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R

R

1

A

K

O

C

S

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j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 145–155

journa l homepage: www.e lsev ier .com/ locate / jmatprotec

ffects of growth rate and temperature gradient on theicrostructure parameters in the directionally solidified

uccinonitrile–7.5 wt.% carbon tetrabromide alloy

. Maraslı a, K. Keslioglua,∗, B. Arslana, H. Kayab, E. Cadırlı c

Erciyes University, Faculty of Arts and Sciences, Department of Physics, 38039 Kayseri, TurkeyErciyes University, Faculty of Education, Department of Science Education, 38039 Kayseri, TurkeyNigde University, Faculty of Arts and Sciences, Department of Physics, 51200 Nigde, Turkey

r t i c l e i n f o

rticle history:

eceived 8 August 2006

eceived in revised form

8 May 2007

ccepted 5 September 2007

a b s t r a c t

Succinonitrile (SCN)–7.5 wt.% carbon tetrabromide (CTB) alloy was unidirectionally solid-

ified with a constant growth rate (V = 33 �m/s) at five different temperature gradients

(G = 4.1–7.6 K/mm) and with a constant temperature gradient (G = 7.6 K/mm) at five different

growth rates (V = 7.2–116.7 �m/s). The primary dendrite arm spacings, secondary dendrite

arm spacings, dendrite tip radius and mushy zone depths were measured. Theoretical

models for the microstructure parameters have been compared with the experimental

observations, and a comparison of our results with the current theoretical models and

previous experimental results have also been made.

eywords:

rganic compounds

rystal growth

olidification

icrostructures

© 2007 Elsevier B.V. All rights reserved.

range of stable spacings. This has been interpreted in such

hase transitions

. Introduction

ver the last 40 years, the formation of dendrite arms duringolidification has been studied extensively and several stud-es (Glicksman and Koss, 1994; Han and Trivedi, 1994; Warrennd Langer, 1993; Makkonen, 2000; Walker and Mullis, 2001) ofirectionally solidification under steady-state conditions haveeen applied to dendritic growth in alloy systems. Dendriticrowth is the ubiquitous form of crystal growth encounteredhen metals, alloys and many other materials solidify under

ow-thermal gradients, a situation which typically occurs in

ost industrial solidification processes (Glicksman and Koss,

994). A dendrite structure is characterized by the microstruc-ure parameters. The microstructure parameters �1, �2, R and

∗ Corresponding author. Tel.: +90 352 4374901x33128; fax: +90 352 43749E-mail address: kesli@erciyes.edu.tr (K. Keslioglu).

924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.jmatprotec.2007.09.011

(d) are shown in Fig. 1. Numerous solidification studies havebeen reported with a view to characterizing microstructureparameters as a function of solidification parameters (Co, Vand G) (Cadırlı et al., 1999, 2000, 2003; Kaya et al., 2005; Ustunet al., 2006).

Recent empirical (Cadırlı et al., 1999, 2000, 2003; Kaya etal., 2005; Ustun et al., 2006) and theoretical (Lu and Hunt,1996; Langer and Muller-Krumbhaar, 1978; Hunt, 1979; Kurzand Fisher, 1981; Trivedi, 1984; Bouchard and Kirkaldy, 1996,1997) studies have claimed the existence of an allowable

33.

a way that no unique spacing selection criterion operatesfor �, and an array with a band of spacing is stable undergiven experimental conditions. A literature survey shows

146 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 145–155

Fig. 1 – Schematic illustrations of methods used for measurements of (a) primary dendrite arm spacing, secondary dendriteradi

arm spacing and the mushy zone depth and (b) dendrite tip

several theoretical models (Lu and Hunt, 1996; Langer andMuller-Krumbhaar, 1978; Hunt, 1979; Kurz and Fisher, 1981;Trivedi, 1984; Bouchard and Kirkaldy, 1996, 1997; Trivedi andSomboonsuk, 1984) used to examine the influence of solid-ification parameters on the microstructure parameters. Themajority of results in the literature show a decrease inspacing with increasing growth rate for a given alloy com-position and with increasing solute concentration for a givengrowth rate (Cadırlı et al., 1999, 2000, 2003; Kaya et al., 2005;Ustun et al., 2006; Sharp and Hellawell, 1969; Spittle andLIoyd, 1979). Besides, the primary arm spacings have beenreported to decrease as temperature gradient or growth rateincreases. Sharp and Hellawell (1969) concluded that Co haslittle effect on primary spacings and Spittle and LIoyd (1979)have found that in the case of steady-state growth withlow G, �1 decreased as Co increases and was independentof Co for high G. Nevertheless, in many cases it has beenassumed that �1 increases as Co increases for any growth con-dition (Bouchard and Kirkaldy, 1997; Okamoto and Kishitake,1975).

