacings (λ* ) mea-

sured on the longitudinal section is larger than the value of

lamellar spacings (λ) measured from the transverse section.

The measured values of the lamellar spacings are given in

Table 1. As shown in Table 1, even some of the λ*m values

are higher than the average λa values. In a longitudinal view,

the lamellar spacings seem to be different in each grain

because the samples were cut at different angles, θ, to the

polished surface. For that reason, the longitudinal sections

are inadequate for making an evaluation of the lamellar

spacings without a geometrical correction. The values of λa

on the transverse section of the sample were observed to be

more reliable than the values of λ on the longitudinal section

of the sample. In addition to the above microstructural char-

acteristics, several solidification faults, such as layer mis-

matches and lamellar terminations, were observed. As shown

in Fig. 4, the α-β boundary tilts toward the β lamella side;

furthermore, a pocked area appears in the liquid in front of

the α-L interface, and α new β lamella eventually grows in

the pocked area where a positive termination forms. By this

dynamic mechanism, the local spacing (λm* ) decreases. The

α-β boundary tilts toward the α lamella side and the local

α-L interface disappears with the α lamella being over-

lapped by two neighbors’ β lamella (negative termination)

[19-21]. Despite the fact that these microstructures are

changed by positive and negative termination mechanisms,

Fig. 3. (a) The chemical composition analysis of the eutectic solid phases by means of SEM EDX: the grey phase (the In2Bi intermetalic solutionphase) and the dark phase (the Sn-rich phase). (b) The chemical composition analysis of the quenched liquid phase (In-21.5 at.% Bi-17.8 at.%Sn) in the ternary alloy by means of SEM EDX.

Dependency of Microstructural Parameters and Microindentation Hardness on the Temperature... 579

the values of λ*m and λ

*M were measured as accurately as

possible on each specimen. Table 1 and Figure 5 give the

values of λa, λa*, λ

*m and λ*

M as a function of the temperature

gradient. The details of the measurements for G, V and λ are

given in [10,12-16].

2.3. The measurement of the microindentation hard-

ness, Hv

The microhardness measurements were made with a stan-

dardized Vickers indenter, with loads of 25 g and a dwell

time of 10 s, and a Fujitech FM-700 model hardness measur-

ing test device. The microhardness value was the average of

at least 10 measurements on the transverse section (HV(tr))

and the longitudinal section (HV(lng)). The minimum impres-

sion spacing (from the centre to the edge of an adjacent

impression) was about three times the diagonal and at least

0.5 μm from the edge of the sample. Table 1 gives the values

of λ, G and HV.

3. RESULTS AND DISCUSSION

A Bridgman-type directional solidification furnace was

used to unidirectionally solidify the In-21.5 at.% Bi-17.8 at.%

Sn ternary eutectic alloy at a constant growth rate (V = 3.2

μm/s) with different temperature gradients (0.91 K/mm to

2.85 K/mm) in order to see how the temperature gradients

(G) affect the lamellar spacings (λ) and microindentation

hardness HV(tr).

3.1. The effect of the temperature gradient on the lamel-

lar spacings

As expected, the formation of microstructures varies with

the temperature gradients at a constant growth rate (V = 3.2

μm/s). As the temperature gradient increases, the lamellar

spacing of the In2Bi-(γ) Sn structure decreases. As shown in

Figs. 2(a) and (b), the highest interlamellar spacing was

obtained at the minimum value of the temperature gradient

(0.91 K/mm). A low temperature gradient allows a more

intense atomic diffusion. Thus, the highest interlamellar

spacing is attributed to the more intense cooperative growth

and to the higher diffusion length. On the other hand, as

shown in Figs. 2(e) and (f), the smallest interlamellar spac-

ing was obtained at the maximum value of the temperature

gradient (G = 2.85 K/mm).

Table 1 and Figure 5 give the variations in the lamellar

Table 1. The values of lamellar spacings (λ),temperature gradient (G) and microhardness (HV) for In-21.5 at.% Bi-17.8 at.% Sn ternary

alloy with a constant growth rate (V = 3.2 µm/s)

Solidification parameters Lamellar spacings Microindentation hardness values

V (μm/s) G (K/mm) λa (μm) λ*a (μm) λ

*m (μm) λ

*M

(μm) HV(tr) (kg/mm

2) HV(lng) (kg/mm

2)

