Journal of Materials Science

, Volume 47, Issue 8, pp 3706–3712

Density and thermal expansion of liquid Al–Si alloys


    • Institut für Materialphysik im WeltraumDeutsches Zentrum für Luft- und Raumfahrt (DLR)
  • Bengt Hallstedt
    • Materials ChemistryRWTH Aachen University
  • Jürgen Brillo
    • Institut für Materialphysik im WeltraumDeutsches Zentrum für Luft- und Raumfahrt (DLR)
  • Ivan Egry
    • Institut für Materialphysik im WeltraumDeutsches Zentrum für Luft- und Raumfahrt (DLR)
  • Michael Schick
    • Materials ChemistryRWTH Aachen University

DOI: 10.1007/s10853-011-6219-8

Cite this article as:
Schmitz, J., Hallstedt, B., Brillo, J. et al. J Mater Sci (2012) 47: 3706. doi:10.1007/s10853-011-6219-8


The density of Al-rich liquid Al–Si alloys was measured contactlessly on electromagnetically levitated samples using optical dilatometry. Data were obtained for samples covering compositions up to 50 at.% Si and in a temperature range between 650 and 1500 °C. The densities can be described as linear functions of temperature with negative slopes. Moreover, they increase monotonically with an increase of Si concentration. In a temperature range between 1100 and 1400 °C, it can be deduced from the composition dependence of the density that virtually no excess volume arises during alloying of the pure elements. For lower temperatures an excess volume is discussed, considering the temperature dependence of Si density literature data. The density data were integrated in a thermodynamic model description of the Al–Si system. In this way volume changes during solidification and changes in phase equilibria as function of pressure can be calculated.



Ternary Al–Cu–Si alloys are technologically widely used as lightweight casting alloys due to their good castability, processability, and mechanical strength, which can be further improved by heat treatment or additive elements [1]. In practice, mainly Al-based alloys are employed, which contain small amounts of the other alloying components and additives. However, there are also some investigations dealing with Si richer alloys. These studies focus on solidification [25] or thermodynamics [612] of the binary or the ternary alloy [13, 14]. Those liquids’ thermophysical properties have hardly been studied [15, 16].

To anticipate and optimize casting processes, a fundamental understanding of solidification is essential. Models with a quantitative prediction capability are needed, based on the thermodynamics of these processes. Using a CALPHAD approach [17] the Gibbs free energy can provide this basis. If the Gibbs energies were accurately known, all other thermophysical properties could be calculated from basic thermodynamic relations. Vice versa Gibbs energies can be determined from sound thermodynamic data. However, for this approach to work, it is not sufficient to explore the Al-rich part of the phase diagram only; a strategy for covering the entire phase diagram must be developed.

Of particular interest for solidification is the knowledge of the density of the alloy melt. When these density data are available, volume changes during solidification and cooling can be calculated. This is a prerequisite for realistic casting simulations and simulation of macro-segregation.

For the fairly small number of binary systems investigated experimentally, the excess volume has been found to be in the order of a few percent of the total volume and no correlation has been found so far with e.g., excess enthalpy (i.e., enthalpy of mixing). The excess volume is, thus, in the same order of magnitude as the volume change during solidification. Therefore, measured volumes, and in particular excess volumes, are important.

Since the expected excess volume is only a few percent, it is necessary to access as large part of the composition range of the considered system as possible to gain highly accurate measurements.

For ternary systems these data are generally sparse and even data of binary alloys are often missing. Hence, our objective is to systematically develop a reliable thermodynamic dataset, first for the binary Al-alloys before addressing the ternaries.

In the liquid Al–Cu system, density and surface tension data have already been reported [18, 19], viscosities are in preparation. With this article, we continue working on the densities of Al–Si, which were measured contactlessly in electromagnetic levitation (EML), a method which enables us to handle high melting and reactive materials.

