Accepted Manuscript

Title: The solid-liquid interfacial energy for solid Zn solutionat the eutectic Zn-Sn-Mg ternary alloy

Author: Canan Alper Billur Buket Saatci

PII: S0040-6031(14)00215-9DOI: http://dx.doi.org/doi:10.1016/j.tca.2014.05.010Reference: TCA 76877

To appear in: Thermochimica Acta

Received date: 17-3-2014Revised date: 1-5-2014Accepted date: 6-5-2014

Please cite this article as: C.A. Billur, B. Saatci, The solid-liquid interfacial energy forsolid Zn solution at the eutectic Zn-Sn-Mg ternary alloy, Thermochimica Acta (2014),http://dx.doi.org/10.1016/j.tca.2014.05.010

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Graphical Abstract (for review)

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The solid-liquid interfacial energy for solid Zn solution at the eutectic Zn-Sn-Mg ternary

alloy

Canan Alper Billur a,*

, Buket Saatçi

aDepartment of Physics, Erciyes University, 38039 Kayseri, Turkey

Abstract

The Gibbs–Thomson coefficient, , the effective entropy change, fS , the solid–

liquid interfacial energy, SL , and the grain boundary energy, GB , for solid Zn solution at

the eutectic Zn-Sn-Mg ternary alloy have been calculated by using the grain boundary groove

method with Bridgman-type directional solidification apparatus.

Keywords: Zn-Sn-Mg ternary alloy, Gibbs–Thomson coefficient, interfacial energy.

∗Corresponding author: Phone: +90 352 207 66 66 /33129; Fax: +90 352 433 4933.

E-mail address:cananbillur@erciyes.edu.tr (Canan A. Billur)

*Manuscript

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1. Introduction

The Pb-Sn alloys are used widely as a soldering material. It has low melting temperature,

good electrical, strength properties and wettability. Due to Pb element in the alloy is toxic to

environmental and human safety, the lead free solders are prompted to be soldering material

[1]. Recently new solder research is being done and many lead free solder alloys are obtained

having different melting temperatures [2-9]. Among the more important of high temperature

lead free solders are Zn-Sn, Au-Sn, Bi- based alloys. These alloys are used in the aerospace

and automotive industries [10]. Each has advantages as well as some disadvantages. Bi-based

alloys are very brittle with Bi, Au-Sn alloy is expensive. Zn-based alloys have good

mechanical, electrical and thermal conductivity properties and Zn-Sn alloy is cheaper [11].

The melting temperature of the Zn-Sn alloy was increased by addition of Mg. At the same

time selecting the eutectic composition of Zn-Sn-Mg alloy provides sudden solidification at a

single temperature.

The purpose of this study is to determine , fS , SL , and GB from the observed grain

boundary groove shapes for solid Zn in Zn-Sn-Mg ternary alloy. Because there is not enough

research on the entropy, fS , the Gibbs-Thomson coefficient, , the solid-liquid interfacial

energy, SL and the grain boundary energy, GB , of Zn-Sn-Mg ternary alloys.

σSL is a significant physical parameter in phase transformations and solidification. Thus,

the numerical information of σSL values is required. For all that, the determine of σSL is very

difficult for alloy systems and it is determined from the thermodynamic description of ,

which is defined as

f

SLr

SrT

. (1)

Where fS is the effective entropy of melting per unit volume, ∆Tr is the curvature under-

cooling, r is the radius of curvature [12].

In the recent years, it has been extensively studied to determine the Gibbs-Thomson

coefficient, and the solid-liquid interfacial energy, SL in the alloy systems. Jácome et al.

used numerical methods based on Butler’s formulation to calculate the Gibbs-Thomson

coefficient, and the solid-liquid interfacial energy, SL in aluminium alloys [12, 13].

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2. Experimental Procedure

2.1. Bridgman type directional solidification apparatus (BTDSA)

Firstly, Gündüz and Hunt were designed to calculate values with a radial heat flow

apparatus (RHFA) in opaque alloys systems [14]. They developed a numerical method to

obtain values by using equation (1). Then, this method was modified by Necmettin et al.

[15] for peritectic systems. To calculate with the numerical method, it is necessary to find

the ratio of thermal conductivity of the equilibrated phases )/( ) ( SLiquidEutecticL KKR , and to

calculate the temperature gradient in the solid, GS, and then to obtain the grain boundary

groove shape. So far, these numerical methods have been implemented by many people [14-

26].

