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REM - International Engineering Journal

On-line version ISSN 2448-167X

REM, Int. Eng. J. vol.70 no.2 Ouro Preto Apr./June 2017

https://doi.org/10.1590/0370-44672016700073 

Metallurgy and materials

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

Marina Fiore1 

Flávio Beneduce Neto2 

Cesar Roberto de Farias Azevedo3 

1Mestranda, 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.

2Professor, 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

3Professor, 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.


Abstract

The thermodynamic optimization of Ti-X-Si systems requires that their respective binary systems be constantly updated. The most recent assessments of the Ti-Si phase diagrams used three sublattices to describe the Ti5Si3 phase. The stable version of this phase diagram indicated the presence of Ti(β)+Ti5Si3→Ti3Si and Ti(β)→Ti(α)+Ti3Si reactions in the Ti-rich corner, while the metastable version featured the presence of a Ti(β)→Ti(α)+Ti5Si3 reaction. The present investigation assessed these phase diagrams using two sublattices to describe the Ti5Si3 phase in order to simplify the optimization of Ti-X-Si systems.

Keywords: phase diagram; Ti-Si phase diagram; thermodynamic modeling; Ti5Si3 phase; sublattice model

1. Introduction

There is a technological interest in the Ti-Si system promoted by the beneficial effect of Si addition for the oxidation and creep resistance of Ti-X-Si alloys (Azevedo, 1996). The earliest Ti-Si experimental phase diagram was obtained in 1952 (Hansen et al., 1952), indicating in the Ti-rich corner the presence of a eutectoid reaction at 1133K, Ti(β) → Ti(α) + Ti5Si3. In 1954, another work confirmed the presence of this eutectoid reaction at 1129K (Sutcliffe, 1954). In 1970, a new experimental version of this phase diagram was proposed (Svechnikov et al., 1970), indicating in the Ti-rich corner the presence of two new reactions (a peritectoid reaction at 1444K, Ti(β) + Ti5Si3 → Ti3Si and a eutectoid reaction at 1133K, Ti(β) → Ti(α) + Ti3Si), instead of the eutectoid reaction previously observed. In late 70´s, however, careful investigations of the eutectoid reaction of the Ti-Si system were performed without showing any evidence on the presence of the Ti3Si phase (Plitcha et al. 1977; Plitcha and Aaronson, 1978). They confirmed instead the presence of Ti5Si3 phase at 1148K, Ti(β) → Ti(α) + Ti5Si3. The first thermodynamic assessment of the Ti-Si phase diagram was performed in 1976 (Kaufmann, 1976) considering the Ti5Si3 phase as a stoichiometric intermetallic. Murray (Murray, 1987) assessed the Ti-Si system assuming the Ti5Si3 phase as a non-stoichiometric phase and the calculated phase diagram was in agreement with one of the previous results (Svechnikov et al., 1970). In 1996, Seifert et al. (Seifert et al., 1996) employed an optimization method for the determination of the variables used for the thermodynamic description of the phases in order to assess the Ti-Si phase diagram from selected experimental data. They described, for instance, the Ti5Si3 phase as a non-stoichiometric compound containing three sublattices, (Ti)3(Ti,Si)2(Si,Ti)3, to represent its D88 crystal structure. Their calculated phase diagram was in good agreement with previous calculated (Murray, 1987) and experimental (Svechnikov et al., 1971) phase diagrams, presenting Ti3Si as the stable phase of the eutectoid reaction. The dispute over the stability of the Ti3Si phase in Ti-Si and Ti-X-Si systems was, however, far from over. Azevedo (Azevedo, 1996; Azevedo and Flower, 1999; Azevedo and Flower, 2000; Azevedo and Flower, 2002) and Bulanova (Bulanova et al., 1997) identified the presence of Ti5Si phase (instead of Ti3Si) after long isothermal heat treatments below the eutectoid temperature. By contrast, the presence of Ti3Si phase was observed by other investigations (Kozlov and Pavlyuk, 2004; Ramos et al., 2006; Costa et al.; 2010; Li et al., 2014). In 2010, the stability of intermetallic phases in the Ti-Si system was studied by ab-initio calculations, indicating that the stability of Ti3Si phase was controversial (Colinet and Tedenac, 2010). Recent ab-initio calculation showed that Ti5Si3 phase was actually more stable than Ti3Si phase at 0 K (Poletaev et al., 2014).

