Surface Tensions of Fe–(30–40Mol%) Si–C Alloys at 1523–1773K

Surface Tensions of Fe(3040 mol%)SiC Alloys at 15231723 K

Takeshi Yoshikawa

Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan

To analyze the Marangoni effect on fluid flow in an FeSi solution during solution growth of SiC, knowledge of the temperature coefficient of surface tension of the solution is essential. In this investigation, the surface tensions of Fe(3040 mol%) Si alloys and alloys with added carbon were measured at 15231723 K by the maximum bubble pressure method. Surface tensions and temperature coefficients were precisely determined. The measured surface tensions were also compared with estimations based on the modified Butler’s model, and the effect of carbon on the surface tension of FeSiC alloys was assessed. [doi:10.2320/matertrans.M2013211]

(Received June 4, 2013; Accepted July 23, 2013; Published September 6, 2013) Keywords: ironsilicon alloy, surface tension, Marangoni effect, surface active effect, modiﬁed Butler’s model

1. Introduction heating.9) A remarkable SiC grown ridge on the seed crystal was observed at the edge of the area that was in contact with Silicon carbide (SiC) is a wide band gap semiconductor, the cylindrical liquid bridge. However, the growth was and is a promising base material for high temperature insignificant in interior regions. Because the growth of the electronics and high-voltage power devices because of its low ridge became larger with larger temperature gradients, the on-resistance and high electrical breakdown field. Physical Marangoni effect might affect the convection around the vapor transport (PVT), based on the sublimation of SiC meniscus of the liquid bridge. powder, is the standard method to produce SiC single To analyze the Marangoni effect on the fluid flow of the crystals. However, this process requires temperatures above solution during the solution growth process, it is essential to 2200 K, resulting in high costs and an inadequate quality of know the temperature and composition dependence of the the grown crystals. surface tension of the FeSiC alloy. The surface tension of Recently, solution growth has been identified as a more binary FeSi1014) and FeC13,1519) alloys has been inves- promising process for producing high quality SiC crystals tigated by many researchers. However, studies on the surface with a smaller dislocation density because the solidliquid tension of FeSiC alloys have been limited and the reported interface is close to the equilibrium state during growth. data are controversial. Belton20) used the sessile drop method Earlier work using solution growth with Si-based solvents, to measure the surface tension of FeSiC alloys with such as SiGe or SiAl solvents, clarified the epitaxial varying Si content (28 mol%) and with a constant C content growth,1,2) but growth rates did not exceed 10 µm/h. The of 12 mol% at 1723 K. He found that increasing the Si growth kinetics of solution growth of SiC was thus regarded content remarkably decreased the surface tension. He to be far slower than conventional sublimation processes in suggested that the decrease was caused by the surface-active which the growth rate is generally larger than 500 µm/h. effect of the associative adsorption of SiC. Kawai et al.13) However, the growth rate was improved by selecting suitable used the sessile drop method to measure the surface tension solvents for carbon solubility, and a growth rate of over of an Fe(110 mol%)Si(13 mol%) C alloy at 1673 100 µm/h was achieved at temperatures above 2000 K using 1923 K, and found its maximum value to be 2 mol% Si at SiTi3,4) and SiCr5,6) solvents by the top-seed growth constant C content. They also found a positive temperature method. dependence for the surface tension of the Fe50 mol% Si The author’s group has attempted to achieve rapid solution alloy, which is anomalous for the endothermic mixing alloy. growth at lower temperature using an FeSi solvent. We have If Belton’s suggestion that the remarkable change in the investigated the phase relation of the FeSiC system, as well surface tension is attributed to SiC adsorption is valid, solutal as the solubility of SiC in the liquid phase, to clarify an Marangoni effect besides thermal effect can affect the fluid optimal solvent composition for rapid SiC growth.7) Fe(35 flow in SiC solution growth conditions. 40 mol%) Si alloy was suitable as a solvent because its SiC In previous studies, Fe(3040 mol%) Si alloys were used solubility was over 100 times greater than that of Si-based as solvent alloys for the solution growth of SiC.8,9) In the alloys or molten silicon. The solution growth was carried out present work, the surface tension of these alloys and those at 16231723 K by a temperature difference method using the with added carbon were measured at 15231723 K by liquid bridge of the FeSi solvent under induction heating.8) maximum bubble pressure method. The estimation was also Because homo-epitaxial growth of 4H- and 6H-SiC was conducted based on Butler’s model.2123) The effect of achieved at a rate of 100200 µm/h, the FeSi solvent was temperature and composition change on the surface tension determined as effective for solution growth. To evaluate the was discussed. diffusion control growth, the solution growth was conducted at 1623 K by the temperature difference method in conditions 2. Alloy Composition designed to suppress natural convection under resistance Fe(3040 mol%) Si alloy was selected as a target alloy +Corresponding author, E-mail: [email protected] composition. The author’s group7) investigated the phase Surface Tensions of Fe(3040 mol%)SiC Alloys at 15231723 K 1969