The measurement of σSL is very difficult with RHFA. Because, the annealing time to

obtain the equilibrated grain boundary groove shape takes a long time and needs more

materials [14-26].

In the RHFA method, a sensitive temperature controller is required for the sample to

remain in equilibrium during experimental procedure. Otherwise, the sample is affected by

external conditions. Therefore, BTDSA was developed for both shortening the annealing time

of the sample and ensuring of stable temperature control. Recently, various binary alloy

systems were studied by using the BTDSA methods [27-30]. A block diagram of BTDSA and

the details are shown in Fig. 1.

2.2. Sample Preparation

The composition of ternary alloys was selected to be Zn-8.5 at. % Sn-3.5 at. % Mg to

obtain the solid Zn solution from the phase diagram.

Otani observed the Zn-Sn-Mg phase diagram using the microscopic method and thermal

analysis over the whole concentration range [31]. However, the Mg2Sn–MgZn2–Sn–Zn region

and binary systems of the Zn-Sn-Mg have been studied in detailed by Gödecke and Sommer

[32]. In the present study, the phase diagram which has been used was first studied by

Sommer and Gödecke [32].

The sample was melted in a vacuum melting furnace by using 4 N Zn, Sn and Mg, then

the alloy was poured into a graphite crucible held in a hot casting furnace which was set

above the eutectic melting point of the alloy, TE, (628 K). The alloy was directionally

solidified from bottom to top (150 mm in length and 10 mm diameter) and placed in a

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BTDSA as given in fig. 1. It was heated up to about 628 K and, then left to reach thermal

equilibrium for about 1 h. After thermal equilibrium of the sample was provided, it was taken

to the cold region by the synchronous motor and the temperature of the specimen was also

controlled with a Eurotherm 9706 type controller to an accuracy of ± 0.01 K during the

experimental study. In these measurements, the growth rate was 41.03x10-4

cm/s. When the

solid–liquid interface was between the 2 and 3 thermocouples, the motor was stopped and it

was again left to reach thermal equilibrium for at least 3 h. Finally, it was quickly quenched

by turning off the input power.

2.3. Measurement of Geometrical Correction for the Groove Coordinates

After the experimental procedure was completed, firstly, the specimen was removed from

the BTDSA and secondly, it was ground and polished by using routine metallographic

polishing techniques. Afterwards, the equilibrated grain boundary groove shapes and

micrometer (0.0001x100=0.01 mm) which was used in this study for the accurate

measurements of the groove coordinate points on the groove shapes were photographed with

a CCD digital camera. This camera has rectangular pixels, and it was placed on the top of an

Olympus BH2 light optical microscope using a 50-times objective. In the present study, the

Adobe Photoshop CS2 software version was used to take the photographs of the equilibrated

grain boundary shapes and the micrometer in the x and y directions. The groove coordinates

on the grain boundary grooves was measured as shown in Ref [15].

2.4. Measurement of Temperature Gradient in the Solid Phase

In order to calculate σSL by using the BTDSA, the values of R and GS was determined

from the temperature gradient measurements on the solid and liquid phases at the same time.

The heat flow away from the interface through the solid phase must balance that of the

heat flow through the liquid phase plus the latent heat generated at the interface and the

steady-state condition, i.e. [33]

VL = KSGS - KLGL (2)

Where V is the growth rate, L is the latent heat, GS and GL are the temperature gradients in the

solid and liquid phases, respectively and KS and KL are the thermal conductivities of the solid

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and liquid phases, respectively. For very low growth rate is 41.03 10-4

cm/sn VL«KSGS, so that

the conductivity ratio, R, is given by

LLSS GKGK , L

S

S

L

G

G

K

KR (3)

The values of R and GS for the same solid phases obtained in this study are given in fig. 2 and

table 1, respectively.

3. Results and Discussion

3.1. The Gibbs-Thomson Coefficient,

The values of were also determined by using Gündüz and Hunt’s method [14]. The

calculations were performed by using eight equilibrated grain boundary groove shapes and the

obtained shapes are shown in fig. 3. The average value of from table 2 is (10.98 ± 0.88) x

10-8

Km for the solid Zn in the Zn-Sn-Mg ternary alloy. So, the total error in the determination

of is about 8% [28].

