A

csrλ

w©

K

1

1

hsttia[[Yt

cc(

0d

Journal of Alloys and Compounds 439 (2007) 114–127

Effect of solidification processing parameters on the cellular spacingsin the Al–0.1 wt% Ti and Al–0.5 wt% Ti alloys

M. Gunduz a,∗, H. Kaya b, E. Cadırlı b, N. Maraslı a,K. Keslioglu a, B. Saatci a

a Erciyes University, Faculty of Arts and Sciences, Department of Physics, Kayseri, Turkeyb Nigde University, Faculty of Arts and Sciences, Department of Physics, Nigde, Turkey

Received 3 July 2006; received in revised form 24 August 2006; accepted 26 August 2006Available online 26 September 2006

bstract

The aim of this work is to investigate the relationship between solidification processing parameters (temperature gradient, G, growth rate, V, andooling rate,T ) and cellular spacing, λ, in the Al–0.1 wt% Ti and Al–0.5 wt% Ti alloys grown at high growth rates. In order to achieve this aim, thepecimens were solidified under argon atmosphere and steady-state conditions upward with different temperature gradients, G at a constant growth

ate, V and with different V at a constant G for the Al–Ti alloys in the Bridgman type directional solidification apparatus. The cellular spacing,was measured and expressed as functions of solidification processing parameters, G, V and T by using a linear regression analysis. The resultsere compared with similar previous experimental work and current theoretical models suggested for cellular growth.2006 Elsevier B.V. All rights reserved.

acing;

foOuucptstHfapβ

b

eywords: Al–Ti alloys; Microstructure; Directional solidification; Cellular sp

. Introduction

.1. Solidification of single phase and peritectic alloys

Solidification of single phase alloys and peritectic growthave been studied [1–5] for about 50 years. Recently peritecticolidification has attracted more attention in experimental andheoretical studies [6–36]. Since many technologically impor-ant materials are peritectics, studies on unidirectional solid-fication of peritectic alloys have been carried out on suchs Zn–Ag [24,25], Sn–Cd [26–28], Pb–Bi [29–33], Zn–Cu11,34,35], Sn–Sb [36], high temperature superalloys Al–Ti16,19], Ni–Ti [15] and Ni–Al [22], superconducting materialsBCO [14,15], magnetic materials Fe–Nd–B [21], and struc-

ural materials Fe–Ni [17,18].Peritectic microstructures are characterized by the growth

ompetition between α primary and a peritectic β phase, whichan both coexist with the liquid at the peritectic temperature TpFig. 1). In case of single growth of the primary phase (Co1) inter-

∗ Corresponding author. Tel.: +90 352 4374937x33126; fax: +90 352 4374933.E-mail address: gunduz@erciyes.edu.tr (M. Gunduz).

uelCBtt

925-8388/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.jallcom.2006.08.246

Crystal growth

ace temperature of the primary phase decreases towards TLα inrder to achieve the steady-state growth with planar interface.n the other hand when peritectic alloy directionally solidifiednder planar growth conditions, the rejection of solute in the liq-id leads to the formation of a solute boundary layer [37]. Theomposition in the liquid at the interface increases as the single-hase solidification and the interface temperature decreases withime until a steady-state growth condition is achieved at theolidus temperature of the alloy. The three phase peritectic reac-ion (L + β → α) cannot occur at Tp but must occur below Tp.owever, below Tp α can also form directly by crystallization

rom liquid and unless the temperature is maintained constantll the α can be produced this way [38]. Once α forms, a threehase interface is produced where the liquid is CLα and hence theis unstable and may dissolve to bring the liquid composition

ack to CLP (Fig. 1). As soon as this happens the liquid becomesndercooled with respect to α and α will grow consuming thexcess B atoms. When the temperature fallen from TL to TP,iquid remote from the β crystals is richer in component B than

LP, because compositions gradients must be established whileatom are withdrawn from the melt to feed the growing β crys-

als [39]. Although the peritectic reaction is normally isothermal,he initial reaction L + β → α is stilled by forming of an envelope

M. Gunduz et al. / Journal of Alloys and

Fig. 1. Hypothetical peritectic phase diagram, showing symbols used for phases,compositions and temperatures (after [38]).

oopα

cttlma

outnitCnotp

Fig. 2. Partial Al–Ti phase diagram (after [71]) and microstructu

Compounds 439 (2007) 114–127 115

f solid α around each β particle. Further transformation thenccurs by diffusion through the peritectic envelope while tem-erature falls below TP. At any given temperature TR (Fig. 1) theenvelope will separate β phase of composition Cβ from liquid

omposition CL but through the thickness �x, of the composi-ion will vary between Cα1 and Cα2 (Fig. 1). Thus, dissolution ofhe β phase by diffusion of the β component through the enve-ope is assisted by a concentration gradient (Cα1 − Cα2)/�x, the

agnitude of which is depend on the relative slopes of the Cα1nd Cα2 lines [40].

