Full text of DOI:10.1557/JMR.2000.0016

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Influence of dendrite arm spacing on the thermal
conductivity of an aluminum-silicon casting alloy
C. Va´zquez-Lo´pez
´
Departamento de F´ısica, Centro de Investigacion y de Estudios Avanzados del IPN, A. P. 14-740,
Me´xico, 07000, D.F., Mexico
A. Caldero´n and M.E. Rodr´ıguez
Centro de Investigacio´n en Ciencia Aplicada y Tecnologia Avanzada del IPN,
Calzada Legaria No. 694, Col. Irrigacio´n, Me´xico 11500, D.F. Mexico
E. Velasco and S. Cano
Corporativo Nemak, S. A. de C. V., A. P. A-100, Monterrey, 66000, N.L. Mexico
R. Cola´s
Facultad de Ingenier´ıa Meca´nica y Ele´ctrica, Universidad Auto´noma de Nuevo Leo´n, A. P. 149-F,
Cd. Universitaria, San Nicola´s de los Garza, 66451, N.L. Mexico
S. Valtierra
Corporativo Nemak, S. A. de C. V., A. P. A-100, Monterrey, 66000, N.L. Mexico
(Received 27 May 1999; accepted 7 October 1999)
The photoacoustic technique and the thermal relaxation method were used to determine
the thermal conductivity of some representative samples obtained from an aluminum-
silicon casting alloy A319. This material was solidified with an imposed unidirectional
thermal gradient to obtain samples with different microstructures characterized by the
secondary dendrite arm spacing, which increases as the solidification rate decreases. It
was found that the thermal conductivity of the alloy decreases with an increase in the
secondary dendrite arm spacing and a decrease in the integral dendrite perimeter.
I. INTRODUCTION
The experimental methods commonly employed
to determine the thermal diffusivity in materials
are of three different types, depending on whether
the measured heat flow is stationary, (conventional
method11) transient or periodic. The American Society
for Testing Materials considers as standard a ver-
sion of the transient technique, the laser flash method,12
to determine the thermal diffusivity. The periodic method
was introduced in 1863 by Ångstrom,13 and involves
heating periodically one end of a rod-shaped sample
and measuring the resulting temperature oscillations at
another point of the rod. The phase lag between the ther-
mal oscillations at any two points gives a precise deter-
mination of the thermal diffusivity. Another method,
applied in this work, which is based on the photoacoustic
(PA) technique14 has been employed extensively15–18
and has the advantage of requiring small quantities of
the material to be analyzed, permitting the determination
of the thermal diffusivity in localized regions of the
material.
The importance of simple thermal diffusivity measure-
ments is crucial in the use of several industrial alloys, in
particular those which are subjected to thermal cycling,
such as aluminum alloys employed in the manufacture of
automotive engines, since power dissipation is an impor-
tant mechanism in engine performance.1
The microstructure which is developed in a casting
depends on its solidification rate.2,3 In the case of the
widely used hypoeutectic aluminum silicon alloys, the typi-
cal microstructure is composed of aluminum dendrites and
a dispersion of the eutectic when made from aluminum and
nearly pure silicon.2,3 The secondary dendrite arm spacing
(DAS) was found to be reduced as the solidification rate
increased,3,4 whereas the shape and distribution of eutec-
tic silicon is affected by a series of parameters such as
solidification rate and chemical composition.5–7
It is a well-known fact that the physical and mechanical
properties of a material depend on its microstruc-
ture,5,6,8,9 but the relationship between the thermo-
physical properties and microstructure is perhaps less
studied, although some reports9,10 indicate that the elec-
trical conductivity depends on the microstructure.
The aim of this work is to determine the possible cor-
relation between the thermophysical properties and the
position-dependent microstructure of a commercial alu-
minum casting alloy of the type A319.
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C. Va´zquez-Lo´pez et al.: Influence of dendrite arm spacing on the thermal conductivity of an aluminum-silicon casting alloy
II. EXPERIMENTAL PROCEDURE
composition of the alloy was determined by optical emis-
sion spectroscopy (spark) as a function of the position.
The averaged values are reported in Table I. The micro-
structure of the samples was determined with a Nikon
Epiphot TME metallographic microscope (Japan), once
the dendrites were revealed with an aqueous solution of
0.05% HF. Measurements of the secondary DAS and of
the total length of the dendrite coastlines, which will be
called the “perimeter” were conducted along different
radial directions, normal to the solidification direction.
The average was obtained from at least 150 branches.