Table 1 Thermodynamic parameters describing the excess properties of the liquid phase for each binary in the FeSiC system.

Ex Excess Gibbs energy; ¦G = XFeXSiLFeSi,liq + XFeXCLFeC,liq + XSiXCLSiC,liq ¹1 Li-j,liq/J·mol Reference 2 3 LFeSi,liq = ¹151128 + 29.125T + (¹33882 ¹ 2.5015T)(XFe ¹ XSi) + (33954 ¹ 11.256T)(XFe ¹ XSi) + (21289 ¹ 0.8650T)(XFe ¹ XSi) 24) 2 LFeC,liq = ¹124320 + 28.500T + (¹19300)(XFe ¹ XC) + (49260 ¹ 19.000T)(XFe ¹ XC) 25)

LSiC,liq = 8700 7)

3.5 3.0 Fe-30mol%Si 2.5 (graphite satd.) Fe-37.5mol%Si 2.0 (SiC satd.)

Mol% C 1.5 Fe-35mol%Si 1.0 (SiC satd.) 0.5 Fe-40mol%Si (SiC satd.) 0 1473 1573 1673 1773 Temperature, T / K

Fig. 1 Estimated solubility of carbon in liquid FeSi alloys saturated with graphite or SiC.

relationship of the FeSiC system at 15231723 K. Graphite or SiC was determined to be in equilibrium with the Fe Si- Fig. 2 Experimental apparatus for the maximum bubble pressure method. based liquid at Si contents smaller or larger than 35 mol%, respectively. The liquid composition determined by experimental data was found to agree with estimations by The furnace was then heated under a H2 gas flow (5 sccm). thermodynamic calculation using the thermodynamic proper- To eliminate the oxygen contamination into the sample, 24) 25) ties of the liquid phase in the binary FeSi, FeC and high purity H2 gas (dew point <¹203 K) was employed and SiC7) systems. passed through silica gel and magnesium perchlorate, sponge For the surface tension measurements of FeSiC alloys titanium heated at 1073 K to remove H2O and oxygen before in the present work, the liquid alloy was saturated with supply to the sample. graphite (Fe30 mol% Si) or SiC (Fe35, 37.5, 40 mol% Si). Measurements were performed after maintaining the target The equilibrium carbon concentrations of the alloys were temperature for more than 0.5 h for FeSi alloys and 1 h for estimated for the respective alloys by thermodynamic FeSiC alloys. First, the position of the melt surface was 7) analysis as described in previous work using the thermo- determined from the pressure change in the Al2O3 capillary dynamic properties listed in Table 1. The calculations as it was lowered at a rate of 0.01 mm/s into the surface. were conducted using a thermodynamic software package The immersion depth of the capillary tip was then controlled (FactSage 6.3). to within 212 mm, and the maximum bubble pressure Figure 1 shows the calculated result of the temperature was measured. The alumina capillary was prepared from dependence of carbon content of the FeSi alloys with an alumina pipe (O.D. 2.0 mm, I.D. 1.5 mm; Degussit) by varying Si content. The carbon content is largest for the polishing and finishing its tip to a sharp edge (3045°) with Fe30 mol% Si alloy, determined as 3.5 mol% at 1723 K. emery paper (#2000). The diameter of the tip was determined by an optical microscope, and the measurement error was 3. Experimental within 10 µm. The motion of the capillary was controlled with an electric actuator (ELS-4; Oriental Motor Co., Ltd.). Surface tension measurements of FeSi alloys and FeSi The pressure in the capillary was measured using a differ- C alloys were carried out using the SiC electric resistance ential pressure transmitters (FKCS22V5; Fuji Electric furnace (Fig. 2). A total of 3040 grams of electric iron Systems Co., Ltd.) calibrated with a water manometer. (99.992% purity, oxygen content; ³60 ppmw, sulfur content; When the capillary is immersed to a depth h (m) in the <5 ppmw) and semiconductor grade silicon (11N purity) liquid and a gas bubble is generated, the pressure difference were charged in an alumina crucible (I.D. 26 mm). To prepare between the inside and outside of the capillary, Ph (Pa), is the FeSiC alloys, a piece of high quality graphite (4N8 caused by the Laplace pressure, "P, as well as the liquid purity) or sintered SiC (99% purity) were placed at the density, as given in the following equation; bottom in the crucible. The reaction tube was evacuated by a P ¼ P þ µgh ð1Þ rotary vacuum pump and fulfilled with purified argon gas. h 1970 T. Yoshikawa

