- Email: [email protected]
Thermodynamic modeling of the Hf–Ti–Si ternary system
Intermetallics 15 (2007) 168e176 www.elsevier.com/locate/intermet
Thermodynamic modeling of the HfeTieSi ternary system Y. Yang a,*, B.P. Bewlay b, Y.A. Chang c a CompuTherm LLC, 437 S. Yellowstone Drive, Madison, WI 53719, USA General Electric Company, GE Global Research Center, 1 Research Circle, Niskayuna, NY 12309, USA c Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA b
Received 14 February 2006; accepted 8 May 2006 Available online 19 June 2006
Abstract A thermodynamic description of the HfeTieSi system was developed using the phenomenological or Calphad approach, based on the critically assessed binary thermodynamic descriptions and experimental data of ternary phase equilibria. The parameters of all ternary phases were optimized using experimentally measured solid-state phase equilibria at 1350 C, melting temperatures of selected alloys, and primary solidification information for metal-rich HfeTieSi alloys. Comparisons between the calculated results and the experimental measurements show that the present modeling can satisfactorily describe the experimental information for the metal-rich region of the HfeTieSi ternary phase diagram for Si concentrations of up to 40 at%. The experimentally identified transition reaction L þ Hf(Ti)2Si / (Hf,Ti)5Si3 þ b(Hf,Ti,Si) at the metal-rich end of the ternary phase diagram is confirmed by this calculation. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: A. Intermetallics, miscellaneous; A. Silicides, various; B. Phase diagrams; B. Thermodynamic and thermochemical properties; E. Phase diagram, prediction
1. Introduction Nb-silicide based in situ composites have been investigated extensively [1e3] for applications as structural materials at temperatures of up to 1200 C. Ti and Hf are added to these composites to improve room temperature fracture toughness and high temperature oxidation resistance [2,4]. Recently, Bewlay et al. [5e8] reported that the creep rate at high temperatures increases significantly when the Nb:(Hf þ Ti) atomic ratio is reduced below w1.5. In order to improve the design of new engineering materials and understand the relationship between microstructure and properties, it is essential to have accurate knowledge of the phase equilibria of the NbeTie HfeSi quaternary system, especially in the metal-rich region. Obtaining such knowledge exclusively from experiments is cumbersome and expensive. Thermodynamic modeling of
* Corresponding author. Fax: þ1 608 262 8353. E-mail address: [email protected] (Y. Yang). 0966-9795/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.intermet.2006.05.002
multi-component systems using the phenomenological or Calphad approach has been shown to be a very efficient tool in this regard [9]. A prerequisite to develop the thermodynamic description of the NbeTieHfeSi system is to obtain thermodynamic descriptions of its four constituent ternary systems. In previous studies, we had developed thermodynamic descriptions of the NbeTieSi [10] and NbeHfeSi [11] systems. The objective of the present study is to develop a thermodyamic description for the metal-rich region of the HfeTieSi system, which will be used to build the thermodynamic database of the NbeTieHfeSi system. 2. Literature data for the HfeTieSi system There is almost no experimental data on phase equilibria for the HfeTieSi ternary system. Recently, Bewlay et al. [12,13] experimentally investigated the partial HfeTieSi liquidus projection (for Si concentrations between 0 and 40 at%) close to the HfeTi binary side, and the solid-state phase equilibria at 1350 C for metal-rich HfeTieSi alloys.
