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Int J Thermophys (2013) 34:267–283 DOI 10.1007/s10765-013-1401-7

Measurements of Microstructural, Mechanical, Electrical, and Thermal Properties of an Al–Ni Alloy A. Aker · H. Kaya

Received: 5 September 2012 / Accepted: 16 January 2013 / Published online: 8 February 2013 © Springer Science+Business Media New York 2013

Abstract The Al–7.5 wt% Ni alloy was directionally solidified upwards with different temperature gradients, G (0.86 K · mm−1 to 4.24 K · mm−1 ) at a constant growth rate, V (8.34 µm · s−1 ). The dependence of dendritic microstructures such as the primary dendrite arm spacing (λ1 ), the secondary dendrite arm spacing (λ2 ), the dendrite tip radius (R), and the mushy zone depth (d) on the temperature gradient were analyzed. The dendritic microstructures in this study were also compared with current theoretical models, and similar previous experimental results. Measurements of the microhardness (HV) and electrical resistivity (ρ) of the directionally solidified samples were carried out. Variations of the electrical resistivity (ρ) with temperature (T ) were also measured by using a standard dc four-point probe technique. And also, the dependence of the microhardness and electrical resistivity on the temperature gradient was analyzed. According to these results, it has been found that the values of HV and ρ increase with increasing values of G. But, the values of HV and ρ decrease with increasing values of dendritic microstructures (λ1 , λ2 , R, and d). It has been also found that, on increasing the values of temperature, the values of ρ increase. The enthalpy of fusion (H ) for the Al–7.5 wt%Ni alloy was determined by a differential scanning calorimeter from a heating trace during the transformation from solid to liquid. Keywords Al–Ni alloy · Dendritic microstructures · Electrical resistivity · Microhardness

A. Aker Department of Physics, Institute of Science and Technology, Erciyes University, 38039 Kayseri, Turkey H. Kaya (B) Department of Science Education, Faculty of Education, Erciyes University, 38039 Kayseri, Turkey e-mail: [email protected]

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1 Introduction Many scientists have been conducting research investigations for several decades to develop new materials, which are stronger, stiffer, more ductile, and lighter than existing materials and also capable of use at elevated temperatures. In the race for the development of new structural materials meeting the requirements of increased specific strength at lower density, epoxy-based composites and aluminum have remained the two favorite contenders. While research in the field of composite materials has yielded very exciting results, aluminum has remained at the center of attention due to its attractive manufacturing costs, its extensive previous use in aircraft structures, and the availability of aluminum manufacturing facilities [1]. It is known that the mechanical and electrical properties of metallic materials are affected by their morphology. The mechanical and electrical properties of directional solidified Al-based alloys which are important commercial materials have been reported in several investigations [2,3] but the results differ from each other. The microstructure evolution during solidification depends on the alloy characteristics and primarily is a function of the temperature profiles at the solidification interface. When a metallic alloy is solidified, the most frequently observed solid morphology is the dendritic microstructure [4–7]. Dendritic microstructures are characterized by microstructure parameters. Numerous solidification studies have been reported with a view to characterizing the microstructure parameters such as a function of the temperature gradient [4–7].

1.1 Dendritic Growth Models Several theoretical models in the literature [8–14] have been used to examine the influence of solidification parameters (G, V ) on dendritic microstructures (λ1 , λ2 , R, and d). Proposed theoretical models in the literature describe λ1 as a function of solidification parameters (G, V , and Co ) by Hunt [8], Trivedi [9], Kurz and Fisher [10], Okamoto and Kishitake [11], and Bouchard and Kirkaldy [12,13]. Hunt [8] allowed for the interaction of the diffusion fields between neighboring cells. The relationship between λ1 and solidification parameters for a spherical dendritic front with the growth condition for dendrites is determined by minimum undercooling. The Hunt model [8] is expressed as λ1 = 2.83

m(k − 1)DΓ Co V

0.25

G −0.5 ,

(1)

where m is the liquidus slope, Γ is the Gibbs–Thomson coefficient, k is the solute partition coefficient, and D is the liquid solute diffusivity. Trivedi [9] has modified Hunt’s model by using the marginal stability criterion to characterize the dendrite primary spacings, λ1 , as a function of solidification parameters and it can be expressed as (Trivedi model [9])