The aim of present work is to experimentally inves-tigate the effect of the temperature gradient and growthrate on the microstructure parameters in the direction-ally solidified SCN–7.5 wt.% CTB alloy and to comparethe results with theoretical models (Lu and Hunt, 1996;Langer and Muller-Krumbhaar, 1978; Hunt, 1979; Kurz andFisher, 1981; Trivedi, 1984; Bouchard and Kirkaldy, 1996,1997; Trivedi and Somboonsuk, 1984) and previous exper-imental results (Han and Trivedi, 1994; Cadırlı et al.,1999, 2000, 2003; Kaya et al., 2005; Ustun et al., 2006;Mullins and Sekarka, 1965; Glicksman and Singh, 1986;Schmidbauer et al., 1993; De Cheveigne et al., 1985; Huanget al., 1993; Taha, 1979; Grugel and Zhou, 1989; Dey andSekhar, 1993; Liu and Kirkaldy, 1994a; Seetharaman et al.,1989; Trivedi and Mason, 1991; Rutter and Chalmers, 1953;

Tiller et al., 1953; Kurz and Fisher, 1989; Esaka and Kurz,1985).

The theoretical models for microstructure parameters arebriefly described as follows.

us.

1.1. Theoretical models for primary dendrite armspacing

Hunt (1979) and Kurz and Fisher (1981) have proposed the the-oretical models to characterize cells/primary dendrite spacing(�1) as a function of growth rate (V), temperature gradients (G)and alloy composition (Co) during steady-state growth condi-tions. At high-growth rate, the results predicted by these twotheories differ only by a constant. The equations representingthese two theories can be expressed, respectively, as

Hunt model:

�1 = 2.83[m (k − 1) D � ]0.25 C0.250 V−0.25 G−0.5 (1)

Kurz and Fisher model:

�1 = 4.3

[m(k − 1)D�

k2

]0.25

C0.250 V−0.25 G−0.5 (2)

where m is the liquidus slope, � the Gibbs–Thomson coef-ficient, k the solute partition coefficient and D is the liquidsolute diffusivity.

Trivedi (1984) has modified the Hunt’s model by using themarginal stability criterion to characterize the dentritic pri-mary arm spacing, �1 as function of G, V and Co and it can beexpressed as

Trivedi model:

�1 = 2.83[m(k − 1)D�L]0.25 C0.250 V−0.25 G−0.5 (3)

where L is a constant depends on the harmonic of perturba-tion.

Lu and Hunt (1996) have proposed a numerical model tocharacterize the dentritic primary arm spacing, �1. The modeldescribes steady- or unsteady-state of an ax symmetric cell or

dendrite and it can be expressed as

Lu and Hunt model:

�′ = 0.07798 V′(a−0.75)(V′ − G′)0.75G′−0.6028 (4)

t e c

w

�

a

a

nsdmpu

�

waK

1

Ldal�

S

�

F(Mt

�

wdodaa(

1

A1Tt

j o u r n a l o f m a t e r i a l s p r o c e s s i n g

here

′ = ��To

�kG′ = G � k

(�To)2V′ = V � k

D �To�To = m Co(k − 1)

k

nd

= −1.131 − 0.1555 log G′ − 0.007589 (log G′)2

Bouchard and Kirkaldy (1996, 1997) have also proposed aumerical model to characterize the dentritic primary armpacing (�1) for unsteady- and steady-state heat-flow con-itions. A heuristically derived steady-state formula, afterodification, has been recommended by these authors for

urposes of predicting primary dendritic spacing in thensteady regime and is given by

Bouchard and Kirkaldy model:

1 = a1

(16C

1/2o Goε�D

(1 − k)mGV

)1/2

(5)

here Goε is a characteristic parameter (600 × 6 K/cm) and

1 is the primary dendrite-calibrating factor (Bouchard andirkaldy, 1997).

.2. Secondary dendrite arm spacing

anger and Muller-Krumbhaar (1978) have carried out aetailed numerical analysis of the wavelength of instabilitieslong the sides of a dendrite and have predicted a scalingaw as �2/R = 2. Using the scaling law �2/R = 2, the variation in

2 for small peclet number conditions given by Trivedi andomboonsuk (1984) as

Trivedi and Somboonsuk model:

2 =(

8�DL

kV�To

)0.5

(6)

or secondary dendrite arm spacing, Bouchard and Kirkaldy1997) have also derived an expression which is very similar to

ullins and Sekarka (1965). This expression independents onemperature gradient and is given by

Bouchard and Kirkaldy model:

2 = 2�a2

(4�

Co(1 − k)2TF

(D

V

)2)1/3

(7)

here a2 is the secondary dendrite-calibrating factor, whichepends on alloy composition and TF is the fusion temperaturef the solvent. The Bouchard and Kirkaldy model additionallyepends on empirical dimensionless calibration parameters,

1 for �1 and a2 for �2 as shown by Eqs. (5) and (7). Theseuthors have proposed different a1 values for different alloysBouchard and Kirkaldy, 1997).

.3. Dendrite tip radius

s mentioned in the previous section, the Hunt model (Hunt,979), the Kurz and Fisher model (Kurz and Fisher, 1981) andrivedi model (Trivedi, 1984) have been applied to find the rela-ionships between R as a function V and Co. According to the

h n o l o g y 2 0 2 ( 2 0 0 8 ) 145–155 147

Hunt model (Hunt, 1979):

R =[

2�D

m(k − 1)

]0.5

C−0.5o V−0.5 (8)

according to the Kurz and Fisher model (Kurz and Fisher, 1981):

R = 2�

[�D

m(k − 1)

]0.5C−0.5

o V−0.5 (9)

and according to the Trivedi model (Trivedi, 1984):

R =[

2k�DL

m(k − 1)

]0.5

C−0.5o V−0.5 (10)

As can be seen from Eqs. (8)–(10) the theoretical models fordendritic tip radius, R are also very similar and the differenceamong them is a constant only.

