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Thermodynamics of gas phase carbothermic reduction of boron-anhydride
Journal of Alloys and Compounds 413 (2006) 198–205
Thermodynamics of gas phase carbothermic reduction of boron-anhydride B.Z. Dacic a , V. Jokanovi´c b,∗ , B. Jokanovi´c c , M.D. Drami´canin b a c
Chemical and Materials Engineering, Auckland University, Auckland, Private Bag 92019, New Zealand b Institute of Nuclear Sciences “Vinˇ ca”, PO Box 522, 11000 Beograd, Serbia and Montenegro TU Clausthal, Institut f¨ur Metallurgie, Department Termochemie und Microkinetik, Clausthal, Germany Received 8 December 2004; accepted 30 March 2005 Available online 31 August 2005
Abstract The upgrading of carbothermic synthesis of the boron-based non-oxide monolithic or composite ceramics powder depends upon the understanding of thermodynamics of carbothermic reduction (CR) of B2 O3(l) . Analysis of relative dominance of relevant equilibriums in CR of B2 O3(l) and the non-stoichiometric computer program for the minimisation of the Gibbs energy of reactions products has been applied to the B–O–C system. Considerably, lower temperature at which the B4 C and boron can thermodynamically be obtained as the pure phase depends upon the extent and the mode of gas phase dilution, and upon the Carbon/B2 O3 molar ratio in the charge (CBMR). © 2005 Elsevier B.V. All rights reserved. Keywords: Carbothermic synthesis; Boron-anhydride; Boron carbide; Gibbs energy
1. Introduction There has been substantial interest in the manufacture of boron based monolithic ceramic B4 C, TiB2 and (B4 C)x (TiB2 )1−x composite powders by CR. Boron carbide is commercially manufactured by CR of boron-anhydride in electric arc furnaces [1]. Two feasible methods for TiB2 synthesis by CR can be described by the following chemical reactions: TiO2 + 0.5B4 C + 1.5C = TiB2 + 2CO or TiO2 + B2 O3 + 5C = TiB2 + 5CO [2]. The temperature gradient within condensed reactants and the augmented partial pressure of CO(g) are probably two most crucial parameters during CR of B2 O3(l) and TiO2(s) within the B4 C and TiB2 synthesis. The consequences of such impediments are: higher needed temperatures and extended reaction time, non-uniform process conditions with consequential chemical and structural non-homogeneity within the product, and a more sintered mass of obtained product than the fine grained one. Experimental results in manufacturing the submicron ∗
Corresponding author. E-mail address: [email protected] (V. Jokanovi´c).
0925-8388/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2005.03.117
powders of B4 C [3] during the rapid heating (105 K/s) of an intimate C/B2 O3 precursor powder (from dried, calcined and milled cornstarch/boric-acid liquid slurry) suggest a mechanism for carbothermic synthesis of carbide (and borides) different than the heterogeneous mechanism expressed for instance by equilibrium, 2B2 O2(g) + 5C(s) = B4 C(s) + 4CO(g) , where a gaseous route to molecular B4 C(s) has been supposed. An assumption has tacitly been made in literature that either B2 O2(g) [4] or B2 O3(g) and BO(g) [5–12], respectively, are the only relevant boronized reacting gas species in B4 C synthesis. These gaseous species are of great importance both to the mechanisms and the rate of B4 C synthesis. Existence of three boron-bearing gaseous species in the vapour phase and, probably, very complex interrelation of their partial pressures with influence on the mechanisms and the rate of carbothermal reduction process make the system challenging for further study. Developing of an improved process for manufacturing stoichiometric boron based monolithic and composite submicron powders by CR, preferably by means of higher partake of the gas phase born B4 C(s) could be the uttermost goal, which greatly depends upon better understanding
B.Z. Dacic et al. / Journal of Alloys and Compounds 413 (2006) 198–205
of thermodynamics of the involved solid/liquid/gas (SLG) phase reactions.
2. Thermodynamics of CR of boron oxide—aspects of non-stoichiometry Calculation of the equilibrium composition of the gas and condensed phases in the system of CR of B2 O3(l) , for a given feed composition, at constant temperature and atmospheric pressure, is the straightforward way to assess the optimum operating conditions and the maximum yield of B4 C(s) . The equilibrium product composition in the CR process was calculated using the CSIRO-Chemix computer program of the
199
minimisation of total Gibbs energy (GEMP) [6] of the presumed products. In the lack of a proof of kinetically inhibited gas mixture composition, it has been supposed that the gas mixture contains B2 O3(g) , B2 O2(g) , BO(g) , CO2(g) , CO(g) and O2(g) . Condensed part of the system can contain one or more of four assumingly pure phases: B2 O3(l) , C(s) , B4 C(s) and B(s) . The exact value of temperature for 20 different CBMR from 0 to 3.5, for which either a condensed phase vanishes or just originates, was calculated by the iteration method. This procedure enables the estimation of boundaries of a single and the mixture of coexisting condensed phases. The effect of the feed composition and temperature on the calculated product composition in CR of 1 mol of B2 O3(l) is shown in Figs. 1 and 2. The characteristic equilibrium yields
Fig. 1. Equilibrium yield of condensed products and dominant gas species vs. temperature, at atmospheric pressure for different CBMR.