The thermal diffusivity was determined by the PA
technique employing the open photoacoustic cell (OPC)
configuration.14 The schematic experimental array is
shown in Fig. 2. In this arrangement the sample is fixed
with vacuum grease at the top of a commercial electret
microphone in order to detect the PA signal. The front air
chamber adjacent to the metallized face of the micro-
phone diaphragm plays the role of the PA chamber. The
experimental setup consists of an 80 mW Ar laser, whose
monochromatic light beam (488 nm line) was mechani-
cally modulated with a variable speed mechanical chop-
per (SRS-model 540) and uniformly focused on the
sample. An interference filter was used in order to avoid
the UV plasma components of the laser. Part of the in-
cident light is converted into heat that propagates through
the sample. Then it induces pressure fluctuations in the
PA cell. A lock-in amplifier (SRS-model 850, Sun-
nyvale, CA) connected to a personal computer through
an IEEE-488 card is used to analyze the output voltage
and the phase lag from the microphone, as a function of
the modulation frequency.
The experimental alloy was obtained from a computer-
controlled instrumented rig, which consisted of a 51-mm-
thick steel plate and a mast in which a given number
(normally eight) of type K (chromel-alumel) thermo-
couples are localized at different heights. The thermo-
couples were connected, during testing, to a solid-state
device used to convert the electromotive force, generated
by the couple, into a linear scale ranging from 0 to 5 V.
The output from these appliances was then applied to an
analog-digital board installed in a PC-compatible computer.
Figure 1 shows a representation indicating the posi-
tions at which the thermocouples were inserted. Cooling
of the bottom surface of the steel was accelerated by
water. The aluminum alloy was poured into an ingot
mould (made of recrystallized alumina) of 150-mm
diameter and 300-mm height, which was covered with a
ceramic fibre blanket in order to assure unidirectional
solidification. The thermocouples were located in this
particular experiment at the ingot-steel plate interface
(which will be called zero distance), and at 1, 2, 4, 8, and
12 cm from the interface. Small samples were cut from
the ingot from positions close to those of the thermo-
couples in order to correlate the thermal evolution during
solidification with the microstructure and thermophysical
properties. The samples were approximately 300-␮m-
thick, and had an area of 0.5 × 0.5 cm2. The chemical
According to the theory of the OPC configuration for
opaque solids, the influence of the thermal diffusivity
process on the magnitude and the phase lag of the mi-
crophone output are given, respectively, by
Co f −1
A =
and
.
(1)
(2)
͌
cosh 2aL͒ − cos 2aL͒
͑
͑
tan aL͒
͑
⌬␸ = −atan
− ␲ 2
ր
ͫ ͬ
tanh aL͒
͑
In these expressions, Co is a factor that depends on the
geometrical and dielectric properties of the microphone,
a ס √␲f/␣ is the thermal diffusion coefficient, f is the
FIG. 1. Experimental casting setup. The thermocouples are used to
monitor the position-dependent solidification process.
TABLE I. Chemical analysis (wt.%) of different heights of the cast ingot (Fig. 1).
Sample
Si
Cu
Fe
Mn
Mg
Zn
Ti
Sr
Al
A
B
C
D
E
F
7.05
7.75
7.70
7.56
7.73
7.82
3.34
3.55
3.50
3.14
3.27
3.38
0.56
0.63
0.67
0.77
0.67
0.59
0.32
0.35
0.39
0.46
0.40
0.31
0.29
0.31
0.30
0.28
0.28
0.31
0.67
0.70
0.70
0.67
0.67
0.69
0.14
0.12
0.12
0.14
0.14
0.11
0.01
0.01
0.01
0.01
0.01
0.01
87.61
86.58
86.61
86.97
86.83
86.77
86
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C. Va´zquez-Lo´pez et al.: Influence of dendrite arm spacing on the thermal conductivity of an aluminum-silicon casting alloy
The heat capacity per unit volume (␳c), where ␳ is the
density and c is the specific heat capacity, can be deter-
mined by the thermal relaxation method21 with the aid of
a vacuum chamber described elsewhere.22 This method
is also known as the temperature-rise method under con-
tinuous light illumination. A diagram of the experimental
set up is shown in Fig. 3. Both surfaces of the sample
were sprayed with black paint, in order to ensure a light
absorbing surface, and a constant heat transfer coeffi-
cient. The sample was then glued to the end of a thin
nylon rod inside the vacuum chamber (10−4 torr). The
optical access was through a glass window. One of the
painted surfaces was then continuously and uniformly
exposed to a laser beam that was expanded, and a thin
thermocouple, attached to the other surface with thermal
paste, was used to monitor the temperature. The tempera-
ture rise is given by
⌬T = P0 1 − e−t/␶
␩
,
(5)
FIG. 2. Experimental setup for the employed photoacoustic technique
in order to measure the thermal diffusivity.