1.4. Mushy zone depth

The mushy zone depth (d) is defined as the distance betweenthe tip and the root of a dendrite trunk. Using constitutionalsupercooling criterion (Trivedi and Mason, 1991; Rutter andChalmers, 1953) for binary alloy systems in the absence ofconvection, the mushy zone depth (d) is given by

d ≈ mCE − Co

G(11)

where CE is the eutectic composition. The mushy zone depth(d) assumed to be equal to the distance between the liquidustemperature (TL) corresponding to Co and the solidus temper-ature (TS) corresponding to CL which is equal to CE when thecomposition of alloy is over the composition of single solidphase (Co > CS). The temperature difference between the liq-uidus and the solidus is given (Kurz and Fisher, 1989) as

�To = TL − TS = −m(CE − Co) (12)

By using Eqs. (11) and (12), (d) can be expressed as

d = �To

G(13)

2. Experimental procedure

SCN–7.5 wt.% CTB alloy was prepared from 99.9% purity ofSCN and 99.9% purity of CTB supplied by Sigma–AldrichChemical Company. The specimen was contained in a glasscell made from two glass cover slips (50 mm long, 24 mmwide and 0.05 mm thick). The slides were stuck togetherwith a silicone elastomer. The slides were placed with theirlargest surface in the x–y plane and spaced a distance ofabout 100–120 �m apart in the z direction to observe thedendrite in x–y plane (2D). Organic materials usually reactwith this type of glue. Before filling the cell with alloy, the

cell was annealed at 523 K to prevent the reaction with theglue.

After filling the cell with alloy, the specimen cell was placedin the temperature gradient stage. The detail of the experi-

148 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 145–155

Table 1a – Dependency of the microstructure parameters for the directionally solidified SCN–7.5 wt.% CTB alloy on thetemperature gradients

Solidification parameters Microstructure parametersa

G (K/mm) V (�m/s) �1 (�m) �2 (�m) R (�m) d (�m) �2/R

4.1 33.0 311.4 ± 15.2 68.4 ± 7.1 34.0 ± 2.5 655.8 ± 15.5 2.014.8 33.0 290.4 ± 15.8 63.6 ± 3.5 31.2 ± 2.2 610.0 ± 19.2 2.045.6 33.0 266.4 ± 14.2 57.2 ± 1.9 28.3 ± 1.9 570.4 ± 23.8 2.026.8 33.0 248.8 ± 11.6 49.5 ± 4.6 25.1 ± 2.0 528.4 ± 17.0 1.977.6 33.0 230.0 ± 12.5 44.5 ± 3.3 22.6 ± 1.7 475.6 ± 10.6 1.97

Constant (k) Correlation coefficients (r)

k1 = 22.4 (�m0.53 K0.47) r1 = −0.999k2 = 2.24 (�m0.42 K0.58) r2 = −0.995k3 = 0.96 (�m0.35 K0.65) r3 = −0.996

0.47 0.53

; (�2/R

k4 = 13.18 (�m K )

a The relationships: �1 = k1G−0.47; �2 = k2G−0.58; R = k3G−0.65; d = k4G−0.53

mental system was given by Trivedi (1984). When one side ofthe cell was heated, the other side of the cell was kept coolwith a water cooling system. The temperature of heater wascontrolled to be ±0.1 K with a Eurotherm 905S type controller.The temperatures in the specimen were measured with theinsulated K type four thermocouples, 50 �m thick which wereplaced perpendicular to heat flow on the sample. The tem-perature gradient in front of the solid–liquid interface on thespecimen during the solidification was observed to be con-stant.

The SCN–7.5 wt.% CTB alloy was solidified in a horizon-tal directional solidification apparatus to directly observethe microstructures using a transmission optical microscope.The SCN–7.5 wt.% CTB alloy was solidified with a con-stant growth rate (V = 33 �m/s) at five different temperaturegradients (G = 4.1–7.6 K/mm) and with a constant tempera-ture gradient (G = 7.6 K/mm) at five different growth rates

(V = 7.2–116.7 �m/s). During the solidification, the photographsof the microstructures were taken with a CCD digital cameraplaced on a transmission Olympus BH2 optical microscopeby using ×5, ×10, and ×20 objectives and the photographs

Table 1b – Dependency of the microstructure parameters for thegrowth rates

Solidification parameters

G (K/mm) V (�m/s) �1 (�m)

7.6 7.2 352.4 ± 10.4 87.6 14.5 279.8 ± 12.0 67.6 33.0 230.0 ± 12.5 47.6 58.9 190.4 ± 14.8 37.6 116.7 176.2 ± 13.1 2

Constant (k)

k5 = 5.62 × 102 (�m1.25 s−0.25)k6 = 2.21 × 102 (�m1.46 s−0.46)k7 = 1.12 × 102 (�m1.48 s−0.48)k8 = 10.96 × 102 (�m1.33 s−0.33)

a The relationships: �1 = k5V−0.25; �2 = k6V−0.46; R = k7V−0.48; d = k8V−0.33; (�2/R

r4 = −0.989

)ave = 2.0.

of a graticula (100 × 0.01 = 1 mm) were also taken with sameobjectives.

