Abstract
Based on an assessment of the available experimental thermochemical and phase diagram information, the phase equilibria involving the condensed phases of the Hf-C system were calculated. The Gibbs energies of the individual phases were described with thermodynamic models. The liquid phase was described as a substitutional solution using the Redlich-Kister formalism for the excess Gibbs energy. Graphite was treated as a stoichiometric phase. The solid solutions of carbon in αHf and βHf as well as the nonstoichiometric phase HfC1-x were described as interstitial solid solutions employing the compound energy model (CEM) with two sublattices. The parameters in the models were determined by computerized optimization using selected experimental data. The temperature dependence of the Gibbs energies of the metastable carbides HfC0.5 and HfC3, which are involved in the CEM for αHf and βHf, were estimated using a method based on the regular behavior of the vibrational entropy of transition metal carbides. A thermodynamic description was obtained, which was used in the calculation of the Hf-C phase diagram. Detailed comparison is made between calculation and experimental data.
Similar content being viewed by others
Cited References
C. Agte and H. Alterthum, “Systems of High-Melting Carbides; Contribution to the Problem of Carbon Fusion,” Z. Tech, Phys., 11, 182–191 (1930) in German (Experimental)
O. Redlich and A.T. Kister, “The Algebraic Representation of Thermodynamic Properties and the Classification of Solids,” Ind. Eng. Chem., 40, 345–348 (1948). (Theory)
P.G. Cotter and J.A. Kohn, “Industrial Diamond Substitutes: I, Physical and X-Ray Study of Hafnium Carbide,” J. Am. Ceram. Soc, 37(9), 415–420 (1954). (Experimental)
F. Benesovsky and E. Rudy, “Contribution to the Systems Zirconium-Carbon and Hafnium-Carbon,” Planseeber. Pulvermetall., 8(2), 66–71 (1960) in German. (Experimental)
D.S. Neel, C.D. Pears, and S. Oglesby Jr., Tech. Rep. WADD-TR-60-924, Wright Air Development Division, Wright-Patterson Air Force Base, OH (1960). (Experimental)
H. Kato and M.I. Copeland, Tech. Rep. USBM-U-887(QPR13), U.S. Atomic Energy Comm.,8pp (1961). (Experimental)
K.I. Portnoi, Yu.V. Levinskii, and V.I. Fadeeva, “Reaction with Carbon of Some Refractory Carbides and Their Solid Solutions,” Izv. Akad. Nauk SSSR, Otd. Tekh Nauk, Met. Toplivo, (2), 147–149(1961) in Russian. (Experimental)
R.G. Avarde, A.I. Avgustinik, Yu.N. Vil'K, Yu.D. Kondrashov, S.S. Nikol'skii.Yu.A. Omel'chenko, and S.S. Ordan'yan, “Phase Diagram of the Hf-HfC System,” Zh. Prikl. Khim., 35, 1976–1980 (1962) in Russian. (Experimental)
H. Bittner and H. Goretzki, “Magnetic Investigation of Carbides TiC, ZrC, HfC, VC, NbC and TaC,” Monatsh. Chem., 93, 1000–1004 (1962) in German. (Experimental)
M.I. Copeland, Tech. Rep. BM-U-952, U.S. Bureau of Mines (1962). (Experimental)
H. Kato and M. Copeland, USBM-U-921, U.S. Atomic Energy Comm., 12–13 (1962); USBM-U-952, U.S. Atomic Energy Comm., 14–16 (1962); USBM-U-978, U.S. Atomic Energy Comm., 5–7 (1962); USBM-U-1001, U.S. Atomic Energy Comm., 7–8 (1962); USBM-U-1031, U.S. Atomic Energy Comm., 19–21 (1963); USBM-U-1057,U.S. Atomic Energy Comm., 14–19(1963). (Experimental)
J.I. Wittebort, Tech. Rep. WADD-TR-60-924, Armed Services Technical Information Agency (1962). (Experimental)
R.P. Adams and R.A. Beall, “Preparation and Evaluation of Fused Hafnium Carbide,” U.S. Bur. Mines, Rep. Invest. 6304,17 pp (1963). (Experimental)
J.A. Coffman, G.M. Kibler, T.F. Lyon, and B.D. Acchione, “Carbonization of Plastics and Refractories Materials Research,” Tech. Rep. WADD-TR-60-646, Part II, Wright Air Development Division, Wright-Patterson Air Force Base, OH (1963). (Experimental)
L.S. Levinson, “High-Temperature Heat Content of Tungsten Carbide and Hafnium Carbide,” J. Chem. Phys. 40(5), 1437–1438 (1964). (Experimental)
A.D. Mah, USBM-6518, U.S. Bureau of Mines (1964). (Experimental)
L. A. McClaine, “Thermodynamic and Kinetic Studies fora Refractory Materials Program,” Tech. Rep. ASD-TDR-62-204, Part III, Air Force Materials Laboratory, Wright-Patterson AFB, OH (1964). (Experimental; #)
R.A. McDonald, F.L. Oetting, and H. Prophet, Proc. Meet. Interagency Chem. Rocket Propulsion Group Thermochem., New York, 1963, CPIA 44, Vol. 1, Johns Hopkins Univ., Appl. Phys. Lab., Silver Spring, MD, 213–245 (1964).
