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

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 (G^ref) is described by Equation 2, while the Gibbs free energy of the ideal solution (G^id) is described by Equation 3 and the excess Gibbs free energy (G^ex) 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.

(1) $G_{\mathrm{phase}}=G^{\mathrm{ref}}+G^{\mathrm{id}}+G^{\mathrm{ex}}$

(2) ${\mathit{G}}_G^{\mathrm{ref}}=x_{\mathrm{Si}}.G_{\mathrm{Si}}^{\mathrm{ref}}+X_{\mathrm{Ti}}.{\mathit{G}}_{\mathrm{Ti}}^{\mathrm{ref}}$

Where: G_i^ref = G_i^SER and x_Si and x_Ti are the molar fraction of the elements.

(3) $G^{\mathrm{id}}=R.T\mathrm{.[}{x}_{\mathrm{Si}}.{\mathrm{Inx}}_{\mathrm{Si}}+x_{\mathrm{Ti}}.{\mathrm{Inx}}_{\mathrm{Ti}}]$

(4) $G^{\mathrm{ex}}=X_{\mathrm{Si}}.x_{\mathrm{Ti}}.L_{\mathrm{phase}}$

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

(5) $L_{\mathrm{phase}}=L_{\mathrm{phase}}^0+L_{\mathrm{phase}}^1(X_{\mathrm{Si}}-X_{\mathrm{Ti}})+\mathrm{.\; .\; .}+L_{\mathrm{phase}}^{\mathit{V}}\mathrm{.(}{X}_{\mathrm{Si}}-X_{\mathrm{Ti}}{)}^{\mathit{V}}$

Where: L^v_phase = a+b.T+...

(6) $f_{\mathrm{orm}}{G}^{{\mathrm{Ti}}_3\mathrm{Si}}-x_{\mathrm{Ti}}.G_{\mathrm{Ti}}^{\mathrm{ref}}-x_{\mathrm{Si}}.G_{\mathrm{Si}}^{\mathrm{ref}}=a+b.T+c.T.\ln (T)$

(7) $G^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}{=}^{\mathit{form}}{G}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}{+}^{\mathit{id}}{G}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}{+}^{\mathit{ex}}{G}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}$

(8) ${}^{\mathit{form}}G^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}=y{\text{'}}_{\mathrm{Ti}}.y{"}_{\mathrm{Ti}}.G_{\mathrm{Ti}:\mathrm{Ti}}^{\mathrm{Ref}}+y{\text{'}}_{\mathrm{Si}}.y{"}_{\mathrm{Ti}}.G_{\mathrm{Si}:\mathrm{Ti}}^{\mathrm{Ref}}.+y{\text{'}}_{\mathrm{Ti}}.y{"}_{\mathrm{Si}}.G_{\mathrm{Ti}:\mathrm{Si}}^{\mathrm{Ref}}+y{\text{'}}_{\mathrm{Si}}.y{"}_{\mathrm{Si}}.G_{\mathrm{Si}:\mathrm{Si}}^{\mathrm{Ref}}$

(9) ${}^{\mathit{id}}G^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}=\mathit{R}.\mathit{T}\mathrm{.\{}5\mathrm{.[}y{\text{'}}_{\mathrm{Si}}.\ln (y{\text{'}}_{\mathrm{Si}})+y{\text{'}}_{\mathrm{Ti}}.\ln (y{\text{'}}_{\mathrm{Ti}}\mathrm{)]}+3\mathrm{.[}y{"}_{\mathrm{Si}}\ln (y{"}_{\mathrm{Si}})+y{"}_{\mathrm{Ti}}\ln (y{"}_{\mathrm{Ti}}\mathrm{)]\}}$

(10) $\begin{array}{c}{}^{\mathit{ex}}\mathit{G}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}=y{\text{'}}_{\mathrm{Ti}}.y{\text{'}}_{\mathrm{Si}}\mathrm{.(}y{"}_{\mathrm{Ti}}.L_{(\mathrm{Ti},\mathrm{Si}:\mathrm{Ti}{)}^{+}}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}y{"}_{\mathrm{Si}}.L_{(\mathrm{Ti},\mathrm{Si}:\mathrm{Si})}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3})+y{"}_{\mathrm{Ti}}.y{"}_{\mathrm{Si}}\mathrm{.(}y{\text{'}}_{\mathrm{Ti}}.L_{({\mathrm{Ti}}^1:\mathrm{Si},\mathrm{Ti})}^{{\mathrm{Ti}}_{5^{S}3}}+y{\text{'}}_{\mathrm{Si}}.L_{(\mathrm{Si}:\mathrm{Si},\mathrm{Ti})}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3})+\\ +y{\text{'}}_{\mathrm{Ti}}.y{\text{'}}_{\mathrm{Si}}.y{"}_{\mathrm{Ti}}.y{"}_{\mathrm{Si}}.L_{(\mathrm{Ti},\mathrm{Si}:\mathrm{Si},\mathrm{Ti})}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}\end{array}$

Where: y_jⁿ 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. V_i1 in [J.(mol of phase)^-1]; V_i2 in [J.(mol of phase)^-1.K^-1].