Y. Yang et al. / Intermetallics 15 (2007) 168e176
The alloys in Refs. [12,13] were prepared using the cold crucible directional solidification technique. Heat treatment was conducted at 1350 C for 100 h. Electron probe microanalysis (EPMA) was used to measure the phase compositions, while X-ray diffraction (XRD) and electron backscatter diffraction (EBSD) were used for crystal structure identification. The alloy melt temperatures were measured using a two wavelength optical pyrometer. The pyrometer was calibrated against both the melting temperature of 99.9% pure Ti (1670 C) and the temperature of the HfeHf2Si eutectic (1830 C) [12]. Fig. 1 shows the partial liquidus projection of the HfeTie Si system close to the HfeTi binary for Si concentrations between 0 and 40 at% proposed by Bewlay et al. [12], together with the experimentally investigated alloy compositions. The phases present in these as-cast alloys and the melting temperature of these alloys are listed in Table 2. The alloy compositions throughout this article are given in atomic percent. There are three primary solidification phases in this portion of liquidus projection: (Hf,Ti)5Si3, Hf(Ti)2Si and b(Hf,Ti,Si). The Ti5Si3 and Hf5Si3 both have hP16 crystal structures and are referred to as (Hf,Ti)5Si3. The Hf2Si with Ti in solid solution is referred to as Hf(Ti)2Si, and b(Hf,Ti,Si) refers to the ternary solid solution based on bcc structure. The denotation of the phase names is explained in Table 1, which also lists the crystal structures in terms of the Pearson symbols and thermodynamic models used. A eutectic groove extends from the L / b(Hf,Si) þ Hf2Si in the HfeSi binary (denoted by e1) to the L / Ti5Si3 þ b(Ti,Si) in the TieSi binary (denoted by e2). Because of the different binary eutectic reactions there is a change in the nature of the liquidus surface, and the eutectic groove, with decreasing Hf and increasing Ti concentration. The phase transition corresponding to the change on the eutectic groove involves four phases, i.e. liquid, b(Hf,Ti,Si), Hf(Ti)2Si and (Hf,Ti)5Si3. Based on microstructural evidence, Bewlay et al. [12] determined that this phase transition is a type II reaction of the form L þ (Hf,Ti)2Si / (Hf,Ti)5Si3 þ b(Hf,Ti,Si), and it occurred at a composition of approximately Hfe50Tie9.5Si. The temperature of this invariant reaction was measured to be 1420 20 C [12]. 40 at% Si
Hf5Si3 Hf2Si
Ti5Si3 3
0.3
0.2
2 (Hf,Ti)2Si
0.1
1 0.0
4 1
(Hf,Ti)5Si3
0.1
0.2
5
(Hf,Ti,Si) 0.3
0.4
0.5
0.6
0.7
0.8
0.9
Hf
1.0
Ti Hf-rich (Hf,Ti,Si)
Ti-rich (Hf,Ti,Si)
Hf-rich (Hf,Ti)5Si3
Hf(Ti)2Si
Ti-rich (Hf,Ti)5Si3
Fig. 1. Experimentally determined liquidus projection of the metal-rich end of the HfeTieSi ternary system [12]. Symbols represent the alloy compositions. The different symbols denote the different primary solidification phases, as shown in the key to the figure.
169
Table 1 Solid phases in the HfeTieSi system Phase symbol
Thermodynamic model
Crystal structure
Phase description
b(Hf,Ti,Si)
(Hf,Ti,Si)1(Va)3
cI2
a(Hf,Ti,Si)
(Hf,Ti,Si)1(Va)0.5
hP2
(Si) Hf(Ti)2Si
(Si) (Hf,Ti)2Si
cF8 tI12
(Hf,Ti)Si
(Hf,Ti)Si
oP8
Hf3Si2
Hf3Si2
tP10
(Hf,Ti)5Si3
(Hf,Ti)5Si3
hP16
(Hf,Ti)5Si4