B.Z. Dacic et al. / Journal of Alloys and Compounds 413 (2006) 198–205
200
rect for the temperatures in Fig. 1 where pure B4 C(s) and pure B(s) is, respectively, the only thermodynamically stable solid phase. In this case, the only requirements imposed by equilibrium thermodynamics for heterogeneous reactions to occur at the same time and to share the (gas) reactants and products is that the concentration of each reacting species remains constant in the time when the overall equilibrium is attained. 2.1. Phase equilibrium—stoichiometric approach
Fig. 2. The phase stability plot for CR of B2 O3(l) .
of pure solid products at related temperatures, inferred from diagrams in Figs. 1 and 2, are shown in Table 1. When CBMR in charge drops from 3.44 to 1.775 and lower, the concentration of B2 O3(g) will increase in the gas phase not only as a thermodynamic consequence of the changed feed composition, which is shown in Fig. 1, but so too kinetically due to reduced surface contact area to B2 O2(g) and BO(g) formation via Eqs. (1) and (2) in Table 2. Partake of more pollard and reactive BO(g) increases with temperature on the expense of B2 O2(g) , and for all estimated CBMR absolutely meet the KP value of Eq. (b). The equilibrium composition of the gas and condensed phases given in Fig. 1, is the definite product composition which meet both the GEMP and the mass conservation principles, and it is thermodynamically correct to assume that the following two reactions are the overall reactions for all possible simultaneous equilibriums involved in CR, giving, respectively, B4 C and pure boron, B2 O3(l) + 3.44 C(s) → nB4 C B4 C + Gas Phase
(A)
B2 O3(l) + 1.775 C(s) → nB B + Gas Phase
(B)
Gas phase in both equilibria stands for the sum of corresponding equilibrium mole fraction of gas species (ni ); nCO CO(g) + nB2 O2 B2 O2(g) + nB2 O3 B2 O3(g) + nBO BO(g) + nCO2 CO2(g) + nO2 O2(g) . The assumption of the simultaneous occurrence of unknown underlying reactions (presumable some of equations listed in Table 2) is corTable 1 Equilibrium yield (EY) of pure B4 C(s) and pure boron Product B4 C(s) B(s) a b
C(s) /B2 O3(s) CBMR
Temperature (◦ C)
EY (%)
3.33 3.44
1593a 1719
93.9 97.4b
2.75 1.775
2045 1791a
87.8b 46.0
The lowest temperature. The maximum yield obtained by the GEMP.
Having assumed that both B2 O2(g) and BO(g) species take part in chemistry of the B4 C synthesis, at considered temperature, proportionally to the mass action low and to their activity, a set of reactions given in Table 2, have been analysed intending to assess the relative dominance of assumed single reactions occurring in CR of B2 O3(l) . The relative dominance of the B2 O2(g) and BO(g) generation and consuming reactions is quantified by means of values of their equilibrium partial pressure (PB2 O2 and PBO ), calculated from the equilibrium constant (KP ) relationships, and are shown in Fig. 3. The PB2 O2 and PBO for separately balanced reaction at equilibrium, when the B2 O2(g) and BO(g) is assumed respectively to be the solo boronised reacting species, were calculated for the assumed PCO = 1 atm. For the sake of the consistent comparison of the PB2 O2 and PBO values for Eqs. (1a) and (2a), calculated from the related expression for KP , and so too for all other reactions involving B2 O3(g) , the needed fixed value of PB2 O3 must be the unique value for each of the single reaction based upon the calculated equilibrium extent (α) for a reaction. For example, for Eq. (1a), α = [KP × P−1 /(1 + KP × P−1 )]1/2 , where the change of mole numbers of gas reactants due to the reaction is one (ν = 1). At 1600 ◦ C and atmospheric pressure PB2 O3 = (1 − α)/(1 + α) = 0.0805 atm. The great sensitivity of estimated PB2 O2 and PBO for Eqs. (1a), (2a), (4a) and (6a) upon the assumed value of PB2 O3 should be taken in account in the case of any arbitrary fixed PB2 O3 value. Notice that if the PB2 O3 of the evaporation Eq. (a), dashed line in Fig. 3, is taken to be the referent activity for the B2 O3(g), (PB2 O3 = 0.0029 atm at 1600 ◦ C) there would be no difference in thermodynamic driving force between the B2 O2(g) generation Eqs. (1) and (1a), and Eqs. (4) and (4a). However, having occurred on the solid/gas instead of on the solid/liquid interface, reactions (1a) and (4a) are kinetically favoured over Eqs. (1) and (4). Points a and b in Fig. 3 represent the invariant conditions for the coexistence of three condensed phases in accordance to the overall equilibrium (A) and (B), reduced to the appropriate stoichiometries inferred as the common solution for Eqs. (1), (3) and (4), and Eqs. (4), (7) and (8), respectively. Temperature TA = 1601.3 ◦ C and TB = 1826 ◦ C define the ratio PB2 O2 /PCO which satisfies quoted pertinent equilibrium for coexistence of the B2 O3(l) + B4 C(s) + C(s) and the B2 O3(l) + B4 C(s) + B(s) phases, respectively. All thermodynamic calculations have been performed by using the JANAF thermodynamics data [7].