The present work will calculate and compare the Ti-rich corner of the stable and metastable Ti-Si phase diagrams, using two sublattices, (Ti,Si)5(Si,Ti)3, to describe the Ti5Si3 phase, assuming that Ti3Si is the stable phase in the eutectoid decomposition of Ti(β) phase. These results will be compared to previous calculated phase diagrams using three sublattices to describe the Ti5Si3 phase (Cost, 1998; Fiori et al., 2016).

2. Methodology

The liquid, Ti(α) and Ti(β) phases are described using Equations 1 to 5. The Gibbs free energy of reference (Gref) is described by Equation 2, while the Gibbs free energy of the ideal solution (Gid) is described by Equation 3 and the excess Gibbs free energy (Gex) of the regular solution is described using the Redlich-Kister polynomial (see Equations 4 and 5) [23]. Additionally, the Gibbs energy for formation of the stoichiometric Ti3Si phase is described using the Kopp-Neumann rule (see Equation 6) and the non-stoichiometric Ti5Si3 phase is described by the Compound Energy Formalism (Lukas, 2007), using a two-sublattices containing Ti and Si, see Equations 7 to 10.

Gphase=Gref+Gid+Gex (1)
GGref=xSi.GSiref+XTi.GTiref (2)

Where: Giref = GiSER and xSi and xTi are the molar fraction of the elements.

Gid=R.T.[xSi.InxSi+xTi.InxTi] (3)
Gex=XSi.xTi.Lphase (4)

Where: Lphase is the Ti-Si interaction parameter in the phase.

Lphase=Lphase0+Lphase1(XSiXTi)+. . .+LphaseV.(XSiXTi)V (5)

Where: Lvphase = a+b.T+...

formGTi3SixTi.GTirefxSi.GSiref=a+b.T+c.T.ln(T) (6)
GTi5Si3=formGTi5Si3+idGTi5Si3+exGTi5Si3 (7)
GTi5Si3form=y'Ti.y"Ti.GTi:TiRef+y'Si.y"Ti.GSi:TiRef.+y'Ti.y"Si.GTi:SiRef+y'Si.y"Si.GSi:SiRef (8)
GTi5Si3id=R. T.{5.[y'Si.ln(y'Si)+y'Ti.ln(y'Ti)]+3.[y"Siln(y"Si)+y"Tiln(y"Ti)]} (9)
GTi5Si3ex=y'Ti.y'Si.(y"Ti.L(Ti,Si:Ti)+Ti5Si3y"Si.L(Ti,Si:Si)Ti5Si3)+y"Ti.y"Si.(y'Ti.L(Ti1:Si,Ti)Ti5S3+y'Si.L(Si:Si,Ti)Ti5Si3)++y'Ti.y'Si.y"Ti.y"Si.L(Ti,Si:Si,Ti)Ti5Si3 (10)

Where: yjn is the site fraction of the element (j) in the sublattice (n).

The parameters and variables used for the thermodynamic description of the Ti5Si3 and Ti3Si phases are listed in Table 1. These variables were calculated from selected experimental data (see Tables 2 and 3) using the Parrot module of the Thermo-Calc software. The variables related to the Ti5Si3 phase were initially calculated during the assessment of the metastable phase diagram (suspending the presence of the Ti3Si phase). These variables were then fixed during the assessment of the stable phase diagram for the calculation of the variables related to the Ti3Si phase. These diagrams were compared to the stable and metastable Ti-Si phase diagrams obtained by Thermocalc software using COST 507 database (Cost, 1998), whose Ti-Si system was based on the assessed version by Seifert et al. (Seifert et al., 1996).

Table 1 Parameters and variables used for the thermodynamic description of the Ti5Si3 - (Ti,Si)5: (Si,Ti)3- and Ti3Si phases. Vi1 in [J.(mol of phase)-1]; Vi2 in [J.(mol of phase)-1.K-1]. 