2.1. Measurements of temperature gradient andgrowth rate

The specimen was slowly melted until the solid–liquid inter-face passed through the second thermocouple by drivingthe specimen cell toward to the heating system. When thesolid–liquid interface was between the second and third ther-mocouples, the synchronous motor was stopped and thespecimen was left to reach thermal equilibrium. After thespecimen reached the steady-state conditions, the solidifica-tion was started by the driving of the specimen toward tocooling system by synchronous motor. While the interfacewas passing the distance between two thermocouples thesolidification time (�t) and temperature difference between

two thermocouples (�T) was recorded and the photographsof the thermocouple positions and solidification microstruc-tures were taken with a CCD digital camera. Thus the valuesof �T, �t and �x were measured accurately and then the tem-

directionally solidified SCN–7.5 wt.% CTB alloy on the

Microstructure parametersa

�2 (�m) R (�m) d (�m) �2/R

5.1 ± 6.4 43.5 ± 1.9 674.8 ± 33.4 1.966.0 ± 5.8 32.2 ± 1.8 596.0 ± 29.8 2.124.5 ± 3.3 22.6 ± 1.7 475.6 ± 10.6 1.974.7 ± 3.3 15.5 ± 0.2 418.6 ± 26.2 2.244.2 ± 2.1 11.8 ± 0.7 343.8 ± 19.1 2.05

Correlation coefficients (r)

r5 = −0.996r6 = −0.992r7 = −0.989r8 = −0.995

)ave = 2.07.

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 145–155 149

Fig. 2 – Typical microstructures of the directionally solidified SCN–7.5 wt.% CTB alloy (a) V = 33 �m/s; G = 4.1 K/mm, (b)V = 33 �m/s; G = 4.8 K/mm, (c) V = 33 �m/s; G = 5.6 K/mm, (d) V = 33 �m/s; G = 6.8 K/mm, (e) V = 33 �m/s; G = 7.6 K/mm, (f)G = 7.6 K/mm; V = 7.2 �m/s, (g) G = 7.6 K/mm; V = 14 �m/s, (h) G = 7.6 K/mm; V = 33.0 �m/s, (i) G = 7.6 K/mm; V = 58.9 �m/s, and (j)G = 7.6 K/mm; V = 116.7 �m/s.

n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 145–155

Fig. 3 – (a) Microstructure parameters as a function oftemperature gradients for the directionally solidifiedSCN–7.5 wt.% CTB alloy with a constant growth rate(V = 33.0 �m/s). (b) Microstructure parameters as a functionof growth rates for the directionally solidified SCN–7.5 wt.%

150 j o u r n a l o f m a t e r i a l s p r o c e s s i

perature gradient, G = (�T/�x) and the growth rate, V = (�x/�t)were determined by using the values of �t, �T and �x.

2.2. Measurements of microstructure parameters

Schematic representation of the microstructure parametersare shown in Fig. 1. The primary dendrite arm spacing (�1)was obtained by measuring the distance between nearest twodendrite tips. The secondary dendrite arm spacing (�2) wasmeasured by averaging the distance between adjacent sidebranches of a primary dendrite as a function of the distancefrom the dendrite tip. The dendrite tip radius (R) was measuredby fitting a suitable circle to the dendrite tip side. The mushyzone depth (d) is also defined by means of region between tipside and root side of the dendrites (Cadırlı et al., 1999, 2000;Kaya et al., 2005; Ustun et al., 2006; Lu and Hunt, 1996). Thisparameter was measured as far from the steady-state con-dition in the dendrites as possible. In the measurements ofmicrostructure parameters, 30–40 values of �1, �2, R and (d) foreach growth rates and each temperature gradients were mea-sured to increase statistical sensitivity. Thus the solidificationparameters and microstructure parameters were measuredand the average values of �1, �2, R and (d) with their standarddeviations are given in Tables 1a and 1b.

3. Results and discussion

SCN–7.5 wt.% CTB alloy was solidified with a constantgrowth rate (V = 33 �m/s) at five different temperaturegradients (G = 4.1–7.6 K/mm) and with a constant tempera-ture gradient (G = 7.6 K/mm) at five different growth rates(V = 7.2–116.7 �m/s) in order to investigate the dependency ofmicrostructures parameters on the growth rate and temper-ature gradient and to find the relationship between them.Typical microstructures of SCN–7.5 wt.% CTB alloy are shownin Fig. 2 and the mean experimental values of the microstruc-ture parameters with the standard variations as a functionof growth rates and temperature gradients are given inTables 1a and 1b. The dependency of the microstructureparameters on the growth rate and temperature gradient wasobtained by linear regression analysis and the results are alsogiven in Tables 1a and 1b.

Fig. 3a and b present the experimental values of primarydendritic arm spacing (�1), secondary dendritic arm spacing(�2), tip radius (R) and mushy zone depth (d) as a function oftemperature gradients (G) and growth rates (V), respectively.

