SIMPLIFICATION OF THE THERMODYNAMIC DESCRIPTION OF THE Ti-Si SYSTEM
SIMPLIFICAÇÃO DA DESCRIÇÃO TERMODINÂMICA DO SISTEMA Ti-Si
Fiore, Marina; Beneduce, Flávio; Azevedo, Cesar Roberto de Farias
http://dx.doi.org/10.4322/2176-1523.1045
Tecnol. Metal. Mater. Min., vol.13, n1, p.91-97, 2016
Abstract
The thermodynamic optimization of ternary or higher order systems containing Ti requires that the Ti-X binary systems are continuously updated. The Ti-Si system has been studied and thermodynamically optimized since de 1950s. The Ti 5 Si 3 phase was initially considered stoichiometric to facilitate the thermodynamic calculations, although experimental results showed that this phase was a non-stoichiometric intermetallic. The most recent optimization of the Ti-Si system described this phase as a non-stoichiometric intermetallic with three sublattices, using the sub-lattice model. The problem of this approach is that it increases considerably the number of variables to be optimized during the calculation of the Ti-Si-X phase diagrams, hindering the convergence of the computational processing. The present work simplifies the optimization of the Ti-Si system, assuming that Ti 5 Si 3 phase is mostly hyper-stoichiometric in relation to Ti. The results showed that this simplification did not significantly affect the phase diagram and the thermodynamic properties calculated for the system.
Keywords
Ti-Si, Thermodynamic optimization, Thermo-calc, Parrot.
Resumo
A otimização termodinâmica de sistemas ternários ou de maior ordem contendo Ti necessita que os sistemas binários Ti-X estejam sempre atualizados. O sistema Ti-Si já foi amplamente estudado e otimizado termodinamicamente. Um dos seus compostos intermediários, a fase Ti 5 Si 3 , foi inicialmente considerada como sendo estequiométrica de modo a facilitar o processo de otimização de variáveis de funções termodinâmicas, embora os resultados experimentais confirmassem a sua não estequiométrica. A otimização mais recente modelou esta fase como sendo não-estequiométrica com três sub-redes. O problema dessa abordagem é que ela pode aumentar significativamente o número de variáveis a serem otimizadas no cálculo de sistemas ternários Ti-Si-X, dificultando a convergência do processamento computacional. O presente trabalho simplifica a otimização do sistema Ti-Si, considerando que a fase Ti 5 Si 3 é sempre hiper-estequiométrica em relação ao Ti. Os resultados mostraram que esta simplificação não afetou significativamente o diagrama de fases e os valores das propriedades termodinâmicas do sistema.
Palavras-chave
Ti-Si, Otimização termodinâmica, Thermo-calc, Parrot.
Referências
1 Azevedo CRF. Phase diagram and phase transformations in Ti-Al-Si system [doctor thesis]. London: Imperial College, Department of Materials; 1996.
2 Azevedo CRF, Flower HM. Experimental and calculated Ti-rich Corner of the Ti-Al-Si Ternary Phase Diagram. Calphad. 2002;26(3):353-373. http://dx.doi.org/10.1016/S0364-5916(02)00050-0.
3 Azevedo CRF, Flower HM. Calculated ternary diagram of Ti–Al–Si system. Materials Science and Technology. 2000;16(4):372-381. http://dx.doi.org/10.1179/026708300101507956.
4 Hansen M. Constitutions of binary alloys. New York: McGraw-Hill Book Company; 1952.
5 Svechnikov VN, Kocherzhisky YA, Yupko LM, Kulik OG, Shinshkin EA. Phase Diagram of the Titanium-Silicon System. Dokl. Akad. SSSR. 1970;193(2):393.
6 Kaufman L. Coupled phase diagrams and thermochemical data for transition metal binary systems-VI. Calphad. 1979;3(1):45-76. http://dx.doi.org/10.1016/0364-5916(79)90020-8.
7 Vahlas C, Chevalier PY, Blanquet E. A Thermodynamic Evaluation of Four Si-M (M=Mo, Ta, Ti, W) Binary System. Calphad. 1989;13(3):273-292. http://dx.doi.org/10.1016/0364-5916(89)90007-2.
8 Seifert HJ, Lukas HL, Petzow G. Thermodynamic Optimization of the Ti-Si system. Mettalkd. 1996;87:2-13.
9 Murray JL. Phase diagrams of titanium binary alloys. Ohio: ASM international; 1987.
10 Crossley FA, Carew WF, Kessler AD. Ti-alloys for elevated temperature application. Chicago: Armour Research Foundation; 1955. p. 52. (WADC Technical Report, 53-101).
11 Crossley FA, Turner DH. Titanium-Rich Corner of the Ti-Al-Si System. Transactions of the Metallurgical Society of AIME. 1958;212(1):60.