3.2±0.09

0.91 8.47±0.49 8.75±0.52 7.03±0.48 9.73±0.59 6.80±0.28 6.16±0.31

1.35 7.63±0.43 8.04±0.50 6.41±0.44 8.93±0.54 7.01±0.32 6.32±0.33

1.80 6.72±0.40 6.97±0.38 5.57±0.37 7.71±0.47 7.08±0.37 6.55±0.37

2.32 5.95±0.38 6.27±0.36 5.04±0.35 6.94±0.39 7.48±0.35 7.01±0.38

2.85 5.28±0.31 5.42±0.29 4.32±0.29 5.99±0.36 7.63±0.34 7.13±0.31

λ: The values of the lamellar spacing obtained from the transverse section of the samplesλ

*: The values of the lamellar spacing obtained from the longitudinal section of the samples

HV(tr): The values of the microindentation hardness obtained from the transverse section of the samplesHV (lng): The values of the microindentation hardness obtained from the longitudinal section of the samples

Fig. 4. (a) Readjustment of local spacing by the positive terminationsand (b) the readjustment of local spacing by the negative terminations.

Fig. 5. Variation of lamellar spacings as a function of the temperaturegradient at a constant growth rate (V = 3.2 µm/s).

580 H. Kaya et al.

spacings (λ) with the temperature gradients (G) at a constant

growth rate (V = 3.2 μm/s). The variation of λ versus G is

essentially linear on a logarithmic scale. As shown in Table 1

and Fig. 5, the data form straight lines and the linear regres-

sion analysis gives the proportionality equation as

(for the constant G) (1)

where k is a constant and m is an exponent value of the tem-

perature gradient. The relation between the interlamellar

spacings and the temperature gradient was determined by

using linear regression analysis; and the results are given in

Table 2. As shown in Table 2 and Fig. 5, the exponent values

of the temperature gradient (G) for λa, λa*, λ

*m and λ

*M are

0.40, 0.42, 0.43, and 0.40, respectively. The dependence of λ

values on the temperature gradient is apparently exponential,

and the average exponential value of the temperature gradient

is 0.41.

The influence of the temperature gradient (G) on the

microstructure parameters has not been considered in theo-

retical studies in terms of binary or ternary eutectic growth.

As shown in Fig. 5 and Table 1, the influence of G on the

microstructure parameters (λa, λa* , λ

*m and λ

*M) cannot be

ignored for eutectic systems. Several authors have investi-

gated the influence of the temperature gradient on the lamel-

lar spacings [10,12-14,16,22,23]. The exponential value

(0.40) obtained for the transverse section in this work is in

quite good agreement with the value of 0.37, which was

obtained by Gündüz et al. [12] for the Al-Si binary eutectic

alloy and by Çadlrll et al. [13] for the Pb-Cd binary eutectic

alloy. This exponential value of 0.40 is somewhat higher

than the values of 0.33, 0.30 and 0.28, which were obtained

by Toloui and Hellawell [22] for the Al-Si binary eutectic

alloy, Çadlrll et al. [10] for the Al-Cu binary eutectic alloy,

and Kaya et al. [14] for the Sn-Zn binary eutectic alloy,

respectively. Moreover, the exponential value of 0.40 is

somewhat smaller than the values of 0.49 and 0.47 obtained

by Çadlrll and Gündüz [16] for the Pb-Sn binary eutectic

alloy and Kaya et al. [23] for the Bi-Cd binary eutectic alloy,

respectively.

3.2. The effect of the growth rate and lamellar spacing

on the microindentation hardness

The mechanical properties such as the microhardness (HV)

of the directional solidified materials also depend on the

solidification parameters, namely the temperature gradient

(G). The relations of the microhardness (HV), the temperature

gradient (G) and the lamellar spacings (λ) can be expressed

as follows [15,24-28]:

(2)

(3)

where m and n are the exponential values of the temperature

gradient and the lamellar spacing, respectively, and k1 and k2

are the constants that can be experimentally determined.

Table 1 and Figure 6 show the variations of the microhard-

ness (HV) as a function of the temperature gradients at a con-

stant growth rate. The value of HV increases as the value of

V increases. The dependence of the microhardness (HV) on

the temperature gradient (G) was determined by using linear

regression analysis; and the results are given in Table 2. The

value of the exponent of the temperature gradient is equal to

0.11 and 0.14 for the transverse and longitudinal sections of

the In-Bi-Sn ternary eutectic alloy, respectively. The expo-

nential value of 0.11, which was obtained in this study, is

fairly close to the value of 0.09, which was obtained by Kaya

et al. [15] for the Al-Si eutectic alloy, and the values of 0.12,

and 0.11, which were obtained by Kaya [24] for Pb-Cd and

λ kGm–

=

Hv

k1Gm

=

Hv

k2λn–

=

Table 2. Dependence of the lamellar spacings and the microhardness

(HV) on the temperature gradient (G) for the directionally solidified In-

21.5 at.% Bi-17.8 at.% Sn ternary alloy at a growth rate (V = 3.2 µm/s)