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201
Table 2 Standard Gibbs energy (G◦ ), standard entropy (S ◦ 298 ), equilibrium temperature (Teql ) and equilibrium constant (KP ) for the B2 O2(g) and BO(g) generation and consumption reactions Reaction
G◦ (J/mol)
aT
S ◦ 298 (J/K)
log KP at 1600 ◦ C
545,870 − 300.281T
1812.1
355.8
−2.12
220,579 − 145.920T
1510.6
150.6
0.42
944,858 − 449.124T
2101.6
520.0
−7.37
619,566 − 294.763T
2101.1
314.3
−4.83
479,103 − 241.953T
1974.1
295.1
−3.00
153,815 − 87.593T
1753.0
89.9
−0.44
1037,689 − 450.333T
2305.0
525.0
−10.34
712,397 − 295.973T
2410.6
319.8
−7.80
451,229 − 225.142T
1997.7
279.1
−2.95
125,937 − 70.782T
1774.4
74.3
−0.41
1049,710 − 448.407T
2342.9
525.7
−10.83
724,419 − 294.046T
2468.5
320.5
−8.29
333,819 − 291.637T
1147.4
303.6
4.33
−24.8
14.83
78.5
−0.17
−3.6
2.45
76.4
0.83
−5.7
3.46
eql ,
(◦ C)
B2 O2(g) and BO(g) generation B2 O3(l) + C(s) = B2 O2(g) + CO(g)
(1)
B2 O3(g) + C(s) = B2 O2(g) + CO(g)
(1a)
B2 O3(l) + C(s) = 2BO(g) + CO(g)
(2)
B2 O3(g) + C(s) = 2BO(g) + CO(g)
(2a)
0.2B4 C(s) + B2 O3(l) = 1.4B2 O2(g) + 0.2CO(g)
(3)
0.2B4 C(s) + B2 O3(g) = 1.4B2 O2(g) + 0.2CO(g)
(3a)
0.2B4 C(s) + B2 O3(l) = 2.8BO(g) + 0.2CO(g)
(4)
0.2B4 C(s) + B2 O3(g) = 2.8BO(g) + 0.2CO(g)
(4a)
B2 O3(l) + B(s) = 1.5B2 O2(g)
(5)
B2 O3(g) + B(s) = 1.5B2 O2(g)
(5a)
B2 O3(l) + B(s) = 3BO(g)
(6)
B2 O3(g) + B(s) = 3BO(g)
(6a)
B2 O2(g) and BO(g) consuming
2B2 O2(g) + 5C(s) = B4 C(s) + 4CO(g)
(7)
4BO(g) + 5C(s) = B4 C(s) + 4CO(g)
(8)
B4 C(s) + 0.5B2 O2(g) = 5B(s) + CO(g)
(9)
B4 C(s) + BO(g) = 5B(s) + CO(g)
(9a)
0.5B2 O2(g) + C(s) = B(s) + CO(g)
(10)
BO(g) + C(s) = B(s) + CO(g)
(10a)
B2 O3(l) = B2 O3(g)
(a)
B2 O2(g) = 2BO(g)
(b)
a
Temperature at which KP = 1.
−464,156 + 6.048T 139,388 − 84.056T −60,104 − 9.630T 94,641 − 75.139T −104,851 − 0.717T
–
1662.9
–
1261.0
–
325,291 − 154.361T
2091.2
205.2
−2.54
398,985 − 148.843T
2690.5
164.0
−5.25
202
B.Z. Dacic et al. / Journal of Alloys and Compounds 413 (2006) 198–205
Fig. 3. Plot of log PB2 O2 and log PBO vs. 1/T for reactions in the B–C–O system.
3. The gas phase dilution in carbothermic reduction To facilitate synthesis of B4 C not only kinetically, by alleviating the transport of gas species, but so too thermodynamically, by boosting the competitive B2 O2(g) and BO(g) generation reactions, a substantial decreasing of the partial pressure of CO(g) is required. To assess this effect, the log P − 1/T relationship has been obtained for the B2 O2(g) and BO(g) generation and consuming reactions considered in Fig. 3a and b, but now for lower PCO = 0.01 atm, and plotted in
Fig. 3c and d. It is apparent from the graphs in Fig. 3 that both temperature and dilution reduce the phase area of B4 C with concomitant expansion of boron field. The lowering of temperature at which B4 C(s) thermodynamically can be obtained, and increasing of the driving force for B4 C nucleating and growth at the unchanged temperature is apparent from the differences of the PB2 O2 values for the B2 O2(g) generation and consuming reaction in Fig. 3. More by vacuuming than by continuous flushing of reaction chamber with Argon, the partial pressure of CO(g) can be kept well below the equilibrium
Fig. 4. Plot of log PB2 O2 and log PBO vs. log PCO at 1600 ◦ C for reactions in the B–C–O system.