(Hf,Ti)5Si4
tP36
HfSi2 Ti3Si TiSi2
HfSi2 Ti3Si TiSi2
oC12 tP32
Ternary solid solution based on bcc Ternary solid solution based on hcp Silicon Solid solution based on Hf2Si Solid solution based on HfSi and NbSi Binary compound Hf3Si2 Solid solution based on Hf5Si3 and Ti5Si3 Solid solution based on Hf5Si4 and Ti5Si4 Binary compound HfSi2 Binary compound Ti3Si Binary compound TiSi2
The solid-state phase equilibria of selected HfeTieSi alloys heat treated at 1350 C for 100 h reported by Bewlay et al. [13] are listed in Table 2. Four phases were observed in these samples, and they were b(Hf,Ti,Si), (Hf,Ti)5Si3, Hf(Ti)2Si, and a(Hf,Ti,Si). One three-phase equilibria region b(Hf,Ti,Si) þ (Hf,Ti)5Si3 þ Hf(Ti)2Si, and three two-phase regions b(Hf,Ti,Si) þ (Hf,Ti)5Si3, b(Hf,Ti,Si) þ Hf(Ti)2Si and a(Hf,Ti,Si) þ Hf(Ti)2Si were observed. The EPMA measurements of the three-phase equilibria b(Hf,Ti,Si) þ (Hf,Ti)5 Si3 þ Hf(Ti)2Si suggest that the maximum solubility of Ti in Hf2Si is 9.8 at% at 1350 C [12]. 3. Thermodynamic modeling of the HfeTieSi system All three constituent binaries of the HfeTieSi system have been thermodynamically modeled. In the present modeling, the thermodynamic parameters of the HfeSi, TieSi, and HfeTi binary systems are taken from Yan et al. [11], Seifert et al. [14] and Bittermann and Rogl [15], respectively. The calculated HfeTi, HfeSi, and TieSi binary phase diagrams are shown in Figs. 2e4, respectively. Neither experimental nor calculated thermodynamic property data for the HfeTieSi ternary system were found in literature. Therefore, the current modeling is based on the experimental information of the liquidus projection and the solid-state phase equilibria discussed in Section 2. The thermodynamic description of the Si-rich region is obtained through extrapolation, again due to lack of experimental data. There are two types of ternary solid solution phases: one is based on the structures of the terminal solid solutions, such as the b(Hf,Ti,Si) phase based on the bcc structure of Hf or Ti, and a(Hf,Ti,Si) based on the hcp structure of Hf or Ti. The second type of solid solution is based on intermetallic compounds such as (Hf,Ti)5Si3 and Hf(Ti)2Si phases. The Gibbs free energy of the first type of ternary solutions is described by the RedlicheKister polynomial [16],
Y. Yang et al. / Intermetallics 15 (2007) 168e176
170
Table 2 Comparison between the calculated and experimental melting temperature and constituent phases in samples Compositions
Tm ( C)
Constituent phases in as-cast samples
Constituent phases in annealed samples at 1350 C
1710 1644
b(Hf,Ti,Si) þ Hf(Ti)2Si b(Hf,Ti,Si) þ Hf(Ti)2Si þ (Hf,Ti)5Si3(<1%)a,b b(Hf,Ti,Si) þ Hf(Ti)2Si b(Hf,Ti,Si) þ Hf(Ti)2Si þ (Hf,Ti)5Si3(<1%) b(Hf,Ti,Si) þ Hf(Ti)2Si b(Hf,Ti,Si) þ Hf(Ti)2Si þ (Hf,Ti)5Si3(1.1%)
a(Hf,Ti,Si) þ Hf(Ti)2Si a(Hf,Ti,Si) þ Hf(Ti)2Si a(Hf,Ti,Si) þ Hf(Ti)2Si a(Hf,Ti,Si) þ Hf(Ti)2Si b(Hf,Ti,Si) þ Hf(Ti)2Si þ a(Hf,Ti,Si) b(Hf,Ti,Si) þ Hf(Ti)2Si þ a(Hf,Ti,Si)
