Microstructural Evolution and Mechanical Properties in Directionally Solidified Sn – 10 . 2 Sb Peritectic Alloy at a Constant Temperature Gradient

Peritectic solidification has attracted more attention in experimental and theoretical studies1 since many technologically important materials are peritectic, such as Sn–Cd2,3, Sn–Sb4,5, Sn-Ag6, Sn–Bi–Zn7, Zn–Cu8,9, Zn–Ag10 lead-free soldering materials, high temperature intermetallics Ti–Al11, Ni–Al12, HF–B13, superconducting materials YBCO14, magnetic materials Nd–Fe–B15, and structural materials Fe–Ni16,17 and Fe–Cr–Ni18. Many interesting microstructures have been found during directional solidification of peritectic alloys, which have drawn much attention since the last four decades4. In the solidification of these alloys, a dendrite structure is the commonly encountered pattern. The microstructural scales involving the primary dendrite arm spacing (PDAS) and the secondary dendritic arm spacing (SDAS) have been carried out in directional solidification of various peritectic alloys, including Pb–Bi19, Zn–Cu19 and Nd–Fe–B20. In fact, PDAS and SDAS in the solidification microstructure determine the final physical properties of peritectic alloys. Therefore, it is of great significance to control the peritectic solidification by different techniques (Bridgman method6,7, Forced Crucible Rotation21, Bridgman-Stockbarger22, Ultrasonic Vibration 5,23, Temperature Gradient Zone Melting24). Tin–antimony alloys are important materials in the industry for their use in die casting alloys, high temperature lead–free solders, manufacture of cable sheathing and battery grids, and in manufacturing acidic accumulators25,26. It is usually applied in the industry as a sliding material such as the bearing babbit alloy. The Sn-Sb peritectic alloy has widespread applications, and is valuable in the industry27. Recently, the study by Rosa et al.,28 has shown that improvement in cell size and corrosion resistance depends on the cooling rate imposed during directional solidification of the Sb–Pb alloy. The investigations of mechanical properties of Sn–Sb alloys are crucial for many industrial applications. However, the effects of growth velocity on the microstructure and mechanical properties of the Sn–10.2 Sb peritectic alloy have not been investigated in a systematic manner. Therefore, the aim of the present work is to study the effect of growth velocity on PDAS, SDAS, microhardness (HV), and compressive strength (σc) for a directionally solidified Sn–10.2 Sb peritectic alloy using the Bridgman method at a constant temperature gradient (G=4.5 K. mm-1), and to compare the results with the previous experimental results for similar alloy systems.


Introduction
Peritectic solidification has attracted more attention in experimental and theoretical studies 1 since many technologically important materials are peritectic, such as Sn-Cd 2,3 , Sn-Sb 4,5 , Sn-Ag 6 , Sn-Bi-Zn 7 , Zn-Cu 8,9 , Zn-Ag 10 lead-free soldering materials, high temperature intermetallics Ti-Al 11 , Ni-Al 12 , HF-B 13 , superconducting materials YBCO 14 , magnetic materials Nd-Fe-B 15 , and structural materials Fe-Ni 16,17 and Fe-Cr-Ni 18 .Many interesting microstructures have been found during directional solidification of peritectic alloys, which have drawn much attention since the last four decades 4 .In the solidification of these alloys, a dendrite structure is the commonly encountered pattern.The microstructural scales involving the primary dendrite arm spacing (PDAS) and the secondary dendritic arm spacing (SDAS) have been carried out in directional solidification of various peritectic alloys, including Pb-Bi 19 , Zn-Cu 19 and Nd-Fe-B 20 .In fact, PDAS and SDAS in the solidification microstructure determine the final physical properties of peritectic alloys.Therefore, it is of great significance to control the peritectic solidification by different techniques (Bridgman method 6,7 , Forced Crucible Rotation 21 , Bridgman-Stockbarger 22 , Ultrasonic Vibration 5,23   , Temperature Gradient Zone Melting 24 ).
Tin-antimony alloys are important materials in the industry for their use in die casting alloys, high temperature lead-free solders, manufacture of cable sheathing and battery grids, and in manufacturing acidic accumulators 25,26 .It is usually applied in the industry as a sliding material such as the bearing babbit alloy.The Sn-Sb peritectic alloy has widespread applications, and is valuable in the industry 27 .Recently, the study by Rosa et al., 28 has shown that improvement in cell size and corrosion resistance depends on the cooling rate imposed during directional solidification of the Sb-Pb alloy.
The investigations of mechanical properties of Sn-Sb alloys are crucial for many industrial applications.However, the effects of growth velocity on the microstructure and mechanical properties of the Sn-10.2Sb peritectic alloy have not been investigated in a systematic manner.Therefore, the aim of the present work is to study the effect of growth velocity on PDAS, SDAS, microhardness (HV), and compressive strength (σ c ) for a directionally solidified Sn-10.2Sb peritectic alloy using the Bridgman method at a constant temperature gradient (G=4.5 K. mm -1 ), and to compare the results with the previous experimental results for similar alloy systems.