B.Z. Dacic et al. / Journal of Alloys and Compounds 413 (2006) 198–205
203
values for Eqs. (1), (1a), (2) and (2a), for the case the total pressure P is 1 atm, increasing the value of the PB2 O2 /PCO ratio (alternatively PBO /PCO ratio) having maintained on that way the independence of KP value from the total pressure. Plots in Fig. 4 show how the difference in thermodynamic driving force between the B2 O2(g) and BO(g) generation and consuming reaction increase with the vacuuming of the system at constant temperature. 3.1. The gas phase dilution and equilibrium yield For the characteristic CBMR-s in Table 1, the effect of the gas phase dilution with Argon (d), defined as the mole number of Argon per 1 mole of B2 O3(s) , and so too the effect of decreasing of the total pressure, by vacuuming, down to 0.01 atm, on the product composition have been calculated at constant temperature and are plotted as the equilibrium yield—PCO graph in Fig. 5. It is apparent from Fig. 5 that dilution of gas phase, at constant temperature, has the same effect on gas species and the condensed phase yields as the increasing temperature has in Fig. 1. For the CBMR = 1.775, Boron can be obtained above the stability region of B4 C(s) only when the partial pressure of the B2 O2(g) and BO(g) are higher than PB2 O2 and PBO for Eqs. (9) and (9a) in Fig. 3. These conditions can be met, when due to the carbon deficiency, soon after the early stage of reduction synthesis B4 C starts reacting with non-reacted B2 O3(l) rendering the reduction to the boron thermodynamically possible—via simultaneously occurring the forward Eqs. (3), (3a), (9) and (9a). Attained for the overall equilibrium, the equilibrium partial pressure for involved gas species calculated by GEMP can be accepted as the unique equilibrium values for all those simultaneous reactions which achieve equilibrium only under the assumed constraint of existence of the single solid product phase. For a considered set of process conditions (CBMR, P/d and T), the equilibrium gas composition calculated by GEMP, is reassessed within the KP value for presumed relevant equilibria in CR. It was done by calculating the new hypothetical ) for equilibrium pressure for B2 O2(g) and BO(g) (P and PBO each single reaction, from the KP relationship by introducing the PCO and PB2 O3 values obtained by GEMP as the true and common equilibrium value for all reactions shown in Fig. 6. Only Eq. (3a) apparently attains equilibrium for the considered conditions (plot in (6a)), where the P curve for Eq. (3a) overlaps the bold PB2 O2 curve calculated by GEMP. Within the applied conjoint stoichiometric and non-stoichiometric equilibrium analysis, this fitting of the values of P and PB2 O2 means that this reaction equilibrates gas species concentration for considered P, T, d, conditions. This fitting could be taken also as an indication of the relevance of the backward Eq. (3a) in the gaseous route to B4 C(s) . The underestimated and the overestimated hypothetical values P for all other reaction can be taken (so long the made presumption of solo existence of B4 C(s) is correct) as the proof of the possibility that reactions occur simultaneously (shearing the gaseous reactants and products) which under
Fig. 5. Equilibrium yield vs. applied dilution of the gas phase for different CBMR.
no circumstances can attain their own equilibrium, in terms of the gas species concentration. In such a scenario of simultaneous occurring reactions involving BO(g) , there is no such equilibrium among considered reactions which equilibrates involved reacting species (Fig. 6b). 3.2. More about thermochemistry of the gas phase carbothermic reduction Neither the practical determination of the KP value (G◦ = −RT lnKP ) for one or more relevant and proven
B.Z. Dacic et al. / Journal of Alloys and Compounds 413 (2006) 198–205
204
Fig. 7. Partition of enthalpy and entropy in Gibbs energy of Eq. (A) vs. gas phase dilution.
of B4 C(s) nucleating in the gas phase, it is quite comprehensive that these features of chemical dynamics of reactive collision are important in terms of achieving the higher total efficiency of the reactions of CR, what is beyond the hitherto done classical thermodynamical consideration. The resource to master quoted parameters, in order to achieve the higher total efficiency of reaction (lower reaction temperature, higher extent of reaction and shorter reaction time) than it can be done merely by vacuuming or by inert gas dilution, when only translation energy is targeting, could be the further tailoring of the configuration entropy of the reacting B2 O2(g) , B2 O3(g) , BO(g) and CO(g) species.
Fig. 6. Equilibrium PB2 O2 and PBO (GEMP) compared with PB 2 O2 and PBO (KP ).
4. Summary equilibrium, nor the GEMP for optimisation of possible products, for considered P and T conditions, distinguish between the enthalpy and entropy contribution in arriving at the equilibrium in the CR process. Hitherto considered effect which the gas phase dilution has on the achievable lowering of temperature at which B4 C(s) and boron become thermodynamically stable pure phase is based upon the mixing gthe increased contribution which term (−R i=1 ni ln xi , where x = n / n ) of the gas i i i g phase entropy Sgas (T,P) = i=1 ni (Si(T,P) − R ln xi ) has in the entropy equation for Eq. (A), S(A) = nB4 C SBo 4 C + Sgas(P,d) − SBo 2 O3 (l) − 3.44SCo (shown in Fig. 7). Notice that Enthalpy of the reaction H(A) is negligently affected by the isothermal change of pressure on which the reaction occurs. Besides this mixing term of reaction entropy there is an avenue of possible ramification which the configuration part of thermal energy, as an chemically important entropy contribution, might has for the overall (thermodynamic + kinetics) efficiency of CR. Even if, for the moment, we disregard: any chemical intuition about geometrical structure of reacting gas species, different angles θ which bring reacting species into effective reaction collisions, the existence of particular active complex, and the possible stereochemical mechanism
Whatever equilibria and mechanism is involved in the process of CR of B2 O3(l) , the Gibbs energy minimisation of the known reacting and product species, together with the analysis of PB2 O2 and PBO for the assumed B2 O2(g) and BO(g) generation and consuming reactions in reduction is the choice in thermodynamical estimation of optimum process conditions for the synthesis of B4 C(s) . Dilution of the gas phase, at constant temperature, has the same effect on gas species and condensed phases yields as the increasing of temperature. More by vacuuming than by continuous flushing with Argon, the crucial PCO can be kept well below the critical equilibrium values needed to promote both the B2 O2(g) and BO(g) generation and consuming reactions.
References [1] J. Scott, Arc Furnace Process for production of B4C, U.S. Patent No. 3,161,471 (1964). [2] J. Kim, C. McMurrty, Ceram. Eng. Sci. Prog. 6 (9–10) (1985) 1313–1320. [3] A. Weimer, et al., J. Am. Ceram. Soc. 75 (9) (1992) 2509–2514. [4] A. Weimer, et al., AIChE J. 37 (5) (1991) 759–768.