In peritectic systems two-phase morphologies have beenbserved under the condition close to the limit of constitutionalndercooling, such as peritectic banding [26,34,41–43] oscilla-ion [33,42,43] and peritectic coupled growth [44–47]. Simulta-eous (coupled) growth of two phases with planar solid/liquidnterface has been suggested to occur in peritectic alloys close tohe peritectic temperature, similar to eutectic alloys [1,26,48,49].oupled growth characterized as a co-operative growth mecha-

ism so that simultaneous growth of two phases from the meltccurs. Coupled growth is characterized by a macroscopicallyhat composite front in which the two phases grow togetherarallel to the growth direction with either lamellar or rod mor-

res observed for Al–0.1 wt% Ti and Al–0.5 wt% Ti alloys.

1 s and

pwb

1p

ccdoMpVhtmttta[

pptfctatm

λ

wc

oasfivwo

λ

Vt

c

λ

wTλ

LtpHtbcecc

cor

λ = 4.09k−0.745o

[Γko

mCo(ko − 1)

]0.41

D0.59V−0.59

(Hunt and Lu; cellular) (4)

16 M. Gunduz et al. / Journal of Alloy

hology. Cellular peritectic coupled growth is only possiblehen both phases are morphologically stable and the liquidetween the cells and dendrites becomes richer in B atoms [50].

.2. Directional solidifications, solidification processingarameters and cellular spacings

In directional solidification experiments, solidification pro-essing parameters, temperature gradient G and growth rate Van be independently controlled so that one may study the depen-ence of microstructural parameter (λ) on either G at constant Vr V at constant G for the constant initial solute composition Co.ost experimental studies have shown that the microstructural

arameters decrease as solidification processing parameters (G,and T ) increase, for the constant Co. The above observations

ave led, over the past decades, to be the establishment of rela-ionships between the solidification processing parameters and

icrostructural parameters. A literature survey shows severalheoretical models [51–53] and numerical models [54–57] usedo examine the influence of solidification processing parame-ers (G, V, Co) on the microstructural parameter, although thegreement between theory and experiment was still in complete58].

Hunt [51], Kurz and Fisher [52] and Trivedi [53] have beenroposed detailed theoretical models to characterize cells andrimary dendrite spacings during steady-state growth condi-ions, as a function of G, V and Co. Hunt attempted to allowor the interaction of the diffusion fields between neighboringells using an approach suggested by Bower et al. [59]. The rela-ionship between solidification processing parameters (G, V, Co)nd λ for a cellular and dendritic front with the growth condi-ion is determined by the minimum undercooling. The Hunt [51]

odel gives,

= 2.83[Γm(ko − 1)D]0.25C0.25o G−0.5V−0.25

(Hunt; cellular/dendritic) (1)

here m is liquidus slope, k is partition coefficient, D is diffusionoefficient in liquid and Γ is Gibbs–Thomson coefficient.

Kurz and Fisher [52] assumed that the shape of the cellr dendrite fully developed, including side branches can bepproximated as an ellipsoidal revolution and using the marginaltability criterion for an isolated dendrite or cell and they simpli-ed their results for the low velocity (V < Vcs/k) and for the highelocity (V > Vcs/k) regimes (where Vcs is the critical velocity athich the planar interface becomes unstable). For V > Vcs/k theybtained as follows.

= 4.3

[Γm(ko − 1)D

k2O

]0.25

C0.25o G−0.5V−0.25

(Kurz and Fisher; cellular/dendritic) (2)

The other theoretical model to characterize λ as function of G,, Co was developed by Trivedi [53]. Trivedi model is a result of

he modification of the Hunt model, and used marginal stability

Fv(s

Compounds 439 (2007) 114–127

riterion. Trivedi model gives

= 2.83[LΓm(ko − 1)D]0.25C0.25o G−0.5V−0.25

(Trivedi; cellular/dendritic) (3)

here L is a constant that depends on the harmonic perturbations.hese theoretical models are very similar at high growth rate forand the difference among them is a constant only. Warren andanger [60,61] proposed a solution of this problem that rather

han a unique value of λ there may be an allowable range ofrimary spacings for any given set of solidification conditions.owever, The Warren and Langer model is unable to account for

he ability of a dendritic array to decrease its primary spacingsy tip splitting or higher-order side branching in response to ahange in solidification conditions. Hunt and Lu [54] and Kurzt al. [56,57] have proposed numerical models to characterizeells and primary dendrite spacings during steady-state growthonditions, as a function of V and Co.

Hunt and Lu [54] have proposed an analytical expression fororresponding cellular spacing from their numerical predictionsf the lower limit of stable cellular/dendritic spacing and is rep-esented by the following equations,

ig. 3. The schematic illustration of the cellular spacings measurements trans-erse and longitudinal sections (a) transverse section; (b) longitudinal section;c) schematic illustration of the microstructure; (d) triangle method for cellularpacing; (e) area counting method for cellular spacing.

M. Gunduz et al. / Journal of Alloys and Compounds 439 (2007) 114–127 117

Table 1The experimental results and relationships between the cellular spacings and solidification processing parameters for Al–0.1 wt% Ti alloy

Al–0.1 wt% Ti alloy system

Solidification parameters Cellular spacings The relationships

G (K/mm) V × 10−3 (mm/s).