Thermodynamic function Parameters Variables
Gibbs energy for the formation of Ti5Si3 GTi:SITi5Si305.GTihcpT+3.GSidiamondT VI1 +V12.T
Gibbs energy for the
formation of hypothetic Ti8
GTi:TiTi5Si308.GTihcpT (40,000 + 20.T)*
Gibbs energy for the formation of hypothetic Si8 GSi:SiTi5Si308.GSidiamondT V21 +V22.T
Gibbs energy for the
formation of hypothetic Ti3Si5
GSi:TiTi5Si303.GTihcpT+5.GSidiamondT V31 + V32.T
Excess Gibbs energy for the
(Si,Ti:Ti) interaction
LSi,Ti:TiTi5Si30 V41 + V42.T**
Excess Gibbs energy for the
(Si,Ti:Si ) interaction
LSi,Ti:SiTi5Si30 V41 +V42.T**
Excess Gibbs energy for the
(Ti: Si,Ti) interaction
LTi:Si,TiTi5Si3 V51 + V52.T**
Excess Gibbs energy for the
(Si:Si,Ti) interaction
LSi:Si,TiTi5Si30 V51 +V52.T**
Excess Gibbs energy for the
(Si,Ti:Si,Ti ) interaction
LSi,Ti:Si:TiTi5si30 V61 +V62.T**
Gibbs energy for the
formation of Ti3Si phase
GTi:SiTi3Si03.GTihcpT+GSidiamondT V71 + V72.T

*(Cost, 1998);

** LSi,Ti:TiTi5Si30=LSi,Ti:SiTi5Si30andLTi:Si,TiTi5Si30=LSi:Si,TiTi5si30 (Lukas, 2007).

Table 2 Enthalpy for the formation of intermetallic phases, Ti-Si system (kJ/mol of phase). 

Ti3Si Ti5Si3 Ti5Si4 TiSi TiSi2 Type Reference
-50.0 - 72.67 -79.0 -77.76 -57.036 Optimization (Svechnikov et al. 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, 1955; Topor and Kleppa, 1996; Maslov et al., 1978)
- - 78.1 - 75.9 -71.5 - 53.5 Experimental (Kematick and Myers, 1996)
- 49 - 73.8 - 78.5 - 72.6 -55 Experimental (Meschel and Kleppa, 1998; Coelho et al., 2006)

Table 3 Experimental values of the Ti-Si invariant reactions (XSi phase: atomic fraction of Si). 

Reaction T(K) Experimental values References
L → Ti5Si3 2401 XSiL=0.375 XSiTi5Si3=0.375 - (Hansen et al., 1952;
Sutcliffe, 1954;
Svechnikov et al. 1970;
Plitcha et al. 1977;
Plitcha and Aaronson, 1978;
Seifert et al. 1996)
L → TiSi2 1773 XSiL=0.667 XSiTiSi2=0.667 -
L → β+Ti5Si3 1613 XSiL=0.137 XSiβ=0.047 XSiTi5Si3=0.36
L → TiSi2+Si 1603 XSiL=0.86 XSiTiSi2=0.667 XSiSi=1
L → TiSi2+TiSi 1747 XSiL=0.641 XSiTiSi=0.5 XSiTiSi2=0.667
L+Ti5Si3 → TI5Si4 2193 XSiL=0.48 XSiTi5Si3=0.398 XSiTi5Si4=0.444
L+Ti5Si3 → TiSi 1843 XSiL=0.60 XSiTi5Si4=0.444 XSiTisi=0.5
β+Ti5Si3 → Ti3Si 1443 XSiβ=0.04 XSiTi5Si3=0.36 XSiTi3Si=0.25
β → α+Ti3Si 1149 XSiβ=0.009 XSiα=0.004 XSiTi3Si=0.25
β → α+Ti5Si3
(metastable)
1133 XSiβ=0.011 XSiα=0.005 XSiTi5Si3=0.365

3. Results and discussion

The calculated values of the variables are shown in Table 4. According to Thermo-Calc User Guide (Thermo, 2015), the order of magnitude of Vi1-type variables should not be higher than 105 and the Vi2-type variables should not be higher than 101. In the present assessments V11 presented an order of magnitude above 105; and V52 above 101. This Vi2-type variable, however, was used to describe the excess term of the enthalpy rather than the entropy for the formation of intermetallic phases. The values of the reduced sum of squares (~ 5 for both optimization procedures) exceeded the advisable maximum value of one (Thermo, 2015). These results indicate that the optimization procedures of the Ti-Si system using two sublattices to describe the Ti5Si3 phase were successful but they can be further improved.

Table 4 Calculated variables, Vi1 in [J.(mol of phase)-1]; Vi2 in [J.(mol of phase)-1.K-1]. 

