Assessment of the Ti-rich corner of the Ti-Si phase diagram using two sublattices to describe the Ti<sub>5</sub>Si<sub>3</sub> phase

Fiore, Marina; Beneduce, Flávio; Azevedo, Cesar Roberto de Farias

doi:10.1590/0370-44672016700073

Marina Fiore

Mestranda, Universidade de São Paulo - USP, Escola Politécnica da Universidade de São Paulo, Engenharia Metalúrgica e de Materiais, São Paulo - São Paulo - Brasil, mah.fiore@gmail.com.

Flávio Beneduce Neto

Professor, Universidade de São Paulo - USP, Escola Politécnica da Universidade de São Paulo, Engenharia Metalúrgica e de Materiais, São Paulo - São Paulo - Brasil, beneduce@gmail.com

Cesar Roberto de Farias Azevedo

Professor, Universidade de São Paulo - USP, Escola Politécnica da Universidade de São Paulo, Engenharia Metalúrgica e de Materiais, São Paulo - São Paulo - Brasil, c.azevedo@usp.br.

Thermodynamic function	Parameters	Variables
Gibbs energy for the formation of Ti₅Si₃	${}^{0}G_{T i : S I}^{{Ti}_{5} {Si}_{3}} - [{5 . G}_{Ti}^{hcp} (T) + {3 . G}_{Si}^{diamond} (T)]$	VI1 +V12.T
Gibbs energy for the formation of hypothetic Ti₈	${}^{0}G_{T i : T i}^{{Ti}_{5} {Si}_{3}} - [{8 . G}_{Ti}^{hcp} (T)]$	(40,000 + 20.T)^* * (Cost, 1998);
Gibbs energy for the formation of hypothetic Si₈	${}^{0}G_{S i : S i}^{{Ti}_{5} {Si}_{3}} - [{8 . G}_{Si}^{diamond} (T)]$	V21 +V22.T
Gibbs energy for the formation of hypothetic Ti₃Si₅	${}^{0}G_{S i : T i}^{{Ti}_{5} {Si}_{3}} - [{3 . G}_{Ti}^{hcp} (T) + {5 . G}_{Si}^{diamond} (T)]$	V31 + V32.T
Excess Gibbs energy for the (Si,Ti:Ti) interaction	${}^{0}L_{S i, T i : T i}^{{Ti}_{5} {Si}_{3}}$	V41 + V42.T^ LSi,Ti:TiTi5Si30=LSi,Ti:SiTi5Si30andLTi:Si,TiTi5Si30=LSi:Si,TiTi5si30 (Lukas, 2007).
Excess Gibbs energy for the (Si,Ti:Si ) interaction	${}^{0}L_{S i, T i : S i}^{{Ti}_{5} {Si}_{3}}$	V41 +V42.T^ LSi,Ti:TiTi5Si30=LSi,Ti:SiTi5Si30andLTi:Si,TiTi5Si30=LSi:Si,TiTi5si30 (Lukas, 2007).
Excess Gibbs energy for the (Ti: Si,Ti) interaction	$L_{T i : S i, T i}^{{Ti}_{5} {Si}_{3}}$	V51 + V52.T^ LSi,Ti:TiTi5Si30=LSi,Ti:SiTi5Si30andLTi:Si,TiTi5Si30=LSi:Si,TiTi5si30 (Lukas, 2007).
Excess Gibbs energy for the (Si:Si,Ti) interaction	${}^{0}L_{S i : S i, T i}^{{Ti}_{5} {Si}_{3}}$	V51 +V52.T^ LSi,Ti:TiTi5Si30=LSi,Ti:SiTi5Si30andLTi:Si,TiTi5Si30=LSi:Si,TiTi5si30 (Lukas, 2007).
Excess Gibbs energy for the (Si,Ti:Si,Ti ) interaction	${}^{0}L_{S i, T i : S i : T i}^{{Ti}_{5} {si}_{3}}$	V61 +V62.T^ LSi,Ti:TiTi5Si30=LSi,Ti:SiTi5Si30andLTi:Si,TiTi5Si30=LSi:Si,TiTi5si30 (Lukas, 2007).
Gibbs energy for the formation of Ti₃Si phase	${}^{0}G_{T i : S i}^{{Ti}_{3} Si} - [{3 . G}_{Ti}^{hcp} (T) + G_{Si}^{diamond} (T)]$	V71 + V72.T