Alloy preparation, directional solidification and metallographic processes
The master alloy Sn-10.2Sb (all compositions are in wt.% unless otherwise noted) was prepared by melting weighed quantities of (≥99.99 wt.%) Sn and (≥99.99 wt.%) Sb metals in a graphite crucible (170 mm length, 30 mm inner diameter, and 40 mm outer diameter), which was placed in a vacuum melting furnace, and the metals were completely melted, taking into account the phase diagram 29 as shown Figure 1.After allowing time for the melt to become homogeneous, the molten master alloy was stirred and quickly poured into the graphite crucibles (ID: 4 mm, OD: 6.4 mm and L: 200 mm) which were placed in a hot filling furnace and then lowered to the cold region of the furnace.The samples were directionally frozen from the bottom to the top to ensure that the samples were full to the brim.One of the prepared samples was positioned in a Bridgman-type furnace.After stabilizing the thermal conditions in the furnace under an argon atmosphere, the sample was withdrawn downwards by approximately 90-100 mm with a known pulling rate by means of a synchronous motor and the sample rapidly quenched.The block diagram of the experimental set up is shown in Figure 2. Samples were solidified under steady state conditions with different V (13.3-266.7 µm.s -1 ) at a constant G (4.5 K. mm -1 ) in order to investigate the effect of V on PDAS, SDAS, HV and σ c .

Measurement of solidification processing parameters (G and V)
The temperature of the Bridgman-type furnace was controlled by a 0.5 mm insulated K-type thermocouple placed between the heating element and alumina tube.The temperature could be controlled to about ±0.1 K during the run.Three insulated K-type 0.5 mm diameter thermocouples with known distances were placed in alumina crucibles which were parallel to the direction of heat flow inside the graphite cylinder (see Figure 2).All of the leads were connected to a data logger interfaced with a computer and the temperature data recorded simultaneously.When the third thermocouple was at the solid-liquid interface and then the first and the second thermocouples in the liquid, their temperatures were used to obtain the temperature gradient G. G was also obtained from the recorded cooling rates (T .= G V ).Both results were similar.G could be kept constant during the run by keeping the temperature of the cooler part and the hotter part of the furnace constant, and the distance between them stable.The positions of the thermocouples were measured by electronic calipers having an accuracy of ±0.02 mm after quench.Careful experimental measurements showed that the pulling rates of the samples were equal to the value of the growth velocities 30 .The solidification time and solidified distance were also measured for the run and their ratio gives the growth velocity.The error in the G and V measurements has been calculated to be about 4%.

Metallographic examination
The unidirectionally grown quenched sample was removed from the alumina crucible, then ground to observe the solid-liquid interface.The longitudinal section of the sample (10 mm), which included the quenched interface, was separated from the sample and set in the cold mounting resin.The longitudinal and transverse sections of this part were ground and polished using diamond paste to a 1 µm finish and etched within the solution of 100 ml H 2 O and 10 g CrO 3 to reveal the microstructure.The microstructures of the samples were investigated by using Olympus BH-2 optical microscopy with LG Honeywell CCD camera.

Measurement of primary and secondary dendrite arm spacing
The primary dendrite arm spacing, PDAS (λ 1 ), was measured on the longitudinal and transverse sections of each sample by using the linear intercept method [30][31][32] .In the linear intercept method, λ 1L is obtained on the longitudinal section by measuring the distance between adjacent dendrite tips.Although λ 1 is independent of the distance behind the quenched interface, to be more precise, the λ 1T measurements on the transverse sections were taken on the plane ≤ 500 µm just behind the tips.The total 50-250 λ 1 were measured using the mean linear intercept method on the longitudinal and transverse sections, depending on the growth conditions.The secondary dendrite arm spacing λ 2 was measured on the longitudinal sections of the samples from the initial adjacent side branches of primary dendrites.Values of λ 2 data reported here were averaged over the 25-50 λ 2 measurements depending on the growth conditions.It has been found that a standard deviation is approximately 5% for λ 1 and λ 2 measurements.

Measurement of microhardness (HV) and compressive strength (σ c )
Microhardness measurements in the present work were made with a DuraScan 20 semiautomatic Microhardness test device using a 300 g load and a dwell time of 10 s.Ten measurements were taken from the longitudinal and transverse sections of each sample.The average values were calculated from these microhardness values.Some errors were inevitable during the microhardness measurements.These errors were owing to factors such as surface quality, inhomogeneities in the microstructure, and the ambiguity of the traces.The error in the microhardness measurements has been calculated to be approximately 5%.
The measurements of the compressive tensile strength were made at room temperature with a Shimadzu AG-IS universal testing machine.Cylindrical compressive test samples with a diameter of 4 mm and gauge length of 6 mm were prepared from the directionally solidified rod samples under different growth velocities.The compressive axis was parallel to the growth direction of the sample.The compressive tests were repeated three times and the average value was taken.It has been found that the standard deviation was approximately 5%.