B.Z. Dacic et al. / Journal of Alloys and Compounds 413 (2006) 198–205 [5] S. Yoon, A. Iha, J. Mater. Sci. 30 (1995) 607–614. [6] A. Turnbull, M. Wadsley, CSIRO-MONASH Thermochemistry Sys., 1992. [7] M. Chose, et al., JANAF, Thermochemical Tables, J. Phys. Chem. Ref. Data 14 (Suppl. 1) (1985). [8] A. Alizadeh, E. Taheri-Nassaj, N. Ehsani, J. Eur. Ceram. Soc. 24 (2004) 3227–3234.
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[9] G. Goller, C. Toy, A. Tekin, C.K. Gupta, High Temp. Mater. Proccess. 15 (1–2) (1996) 117–122. [10] F. Thevenot, J. Eur. Ceram. Soc. 6 (1990) 205–225. [11] D.K. Bose, K. Nair, C.K. Gupta, High Temp. Mater. Proccess. 7 (2–3) (1986) 133–140. [12] L.E. Toth, Transition Metal Carbides and Nitrides, Academic Press, New York, 1971.
Thermodynamics of gas phase carbothermic reduction of boron-anhydride B.Z. Dacic a , V. Jokanovi´c b,∗ , B. Jokanovi´c c , M.D. Drami´canin b a c
Chemical and Materials Engineering, Auckland University, Auckland, Private Bag 92019, New Zealand b Institute of Nuclear Sciences “Vinˇ ca”, PO Box 522, 11000 Beograd, Serbia and Montenegro TU Clausthal, Institut f¨ur Metallurgie, Department Termochemie und Microkinetik, Clausthal, Germany Received 8 December 2004; accepted 30 March 2005 Available online 31 August 2005
Abstract The upgrading of carbothermic synthesis of the boron-based non-oxide monolithic or composite ceramics powder depends upon the understanding of thermodynamics of carbothermic reduction (CR) of B2 O3(l) . Analysis of relative dominance of relevant equilibriums in CR of B2 O3(l) and the non-stoichiometric computer program for the minimisation of the Gibbs energy of reactions products has been applied to the B–O–C system. Considerably, lower temperature at which the B4 C and boron can thermodynamically be obtained as the pure phase depends upon the extent and the mode of gas phase dilution, and upon the Carbon/B2 O3 molar ratio in the charge (CBMR). © 2005 Elsevier B.V. All rights reserved. Keywords: Carbothermic synthesis; Boron-anhydride; Boron carbide; Gibbs energy
1. Introduction There has been substantial interest in the manufacture of boron based monolithic ceramic B4 C, TiB2 and (B4 C)x (TiB2 )1−x composite powders by CR. Boron carbide is commercially manufactured by CR of boron-anhydride in electric arc furnaces [1]. Two feasible methods for TiB2 synthesis by CR can be described by the following chemical reactions: TiO2 + 0.5B4 C + 1.5C = TiB2 + 2CO or TiO2 + B2 O3 + 5C = TiB2 + 5CO [2]. The temperature gradient within condensed reactants and the augmented partial pressure of CO(g) are probably two most crucial parameters during CR of B2 O3(l) and TiO2(s) within the B4 C and TiB2 synthesis. The consequences of such impediments are: higher needed temperatures and extended reaction time, non-uniform process conditions with consequential chemical and structural non-homogeneity within the product, and a more sintered mass of obtained product than the fine grained one. Experimental results in manufacturing the submicron ∗
Corresponding author. E-mail address: [email protected] (V. Jokanovi´c).
0925-8388/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2005.03.117
powders of B4 C [3] during the rapid heating (105 K/s) of an intimate C/B2 O3 precursor powder (from dried, calcined and milled cornstarch/boric-acid liquid slurry) suggest a mechanism for carbothermic synthesis of carbide (and borides) different than the heterogeneous mechanism expressed for instance by equilibrium, 2B2 O2(g) + 5C(s) = B4 C(s) + 4CO(g) , where a gaseous route to molecular B4 C(s) has been supposed. An assumption has tacitly been made in literature that either B2 O2(g) [4] or B2 O3(g) and BO(g) [5–12], respectively, are the only relevant boronized reacting gas species in B4 C synthesis. These gaseous species are of great importance both to the mechanisms and the rate of B4 C synthesis. Existence of three boron-bearing gaseous species in the vapour phase and, probably, very complex interrelation of their partial pressures with influence on the mechanisms and the rate of carbothermal reduction process make the system challenging for further study. Developing of an improved process for manufacturing stoichiometric boron based monolithic and composite submicron powders by CR, preferably by means of higher partake of the gas phase born B4 C(s) could be the uttermost goal, which greatly depends upon better understanding
B.Z. Dacic et al. / Journal of Alloys and Compounds 413 (2006) 198–205
of thermodynamics of the involved solid/liquid/gas (SLG) phase reactions.
2. Thermodynamics of CR of boron oxide—aspects of non-stoichiometry Calculation of the equilibrium composition of the gas and condensed phases in the system of CR of B2 O3(l) , for a given feed composition, at constant temperature and atmospheric pressure, is the straightforward way to assess the optimum operating conditions and the maximum yield of B4 C(s) . The equilibrium product composition in the CR process was calculated using the CSIRO-Chemix computer program of the
199
minimisation of total Gibbs energy (GEMP) [6] of the presumed products. In the lack of a proof of kinetically inhibited gas mixture composition, it has been supposed that the gas mixture contains B2 O3(g) , B2 O2(g) , BO(g) , CO2(g) , CO(g) and O2(g) . Condensed part of the system can contain one or more of four assumingly pure phases: B2 O3(l) , C(s) , B4 C(s) and B(s) . The exact value of temperature for 20 different CBMR from 0 to 3.5, for which either a condensed phase vanishes or just originates, was calculated by the iteration method. This procedure enables the estimation of boundaries of a single and the mixture of coexisting condensed phases. The effect of the feed composition and temperature on the calculated product composition in CR of 1 mol of B2 O3(l) is shown in Figs. 1 and 2. The characteristic equilibrium yields
Fig. 1. Equilibrium yield of condensed products and dominant gas species vs. temperature, at atmospheric pressure for different CBMR.