T (K/s) λ* (�m) λ∗∗tr (�m) λ∗∗

ar (�m)

3.8 8.2 0.034 95.2 ± 2.9 98.9 ± 8.2 107.1 ± 8.7 λ* = k1G−0.51,λ* = k2V−0.27,λ∗ =k3(T )−0.32,λ∗∗

a =k4G

−0.54,λ∗∗

a =k5V

−0.27,λ∗∗

a =k6(T )−0.32

5.1 8.3 0.045 83.0 ± 2.4 84.4 ± 11.3 90.5 ± 13.26.2 8.3 0.052 77.4 ± 2.1 74.4 ± 9.2 80.2 ± 11.17.3 8.4 0.061 66.8 ± 1.9 68.0 ± 7.5 71.3 ± 6.69.1 8.3 0.070 61.1 ± 1.7 62.6 ± 4.5 65.8 ± 6.29.1 16.6 0.133 51.0 ± 2.0 53.9 ± 5.8 56.7 ± 6.19.1 42.8 0.327 38.3 ± 2.9 40.6 ± 5.0 43.5 ± 5.19.1 81.0 0.745 32.2 ± 1.2 34.4 ± 4.3 36.6 ± 4.19.1 166.0 1.300 27.2 ± 1.8 27.4 ± 2.7 29.1 ± 2.2

Constant (k) Correlation coefficients (r)

k1 = 5.62 (�m0.49 K0.51) r1 = −0.989k2 = 107.2 (�m1.27 s−0.27) r2 = −0.994k3 = 27.5 (�m K0.32 s−0.32) r3 = −0.984k4 = 4.83 (�m0.46 K0.54) r4 = −0.994k5 = 114.8 (�m1.27 s−0.27) r5 = −0.994k6 = 28.8 (�m K0.32 s−0.32) r6 = −0.984

λ*: The values of the cellular spacing measured from the longitudinal section of the samples; λ∗∗tr : the values of the cellular spacing measured from the transverse

s ular sc e trano

AK

λ

b

(tew

TT

A

S

G

11111

C

kkkkkk

B

ection of the samples using by the triangle method; λ∗∗ar : the values of the cell

ounting method; and λ∗∗a : average values of cellular spacing measured from th

f G at a constant V, and also, increase of Vat a constant G.

good approximation for λ at high growth velocity is given byurz et al. [56,57] as,

[ΓDko

]0.5−0.5

= 4π

mCo(ko − 1)V (Kurz et al.; cellular) (5)

The theoretical models for high growth rate were chosenecause the experiments were carried out for high growth rates

csSg

able 2he experimental results and relationships between the cellular spacings and solidific

l–0.5 wt% Ti peritectic alloy system

olidification parameters Cellular spa

(K/mm) V × 10−3 (mm/s).

T (K/s) λ* (�m)

5.1 8.4 0.039 94.5 ± 2.66.3 8.3 0.048 80.1 ± 3.07.6 8.2 0.058 75.4 ± 2.78.9 8.4 0.066 69.0 ± 2.90.3 8.3 0.079 64.0 ± 2.10.3 16.6 0.165 53.3 ± 2.20.3 43.0 0.407 43.9 ± 2.10.3 83.0 0.790 35.1 ± 1.80.3 165.0 1.45 26.8 ± 1.9

onstant (k)

7 = 5.62 (�m0.47 K0.53)

8 = 117.5 (�m1.28 s−0.28)

9 = 30.9 (�m K0.31 s−0.31)

10 = 5.50 (�m0.46 K0.54)

11 = 112.2 (�m1.25 s−0.25)

12 = 33.9 (�m K0.29 s−0.29)

old values are used to emphasize the increase of G at a constant V, and also, increas

pacing measured from the transverse section of the samples using by the areasverse section of the samples. Bold values are used to emphasize the increase

V > Vcs) and the experimental results were compared withhe results obtained by the theoretical models. Also severalxperimental studies in the literature [62–70] have comparedith these theoretical predictions under steady-state growth

onditions, for alloys of different systems: Pb–Sb [62,63],uccinonitrile–acetone [64,65], Al–Cu [66,67], Al–Zn [68,69],n–Pb [70], and a agreement between theory and experiment isenerally reported.

ation processing parameters for Al–0.5 wt% Ti alloy

cings The relationships

λ∗∗tr (�m) λ∗∗

ar (�m)

96.1 ± 4.8 103.5 ± 6.1 λ* = k7G−0.53,λ* = k8V−0.28,λ∗ =k9(T )−0.31,λ∗∗

a =k10G

−0.54,λ∗∗

a =k11V

−0.25,λ∗∗

a =k12(T )−0.29

82.6 ± 5.0 97.5 ± 5.275.9 ± 5.3 89.8 ± 4.570.4 ± 4.5 76.2 ± 4.664.7 ± 4.3 67.4 ± 4.756.2 ± 4.0 57.9 ± 4.444.8 ± 2.7 45.8 ± 3.036.7 ± 2.2 39.4 ± 2.930.5 ± 2.1 34.3 ± 2.0

Correlation coefficients (r)

r7 = −0.989r8 = −0.989r9 = −0.989r10 = −0.994r11 = −0.994r12 = −0.989

e of Vat a constant G.