V.I. Zehlankin and V.S. Kutsev, “Variation of the Heat of Formation of Hafnium Carbides with Composition,” Russ. J. Phys. Chem., 38(3), 302–303 (1964). (Experimental)
E. Rudy, “Ternary Phase Equilibria in Transition Metal-Boron-Carbon-Silicon Systems. Part 1. Related Binary Systems. Vol. 4. Hf-C System,” Tech. Rep. AFML-TR-65-2, Part I, Vol. IV, Air Force Materials Laboratory, Wright-Patterson AFB, OH, 62 pp (1965). (Experimental;#)
R.V. Sara, “The Hafnium-Carbon System,” Trans. Metall. Soc. AIME, 233(9), 1683–1691 (1965). (Experimental)
L.M. Adelsberg, L.H. Cadoff, and J.M. Tobin, “Group IV-B and V-B Metal Carbide-Carbon Eutectic Temperatures,” J. Am. Ceram. Soc. 49(10), 573–574 (1966). (Experimental)
V.V. Fesenko, A.S. Bolgar, and S.P. Gordienko, “Vaporization Rate, Vapor Pressure, Composition Discontinuity, and Some Thermodynamic Properties of Refractory Compounds at Temperatures up to 3000°,” Rev. Hautes Tempér. Réfract., 5(3), 261–271 (1966) in French. (Experimental)
H.L. Schick, Thermodynamics of Certain Refractory Compounds, Vol. 1, Academic Press, New York (1966). (Experimental)
L.M. Adelsberg and L.H. Cadoff, “The Reactions of Liquid Titanium and Hafnium with Carbon,” Trans. Metall. Soc. AIME, 239(6), 933–935 (1967). (Experimental)
A.S. Bolgar, E.A. Gusyeva, and V.V. Fesenko, “Thermodynamic Properties of Zirconium and Hafnium Carbides over the Range of 298-2500 °K,” Pomshk. Metall., 49(1), 40–43 (1967) in Russian. (Experimental)
D.K. Deardorff, M.I. Copeland, and R.P. Adams, “The Hafnium-Carbon Phase Diagram,” U.S. Bur. Mines, Rep. Invest. 6983,16 pp (1967). (Experimental)
M. Hoch, “The Role of the Defect Interaction Energy on the Stability of Interstitial Phases,” Phase Stability of Metals and Alloys, P.S. Rudman, J. Stringer, and R.I. Jaffee, Ed., McGraw-Hill, New York (1967). (Theory)
E.K. Storms, The Refractory Carbides, Vol. 2, Refractory Materi-als, Academic Press, New York (1967). (Compilation; #)
E. Rudy, “Ternary Phase Equilibria in Transition Metal-Boron-Carbon-Silicon Systems. Part V., Compendium of Phase Diagram Data,” Tech. Rep. AFML-TR-65-2, Part V, Air Force Materials Laboratory, Wright-Patterson AFB, OH, 165–167 (1969). (Review; #)
E.A. Guseva, A.G. Turchanin, V.V. Morozov, A.S. Bolgar, and V.V. Fesenko, “An Experimental Study of the Heat Content of Hafnium Carbide in the Region of Homogeneity at High Temperatures,” Zh. Fiz. Khim., 45(11), 2948 (1971) in Russian. (Experimental)
L.E. Toth, Transition Metal Carbides and Nitrides, Academic Press, New York (1971). (Compilation; #)
V.N. Zagryazkin, E.V. Fiveisky, and A.S. Panov, “Thermodynamic Properties of the Monocarbides of Transition Metals. II. Thermodynamic Properties of the Monocarbides of Group IV-V Transition Metals,” Zh. Fiz, Khim., 47(8), 1951–1955 (1973) in Russian; TR: Russ. J. Phys. Chem., 47(8), 1099–1101 (1973). (Theory)