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m (k − 1) DΓ LCo λ1 = 2.83 V

0.25

G −0.5 ,

(2)

where L is a constant depending on harmonic perturbations. According to Trivedi [9], L can be any value between 10 and 28 for dendritic growth. Kurz and Fisher [10] have developed a theoretical model to formulate the correlation between the primary dendrite/cellular spacing and solidification parameters by applying the marginal stability criterion. They have approximated the morphology of the dendrite to be an ellipsoid of revolution. Kurz and Fisher [10] have also assumed that the dendrites/cells are located on the corners of a hexagon. The Kurz–Fisher model may be applied according to the growth rate condition. According to the Kurz– Fisher model [10], the primary dendrite/cellular spacing, λ for the high growth rates (V > Vcs /k) is given by λ1 = 2.83

m (k − 1) DΓ Co k2 V

0.25

G −0.5 .

(3)

Hunt, Trivedi, and Kurz–Fisher models are very similar at high growth rates for λ1 , and the difference among them is only a constant. Okamoto and Kishitake [11] have proposed a simplified method for correlating primary dendrite spacing with solidification parameters. They have assumed the secondary dendrite arms to be plates that become thicker as the solidification proceeds. The Okamoto–Kishitake model [11] is given by the following equation: λ1 = 2ε

−m6Co D(1 − k) V

0.5

G −0.5 ,

(4)

where ε is a constant less than unity. From experiments with several aluminum alloys, the value of ε was found to be near 0.5 [11]. Bouchard and Kirkaldy [12,13] have also proposed a numerical model to characterize the dendrite primary spacings, λ1 , for unsteady-state and steady-state heat flow conditions. The Bouchard and Kirkaldy model [12,13] is expressed as λ1 = a 1

1/2

16Co G o εΓ D (1 − k)mV

0.5 G −0.5 ,

(5)

where G o ε is a characteristic parameter, which is about 600 × 6 K · cm−1 , and a1 is the primary dendrite calibrating factor, which depends on the alloy composition (see Appendix). The mushy zone depth, d, is defined as the distance between the tip and the root of a dendrite trunk. Rutter and Chalmers [14] have derived a mushy zone depth formula from the constitutional supercooling criterion in the absence of convection and it is given by d≈

CL − Co TL − TS =m , G G

(6)