͓
͔
ր
where P0 is the incident light intensity, ␩ ס 4⑀␴T30, and
modulation frequency, ␣ is the thermal diffusivity of the
sample and L its thickness. For many samples, the ther-
mal diffusivity, ␣, can be obtained by means of fitting
either the signal amplitude or its phase-lag using the Eqs.
(1) and (2) in the range of high modulation-frequency,
corresponding to a thermally thick regime (a ӷ 1). Care
should be taken when fitting, in order to avoid the fre-
quency interval at which the noise-to-signal ratio is con-
siderable or at which the thermoelastic effect is
present.14,19
L␳c
8⑀␴T30
␶ =
,
(6)
In the frequency range 0 < f ഛ (␲/2)2 fc, where
a
L2␲
fc =
is the cutoff frequency
,
(3)
the phase Eq. (2) is approximately given by
1
3␲
⌬␸ = −
f +
,
(4)
␲fc
4
and the relative error in this approximation is smaller
than 1.2%.20 Hence, by means of fitting the experimental
data of the PA signal phase using the simple linear equa-
tion [Eq. (4)] the cutoff frequency fc can be obtained, and
then, from Eq. (3) the thermal diffusivity of the sample
can be deduced. This last method is most suitable for
materials with high heat diffusion capacity such as met-
als, or some semiconductors, as well as for samples
whose thickness is small. Since for these materials, the
thermally thick regime can occur in hundreds or several
thousands of Hz with the inconvenience that the noise-
to-signal ratio becomes important and that the ther-
moelastic binding mechanism is present.
FIG. 3. The vacuum chamber for the thermal relaxation method used
to determine the heat capacity per unit volume.
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C. Va´zquez-Lo´pez et al.: Influence of dendrite arm spacing on the thermal conductivity of an aluminum-silicon casting alloy
where ␴ ס 5.67 × 10−12 W/cm2K4 is the Stefan–
Boltzmann constant, ⑀ is the emissivity (which is close to
one), T0 is the ambient temperature in Kelvin, and L is
the sample thickness in centimeters. Equation (5) is em-
ployed with the experimental data gathered, and ␶ is the
parameter that has to be adjusted to determine ␳c. After
reaching experimental saturation in temperature, described
by Eq. (5), the value of ␳c can be confirmed by turning off
the incident light, in which case the temperature decay
will be described by
⌬T = P0 e−t/␶
␩
,
(7)
ր
and the decay relaxation time ␶ should be the same as that
in Eq. (5).
FIG. 4. Optical micrographs at different positions within the ingot.
88
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C. Va´zquez-Lo´pez et al.: Influence of dendrite arm spacing on the thermal conductivity of an aluminum-silicon casting alloy
by other researchers23–27 are also shown. The DAS data
III. RESULTS AND DISCUSSION
obtained in this work are close to those reported by
Typical microstructures of the samples are shown in
Fig. 4, in which the dominance of the dendrites over sec-
ondary precipitates can be appreciated. The secondary den-
Granger and Ting.26
Typical results of the variation of the PA phase lag as
a function of the modulation frequency are shown in Fig. 6.
drite arm spacing and the perimeter of dendrites were
The continuous lines are the results of least square fit-
determined. These microstructural parameters are reported
tings to the expression given in Eq. (4), from which the
in Table II. Also in this table the solidification rate for each
thermal diffusivities of the samples were determined, and
sample is reported. DAS is related to the solidification rate
are listed in Table II. There is a decrease of 20% in the
in Fig. 5 (solid circles), and as the rate increases, their size
thermal diffusivity from the bottom to 12-cm height of
is reduced. The relationship found in this work is
the ingot (Fig. 1), while the DAS increases by a factor of
␭ = 36.1R−0.34
,
(8)
four. The decrease of the thermal diffusivity cannot be
explained in terms of the chemical composition of the
samples, in which a variation of the silicon content of
0.77% in weight occurs. More important than the amount
where ␭ (measured in ␮m) is the DAS and R is the
solidification rate, which was obtained by thermal analy-
sis of the solidification curves.28 In Fig. 5 data reported
TABLE II. Microstructure and thermal characterization parameters.