118 M. Gunduz et al. / Journal of Alloys and Compounds 439 (2007) 114–127

F i alloy( (c1) ll ) long

mpsih

ao

ig. 4. Variation of cellular spacings of the directionally solidified Al–0.1 wt% Tb1) longitudinal section, (b2) transverse section (G = 6.2 K/mm, V = 8.3 �m/);ongitudinal section, (d2) transverse section (G = 9.1 K/mm, V = 42.8 �m/s); (e1

The aim of this work is to obtain more insight into theicrostructure and phase selection of the single phase and the

eritectic growth and to investigate the relationship betweenolidification processing parameters (G, V, T ) and cellular spac-ng, in the Al–0.1 wt% Ti and Al–0.5 wt% Ti alloys grown atigh growth rates. In the Al rich Al–Ti alloys, solute pile up

sitt

, (a1) longitudinal section, (a2) transverse section (G = 3.8 K/mm, V = 8.2 �m/s);ongitudinal section, (c2) transverse section (G = 9.1 K/mm, V = 8.3 �m/s); (d1)itudinal section, (e2) transverse section (G = 9.1 K/mm, V = 166 �m/s).

t growing interface does not cause convection because densityf Ti is larger than that of Al. Therefore the Al–Ti system was

elected as a model system to investigate the cellular structuren peritectic alloys. Al rich Al–Ti alloy is excellent alloy systemo study coupled growth for three main reasons: first, in con-rast to many other peritectic systems, the mushy zone range is

M. Gunduz et al. / Journal of Alloys and Compounds 439 (2007) 114–127 119

F i alloy( c1) lol longi

sitiPt

2

ig. 5. Variation of cellular spacings of the directionally solidified Al–0.5 wt% Tb1) longitudinal section, (b2) transverse section (G = 7.6 K/mm, V = 8.2 �m/); (ongitudinal section, (d2) transverse section (G = 10.3 K/mm, V = 43 �m/s); (e1)

mall [71] (∼5 K) which values it convenient to carry out exper-ments (Fig. 2), secondly, the small density difference between

he solute and the solvent limits the amount of convection presentn the melt as compared to other alloy systems such as Cu–Zn,b–Bi, Sn–Cd, thirdly, all necessary physical parameters related

o Al–Ti system are well known.

Avai

, (a1) longitudinal section, (a2) transverse section (G = 5.1 K/mm, V = 8.4 �m/s);ngitudinal section, (c2) transverse section (G = 10.3 K/mm, V = 8.3 �m/s); (d1)tudinal section, (e2) transverse section (G = 10.3 K/mm, V = 165 �m/s).

. Experimental procedure

Al–Ti alloys containing 0.1 and 0.5 wt% Ti were prepared from high-purityl (99.99%) and Ti (99.99%). Bulk alloy of each composition was melted byacuum melting furnace. After allowing time for melt homogenization, moltenlloy was poured into the prepared 13 graphite crucibles (250 mm in length 4 mm.d. and 6.35 mm o.d.) in a hot filling furnace. Then each specimen was positioned

120 M. Gunduz et al. / Journal of Alloys and Compounds 439 (2007) 114–127

F Ti all s fro

imaowa(aGsr

2a

Rtp

piotcr[

tsmato

ig. 6. Scanning electron micrographs of the directionally solidified Al–0.1 wt%ongitudinal section area; (b1) transverse section, (b2) higher magnification view

n a graphite cylinder (300 mm in length 10 mm i.d. and 40 mm o.d.) in a Bridg-an type furnace. After stabilizing the thermal conditions in the furnace under

n argon atmosphere, the specimen was grown by pulling it downwards at vari-us constant rates by means of different speed synchronous motors. Specimensere solidified under steady-state conditions with different G (3.8–9.1 K/mm)

t constant V (8.3 �m/s) and with different V (8.3–166 �m/s) at a constant G9.1 K/mm) for Al–0.1 wt% Ti alloy and with different G (5.1–10.3 K/mm)t a constant V (8.3 �m/s) and with different V (8.3–165 �m/s) at a constant

(10.3 K/mm) for Al–0.5 wt% Ti alloy (Tables 1 and 2). After 100–120 mmteady-state growth of the samples, the samples were quenched by pulling themapidly into the water reservoir.

.1. Measurement of temperature gradients, G growth rates, Vnd cooling rates, T

The temperature of the Bridgman type furnace was controlled by a Pt/Pt-13%h thermocouple placed between the heating element and the alumina tube. The

emperature could be controlled to about ±0.1 K during the run. The thermocou-les were placed capillary alumina tubes (0.8 mm i.d., 1.2 mm o.d.) which were

ctttt

loy (a1) longitudinal section, (a2, a3) higher magnification views from the samem the same transverse section area (G = 9.1 K/mm, V = 8.3 �m/s).

ositioned approximately 10 mm apart and parallel to the heat flow directionnside the crucible. Throughout the experiment, temperature distribution wasbtained by measuring the temperature in the sample by three chromel/alumelhermocouples (type-K). All the thermocouple leads were taken to an ice/waterold junction, then to a WPA analog potentiometer and to a Kipp–Zonen chartecorder capable of recording to 1 �V. (The experimental details are given in72].)

