The B-rich side of the B–C phase diagram

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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The B-rich side of the B–C phase diagram Peter F. Rogl a,n, Jan Vrestal b, Takaho Tanaka c, Satoshi Takenouchi d a

Institute of Physical Chemistry, University of Vienna, Währingerstr. 42; A-1090 Wien, Austria Masaryk University, CEITEC, Kamenice 753/5, Brno, Czech Republic Scientific Information Office, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan d Technical Support Section, National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan b c

art ic l e i nf o

Keywords: Beta boron (ßB) peritectic melting Floating zone method B–C phase diagram modeling Ternary metal–boron–carbon systems

a b s t r a c t The melting behavior of ß-boron at the boron-rich side of the B–C binary phase diagram is a long standing question whether eutectic or peritectic. Floating zone experiments have been employed to determine the melting type on a series of C-containing feed-rods prepared by powder metallurgy and sinter techniques. Melting point data as a function of carbon-content clearly yielded a peritectic reaction isotherm: L+B4+δC ¼(ßB). The partition coefficient of carbon is  2.6. The experimental melting point data were used to improve the existing thermodynamic modeling of the system B–C. Relative to the thermodynamically accepted melting point of pure ßB (TM ¼2075 1C), the calculated reaction isotherm is determined at 2100.6 1C, a peritectic point at 0.75 at% C and a maximum solid solubility of 1.43 at% C in (ßB) at reaction temperature. With the new melting data the refractory system Hf–B–C has been recalculated and the liquidus surface is presented. The influence of the melting behavior of (ßB) on the phase reactions in the B-rich corner of M–B–C diagrams will be discussed and demonstrated in case of the Ti–B–C system. & 2013 Elsevier Ltd. All rights reserved.

1. Introduction Liquidus and solidus lines in the boron-rich part of the B–C phase diagram are by far not well determined. Several versions of the phase diagram exist, which all differ in the number and formation of binary phases and particularly in the melting behavior of the boron-rich corner. Whilst the early diagrams of Samsonov and coworkers [1,2] and even later those of Ekbom [3] include various variants of the B4+δC structure as individual compounds (see Fig. 1), later versions of Dolloff [4] and of Elliott and coworkers [5,6] concluded on a single intermediate phase B4+δC with a large but varying homogeneous region (see Figs. 1 and 2). Although compounds such as B13C2, B13C3, B51C, B48B2C2, B49C3 and B8C have been synthesized by CVD and have been characterized by single crystal X-ray structure analyses [7,8], more recent structural investigations of the B4+δC homogeneity region confirm the existence of only one intermediate phase to be stable in thermodynamic equilibrium for the B–C binary system [9,10]. CVD-grown crystals of composition B2C and B12C to B17C have been obtained, but lack crystallographic analyses [11]. B–C phase diagrams with only one phase, B4+δC, exhibiting a large range of existence are known from the research groups of Thevenot and

n

Corresponding author. Tel.: +43 1 4277 52456; fax: +43 1 4277 9524. E-mail address: [email protected] (P.F. Rogl).

Bouchancourt [12–15], Beauvy [16], Gosset [17] and from Schwetz and Karduck [18] (see Fig. 2). Particularly the carbon-poor phase boundary of B4+δC was carefully investigated by Bouchancourt and Thevenot [12–15] relying on metallography, X-ray and electron probe micro-analyses (EPMA) and was located at 8.8 at% C with little variation in the temperature region from 1500 1C to about 2075 1C. Some controversy existed for the C-rich phase boundary of B4+δC, which was located at about 20 at% C [4–6,12–15], but was in a reinvestigation by Beauvy [16], via chemical analyses on commercially available B4+δC powder grades, located at 21.6 at% C at 1800 1C rising monotonously to 24.3 at% C at the eutectic B4 +δC+C (no detailed temperature given). The most reliable determination of the C-rich boundary by means of carefully calibrated EPMA on a B4+δC grain extending far into graphite was presented by Schwetz and Karduck [18] moving from 18.8 at% C at 1200 1C to 19.2 at% C at 2384 1C (eutectic B4+δC+C) and yielding 8.6 at% C for the B-rich boundary. The solubility of boron in graphite was determined from lattice parameter measurements to vary from 1 at% B at 1800 1C to 2.35 at% B at the temperature of 2350 1C near the eutectic B4+δC+C [19]. Despite most of these investigations contributed also to the knowledge of the liquidus in the B–C system, the large discrepancies concerning the liquidus data, as presented by various research groups [1,4–6,20], is obvious from Fig. 3. These differences essentially arose from the difficulties to handle the aggressive boron-rich melts in crucibles at high temperatures or to reach reliable temperature