Thermodynamic function	Parameters	Variables
Gibbs energy for the formation of Ti5Si3	${}^{0}G_{Ti:SI}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}-\left[{5.G}_{\mathrm{Ti}}^{\mathrm{hcp}}\left(T\right)+{3.G}_{\mathrm{Si}}^{\mathrm{diamond}}\left(T\right)\right]$	VI1 +V12.T
Gibbs energy for the formation of hypothetic Ti8	${}^{0}G_{Ti:Ti}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}-\left[{8.G}_{\mathrm{Ti}}^{\mathrm{hcp}}\left(T\right)\right]$	(40,000 + 20.T)*
Gibbs energy for the formation of hypothetic Si8	${}^{0}G_{Si:Si}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}-\left[{8.G}_{\mathrm{Si}}^{\mathrm{diamond}}\left(T\right)\right]$	V21 +V22.T
Gibbs energy for the formation of hypothetic Ti3Si5	${}^{0}G_{Si:Ti}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}-\left[{3.G}_{\mathrm{Ti}}^{\mathrm{hcp}}\left(T\right)+{5.G}_{\mathrm{Si}}^{\mathrm{diamond}}\left(T\right)\right]$	V31 + V32.T
Excess Gibbs energy for the (Si,Ti:Ti) interaction	${}^{0}L_{Si,Ti:Ti}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}$	V41 + V42.T**
Excess Gibbs energy for the (Si,Ti:Si ) interaction	${}^{0}L_{Si,Ti:Si}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}$	V41 +V42.T**
Excess Gibbs energy for the (Ti: Si,Ti) interaction	$L_{Ti:Si,Ti}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}$	V51 + V52.T**
Excess Gibbs energy for the (Si:Si,Ti) interaction	${}^{0}L_{Si:Si,Ti}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}$	V51 +V52.T**
Excess Gibbs energy for the (Si,Ti:Si,Ti ) interaction	${}^{0}L_{Si,Ti:Si:Ti}^{{\mathrm{Ti}}_5{\mathrm{si}}_3}$	V61 +V62.T**
Gibbs energy for the formation of Ti3Si phase	${}^{0}G_{Ti:Si}^{{\mathrm{Ti}}_3\mathrm{Si}}-\left[{3.G}_{\mathrm{Ti}}^{\mathrm{hcp}}\left(T\right)+G_{\mathrm{Si}}^{\mathrm{diamond}}\left(T\right)\right]$	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 (X_Si ^phase: atomic fraction of Si).

Reaction	T(K)	Experimental values			References
L → Ti5Si3	2401	$X_{\mathrm{Si}}^L=0.375$	$X_{\mathrm{Si}}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}=0.375$	-	(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	$X_{\mathrm{Si}}^L=0.667$	$X_{\mathrm{Si}}^{{\mathrm{TiSi}}_2}=0.667$	-
L → β+Ti5Si3	1613	$X_{\mathrm{Si}}^L=0.137$	$X_{\mathrm{Si}}^{\mathit{\beta }}=0.047$	$X_{\mathrm{Si}}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}=0.36$
L → TiSi2+Si	1603	$X_{\mathrm{Si}}^L=0.86$	$X_{\mathrm{Si}}^{{\mathrm{TiSi}}_2}=0.667$	$X_{\mathrm{Si}}^{\mathrm{Si}}=1$
L → TiSi2+TiSi	1747	$X_{\mathrm{Si}}^L=0.641$	$X_{\mathrm{Si}}^{\mathrm{TiSi}}=0.5$	$X_{\mathrm{Si}}^{{\mathrm{TiSi}}_2}=0.667$
L+Ti5Si3 → TI5Si4	2193	$X_{\mathrm{Si}}^L=0.48$	$X_{\mathrm{Si}}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}=0.398$	$X_{\mathrm{Si}}^{{\mathrm{Ti}}_5{\mathrm{Si}}_4}=0.444$
L+Ti5Si3 → TiSi	1843	$X_{\mathrm{Si}}^L=0.60$	$X_{\mathrm{Si}}^{{\mathrm{Ti}}_5{\mathrm{Si}}_4}=0.444$	$X_{\mathrm{Si}}^{\mathrm{Tisi}}=0.5$
β+Ti5Si3 → Ti3Si	1443	$X_{\mathrm{Si}}^{\mathit{\beta }}=0.04$	$X_{\mathrm{Si}}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}=0.36$	$X_{\mathrm{Si}}^{{\mathrm{Ti}}_3\mathrm{Si}}=0.25$
β → α+Ti3Si	1149	$X_{\mathrm{Si}}^{\mathit{\beta }}=0.009$	$X_{\mathrm{Si}}^{\mathit{\alpha }}=0.004$	$X_{\mathrm{Si}}^{{\mathrm{Ti}}_3\mathrm{Si}}=0.25$
β → α+Ti5Si3 (metastable)	1133	$X_{\mathrm{Si}}^{\mathit{\beta }}=0.011$	$X_{\mathrm{Si}}^{\mathit{\alpha }}=0.005$	$X_{\mathrm{Si}}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}=0.365$

