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High Temperatures-High Pressures, Vol. 38, pp. 245–257
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Density and surface tension of liquid
iron oxides*
F. Millot1,**, J.C. Rifflet1, G. Wille2 and V. Sarou-Kanian1
CEMHTI/CNRS Orleans Université Orléans
2
BRGM Orleans
1
Received:
October 1, 2008. Accepted:
December 17, 2008.
New data are presented for the density ρ and the surface tension σ of the
liquid oxides FeOX in the range of x between 1.05 and 1.35 and temperatures
T from 1865 to 2155 K. The results obtained with contactless techniques
indicate that ρ. and σ are almost constant with T and x within uncertainties.
Practical values are ρ = 4.35 ± 0.1g/cm3 and σ = 0.59 ± 0.02 N/m.
Keywords: Iron oxide, melt, surface tension, density, levitation.
1 INTRODUCTION
The density of liquid iron oxides is not accurately known. There are only few
sources of data obtained with the Archimedean method [1–3]. Reported density
values range from 4500 Kg/m3 [1,2] to 3800–4300 Kg/m3 [3] in small domains
of temperature (1680K<T<1880 K) and composition (1.05<[O]/[Fe]<1.2).
In this paper we report values of the density and surface tension of liquid
iron oxides obtained with containerless experimental techniques which have
been developed by our group during the last ten years [4–6].
2 EXPERIMENTAL
Figure 1 is a scheme of the aerodynamic levitation furnace. 2–3 mm diameter
drops are maintained stable on a gas flowing through a convergent-divergent
copper nozzle. Its convergent and divergent parts act also as a concentrating
*Paper presented at the 18th European Conference on Thermophysical Properties, Pau, 2008.
**Corresponding author: [email protected]
245
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F. Millot et al.
optical pyrometer λ=0.85µm
CO2 Laser
Fast CCD Camera
Chamber
Droplet
Nozzle
Motion
Analyzer
Water
cooling
Levitation gas
Oxygen analyzer
CO2 Laser
optical pyrometer λ=0.85µm
Figure 1
Experimental set up.
optics for the 8 mm diameter 10.6 µm laser rays that heat the top and the bottom of the sample. 240 Watt effective heating are available allowing heating
up to 3300 K in favourable cases. Liquid drop can be maintained pollution free
and stable during very long time (hours) with movements of the gravity centre
of a few microns only although convection movements are expected from the
shear of the flowing gas and the surface deposition of the laser energy.
The gas for levitation is a mixture of argon and oxygen obtained from
electronic flow-regulators. The oxygen partial pressure of the gas (10–5 – 105
Pa) is also measured with a ZrO2/Y2O3 solid oxide electrolytic cell having a
Pd/PdO reference electrode and working at T = 907 K.
Thermophysical measurements of the properties of a liquid levitating sample are performed with contactless methods:
The temperature is estimated from two optical pyrometers aiming at the
top and bottom of the drop. This supposes knowledge of the emissivity of
the sample at the wavelength (0.85 µm) of the pyrometers. In general, emissivity is not accurately known and temperature uncertainties of 20–50 K are
reasonable.
In practice, temperatures are obtained from a calibration of pyrometers at
the solidification of liquid alumina drops cooling freely under argon atmosphere. This corresponds to an emissivity of approximately 0.9 and temperature of 2327 K [8].
The initial product is Fe2O3 powder (Specpure from Johnson Matthey). It
is compacted with an uniaxial press. Small pieces of the compact are introduced in the levitation nozzle and quickly melted to obtain drops.
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Density and Surface Tension of Liquid Iron Oxides
247
Fe2O3 is melted in the levitation furnace with an Ar/O2 gas. The partial
pressure of the gas is measured with the electrolytic cell and the power of the
two lasers is adjusted in order to have only small differences of temperature
between the top and the bottom of the drop. After these settings, the levitating
drop is left in the gas during 15 minutes. Finally, 1250 images are recorded
with exposure times of 1ms in order to determine density and surface tension.
Just after this, lasers are shut off allowing the free cooling and crystallization
of the drop. During this last period, the signal of the two pyrometers is
recorded as shown on various examples on figure 2.
The cold drop is then weighed with a precision of 10–5 g.
