Regular Article
Viscosity of Molten Fe–B Alloy
2015 Volume 55 Issue 3 Pages 500-503
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2015 Volume 55 Issue 3 Pages 500-503
The viscosities of molten Fe–B alloys (Fe–12.5, 25, 37.5 mol% B alloy) were measured by using an oscillating viscometer. The viscosity measurements were carried out using 99.5% alumina crucible up to about 1873 K from the liquids temperatures. The viscosities of all alloys were higher than that of pure iron, and the obtained results showed very good Arrhenius type linearity, which indicates that no considerable change of liquid structure exists in each system at the temperatures studied. The viscosity and the activation energy for viscous flow of Fe–B alloy increased monotonously with increasing boron content, which also showed that there is no considerable change in the liquid structure and the mechanism of viscous flow. The viscosity of molten Fe–C alloy previously measured by the authors slightly decreased with increasing carbon content, which was totally different with the behavior of viscosity of Fe–B alloy. It was expected that the interatomic attracting force between the iron and boron was larger than that of iron and carbon because the free energies of formation of Fe2B and FeB in Fe–B system are larger than that of Fe3C in Fe–C system.
An iron-based alloy is one of the most important industrial material. However, the reported viscosities of molten iron alloys are significantly different due to the difficulty on the measurement of thermophysical properties of high temperature melts. Therefore, the reliability of the viscosities was low. Based on the background, one of the authors systematically measured the viscosities of molten iron group elements and their alloy with high reliability.1) It was also revealed that carbon of nonmetallic elements does not give significant influence on the viscosity of Fe–C melt.2) The viscosities of molten Fe–B alloys were measured in order to investigate the effect of boron as a light element to the viscosity of molten iron-based alloy in this study.
Ferro boron is industrially used as a boron source for magnet materials and others. The materials are usually processed through a casting, and it is important for obtaining high performance to control the metallic structure after solidification. The viscosity measurement of molten Fe–B alloy is also important from the practical viewpoints because the viscous flow of melts give strong influence on the solidification process. For instance, in a mold casting, if melts do not keep sufficiently low viscosity, solidification progresses before the melts spread to entire mold.3)
The viscosities of the melts in iron rich side were measured by using an oscillating viscometer, and behavior of viscous flow of the melts was investigated. Differences between the systems of Fe–B and Fe–C were also discussed.
Fe–B alloys were prepared in a calcia crucible by an induction melting of an electrolytic iron (> 99.9%) and a pure boron (> 99.5%) under vacuum. The compositions were Fe–12.5 mol% B, Fe–25 mol%B and Fe–37.5 mol% B. The representative phase diagram of Fe–B system is shown in Fig. 1.4) The sample compositions and measurement temperature range are also indicated in the figure.
Phase diagram for the Fe–B system4) and compositions and temperature region for the viscosity measurement. Full lines indicate phase boundaries calculated from interstitial model, and dashed lines indicate those calculated from substitutional model.
The oscillating crucible method was used in this study. The method is most suitable for high temperature molten metals due to the high precision in low viscosity range and the flexibility in the choice of container material used in the apparatus. Since the principle of measurement and the experimental apparatus have been described in detail in the previous article,5) the important points are described below.
A crucible containing molten alloy sample is suspended, and a rotational oscillation is given to the crucible electromagnetically. The oscillation was damped due to the internal friction of molten alloy. Viscosity is determined from the factors such as the period of oscillation and the logarithmic decrement. The crucible was connected to a mirror block and an inertia disk made of aluminum, and whole of them was suspended by a thin wire made of platinum-13% rhodium alloy. A laser light is irradiated to the mirror. The reflection light is detected by the photo-detectors, and the logarithmic decrement is determined.
A furnace which consists of stacked three spiral MoSi2 heaters controlled independently was used. To minimize the thermal radiation vertically, about 20 thermal reflective protection plates made of tungsten were placed in an outer alumina tube. As a result, excellent temperature uniformity within 0.5 K around whole length of the crucible was achieved. Helium with low viscosity was introduced into the apparatus. Zirconium sponge as an oxygen absorber was placed just under the crucible in order to remove the oxygen in the atmosphere. A crucible made of 99.5% alumina was used. Determination of the moment of inertia of suspended system and logarithmic decrement for empty crucible was carried out at room temperature and high temperature in advance. Temperature dependences of a logarithmic decrement and a moment of inertia were measured to use for the calculation of viscosity.