S.E. Buravoi and M.L. Taubin, “Thermophysical Properties of Carbides of Titanium, Zirconium, Hafnium and Niobium at 50-1000 °C,” Inorganic Mater., 10, 319–321 (1974). (Experimental)
V.N. Eremenko, T.Ya. Velikanova, and S.V. Shabanova, “Phase Diagram of the Hafnium-Carbon Binary System,” Strukt. Faz, Fazouye Prevrashch. Diagr. Sostoyaniya, O.S. Ivanov and Z.M. Alekseeva, Ed., Nauka, Moscow, 129–132 (1974) in Russian. (Experimental; #)
F. J. Kohl and C. A. Steams, “Vaporization and Dissociation Energies of the Molecular Carbides of Titanium, Zirconium, Hafnium and Thorium,” High Temp. Sci., 6, 284–302 (1974). (Experimental)
N. Kornilov, N.V. Chelovskaya, V.I. Zhelankin, and G.P. Shveikin, “Enthalpies of Formation of Hafnium Carbides,” J. Chem. Thermodyn., 9(7), 629–642 (1977). (Experimental)
E.F. Westrum, Jr. and G. Feick, “Heat Capacities of HfB2.035 and HfC0.968 from 5 to 350 K,” J. Chem. Thermodyn., 9, 293–299 (1977). (Experimental)
V.M. Maslov, A.S. Neganov, I.P. Borovinskaya, and A.G. Merzhanov, “Self-Propagating High-Temperature Synthesis as a Method for Determination of the Heat of Formation of Refractory Compounds,” Fiz, Goreniya Vzryva, 14(6), 73–82 (1978) in Russian. (Experimental)
P.J. Spencer, O. Kubaschewski-von Goldbeck, R. Ferro, R. Marazza, K. Girgis, and O. Kubaschewski, Hafnium Physico-Chemical Properties of Its Compounds and Alloys, K.L. Komarek, Ed., Atomic Energy Review, Special Issue No. 8, IAEA, Vienna (1981). (Compilation; #)
A.G. Turchanin and A.E. Polyakov, “Thermodynamic Properties of Hafnium Carbide in the Temperature Range 0-3000 °K,” Izv. Akad. NaukSSSR, Neorg. Mater., 18(3), 404–406 (1982) in Russian; TR: Inorganic Mater., 18(3), 335–338 (1982). (Compilation)
J. Rosén and G. Grimvall, “Anharmonic Lattice Vibrations in Simple Metals,” Phys. Rev., B27(12), 7199–7208 (1983). (Theory)
B. Sundman, B. Jansson, and J.-O. Andersson, “The Thermo-Calc Databank System,” Calphad, 9, 153–190 (1985). (Theory)
J.-O. Andersson, A. Fernandez Guillermet, M. Hillert, B. Jansson, and B. Sundman, “A Compound-Energy Model of Ordering in a Phase with Sites of Different Coordination Numbers,” Acta Metall., 34(3), 437–445 (1986). (Theory)
G. Grimvall and M. Thiessen, “The Strength of Interatomic Forces,” Science of Hard Materials, E.A. Almond, C.A. Brookes, and R. Warten, Ed., Inst. Phys. Conf. Ser. No. 75: Chapter 1,61–67 (1986). (Theory)
A.G. Turchanin, “Thermodynamics of Cubic Refractory Carbides of Group IV Transition Metals of Variable Composition in the Range 1200-2500 °K,” Izv. Akad. Nauk SSSR, Neorg. Mater, 22(8), 1299–1302 (1986) in Russian; TR: Inorganic Mater., 22(8), 1136–1139 (1986). (Compilation)
J.-O. Andersson, “ AThermodynamic Evaluation of the Fe-Cr-C System,” Metall. Trans., 19A, 627–636 (1988).