The thermocouples were, recorded simultaneously for measurement of theemperature gradients on the solid/liquid interface in the liquid. When theecond thermocouple was at the solid–liquid interface and then third ther-ocouple in the liquid their temperatures were used to obtain the temper-

ture gradient, G. The positions of the thermocouples were measured afterhe quench. The cooling water level was always kept at the same position inrder to check the furnace temperature. Thus, the sample temperature was

onstant. The temperature gradient can be altered by changing the tempera-ure of the sample and/or the distance between the cooling water level andhe hot stage. G can be kept constant during the run by keeping the tempera-ure of the cooler and the hotter part of the furnace and the distance betweenhem.

M. Gunduz et al. / Journal of Alloys and Compounds 439 (2007) 114–127 121

F Ti all s fro

morawt

tt

2

gt

iivtamp

2

ig. 7. Scanning electron micrographs of the directionally solidified Al–0.5 wt%ongitudinal section area; (b1) transverse section, (b2) higher magnification view

The growth rate was calculated with two different methods. In the firstethod, the values for the growth rate were calculated from the measurements

f the time taken for the solid/liquid interface to pass the thermocouples sepa-ated by a known distance. In the second method, the total solidification timend solidification distance (on the longitudinal section of the polished sample)ere measured. The ratio of the distances to the times was measured to obtain

he growth rates and these were similar for both methods.The cooling rate T was determined from the cooling curves obtained by

he Kipp–Zonen recorder during the directional solidification process of eachhermocouple. The values are given in Tables 1 and 2.

.2. Metallographic analysis

The unidirectionally grown quenched specimens were removed from theraphite crucible, then ground to observe the solid–liquid interface, and longi-udinal (parallel to the growth direction) section, which included the quenched

tw(js

loy (a1) longitudinal section, (a2, a3) higher magnification views from the samem the same transverse section area (G = 10.3 K/mm, V = 8.3 �m/s).

nterface, was separated from the specimen. Then the samples included quenchnterface was cold-mounted with epoxy-resin. Thereafter, longitudinal and trans-erse sections of the samples were observed with standard metallographicechniques. An etchant made up of 5-ml hydrofluoric acid, 5-ml nitric acidnd 95-ml water was used to provide a suitable contrast for Al–Ti alloys. Theicrostructure of the specimen was investigated by the light microscope (Olym-

us, BH-2) and scanning electron microscopy (LEO-l).

.3. Measurement of cellular spacings, λ

The λ values measured on the transverse sections gave more accurate results

han the λ values measured on the longitudinal section. Two different methodsere used for measurement of the cellular spacings on the transverse sections

Fig. 3). The first method is the triangle method [73]. The triangle occurred byoining the three neighbor hexagonal centers and sides of the triangle corre-ponded to λ (Fig. 3d). In this method at least 200–300 cellular spacings λ∗∗

tr

1 s and

viw

λ

wfooom

3

(VT

((ttsap

3s

a

Frs

22 M. Gunduz et al. / Journal of Alloy

alues were measured for each specimen. The second method is the area count-ng method [73–76]. In this method, the average cellular spacing values, λ∗∗

arere calculated from,

∗∗ar = B

M

(A

N

)0.5

(6)

here B (1.075 for hexagonal structures) is correction factor, M the magnificationactor, A the total specimen cross-section area and N the number of hexagonaln the cross-section. λ∗∗

ar values were measured on the cross-section, at leastn five different regions for each specimen in this method (Fig. 3e). λa values,btained from average values of the area counting method, λ∗∗

a and the triangleethod, λ∗∗

tr are given in Tables 1 and 2.

. Result and discussion

A series of experiments were carried out at a constant G9.1 K/mm) with different V (8.3–166) �m/s and at a constant

(8.3 �m/s) with different G (3.8–9.1 K/mm) for Al–0.1 wt%i alloy and also at a constant G (10.3 K/mm) with different V

Go(T

ig. 8. (a) Variation of cellular spacing λ, with temperature gradients G, at a constaates V, at a constant temperature gradient (G = 9.1 K/mm); (c) variation of cellular spystem.

Compounds 439 (2007) 114–127

8.3–165 �m/s) and at a constant V (8.3 �m/s) with different G5.1–10.3 K/mm) for Al–0.5 wt% Ti alloy. Figs. 3–7 show longi-udinal and transverse views of the samples studied to examinehe effect of solidification processing parameters on the cellularpacing. The measured cellular spacing with standard deviationsnd relationships between cellular spacing and the solidificationrocessing parameters are given in Tables 1 and 2.

.1. Effect of the temperature gradient on the cellularpacing

The photographs of the unidirectionally solidified Al–Tilloys are shown in Figs. 4–7. In order to determine λ versus

dependency, measurements of cellular spacings were madever a range of temperature gradients at a constant velocityV = 8.3 �m/s) for Al–0.1 wt% Ti and Al–0.5 wt% Ti alloys.he plots of the log λ versus log G data obtained at constant

nt growth rate (V = 8.3 �m/s); (b) variation of cellular spacing λ, with growthacing λ, with cooling rates T of the directionally solidified Al–0.1 wt% Ti alloy

M. Gunduz et al. / Journal of Alloys and Compounds 439 (2007) 114–127 123

F onstar llulara

vAFbs

λ

Apv0TgAoto

nEwAaFbas

3

ig. 9. (a) Variation of cellular spacing λ, with temperature gradients G, at a cates V, at a constant temperature gradient (G = 10.3 K/mm); (c) variation of celloy system.