As can be seen from Fig. 3a and Table 1a, the values of �1,�2, R and (d) decrease as the value of (G) increases at a constantCoV and the average exponent value of �1, �2, R and (d) in thedirectionally solidified SCN–7.5 wt.% CTB alloy with a constantgrowth rate (V = 33 �m/s) at different temperature gradients(G = 4.1–7.6 K/mm) was found to be −0.47, −0.58, −0.65 and−0.53, respectively.

From Fig. 3b and Table 1b, the values of �1, �2, R and (d)also decrease as the growth rate increase at a constant CoGand the average exponent value of � , � , R and (d) in the

1 2

directionally solidified SCN–7.5 wt.% CTB alloy with a constanttemperature gradient (G = 7.6 K/mm) at different growth rates(V = 7.2–116.7 �m/s) was found to be −0.25, −0.46, −0.48 and−0.33, respectively.

CTB alloy with a constant temperature gradient(G = 7.6 K/mm).

A number of experimental studies have been reported inthe literature to characterize the variations in the �1, �2, R and

(d) as a function of (V) and (G). Available experimental resultsrelated to the values of �1, �2, R and (d) can be found in Table 2.As can be seen from Tables 1a, 1b and 2, the exponent values of�1, �2, R and (d) in the directionally solidified SCN–7.5 wt.% CTB

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 145–155 151

Table 2 – A comparison of the experimental results of the microstructure parameters with previous experimental works

Pure or alloy system Temperature gradient Relationships References

Temperaturegradient G

Growth rate V(�m/s)

SCN–7.5 wt.% CTB 4.1–7.6 7.2–116.7 �1 = 22.4G−0.47 This workSCN–7.5 wt.% CTB 4.1–7.6 7.2–116.7 �1 = 562V−0.25 This workSCN–13 wt.% ACE 2 7.25–11.35 �1 = kV−0.58 Han and Trivedi (1994)SCN–(5–20) wt.% Salol 4.5 6.7–112.4 �1 = kV−0.26 Cadırlı et al. (2003)PVA 1.64 0.7–85.8 �1 = kV−0.32 Cadırlı et al. (1999)PVA 1.64–4.86 9.6 �1 = kG−0.36 Cadırlı et al. (1999)Camphene 6.94 6.6–116.5 �1 = kV−0.25 Cadırlı et al. (2000)Camphene 2.25–6.94 6.6 �1 = kG−0.47 Cadırlı et al. (2000)SCN–(5,10,20,40) wt.% CTB 7.5 6.5–103.4 �1 = 584.7V−0.25 Kaya et al. (2005)SCN–3.6 wt.% ACE 3.5–5.7 6.5–113 �1 = 9.7G−0.50 Ustun et al. (2006)SCN–3.6 wt.% ACE 3.5–5.7 6.5–113 �1 = 240.1V−0.25 Ustun et al. (2006)KCl–5 mol.% CsCl 3 13–130 �1 = kV−0.42 Schmidbauer et al. (1993)CBr4 7 7–100 �1 = kV−0.55 De Cheveigne et al. (1985)SCN–25 wt.% ETH 4.8–10.8 3–54 �1 = 470V−0.33 Huang et al. (1993)SCN–2.5 wt.% Benzyl 1.6–9.5 56–92 �1 = kG−0.50V−0.25 Taha (1979)SCN–(0.15–5) wt.% ACE 3.8 48–225 �1 = kG−0.50V−0.25 Taha (1979)SCN–1.4 wt.% H2O 6.24 140 �1 = kG−0.50 Grugel and Zhou (1989)Salol 5.4 5–75 �1 = k(GV)−0.50 Dey and Sekhar (1993)

SCN–(0.001–0.004) mol.% Salol 6–15 60–160 �1 = 0.16G−1/3 V−1/3¦X−1/3o Liu and Kirkaldy (1994a)

