ISSN 0018-151X, High Temperature, 2014, Vol. 52, No. 3, pp. 386–390. © Pleiades Publishing, Ltd., 2014.
386
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INTRODUCTION
Pure liquid metals have been studied since many
decades and their fundamental properties may be con-
sidered on a firm basis (e.g. [1]) especially due to the
studies conducted the ‘60 and the ’70 by such authors
as Grosse (1961), Ziman (1961), Edwards (1962),
Allen (1963), Faber (1966), Ashcroft (1966), Ascarelli
(1969), Lang (1970), and Filippov (1966) (see [1] for
more details). However, the same is not true for alloys
which are still under investigation. In the last years,
there have been investigations of some alloys, such as
Al–Cu, Pb–Bi and Pb–Sn [2], but the experimental
data are sometimes contradictory. This work aims at
providing a method for estimating the main physical
properties at standard pressure (i.e. one atmosphere)
to describe metal alloys in the liquid state in order to
offer a reliable approximated approach. Density, sur-
face tension, electrical resistivity and, consequently,
thermal conductivity are the considered values. Given
these literature data (i.e. [3–9]), we choose to test the
model on the Al–Cu and Al–Si systems. These alloys
have been investigated during the recent years with the
most qualified experimental methods and the data
obtained seem to be consistent.
DENSITY
Density is important because it determines the
mass flow and influences the heat transfer [10]. It also
determines the solidification transformation [11]. In
the model we previously proposed [12], it was shown
that density influences the relationship between vis-
cosity and temperature.
1
The article is published in the original.
On the one hand, the density of an alloy may be
determined only experimentally because the models
proposed in literature are inadequate to satisfy the
industrial needs which often involve complex chemi-
cal compositions. On the other hand, the knowledge
of this property is essential for simulating and setting
the design of every metallurgical process. Here, a new
model is presented for estimating the density of a
binary alloy and it is compared with the most recent
assessed data.
We begin by considering the alloy as an ideal solu-
tion of two elements A and B. Under this hypothesis
the alloy is studied as an ideal mixture of gases, where
the properties of the AB solution are determined by the
sum of the fraction ρ
AB,
of the alloying elements.
According to this model we consider the density of the
alloy under ideal condition ρ
AB,id
to be expressed with
the “linear mixture rule” as:
(1)
where ρ
A
, ρ
B
are the density of pure metals A and B, X
A
and X
B
are the components mass fraction of each pure
element for which this property is valid
Now, we compare the ideal properties with the
experimental values. Given the importance for indus-
tries and the availability of experimental data in litera-
ture we choose to conduct the investigation under two
well-tested systems: Al–Cu and Al–Si.
By an empirical examination one may observe that
along the liquidus line this proportion holds:
(2)
where and T
L
are the density and the temperature
of the alloy along the liquidus line. Using an ideal mix-
ing ratio, the melting temperature of the alloy T* is
,
,
AB A A B B
X X ρ = ρ + ρ
id
1.
A B
X X + =
1
,
,
AB L
AB
T
T
ρ
=
ρ
id
*
AB
ρ
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Empirical Model for the Estimation of Thermophysical Properties
of Liquid Metal Alloys
1
D. Ceotto
a
and F. Miani
b
a
DIEGM—Universitá degli Studi di Udine
b
DICA—Universit@a degli Studi di Udine 33100 Udine (Italy)
e-mail: diego.ceotto@uniud.it
Received July 19, 2013
Abstract—A model for calculating the main properties of liquid metal binary alloys at standard pressure
based on experimental data observation is presented. Given the characteristics of the pure metals, the model
allows to calculate density, surface tension, electrical resistivity and thermal conductivity of binary alloys at
various concentrations along the liquidus line. Some preliminary comparisons for Al–Si and Al–Cu systems
are in satisfactory agreement with the model.
DOI: 10.1134/S0018151X14030249
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THERMOPHYSICAL PROPERTIES
OF MATERIALS