B.Z. Dacic et al. / Journal of Alloys and Compounds 413 (2006) 198–205
200
rect for the temperatures in Fig. 1 where pure B4 C(s) and pure B(s) is, respectively, the only thermodynamically stable solid phase. In this case, the only requirements imposed by equilibrium thermodynamics for heterogeneous reactions to occur at the same time and to share the (gas) reactants and products is that the concentration of each reacting species remains constant in the time when the overall equilibrium is attained. 2.1. Phase equilibrium—stoichiometric approach
Fig. 2. The phase stability plot for CR of B2 O3(l) .
of pure solid products at related temperatures, inferred from diagrams in Figs. 1 and 2, are shown in Table 1. When CBMR in charge drops from 3.44 to 1.775 and lower, the concentration of B2 O3(g) will increase in the gas phase not only as a thermodynamic consequence of the changed feed composition, which is shown in Fig. 1, but so too kinetically due to reduced surface contact area to B2 O2(g) and BO(g) formation via Eqs. (1) and (2) in Table 2. Partake of more pollard and reactive BO(g) increases with temperature on the expense of B2 O2(g) , and for all estimated CBMR absolutely meet the KP value of Eq. (b). The equilibrium composition of the gas and condensed phases given in Fig. 1, is the definite product composition which meet both the GEMP and the mass conservation principles, and it is thermodynamically correct to assume that the following two reactions are the overall reactions for all possible simultaneous equilibriums involved in CR, giving, respectively, B4 C and pure boron, B2 O3(l) + 3.44 C(s) → nB4 C B4 C + Gas Phase
(A)
B2 O3(l) + 1.775 C(s) → nB B + Gas Phase
(B)
Gas phase in both equilibria stands for the sum of corresponding equilibrium mole fraction of gas species (ni ); nCO CO(g) + nB2 O2 B2 O2(g) + nB2 O3 B2 O3(g) + nBO BO(g) + nCO2 CO2(g) + nO2 O2(g) . The assumption of the simultaneous occurrence of unknown underlying reactions (presumable some of equations listed in Table 2) is corTable 1 Equilibrium yield (EY) of pure B4 C(s) and pure boron Product B4 C(s) B(s) a b
C(s) /B2 O3(s) CBMR
Temperature (◦ C)
EY (%)
3.33 3.44
1593a 1719
93.9 97.4b
2.75 1.775
2045 1791a
87.8b 46.0
The lowest temperature. The maximum yield obtained by the GEMP.
Having assumed that both B2 O2(g) and BO(g) species take part in chemistry of the B4 C synthesis, at considered temperature, proportionally to the mass action low and to their activity, a set of reactions given in Table 2, have been analysed intending to assess the relative dominance of assumed single reactions occurring in CR of B2 O3(l) . The relative dominance of the B2 O2(g) and BO(g) generation and consuming reactions is quantified by means of values of their equilibrium partial pressure (PB2 O2 and PBO ), calculated from the equilibrium constant (KP ) relationships, and are shown in Fig. 3. The PB2 O2 and PBO for separately balanced reaction at equilibrium, when the B2 O2(g) and BO(g) is assumed respectively to be the solo boronised reacting species, were calculated for the assumed PCO = 1 atm. For the sake of the consistent comparison of the PB2 O2 and PBO values for Eqs. (1a) and (2a), calculated from the related expression for KP , and so too for all other reactions involving B2 O3(g) , the needed fixed value of PB2 O3 must be the unique value for each of the single reaction based upon the calculated equilibrium extent (α) for a reaction. For example, for Eq. (1a), α = [KP × P−1 /(1 + KP × P−1 )]1/2 , where the change of mole numbers of gas reactants due to the reaction is one (ν = 1). At 1600 ◦ C and atmospheric pressure PB2 O3 = (1 − α)/(1 + α) = 0.0805 atm. The great sensitivity of estimated PB2 O2 and PBO for Eqs. (1a), (2a), (4a) and (6a) upon the assumed value of PB2 O3 should be taken in account in the case of any arbitrary fixed PB2 O3 value. Notice that if the PB2 O3 of the evaporation Eq. (a), dashed line in Fig. 3, is taken to be the referent activity for the B2 O3(g), (PB2 O3 = 0.0029 atm at 1600 ◦ C) there would be no difference in thermodynamic driving force between the B2 O2(g) generation Eqs. (1) and (1a), and Eqs. (4) and (4a). However, having occurred on the solid/gas instead of on the solid/liquid interface, reactions (1a) and (4a) are kinetically favoured over Eqs. (1) and (4). Points a and b in Fig. 3 represent the invariant conditions for the coexistence of three condensed phases in accordance to the overall equilibrium (A) and (B), reduced to the appropriate stoichiometries inferred as the common solution for Eqs. (1), (3) and (4), and Eqs. (4), (7) and (8), respectively. Temperature TA = 1601.3 ◦ C and TB = 1826 ◦ C define the ratio PB2 O2 /PCO which satisfies quoted pertinent equilibrium for coexistence of the B2 O3(l) + B4 C(s) + C(s) and the B2 O3(l) + B4 C(s) + B(s) phases, respectively. All thermodynamic calculations have been performed by using the JANAF thermodynamics data [7].