Description Variables Calculated values
Gibbs energy for the formation of Ti5Si3 V11 -592,126.51
V12 6.055
Gibbs energy for the formation of hypothetic Si8 V21 -36,405.66
V22 12.595
Gibbs energy for the formation of hypothetic Ti3Si5 V31 -15,172.13
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
V62 -14.165
Gibbs energy for the formation of Ti3Si V71 -200,788.05
V72 2.737

Table 5 compares the values of the experimental and the calculated equilibria and the enthalpies for the formation of Ti3Si and Ti5Si3 phases. Six out of the 38 calculated values presented relative deviation above 5% in relation to the experimental data. Two of these deviations were originated in the equilibria involving the liquid phase and they could be decreased by the use of a more complex model for the thermodynamic description of the liquid phase (Lukas, 2007; Seifert et al., 1996; Fiori et al., 2016). The other values were found for the β +Ti5Si3→Ti3Si, β→α+Ti3Si and β→α+Ti5Si3 reactions, indicating that further experiments in these critical regions of the Ti-rich corner of the Ti-Si phase diagram are needed to improve the results of the present optimization procedures; and to define which one of the eutectoid reactions is actually the stable one (β→α+Ti3Si or β→α+Ti5Si3).

Table 5 Main experimental and calculated values of the Ti-Si system. 

Reaction Parameter Experimental Calculated Deviation (%)
L → Ti5Si3 T(K) 2403 2394 0.4
XSiTi5Si3 0.375 0.375 0
L → TiSi2 T(K) 1773 1757 1
XSiTiSi2 0.667 0.667 0
L → β+ Ti5Si3 T(K) 1613 1626 0.6
XSiL 0.137 0.127 7
XSiβ 0.047 0.044 4
XSiTi5Si3 0.36 0.35 5
L → TiSi2+Si T(K) 1603 1604 0.1
XSiL 0.86 0.815 5
XSiTiSi2 0.667 0.667 0
XSiSi 1 1 0
L → TiSi2+TiSi T(K) 1747 1747 0
XSiL 0.641 0.637 0.7
XSiTi 0.5 0.50 0
XSiTiSi2 0.667 0.667 0
L+Ti5Si3 → Ti5Si4 T(K) 2193 2210 0.8
XSiL 0.477 0.476 0.2
XSiTi5Si3 0.405 0.375 6
XSiTi5Si4 0.444 0.444 0
L+Ti5Si4 → TiSi T(K) 1843 1843 0
XSiL 0.60 0.604 0.7
XSiTi5Si4 0.444 0.444 0
XSiTiSi 0.5 0.5 0
β +Ti5Si3 → Ti3Si T(K) 1443 1457 0.1
XSiβ 0.04 0.033 18
XSiTi5Si3 0.36 0.353 2
XSiTi3Si 0.25 0.25 0
β → α+ Ti3Si T(K) 1149 1142 0.8
XSiβ 0.009 0.010 6
XSiα 0.004 0.0042 5
XSiTi3Si 0.25 0.25 0
HformTi3Si (J/mol of phase) -47,850 -50,197 5
β → α+ Ti5Si3(metastable) T(K) 1133 1138 0.4
XSiβ 0.011 0.013 18
XSiα 0.005 0.0054 8
XSiTi5Si3 0.365 0.36 1.4
HformTi5Si3 (J/mol of phase) -73,874 -74,016 0.2

Figure 1-a shows a general view of the calculated stable Ti-Si phase diagram, indicating that the position of the phase boundaries are in fair agreement with previous results (Svechnikov et al. 1970; Fiore et al. 2016), except for the narrower solubility range of the Ti5Si3 phase field. Figure 1-b shows a detail of the Ti-rich corner near the eutectoid reaction, indicating that there are no experimental data to validate the position of the calculated Ti(α) and Ti(β) solvus lines. The present assessment showed lower Si-solubility in the Ti(α) and Ti(β) phases when compared to the calculated phase diagram using COST 507 database (Cost, 1998), without any change in the eutectoid temperature.

Figure 1 Stable Ti-Si phase diagram. a) General view of the phase diagram (β+Ti5Si3→Ti3Si and β→α+Ti3Si reactions) compared with the latest assessment (Fiore et al., 2016); b) Detail of the eutectoid reaction, Ti(β)→Ti(α)+Ti3Si in the Ti-rich corner, compared with previous assessment by COST 507 database (Cost, 1998). 