Density and molar volume of binary mixtures

Within a temperature interval, (T−TL), which is small enough, the density, ρ(T), of a liquid metal can be considered as a linear function of temperature, T:
$$ \rho (T) = \rho_{\text{L}} + \rho_{T} (T - T_{\text{L}} ) $$
Here, TL is the liquidus temperature, ρL is the density at TL and ρT its temperature coefficient ∂ρ/∂T.
From these quantities, the volume expansion coefficient \( \beta = \frac{1}{V}\frac{\partial V}{\partial T} \) can be calculated:
$$ \beta = - \frac{{\rho_{T} }}{{\rho_{\text{L}} }} $$
In multicomponent mixtures, the different elements usually establish additional interactions among each other. This is the reason, why in alloying not only the sum of the weighted molar volumes of the pure components, i, has to be considered, but also an excess volume, which accounts for these interactions.
In a binary liquid system (i = 1, 2) the molar volume, V, can be written [20].
$$ V = \sum\limits_{i = 1}^{2} {x_{i} \cdot \frac{{M_{i} }}{{\rho_{i} }} + V^{E} } $$
The molar volumes of the pure components are here written by considering the molar masses, Mi, of each component and their densities, ρi, at a certain temperature. These are weighted by the atomic concentrations xi. Deviations of V from ideal mixing behavior are included by the excess volume, VE. That means, for VE = 0 Eq. 3 is a simple linear combination of pure component molar volumes and describes an ideal mixing without volume change.
From Eq. 3 the composition dependence of the binary system’s density is deduced:
$$ \rho (x_{i} ) = \frac{M}{V} = \frac{{\sum\nolimits_{i = 1}^{2} {x_{i} \cdot M_{i} } }}{{\sum\nolimits_{i = 1}^{2} {x_{i} \cdot \frac{{M_{i} }}{{\rho_{i} }} + V^{E} } }} $$
In most cases, VE does not vanish. When atoms are of similar size and have no preferred coordination with either similar or different atoms, they are stochastically distributed in the solution. In this situation, the temperature and composition dependence of VE can be split by an approximation, which is symmetric in the alloy composition [20, 21]:
$$ V^{E} \left( {x_{1} ,x_{2} ,T} \right) = x_{1} x_{2} V_{0} (T) $$
Here, the composition dependence is incorporated in the product of the atomic concentrations xi (i = 1, 2) of the alloy components. Hence, the whole system can be described by a coefficient V0, which is a function of temperature, but independent of composition.

Thermodynamic modeling

Volume data are usually not included in thermodynamic databases so far. In the form of Eqs. 3 and 5, they can easily be added to existing thermodynamic model descriptions. To each Gibbs energy parameter in the thermodynamic description a term of the form (PP0)V is added;
$$ G(P,T) = G(T) + (P - P_{0} )V , $$
where G is the Gibbs energy, P is the pressure, P0 the normal pressure (1 bar) and V the volume. The thermodynamic description of the Al–Si system from Feufel et al. [22] was used. Volume data for solid and liquid Al and Si from [23] and excess volumes from the present work were added to this description. The data for liquid Al were adjusted to match the evaluation of Assael et al. [24]. The modified volume used for liquid Al is V = 9.9044 + 1.548 × 10−3T cm3/mol, where T is in K.


Electromagnetic levitation (EML)

Experiments were performed in a stainless steel high vacuum chamber described in detail elsewhere [25, 26]. It was evacuated to 10−7 mbar and then filled with 750 mbar Ar (purity: 99.9999 vol.%). The pre-alloyed sample was positioned in the center of a levitation coil to which an alternating current of typically 300 kHz and about 200 A is applied. Its inhomogeneous electromagnetic field induces eddy currents inside the electrically conductive sample. The forces arising from interaction of these currents with the field levitate the sample stably against gravity. A detailed consideration of the EML-principle is given in literature [27].