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where d is the mushy zone depth and defined as the distance between the tip and the root of a dendrite trunk, TL and TS are liquidus and solidus temperatures of the solvent, respectively, and CL is the liquid composition. The aim of this study was to experimentally investigate the dependence of the dendritic microstructures (λ1 , λ2 , R, and d) on the temperature gradient, compare the results with current theoretical models [8–14] and also, investigate the mechanical and electrical properties of the directionally solidified Al–7 wt%Ni alloy. 2 Experimental Details 2.1 Material Preparation and Solidification Al–7.5 wt%Ni samples were prepared by melting weighed amounts of Al and Ni of (>99.9 %) high purity metals in a graphite crucible which was placed into the vacuum melting furnace. The homogenized molten alloy was poured into graphite crucibles (6.35 mm OD, 4 mm ID, and 250 mm in length) which were placed in a hot filling furnace. Then, each specimen was taken from the hot filling furnace, and it was positioned in a graphite cylinder (300 mm in length, 10 mm ID, and 40 mm OD) in a Bridgman-type furnace [6,7]. After stabilizing the thermal conditions in the furnace under an argon atmosphere, the specimen was grown by pulling it downward at different temperature gradients, G (0.86 K · mm−1 to 4.24 K · mm−1 ) at a constant growth rate, V ( 8.34 µm · s−1 ) by means of synchronous motors. After ∼10 cm steady-state growth of the samples, they were quenched by pulling rapidly into the water reservoir. The temperature of water in the reservoir was kept at ∼10 ◦ C to an uncertainty of 0.01 K using a Poly Science digital 9102 model heating/refrigerating circulating bath, and the temperature in the sample was controlled to an uncertainty of 0.01 K by using a Eurotherm 2604 type controller. 2.2 Metallographic Process The quenched sample was removed from the graphite crucible and cut into lengths of typically 8 mm. The longitudinal and transverse sections of the ground samples were then cold mounted with epoxy resin. The longitudinal and transverse sections were ground flat with (180, 500, 1000, and 2500) grit SiC paper, and then polished with (6, 3, 1, 0.25, and 0.05) µm diamond paste. After polishing, the samples were etched with a solution (75 mL H2 O, 10 mL HCl, 12 mL NHO3 , and 3 mL HF, for 8 s to 10 s). After metallographic preparation, the microstructures of the samples were revealed. The microstructures were characterized from both transverse and longitudinal sections of samples using an Olympus BX-51 optical microscope. Typical images of growth morphologies of the directionally solidified Al–7.5 wt%Ni alloy are shown in Fig. 1. 2.3 Measurements of Growth Parameters The temperature in the sample was measured by using three K-type 0.25 mm in diameter insulated thermocouples fixed within the sample with a spacing of 8 mm to 16 mm.

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λ1(tr)

λ1(ar) = (1/M)(A/N)0.5

λ2=L/(n-1)

λ1(L)

d

(a) r

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 1 Schematic illustration of the dendritic spacing measurements of longitudinal and transverse sections: (a) longitudinal and (b) transverse sections (M magnification factor, A total area, N number of primary dendrites, L length, n number of secondary arms). Optical micrographs of the directional solidified Al– 7.5 wt%Ni alloy; (c) longitudinal and (d) transverse sections (V = 8.34 µm · s−1 and G = 0.86 K · mm−1 ), (e) longitudinal, and (f) transverse sections (V = 8.34 µm · s−1 and G = 2.91 K · mm−1 )

All the thermocouples’ ends were then connected to a measurement unit consisting of a data-logger and a computer. The cooling rates were recorded by using the datalogger via the computer during growth. When the solid/liquid interface was at the

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Table 1 Solidification processing parameters, microstructures, microhardness, and electrical resistivity for directional solidified Al–7.5 wt%Ni alloy and the relationships between them V G λ1(ave) (µm · s−1 ) (K · mm−1 ) (µm)

8.34

λ2 (µm)

R (µm)

d (µm)

HV ρ × 10−6 (kg · mm−2 ) ( · mm)

T (K)

0.86

516.50

88.94

45.44

1823.25 37.59

9.63

300

1.08

482.32

74.23

36.05

1512.9

40.44

9.65

400

1.87

373.73

65.01

32.11

1108.53 42.52

9.99

520

2.91

295.54

59.85

27.85

850.17

43.74

10.15

620

4.24

248.27

50.38

23.22

508.96

46.12

10.24

720

Experimental relationships

Regression constant (k)

Correlation coefficient (r)

λ1(ave) = k1 G −0.47

k1 = 19.05 µm0.53 · K0.47

r1 = −0.998

λ2 = k2 G −0.35 R = k3 G −0.38

k2 = 9.06 µm0.65 · K0.35

r2 = −0.977

k3 = 3.02 µm0.62 · K0.38 k4 = 9.77 µm0.24 · K0.76 k5 = 0.21 K−0.12 · kg · mm−1.88 k6 = 0.18 kg · mm−1.76 k7 = 0.08 kg · mm−1.64 k8 = 0.07 kg · mm−1.70 k9 = 0.21 kg · mm−1.85 k10 = 9.68 × 10−6 · mm1.048 · K−0.048 k11 = 9.10 × 10−6 · mm1.09 k12 = 7.09 × 10−6 · mm1.12 k13 = 6.93 × 10−6 · mm1.10 k14 = 9.98 × 10−6 · mm1.05 k15 = 3.40 × 10−8 · K−1.17