Position in
the alloy
(cm)
Dendrite
perimeter
(mm)
Dendrite
arm spacing
(␮m)
Heat
capacity/vol
(J/cm3K)
Thermal
diffusivity
(cm2/s)
Thermal
conductivity
(W/mK)
Solidification
rate (K/s)
Sample
A
B
C
D
E
F
0
1
2
4
8
3.35
1.43
0.48
0.24
0.11
0.06
44.1
32.0
30.1
15.1
12.5
6.3
23.4
34.4
40.8
55.8
71.2
104.2
1.11
0.95
0.90
0.88
0.82
0.85
0.98
0.97
0.95
0.93
0.92
0.91
108.8
91.7
85.5
81.8
75.3
77.3
12
FIG. 5. Relationship between DAS and solidification rate (filled
circles). Results from other researchers are included for comparison.
FIG. 6. Experimental results (open symbols) and fitting of Eq. (4)
(continuous lines) of the PA phase lag.
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C. Va´zquez-Lo´pez et al.: Influence of dendrite arm spacing on the thermal conductivity of an aluminum-silicon casting alloy
of silicon is its distribution in the alloy, since Si will act
as a thermal barrier.29 It was found in the present study
that the degree of modification was the same for all the
samples. The decrease is related to the dendrite param-
eter DAS, which determines the form of the aluminum
channels. Since the thermal diffusivity measures essen-
tially the thermalization time within the sample (the
greater the thermal diffusivity, the less the heating time),
a greater thermal diffusivity is expected near the bottom
of the ingot, where the DAS is finest.
Figure 7 shows a typical result of thermal relaxation
experiments. The solid lines correspond to the best fits of
Eq. (5) (increasing temperature) and Eq. (7) (decreasing
temperature) to the experimental data, from which the
value of ␳c is deduced, Table II.
The dependence of the thermal conductivity, k ס ␣␳c,
on the DAS is shown in Fig. 8. The behavior corresponds
to an allometric function of the form:
−0.253
k = 230␭
.
(9)
The dependence of the conductivity on the dendrite pe-
rimeter is shown in Fig. 9. The variation in the thermal
conductivity as a function of the dendrite perimeter fol-
lows a linear trend.
FIG. 8. Variation in thermal conductivity as a function of secondary
dendrite arm spacing.
FIG. 7. (a) Experimental increase of temperature and fitting of Eq. (5)
(continuous curve) under continuous illumination. (b) Decrease of tem-
perature after turning off the light, with fitting of Eq. (7) (continuous line).
FIG. 9. Variation in thermal conductivity as a function of dendrite
perimeter.
90
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C. Va´zquez-Lo´pez et al.: Influence of dendrite arm spacing on the thermal conductivity of an aluminum-silicon casting alloy
10. J.E. Hatch, Aluminum Properties and Physical Metallurgy (ASM,
Metals Park, OH, 1984).
11. P.K. Kuo, L. Wei, and R.L. Thomas in Photoacoustic and Pho-
These results indicate that the thermal conductivity is
increased when the microstructure is refined, which
means that an adequate design in terms of mechanical
properties, will also enhance the thermophysical ones,
which will benefit the resistance to thermal fatigue.30
tothermal Phenomena III, Springer Series in Optical Sciences Vol.
69, edited by Theodor Tamir (Springer-Verlag, Berlin, 1992).
12. E. Feit and H. Shaw, Am. Ceram. Soc. Bull. 70, 125 (1991).
13. A.J. Ångstrom, Phil. Mag. 26, 130 (1863).
14. L.F. Perondi and L.C.M. Miranda, J. Appl. Phys. 62, 2955 (1987).
15. M.E. Rodr´ıguez, J. M. Ya´n˜ez, A. Cruz, J.J. Alvarado, O. Zelaya,
F. Sa´nchez, H. Vargas, J.D. Figueroa, F. Mart´ınez, J. Mart´ınez,
J. Gonza´lez, and L.C.M. Miranda, Z. Lebensm, Unters Forsch.
201, 236 (1995).
16. M. Ya´n˜ez, M.E. Rodr´ıguez, J.J. Alvarado, O. Zelaya, F. Sa´nchez,
A. Cruz, H. Vargas, J.D.C. Figueroa, F. Mart´ınez, J. Mart´ınez,
J. Gonza´lez, C. Argu¨ello, and L.C.M. Miranda, Analyst bf. 120,
1953 (1995).