Beneficial effect of the inherent ohmic losses of these currents is the heating and melting of the sample, which is realized simultaneously with EML. As levitation and heating are coupled, a certain desired temperature can only be adjusted within narrow limits by changing the levitation power. During our measurements, the forced cooling in a laminar flow of Ar or even He gas could be avoided, since reducing the levitation power was sufficient to cool the samples to the desired temperatures. Only for solidification additional cooling by He gas flow was needed.

The measurement procedure is to start at a certain levitation power at high temperatures and reduce the power stepwise to reach lower temperatures. Measurements are then performed in thermal equilibrium.

The sample temperature is measured by an infrared pyrometer. As the emissivity is generally not known, the pyrometer output signal, TP, has to be recalibrated using the known liquidus temperature, TL, of each sample as a calibration point. For most liquid metals, the emissivity within a limited wavelength band is almost independent of the temperature [28]. Hence, for calibration a constant emissivity within the operating wavelength range of the pyrometer can be assumed. The exact calibration procedure is described, for instance, in [29].

Optical dilatometry

Densities of the liquid droplets are determined by taking side view shadowgraph images and calculating its volume at different temperatures. The technique is thoroughly described in [25].

In principle, the levitated sample is illuminated from the back side by an expanded HeNe-laser beam. An interference filter removes thermal radiation of the sample and a pinhole eliminates scattered nonparallel light rays from the beam. The images are recorded by a CCD-camera and analyzed by an edge detection algorithm to determine the edge curve of the 2D-projection of the sample. In order to evaluate the liquid sample volume, 3D-information must be gained from these images.

The surface of a levitated droplet performs oscillations around its rest position, which is axially symmetric to the symmetry-axis of the electromagnetic field providing the levitating force. Since not every oscillation mode is symmetric to this axis, a single frame is not necessarily axially symmetric, when it does not incidentally capture the rest position of the sample. In averaging over 1000 of these frames, these oscillations (usually in the order of 50 Hz) are eliminated and one obtains an edge curve, which is symmetric to the vertical sample axis [25]. This curve is then fitted by Legendre polynomials and gives the sample volume, when it is integrated over space assuming rotational z-axis symmetry:
$$ V_{P} = \tfrac{2}{3}\pi \int\limits_{0}^{\pi} {<R(\varphi) >^{3}\sin (\varphi)d\varphi } $$
Here, R(φ) is the fitted average 2D-edge curve and φ is the polar angle. The sample volume, Vp, is only obtained in pixel units. It must be calibrated to the real volume, V, by a comparison to reference volumes, which is also described in [25]. From the mass, m, of the processed sample the density is calculated, provided evaporation during the measurement was negligible.

Sample preparation

Samples with a diameter of about 6 mm were made of Si and Al metal with a purity of 99.999% (metals basis). Mass adjustment and surface cleaning was achieved by pinching off pieces and ultrasonic treatment. Despite the contact with crucible material, the samples needed to be pre-alloyed within an arc melting furnace, since otherwise the solid semiconducting Si could not have been processed in EML. Alloying was completed in the EML apparatus by heating the samples to about 1500 °C. At the same step, oxygen contaminations were removed by keeping the sample at this temperature until no bright oxide spots could be observed on the surface. After this alloying procedure and the subsequent experiment, the mass loss of the about 300 mg samples was less than 3 mg. If this evaporation affected only one component (Al), the change of the alloy composition would amount 0.2 at.% at most. For comparison and to check the reproducibility of the data, also samples prepared in vacuum induction melting and in electron beam melting were measured. The inductively molten samples were obtained from our cooperation partners in Jena1, the electron beam samples from Clausthal.2


Measurements were performed at temperatures, where evaporation was negligible. Levitation became more and more unstable, the colder the samples got and the more Si they contained. Hence, a limited temperature interval was accessible, which, however, is quite broad for most samples (800–1400 °C).