r3 = −0.975

D = k4 G −0.76 H V = k5 G 0.12 H V = k6 (λ1 )−0.24 H V = k7 (λ2 )−0.36 H V = k8 (R)−0.30 H V = k9 (d)−0.15 ρ = k10 G 0.048 ρ = k11 (λ1 )−0.09 ρ = k12 (λ2 )−0.12 ρ = k13 (R)−0.10 ρ = k14 (d)−0.05 ρ = k15 T 1.17

r4 = −0.983 r5 = 0.982 r6 = −0.957 r7 = −0.998 r8 = −0.995 r9 = −0.962 r10 = 0.975 r11 = −0.982 r12 = −0.943 r13 = −0.934 r14 = −0.943 r15 = 0.999

second thermocouple, the temperature difference (T ) between the thermocouples was read from the data-logger record. The temperature gradient (G = T /X ) for each sample was determined using the measured value of T and the known value of X . The time taken for the solid–liquid interface to pass through the thermocouples separated by known distances was read from the data-logger record. Thus, the value of growth rate (V = X/t) for each sample was determined using the measured values of t and X . The measured values of G and V are given in Table 1. 2.4 Measurements of Microstructure Parameters (λ1 , λ2 , and R) As shown in Fig. 1, three different λ1 values were measured from the samples. The primary dendrite arm spacings, λ1(L) , were obtained by measuring the distance between the nearest two dendrites tips (Fig. 1a) on the longitudinal section. Two different methods were used to measure the λ1 values on the transverse sections (Fig. 1b). The first

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method is the triangle method [15]. A triangle is formed by joining the three neighboring dendrite centers, and the sides of the triangle corresponded to λ1(tr) . The second method is the area counting method [15]. The values of λ1(ar) were measured on the cross section of the sample (see Fig. 1b). In this method, the average primary dendrite arm spacings, λ1(ar) , were determined from λ1(ar) =

1 M

A N

0.5 ,

(7)

where M is the magnification factor, A is the total specimen cross-sectional area, and N is the number of primary dendrites on the cross section. λ1 represents the arithmetic average values of λ1(L) , λ1(tr) , and λ1(ar) . The secondary dendrite arm spacings, λ2 , were measured by averaging the distance between adjacent side branches of a primary dendrite on the longitudinal section. The dendrite tip radius (R) was measured by fitting a suitable circle to the dendrite tip side (see Fig. 1a). The mushy zone depth (d) is also defined by means of the region between the tip side and root side of the dendrites (see Fig. 1a). Each of the side-branch spacings data reported here is the average of the λ1 , λ2 , R, and d values from 18 to 20 primary dendrites for each specimen. Microstructure parameters were measured as far from the steady-state condition in the dendrites as possible, and taken to be the average value of these measurements. The measured values of λ1 , λ2 , R, and d are given in Fig. 2 and Table 1. 2.5 Measurement of Microhardness One of the purposes of this investigation was to obtain the relationships among the temperature gradient, dendritic microstructures, and microhardness for the directionally solidified Al–7.5 wt%Ni alloy. The mechanical properties of any solidified materials are usually determined with a hardness test, a tensile strength test, a ductility test, etc. Since true tensile strength testing of solidified alloys gave inconsistent results with a wide scatter due to the strong dependence on the solidified sample surface quality, the mechanical properties were monitored by hardness testing, which is one of the easiest and most straightforward techniques. The Vickers hardness (HV ) is the ratio of a load applied to the indenter to the surface area of the indentation. This is given by HV =

2P sin(θ/2) , d2

(8)

where HV is the Vickers microhardness in kg · mm−2 , P is the applied load (kg), d is the mean diagonal of the indentation (mm), and θ is the angle between opposite faces of the diagonal indenter (136◦ ). Microhardness measurements in this study were made with a Future-Tech FM-700 model hardness measuring test device using a (100 to 300) g load and a dwell time of 10 s giving a typical indentation depth of about 40 µm to 60 µm, which is significantly smaller than the original solidified samples. The microhardness was the average of at least 30 measurements on the transverse,