R. Berkane, “Thermodynamic Study of Chromium, Titanium, Zirconium and Hafnium Carbides by High Temperature Calorimetry Numerical Modeling of the Phase Diagram,” Thesis, Université de Nancy I (1989). (Experimental)
A. Fernández Guillemet and G. Grimvall “Cohesive Properties and Vibrational Entropy of 3d Transition-Metal Compounds: MX (NaCl) (X=C, N, O, S), Complex Carbides and Nitrides,” Phys. Rev., 040(15), 10582–10593 (1989). (Theory)
A. Fernández Guillemet and G. Grimvall, “Homology of Interatomic Forces and Debye Temperatures in Transition Metals,” Phys. Rev., B40(3), 1521–1527 (1989). (Theory)
A. Fernández Guillemet and G. Grimvall, “Correlations for Bonding Properties and Vibrational Entropy in 3d-Transition Metal Compounds, with Application to the CALPHAD Treatment of a MetastableCr-CPhase,”Z Metallkd., 81, 521–524 (1990). (Theory)
H. Okamoto, “The C-Hf (Carbon-Hafnium) System,” Bull. Alloy Phase Diagrams, 11(4), 369–403 (1990). (Compilation; #)
B. Sundman, “Review of Alloys Modelling,” An. Fisica, Serie B 86, 69–82 (1990). (Theory)
A.T. Dinsdale, “SGTE Data for Pure Elements,” Calphad, 15, 319–427 (1991). (Compilation)
A. Fernández Guillemet, “Predictive Approach to Thermodynamic Properties of Metastable Cr3C Carbide,” Int. J. Thermophys., 12(5), 919–936 (1991). (Theory)
A. Fernández Guillemet and W. Huang, “Thermodynamic Analysis of Stable and Metastable Carbides in the Mn-V-C System and Predicted Phase Diagrarn” Int. J. Thermophys., 12(6), 1077–1102 (1991). (Theory)
A. Fernández Guillemet and G. Grimvall, “Cohesive Properties and Vibrational Entropy of 3d-Transition Metal Carbides,” J. Phys. Chem. Solids 53(1), 105–125 (1992). (Theory)
S. Jonsson, Thesis, Royal Institute of Technology, Stockholm, Sweden (1992).
S. Wolfram, MATHEMATICA, A System for Doing Mathematics by Computer, Addison-Wesley, Massachusetts (1992).
A. Fernández Guillemet and S. Jonsson, “Thermodynamic Analysis of Stable and Metastable W Nitrides and Calculation of the W-N Phase Diagram,” Z Metallkd. 84(2), 106–117 (1993). (Theory)
O. Kubaschewski, C.B. Alcock, and P.J. Spencer, Materials Thermochemistry, 6th ed., Pergamon Press, Oxford (1993). (Compilation)
A. Fernández Guillemet, “Analysis ofThermochemical Properties and Phase Stability in the Zirconium-Carbon System,” J. Alloys Compd., 217, 69–89 (1995). (Theory)
H. Bittermann and P. Rogl, “Critical Assessment and Thermodynamic Calculation of the Ternary System Boron-Carbon-Hafnium (B-C-Hf),” Thesis, Institute of Physical Chemistry at the University of Vienna(1997). (Compilation)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bittermann, H., Rogl, P. Critical assessment and thermodynamic calculation of the binary system hafnium-carbon (Hf-C). JPE 18, 344–356 (1997). https://doi.org/10.1007/s11669-997-0061-3
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s11669-997-0061-3