The measured densities are displayed in Fig. 1. They can be fitted linearly by Eq. 1. The obtained densities ρL at liquidus temperature, TL, and the slopes of the curves (temperature coefficients), ρT, are compiled in Table 1 for each measured sample. There, also the volume expansion coefficient, β, is calculated from Eq. 2.
Fig. 1

Density of liquid Al–Si versus temperature. The solid lines represent linear fits to the data. The samples denoted by FSU or TUC were obtained from Jena (see footnote 1) or Clausthal (see footnote 2), respectively. For comparison, literature data [23] (partly combined with [24], see text) of the pure components are also depicted

Table 1

Fit parameters for the density and thermal expansion of each of the investigated Al–Si samples. The samples, denoted by FSU or TUC were obtained from Jena (see footnote 1) or Clausthal (see footnote 2), respectively


TL, °C

ρL, g cm−3

ρT, 10−4 g cm−3K−1

β, 10−5 K−1



2.36 ± 0.01

−3.0 ± 0.1

12.8 ± 0.1



2.46 ± 0.01

−2.1 ± 0.1

13.1 ± 0.3



2.44 ± 0.01

−2.3 ± 0.1

8.9 ± 0.1



2.37 ± 0.02

−1.6 ± 0.2

6.8 ± 1.0

Al70Si30 (FSU)


2.40 ± 0.02

−1.7 ± 0.2

7.0 ± 0.9

Al70Si30 (TUC)


2.39 ± 0.02

−1.8 ± 0.2

7.0 ± 0.7

Al60Si40 (TUC)


2.42 ± 0.01

−2.9 ± 0.1

11.9 ± 0.3

Al50Si50 (TUC)


2.46 ± 0.03

−3.2 ± 0.2

12.9 ± 1.0

Literature data of the pure components are denoted as dashed lines in Fig. 1. The literature data for Al [23] were adjusted to match those of [24] in temperature interval 660–920 °C. The ones of pure Si [23, 30] remained unmodified. The data in [23] (dashed line in Fig. 1) are fitted using a linear temperature dependence of the volume.

The measured Al-densities fit the reported data quite well, except for the values measured above 1450 °C. There, a steeper slope arises, leading to lower density values. This effect must be due to evaporation of sample material during measurement at these elevated temperatures. In this temperature region, the mass loss of 3% disturbs recalibrating sample volumes to densities with the processed sample mass. Below 1450 °C no evaporation occurs, so the mass during the lower T measurements stays constant.

Measurements were started at high temperatures and data were acquired after subsequent cooling steps. This means that at high temperatures evaporation leads to a change of sample mass between different data points. Later on, at lower temperatures, no evaporation occurs, and the sample mass stays constant. Since these data are evaluated using the mass of the processed sample, the lower temperature densities are determined correctly, while the values at higher temperatures are underestimated. For this reason, recalibrated densities of Al up to 1450 °C are reliable and only these data are evaluated in the linear fitting.

In all the data of the other samples, where the overall mass loss was less than 1%, this effect does not occur. In these cases, the major evaporation was during the alloying and surface cleaning step at more elevated temperatures. Hence, for these samples the recalibration by the processed sample mass is valid throughout the whole measurement range.

At first glance the value of the Al80Si20 sample seems to be quite high. But the composition dependence depicted in Fig. 2 visualizes that this scatter is within the small uncertainties of the measurement principle which are of 1% [25].
Fig. 2

Composition dependence of the liquid Al–Si density at 1200 °C. The pure component data were taken from literature [23, 24, 30]. The lines represent fits of Eq. 5 to the data, giving an excess volume, VE, of zero

The same holds for the Al70Si30 alloys, where we compared samples created by different methods. Within the measurement uncertainties, density values are the same. The completely homogeneous samples, obtained from our project partners, levitated more stably from the beginning. The pre-alloyed samples only became stable after they were heated above the melting temperature of pure Si. For this reason, only fully alloyed initial samples were used for Si-contents above 30 at.% .