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(a)

(b) 2000

λ1(ave) λ2 R d

4000 2000

This work Trivedi Bouchard-Kirkaldy model Okamoto-Kishitake model Hunt model Kurz-Fisher model

1500 1000

500

λ1,μm

λ1,λ2 ,R,d, μm

1000

400 200

200 100

150 100

40 20

50 0.7

1

2

G, K·mm

3

4

5

8

10

-1

15

20

G-0.50

(c) 5000 This work

d, μm

3000

Rutter and Chalmers Model

1000 700 500 300

100 0.0006

0.001

0.0015 0.002

G, K·μm

0.004

-1

Fig. 2 (a) Variation of dendritic microstructures with temperature gradient at constant V (8.34 µm · s−1 ), (b) comparison of experimental λ1 values with values of λ1 predicted by theoretical models as a function of G −0.50 , and (c) comparison of experimental d values with values of d predicted by the Rutters and Chalmers model as a function of G

HV T , and the longitudinal sections, HV L . HV represents the arithmetic average values of HV T and HV L . The measured values of G, V , and HV are also given in Table 1, and the variations of microhardness with the solidification processing parameters are plotted and given in Fig. 3. 2.6 Measurement of Electrical Resistivity Another purpose of this investigation was to obtain the relationships among the temperature gradient, dendritic microstructures, and electrical resistivity for the Al–7.5 wt%Ni samples. The electrical resistivity of directionally solidified samples was measured by the dc four-point probe method [16]. The four-point probe method is

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(a) 70 V= 0.0083 mm·s -1 (constant)

HV, kg·mm- 2

60

50

40

30 0.8

1

2

4

G, K·mm- 1

(b) 55 λ1-HV λ2-HV R-HV d-HV

HV, kg·mm

-2

50

40

35 0.02

1.0

0.1

2.0

λ1,λ2, R, d, mm Fig. 3 (a) Variation of microhardness as a function of temperature gradient and (b) variation of microhardness as a function of dendritic microstructures

the most widely used technique for electrical profile measurements of materials. The method has proven to be a convenient tool for resistivity measurements. A four-point probe measurement is performed by making four electrical contacts to a sample surface. Two of the probes are used to source current and the other two probes are used to measure voltage; the use of four probes eliminates measurement errors due to the probe resistance, the spreading resistance under each probe, and the contact resistance between each metal probe and the material [16]. In this study, as the sample thickness (t) is much greater than the probe spacing (s), the following equations were used to calculate the electrical resistivity value of the sample [17]. The differential resistance (R) can be expressed as R=ρ

dx A

,

(9)

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where A is the cross-sectional area of the sample and dx is the differential distance. By integrating between the inner probe tips where the voltage is measured, the resistance can be expressed as x2 R=

ρ ρ , dx = 2 2π x 2π s

(10)

x1

where x is the distance from the outermost probe tip as shown in Fig. 4. Due to the superposition of the current at the outer two tips, the resistance R=

V 2I

(11)

and thus, the bulk resistivity of the solder sample can be expressed as ρ = 2π s

V 2I

,

(12)