Composition analysis of the phases (EDS Analysis)
EDS analysis was performed to determine the composition of the phases in the Sn-10.2Sb (mass fraction) peritectic alloy at 20 keV using X-ray lines.According to the EDS analysis results shown in Figure 3, three different phases (dark gray quenched liquid phase, light gray dendritic matrix phase, and white SnSb intermetallic phase) grew during the directional solidification of Sn-10.2Sb alloy.The composition of the dendritic matrix phase (β-Sn) was Sn-10.16Sb (wt.%), and that of the dark gray quenched liquid phase was Sn-6.39 Sb (wt.%).Also, the white phase (SnSb intermetallic phase) was Sn-43.76Sb (wt.%).These determined compositions are very close to values of nominal compositions (Figure 1).

The effect of growth velocity on dendritic spacings
The Sn-10.2 Sb peritectic alloy was directionally solidified at steady state conditions with different growth velocities (V=13.3-266.7 µm.s -1 ) at a constant temperature gradient (G =4.5 K. mm -1 ).The optical micrographs of longitudinal and transverse sections of the directionally solidified Sn-10.2Sb peritectic alloy prepared under different solidification parameters are given in Figure 4.As seen in Figure 4, the microstructure is dendritic form.The PDAS was measured from the longitudinal and transverse sections and SDAS was measured from the longitudinal section of the samples grown at different V.As seen in Figure 5, an increase in growth velocity caused a decrease of the PDAS and SDAS at a constant temperature gradient (4.5 K. mm -1 ).When the growth velocity was increased from 13.3 to 266.7 µm.s -1 , the λ 1L value decreased from 82.1 to 39.3 µm and the λ 1T value decreased from 78.1 to 36.2 µm.Similarly, when the growth velocity was increased from 26.7 to 266.7 µm.s -1 , the λ 2 value decreased from 40.4 to 15.3 µm.Secondary dendrite arms were not observed for 13.3 µm.s -1 growth velocity, because the microstructure is cellular or cellular-dendritic (see Figure 4).The dependency of λ 1 and λ 2 on V was determined by a linear regression analysis.From the experimental results, the relationship between microstructure parameters (λ 1 , λ 2 ) and growth velocity (V) can be established as follows:    42 and Jesse,Giller 43 and also the 0.50 predicted by Kurz et al., 44 numerical models for dendritic spacings.This discrepancy might be due to rapid solidification conditions for the numerical model 44 , because under rapid solidification conditions, m (liquidus slope) and k (distribution coefficient) cannot be constant and k becomes a function of growth velocity. 45As can be seen from the theoretical and numerical models, coefficients of λ 1 and λ 2 are functions of m and k.Thus, the rapid solidification and unsteady conditions cannot apply to steady state conditions case.The exponent value (0.46) of λ 2 is in good agreement with the values 0.42 and 0.47 obtained by Şahin et al. 38 and Kaya et al. 46 respectively.In the present work, the λ 2 values experimentally obtained as a function of growth velocity have been compared with the values of λ 2 calculated from the Trivedi-Somboonsuk 47 and the Bouchard-Kirkaldy 48,49 models.Our experimental values agree with the calculated Table 1.The relationships between the dendritic spacings (λ 1 , λ 2 ), mechanical properties (HV L , HV T , σ c ) and the growth velocity (V)