We have also characterized the cold drops in order to determine the ratio
[O]/[Fe]. The drops have been heat treated in air in an alumina single crystalline crucible which was obtained by machining a plate of a Verneuil single
crystal in order to manage small cavities to receive drops. After a treatment of
2 days at 1000ºC and 1 day at 1200ºC we obtain a drop constituted of Fe2O3.
No pollution of the alumina single crystal by iron oxide can be detected (see
figure 3b) contrary to the common observation of a pollution leading to the
darkening of alumina polycrystalline crucibles. The change of the weight of
the drop before and after the thermal treatment is a direct measurement of
[O]/[Fe] with the formula:
[O]/[Fe] = 1.5–4.99*(1–mi/mf)
2400
Temperature (K)
2200
2000
3
1800
1600
2
1
1400
1200
1000
0
2
4
6
8
time (s)
Figure 2
Cooling curves and solidification: 1-in argon, 2- in Ar/3*10-2O2, 3-Ar/0.3O2.
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F. Millot et al.
Figure 3
Drop picture immediately after laser processing (up) and after re-oxidation to Fe2O3 (down).
where mi and mf are the initial and final weight of the drop after the heat tre­
at­ment. Weight changes mf-mi are between 1 to 5 mg depending on samples.
3 RESULTS
In this experimental study, we have to define and measure various quantities:
––
––
––
––
The temperature of the experiment.
The composition of the sample.
The surface tension of the sample.
The density of the sample.
3.1 Temperature T
Figure 2 presents the recordings of the two pyrometers aiming at the top
and the bottom of three samples that have approximately the same weight
(≈ 40 mg) denoted as 1, 2 and 3.
The three recordings represent the free cooling of drops after the shut
down of lasers at time t = 1s. The first part of the curves (from 1 to 3 s) is the
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Density and Surface Tension of Liquid Iron Oxides
249
cooling of the liquid. The jump at t ≈ 3s corresponds to the beginning of
solidification of the undercooled liquid. The right side of curves are the solidification and finally the cooling of solids. The main difference between the
three samples is the nature of the flowing Ar/O2 gas mixture. 1 is almost pure
argon (Po2 ≈ 10–5 atm.), 2 contains 3*10–2 parts of O2 and 3 contains 0.3 parts
of O2. There are, however, striking differences between the three curves of
figure 2:
–– The cooling rate of the liquid is different for the three curves, being much
smaller in Ar/0.3 O2 than in pure argon.
–– The two pyrometers indicate the same temperature of the liquid for the
sample flown in argon (1) but different curves for the argon containing
oxygen curves 2 and 3, the temperature of the bottom of the drop being
higher than that of the top.
These differences could be satisfactorily explained if an exothermic
absorption of oxygen happens during the cooling of the drop (which is what
we expect from thermodynamics). They have the consequence that the composition of the drop which is measured after its cooling is certainly representative of its composition at the moment of the solidification but it may have
changed during the cooling period of the liquid and may present composition
gradients in the temperature gradients when the lasers are heating.
The figure 4 has been obtained by comparing the classical phase diagram
obtained by Muan [9] and Darken and Gurry [10] with the temperature at the
beginning of solidification (see figure 2). We observe a 20 K systematic dif-
1900
M+L
L
Temperature (K)
1800
M
L+M
1700
M+H
1600
W+Fe
W+M
W
1500
1,0
1,1
1,2
1,3
1,4
1,5
composition x in FeOX
Figure 4
Liquidus temperature versus measured composition x compared to the phase diagram of the
Fe/O system.
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F. Millot et al.
ference between the phase diagram liquidus temperature and the points corresponding to almost congruent solidification (wustite between 1.05 and 1.2
and magnetite between 1.33 and 1.35). The agreement is then correct since it
reproduces the essential features of the phase diagram and it confirms the fact
that the composition of drops is representative of their state at the moment of
the solidification.
These data also confirm that our temperature measurements are representative of the temperature of the drops. We have also examined (not reported
in detail) that there is only slight differences between the emissivity of the
solid and liquid iron oxides by performing solidifications without or few
undercooling of the liquid.
3.2 Composition [O]/[Fe]
As early explained, the composition of the drops have been obtained after the
experiment by their weight change after oxidation to Fe2O3. We have also
anticipated the fact that oxygen is able to react very quickly with the liquid
during its cooling making the final measurement of the composition different
from that of the liquid of interest.