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Please cite this article as: P.F. Rogl, et al., The B-rich side of the B–C phase diagram, Calphad (2013), http://dx.doi.org/10.1016/j. calphad.2013.07.016i

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Fig. 1. Various versions of the phase diagram for the system B–C according to Samsonov [1], Zhuravlev [2], Ekbom [3] and Dolloff [4].

Fig. 2. Various versions of the phase diagram for the system B–C according to Elliott [5], Bouchancourt [12–15], Beauvy [16] and Schwetz [18].

measurements on pyramidal sinter-cones or via direct heating of sintered semiconducting specimens employing the Pirani method. Although the pressure dependence of the melting point of boron carbide was determined for the range from 2.5 to 7.7 GPa and revealed a negative slope,  137 6 K/GPa, a melting point of 24507 50 1C was used as the most reliable value for binary boron

carbide [21]. Particularly the melting behavior of ß-boron at the boron-rich side of the B–C binary phase diagram has long been an un-clarified problem because of the difficulty to determine the narrow two-phase field between the liquidus and solidus curves. Therefore without detailed experimental verification some research groups favoured a boron rich eutectic (L¼ (ßB)+B4+δC

Please cite this article as: P.F. Rogl, et al., The B-rich side of the B–C phase diagram, Calphad (2013), http://dx.doi.org/10.1016/j. calphad.2013.07.016i

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[1,2,4]) whereas some others reported a depleted reaction [5,6,18,20]. Bouchancourt et al. mentioned that electron melting experiments of boron with C-impurities revealed a smaller C-content of the melt and therefore suggested [12–15] a peritectic reaction L+B4+δC2(ßB), which was also chosen in some other papers on the B–C phase diagram [3,16]. The latest B–C phase diagram compilation by Okamoto [22] adopted a eutectic melting behavior of ß-boron on the basis of the phase diagram presented by Dolloff [4]. The peritectic version of the B-rich liquidus, however, is backed by the experimentally determined solubility of 1 at% C at 1300 1C [23–25]. Although no clear experimental evidence was available in the literature, the demand for a thermodynamic description of the B–C system forced either the decision of a eutectic melting behavior (used by Lim and Lukas [26], and Duschanek et al. [27]) or a decision in favor of a peritectic reaction (used by Kasper [28] and Rogl and Bittermann [29,30]). Zone melting is a very convenient method for determining the relation between liquidus and solidus curves: in a zone melting crystal growth experiment the chemical composition of the quenched molten zone and that of the zone-end part crystal correspond to one set of data points on the liquidus curve and the solidus curve at the same temperature (crystal growth temperature), respectively. By repeating such experiments using raw rods having a different chemical composition one can determine the liquidus and solidus curves. This concept is schematically illustrated in Fig. 4. The aim of the present investigation is three-fold: (i) to determine the liquidus and solidus curves of ß-boron at the boron end side of the B–C phase diagram using the floating zone method, (ii) to introduce the new data into a renewed thermodynamic modeling of the B–C phase diagram, and (iii) to evaluate the influence of the binary reaction data on the phase relations in the very boron rich corner of the ternary systems M–B–C (see for instance the compilation by P. Rogl [30]). The present research is

T, °C 2500

2390°C

2400

2375°C

2300

2000

meant to support the recently revived interest in the unusual but outstanding high-temperature properties [31,32] and particularly the excellent high-temperature thermoelectric behavior of boroncarbide [33,34].