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201
Table 2 Standard Gibbs energy (G◦ ), standard entropy (S ◦ 298 ), equilibrium temperature (Teql ) and equilibrium constant (KP ) for the B2 O2(g) and BO(g) generation and consumption reactions Reaction
G◦ (J/mol)
aT
S ◦ 298 (J/K)
log KP at 1600 ◦ C
545,870 − 300.281T
1812.1
355.8
−2.12
220,579 − 145.920T
1510.6
150.6
0.42
944,858 − 449.124T
2101.6
520.0
−7.37
619,566 − 294.763T
2101.1
314.3
−4.83
479,103 − 241.953T
1974.1
295.1
−3.00
153,815 − 87.593T
1753.0
89.9
−0.44
1037,689 − 450.333T
2305.0
525.0
−10.34
712,397 − 295.973T
2410.6
319.8
−7.80
451,229 − 225.142T
1997.7
279.1
−2.95
125,937 − 70.782T
1774.4
74.3
−0.41
1049,710 − 448.407T
2342.9
525.7
−10.83
724,419 − 294.046T
2468.5
320.5
−8.29
333,819 − 291.637T
1147.4
303.6
4.33
−24.8
14.83
78.5
−0.17
−3.6
2.45
76.4
0.83
−5.7
3.46
eql ,
(◦ C)
B2 O2(g) and BO(g) generation B2 O3(l) + C(s) = B2 O2(g) + CO(g)
(1)
B2 O3(g) + C(s) = B2 O2(g) + CO(g)
(1a)
B2 O3(l) + C(s) = 2BO(g) + CO(g)
(2)
B2 O3(g) + C(s) = 2BO(g) + CO(g)
(2a)
0.2B4 C(s) + B2 O3(l) = 1.4B2 O2(g) + 0.2CO(g)
(3)
0.2B4 C(s) + B2 O3(g) = 1.4B2 O2(g) + 0.2CO(g)
(3a)
0.2B4 C(s) + B2 O3(l) = 2.8BO(g) + 0.2CO(g)
(4)
0.2B4 C(s) + B2 O3(g) = 2.8BO(g) + 0.2CO(g)
(4a)
B2 O3(l) + B(s) = 1.5B2 O2(g)
(5)
B2 O3(g) + B(s) = 1.5B2 O2(g)
(5a)
B2 O3(l) + B(s) = 3BO(g)
(6)
B2 O3(g) + B(s) = 3BO(g)
(6a)
B2 O2(g) and BO(g) consuming
2B2 O2(g) + 5C(s) = B4 C(s) + 4CO(g)
(7)
4BO(g) + 5C(s) = B4 C(s) + 4CO(g)
(8)
B4 C(s) + 0.5B2 O2(g) = 5B(s) + CO(g)
(9)
B4 C(s) + BO(g) = 5B(s) + CO(g)
(9a)
0.5B2 O2(g) + C(s) = B(s) + CO(g)
(10)
BO(g) + C(s) = B(s) + CO(g)
(10a)
B2 O3(l) = B2 O3(g)
(a)
B2 O2(g) = 2BO(g)
(b)
a
Temperature at which KP = 1.
−464,156 + 6.048T 139,388 − 84.056T −60,104 − 9.630T 94,641 − 75.139T −104,851 − 0.717T
–
1662.9
–
1261.0
–
325,291 − 154.361T
2091.2
205.2
−2.54
398,985 − 148.843T
2690.5
164.0
−5.25
202
B.Z. Dacic et al. / Journal of Alloys and Compounds 413 (2006) 198–205
Fig. 3. Plot of log PB2 O2 and log PBO vs. 1/T for reactions in the B–C–O system.
3. The gas phase dilution in carbothermic reduction To facilitate synthesis of B4 C not only kinetically, by alleviating the transport of gas species, but so too thermodynamically, by boosting the competitive B2 O2(g) and BO(g) generation reactions, a substantial decreasing of the partial pressure of CO(g) is required. To assess this effect, the log P − 1/T relationship has been obtained for the B2 O2(g) and BO(g) generation and consuming reactions considered in Fig. 3a and b, but now for lower PCO = 0.01 atm, and plotted in
Fig. 3c and d. It is apparent from the graphs in Fig. 3 that both temperature and dilution reduce the phase area of B4 C with concomitant expansion of boron field. The lowering of temperature at which B4 C(s) thermodynamically can be obtained, and increasing of the driving force for B4 C nucleating and growth at the unchanged temperature is apparent from the differences of the PB2 O2 values for the B2 O2(g) generation and consuming reaction in Fig. 3. More by vacuuming than by continuous flushing of reaction chamber with Argon, the partial pressure of CO(g) can be kept well below the equilibrium
Fig. 4. Plot of log PB2 O2 and log PBO vs. log PCO at 1600 ◦ C for reactions in the B–C–O system.