Hf(Ti)2Si þ b(Hf,Ti,Si) b(Hf,Ti,Si) þ Hf(Ti)2Si þ (Hf,Ti)5Si3(4%) Hf(Ti)2Si þ b(Hf,Ti,Si) Hf(Ti)2Si þ b(Hf,Ti,Si) þ (Hf,Ti)5Si3(<1%) Hf(Ti)2Si þ b(Hf,Ti,Si) b(Hf,Ti,Si) þ Hf(Ti)2Si þ (Hf,Ti)5Si3(2%) Hf(Ti)2Si þ b(Hf,Ti,Si) b(Hf,Ti,Si) þ Hf(Ti)2Si þ (Hf,Ti)5Si3(6%) Hf(Ti)2Si þ b(Hf,Ti,Si) þ (Hf,Ti)5Si3 Hf(Ti)2Si þ b(Hf,Ti,Si) þ (Hf,Ti)5Si3 Hf(Ti)2Si þ b(Hf,Ti,Si) þ (Hf,Ti)5Si3 Hf(Ti)2Si þ b(Hf,Ti,Si) þ (Hf,Ti)5Si3 b(Hf,Si) þ Hf2Si Hf2Si þ b(Hf,Si)
Hf(Ti)2Si þ b(Hf,Ti,Si) Hf(Ti)2Si þ b(Hf,Ti,Si)
Group 1 Hfe10Tie10Si Hfe10Tie5Si Hfe20Tie5Si Group 2 Hfe30Tie10Si Hfe10Tie16Si
1530 1507 1720 1708
Hfe20Tie16Si Hfe30Tie16Si Hfe40Tie9Si Hfe42Tie10Si
1420 1430 1415 1430
Hfe12Si Hfe20Si Group 3 Hfe50Tie9.5Si
1420 1412
Hfe30Tie25Si Group 4 Hfe60Tie25Si
a b
1340 1382
b(Hf,Ti,Si) þ (Hf,Ti)5Si3 b(Hf,Ti,Si) þ (Hf,Ti)5Si3
b(Hf,Ti,Si) þ (Hf,Ti)5Si3 b(Hf,Ti,Si) þ (Hf,Ti)5Si3 b(Ti) þ Ti5Si3 (Hf,Ti)5Si3 þ b(Hf,Ti,Si) b(Hf,Ti,Si) þ (Hf,Ti)5Si3
(Hf,Ti)5Si3 þ b(Hf,Ti,Si) b(Hf,Ti,Si) þ (Hf,Ti)5Si3
Italic font denotes the calculated results and normal font the experimental results. The number denotes the calculated mole fraction of the phase.
G4m ¼xTi 0 G4Ti þ xHf 0 G4Hf þ xSi 0 G4Si þ RT xTi ln xTi þ xHf ln xHf þ xSi ln xSi þ ex G4m
L4Hf;Ti;Si ¼ xTi L4Ti þ xHf L4Hf þ xSi L4Si
G4m ¼ xTi xSi L4Ti;Si þ xHf xSi L4Hf;Si þ xTi xHf L4Hf;Ti þ xTi xHf xSi L4Hf;Ti;Si
ð3Þ
ð1Þ
where xTi , xHf and xSi are the mole fractions of Ti, Hf and Si, respectively. 0 G4Ti , 0 G4Hf and 0 G4Si are the 4 phase molar Gibbs energies of element Ti, Hf and Si, respectively. ex G4m is the excess Gibbs energy term of 4 phase. It is expressed by the following equation: ex
(Hf,Ti)5Si3 þ Hf(Ti)2Si þ b(Hf,Ti,Si) (Hf,Ti)5Si3 þ Hf(Ti)2Si þ b(Hf,Ti,Si)
(Hf,Ti)5Si3 þ b(Hf,Ti,Si) (Hf,Ti)5Si3 þ b(Hf,Ti,Si)
Group 5 Hfe85Tie5Si Tie13.5Si Hfe60Tie10Si
Hf5Si3 þ b(Hf,Ti,Si) b(Hf,Ti,Si) þ (Hf,Ti)5Si3 þ Hf(Ti)2Si(2%) (Hf,Ti)5Si3 þ Hf(Ti)2Si þ b(Hf,Ti,Si) (Hf,Ti)5Si3 þ Hf(Ti)2Si þ b(Hf,Ti,Si)
ð2Þ
the parameters denoted by L4Hf;Si, L4Ti;Si and L4Hf;Ti are the interaction parameters from the HfeSi, TieSi and HfeTi binaries, respectively. L4Hf;Ti;Si is the ternary interaction parameter, which is usually expressed by the following equation:
L4Hf , L4Ti and L4Si make the major contributions to the liquidus surfaces in Hf-rich, Ti-rich and Si-rich corners of the HfeTie Si system, respectively. The compound energy formalism developed by Hillert and Staffansson [17] was used to describe the second type of ternary solid solutions with a form of (Hf,Ti)p(Si)q. The Gibbs free energy of such phases for one mole of atoms can be described by the following equation: G4ðHf;TiÞ
p Siq
p ¼yITi 0 G4Ti:Si þ yIHf 0 G4Hf:Si þ pþq RT yITi ln yITi þ yIHf ln yIHf þ yITi yIHf L4Hf;Ti:Si ð4Þ
in which yITi and yIHf are the site fractions of Ti and Hf on the first sublattice, respectively. 0 G4Ti:Si and 0 G4Hf:Si are the Gibbs
Y. Yang et al. / Intermetallics 15 (2007) 168e176 2500
2400
2100
2040
171
L
0.48,1929
900
L
0.61,1570 0.667,1488
960
TiSi2
0.15, 1328
TiSi
0.86,1330
1320
Ti5Si4
(Hf,Ti)
1300
1680
Ti5Si3
1700
Ti3Si
Temperature (ºC)
Temperature (ºC)
0.375,2127
(Si)
(Hf,Ti)
500 0
0.1
0.2
0.3
Hf
0.4
0.5
0.6
0.7
0.8
0.9
Mole fraction of Ti
1
Ti
600 0
0.1
0.2
0.3
Ti
0.4
0.5
0.6
0.7
0.8
0.9
Mole fraction of Si
1
Si
Fig. 2. The HfeTi phase diagram calculated in the present study. The thermodynamic description is taken from Ref. [15].