2. Experimental details The floating zone (FZ) technique employing a xenon lamp image furnace (Crystal Systems, Inc., Japan) was used for the zone melting of ß-boron because of unavailability of crucible materials that can contain the very reactive boron melt at approximately 2100 1C. Starting powders for FZ were amorphous boron (SB-Boron Inc., USA) and hydrocarbon. A desired small amount of carbon was added to the amorphous boron to form a FZ feed sintered rod that was heated at 1700 1C in a high frequency furnace with a graphite susceptor tube under vacuum for 1 h. After the molten zone was passed through the feed rod 4 times of the zone length the zone pass was quenched. To quench the molten zone the power supply of the xenon lamps was switched off, and the molten zone and the crystal were synchronously pulled away from the image focus point of the hot tungsten electrodes of the xenon lamps at a speed of  10 mm/s. The processing temperatures and cooling rates were measured by optical pyrometry with respect to careful calibration on metallic materials under RF-heating. From these measurements cooling rates of the molten zone are about  300 1C/s, and the temperature gradient along the growth direction just below the molten zone is about 100 1C/mm at  2000 1C. Although after a few seconds, the cooling rate has slowed down, the diffusion of B and C at the interface between the molten zone and the grown crystal should be small. The frozen molten zone and the zone-end part of the crystal obtained were cut by a spark erosion cutter. Both corresponding sample pieces were independently crushed to powders in a stainless-steel mortar and the stainless-steel contamination was extracted by a dilute HCl solution and rinsed. Carbon contents were determined by a volumetric combustion method using a carbon analyzer (WR-12, Leco Co., USA). Standard deviation of the chemical analysis was within 72%.

3. Results and discussion 3.1. Melting of C-added ß-boron from FZ -experiments

2200 2100

3

2150°C

2080°C 2075°C

1958 Samsonov 1960 Dolloff 1961 Elliott 1971 Kieffer

1900

0

10

20 at.% C 30

40

Fig. 3. Liquidus in the system B–C after various research groups.

Six data sets were obtained, which enabled us to depict liquidus and solidus curves of ß-boron at the boron end side of the B–C phase diagram as shown in Fig. 5, where the temperature scale is relative to the thermodynamically accepted melting point of pure ßB (TM ¼ 2075 1C [35]). The average partition coefficient of carbon is  2.6, i.e., the addition of a small amount of carbon to ßboron increases its melting temperature. Thus the present result clearly indicates that the melting behavior of ß-boron for carbon addition is not of eutectic but of peritectic nature.

Fig. 4. Schematic illustration of determining melting behavior by the zone melting method; right image shows molten zone and zone-end crystal in experiment.

Please cite this article as: P.F. Rogl, et al., The B-rich side of the B–C phase diagram, Calphad (2013), http://dx.doi.org/10.1016/j. calphad.2013.07.016i

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of B in graphite follows the substitutional model and data from Lowell [19]. The selection of experimental solidus and liquidus values (for the solidification of B4+δC and graphite but including the thermodynamically established melting point of B [35]) as well as the thermodynamic data for B4+δC remains unchanged since the first reliable calculation by Kasper [28] and by Bittermann [36], respectively. Table 1 summarizes the coefficients used for the new description of the phases and compares them with the values used by Kasper [28] and by Bittermann [36], respectively, in the previous versions of the B–C diagram calculations. Table 1 shows that on keeping a minimum number of variables the change of only two coefficients yields a quite satisfactory description of the liquidus and solidus for the (ßB) phase within the error bars of composition (70.3 at%) and temperature (7 20 1C) (see Fig.5).

3.2. Thermodynamic modeling of the B–C system Although the latest thermodynamic modeling of the B–C system by Bittermann [29,36] already assumed a peritectic melting behavior of (ßB), the new experimental data make a new modeling of the liquidus/solidus necessary. The modeling of this work thereby still relies on the description of the liquid via the Redlich–Kister–Muggianu formalism as adopted in the previous CALPHAD calculations [26–30,36] as well as on the Compound Energy Formalism (CEF) used for the description of the solid phases. As summarized in a recent review on ßB and B4+δC by Werheit et al. [37], we can still rely on the maximal carbon solubility of about 1 at% C at 1300 1C in ßB with C in the polar sites of the B12-octahedra, as well as on a substitutional model incorporating maximally one C-atom in B11C octahedra and three species, B2C, BC2, B□B (□ denotes a vacancy), competing for the chains linking the three-center bonds in B4+δC [25]. The solubility