The Effect of growth velocity on microhardness and compressive strength
The high microhardness and compressive strength are reported to arise from the dendritic matrix due to Hall-Petch-type mechanism 50,51 .The Hall-Petch-type relationships between the growth velocity (V) and mechanical properties (HV, σ c ), can be expressed as follows, where d, e and f are the exponent values relating to the V and the k 4 , k 5 and k 6 are constants which can be experimentally determined (Table 1).According to Eqs. ( 3) and ( 4), the microhardness and compressive strength change with the growth velocity.At a constant temperature gradient (4.5 K/mm), an increase in the growth velocity resulted in increased microhardness (Figure 6).When the growth velocity was increased from 13.3.3 to 266.7 µm.s -1 , the HV L increased from 16.8 to 21.7 kg.mm -2 and the HV T increased from 18.1 to 23.3 kg.mm -2 .The exponent value of V (0.08) obtained from this study as a function of HV is in agreement with the values of 0.06, 0.06, 0.07 and 0.09 reported by Çadırlı et al. 52 for Sn-23Bi-5Zn (wt%) alloy, by Hu et al. 53 for Sn-58 wt% Bi eutectic alloy, by Vnuk et al. 54 for Sn-Zn eutectic alloy, and by Böyük and Maraşlı 55 for Sn-3.5Ag-0.9Cu(wt%) eutectic alloy respectively.The exponent value of V (0.08) is slightly lower than the values of 0.11 reported by Hu et al. 56 for Sn-1.0 wt% Cu.As seen in Figure 7(a), compressive strength (σ c ) values increased with increasing V, but strain (%) values decreased.The maximum compressive strength of studied alloy reaches 107 MPa (Figure 7(b)).The factor responsible for higher compressive strength in the investigated alloys is fineness of the dendritic and SnSb intermetallic phases.Similar trends were observed by some researchers for different multicomponent alloys [57][58][59] .It can be seen from these figures that the σ c values increased by approximately 36% with increasing V for the studied alloy.The exponent value of V is equal to 0.10.This exponent value is smaller than the values of 0.20 and 0.23 obtained by Siewert et al., 60,61 for some soldering alloys.These discrepancies are due to factors such as composition, temperature gradient, microsegregation and presence of intermetallic phases.

Conclusions
In this work, microstructural properties of the directionally solidified Sn-10.2Sb peritectic alloy were investigated.The results are summarized as follows: (1) The effects of growth velocity on PDAS and SDAS were investigated.Increasing of growth velocity was observed to result in finer microstructures.
(2) Experimental relationships show that the dependency of the λ 2 on growth velocity is stronger than λ 1 .
(3) The exponent values (0.24 and 0.25) obtained in this experimental study for PDAS and SDAS are in agreement with the exponent value (0.25) predicted by theoretical models [39][40][41]47 for the steady state conditions. Howver , Kurz-Giovanola-Trivedi 44 for rapid solidification conditions (for λ 1 ) and Bouchard-Kirkaldy models 48,49 for the unsteady state conditions (for λ 2 ) do not agree with the experimental results.
(4) Increasing of growth velocity resulted in finer dendritic microstructures, thereby resulting in increased microhardness and compressive strength.The establishment of the relationships between HV L , HV T , σ c and V have been obtained as HV L =k 4 V -0.09 , HV T =k 5 V -0.08 and σ c =k 6 V -0.10

Figure 2 .
Figure 2. (a) Block diagram of the experimental setup, (b) The details of the Bridgman-type directional solidification furnace b and c are exponent values for the growth velocity, and k 1 , k 2 and k 3 are constants which can be experimentally determined.According to Eqs. (1) and (2), PDAS and SDAS change with the growth velocity.The exponent values (a, b) of V were found to be 0.24 and 0.25 for λ 1 values obtained from longitudinal and transverse sections of samples respectively.Similarly, the exponent value (c) of V found to be 0.46 for λ 2 value was obtained from longitudinal sections of samples.The exponent values (a, b and c) and experimental constants (k 1 , k 2 and k 3 ) are given in Table 1.The exponent values (0.24 and 0.25) of λ 1 are in agreement with the values 0.25, 0.23, 0.27, 0.26, 0.25 and 0.28 obtained

. 1 (λ
MPa. µm 0.10 .s -01L : the values of the PDAS measured from the longitudinal section of the samples; λ 1T : the values of the PDAS measured from the transverse section of the samples; λ 2 : the values of the SDAS measured from the longitudinal section of the samples; HV L : the values of the microhardness measured from the longitudinal section of the samples; HV T : the values of the microhardness measured from the transverse section of the samples; σ c : the values of the compressive strength measured from the longitudinal section of the samples values of λ 2 from the Trivedi-Somboonsuk steady state model47 as a function of (V) 0.5 .In contrast, the calculated values of λ 2 with the Bouchard-Kirkaldy unsteady state model48,49 as a function of V 0.67 do not agree with our experimental values.There is a clear difference between the exponent values obtained in the Trivedi-Somboonsuk and the Bouchard-Kirkaldy models.Briefly, the results of our experiments (which were carried out under steady state conditions), agree with the results of the steady state theoretical models.

Figure 5 .
Figure 5.The variation of PDAS and SDAS with growth velocity at a constant temperature gradient

Figure 6 .Figure 7 .
Figure 6.The variation of microhardness with growth velocity at a constant temperature gradient 41, Lapin et al.34, Kloosterman and Hosson 35 , Pryds et al.36, Gündüz et al.37, and Şahin et al.38respectively. The exponent values are also in agreement with the value 0.25 predicted by Hunt 39 , Kurz,Fisher 40 and Trivedi41 theoretical models for steady state conditions.On the other hand, our exponent values (0.24 and 0.25) are less than the values of 0.40 and 0.41 obtained byMiyata et al.