The alloy samples were melted at higher temperature over liquidus, and the viscosity measurement was conducted in heating process. After the measurement at highest temperature around 1873 K, the viscosity measurement was continued in cooling process. The measurement was continued even under the liquidus temperature until solidification was confirmed because supercooling is observed in cooling process in most cases. The density measured by Ostrovskii was used for the viscosity calculation.6) After the experiment, Fe–B alloy samples were easily detached from the alumina crucible. There is no form change such as flaking and deformation on the inner wall of the crucible. Namely, it was considered that there was no reaction between Fe–B alloy melts and the alumina crucible.
The viscosities measured are tabulated in Table 1. The order of the data is the order of measurement. The temperature range, the lines determined by a least-square method, and the activation energy for viscous flow are summarized in Table 2. The viscosities are also plotted in Fig. 2. The viscosity of pure iron reported by one of the authors1,7) was also shown in the figure. The data obtained were in good agreement in both heating and cooling processes and the plotted points in both runs were not distinguished in the figure. The viscosities of molten Fe–B alloys are higher than that of molten pure iron. All data showed good Arrhenius type linearity, which indicates that change of mechanism of viscous flow does not occur in the temperature region in this study. Ladyanov et al. measured the viscosities of molten Fe–B alloys using the oscillating viscometer and reported distinct ramifications on viscosities between heating and cooling processes, then they called the phenomenon viscosity hysteresis.8) However, no rational basis was found for the anomalous phenomenon of viscosity and such a phenomenon was not observed in this study as mentioned above.
| Fe–12.5 mol% B | Fe–25 mol% B | Fe–37.5 mol% B | |||
|---|---|---|---|---|---|
| Temperature, T/K | Viscosity, η/mPa·s | Temperature, T/K | Viscosity, η/mPa·s | Temperature, T/K | Viscosity, η/mPa·s |
| 1570.1 | 12.652 | 1698.1 | 10.696 | 1718.8 | 12.230 |
| 1610.8 | 11.185 | 1744.9 | 9.344 | 1751.0 | 11.009 |
| 1648.3 | 10.053 | 1789.9 | 8.308 | 1813.9 | 8.408 |
| 1689.2 | 9.065 | 1832.5 | 7.510 | 1846.7 | 7.661 |
| 1731.6 | 8.205 | 1873.4 | 6.869 | 1876.5 | 7.135 |
| 1792.8 | 7.203 | 1854.6 | 7.166 | 1862.9 | 7.484 |
| 1774.6 | 7.502 | 1815.5 | 7.842 | 1833.2 | 8.071 |
| 1813.2 | 6.907 | 1777.1 | 8.617 | 1803.1 | 8.846 |
| 1854.6 | 6.386 | 1755.9 | 9.108 | 1772.7 | 9.700 |
| 1875.8 | 6.170 | 1726.5 | 9.909 | 1742.2 | 10.746 |
| 1837.2 | 6.639 | 1674.2 | 11.580 | 1709.4 | 12.693 |
| 1735.2 | 8.173 | 1654.0 | 12.461 | 1752.8 | 10.887 |
| 1755.6 | 7.805 | 1632.9 | 13.540 | 1787.6 | 9.241 |
| 1712.3 | 8.653 | 1611.9 | 14.779 | 1825.5 | 8.280 |
| 1673.9 | 9.406 | 1590.6 | 16.180 | 1846.0 | 7.929 |
| 1632.7 | 10.525 | 1817.2 | 8.542 | ||
| 1590.3 | 11.848 | 1781.6 | 9.546 | ||
| 1549.7 | 13.508 | 1765.8 | 10.015 | ||
| 1755.0 | 10.316 | ||||
| 1734.3 | 11.118 | ||||
| 1723.8 | 11.477 | ||||
| 1713.5 | 12.086 | ||||
| Sample | Temperature range measured, T/K | Viscosity of melts, log (η / mPa·s) = a + b/T | log (η / mPa·s) at 1873 K | Activation energy, E/kJ·mol–1 | |
|---|---|---|---|---|---|
| a | b | ||||
| Fe–12.5 mol% B | 1550–1876 | –0.826 | 3020 | 6.116 | 57.8 |
| Fe–25 mol% B | 1591–1873 | –1.239 | 3870 | 6.711 | 74.0 |
| Fe–37.5 mol% B | 1714–1877 | –1.630 | 4651 | 7.141 | 88.9 |
Viscosities of molten Fe–B alloys.