where 2π s is the resistivity correction factor, V is the potential difference measured across the probes, and I is the current through the probes. When a constant current was applied on the sample with a Keithley 2400 sourcemeter, the potential drops on the samples were measured with a Keithley 2700 multimeter connected to a computer. As seen from Fig. 4, platinum wires, 0.5 mm in diameter, were used as the probes of the current and potential. The specimen thickness (4 mm) and width (20 mm) were measured to an accuracy of 1 µm using a digital micrometer. The resistance data were converted to resistivity values with the measured specimen dimensions. The electrical resistivities of all the solidified samples were measured by the dc four-point probe method at room temperature. The measurement of the electrical resistivity of the cast sample was also measured depending on the temperature. The dependence of the electrical resistivity on the temperature gradient, microstructures, and temperature were analyzed. Measured ρ values are given in Table 1 and Figs. 5 and 6. 3 Results and Discussion 3.1 Dependence of the Microstructures on the Temperature Gradient Al–7.5 wt%Ni bulk samples were directionally solidified under different temperature gradients, G(0.86 K · mm−1 to 4.24 K · mm−1 ) and constant growth rate, V (8.34 µm · s−1 ) conditions. Microstructure features (Fig. 1) of the grown samples were analyzed, and the influence of the temperature gradient on the microstructure parameters ( λ1 , λ2 , R, and d) was examined. The dependence of microstructures on the temperature gradient was determined by a linear regression analysis. From the experimental results, the relationship between microstructures and the temperature gradient can be written as

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0.015 T=100 T=273 T=300 T=350

o o o

K K K K

o

Current (A)

Computer 0.010

0.005

Voltage (V) -0.04

-0.03

0.000 -0.02

-0.01

0.00

0.01

0.02

0.03

0.04

-0.005

-0.010

-0.015

Keithley 2400 Sourcemeter Keithley 2700 Multimeter

Probe tip S

Solid

S

S

Quenched liquid

Solid-liquid interface

Epoxy-resin mold Directionally solidified sample (longitudinal section) Fig. 4 Schematic diagram showing the four probes used for the electrical resistivity measurements

(λ1 , λ2 , R, d) = kG −a ,

(13)

where k is the proportionality constant and a is the exponent value of G. As can be seen from Table 1 and Fig. 2a, the values of λ1 , λ2 , R, and d decrease with increasing values of G. The average exponent values of G for λ1 , λ2 , R, and d were found to be −0.47, −0.35, −0.38, and −0.76, respectively. Comparisons of the measured λ1 values in this study with the calculated λ1 values by theoretical models [8–14] are given in Fig. 2b. The thermophysical parameters of the Al–7.5 wt%Ni alloy used in the λ1 , λ2 , R, and d calculations of the theoretical models are given in the Appendix. As can be seen from Fig. 2b, the experimental λ1 values are in good agreement with the calculated λ1 values by Trivedi [9], Okamoto– Kishitake [11], and Bouchard–Kirkaldy [12,13] models, but the calculated lines of λ1 by the Hunt [8] and Kurz–Fisher [10] models give smaller and some higher values than the experimental values, respectively. It can be seen from Fig. 2c, the calculated d values by Rutters and Chalmers [14] are in good agreement with the experimental d values.

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Int J Thermophys (2013) 34:267–283 1.2x10-5

ρ, Ω·mm

(a)

10-5 9.5x10-6 9.0x10-6

8.5x10-6 1

0.7

2

3

5

G, K·mm -1 1.06x10-5

λ1-ρ

(b)

λ2-ρ

ρ, Ω·mm

R-ρ d-ρ

10-5

9.5x10-6

0.02

0.1

1.0

2.0

λ1,λ2, R, d, mm Fig. 5 (a) Variation of electrical resistivity as a function of temperature gradient and (b) variation of electrical resistivity as a function of microstructures

The exponent values of G for λ1 , λ2 , R, and d obtained in the literature are in the range of (0.46 to 0.58), (0.39 to 0.60), (0.45 to 0.65), and (0.50 to 0.90), respectively, by different researchers [4–7] for the Al alloy systems. It can be say that the exponent values of G for λ1 , λ2 , R, and d obtained in this study are in agreement with the literature.