In order to examine this point we have compared the compositions that we
have determined after experiment with the composition that we should have
expected from the oxygen pressure above the drop at the temperature T of the
liquid. However, we have already remarked that the drop should present temperature gradients, particularly when the lasers are heating it. This point is
easily revealed if we transform the beginning of the cooling curve of the liquid as shown in figure 2 to a new curve expressing the variations of the inverse
of the cube of the temperature 1/T3 vs time t (see an example in figure 5). The
transition from the steady state of the drop with the lasers impinging the surface to their free cooling having an approximate linear relation between time
and 1/T3 is characterized by a short unsteady period of time (between points
A and B) when the temperature gradients that were produced by the deposition of energy of the lasers on the surface of the drop almost vanish. The point
A and B correspond to a temperature difference of approximately 80 K and
point B is the temperature that we should use to guess at the mean temperature of the liquid instead of point A which represents the laser overheated
surface of the drop.
In order to calculate the liquid compositions from the values of the temperature and the partial pressure of oxygen of the Ar/O2 mixture flowing the
liquid sample, we have used the data of Darken and Gurry [10]:
From the partial molal heat of solution of oxygen in liquid of composition
x = [O]/[Fe] and temperature T(K) in the gas at pO2 (atm), we deduce:
245-257 pp HTHP_1036.indd 250
R  ∂log(p O2 ) 
= -145660 + 69500x 2  ∂(1/T)  x
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Density and Surface Tension of Liquid Iron Oxides
251
-10
2,0x10
-10
1,8x10
-10
1/T3 (K-3)
1,6x10
-10
1,4x10
B
-10
1,2x10
-10
1,0x10
A
-11
8,0x10
0
1
2
time t (s)
Figure 5
1/T3 versus time cooling curve showing the unsteady period A to B.
And the approximate linear relationship between x and log (pO2) at 1873K is:
 log(p )
O2  1873K = 21.8x - 30.19 
By combination, we obtain:
x=
log(p O2 ) + 30.19 + 63662* (1/T -1/1873)
21.8 + 30376* (1/T -1/1873)
The calculation of the composition x has been performed at the point B of
figure 5 which represents the mean temperature of the liquid under study. We
have also calculated the composition x of the liquid for an infinitely fast
exchange of oxygen between the gas and the liquid leading to an equilibrium
value immediately before the beginning of the solidification (see figure 2).
These values have been plotted vs the composition x that we have determined
experimentally after the experiment and appear on figure 6 with a straight line
which represents the perfect agreement between measured and calculated
values. We observe from figure 6 that the composition of the liquid was correctly measured for compositions in the range 1.10–1.30 which corresponds
to oxygen poor Ar/O2 mixtures (PO2 ≤ 10−2 atm.). On the contrary, the oxygen
rich Ar/O2 mixtures (PO2 ≥ 10−1 atm.) corresponding to x > 1.35 can equilibrate very fast with the drops since the final composition represents approxi-
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F. Millot et al.
1,45
x calculated from PO2 and T
1,40
1,35
1,30
1,25
1,20
1,15
1,10
1,05
1,00
1,00 1,05 1,10 1,15 1,20 1,25 1,30 1,35 1,40 1,45
x of FeOX measured after experiment
Figure 6
Composition [O]/[Fe] calculated from T, pO [10] versus composition measured after the cooling
2
of the sample. # mean temperature of the liquid during experiments, +temperature of the liquid
sample just before the solidification.
mately that of the liquid just before the solidification (some additional
oxidation of the solid during the cooling cannot be completely excluded
which is consistent with the slight deviations of the “cross” points with the
straight line of figure 6). The apparent diffusion coefficient is of the order of
10-2 cm2/s which is at least two order of magnitude higher than classical values in quiet liquids. This comparison again points the importance of the
movements of the liquid in the levitated drops.
Finally, these comparisons between measured and calculated values of the
composition show that we should use the calculated composition of the liquid
at the temperature of interest.