SCN–5.5 mol.% ACE – – �1˛V−0.27 Somboonsuk et al. (1984)SCN–4 wt.% ACE 6.7 1–100 �1 = kV−0.37 Billia and Trivedi (1993)SCN 50 45–500 �˛V−0.20G−3/4 Shangguan (1988)SCN–ACE 5.6–35 8.57–194 �1 = 535.2G−0.81 Ma (2004)SCN–%2.5 ETH 48 3–54.2 �1 = 679.2V−0.40 Ma (2002)SCN–salol 26–35 1–25 �1 = 60(GV)−0.33 Trivedi et al. (2003)SCN–7.5 wt.% CTB 4.1–7.6 7.2–116.7 �2 = 2.24G−0.58 This workSCN–7.5 wt.% CTB 4.1–7.6 7.2–116.7 �2 = 221V−0.46 This workPVA 1.64 .7–85.8 �2 = kV−0.43 Cadırlı et al. (1999)PVA 1.644.86 9.6 �2 = kG−0.29 Cadırlı et al. (1999)Camphene 6.94 6.6–116.5 �2 = kV−0.24 Cadırlı et al. (2000)SCN–(5,10,20,40) wt.% CTB 7.5 6.5–103.4 �2 = 177V−0.46 Kaya et al. (2005)SCN–3.6 wt.% ACE 3.5–5.7 6.5–113 �2 = 1.4G−0.50 Ustun et al. (2006)SCN–3.6 wt.% ACE 3.5–5.7 6.5–113 �2 = 49.5V−0.48 Ustun et al. (2006)CBr4–(8–10.5) wt.% C2Cl6 3 0.2–20 �2˛V−0.44 Seetharaman et al. (1989)PVA–0.82 wt.% ETH 0.85–2.26 0.3–80 �2˛V−0.58 Trivedi and Mason (1991)SCN–1.3 wt.% ACE 1.6–9.7 1.6–250 �2˛V−0.51 Esaka and Kurz (1985)SCN–5.5 mol.% ACE 6.7 0.4–100 �2˛V−0.56 Somboonsuk et al. (1984)SCN–4 wt.% ACE 6.7 1–100 �2 = kV−0.56 Huang and Glicksman (1981)SCN–(5–20) wt.% Salol 4.5 6.7–112.4 R = kV−0.45 Cadırlı et al. (2003)SCN–7.5 wt.% CTB 4.1–7.6 7.2–116.7 R = 0.96G−0.65 This workSCN–7.5 wt.% CTB 4.1–7.6 7.2–116.7 R = 112V−0.48 This workPVA 1.6 6.7–85.8 R = kV−0.50 Cadırlı et al. (1999)PVA 1.644.86 9.6 R = kG−0.46 Cadırlı et al. (1999)Camphene 6.94 6.6–116.5 R = kV−0.24 Cadırlı et al. (2000)Camphene 2.25–6.94 6.6 R = kG−0.50 Cadırlı et al. (2000)SCN–(5,10,20,40) wt.% CTB 7.5 6.5–103.4 R = 090V−0.46 Kaya et al. (2005)SCN–3.6 wt.% ACE 3.5–5.7 6.5–113 R = 0.5G−0.50 Ustun et al. (2006)SCN–3.6 wt.% ACE 3.5–5.7 6.5–113 R = 20.5V−0.50 Ustun et al. (2006)CBr4–(8–10.5) wt.% C2Cl6 3 0.2–20 R˛V−0.53 Seetharaman et al. (1989)PVA–0.82 wt.% ETH 0.85–2.26 0.3–80 R˛V−0.54 Trivedi and Mason (1991)SCN–1.3 wt.% ACE 1.6–9.7 1.6–250 R˛V−0.53 Esaka and Kurz (1985)SCN–2 wt.% H2O 2.4–3.3 0.76–105 R˛V−0.43 Cattaneo et al. (1994)SCN–5.5 mol.% ACE 6.7 0.4–100 R˛V−0.53. Somboonsuk et al. (1984)CBr4–Hexacloroethane 3 0.2–20 R˛V−0.53 Somboonsuk et al. (1984)CBr4–C2Cl6 3 0.2–20 R˛V−0.47 Somboonsuk et al. (1984)SCN–%2.5 ETH 48 3–54.2 R = 22V−0.50 Ma (2002)NaCl – 30–100 R = 59.34V−0.531 Gorbunov (1992)PVA 0.001–1.1 ◦C/s 1–100 R = 1.41V−0.5 Glicksman (1984)SCN–7.5 wt.% CTB 4.1–7.6 7.2116.7 d = 13.2G−0.53 This workSCN–7.5 wt.% CTB 4.1–7.6 7.2116.7 d = 1096V−0.33 This workPVA 1.64 0.7–85.8 d = kV−0.45 Cadırlı et al. (1999)PVA 1.64–0.864 19.6 d = kG−0.33 Cadırlı et al. (1999)

152 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 145–155

Table 2 (Continued )

Pure or alloy system Temperature gradient Relationships References

Temperaturegradient G

Growth rate V(�m/s)

PVA 1.64–0.86 0.7–85.8 d = k(GV)−0.44 Cadırlı et al. (1999)Camphene 6.94 6.6–116.5 d = kV−0.22 Cadırlı et al. (2000)Camphene 2.25–6.94 6.6–116.5 d = kG−0.65 Cadırlı et al. (2000)Camphene 2.25–6.94 6.6–116.5 d = k(GV)−0.34 Cadırlı et al. (2000)SCN–3.6 wt.% ACE 3.5–5.7 6.5–113 d = 18.4G−0.49 Ustun et al. (2006)SCN–3.6 wt.% ACE 3.5–5.7 6.5–113 d = 351.7V−0.25 Ustun et al. (2006)

PVA: pivalic acid, SCN: succinonitrile, ACE: acetone, ETH: ethanol, and CTB: carbon tetrabromide.

Table 3 – A comparison of �2/R values obtained in present work with previous theoretical and experimental works

Pure or alloy system �2/R values References

– 2.10 (theoretical value) Langer and Muller-Krumbhaar (1978)SCN–7.5 wt.% CTB 2.07 This workPVA 4.64 Cadırlı et al. (1999)Camphene 3.33 Cadırlı et al. (2000)SCN–5 wt.% CTB 2.12 Kaya et al. (2005)SCN–10 wt.% CTB 2.10 Kaya et al. (2005)SCN–20 wt.% CTB 2.07 Kaya et al. (2005)SCN–40 wt.% CTB 2.03 Kaya et al. (2005)SCN–3.6 wt.% ACE 2.6 Ustun et al. (2006)SCN–ACE 2.0 Trivedi and Somboonsuk (1984)SCN 2.5 Glicksman and Singh (1986)CBr4–10.5 wt.% C2Cl6 3.18 Seetharaman et al. (1989)CBr4–7.9 wt.% C2Cl6 3.47 Seetharaman et al. (1989)PVA–0.82 wt.% ETH 3.8 Trivedi and Mason (1991)H2O–NH4Cl 4.68 Honjo and Sawada (1982)SCN–5.6 wt.% H2O 2.8 Liu et al. (2002)