3.2. The Effective Entropy Change, fS

To calculate SL , it is also necessary to know fS . fS for alloy systems is given by [14]

LLSL

LSEf

CCVm

CCRTS

)1(

)(

(4a)

)(CfVm

RTS

SL

Ef (4b)

Where R is the gas constant, TE the eutectic point (628 K), and CL and CS are the composition

of the equilibrated liquid and solid phases in at. %, respectively, mL is the liquidus slope, VS

is molar volume of the solid [14]. The other required parameters can be obtained from the Zn-

Sn-Mg phase diagram, which was studied by Sommer and Gödecke [32]. The obtained

fS value is (1.20 ± 0.06 x106) x 10

6 J/Km

3 for the present study (Table 3). The estimated

error in fS was estimated to be about 5 % [35].

A

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3.3. The Solid-Liquid Surface Energy, SL

If , fS are correctly measured or known, SL can be calculated by using equation (1)

for opaque alloy systems.

In the present study, SL for the Zn solid solution in equilibrium with the Zn-Sn-Mg

liquid solution was found to be (131.82± 17.14) mJ/m2

and the experimental error is about 13

%. The values of and SL with standard deviations are given in table 1. The other

experimentally determined values of SL were compared with the previous study in table 4.

3.4. The Grain Boundary Energy, GB

The interfacial energy of the solid Zn in equilibrium with the eutectic Zn-Sn-Mg liquid

was considered to be isotropic in this study. When SL is isotropic, it is equal to the surface

tension [36]. By using the balance of forces at the grain boundary groove, this is possible to

determine SL and GB . When SL is not anisotropic, the force balance can be given as

B

B

SLA

A

SLSS cos cos (5)

Where A and B are the angles that the solid-liquid interfaces make with the y-axis. If the

grains on either side of the grain boundary are the same, GB can be given as

cosθσ2σ SLGB (6)

Where 2

BA is the angle that the solid-liquid interfaces make with the y axis [6]. By

using Taylor expansion for parts at the base of the groove, the A and B angles in the cusp

were obtained from the cusp coordinates [15].

GB was calculated from the equation (6) using the related SL and for the groove

shapes in Figure 3. The average grain boundary value for the eight grain boundary groove

shapes was found to be GB = 242.58 ± 33.96 mJ/m2. A comparison of our results with the

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previous study is also provided in table 4. The obtained results are in good agreement with the

result in the literature [20, 25, 28, 29, 37-41]. Therefore, the total experimental error in the

resulting grain boundary energy is about 14 % obtained together with a determined 1 % error

of θ.

4. Conclusions

The equilibrated grain boundary groove shapes were obtained for the solid Zn solution in

equilibrium with the Zn-Sn-Mg eutectic liquid with a BTDSA, and Γ was calculated by using

eight of the groove shapes as Γ= (10.98 ± 0.88) x 10-8

Km. fS was determined to be (1.20 ±

0.06 x106) x 10

6 J/Km

3 by using the phase diagrams [32] and related parameters. SL was

calculated to be SL = (131.82± 17.14) mJ/m2 by using Γ and fS . GB was determined to be

GB =(242.58 ± 33.96) mJ/m2

by using the equilibrated shapes and the related SL . The total

experimental error in the resulting grain boundary energy is about 14 %. This experimental

error is obtained by the sum of the Gibbs-Thomson Coefficient, , the Effective Entropy

Change, fS , the angle θ, 8 % , 5 % , 1 % respectively.

Acknowledgement

The results of this paper are in the frame of project FBD-10-3263 financed by the Erciyes

University Research Fund.

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Table 3.

System Zn-Sn-Mg

Composition of solid Phases, CS Solid Zn

Compositions of Quenched Liquid Phase, CL Eutectic Liquid (Zn-8.5 at. % Sn-3.5 at. % Mg)

The value of f (c) for solid Zn 1.14

Melting Temperature, TM(K) 628

Liquidus slope of solid Zn, mL(K/at.fr) 521

Crystal Structure Hexagonal A3

Lattice parameters )(0

A a=2.664, c=4.945

n 6

Molar Volume of Solid Zn, VSx10-6

(m3) 9.16

M(g) 65.37

d(g/cm3) 7.13

Entropy Change of fusion for solid Zn, *S (J/Km3) 1.2 ± 0.06 x10

6

Table(s)

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Table Captions

Table 1. The values of R and GS for the same solid phases obtained in this study

Table 2. Gibbs-Thomson coefficients for the solid Zn phase in equilibrium with the eutectic

Zn-8.5 at. % Sn-3.5 at. % Mg liquid.

Table 3. Some physical properties of solid Zn phase in the Zn-Sn-Mg ternary system

Table 4. A comparison of the temperature, , SL , GB values for solid Zn phase obtained in

the present work with the values of the temperature, , SL , GB obtained in previous works

Table(s)

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Table 1.