12 Schob VO, Nowotny H, Benesovsky F. The ternary system (Titanium, Zirconium, Hafnium) aluminum-silicon. Planseeberichte für Pulvermetallurgie. 1962;10:65-71.
13 Wu JS, Beaven PA, Wagner R. The Ti 3 (AI,Si)+Ti 5 (Si,AI) 3 eutectic reaction in the Ti-AI-Si system. Scripta Metallurgica et Materialia. 1990;24(1):207-212. http://dx.doi.org/10.1016/0956-716X(90)90593-6.
14 Azevedo CRF, Flower H. Microstructure and phase relationships in Ti-Al-Si system. Materials Science and Technology. Institute of Materials. 1999;15(8):869-877.
15 Bulanova M, Tretyachenko L, Golovkova M, Meleshevich K. Phase Equilibria in the α-Ti-Al-Si Region of the Ti-Si-Al System. Journal of Phase Equilibria and Diffusion. 2004;25(3):209-229. http://dx.doi.org/10.1007/s11669-004-0110-0.
16 Perrot, P. Al-Si-Ti (Aluminium - Silicon - Titanium). Light Metal Systems. Part 4. Landolt-Börnstein - Group IV. Physical Chemistry. 2006;11:1-15.
17 Meschel SV, Kleppa OJ. Standard enthalpies of formation of some 3d transition metal silicides by high temperature direct synthesis calorimetry. Journal of Alloys and Compounds. 1998;276(1-2):128-135. http://dx.doi.org/10.1016/S0925-8388(97)00528-8.
18 Kematick RJ, Myers CE. Thermodynamics of the phase formation of the titanium silicides. Chemistry of Materials. 1996;8(1):287-291. http://dx.doi.org/10.1021/cm950386q.
19 Colinet C, Tedenac JC. First-principles calculations of phase stability in the Ti–Zr–Si ternary system. Calphad. 2012;37:94-99. http://dx.doi.org/10.1016/j.calphad.2012.02.003.
20 Coelho GC, David N, Gachon JC, Nunes CA, Fiorani JM, Vilasi M. Enthalpies of formation of intermediate phases of the systems Ti–Si, Ti–B e Ti–Si–B measured by calorimetry of direct synthesis. In: Associação Brasileira de Metalurgia e Materiais. Proceedings of the 61st Anual Congress of ABM; 2006; Rio de Janeiro, Brasil. São Paulo: ABM; 2006. p. 1300-1308.
21 Topor L, Kleppa OJ. Standard enthalpies of formation of TiSi2 and VSi2 by high-temperature calorimetry. Metallurgical Transactions A: Physical Metallurgy and Materials Science. 1986;17(7):1217-1221. http://dx.doi.org/10.1007/BF02665321.
22 Maslov VM, Neganov AS, Borovinskaya IP, Merzhanov AG. Self-propagating high-temperature synthesis as a method for determination of the heat of formation of refractory compounds. Combustion, Explosion, and Shock Waves. 1978;14(6):759-767. http://dx.doi.org/10.1007/BF00786108.
23 Robins DA, Jenkins I. The heats of formation of some transition metal silicides. Acta Metallurgica. 1955;3(6):598- 603. http://dx.doi.org/10.1016/0001-6160(55)90120-6.
24 Engqvist J, Myers C, Carlsson JO. Selective deposition of TiSi 2 from H 2 -TiCI 4 gas mixtures and Si: Aspects of thermodynamics including critical evaluation of thermochemical data in the Ti-Si system. Journal of the Electrochemical Society. 1992;139(11):3197-3205. http://dx.doi.org/10.1149/1.2069053.
25 Lukas HL, Fries SG, Sundman B. Computational thermodynamics: the Calphad Method. Cambridge: Cambridge University Press; 2007.
26 Dinsdale AT. Sgte data for pure elements. Calphad. 1991;15(4):317-425. http://dx.doi.org/10.1016/0364-5916(91)90030-N.
2 Azevedo CRF, Flower HM. Experimental and calculated Ti-rich Corner of the Ti-Al-Si Ternary Phase Diagram. Calphad. 2002;26(3):353-373. http://dx.doi.org/10.1016/S0364-5916(02)00050-0.
3 Azevedo CRF, Flower HM. Calculated ternary diagram of Ti–Al–Si system. Materials Science and Technology. 2000;16(4):372-381. http://dx.doi.org/10.1179/026708300101507956.
4 Hansen M. Constitutions of binary alloys. New York: McGraw-Hill Book Company; 1952.
5 Svechnikov VN, Kocherzhisky YA, Yupko LM, Kulik OG, Shinshkin EA. Phase Diagram of the Titanium-Silicon System. Dokl. Akad. SSSR. 1970;193(2):393.
6 Kaufman L. Coupled phase diagrams and thermochemical data for transition metal binary systems-VI. Calphad. 1979;3(1):45-76. http://dx.doi.org/10.1016/0364-5916(79)90020-8.