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203
values for Eqs. (1), (1a), (2) and (2a), for the case the total pressure P is 1 atm, increasing the value of the PB2 O2 /PCO ratio (alternatively PBO /PCO ratio) having maintained on that way the independence of KP value from the total pressure. Plots in Fig. 4 show how the difference in thermodynamic driving force between the B2 O2(g) and BO(g) generation and consuming reaction increase with the vacuuming of the system at constant temperature. 3.1. The gas phase dilution and equilibrium yield For the characteristic CBMR-s in Table 1, the effect of the gas phase dilution with Argon (d), defined as the mole number of Argon per 1 mole of B2 O3(s) , and so too the effect of decreasing of the total pressure, by vacuuming, down to 0.01 atm, on the product composition have been calculated at constant temperature and are plotted as the equilibrium yield—PCO graph in Fig. 5. It is apparent from Fig. 5 that dilution of gas phase, at constant temperature, has the same effect on gas species and the condensed phase yields as the increasing temperature has in Fig. 1. For the CBMR = 1.775, Boron can be obtained above the stability region of B4 C(s) only when the partial pressure of the B2 O2(g) and BO(g) are higher than PB2 O2 and PBO for Eqs. (9) and (9a) in Fig. 3. These conditions can be met, when due to the carbon deficiency, soon after the early stage of reduction synthesis B4 C starts reacting with non-reacted B2 O3(l) rendering the reduction to the boron thermodynamically possible—via simultaneously occurring the forward Eqs. (3), (3a), (9) and (9a). Attained for the overall equilibrium, the equilibrium partial pressure for involved gas species calculated by GEMP can be accepted as the unique equilibrium values for all those simultaneous reactions which achieve equilibrium only under the assumed constraint of existence of the single solid product phase. For a considered set of process conditions (CBMR, P/d and T), the equilibrium gas composition calculated by GEMP, is reassessed within the KP value for presumed relevant equilibria in CR. It was done by calculating the new hypothetical ) for equilibrium pressure for B2 O2(g) and BO(g) (P and PBO each single reaction, from the KP relationship by introducing the PCO and PB2 O3 values obtained by GEMP as the true and common equilibrium value for all reactions shown in Fig. 6. Only Eq. (3a) apparently attains equilibrium for the considered conditions (plot in (6a)), where the P curve for Eq. (3a) overlaps the bold PB2 O2 curve calculated by GEMP. Within the applied conjoint stoichiometric and non-stoichiometric equilibrium analysis, this fitting of the values of P and PB2 O2 means that this reaction equilibrates gas species concentration for considered P, T, d, conditions. This fitting could be taken also as an indication of the relevance of the backward Eq. (3a) in the gaseous route to B4 C(s) . The underestimated and the overestimated hypothetical values P for all other reaction can be taken (so long the made presumption of solo existence of B4 C(s) is correct) as the proof of the possibility that reactions occur simultaneously (shearing the gaseous reactants and products) which under
Fig. 5. Equilibrium yield vs. applied dilution of the gas phase for different CBMR.
no circumstances can attain their own equilibrium, in terms of the gas species concentration. In such a scenario of simultaneous occurring reactions involving BO(g) , there is no such equilibrium among considered reactions which equilibrates involved reacting species (Fig. 6b). 3.2. More about thermochemistry of the gas phase carbothermic reduction Neither the practical determination of the KP value (G◦ = −RT lnKP ) for one or more relevant and proven
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204
Fig. 7. Partition of enthalpy and entropy in Gibbs energy of Eq. (A) vs. gas phase dilution.
of B4 C(s) nucleating in the gas phase, it is quite comprehensive that these features of chemical dynamics of reactive collision are important in terms of achieving the higher total efficiency of the reactions of CR, what is beyond the hitherto done classical thermodynamical consideration. The resource to master quoted parameters, in order to achieve the higher total efficiency of reaction (lower reaction temperature, higher extent of reaction and shorter reaction time) than it can be done merely by vacuuming or by inert gas dilution, when only translation energy is targeting, could be the further tailoring of the configuration entropy of the reacting B2 O2(g) , B2 O3(g) , BO(g) and CO(g) species.
Fig. 6. Equilibrium PB2 O2 and PBO (GEMP) compared with PB 2 O2 and PBO (KP ).
4. Summary equilibrium, nor the GEMP for optimisation of possible products, for considered P and T conditions, distinguish between the enthalpy and entropy contribution in arriving at the equilibrium in the CR process. Hitherto considered effect which the gas phase dilution has on the achievable lowering of temperature at which B4 C(s) and boron become thermodynamically stable pure phase is based upon the mixing gthe increased contribution which term (−R i=1 ni ln xi , where x = n / n ) of the gas i i i g phase entropy Sgas (T,P) = i=1 ni (Si(T,P) − R ln xi ) has in the entropy equation for Eq. (A), S(A) = nB4 C SBo 4 C + Sgas(P,d) − SBo 2 O3 (l) − 3.44SCo (shown in Fig. 7). Notice that Enthalpy of the reaction H(A) is negligently affected by the isothermal change of pressure on which the reaction occurs. Besides this mixing term of reaction entropy there is an avenue of possible ramification which the configuration part of thermal energy, as an chemically important entropy contribution, might has for the overall (thermodynamic + kinetics) efficiency of CR. Even if, for the moment, we disregard: any chemical intuition about geometrical structure of reacting gas species, different angles θ which bring reacting species into effective reaction collisions, the existence of particular active complex, and the possible stereochemical mechanism
Whatever equilibria and mechanism is involved in the process of CR of B2 O3(l) , the Gibbs energy minimisation of the known reacting and product species, together with the analysis of PB2 O2 and PBO for the assumed B2 O2(g) and BO(g) generation and consuming reactions in reduction is the choice in thermodynamical estimation of optimum process conditions for the synthesis of B4 C(s) . Dilution of the gas phase, at constant temperature, has the same effect on gas species and condensed phases yields as the increasing of temperature. More by vacuuming than by continuous flushing with Argon, the crucial PCO can be kept well below the critical equilibrium values needed to promote both the B2 O2(g) and BO(g) generation and consuming reactions.
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