The composition dependence of viscosities at 1723 to 1873 K, calculated from the regression lines, is shown in Fig. 3. The viscosities increase with an increase of boron concentration almost linearly. At higher temperature, increment of viscosity is getting decrease with increasing boron concentration. It may be due to the weaking of Fe–B bond in the melt.
Isothermal viscosities of molten Fe–B alloys.
The composition dependency of viscosities at 1773 K is shown in Fig. 4 with literature values.9,10) Ladyanov et al. measured the viscosities using an oscillating viscometer,9) but systematic trend is not observed, and the scatter of plots is large. Tomut et al. also measured the viscosities using an oscillating viscometer,10) but change on viscosity is significantly large. The viscosities measured in this study shows systematic trend compared with the literature values and is considered to be more reliable. It is also considered that the most effective measurement factor is temperature homogeneity around whole length of the crucible because excellent temperature homogeneity suppresses the convection of melts disturbing normal flow of melts in oscillation movement.
The activation energy for the viscous flow of molten Fe–B alloys calculated from the Arrhenius plot is shown in Fig. 5. The activation energy linearly increases with an increase of boron concentration in the composition range in this study. This indicates that the bond between iron and boron is relatively strong.
Activation energy for the viscous flow of molten Fe–B alloys.
A comparison on composition dependency of viscosities of Fe–B and Fe–C systems at 1873 K is shown in Fig. 6. The viscosity of molten Fe–B alloy increases with an increase of boron concentration, but the viscosity of molten Fe–C alloy slightly decreases with an increase of carbon concentration. Namely, the effect of boron and carbon on the viscosity is different although the cause is not clear, but it may be because of difference on the style of alloy formation with iron. Carbon forms a solid solution (γ phase, solubility of C at 1400 K is 8 mol%) as an interstitial atom in iron lattice in wide composition range on the phase diagram.11) On the other hand, the solubility of boron into iron is significantly small (solubility of B at 1400 K is 0.02 mol%). It means that boron does not form solid solution as an interstitial atom with iron.4) Cementite (Fe3C) equilibrating with Fe (γ) is a metastable phase, but Fe2B and FeB as stable intermetallic compounds exist in Fe–B system. Although the relationship between thermodynamic quantities and viscosity is not fully revealed theoretically, Seetharaman et al. reported that there would be a relationship between Gibbs energy and viscosity in metallic melts comprised of simple bonds.12) Standard Gibbs free energy changes of formation of Fe2B (–69.5 kJ·mol–1 at 298 K) and FeB (–70.0 kJ·mol–1 at 298 K) are significantly lower than that of Fe3C (+20.0 kJ·mol–1 at 298 K),13) which indicates that the bond between iron and boron is significantly stronger than the bond between iron and carbon. Molar volumes of molten iron alloy decrease with the addition of boron or carbon because atomic sizes of light elements are small compared to that of iron.2,7) Consequently, the viscosity of Fe–B system may be increased because the resistance to shear stress in liquid increased by the strong attracting force between the iron and boron.
Viscosities of molten Fe–B alloy and Fe–C alloy2) at 1873 K.
The viscosities of molten Fe–B alloy (Fe–12.5, 25, 37.5 mol% B alloy) were measured using the oscillating viscometer in order to investigate the effect of boron as a light element to the viscosity of molten iron-based alloy in this study. The viscosities of all alloy compositions were higher than that of pure iron, and the obtained results showed very good Arrhenius type linearity, which indicates that no considerable change of liquid structure exists in each system at the temperatures studied. The viscosity and activation energy for the viscous flow of Fe–B alloy increased monotonously with increasing boron content. The viscosity of molten Fe–C alloy previously measured by the authors was compared to the behavior of viscosity of Fe–B alloy.