Table 2 Uncertainty of the surface tension measurements.

Uncertainty Equipment specification Relative standard uncertainty Factor pffiffiffi for measurement ð= 3Þ on surface tension Capillary tip diameter 0.0072 mm 0.45% Pressure measurement 6.7 Pa 6.9 Pa 0.30% Surface position 0.042 mm 0.012 mm 0.081% Immersion depth ® 0.012 mm 0.022% Combined relative standard uncertainty 0.55% Expanded relative standard uncertainty 1.1% (coverage factor, k = 2)

4800

/ Pa 7 P 4600

-3 6 4400

/ g·cm 5 4200 d Gertman, 1773K 4000 4 Dzhemilev, 1823K

Density, Density, Kawai, 1723K Dumay, 1723K

Maximum bubble pressure, Maximum bubble 3800 3 0 2 4 6 8 10 12 Present work, 1523 - 1723K Capillary immersion depth, h / mm 0 20 40 60 80 100 Fig. 3 Maximum bubble pressure against capillary immersion depth (Fe Mol% Si 30 mol%Si, 1723 K). Fig. 4 Density of liquid FeSi alloy. where µ (kg/m3) is the density of the liquid. When the bubble has a truly spherical shape, the Laplace pressure, "P,is of the liquid. The surface tension was determined from the described as below. intercept (Laplace pressure) using the Schrödinger equation ’ 2· (eq. (4)) to correct for the deformation of the bubble s P ¼ ð2Þ hemispherical shape caused by the gravimetric effect.27) r rP 2 µgr 1 µgr 2 Here, · (N/m) is the surface tension of the liquid solution, £ ¼ 1 ð4Þ 2 3 P 6 P and r (m) is the curvature of the gas bubble. The pressure in the capillary reaches the maximum bubble pressure when Uncertainty in measuring the surface tension in the present the bubble has the smallest curvature, which is generally work is summarized in Table 2 along with uncertainties of obtained with a hemispherical bubble at the inner edge of elemental factors, which were evaluated by following “ISO the capillary tip for wetting conditions between the capillary Guide to the Expression of Uncertainty in Measurement”.28) and liquid, and at the outer edge for a non-wetting condition such as between alumina and an FeSi alloy. However, an 4. Results and Discussion unfavorable increase in bubble pressure was sometimes observed in the non-wetting condition, and was determined to 4.1 Surface tension of FeSi alloys be caused by the metastable bubble formation at the inner Experimental data of the surface tensions and densities of edge of the capillary tip followed by its rapid shift to the the FeSi alloys are summarized in Table 3. The densities outer diameter.26) The capillary tip was prepared to be a sharp of FeSi alloys measured at 15231723 K are plotted edge, and the curvature was determined at a tip radius. against alloy composition in Fig. 4 along with the reported Figure 3 shows an example of the measured maximum data.13,2931) All of the experimental values exhibit positive bubble pressure against the capillary immersion depth, where deviation from the broken curve expected with ideal mixing, it was corrected from the displacement controlled by the which can be explained by the attractive interactions between actuator, hA, using the following equation, considering the Fe and Si in the alloy. The present data agree fairly well with excluded volume of liquid by the capillary. data from Kawai et al.,13) Dzhemilev et al.30) and Dumay and 31) 0 Cramb. h R2 h ¼ ð3Þ The measured surface tensions of the FeSi alloys are R2 r 2 o shown against alloy composition in Fig. 5 along with the 1014) Here, R (m) and ro (m) are the inner radius of the crucible and literature data. The present data are higher than the outer radius of the capillary, respectively. The slope of the previously obtained results, even considering the difference regression line in Fig. 3 allows us to determine the density in measurement temperature. The measured data were then Surface Tensions of Fe(3040 mol%)SiC Alloys at 15231723 K 1971