Fig. 4. The TieSi phase diagram calculated in the present study. The thermodynamic description is taken from Ref. [14].
energies of the compounds TipSiq and HfpSiq with the structure of 4. L4Hf;Ti:Si represents the interaction between Hf and Ti in the first sublattice with only Si present in the second sublattice. It is expressed as the following equation:
treated as binary compounds due to the lack of solubility data of Hf in Ti3Si and TiSi2, and Ti in HfSi2 and Hf3Si2. The optimization was performed in the parrot module of Thermo-Calc [18], and Pandat [19] was used to calculate the phase diagrams and solidification paths. The optimization procedure begins with solid-state phase equilibria at 1350 C, and then it proceeds to the liquidus surface. The optimized parameters in this study are listed in Table 3.
L4Hf;Ti;Si ¼ 0 L4Hf;Ti:Si þ yIHf yITi 1 L4Hf;Ti:Si
ð5Þ
In the present modeling, the Gibbs energies of b(Hf,Si,Ti), a(Hf,Si,Ti) and liquid were described by Eq. (1). Hf5Si3 and Ti5Si3 are treated as one phase denoted by (Hf,Ti)5Si3 due to their similar crystal structures. Similarly, Hf5Si4 and Ti5Si4 are denoted by (Hf,Ti)5Si4, and HfSi and TiSi by (Hf,Ti)Si. The Gibbs free energies of Hf(Ti)2Si, (Hf,Ti)5Si3, (Hf,Ti)5Si4 are described by Eq. (4). Ti3Si, TiSi2, HfSi2, and Hf3Si2 are 2600 0.4, 2466 0.30, 2354
Hf5Si3 Hf5Si4
0
0.1
0.2
0.3
0.4
0.5
Table 2 lists the good agreement between the calculated and experimentally observed constituent phases in those samples annealed at 1350 C. The calculated 1350 C isothermal section is shown in Fig. 5, together with the experimentally investigated alloy compositions, and the compositions of the phases in these alloys. The experimentally measured three-phase and two-phase equilibria are reasonably well described by this calculation. The calculated maximum solubility of Ti in Hf(Ti)2Si at 1350 C is 10.0%, which agrees very well with the EPMA measurement of 9.8%. In addition to the 1350 C isothermal section, we also calculated isothermal sections at 1000 and 1600 C, as shown in Figs. 6 and 7, respectively. The 1000 C isotherm displays a similar phase relationship to Table 3 The optimized parameters in the study for the HfeTieSi system
0.89, 1329
(Si)
1000
Hf
4.1. Isothermal sections at 1350, 1000 and 1600 C
0.76, 1539
HfSi2
Hf3Si2
0.12,1824
Hf2Si
1400
0.58, 2147
HfSi
β(Hf,Si)
1800
0.21, 2092
α(Hf,Si)
Temperature (ºC)
2200
L
0.51, 2320
4. Results and discussion
0.6
Mole fraction of Si
0.7
0.8
0.9
1
Si
Fig. 3. The HfeSi phase diagram calculated in the present study. The thermodynamic description is taken from Ref. [11].