elocity are shown in Figs. 8a and 9a for Al–0.1 wt% Ti andl–0.5 wt% Ti alloy systems, respectively. As can be seen fromigs. 8a and 9a, a mathematical relationship can be describedetween λ and G by linear regression analysis for each compo-ition as

= k1G−a (7)

s can be seen from Figs. 8a and 9a, λ changed inverselyroportional to G. The exponent values (obtained from trans-erse section) of the temperature gradient equal to 0.56 and.57 for Al–0.1 wt% Ti and Al–0.5 wt% Ti alloys, respectively.he exponent values of the temperature gradients for the lon-itudinal section equal to 0.52 and 0.50 for Al–0.1 wt% Ti and

l–0.5 wt% Ti alloys, respectively. As can be seen from Table 3,ur exponent values (0.52–0.57) are in good agreement withhe values of 0.50, 0.50, 0.50, 0.50, 0.50 and (0.52 and 0.57)btained by Lapin et al. [77] for Ni–Al–Cr–Fr system, McCart-

Vcog

nt growth rate (V = 8.3 �m/s); (b) variation of cellular spacing λ, with growthspacing λ, with cooling rates T of the directionally solidified Al–0.5 wt% Ti

ey and Hunt [78] for Al–0.63 at% Mg–1.39 at% Si system,shalman et al. [79] for PWA1480 system, Young and Kirk-ood [80] for Al–(2.4–10.1) wt% Cu systems, Taha [81] forl–(5.7–20) wt% Cu systems, Jin [82] for Fe–8 at% Ni system

nd Tunca and Smith [83] for Zn–8 wt% Al system, respectively.urthermore, these experimental exponent values were found toe very close to the value 0.50 predicted by Hunt [51] Kurznd Fisher [52] and Trivedi [53] theoretical models for cellularpacings.

.2. Effect of the growth rate on the cellular spacing

Figs. 8b and 9b, Tables 1 and 2 show variation of λ with

at the constant G (9.1 K/mm) for Al–0.1 wt% Ti alloy and a

onstant G (10.3 K/mm) for Al–0.5 wt% Ti alloy. The variationf λ on the log λ versus log V plot is essentially linear for therowth rate ranges (8.3–165) �m/s. A linear regression analysis

124 M. Gunduz et al. / Journal of Alloys and Compounds 439 (2007) 114–127

Table 3The experimental results for some metallic alloys in the literature

Composition Range of G (K/mm) Range of V (�m/s) Relationship Range of λ1 (�m) Ref.

Al–(70–80 at% Ni) alloys – 500–5000 λ = 1200V−0.50 – [6]Zn–1.5–7.4Cu peritectic alloys 15 20–4820 λ1 = (216–316)V−0.50 – [10]

Zn–1.53–7.37Cu peritectic alloys 15 20–4820 λ1 = 310V−0.50 3.5–103 [11]λ1 = 540V−0.59

Zn–3.37 wt% Cu peritectic – 500–4500 λ = 216V−0.50 2.8–8 [35]Fe–Ni peritectic alloys 9–10 5–33 – 10–120 [47]

Al–(3–24) wt% Cu 1.5–7.4 8–490 λ1 = kG−0.30 120–750 [66]λ1 = k2V−0.23

Al–4.5 wt% Cu 8.8 10–240 λ1 = kV−0.38 7.5–90 [67]Al–0.53 wt% Zn λmin = 731.3V−0.375

Al–0.26 wt% Mn 8.8 10–200 λmax = 8674.1V−0.526 457–1141 [67]

Pb–(5–95) wt% Sn 0.8–5.5 7–467 λ1 = kG−n (n = 0.32–0.71) 45.2–146.7 [70]λ1 = kV−n (n = 0.29–0.40)

Pb–19 wt% Sn 1.1–37 20 λ1 = kG−0.32 35.2–182 [75]Pb–8 wt% Au 40 2–407 λ1 = kV−0.44

Ni–Al–Cr–Fr 15 2.78–118 λ1 = 1.24 × 10−3G−0.50V−0.25 80–200 [77]Al–0.63 at% Mg–1.39 at% Si 0.3–18.5 7.7–1000 λ1 = 62G−0.50V−0.25 48–1270 [78]PWA1480

(Ni–12Ta–10Cr–5Co–5Al–4W–1.5Ti)25.5 100–233 λ1 = 102G−0.50V−0.25 167–195 [79]

Al–2.4 wt% Cu λ1 = kG−0.50V−0.50

Al–4.4 wt% Cu 5–13 50–500 λ1 = kG−0.50V−0.36 132–630 [80]Al–10.1 wt% Cu λ1 = kG−0.50V−0.43

Al–(5.7–20) wt% Cu 2–9 7–430 λ1 = 55G−0.50V−0.25 160–500 [81]Fe–8 at% Ni 11–42 4.1–102.8 λ1 = 41G−0.50V−0.25 77.5–850 [82]Zn-6.5 wt% Al 7.5–10.5 10–1000 λ1 = kV−m (m = 0.25–0.27)Zn–8 wt% Al 7.5–12 10–1000 λ1 = kV−m (m = 0.24–0.29)