Table 3 Experimental results for FeSi binary alloys.

Fe30 mol%Si (1) Fe30 mol%Si (2) Fe35 mol%Si (1) Fe35 mol%Si (2) Fe37.5 mol%Si Fe40 mol%Si (1) Fe40 mol%Si (2) T/K £/ d/ £/ d/ £/ d/ £/ d/ £/ d/ T/K £/ d/ £/ d/ mN·m¹1 g·m¹3 mN·m¹1 g·m¹3 mN·m¹1 g·m¹3 mN·m¹1 g·m¹3 mN·m¹1 g·m¹3 mN·m¹1 g·m¹3 mN·m¹1 g·m¹3 1523 1625 6.086 1628 6.086 1553 5.935 1573 1624 6.122 1616 6.032 1537 5.979 1559 5.958 1493 5.970 1598 1409 5.747 1428 5.764 1623 1605 6.021 1602 6.052 1526 5.868 1530 5.977 1475 5.873 1623 1410 5.704 1414 5.799 1673 1570 6.031 1586 5.988 1506 5.961 1501 5.878 1457 5.937 1673 1396 5.783 1402 5.767 1723 1552 5.988 1565 6.031 1489 5.939 1486 5.869 1450 5.904 1723 1392 5.644 1407 5.671 d£/dT ¹0.402 ¹0.310 ¹0.319 ¹0.497 ¹0.296 ¹0.159 ¹0.162

Table 4 Surface tensions and densities of pure iron and silicon.

Element Surface tension, £/mN·m¹1 Density, d/g·cm¹3 32) ¹3 33) Fe £Fe = 1925 ¹ 0.455(T ¹ 1808) µFe = 7.035 0.926 © 10 (T ¹ 1811) 34) ¹3 35) Si £Si = 732 ¹ 0.086 (T ¹ 1685) µSi = 2.510 0.271 © 10 (T ¹ 1687)

compared with the semi-empirical theory based on Butler’s 2000 model21,22) with the modiﬁcation by Tanaka et al.23) In this -1 Estimation m

· model, the surface tension of the AB binary alloy is 1800 1523 K described by the following equation, which indicates the 1723 K