Phase symbol
Thermodynamic model
Model parameters (J/mol)
b(Hf,Ti,Si) Liquid
(Hf,Ti,Si)1(Va)3 (Hf,Ti,Si)
Hf(Ti)2Si (Hf,Ti)5Si3
(Hf,Ti)0.667Si0.333 (Hf,Ti)5Si3
L0Hf;Si;Ti:Va ¼ L2Hf;Si;Ti:Va ¼ 236 445 L0Hf;Si;Ti ¼ L2Hf;Si;Ti ¼ 80 986 L1Hf;Si;Ti ¼ 31 387 L0Hf;Ti:Si ¼ 161 575 þ 30 T L0Hf;Ti:Si ¼ 370 706 þ 178 T L1Hf;Ti:Si ¼ 274 336 þ 140 T
Y. Yang et al. / Intermetallics 15 (2007) 168e176
172 Si
Phasecomposition Alloy composition
Liq
Liq
Si of
TiSi2
tio n
Si of
HfSi2
0.4
Mo
(Hf,Ti)Si (Hf,Ti)5Si4
Hf3Si2
0.6
le fra c
0.6
tio n le fra c
Si
0.8
0.8
Mo
1
T=1600ºC
1
T=1350ºC
(Hf,Ti)Si (Hf,Ti)5Si4
0.4
(Hf,Ti)5Si3
Hf3Si2 Hf(Ti)2Si
(Hf,Ti)5Si3
Hf(Ti)2Si
0.2
0.2 Liq
0
Liq 0
0
α(Hf,Ti,Si)
0.2
0.4
Hf
0.6
0.8 β(Hf,Ti,Si) 1
Mole fraction of Ti
Ti
Fig. 5. Comparison between the calculated isothermal section and the experimental measurements at 1350 C [13]. The solid circles refer to bulk alloy compositions, and the solid squares refer to phase compositions.
that at 1350 C. The solubility of Ti in Hf(Ti)2Si at 1000 C is 11.3%, and it is slightly higher than that at 1350 C. The solubility of Ti in Hf(Ti)2Si at 1600 C is calculated to be 8.7%. The calculated results at these three temperatures (1600, 1350 and 1000 C) suggest that the solubility of Ti in Hf(Ti)2Si decreases with temperature. The major difference between 1350 and 1000 C isotherms is that b(Hf,Ti,Si) and (Hf,Ti)5Si3 of the three-phase equilibria b(Hf,Ti,Si) þ (Hf,Ti)5Si3 þ Hf (Ti)2Si contain more Ti at 1000 C. The 1600 C isotherm is above the transition temperature of the reaction L þ H f(Ti)2Si / (Hf,Ti)5Si3 þ b(Hf,Ti,Si) at 1430 C. Therefore, the two three-phase equilibria of L þ b(Hf,Ti,Si) þ Hf(Ti)2Si 1
T= 1000ºC
Si
Mo le
fra ctio no
fS
i
0.8
HfSi2
TiSi2
0.6 (Hf,Ti)Si (Hf,Ti)5Si4
Hf3Si2 0.4
(Hf,Ti)5Si3
Hf(Ti)2Si Ti3Si
0.2
0
0 α(Hf,Ti,Si) 0.2
Hf
0.4
0.6
Mole fraction of Ti
0.8 β(Hf,Ti,Si) 1
Ti
Fig. 6. The HfeTieSi isothermal section at 1000 C calculated in the present study.