The relationships Constant (k)Correlation

coefficients (r)

λa= k1 G-0.40

k1= 8.43 (K0.40

. μm0.60

) r1= -0.981

λa* = k2 G

-0.42k2= 8.71 (K

0.42. μm

0.58) r2= -0.981

λm*

= k3 G-0.43

k3= 7.00 (K0.43

. μm0.57

) r3= -0.982

λM*

= k4 G-0.40

k4= 9.49 (K0.40

. μm0.60

) r4= -0.981

Hv(tr) = k5 G0.11

k5= 6.81 (kg.mm-1.90

. K -0.10

) r5= 0.965

Hv(tr) = k6 λ -0.23

k6= 10.96 (kg.mm-1.77

) r6 = -0.977

Hv(ln g) = k7 G0.14

k7= 6.15 (kg.mm-1.86

. K -0.14

) r7 = 0.969

Hv(ln g) = k8 λ -0.32

k8= 12.47 (kg.mm-1.68

) r8 = -0.978

Fig. 6. Variation of the microindentation hardness, HV, as a function ofthe temperature gradient for the directionally solidified In-21.5 at.%Bi-17.8 at.% Sn ternary eutectic alloy at a constant growth rate (V = 3.2µm/s).

Dependency of Microstructural Parameters and Microindentation Hardness on the Temperature... 581

Bi-Cd eutectic alloys, respectively. The exponential value of

0.11 is greater than the values of 0.05 and 0.04, which were

obtained respectively by Yllmaz and Elliott [25] for Al-Si

eutectic alloy and Kaya [24] for the Sn-Zn eutectic alloy

under similar solidification conditions.

As shown in Table 1 and Fig. 7, when V is constant, the

value of HV decreases as the value of λ increases. The depen-

dence of the microhardness (HV) on the lamellar spacings (λ)

was also determined by using binary regression analysis; and

the results are given in Table 2. The values of the exponent

of the lamellar spacing are equal to 0.23 and 0.32 for the

transverse and longitudinal sections of the same ternary

alloy, respectively. These values are in good agreement with

the values of 0.20, 0.22, and 0.18, which were obtained by

Kaya et al. [26] for a different alloy system, Khan et al. [27]

and Kaya et al. [15] for the Al-Si eutectic system. On the

other hand, these values are higher than the value of 0.08,

which was obtained by Yllmaz and Eliot [25] for the Al-Si

eutectic alloy; moreover, they fail to confirm the value of

0.5, which was suggested by Telli and Klsakürek [28] for Al-

Si eutectic alloys.

4. CONCLUSION

The microstructures produced at a constant growth rate

(V = 3.2 μm/s) with different temperature gradients (0.91 K/

mm to 2.85 K/mm) tended to form a two-phase lamellar

structure. The lamellar spacing is strongly dependent on the

growth rate because, as shown in Table 1, the increase in the

growth rate causes microstructural refinement. As shown in

Figs. 2(a) and (b), the highest lamellar spacing was obtained

with the lowest temperature gradient (0.91 K/mm). On the

other hand, as shown in Figs. 2(e) and (f), the smallest lamel-

lar spacing was obtained with the highest temperature gradi-

ent (2.85 K/mm).

Lamellar spacings (λ) decrease inversely as the tempera-

ture gradient increases for the directionally solidified In-Bi-

Sn ternary eutectic alloy at a growth rate with different tem-

perature gradients. The relation between these parameters

can be obtained by binary regression analysis as follows:

where k1 = 8.43 (K0.44

. μm0.56

). This exponential value is in

good agreement with the results of some other experimental

works [12,13]. The value of microhardness (HV) for the direc-

tionally solidified In-21.5 at.% Bi-17.8 at.% Sn ternary eutec-

tic alloy with a constant growth rates (G = 0.91 K/mm) increases

as the value of the temperature gradient (V) increases and as

the value of the lamellar spacing (λ) decreases; furthermore,

the relations between these parameters was been found to

be HV = k5G0.11

and HV = k6λ-0.23

for the transverse sections.

These exponential values are generally in good agreement

with the results of previous experimental works [15,24-

28].

ACKNOWLEDGMENT

This research was supported financially by the Scientific

and Technical Research Council of Turkey under contract no

105T481. The authors are grateful to the Scientific and Tech-

nical Research Council of Turkey for their financial support.

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