Ti₃Si	Ti₅Si₃	Ti₅Si₄	TiSi	TiSi₂	Type	Reference
-50.0	- 72.67	-79.0	-77.76	-57.036	Optimization	(*Svechnikov et al.* 1970**SVECHNIKOV V. N., KOCHERZHISKY Y. A., YUPKO L. M., KULIK, O.G., SHINSHKIN, E. A. Phase diagram of the titanium-silicon system. Dokl. Akad. SSSR, v. 193, n. 2, p.393-396, 1970.)
- 47.11	- 72.53	-74.63	- 72.23	-49.87	Ab-initio	(Colinet and Tedenac, 2014)
-	- 72.52	-	-	- 56.97	Experimental	(Robins and Jenkins, 1955ROBINS, D. A., JENSKINS, I. The heats of formation of some transition metal silicides. Acta Metallurgica. v.3, p.598-603, 1955.; Topor and Kleppa, 1996; *Maslov et al., 1978*MASLOV, V.M., NEGANOV, A.S., BOROVINSKAYA, I.P., AND MERZHANOV, A.G. Self-propagating high-temperature synthesis as a method for determination of the heat of formation of refractory compounds. Combust. Explos. Shock Waves, v. 14, n. 6, p.759-767, 1978.)
-	- 78.1	- 75.9	-71.5	- 53.5	Experimental	(Kematick and Myers, 1996KEMATICK, R. J., MYERS, C. E. Thermodynamics of the Phase Formation of the Titanium Silicides. Chemistry of Materials, v. 8, n. 1, p.287-291, 1996.)
- 49	- 73.8	- 78.5	- 72.6	-55	Experimental	(Meschel and Kleppa, 1998MESCHEL, S., KLEPPA, O. Standard enthalpies of formation of some 3d transition metal silicides by high temperature direct synthesis calorimetry. Journal of Alloys and Compounds, v. 267, n. 1-2, p.128-135, 1998.; *Coelho et al., 2006*COELHO, G. C., DAVID, N., GACHON, J. C., NUNES, C. A., FIORANI, J. M., VILASI, M. Entalpias de formação de fases intermetálicas dos sistemas Ti-Si, Ti-B e Ti-Si-B medidas por calorimetria de síntese direta. In: CONGRESSO DA ABM, 61, Rio de Janeiro. Anais... São Paulo, Associação Brasileira de Metalurgia e Materiais, 2006. p. 1300-1308.)