17. A. Caldero´n, J.J. Alvarado Gil, Y. Gurevich, A. Cruz Orea,
I. Delgadillo, H. Vargas, and L.C.M. Miranda, Phys. Rev. Lett. 79,
5022 (1997).
18. A. Cruz-Orea, I. Delgadillo, H. Vargas, A. Gudin˜o, E. Marin,
C. Va´zquez-Lo´pez, A. Caldero´n, and J.J. Alvarado, J. Appl. Phys.
79, 8951 (1996).
19. G. Rousset, F. Lepoutre, and L. Bertrand J. Appl. Phys. 54, 2383
(1983).
20. A. Caldero´n, R.A. Mun˜oz Herna´ndez, S.A. Toma´s, A. Cruz Orea,
and F. Sa´nchez Sinencio, J. Appl. Phys. 84, 6327 (1998).
21. I. Hatta, Rev. Sci. Inst. 50, 292 (1979).
22. G. Gutie´rrez-Jua´rez, O. Zelaya, Juan J. Alvarado-Gil, H. Vargas,
H. de O. Pastore, J.S. Barone, M. Herna´ndez, and L. Ban˜os,
J. Chem. Soc., Faraday Trans. 92, 2651 (1996).
IV. CONCLUSIONS
The thermophysical properties of a series of samples
of an aluminum casting alloy were determined as a func-
tion of the principal microstructural parameters, namely
the secondary dendrite arm spacing and the integral den-
drite perimeter. The measurements were performed using
the photoacoustic effect and the thermal relaxation
method. It was found that the effective thermal conduc-
tivity increases linearly with the dendrite perimeter.
ACKNOWLEDGMENTS
This work was partially supported by Consejo Nacio-
nal de Ciencia y Tecnología (CONACyT), Me´xico. The
authors would like to thank Eng. Blanca Zendejas for her
valuable technical support. The support of Corporativo
Nemak S.A. de C.V. is also acknowledged.
23. C.H. Caceres, C.J. Davidson, and J.R. Griffiths, Mater. Sci. Eng.
A197, 171 (1995).
REFERENCES
24. R.E. Spear and G.R. Gardner, Trans. AFS. 71, 209 (1963).
25. Q.S. Hamed and R. Elliot, Cast Metals. 6, 36 (1993).
26. D.A. Granger and E. Ting, in Structures in Directionally Solidified
Aluminum Foundry Alloy, edited by D.M. Stefanescu, G.J. Ab-
baschian, and R.J. Bayuzick (The Metallurgical Society, London,
United Kingdom, 1988), p. A356.
27. J.C. Jaques and W. Hotz, Cast Metals. 4, 200 (1992).
28. E. Velasco, F. Hernandez, J.G. de la Rosa, S. Valtierra, J.F. Mo-
jica, and R. Colas in Light Metals, edited by B. Welch (TMS,
Warrendale, PA, 1998) p. 993.
1. P.M. Norris, M.C. Hastings, and W.J. Wepfer, J. Exp. Heat. Trans.
7, 43 (1994).
2. J.A. Horwath and L.F. Mondolfo, Acta Metall. 10, 1037 (1962).
3. M.C. Flemings, T.Z. Kattamis, and B.P. Bardes, AFS Trans. 88,
695 (1980).
4. R.M. Kotschi and C.R. Loper, Jr., AFS Trans. 85, 425 (1977).
5. J. Campbell, Castings (Butterworth-Heinemann, London, 1991).
6. I.J. Polmear, Light Alloys (Arnold, a division of Hodder Headline
PLC, London, 1996).
7. J.L. Carbajal, C. Casado, J.F. Mojica, and S. Valtierra, 3rd. Int.
Conf. Molten Aluminum Processing (AFS, Des Plaines, IL, 1992),
p. 141.
29. J.E. Gruzleski and B.M. Closset, The Treatment of Liquid Alumi-
num-Silicon Alloys (AFS, Des Plaines, 1990).
30. R.B. Gundlach, Thermal Fatigue Resistance of Aluminum Alloy
319 (Climax Research Services, Cleveland, OH, 1993).
8. L. Mondolfo, Aluminum Alloys, Structure and Properties (Butter-
worth, London, 1986).
9. L. Backerud and E. Krol, Solidification Characteristics of Alumi-
num Alloys (Foundry Alloys, Skan Aluminum, Oslo, 1990), Vol. 2.
J. Mater. Res., Vol. 15, No. 1, Jan 2000
Downloaded: 14 Mar 2015
91
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