7 Vahlas C, Chevalier PY, Blanquet E. A Thermodynamic Evaluation of Four Si-M (M=Mo, Ta, Ti, W) Binary System. Calphad. 1989;13(3):273-292. http://dx.doi.org/10.1016/0364-5916(89)90007-2.
8 Seifert HJ, Lukas HL, Petzow G. Thermodynamic Optimization of the Ti-Si system. Mettalkd. 1996;87:2-13.
9 Murray JL. Phase diagrams of titanium binary alloys. Ohio: ASM international; 1987.
10 Crossley FA, Carew WF, Kessler AD. Ti-alloys for elevated temperature application. Chicago: Armour Research Foundation; 1955. p. 52. (WADC Technical Report, 53-101).
11 Crossley FA, Turner DH. Titanium-Rich Corner of the Ti-Al-Si System. Transactions of the Metallurgical Society of AIME. 1958;212(1):60.
12 Schob VO, Nowotny H, Benesovsky F. The ternary system (Titanium, Zirconium, Hafnium) aluminum-silicon. Planseeberichte für Pulvermetallurgie. 1962;10:65-71.
13 Wu JS, Beaven PA, Wagner R. The Ti 3 (AI,Si)+Ti 5 (Si,AI) 3 eutectic reaction in the Ti-AI-Si system. Scripta Metallurgica et Materialia. 1990;24(1):207-212. http://dx.doi.org/10.1016/0956-716X(90)90593-6.
14 Azevedo CRF, Flower H. Microstructure and phase relationships in Ti-Al-Si system. Materials Science and Technology. Institute of Materials. 1999;15(8):869-877.
15 Bulanova M, Tretyachenko L, Golovkova M, Meleshevich K. Phase Equilibria in the α-Ti-Al-Si Region of the Ti-Si-Al System. Journal of Phase Equilibria and Diffusion. 2004;25(3):209-229. http://dx.doi.org/10.1007/s11669-004-0110-0.
16 Perrot, P. Al-Si-Ti (Aluminium - Silicon - Titanium). Light Metal Systems. Part 4. Landolt-Börnstein - Group IV. Physical Chemistry. 2006;11:1-15.
17 Meschel SV, Kleppa OJ. Standard enthalpies of formation of some 3d transition metal silicides by high temperature direct synthesis calorimetry. Journal of Alloys and Compounds. 1998;276(1-2):128-135. http://dx.doi.org/10.1016/S0925-8388(97)00528-8.
18 Kematick RJ, Myers CE. Thermodynamics of the phase formation of the titanium silicides. Chemistry of Materials. 1996;8(1):287-291. http://dx.doi.org/10.1021/cm950386q.
19 Colinet C, Tedenac JC. First-principles calculations of phase stability in the Ti–Zr–Si ternary system. Calphad. 2012;37:94-99. http://dx.doi.org/10.1016/j.calphad.2012.02.003.
20 Coelho GC, David N, Gachon JC, Nunes CA, Fiorani JM, Vilasi M. Enthalpies of formation of intermediate phases of the systems Ti–Si, Ti–B e Ti–Si–B measured by calorimetry of direct synthesis. In: Associação Brasileira de Metalurgia e Materiais. Proceedings of the 61st Anual Congress of ABM; 2006; Rio de Janeiro, Brasil. São Paulo: ABM; 2006. p. 1300-1308.
21 Topor L, Kleppa OJ. Standard enthalpies of formation of TiSi2 and VSi2 by high-temperature calorimetry. Metallurgical Transactions A: Physical Metallurgy and Materials Science. 1986;17(7):1217-1221. http://dx.doi.org/10.1007/BF02665321.
22 Maslov VM, Neganov AS, Borovinskaya IP, Merzhanov AG. Self-propagating high-temperature synthesis as a method for determination of the heat of formation of refractory compounds. Combustion, Explosion, and Shock Waves. 1978;14(6):759-767. http://dx.doi.org/10.1007/BF00786108.
23 Robins DA, Jenkins I. The heats of formation of some transition metal silicides. Acta Metallurgica. 1955;3(6):598- 603. http://dx.doi.org/10.1016/0001-6160(55)90120-6.
24 Engqvist J, Myers C, Carlsson JO. Selective deposition of TiSi 2 from H 2 -TiCI 4 gas mixtures and Si: Aspects of thermodynamics including critical evaluation of thermochemical data in the Ti-Si system. Journal of the Electrochemical Society. 1992;139(11):3197-3205. http://dx.doi.org/10.1149/1.2069053.
25 Lukas HL, Fries SG, Sundman B. Computational thermodynamics: the Calphad Method. Cambridge: Cambridge University Press; 2007.
26 Dinsdale AT. Sgte data for pure elements. Calphad. 1991;15(4):317-425. http://dx.doi.org/10.1016/0364-5916(91)90030-N.
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