/ mN 1600 equality of the chemical potentials of the components γ between the surface monolayer phase and bulk phase; 1400 surface RT 1 X 1 Popel, 1823 K £ ¼ £ þ ln B þ ðG Ex,surface G Ex,bulkÞ 1200 A S 1 Xbulk S A A Levin, 1823 K A B A Ixanov, 1823 K 1000 RT Xsurface Kawai, 1773 K ¼ £ þ B þ 1 ð Ex,surface Ex,bulkÞ ð Þ B ln G G ; 5 Brooks, 1823 K bulk B B tension, Surface SB XB SB 800 Presentwork, 1523 - 1723K £ where i and Si are the surface tension and molar surface area 0 20 40 60 80 100 surface bulk of pure liquid i, respectively. Xi and Xi are mole Mol%Si fractions of component i in the surface and bulk phases, Ex,surface Ex,bulk Fig. 5 Composition dependence of surface tension of liquid FeSi alloys. respectively. Gi and Gi are excess partial molar Gibbs energy of i in the surface and bulk phases, respectively. Molar surface area is calculated from the molar volume of i, Vi, as given in eq. (6). active effects of contaminated oxygen and sulfur, as pointed out by Keene.36) In the present work, the oxygen and S ¼ 1:091N 1=3V 2=3 ð6Þ i AV i sulfur contents of selected samples were analyzed after NAV is Avogadro’s constant. Excess partial molar Gibbs the experiment, and respective maximum values of 5 and energy of i in the surface monolayer was suggested as 7 ppmw were found. Their effects were thus assumed to be described by the following equation,23) which was derived by negligible, considering their effects on surface tension of the coordination number of the surface atoms. iron alloys.3740) In addition, the weight loss of the alloy was Zsurface less than 0.2 g so that the change in the matrix composition G Ex,surfaceðT;XsurfaceÞ¼ G Ex,bulkðT;XsurfaceÞ was insignificant. B B Zbulk B B Figure 6 shows the temperature dependence of the ¼ : G Ex,bulkðT;XsurfaceÞðÞ 0 83 B B 7 measured surface tension. All the alloys showed a negative Solving eq. (5) by substituting the excess Gibbs energy of temperature dependence to the surface tension. Kawai FeSi alloys in Table 1 and the physical properties listed in et al.13) reported a positive temperature coefficient for certain Table 4,3235) the surface tension and the surface concen- compositions of the FeSi alloy (Fe50 mol%Si alloy), but tration can be calculated as a function of alloy composition. such tendencies were not noted here. The experimental data In Fig. 5, the estimated composition dependence of the agree well with the broken lines in Fig. 6, which were surface tension at 1523 and 1723 K are shown as broken estimated using eq. (5), although it was found that the and dashed curves, respectively. As most of present data experimental data tended to be slightly larger than the measured at 15231723 K range within the two estimated estimation. Accordingly, the surface tension of the binary curves, they are reproduced fairly well using the modified Fe(3040 mol%) Si alloys were determined precisely in the Butler’s model. Hence, earlier data are speculated to include present work, and were found to exhibit a negative temper- some experimental errors, presumably caused by surface ature coefficient. 1972 T. Yoshikawa

1650 1650 -1 -1 m

· 1600 1600 30%Si / mN γ 1550 / mN·m 1550 γ 35%Si 1500 1500 37.5%Si 1450 30%Si 1450 30mol%Si 35%Si 35mol%Si 40%Si 1400 37.5%Si 37.5mol%Si 1400 40mol%Si 40%Si Surface tension, Surface

Surface tension, Surface Estimation for ternary 1350 Estimation 1350 Estimation for binary 1523 1573 1623 1673 1723 1523 1573 1623 1673 1723 Temperature, T / K Temperature, T / K Fig. 6 Temperature dependence of surface tension of liquid Fe30 Fig. 7 Temperature dependence of surface tension of liquid Fe30 40 mol%Si alloys. 40 mol%Si alloys saturated with graphite or SiC. Large white marks are the values determined for ternary alloys and small black marks are the values for binary alloys in Fig. 6.

Table 5 Experimental results for FeSiC ternary alloys.

Fe35 mol%SiSiC Fe35 mol%SiSiC Fe40 mol%SiSiC Fe40 mol%SiSiC Fe30 mol%SiC Fe37.5 mol%SiSiC (1) (2) (1) (2) T/K T/K £/ d/ £/ d/ £/ d/ £/ d/ £/ d/ £/ d/ mN·m¹1 g·cm¹3 mN·m¹1 g·cm¹3 mN·m¹1 g·cm¹3 mN·m¹1 g·cm¹3 mN·m¹1 g·cm¹3 mN·m¹1 g·cm¹3 1523 1624 6.105 1540 5.912 1548 5.967 1573 1616 5.989 1514 5.818 1500 5.844 1478 5.847 1598 1433 5.711 1623 1594 5.956 1475 5.703 1504 5.889 1450 5.837 1623 1414 5.695 1421 5.763 1673 1576 5.919 1452 5.856 1476 5.841 1444 5.846 1673 1365 5.649 1396 5.711 1523 1542 5.902 1434 5.712 1469 5.822 1417 5.844 1723 1364 5.611 1378 5.767 d£/dT ¹0.409 ¹0.548 ¹0.365 ¹0.378 ¹0.592 ¹0.426