3.2 Dependence of the Microhardness on the Temperature Gradient and Microstructures The dependence of the microhardness on the temperature gradient was investigated by several authors [18–21]. It can be seen from Table 1 and Fig. 3a that an increase in the temperature gradient leads to an increase in the microhardness. The dependence of the microhardness on the temperature gradient was determined by using linear regression analysis, and the relationship between them can be expressed as

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(a) 3.0x10-4 Al Ni Al-7wt%Ni [this work]

-4

2.5x10

ρ, Ω·mm

2.0x10-4

1.5x10-4

10-4

5.0x10-5

300

(b)

400

500

600

700

800

T, K 10 Al-7.5 wt %Ni

Heat flow, mW

0

-10

-20

Rate: 10 K·min-1 Area:1378.80 mJ Onset: 941.45 K Peak. 932.55 K End:960.12 K

-30

750

800

850

900

950

1000

Temperature, K

Fig. 6 (a) Variation of electrical resistivity as a function of temperature and (b) heat flow curve versus temperature for Al–7.5 wt%Ni alloy at heating rate of 10 K · min−1

HV = kG b ,

(14)

where k is a constant and b is the exponent value of G. In this study, the exponent value of G was obtained to be 0.12. The exponent values of G are in good agreement with those obtained in the literature in the range of (0.09 to 0.23) by different researchers [18–21] for Al-based alloys, such as Al–Ni, Al–Si, Al–Cu, and Al–Ti. The dependence of the microhardness on the microstructure was investigated by several researchers [18–27]. It can be seen from Table 1 and Fig. 3b that a decrease in the microstructures leads to an increase in the microhardness. The dependence of the microstructures on the microhardness can be expressed as HV = k(λ1 , λ2 , R, d)−c ,

(15)

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where values of k are the proportionality constants and given in Table 1. In this study, the values of the exponent relating to the microstructure parameters (λ1 , λ2 , R, and d) were obtained to be: −0.24, −0.36, −0.30, and −0.15, respectively. The exponent values of microstructures (λ1 , λ2 , R, and d) obtained in the literature are in the range of (0.19 to 0.43) for λ1 [18–26], (0.21 to 0.35) for λ2 [18–27], (0.23 to 0.30) for R [18–27], and (0.20 to 0.40) for d [18–27] for Al alloy systems under similar solidification conditions. It can be observed that the exponent values of microstructure (λ1 , λ2 , R, and d) in this study are generally in agreement with obtained values in the literature. Some differences of the exponent values might be due to different alloy compositions, different microstructures, and experimental errors. 3.3 Dependence of the Electrical Resistivity on the Temperature Gradient and Microstructures It can be seen from Table 1 and Fig. 5a that the temperature gradient leads to an increase in the electrical resistivity. The dependence of the electrical resistivity on the temperature gradient can be expressed as ρ = kG d ,

(16)

where k is a constant and given in Table 1. The exponent value of G in this study is 0.048 and very close to the value of 0.043 obtained by Kaya et al. [20] for the Al–5.7 wt%Ni eutectic composition under a similar solidification condition. The variation of the electrical resistivity (ρ) as a function of the microstructures are given in Table 1 and Fig. 5b. It can be observed that an increase in the microstructure values leads to a decrease in the electrical resistivity values. From linear regression analysis, the dependence of λ1 , λ2 , R, and d on ρ can be represented as ρ = k(λ1 , λ2 , R, d)−e ,

(17)

The exponent values of λ1 , λ2 , R, and d were obtained to be 0.09, 0.12, 0.10, and 0.05, respectively. Exponent values in this study are very close to the value of 0.13 obtained by Kaya et al. [20] for the Al–5.7 wt%Ni eutectic composition under a similar solidification condition. Because of the changes of the resistivity of pure metals and alloys depending on the microstructure evolution, such a tendency is quite a natural result. A change of resistivity can be interpreted as indicating that some other mechanisms, such as electron–electron interaction, grain boundary/impurity scattering, etc., is involved in the electrical conduction process [28]. A similar trend is supported by Boekelheide et al. [29]. 3.4 Thermal Properties of Al–Ni Alloy The variation of the electrical resistivity with temperature in the range of 300 K to 720 K was measured (see Fig. 6a). The dependence of the temperature on the electrical resistivity can be expressed as

123


ρ = kT 1.17 (k = 3.40 × 10−8 · K−1.17 ).