In Figs. 2, 3 and 4, the composition dependence of ρ is depicted at different temperatures, together with literature data [23, 24, 30] of the pure components. The density increases monotonically with increasing Si-content. The considered density range between pure Al and Si is quite narrow and scatter of the data is within the measurement uncertainties of only 1%.
Fig. 3

Composition dependence of the liquid Al–Si density at 1000 °C with the extrapolated pure component data from literature [23, 24, 30]. There, in the undercooled region of Si different behavior is discussed and considered in the evaluation of our data. The lines represent fits of Eq. 5 to each of the datasets. With the second, a slight deviation of VE of from zero might occur
Fig. 4

Composition dependence of the liquid Al–Si density at 800 °C with the extrapolated pure component data from literature [23, 24, 30]. Considering the different existing datasets of Si, both fits to the data are equally good. In either case the excess volume, VE, does only differ little from zero

For liquid Si, there are two classes of datasets [23, 30]. Starting from quite similar density values above TL, one dataset [23] observes a linear behavior during undercooling to about 1100 °C. The other [30] reports a T2-behavior within the same temperature region and extrapolates a maximum around 900 °C.

Since our measurements were performed in this undercooled temperature range of pure Si and it is not trivial to select between those reported data, we checked the extrapolations of both datasets with regard to composition-dependent volume effects during alloying.

In Figs. 2, 3 and 4, the composition dependence of the alloy density is fitted by Eq. 4. The black lines are reduced χ2-fits to the data using one Si dataset [23] the grey curves employ the other [30]. The full lines represent fits, where ρAl, ρSi, and VE were varied. These fit parameters are compiled in Tables 2 and 3. As a guide to the eye, VE was set to zero in the dashed line fits.
Table 2

Fit parameters for the excess volume and densities of Al and Si at different temperatures, utilizing pure metal data from Ref. [23]

T, °C

V0, cm3 mol−1

ρAl, g cm−3

ρSi, g cm−3


0.5 ± 0.6

2.31 ± 0.03

2.79 ± 0.03


0.6 ± 0.6

2.31 ± 0.03

2.74 ± 0.03


0.2 ± 0.5

2.26 ± 0.02

2.70 ± 0.03


0.0 ± 0.5

2.24 ± 0.02

2.66 ± 0.02


−0.1 ± 0.3

2.21 ± 0.02

2.62 ± 0.01


−0.2 ± 0.4

2.19 ± 0.02

2.58 ± 0.02


−0.3 ± 0.4

2.17 ± 0.02

2.54 ± 0.02

Table 3

Fit parameters for the excess volume and densities of Al and Si at different temperatures, utilizing pure Si data from Ref. [30]

T, °C

V0, cm3 mol−1

ρAl, g cm−3

ρSi, g cm−3


−0.6 ± 0.4

2.30 ± 0.03

2.63 ± 0.04


−0.1 ± 0.6

2.30 ± 0.3

2.63 ± 0.04


−0.3 ± 0.5

2.26 ± 0.02

2.63 ± 0.03


−0.2 ± 0.4

2.24 ± 0.02

2.62 ± 0.02


−0.2 ± 0.4

2.21 ± 0.02

2.62 ± 0.02


0.0 ± 0.4

2.20 ± 0.02

2.60 ± 0.02


0.01 ± 0.4

2.17 ± 0.02

2.58 ± 0.2

The main difference in the fits originates from the single Si-datapoints. The fits start to deviate from each other at Si concentrations of about 50 at.%. The Al50Si50 data seem to be slightly higher than the fits, implying higher values for Si-rich alloys. Since we focused on the Al-rich side of the alloy, no final statement can be given about the Si-rich densities.