4.2 Surface tension of FeSiC alloys in the system, as shown in eq. (5), the surface tension of Experimental data of the surface tensions and densities of “pure liquid carbon”, £C, is not available. Additionally, the FeSiC alloys are summarized in Table 5. The densities of chemical state of carbon at the melt surface has not yet been the FeSiC alloys are similar to those of the binary FeSi proven. Keene36) summarized the surface tension of FeC alloys in Table 3. alloys and suggested that it decreased with increasing carbon The surface tensions of the FeSiC alloys are plotted in content. However, Jimbo and Cramb18) measured the carbon Fig. 7 along with the binary data (as small black marks). All effect on the surface tension of iron in a controlled CO/CO2 of the FeSiC alloys showed negative temperature de- atmosphere and found that it had a tendency to increase with pendence. The surface tension of the Fe30 mol% SiC alloy increasing carbon content. They mentioned that the decrease was comparable to that of the Fe30 mol% Si binary alloy. in surface tension with the addition of carbon in other The Fe(35, 37.5, 40 mol%)SiC alloys showed slightly works might be caused by sulfur contamination, as there is a lower values than did their corresponding binary alloys. strong increasing effect of carbon on sulfur activity. Lee and Belton20) suggested a significant decrease in surface tension Morita19) also suggested an increase in surface tension of Fe owing to the surface active effect by associative “SiC” C alloys with increased carbon content. Kojima and Susa41) formation at the melt surface. However, it was not observed conducted a molecular dynamics simulation of the surface in this study. The following discussion is given without melting of an FeC alloy. They found that the temperature of taking into account any of the surface active effects on the the surface melting decreased by increasing the total carbon present alloy system. content. However, there were no C atoms present on the Because the modified Butler’s model reproduces the outer-most monolayer of the melting surface phase. From measured surface tension of the FeSi binary alloys, as these previous studies, it can be considered that carbon does shown in Fig. 6, estimations of the surface tension of the Fe not segregate at the alloy surface, resulting in insignificant SiC ternary alloys were also carried out using this model. surface active effects. Therefore, the following assumptions It is possible in principal to extend the model to the ternary have been made to estimate the surface tension of FeSiC system, but dealing with the added carbon remains an issue. alloys; (1) carbon cannot exist at the surface monolayer Although the surface tension can be derived through the phase, (2) the excess Gibbs energy of the surface is the same equalities in chemical potentials for all components contained as the binary FeSi alloy without any contributions from Surface Tensions of Fe(3040 mol%)SiC Alloys at 15231723 K 1973

carbon. The surface tension of the FeSiC alloys were then method. An estimation of the surface tension was also estimated by using the bulk composition (Fig. 1), the excess conducted based on the modified Butler’s model. The Gibbs energy of the FeSiC alloy in Table 1 and the following results were obtained. physical properties in Table 4. (1) Surface tensions of FeSi binary alloys were precisely Estimated results are shown as dashed curves in Fig. 7 determined and were larger than previously reported and reproduce the measured values fairly well. When the values. The measured values were reproduced well estimated curves are compared between binary and ternary using the modified Butler’s model. alloys, the curves for 30% Si are comparable. Curves for (2) Measured surface tensions of the FeSiC alloys were ternary alloys of 35, 37.5 and 40 mol% Si are located lower comparable with FeSi binary alloys at graphite than those for their corresponding binary alloys, and the saturation and were smaller at SiC saturation. The differences become larger with increased temperature. In the estimation was conducted under the assumption ternary alloys of 35, 37.5 and 40 mol% Si, SiC dissolves into that no carbon existed at the melt surface and the alloy so that the content of silicon beside carbon is larger reproduced the experimental data well. It was thus than in the corresponding binary alloy. indicated that surface active effects of carbon or Consequently, the surface tension of the FeSiC alloy associative SiC were negligible for FeSiC alloys. was acceptably reproduced by the estimation, with the (3) Temperature coefficients of the surface tension of assumption that no carbon exists at the melt surface, FeSiC alloys were determined, which suggest the indicating a negligible surface active effect of carbon or significance of the Marangoni effect on the fluid flow of associative SiC on the FeSiC alloy. The lower surface an FeSi based solution during the solution growth of tension of the ternary alloy compared with the binary alloy is SiC. presumably caused by the change in silicon content owing to the dissolution of SiC into the alloy. Acknowledgement

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