281

(18)

It is observed that an increase in the temperature (300 K to 720 K) values leads to an increase in the electrical resistivity values (0.96 to 1.024) ×10−5 · mm. Comparisons of the electrical resistivity as a function of temperature are given in Fig. 6a for pure aluminum [30], pure nickel, and a casting Al–Ni alloy. As can be seen from Fig. 6a, the electrical resistivity values (4.66 to 11.43) ×10−5 · mm in this study are higher than the values (2.75 to 7.61) ×10−5 · mm for pure aluminum [30], and smaller than the values (8.82 to 34.43) ×10−5 · mm for pure nickel [30]. The value of ρ(2.75 × 10−5 · mm) at room temperature in this study is very close to the value of 4.25 × 10−5 · mm obtained by Brandt and Neuer [31] for the Al–12 wt%Si alloy at room temperature. The Al–7.5 wt%Ni alloy was heated at a rate of 10 K · min−1 from room temperature to 1020 K by using a Perkin Elmer Diamond model DSC and the heat flow versus temperature for Al–7.5 wt%Ni alloy is given in Fig. 6b. As can be seen from Fig. 6, the melting temperature of Al–7.5 wt%Ni was determined to be 941.45 K. The values of the enthalpy of fusion (H ) and the specific heat (C p ) for the Al– 7.5 wt%Ni alloy were also calculated to be 83.28 J · g−1 , and 0.283 J · g−1 · K−1 , respectively, from the graph of the heat flow versus temperature. The recommended values of the enthalpy of fusion (H ) and the specific heat (C p ) for pure Al and Ni are 396.96 J · g−1 , 297.83 J · g−1 , 0.897 J · g−1 · K−1 , and 0.444 J · g−1 · K−1 , respectively [32], at the melting temperature (912.9 K). 4 Conclusions The principal results of this study can be summarized as follows. 1. Experimental observations show that the values of λ1 and λ2 decrease as V increases. The relationships between microstructure parameters (λ1 and λ2 ) and the growth rate have been obtained to be λ1 = 851.1V −0.28 and λ2 = 124.2V −0.46 . 2. The experimental results on the measurements of λ1 were compared with the results of theoretical models for the calculation of λ1 [8–13]. The predicted λ1 values by the Trivedi [9] and Okamoto–Kishitake [11] models agree with the experimental λ1 values, but the predicted values of λ1 by the Hunt [8], Kurz– Fisher [10], Bouchard–Kirkaldy [12,13], and Okamoto–Kishitake [14] models do not agree with the experimental λ1 values. 3. The values of HV for the directionally solidified Al–7.5 wt%Ni alloy have been measured. It was found that the values of microhardness increase with increasing values of V as well as with decreasing values of the dendritic spacings. 4. It was found that the values of ρ increase with increasing values of the temperature gradient as well as with decreasing values of the dendritic spacings. 5. The Al–5.7 wt%Ni eutectic alloy was heated at a rate of 10 K · min−1 from 300 K to 720 K. From the plot of heat flow versus temperature, the melting temperature,

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the enthalpy of fusion, and the specific heat were found to be 941.45 K, 83.28 J · g−1 , and 0.283 J · g−1 · K−1 , respectively. Appendix: Some Thermophysical Parameters of the Al-rich Al–Ni Alloy

Composition Co

7.0 wt%

[33]

Liquidus slope (m)

−2.72, 9.64 K · wt%−1

[33]

Diffusion coefficient in the liquid (D)

5000 µm2 · s−1

[34]

Equilibrium partition coefficient (k)

0.3125

[33]

Gibbs–Thomson coefficient (Γ )

0.2 K · µm

[30]

Harmonic perturbations (L)

(10 to 28) mJ · m−2

[9]

Equilibrium melting point of Al–7.5 wt%Ni (Te )

938.60 K

[33]

Primary dendrite-calibrating factor (a1 )

250

[13]

Characteristic parameter (G o ε)

600 × 6 K · cm−1

[13]

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.

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