Reaction	T(K)	Experimental values			References
L → Ti₅Si₃	2401	$X_{Si}^{L} = 0.375$	$X_{Si}^{{Ti}_{5} {Si}_{3}} = 0.375$	-	(Hansen et al., 1952HANSEN, M., KESSLER, H. D., MCPHERSON, D. J. Ti-Si phase diagram. Transactions ASM, v.44, p.518-538, 1952.; Sutcliffe, 1954SUTCLIFFE, D. A. Alliage de titane et de silicium. Revue de Metallurgie, n.3, p.524- 536, 1954.; Svechnikov et al. 1970SVECHNIKOV V. N., KOCHERZHISKY Y. A., YUPKO L. M., KULIK, O.G., SHINSHKIN, E. A. Phase diagram of the titanium-silicon system. Dokl. Akad. SSSR, v. 193, n. 2, p.393-396, 1970.; Plitcha et al. 1977PLICHTA M. R., WILLIAMS, J. C., AARONSON, H. I. On the existence of the β→αm transformation in the alloy systems Ti-Ag, Ti-Au, and Ti-Si. Metallurgical Transactions A, v. 8, p.1885-1892, 1977; Plitcha and Aaronson, 1978PLITCHA, M. R., AARONSON, H. I. The thermodynamic and kinetics of the β->αm transformation in three Ti-X systems. Acta Metallurgica, v. 26, p.1293-1305, 1978.; Seifert et al. 1996SEIFERT, H. J., LUKAS, H. L., PETZOW, G. Thermodynamic optimization of the Ti-Si system. Z. Mettalkd, v. 87, p.2-13, 1996.)
L → TiSi₂	1773	$X_{Si}^{L} = 0.667$	$X_{Si}^{{TiSi}_{2}} = 0.667$	-
L → β+Ti₅Si₃	1613	$X_{Si}^{L} = 0.137$	$X_{Si}^{β} = 0.047$	$X_{Si}^{{Ti}_{5} {Si}_{3}} = 0.36$
L → TiSi₂+Si	1603	$X_{Si}^{L} = 0.86$	$X_{Si}^{{TiSi}_{2}} = 0.667$	$X_{Si}^{Si} = 1$
L → TiSi₂+TiSi	1747	$X_{Si}^{L} = 0.641$	$X_{Si}^{TiSi} = 0.5$	$X_{Si}^{{TiSi}_{2}} = 0.667$
L+Ti₅Si₃ → TI₅Si₄	2193	$X_{Si}^{L} = 0.48$	$X_{Si}^{{Ti}_{5} {Si}_{3}} = 0.398$	$X_{Si}^{{Ti}_{5} {Si}_{4}} = 0.444$
L+Ti₅Si₃ → TiSi	1843	$X_{Si}^{L} = 0.60$	$X_{Si}^{{Ti}_{5} {Si}_{4}} = 0.444$	$X_{Si}^{Tisi} = 0.5$
β+Ti₅Si₃ → Ti₃Si	1443	$X_{Si}^{β} = 0.04$	$X_{Si}^{{Ti}_{5} {Si}_{3}} = 0.36$	$X_{Si}^{{Ti}_{3} Si} = 0.25$
β → α+Ti₃Si	1149	$X_{Si}^{β} = 0.009$	$X_{Si}^{α} = 0.004$	$X_{Si}^{{Ti}_{3} Si} = 0.25$
β → α+Ti₅Si₃ (metastable)	1133	$X_{Si}^{β} = 0.011$	$X_{Si}^{α} = 0.005$	$X_{Si}^{{Ti}_{5} {Si}_{3}} = 0.365$

Description	Variables	Calculated values
Gibbs energy for the formation of Ti₅Si₃	V11	-592,126.51
Gibbs energy for the formation of Ti₅Si₃	V12	6.055
Gibbs energy for the formation of hypothetic Si₈	V21	-36,405.66
Gibbs energy for the formation of hypothetic Si₈	V22	12.595
Gibbs energy for the formation of hypothetic Ti₃Si₅	V31	-15,172.13
Gibbs energy for the formation of hypothetic Ti₃Si₅	V32	5.055
Excess terms, (Si,Ti:Ti) and (Si,Ti:Ti) interactions, Ti₅Si₃	V41	49,843.69
	V42	-16.271
Excess terms, (Si:Si,Ti) and (Ti:Si,Ti) interactions, Ti₅Si₃	V51	-624.781
	V52	335.78
Excess term, (Si,Ti:Si,Ti) interaction, Ti₅Si₃	V61	-226.340
Excess term, (Si,Ti:Si,Ti) interaction, Ti₅Si₃	V62	-14.165
Gibbs energy for the formation of Ti₃Si	V71	-200,788.05
Gibbs energy for the formation of Ti₃Si	V72	2.737