3.3 Surface tension σ
The surface tension acts as a spring counteracting the temporal deformations
of the drop induced by external forces (gas shear, laser interaction etc…). This
makes characteristic frequencies νi of drops of known weight m to be directly
related to surface tension σ. In case of a drop with no external force on it,
3π ⋅ m ⋅ ν 22
there is only one characteristic frequency ν2 and the result is: σ =
8
[11]. In other cases, deformation, rotation and precession play a direct role on
the frequency spectrum of the drop [6]. However, for moderate deviation from
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Density and Surface Tension of Liquid Iron Oxides
253
the spherical drop and observation nearly along the rotation axis, five characteristic frequencies can be identified and related to surface tension:
2
2

(ν2-1 + ν2+1 ) (ν2-2 + ν2+2 ) 
1

ν 22 = ν 220 +
+

5 
2
2

A typical result of the treatment of images is shown on figure 7. It was
obtained on a 51.33 mg drop at t = 1862 K under argon. The relative amplitude of vibration of the surface is approximately 4*10–3. The Fourier transform of the surface and orientation of the drop is interpreted with the five
peak frequency spectrum which is characteristic of a rotating and slightly
deformed drop [6]. The precession of the rotation axis is also responsible for
the comb shape of the peaks. This example illustrates the fact that it is difficult to assess the exact position of the various frequencies. Selection rules are
helpful to do that since ν0 can only be found in the surface spectrum, ν±2
appears only in the orientation spectrum and finally ν±1 is appearing in the
two spectra. We have also ν 2 - ν-2 = 2*(ν1 - ν-1 ) .
The final result is shown on figure 8. We observe almost the same value of
the surface tension (σ = 0.59 ± 0.02 N/m) whatever the temperature or the
composition. The comparison with literature indicates similar trends with the
results of Kidd and Gaskell [12] and those of Bhattacharyya and Gaskell [13].
ν -2
ν -1
ν0 ν1
ν2
amplitude (a.u.)
40
orientation
20
surface
0
85
90
95
100
105
110
115
120
125
Frequency (Hz)
Figure 7
Fourier transform of the oscillations of the surface and the orientation of a liquid sample and
determination of the characteristic frequencies νi.
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F. Millot et al.
0,65
Maurakh (T=1873K)
Kozakevitch (T=1673K)
Okunev (T=1673K)
Kawaï (T=1650-1700K)
Kidd et Gaskell t=1733K
Kidd T=1683K
Bhattacharyya (T=1708K)
This work (T=2112-2155K)
This work (T=1862K)
This work (T=2017-2054K)
This work (T=1916-1956K)
surface tension (N/m)
0,60
0,55
0,50
0,45
0,40
0,35
1,0
1,1
1,2
1,3
1,4
1,5
1,6
composition X of FeO X
Figure 8
Surface tension obtained in this study at different temperatures versus the calculated composition
of the liquid at T, pO2 are compared with Kidd and Gaskell [12], Bhattacharyya and Gaskell [13],
Kozakevitch [15], Okunev and Galimov [16], Kawai et al [17], Maurakh et al [18], data.
Another interesting result comes from the relative position of the three characteristic frequencies ν0*, ν1* and ν2* of the non rotating drop. These are easily
obtained by taking the average position of the 0, ±1 and ±2 frequencies of the
rotating drop. These frequencies are directly related to the two permanent distortions ε2 and ε4 that describe the deviation from sphericity [14]:
ν 0 * = ν * (1 - 0.6758 ε2 - 2.176 ε 4)
ν1 * = ν * (1 - 0.3379 ε2 + 1.4507 ε 4)
ν 2 * = ν * (1 + 0.6758 ε2 - 0.3627 ε 4)
where ν* is the arithmetic mean value of the five characteristic frequencies.
The calculation of ε2 and ε4 from our data indicate that ε4 is always smaller
than 1.5% whereas ε2 is between 2 and 10%. These large deformations which
concern mainly the flattening of the drop along the vertical axis are in part
produced by the rotation force on the drop. They will influence our methodology for the determination of density.
3.4 Density ρ
The density is the ratio of the weight to the liquid volume. Weight is measured immediately after the cooling of the drop which lasts a few seconds
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Density and Surface Tension of Liquid Iron Oxides
255
after an experiment. Volume V is obtained indirectly from the measurement
of the surface S of the images of the drop. For small enough mass and not too
high rotation rates, the deformation from sphere of the drop is less than 1%
inducing only small uncertainty in the simplified formula of the sphere:
V = S3/2 / 36π . In case of deviation from spherical shape, corrections must
be done. For instance, with a static deformation ε2 corresponding to the flat2
ness of the drop the volume becomes V =
(1 - ε2 ) (1 + ε2 )S3/2
36π
.