NH4Cl–70 wt.% H2O 4.02SCN 3.0SCN 3.0

alloy with a constant growth rate at different temperature gra-dients and with a constant temperature gradient at differentgrowth rates obtained in the present work are in good agree-ment with the exponent values of �1, �2, R and (d) for the samealloys and different organic materials obtained by previousworkers (Cadırlı et al., 1999, 2000, 2003; Kaya et al., 2005; Ustunet al., 2006; Taha, 1979; Grugel and Zhou, 1989; Dey and Sekhar,1993; Liu and Kirkaldy, 1993, 1994b; Seetharaman et al., 1989;Trivedi and Mason, 1991; Rutter and Chalmers, 1953; Tiller etal., 1953; Kurz and Fisher, 1989; Esaka and Kurz, 1985; Cattaneo

et al., 1994; Somboonsuk et al., 1984; Billia and Trivedi, 1993;Shangguan, 1988; Ma, 2002, 2004; Trivedi et al., 2003; Gorbunov,1992; Glicksman, 1984; Honjo and Sawada, 1982; Liu et al., 2002;Hansen et al., 2002; Huang and Glicksman, 1981).

Table 4 – Physical properties of SCN–CTB alloys used in the calc

Liquidus slope (m) 2.25 (K/wt.%) or 0.225 ×Liquid diffusion coefficient (D) 2 × 10−5 (cm2/s)Equilibrium partition coefficient (k) 0.2

The Gibbs–Thomson coefficient (� ) 5.56 × 10−8 (Km)The harmonic perturbations 10 (mJ/m2)Equilibrium melting point of SCN (Te) 331.24 (K)

Hansen et al. (2002)Hansen et al. (2002)Huang and Glicksman (1981)

The comparisons of the experimentally obtained �1 val-ues in present work with the calculated �1 values by Hunt(1979), Kurz and Fisher (1981), Trivedi (1984), Lu and Hunt(1996) and Bouchard and Kirkaldy (1996, 1997) models forSCN–7.5 wt.% CTB alloy are given in Fig. 4. As can be seen fromFig. 4, the calculated line of �1 with Kurz and Fisher (1981),Trivedi (1984), Lu and Hunt (1996) and Hunt (1979) models areslightly upper, slightly lower and fairly below our experimen-tal values, respectively, and the calculated values of �1 withBouchard and Kirkaldy (1996) model are in good agreement

with our experimental results at high-growth rates but slightlylower than the experimental values at low-growth rates. Itcan be seen from Fig. 4 that the values of �1 experimentallyobtained in present work are very close the calculated values

ulations

103 (Kmol−1 fr−1) Rai and Rai (1998)Venugopalan and Kirkaldy (1984)Liu and Kirkaldy (1993, 1994a,b) andGandin et al. (1996)Maraslı et al. (2003)Trivedi (1984)Venugopalan and Kirkaldy (1984) andGandin et al. (1996)

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 145–155 153

Fig. 4 – Comparison of the experimental and theoreticalprimary dendrite arm spacing as a function of growth ratesfor directionally solidified SCN–7.5 wt.% CTB alloy with aconstant temperature gradient.

Fig. 5 – Comparison of the experimental and theoreticalsecondary dendrite arm spacing as a function of growth

rates for directionally solidified SCN–7.5 wt.% CTB alloywith a constant temperature gradient.

of �1 with Kurz and Fisher (1981) model for SCN–7.5 wt.% CTBalloy.

The variations in the values of �2 experimentally obtainedwith a constant G at different V in present work have beencompared with the values of �2 calculated from Trivedi andSomboonsuk (1984) and Bouchard and Kirkaldy (1996, 1997)models and the comparisons are given in Fig. 5. As it can beseen from Fig. 5, the calculated line of �2 with Trivedi andSomboonsuk (1984) model as a function of V is in good agree-ment with our experimental values and the calculated line of

�2 with Bouchard and Kirkaldy (1996, 1997) model as functionof V is slightly lower than the our experimental values.

Fig. 6a shows the comparisons of the experimentallyobtained R values as a function of V with the calculated R val-

154 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t

Fig. 6 – (a) Comparison of the experimental and theoreticaldendrite tip radius as a function of growth rates fordirectionally solidified SCN–7.5 wt.% CTB alloy with aconstant temperature gradient. (b) Comparison of theexperimental and Ruther Chalmers theoretical dendritemushy zone depth as a function of inverse of temperature

gradients for the directionally solidified SCN–7.5 wt.% CTBalloy with a constant growth rate.

ues from Hunt (1979), Kurz and Fisher (1981) and Trivedi (1984)the models. It can be seen from Fig. 6a, the calculated valuesof R with Trivedi (1984) model for SCN–7.5 wt.% CTB alloy is ingood agreement with our experimental values.