3.3. Thermodynamic modeling of the Hf–B–C system Introducing the new B–C system into the modeling of the Hf–B–C system, as performed by Bittermann [36] (see also Refs. [29,30]), changes slightly the location of the transition reaction U1 (L+B4+δC2(ßB)+HfB2) nearest to the boron-rich corner of the diagram from 2364 K (¼ 2091 1C) [29,30,36] to 2362.65 K (¼2089.5 1C). The phase compositions can be read from the partial isothermal section given in Fig. 6. 3.4. Influence of the melting behavior of ßB on the phase equilibria in the B-rich corner of M–B–C systems In order to demonstrate the influence of the melting behavior in the binary B-C system on the constitution of the ternary M–B–C systems, we choose the Ti–B–C system. Considering the difficulties to handle melting point experiments with B-rich alloys, the melting behavior in the boron-rich region is not well established, neither for binary metal borides nor for metal–boron-carbide systems. In most cases a ternary eutectic reaction was reported: L2(ßB)+B4+δC+MBx, where MBx represents the metal boride richest in boron [30,38–40]. Although the melting point of B was set at  2100 1C [38], the adjoining ternary eutectic was given at thermodynamically unreliably low temperatures depressed by

Fig. 5. Thermodynamic modeling of the B–C system showing the B-rich part. Square symbols (blue) denote the solidus points and red circles denote liquidus points extracted from the floating zone experiment. The solid lines correspond to the thermodynamic optimization. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Table 1 Thermodynamic parameters for system B–C (in J/mol). Phase

Liquid

ßB

Model

R–K

CEF R–K

Cgraph

R–K

B4+δC

CEF

Parameter

Data from ref. [28]

Data from ref. [30,36] Values in italics: this work

K1

K2

K1

K2

0 liq: LB;C

 67045.26

4.46969

 67045.16

1 liq: LB;C

 36683.57

2.44551

 36682.57

βB graphite GβB B:C 93GB:C 12GC 0 βB LB:B;C 0 graphite LB;C graphite 0 B4þδ C G B11 C:CBC 12GβB B 3GC B C 4þδ graphite 0 G B11 C:CBB 13GβB B 2GC βB graphite 0 B4þδ C G B11 C:BVaB 13GB GC graphite 0 B4þδ C G B12 :CBC 13GβB B 2GC
βB 0 B4þδ C 1 G B12 :CBB  14 þ 14 GB Ggraphite C graphite 0 B4þδ C G B12 :CBB 14GβB B GC 0 B4þδ C G B12 :BVaB 14GβB B

10,000

–

1,000,000

4.46969 3.06969 2.44551 1.04551 –

 1636713.01

–

 2769690.3

–

 34385.95

8.6792

 34385.95

8.6792

 311207.416

11.5310464

 347121.82

22.909095

 293453.353

11.5310464

 304040.52

22.909095

 148993.047

11.5310464

 170978.12

22.909095

 283453.45

11.5310464

 294040.52

22.909095

 138993.047

11.5310464

–

–

–169978.12

22.909095

10,000

22.909095

0

10,000

11.5310464

R–K ¼Redlich Kister Formalism. CEF ¼Compound Energy Formalism. Sublattice models used: “B4+δC”: (B12, B11C)1(B2Va, C2B, B2C)1 and “ßB”: (B)93(B,C)12.

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Fig. 6. System Hf-B-C; upper panel depicts the calculated liquidus surface based on the newly modeled B–C system with peritectic melting behavior of (βB). Lower left shows a closeup of the liquidus surface for the B-rich corner. Lower right gives the phase relations for the B-rich corner at the temperature T of the reaction U1 (L+B4+δC2(ßB)+HfB2).