Zn–11 wt% Al 7.5–12 10–1000 λ1 = kV−m (m = 0.25–0.30) – [83]λ1 = kG−0.57

Zn–8 wt% Al 2.8–12 53–100 λ1 = kG−0.52

Zn–(2.17) wt% Cu peritectic alloys – 20–4800 λ1 = 316V−0.50 4.3–16.3 [84]Fe–C–Mn–Si 0.09, 0.15C/1.4Mn/0.4Si 1.02–7.02 33–340 λ1 = 53G−0.50V−0.25 144–859 [85]Al–40 wt% Cu 3 4.2–42 λ1 = kV−0.32 – [86]Pb–5.10 at% Sb 0.5–4.5 50–120 λ1 = 19G−0.50V−0.25 80–200 [87]Al–11 wt% Mg – – λ1 = k(GV)−0.33 – [88]Al–(9.5–28.1) wt% Fe 1–13 10–6400 λ1 = kG−0.50V−0.25 – [89]Ni base superalloy (IN738LC)a 5–8.5 16–333 λ1 = 954(GV)−0.31 120–750 [90]Pb–5.7 at% Sb 2–19.7 8–218 λ1 = 24G−0.50V−0.25 66–118 [91]F

g

λ

Fdtr

rsr0[YK

an0ePaFhvaL

e–(3.5–4.5) at% Ni peritectic alloys 18 3–30

a Ni–(15.9Cr–8.1Co–3.3Ti–3.4Al–3W–1.9Mo–1.6Ta–0.8Nb–0.11C) wt%.

ives the proportionality equation as

= k2V−b (8)

igs. 8b and 9b show clearly that an increase in V produce aecrease in λ. The exponent value of the growth rate b is equalo 0.26 and 0.24 for the Al–0.1 wt% Ti and Al–0.5 wt% Ti alloys,espectively.

Decreasing of cellular spacings, λ with increasing growthates, V was determined by various workers for different alloyystems [6,77,84,93–98]. The exponent values of the growthates, b values 0.40, 0.41 0.25, 0.50, 0.25, 0.23, 0.27, 0.54 and

.26 obtained by Miyata et al. [93] for Al–Cu, Jesse and Giller94] for Cd–Zn, Sharp [95] for Al–Cu, Ma et al. [84] for Zn–Cu,ang et al. [96] for Cu–Mn, Lapin et al. [77] for Ni–Al–Cr–Fe,loosterman and Hosson [6] for TiN, Feng et al. [97] for Al–Zn

frea

– 80–225 [92]

nd Pryds et al. [98] for Fe–Cr–C alloy, respectively. Our expo-ent values (0.26 and 0.24) is in good agreement with the values.25, 0.25, 0.23, 0.27, and 0.26 obtained by Sharp [95], Yangt al. [96], Lapin et al. [77], Kloosterman and Hosson [6] andryds et al. [98], respectively. These exponent values are in goodgreement with the value 0.25 predicted by Hunt [51], Kurz andisher [52] and Trivedi [53] theoretical models. On the otherand, these exponent values (0.26 and 0.24) are less than thealues of 0.40 and 0.41 obtained by Miyata et al. [93] and Jessend Giller [94] and also (0.59 and 0.50) predicted by Hunt andu [54] and Kurz et al. [56,57] numerical models, respectively,

or cellular spacings. This might be due to the higher growthate exponent for the numerical models. On the other hand thexperimental λ values and the numerically obtained λ valuesgree quite well for the growth rates between 15 and 150 �m/s.

M. Gunduz et al. / Journal of Alloys and Compounds 439 (2007) 114–127 125

F ork anA

3

irtsiie

λ

Tf

S0aan0a

3

FA

ig. 10. Comparison of cellular spacings, λ obtained with the experimental wl–0.5 wt% Ti alloy.

.3. Effect of the cooling rate on the cellular spacing

Experimentally measured cooling rate (T ) values are givenn Tables 1 and 2 for Al–0.1 wt% Ti and Al–0.5 wt% Ti alloys,espectively. As can be seen from Figs. 8c and 9c, the varia-ions of λ versus T plot is essentially linear on the logarithmiccale. Figs. 8c and 9c, Tables 1 and 2 show clearly that anncrease in cooling rate, T leads to a decrease in cellular spac-ngs, λ. The linear regression analysis gives the proportionalityquation as,

= k3T−c (9)

he exponent value of the cooling rate c is equal to 0.33 and 0.32or the Al–0.1 wt% Ti and Al–0.5 wt% Ti alloys, respectively.

ffT

ig. 11. Comparison of cellular spacings, λ obtained with the experimental work al–0.5 wt% Ti alloy.

d with the theoretical models [50,52,53] (a) for Al–0.1 wt% Ti alloy; (b) for

imilar exponent values in the literature for different alloys 0.55,.25, 0.35, 0.36 were obtained by Rocha et al. [69] for Sn–Pblloys, David and Vitek [99], Gunduz and Cadırlı [66] for Al–Culloys, by Cadırlı and Gunduz [70] for Pb–Sn alloys. These expo-ent values (0.33 and 0.32) are close to the values 0.25, 0.35 and.36 obtained by David and Vitek [99], Gunduz and Cadırlı [66]nd Cadırlı and Gunduz [70], respectively.