Comparing fits with adjustable VE and those with VE = 0, one might observe slight differences between them, intensifying with decreasing T. But even at 800 °C the deviation of the measured molar volume from the ideal one is only in the order of 2%, which is more due to the scatter of the data. In Fig. 5, the temperature dependence of the fitted VE is evaluated, considering V0 from Eq. 5. There, for both of the evaluated Si-densities, V0 virtually vanishes considering its uncertainty.
Fig. 5

Temperature dependence of VE, visualized by the coefficient V0 fitted with different Si densities [23, 30]. The dashed line is placed at zero. Within the uncertainties, V0 and VE equal zero

The observed simple additivity of molar volumes in the Al–Si system implies comparable nearest–neighbor interactions regardless of the kind of atoms involved. In literature [15], at temperatures 20 K above TL and Si contents higher than 40 at.%, a virtually instantaneous change in the average coordination number of the Al–Si alloy atoms was observed by neutron diffraction. This was explained by formation of tetrahedrally coordinated Si atoms only in the Si-rich liquid. For Si concentrations below 40 at.% the average coordination of the atoms stayed almost constant and decreased to another constant value upon increasing the Si content by 10 at.% to 50 at.%. The mean distance of atoms within the pure liquids and the alloys was comparable.

Considering this, for low Si contents, an ideal mixing seems plausible. In case the Si tetrahedral short-range order should establish in Si-rich Al–Si alloys, the atomic interactions within the system cannot be equal. Against this background the observed ideal mixing is not trivial and should be examined in more detail by extending density measurements to alloys with higher Si-contents.

Using the thermodynamic description for Al–Si including volume data (with zero excess volume) with the modified Gibbs energy expressions according to Eq. 6, the density as function of temperature can be calculated with standard thermodynamic software such as Thermo-Calc [31] for any composition, including any phase transformations, such as solidification. An example for an Al–6 at.% Si alloy is shown in Fig. 6. Including volume data in the thermodynamic description means, that pressure dependence of the Gibbs energy is incorporated. This can be used to calculate phase equilibria as function of pressure. In Fig. 7, the Al–Si phase diagram is calculated at different pressures. Such calculations can be considered reasonably accurate at moderate pressure. High pressure differences in compressibility, which is currently not modeled, will lead to deviations from reality of such “simple” calculations. For pressures above about 1 GPa (10 kbar), depending on material, it is probably necessary to consider the compressibilities to reach acceptable accuracy.
Fig. 6

Calculated density as function of temperature for an Al–6 at.% Si alloy
Fig. 7

Calculated Al–Si phase diagram in the Al-rich part at normal pressure (1 bar, solid lines), 1 kbar (dotted lines) and 10 kbar (1 GPa, dashed lines). Note that the Al liquidus increases with pressure since the volume of Al increases on melting, whereas the Si liquidus decreases with pressure since the volume of Si decreases on melting. This leads to a considerable shift of the eutectic composition


The density and thermal expansion of liquid Al–Si alloys was determined experimentally as a function of temperature and composition up to Si-concentrations of 50 at.%. The density can be described by a linear combination of the pure metals' molar volumes and hence, no pronounced excess volume was found. On the other hand, there are experiments [15], suggesting strong interactions in Al–Si melts with Si-contents above 50 at.%. Addressing densities of those alloys experimentally could be worthwhile to gain more insight into this system.

By including the experimental density data to the thermodynamic description, the modeling is capable of including moderate pressure dependencies.


M. Rettenmayr, A. Löffler, Institut für Materialwissenschaft und Werkstofftechnologie, Friedrich-Schiller-Universität Jena, 07743 Jena, Germany.


R. Schmid-Fetzer, J. Gröbner, Institut für Metallurgie, TU Clausthal, 38678 Clausthal-Zellerfeld, Germany.



Within the framework of PAK 461 this study was financially supported by the “Deutsche Forschungsgemeinschaft” under grant numbers EG 93/8-1 and HA 5382/3-1. This is gratefully acknowledged. Further, we would like to thank our cooperation partners Rainer Schmid-Fetzer, Joachim Gröbner, Markus Rettenmayr, and Andrea Löffler for sharing their expertise and for the preparation of high quality samples.

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© Springer Science+Business Media, LLC 2012