A comparison of the experimentally obtained mushy zonedepth (d) values as an inverse function of G in present workwith the calculated d values by Rutter and Chalmers (1953)model is given in Fig. 6b and the calculated line of d with

Rutter and Chalmers (1953) model is quite upper than ourexperimental results.

The value of �2/R for undercooled dendrites was esti-mated to be 2.1 by Langer and Muller-Krumbhaar (1978). In

e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 145–155

the present work, the average value of �2/R for directionallysolidified SCN–7.5 wt.% CTB alloy with a constant tempera-ture gradient has been found to be 2.07 (see Table 1b). As itcan be seen from Tables 1b and 3, the average value of �2/Robtained in present work for SCN–7.5 wt.% CTB alloy is in goodagreement with the value of �2/R estimated by Langer andMuller-Krumbhaar (1978).

A comparison of �2/R values obtained in present work withthe previous experimental works (Cadırlı et al., 1999, 2000;Kaya et al., 2005; Ustun et al., 2006; Trivedi and Somboonsuk,1984; Glicksman and Singh, 1986; Seetharaman et al., 1989;Trivedi and Mason, 1991; Billia and Trivedi, 1993; Shangguan,1988; Ma, 2002, 2004) is also given in Table 3. The average valueof �2/R obtained in the present work for SCN–7.5 wt.% CTB alloyis approximately equal to the value of �2/R estimated by Langerand Muller-Krumbhaar (1978) for pure substances. In addition,the experimental value (2.07) is also very close to 2.1, 2.0, 2.6,2.5 and 2.8 values reported by Kaya et al. (2005) for SCN–CTBalloys, Trivedi and Somboonsuk (1984) for SCN–ACE, Ustun etal. (2006) for SCN–2.6 wt.% ACE, Glicksman and Singh (1986) forSCN and Liu et al. (2002) for SCN–5.6 wt.% H2O alloy, respec-tively. As can bee seen from Table 3 the experimental valuesare quite different from some of the other experimental resultsgiven by Cadırlı et al. (1999, 2000), Glicksman and Singh (1986),Seetharaman et al. (1989), Trivedi and Mason (1991), Honjo andSawada (1982), Hansen et al. (2002) and Huang and Glicksman(1981). The physical parameters of SCN–CTB alloy used in �1,�2, R and d calculations with the theoretical models are givenin Table 4.

4. Conclusions

(a) The dependency of �1, �2, R and (d) on the (G) and (V) for thedirectionally solidified SCN–7.5 wt.% CTB alloy was inves-tigated. Our experimental observations show that thevalues of �1, �2, R and (d) decrease as the values of (G) and(V) increase. The relationships between the microstruc-ture parameters and the solidification parameters witha constant solute composition have been obtained tobe �1 = k1 G−0.47, �2 = k2 G−0.58, R = k3 G−0.65, d = k4 G−0.53,�1 = k5 V−0.25, �2 = k6 V−0.46, R = k7 V−0.48 and d = k8 V−0.33 bylinear regression analysis. These exponent values showthat the dependencies of �2, R and (d) on the (G) and (V)are stronger than �1.

(b) A comparison of the exponent values of �1, �2, R and (d) fordirectionally solidified SCN–7.5 wt.% CTB with a constantgrowth rate at different temperature gradients or with aconstant temperature gradient at different growth ratesobtained in present work with the theoretical models andprevious experimental works have been made. From thecomparison, it can be seen that the exponent value of �1 isin a good agreement with the theoretical exponent valuesof �1 and the average exponent values of �2, R and (d) areslightly lower than the theoretical values.

(c) The values of �1, �2 R and (d) for directionally solidi-fied SCN–7.5 wt.% CTB with a constant growth rate at

different temperature gradient or with a constant tem-perature gradient at different growth rates measured inpresent work have been compared with the calculatedvalues of �1, �2, R and (d) from Kurz and Fisher (1981),

t e c

(

A

TRUs

r

B

BBC

C

C

C

D

DEG

GG

j o u r n a l o f m a t e r i a l s p r o c e s s i n g

Trivedi (1984), Bouchard and Kirkaldy (1996, 1997), Lu andHunt (1996), Trivedi and Somboonsuk (1984) and Rutterand Chalmers (1953) models and it was seen that theexperimental results are mostly in good agreement withthe calculated values from Kurz and Fisher (1981), Trivedi(1984), Bouchard and Kirkaldy (1996, 1997), Trivedi andSomboonsuk (1984) and Rutter and Chalmers (1953) mod-els.

d) Langer and Muller-Krumbhaar (1978) have carried out adetailed numerical analysis of the wavelength of instabili-ties along the sides of a dendrite according to undercoolingand have predicted the values of �2/R to be 2.1. In thepresent work, the average value of �2/R for SCN–7.5 wt.%CTB alloy was found to be 2.07 and this value is very closeto 2.1 predicted by Langer and Muller-Krumbhaar (1978). Acomparison of �2/R values obtained in present work withthe values of �2/R obtained from theoretical and previousexperimental works have also been made.

cknowledgements

his project was supported by Erciyes University Scientificesearch Project Unit. The authors are grateful to Erciyesniversity Scientific Research Project Unit for their financialupports.

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