Reaction	Parameter	Experimental	Calculated	Deviation (%)
L → Ti₅Si₃	T(K)	2403	2394	0.4
L → Ti₅Si₃	$X_{Si}^{{Ti}_{5} {Si}_{3}}$	0.375	0.375	0
L → TiSi₂	T(K)	1773	1757	1
L → TiSi₂	$X_{Si}^{{TiSi}_{2}}$	0.667	0.667	0
L → β+ Ti₅Si₃	T(K)	1613	1626	0.6
	$X_{Si}^{L}$	0.137	0.127	7
	$X_{Si}^{β}$	0.047	0.044	4
	$X_{Si}^{{Ti}_{5} {Si}_{3}}$	0.36	0.35	5
L → TiSi₂+Si	T(K)	1603	1604	0.1
	$X_{Si}^{L}$	0.86	0.815	5
	$X_{Si}^{{TiSi}_{2}}$	0.667	0.667	0
	$X_{Si}^{Si}$	1	1	0
L → TiSi₂+TiSi	T(K)	1747	1747	0
	$X_{Si}^{L}$	0.641	0.637	0.7
	$X_{Si}^{Ti}$	0.5	0.50	0
	$X_{Si}^{{TiSi}_{2}}$	0.667	0.667	0
L+Ti₅Si₃ → Ti₅Si₄	T(K)	2193	2210	0.8
	$X_{Si}^{L}$	0.477	0.476	0.2
	$X_{Si}^{{Ti}_{5} {Si}_{3}}$	0.405	0.375	6
	$X_{Si}^{{Ti}_{5} {Si}_{4}}$	0.444	0.444	0
L+Ti₅Si₄ → TiSi	T(K)	1843	1843	0
	$X_{Si}^{L}$	0.60	0.604	0.7
	$X_{Si}^{{Ti}_{5} {Si}_{4}}$	0.444	0.444	0
	$X_{Si}^{TiSi}$	0.5	0.5	0
β +Ti₅Si₃ → Ti₃Si	T(K)	1443	1457	0.1
	$X_{Si}^{β}$	0.04	0.033	18
	$X_{Si}^{{Ti}_{5} {Si}_{3}}$	0.36	0.353	2
	$X_{Si}^{{Ti}_{3} Si}$	0.25	0.25	0
β → α+ Ti₃Si	T(K)	1149	1142	0.8
	$X_{Si}^{β}$	0.009	0.010	6
	$X_{Si}^{α}$	0.004	0.0042	5
	$X_{Si}^{{Ti}_{3} Si}$	0.25	0.25	0
	$H_{form}^{{Ti}_{3} Si}$ (J/mol of phase)	-47,850	-50,197	5
β → α+ Ti₅Si₃(metastable)	T(K)	1133	1138	0.4
	$X_{Si}^{β}$	0.011	0.013	18
	$X_{Si}^{α}$	0.005	0.0054	8
	$X_{Si}^{{Ti}_{5} {Si}_{3}}$	0.365	0.36	1.4
	$H_{form}^{{Ti}_{5} {Si}_{3}}$ (J/mol of phase)	-73,874	-74,016	0.2

\begin{matrix} {}^{ex}G^{{Ti}_{5} {Si}_{3}} = y'_{Ti} . y'_{Si} .(y "_{Ti} . L_{(Ti, Si : Ti)^{+}}^{{Ti}_{5} {Si}_{3}} y "_{Si} . L_{(Ti, Si : Si)}^{{Ti}_{5} {Si}_{3}}) + y "_{Ti} . y "_{Si} .(y'_{Ti} . L_{({Ti}^{1} : Si, Ti)}^{{Ti}_{5^{S} 3}} + y'_{Si} . L_{(Si : Si, Ti)}^{{Ti}_{5} {Si}_{3}}) + \\ + y'_{Ti} . y'_{Si} . y "_{Ti} . y "_{Si} . L_{(Ti, Si : Si, Ti)}^{{Ti}_{5} {Si}_{3}} \end{matrix}

[TFN1] ^*
(Cost, 1998COST 507. Definition of Thermochemical and Thermophysical Properties to Provide a Database for the Development of New Light Alloys. European Cooperation in the Field of Scientific and Technical Research, European Commission. Proceedings of the Final Workshop of COST 507, Vaals, the Netherlands, 1998.);

[TFN2] ^**
LSi,Ti:TiTi5Si30=LSi,Ti:SiTi5Si30andLTi:Si,TiTi5Si30=LSi:Si,TiTi5si30 (Lukas, 2007LUKAS, H. L., FRIES, S. G., SUNDMAN, B. Computational thermodynamics: the calphad method. Cambridge University Press, 2007.).

Brasil

Brasil

Assessment of the Ti-rich corner of the Ti-Si phase diagram using two sublattices to describe the Ti₅Si₃ phase

Abstract

Brasil

Brasil

Assessment of the Ti-rich corner of the Ti-Si phase diagram using two sublattices to describe the Ti5Si3 phase

Abstract

Assessment of the Ti-rich corner of the Ti-Si phase diagram using two sublattices to describe the Ti₅Si₃ phase