0 α(Hf,Ti,Si) 0.2
Hf
0.4
0.6
Mole fraction of Ti
0.8 β(Hf,Ti,Si) 1
Ti
Fig. 7. The HfeTieSi isothermal section at 1600 C calculated in the present study.
and L þ Hf(Ti)2Si þ (Hf,Ti)5Si3 are calculated to exist in the 1600 C isothermal section, instead of b(Hf,Ti,Si) þ (Hf,Ti)5Si3 þ Hf(Ti)2Si and L þ b(Hf,Ti,Si) þ (Hf,Ti)5Si3. Further experimental data are required to validate the calculated isotherms at 1000 and 1600 C. 4.2. Liquidus projection The calculated liquidus projection is shown in Fig. 8, together with alloy compositions investigated by Bewlay et al. [12]. It shows three primary phase regimes: (Hf,Ti)5Si3, Hf(Ti)2Si and b(Hf,Ti,Si) in the metal-rich region for Si concentrations from 0 to 40%. The symbols in this figure refer to the experimentally investigated alloy compositions from the five groups in Table 2. Details on the definition of these five groups will be discussed in Section 4.3. The calculated primary phases of solidification according to the Scheil model are in accord with the experimentally observed results. The observed type II invariant reaction L þ Hf(Ti)2Si / (Hf,Ti)5Si3 þ b(Hf,Ti,Si) is confirmed by the calculation. The calculated temperature of this reaction (1430 C) is in accordance with the experimental measurement (w1420 C). The liquid composition of this invariant reaction was determined through microstructure analysis of selected as-cast alloys [12]. The Ti concentration of the liquid at this invariant reaction is between 42 and 50 at%, while the Si concentration is between 9 and 10 at%. The Si concentration of the liquid at this invariant reaction is determined more precisely than the Ti concentration. The calculated liquid composition of this reaction Hfe51Tie 9.9Si is in good agreement with the composition Hfe50Tie 9.5Si [12] within experimental error. The current thermodynamic modeling also takes the melting temperature measurements [12] of the alloys into consideration. During the thermodynamic modeling, we found that the measured melting temperatures of those alloys with
Y. Yang et al. / Intermetallics 15 (2007) 168e176
(Si) HfSi2
0.8
TiSi2
Calculation Hf-rich (Hf,Ti,Si) Hf(Ti)2Si Hf-rich(Hf,Ti)5Si3 Ti-rich(Hf,Ti)5Si3 Ti-rich (Hf,Ti,Si)
(Hf,Ti)Si
(Hf,Ti)5Si4 0.4
Hf 3 Si 2
Mo
le fra c
tio n
of
Si
0.6
(Hf,Ti)5Si3 0.2
(Hf,Ti)2Si (Hf,Ti,Si) 0.0 0
Hf
0.2
0.4
0.6
Mole fraction of Ti
0.8
1
solidification regimes are Hf-rich b(Hf,Ti,Si), Hf(Ti)2Si-rich, Hf-rich (Hf,Ti)5Si3, Ti-rich (Hf,Ti)5Si3, and Ti-rich b(Hf,Ti,Si) primary solidification regions. Five representative alloy compositions with one alloy from each group were selected for simulations. Solidification path simulations were performed using the Scheil [20] and lever-rule models. The Scheil model assumes no diffusion in the solid and thermodynamic equilibrium is maintained at liquidesolid interface only. The leverrule model assumes complete mixing in the solid, and the total solid and liquid are in thermodynamic equilibrium. Both models require thermodynamic information only and are integrated into the solidification simulation module of Pandat [19]. These two models represent two extreme cases of solidification. The simulation results show that the solidification microstructure in the DS experiments is closer to that predicted by the Scheil model. Therefore, comparisons between predicted phases by the Scheil solidification simulations and the observed phases in as-cast alloys are given in this paper, as shown in Figs. 9e13.
Ti
Fig. 8. The calculated liquidus projection of the HfeTieSi system compared with experimental data. Symbols represent the alloy compositions. The different symbols denote the different primary solidification phases, as shown in the key to the figure.