Various calibrations have been used in order to measure the size of image
pixels (calibrated drops and calibrated arrays of micrometric lines) with an
absolute uncertainty of 1/1000.
The density of the liquid iron oxides is represented for four different temperature ranges on figure 9 and it covers the domain of compositions x going
from 1.05 to 1.35. The weights of samples are between 40–70 mg and 3 extra
samples between 90–115 mg.
Glorieux [19] have proposed a limit for the non-dimensional parameter
mg/σr = 0.7 (σ = surface tension and r = radius of the drop) in order to have
negligible deviations (<1%) from the spherical shape of a drop in order to
evaluate the density of a levitated liquid. In the case of liquid iron oxides this
means that drop weight should be lower than 150 mg. We have, however,
6,0
5,8
3
density (g/cm )
5,6
5,4
5,2
5,0
4,8
4,6
4,4
This work (T=2112-2155K)
This work (T=1862K)
This work (T=2017-2054K)
This work (T=1916-1956K)
Hara (T=1743-1881K)
Mori (T=1723K)
Mori (T=1748K)
Mori (T=1773K)
Mori (T=1798K)
Lee (T=1773K)
4,2
4,0
3,8
3,6
1,05 1,10 1,15 1,20 1,25 1,30 1,35 1,40 1,45
composition X of FeO X
Figure 9
Experimental densities corrected for the deformations of the drop (see text). Comparison with
literature data: Lee and Gaskell [1], Hara et al [2], Mori and Suzuki [3].
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F. Millot et al.
deduced in paragraph 3.2 from the frequency spectrum of the liquid iron
oxides that the weight of the drop is not the only parameter that can change
the spherical shape. For this reason we have applied corrections with ε2 distortions deduced from characteristic frequency measurements.
The precision on the density data is calculated from the ratio of the number of pixels of the perimeter to the number of pixels of the surface of the
images recorded with the high speed camera. Characteristic values for our
samples are ∆ρ/ρ = 3%. The error coming from the weight of the drop is
much smaller (1/1000).
Figure 9 clearly shows that the density of liquid oxides are only weakly dep­
endent on the composition [O]/[Fe]. A practical value is: ρ = 4.35 ± 0.1 g/cm3.
It is also observed that the relatively bad precision (3%) of the density
values do not permit to seriously predict its temperature dependence.
Comparison with the conflictive previous results of Mori and Suzuki [3]
and Hara et al [2] which include in their analysis the results of Lee and Gaskell
[1] indicate agreement with Hara on the fact that the comparable densities
should not change significantly with the composition of the liquid and also on
the fact that the temperature coefficient of the density should be sufficiently
small in order to not be detected in our data. This means that it should be less
than (∆ρ/ρ)∆T = 1.2*10-4K-1, where ∆ρ/ρ = 0.1/4.35 is the total scatter of
the density values and ∆T = 200 K is the domain of temperature of our study
(the values of this temperature coefficient are 7*10-5K-1 for Hara et al [2] and
between 2.5*10-4K-1 and 4.8*10-4K-1 for Mori and Suzuki from their data).
CONCLUSION
The surface tension and density of the liquid oxides have been measured with
contactless methods in the temperature domain 1865–2155 K and composition [O]/[Fe] ranging from 1.05 to 1.35.
The temperature and composition has been carefully evaluated by comparing our measurements with the thermodynamic properties of the iron/oxygen system previously reported in the literature.
The experimental data obtained for density as well as for surface tension
is particularly simple since it reduces to ρ = 4.35 ± 0.1 g/cm3 and σ = 0.59 ± 
0.02 N/m with almost no change with temperature and composition. These
data permit to choose density values between conflictive results [2,3].
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  [3] Mori K., Suzuki K. Trans. ISIJ 8 (1968) 382.
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Density and Surface Tension of Liquid Iron Oxides
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[19] Glorieux B. Thèse University of Orléans, (France) 2000.
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