.4. Effect of composition on the cellular spacing

As can be seen from Tables 1 and 2, the values of λ measuredrom Al–0.5 wt% Ti alloy are higher than Al–0.1 wt% Ti alloyor same G and V values (G = 5.1, 6.2, 7.3 K/mm; V = 8.3 �m/s).his result is agreed with the theoretical models because accord-

nd with the numerical models [57,59,60] (a) for Al–0.1 wt% Ti alloy; (b) for

1 s and

iCatT

3t

t[ampatmrlbvgmwCeairλ

mT

ct

4

wcoctoiλ

T

1

2

3

4

5

A

ACf

AA

P

MCSGDDT

R

26 M. Gunduz et al. / Journal of Alloy

ng to Eqs. (1)–(3) λ increase with the increasing composition,o. Furthermore, the exponent values of the growth rate (0.27)nd cooling rate (0.32) for Al–0.1 wt% Ti alloy are bigger thanhe growth rate (0.25) and the cooling rate (0.29) for Al–0.5 wt%i alloy.

.5. The comparison of the experimental results withheoretical models

The comparison of the experimentally obtained λ values withhe calculated λ values by the theoretical models (Hunt model51], the Kurz and Fisher model [52], the Trivedi model [53])nd numerical models (Hunt and Lu model [54] and Kurz et al.odel [56,57]) is given in Figs. 10 and 11. The thermophysical

arameters of Al–Ti alloys used in λ calculations for the modelsre given in Appendix A. Fig. 10a and b shows the comparison ofhe experimental cellular spacing, λ values with the theoretical

odels [50,52,53] for Al–0.1 wt% Ti and Al–0.5 wt% Ti alloys,espectively. As can be seen in Fig. 10a and b the calculatedine of λ with the Kurz–Fisher model and Trivedi model foroth compositions is fairly higher than the our experimentalalues, but the calculated λ value with the Hunt model is inood agreement with our experimental values. The numericalodel presented by Hunt and Lu [54] and Kurz et al. [56,57]ere also used to calculate values of λ as a function of V ando for constant temperature gradient. The comparison of ourxperimental values of λ with calculated values of λ by Huntnd Lu [54] and Kurz et al. [56,57] numerical models are givenn Fig. 11a and b. As can be seen in Fig. 11, our experimentalesults are in quite good agreement with calculated values of

by Hunt–Lu model at high growth rates and by Kurz et al.odels at low growth rates for Al–0.1 wt% Ti and Al–0.5 wt%i alloys.

Discrepancies are noticed between experimental and the cal-ulated values for growth rates smaller than 15 �m/s and higherhan 150 �m/s.

. Summary and conclusions

In the present study, Al–0.1 wt% Ti and Al–0.5 wt% Ti alloysere solidified unidirectionally upwards under various solidifi-

ation conditions. The formation of the cellular structure wasbserved from the Al–0.1 wt% Ti and Al–0.5 wt% Ti alloys butell lengths relating to Al–0.5 wt% Ti composition are shorterhan Al–0.1 wt% Ti composition. The microstructural featuresbserved from the longitudinal and transverse views of the spec-mens studied for examining the influence of cellular spacing,, depend on solidification processing parameters (G, V and T ).he principal results can be summarized as follows.

. Cellular spacings measured from the transverse sections,λ∗∗

a are more reliable than the cellular spacings measuredfrom the longitudinal sections, λ∗

a of the directionally solid-

ified Al–0.1 wt% Ti and Al–0.1 wt% Ti alloys (Fig. 3 andTables 1 and 2).

. It was seen that the values of λ decreases as the values of G, Vand T increase. The range of temperature gradients exponents

Compounds 439 (2007) 114–127

(a = 0.52–0.57) is good agreement with the previous experi-mental works [77–83]. The range of growth rate exponents(b = 0.24–0.26) is very close to the previous experimentalworks [6,77,95,96,98] and also the range of cooling rateexponents (c = 0.32–0.33) are very close to previous experi-mental works [66,70,99].

. As can be seen from Fig. 10a and b, the experimental λ valuesare very close to results obtained by the Hunt model [51] butthe predicted λ values with the Kurz and Fisher [52] and theTrivedi model [53] are fairly higher than our experimental λ

values.. The experimental λ values agree quite well with the values

obtained by Hunt and Lu [54] numerical model at high growthrates and Kurz et al. [56,57] numerical models at low growthrates.

. As can be seen from Tables 1 and 2, λ values for theAl–0.5 wt% Ti alloy are larger than the λ values for theAl–0.1 wt% Ti alloy for same G and V values. This resultis also agreed with the theoretical models.

cknowledgments

This research was financially supported by the The Scientificnd Technical Research Council of Turkey (TUBITAK Underontract No: MISAG-125). Authors are grateful to TUBITAK

or their financial support.

ppendix A. Thermophysical parameters of Al richl–Ti alloys

roperty Symbol Unit Value Ref.

elting point Tm K 938omposition Co wt% 0.1 and 0.5lope of liquid line mL K/wt% 46.62 [100]ibbs–Thomson coefficient Γ �m K 0.131 [101]iffusion coefficient (liquid) DL �m2/s 2720 [102]istribution coefficient ko – 0.94 [102]he harmonic perturbations L mJ/m2 10 [103]

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