Figure 2-a shows the calculated metastable Ti-Si phase diagram, indicating that the position of the phase boundaries are in good agreement with previous experimental (Hansen et al, 1952; Sutcliffe, 1954) and calculated (Fiore et al. 2016) phase diagrams, except for the narrower solubility range of the Ti5Si3 phase field. The shape of this phase field resembles a previous result, which described the Ti5Si3 phase as Ti3Ti2(Ti,Si)3 (Beneduce et al., 2016). Figure 2-b shows a detail of the Ti-rich corner near the eutectoid reaction, comparing the present assessment with previous experimental (Plitcha et al. 1977; Plitcha and Aaronson, 1978) and calculated (Cost, 1998; Fiore et al. 2016) phase diagrams. The present assessment showed smaller Si-solubility in the Ti(α) and Ti(β) phases when compared to the calculated phase diagram using COST 507 database (Cost, 1998) and a slightly higher value for the eutectoid temperature. The slope of the Ti(α) solvus line showed a typical inclination, unlike the one obtained by COST 507 database (Cost, 1998), indicating that the Si solubility of the Ti(α) phase decreased with decreasing temperature. This result is agreement with the most recent assessment of the metastable Ti-Si phase diagram (Fiore et al. 2016).

Figure 2 Metastable Ti-Si phase diagram. a) General view of the Ti-Si phase diagram (β→α+Ti5Si3 reaction) compared with the latest assessment (Fiore et al., 2016); b) Detail of the eutectoid reaction, Ti(β)→Ti(α)+Ti5Si3, in the Ti-rich corner, compared with previous assessment by COST 507 database (Cost, 1998) with suspended Ti3Si phase. 

The position of the Ti5Si3 phase field in both assessments was slightly shifted towards smaller Si contents. Additionally, its Si-solubility range was comparatively narrower and presented a maximum of 37.5at%. This maximum Si-solubility value suggests that the present thermodynamic description of the excess terms of the (Ti,Si)5(Si,Ti)3 phase was not able to induce the presence of Si atoms on the Ti sublattice. In this sense, the hypothesis that the interaction between Si and Ti on each sublattice is independent of the occupation of the other sublattice ( LSi,Ti:TiTi5Si30=LSi,Ti:SiTi5Si30andLTi,Si:TiTi5Si30=LSi,Si:TiTi5Si30 ), see Table 1) should be further analyzed. For instance, another hypothesis, assuming that the interaction parameters on the two sublattices are symmetrical ( LSi,Ti:TiTi5Si30=LSi,Ti:SiTi5Si30andLTi,Si:TiTi5Si30=LSi,Si:TiTi5Si30 ), can be investigated. Finally, the description of the Ti5Si3 phase using only two sublattices presented promising results for the assessment of Ti-X-Si phase diagrams.

4. Conclusions

  • The assessed versions of the stable and metastable Ti-Si phase diagrams, using only two sublattices to describe the Ti5Si3 phase, were in fair agreement with previous experimental and calculated phase diagrams.

  • The slope of the Ti(α) solvus line of the assessed metastable Ti-Si phase diagram showed a typical inclination, indicating that the Si-solubility of the Ti(α) phase decreased with decreasing temperature.

  • The position of the Ti5Si3 phase field in both assessments was slightly shifted towards smaller Si contents. Additionally, its Si-solubility range was comparativelly much narrower than expected and presented a maximum value of 37.5at%.

  • The assessment of the Ti-Si phase diagram using two sublattices to describe the Ti5Si3 phase might be further improved by the inclusion of new experimental data near the eutectoid reaction of the Ti-rich corner of the Ti-Si phase diagram. In this sense, further experimental work is needed to define which eutectoid reaction (β→α+Ti3Si or β→α+Ti5Si3) is stable.

  • Finally, the use of a more complex description for the liquid phase and another thermodynamic description for the excess terms of the Ti5Si3 phase might be useful to improve the quality of the assessed phase diagrams.

Acknowledgments

The authors would like to thank the kind collaboration of Prof. V. Pastoukhov, Prof. S. Wolynec, Prof. C. G. Schön and Prof. L.T.F. Eleno, all from Universidade de São Paulo, and Dr. A. H. Feller. The present investigation was funded by the Ministry of Education from Brazil (Coordination for the Improvement of Higher Education Personnel, CAPES) in a form of a MEng. scholarship to Ms. M. Fiore.

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Received: June 13, 2016; Accepted: November 28, 2016

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