Alloy Phases Melting Temparature(K) GS (K/mm)

Zn-Sn-Mg

Liquid (Zn-8.5at.%Sn-3.5 at.%Mg)

Solid(Zn)

628

4.98

0.99

Table(s)

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Table 2.

(10.98 ±0.88)× Km

Groove no

GS (K/mm)

Gibbs-Thomson coefficient

1 4.4 4.2

4.98

11.30 11.21

2 1.1 0.3 11.15 11.15

3 1.4 4.0 9.82 9.80

4 4.4 9.9 10.70 10.64

5 22.0 9.0 11.94 11.86

6 29.6 19.6 10.56 10.69

7 5.0 0.8 10.90 11.41

8 45.5 20.7 11.31 11.31

Table(s)

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Table 4. A comparison of the temperature, , SL , GB values for solid Zn phase obtained in the present work with the values of the

temperature, , SL , GB obtained in previous works

System

Solid phase Liquid phase x10-8

(Km) σSLx10-3

(Jm-2

) σGBx10-3

(Jm-2

)

Zn-Cu ɛ(CuZn5) (Zn-12 at % Cu)[37] Zn-1.75 at % Cu[30] 4.9±0.3[30] 76.0±9.1[30] 150.3±19.5[30]

Zn-Cd Zn (Zn-0.76 at % Cd)[20] Zn-26.9 at % Cd[20] 2.5±0.1[20] 165.5±19.0[20] 317.8±39.9[20]

Sn-99.9wt%Zn[25] Sn-9wt%Zn[25] 2.32±0.13[25] 120.87±13.29[25] 194.76±23.37[25]

Mg-Zn Zn-0.4 at % Mg[38] Zn-7.8 at % Mg[38] 10.64±0.43[38] 89.16±8.02[38] 172.97±20.76[38]

Zn-Al Znβ(Al-66.5 at % Zn)[39] Al-88.7 at % Zn[39] 3.41±0.14[39] 106.94±9.62[39] 204.72±22.52[39]

Zn(Zn-2.4 at % Al)[28] Zn-11.3 at % Al[28] 6.41±0.51[28] 103.33±13.4[28] 204.11±30.62[28]

Zn(Zn-2.4 at % Al)[40] Zn-11.3 at % Al[40] 5.80±0.18[40] 93.49±8.41[40] 182.30±18.23[40]

Zn-Al-Bi Zn(Zn- 3 at % Al -0.3 at % Bi)[41] Zn-12.7 at % Al-1.6 at % Bi[41] 5.1±0.4[41] 80.1±9.6[41] 158.6±20.6[41]

Zn-Sn-Mg Zn[PW] Zn-8.5 at % Sn-3.5 at % Mg[PW] 10.98±0.88[PW] 131.82±17.14[PW] 242.58±33.96[PW]

Table(s)

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Fig. 1.

TC-08 Data Logger

Bri

dg

ma

n t

yp

e

soli

dif

ica

tio

n

furn

ace

Variac

Eurotherm 9706

type controller.

Synchronous

motors

Hea

tin

g /

Ref

rigera

tin

g

Cir

cula

tor

Directional

control unit

Power

outlet

Computer

wate

r co

oli

ng

Circulator input

wate

r co

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ng o

utl

et

wate

r co

oli

ng i

np

ut

Circulator outlet

Figure(s)

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Fig. 3

50 µm

50

µm

50

µm

50

µm

50

µm

50 µm

50 µm

50 µm

Solid Zn solution Solid Zn solution

Solid Zn solution Solid Zn solution

Eutectic Zn-Sn-Mg liquid Eutectic Zn-Sn-Mg liquid

Eutectic Zn-Sn-Mg liquid Eutectic Zn-Sn-Mg liquid

Figure(s)

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Figure Captions

Fig.1 The block diagram of the experimental system.

Fig. 2 The value of R is obtained in this study.

Fig. 3 Typical grain boundary groove shapes for the solid Zn phase in equilibrium with the

eutectic Zn-8.5 at. % Sn-3.5 at. % Mg liquid.

Figure(s)

Page 20 of 20

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Distance (cm)

6,5 7,0 7,5 8,0 8,5 9,0 9,5 10,0 10,5

Tem

pera

ture

(o K

)

540

560

580

600

620

640

660

680

700

720

740

760

Liquid Phase

Solid Phase

GS=4.982 K/mm

GL=6.210 K/mm

TM=628 0K

R=Gk/Gs=0.986

Fig. 2

Figure(s)