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, V_i1 in [J.(mol of phase)^-1]; V_i2 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
	$X_{\mathrm{Si}}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}$	0.375	0.375	0
L → TiSi2	T(K)	1773	1757	1
	$X_{\mathrm{Si}}^{{\mathrm{TiSi}}_2}$	0.667	0.667	0
L → β+ Ti5Si3	T(K)	1613	1626	0.6
	$X_{\mathrm{Si}}^L$	0.137	0.127	7
	$X_{\mathrm{Si}}^{\mathit{\beta }}$	0.047	0.044	4
	$X_{\mathrm{Si}}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}$	0.36	0.35	5
L → TiSi2+Si	T(K)	1603	1604	0.1
	$X_{\mathrm{Si}}^L$	0.86	0.815	5
	$X_{\mathrm{Si}}^{{\mathrm{TiSi}}_2}$	0.667	0.667	0
	$X_{\mathrm{Si}}^{\mathrm{Si}}$	1	1	0
L → TiSi2+TiSi	T(K)	1747	1747	0
	$X_{\mathrm{Si}}^L$	0.641	0.637	0.7
	$X_{\mathrm{Si}}^{\mathrm{Ti}}$	0.5	0.50	0
	$X_{\mathrm{Si}}^{{\mathrm{TiSi}}_2}$	0.667	0.667	0
L+Ti5Si3 → Ti5Si4	T(K)	2193	2210	0.8
	$X_{\mathrm{Si}}^L$	0.477	0.476	0.2
	$X_{\mathrm{Si}}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}$	0.405	0.375	6
	$X_{\mathrm{Si}}^{{\mathrm{Ti}}_5{\mathrm{Si}}_4}$	0.444	0.444	0
L+Ti5Si4 → TiSi	T(K)	1843	1843	0
	$X_{\mathrm{Si}}^L$	0.60	0.604	0.7
	$X_{\mathrm{Si}}^{{\mathrm{Ti}}_5{\mathrm{Si}}_4}$	0.444	0.444	0
	$X_{\mathrm{Si}}^{\mathrm{TiSi}}$	0.5	0.5	0
β +Ti5Si3 → Ti3Si	T(K)	1443	1457	0.1
	$X_{\mathrm{Si}}^{\mathit{\beta }}$	0.04	0.033	18
	$X_{\mathrm{Si}}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}$	0.36	0.353	2
	$X_{\mathrm{Si}}^{{\mathrm{Ti}}_3\mathrm{Si}}$	0.25	0.25	0
β → α+ Ti3Si	T(K)	1149	1142	0.8
	$X_{\mathrm{Si}}^{\mathit{\beta }}$	0.009	0.010	6
	$X_{\mathrm{Si}}^{\mathit{\alpha }}$	0.004	0.0042	5
	$X_{\mathrm{Si}}^{{\mathrm{Ti}}_3\mathrm{Si}}$	0.25	0.25	0
	$H_{\mathrm{form}}^{{\mathrm{Ti}}_3\mathrm{Si}}$ (J/mol of phase)	-47,850	-50,197	5
β → α+ Ti5Si3(metastable)	T(K)	1133	1138	0.4
	$X_{\mathrm{Si}}^{\mathit{\beta }}$	0.011	0.013	18
	$X_{\mathrm{Si}}^{\mathit{\alpha }}$	0.005	0.0054	8
	$X_{\mathrm{Si}}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}$	0.365	0.36	1.4
	$H_{\mathrm{form}}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}$ (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 ($\left({}^{0}L_{Si,Ti:Ti}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}={}^{0}L_{Si,Ti:Si}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}\mathrm{and}{}^{0}L_{Ti,Si:Ti}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}={}^{0}L_{Si,Si:Ti}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}\right)$), see Table 1) should be further analyzed. For instance, another hypothesis, assuming that the interaction parameters on the two sublattices are symmetrical ($\left({}^{0}L_{Si,Ti:Ti}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}={}^{0}L_{Si,Ti:Si}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}\mathrm{and}{}^{0}L_{Ti,Si:Ti}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}={}^{0}L_{Si,Si:Ti}^{{\mathrm{Ti}}_5{\mathrm{Si}}_3}\right)$), 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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Publication Dates

• Publication in this collection
  Apr-Jun 2017

History

• Received
  13 June 2016
• Accepted
  28 Nov 2016