100 1C on C and M additions. Avoiding ternary interaction parameters to stabilize the boron-rich liquid results in a compromise accepting ternary reaction temperatures higher than those experimentally reported. It should be mentioned, that the depleted nature of most of these reactions did not allow a clear metallographic decision for a ternary eutectic much for the same reasons a binary ßB-eutectic was erroneously reported at  30 1C lower than the peritectic established in this work. Furthermore the semiconducting nature of B-rich samples does not allow a proper determination of Pirani technique-based temperature determinations, which therefore might suffer from error bars as high as  30 to 100 1C. An early modeling of the Ti–B–C system on the basis of a eutectic melting of ßB in the B–C system was performed by

Duschanek et al. [27] and tried to respect the experimental ternary low lying eutectic L2(ßB)+B4+δC+TiB2 at 2016 1C [38]. The corresponding liquidus projection is given in Fig. 7a expanding the Brich section to a fine grid. Accepting the new peritectic melting of binary (ßB) at 21011 (see Sections 3.1 and 3.2) and incorporating the new B–C values into the modeling of the Ti–B–C system, as done earlier with a peritectic ßB melting behavior [28], the calculation reveals consistency with the main body of the phase diagram [27], but for the B-rich part arrives at a reaction temperature somewhat higher than for the ternary eutectic measured, but now the C-solubility in ßB enables instead a transition reaction L+B4+δC2(ßB)+TiB2 at 2085 1C (Fig. 7b). Fig. 7 compares the liquidus surfaces of both versions. As a general feature for most

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Fig. 7. System Ti–B–C; upper panel depicts the calculated liquidus surface based on the newly modeled B–C system with peritectic melting behavior of (βB). Lower panels show a closeup of the liquidus surface for the B-rich corner and compare the thermodynamic calculation for the version with the binary peritectic L+B4+δC2(ßB) (left lower panel) with the calculation for the version with binary eutectic L2(ßB)+B4+δC after Duschanek et al. [27] (right lower panel).

of the refractory M–B–C systems, the influence of the peritectic reaction in the B–C binary favors a ternary transition reaction U (L +B4+δC2(ßB)+MBx) over a ternary eutectic E (L2(ßB)+B4+δC +MBx) where MBx represents the metal boride richest in boron and if one excludes specially stabilizing ternary interaction parameters in the liquid phase. The corresponding.tdb files for the calculations of the ternary systems {Ti,Hf}–B–C based on the new modeling of the B–C diagram are included as supplementary material.

4. Conclusion Floating zone experiments in this work have been employed to determine the melting type of ß-boron at the boron-rich side of the B–C binary phase diagram on a series of C-containing feed-rods prepared by powder metallurgy and sinter techniques.

Melting point data as a function of carbon-content clearly define a peritectic reaction isotherm: L+B4+δC ¼(ßB) with a partition coefficient of carbon at  2.6. The new experimental melting point data were used for thermodynamic modeling of the B–C diagram. Relative to the thermodynamically accepted melting point of pure ßB (TM ¼ 2075 1C), the calculated reaction isotherm is determined at 2100.6 1C with a peritectic point at 0.75 at% C and a maximum solid solubility of 1.43 at% C in (ßB). Based on the new melting data the refractory system Hf–B–C has been recalculated and the liquidus surface is presented. The influence of the melting behavior of (ßB) on the phase reactions in the B-rich corner of M–B–C diagrams is discussed and demonstrated in case of the Ti–B–C system. In general and excluding ternary interaction parameters in the liquid phase, the peritectic reaction in the B–C binary favors a ternary transition reaction U (L+B4+δC2(ßB)+MBx) over a ternary eutectic E (L2(ßB)+B4+δC+MBx) where MBx represents the metal boride richest in boron.

Please cite this article as: P.F. Rogl, et al., The B-rich side of the B–C phase diagram, Calphad (2013), http://dx.doi.org/10.1016/j. calphad.2013.07.016i

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Acknowledgments J.V. and P.R. acknowledge the financial support of the OEAD (Project CZ12/2013) and the Ministry of Education of the Czech Republic (Project: 7AMB13AT019) and CEITEC (CZ.1.05/1.1.00/02.0068). Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.calphad.2013.07. 016.

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Please cite this article as: P.F. Rogl, et al., The B-rich side of the B–C phase diagram, Calphad (2013), http://dx.doi.org/10.1016/j. calphad.2013.07.016i