a wide freezing range cannot be reconciled with those with a narrow freezing range and with the temperature of the transition reaction II1. This suggests that the method used by Bewlay et al. [12] in measuring the melting points of alloys, with wide freezing ranges, may have large uncertainties. Accordingly, the measured melting points for these alloys were not included in Table 2. Table 2 also compares the phases observed in the as-cast microstructure and the phases predicted by the Scheil solidification simulation. The calculation suggests that the (Hf,Ti)5Si3 phase should be present in the solidification microstructure of all these alloys, but it was only observed experimentally in some of them. This may be due to the small volume fraction of (Hf,Ti)5Si3. In general, the comparisons in Table 2 show reasonable agreement between the calculated results and experimental measurements. Three other invariant reactions are identified using the thermodynamic calculation. They are L þ (Hf,Ti)5Si3 / Hf3Si2 þ (Hf,Ti)5Si4, L þ (Hf,Ti) / HfSi2 þ TiSi2 and L / HfSi2 þ TiSi2 þ (Si). These reactions are calculated based on the extrapolated thermodynamic descriptions of relevant phases. While the calculated compositions and temperatures may deviate from the actual values, the topological features of these three reactions are considered to be correct. The currently calculated phase diagram can therefore serve as a design tool to efficiently select critical alloy compositions for further experimental investigation of these three reactions. 4.3. Solidification path simulation
4.3.1. Hfe10Tie5Si in the Hf-rich b(Hf,Ti,Si) primary phase regime Fig. 9 shows the simulated solidification sequence along with the experimental observation (shown in the right-corner box) for the Hfe10Tie5Si alloy located in the Hf-rich b(Hf,Ti,Si) primary phase regime. The calculated solidification sequences show that the first phase to solidify is b(Hf,Ti,Si), then the liquid composition follows the L / Hf(Ti)2Si þ b(Hf,Ti,Si) eutectic valley until it reaches the invariant reaction of L þ Hf(Ti)2Si / (Hf,Ti)5Si3 þ b(Hf,Ti,Si). Then the liquid continues to solidify by following the eutectic valley of L / (Hf,Ti)5Si3 þ b(Hf,Ti,Si). The final point of the Scheil simulation is the L / Ti5Si3 þ b(Ti,Si) binary eutectic reaction. The mole fraction of the (Hf,Ti)5Si3 þ b(Hf,Ti,Si) eutectic is calculated to be very small (<1%). The simulated 2100 Hf-10Ti-5Si β(Hf,Ti,Si) dendrite
2000
β(Hf,Ti,Si)+Hf(Ti)2Si eutectic 1900
Temperature_Celsius
Si 1
Liquidus projection
173
L->β(Hf,Ti,Si)
1800 1700
L->β(Hf,Ti,Si)+Hf(Ti)2Si 1600 1500 1400 L->β(Hf,Ti,Si)+(Hf,Ti)5Si3 1300 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Fraction of Solid
As-cast microstructures of a series of alloys from the five groups corresponding to the five regimes on the liquidus surface have been analyzed by Bewlay et al. [12]. These five
Fig. 9. Comparison between the calculated solidification path of the Hfe 10Tie5Si alloy and the experimental observations [12] shown in the rightcorner box.
Y. Yang et al. / Intermetallics 15 (2007) 168e176
174
2000
2200
Temperature_Celsius
2000 1900
1900
Hf(Ti)2Si peritectic β(Hf,Ti,Si)+Hf(Ti)2Si eutectic β(Hf,Ti,Si)+(Hf,Ti)5Si3 eutectic
1800
Temperature_Celsius
2100
Hf-30Ti-25Si (Hf,Ti)5Si3 dendrite
L->(Hf,Ti)5Si3
1800 1700 1600 1500
L->Hf(Ti)2Si
1400
L->β(Hf,Ti,Si)+Hf(Ti)2Si
Hf-60Ti-25Si (Hf,Ti)5Si3 dendrite β(Hf,Ti,Si)+(Hf,Ti)5Si3 eutectic
1700 L->(Hf,Ti)5Si3
1600
1500 L->β(Hf,Ti,Si)+(Hf,Ti)5Si3
1400 L->β(Hf,Ti,Si)+(Hf,Ti)5Si3
1300 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1300
1
0
0.1
0.2
0.3
Fraction of Solid
0.4
0.5
0.6
0.7
0.8
0.9
1
Fraction of Solid
Fig. 10. Comparison between the calculated solidification path of the Hfe 30Tie25Si alloy and the experimental observations [12] shown in the rightcorner box.
Fig. 12. Comparison between the calculated solidification path of the Hfe 60Tie25Si alloy and the experimental observations [12] shown in the rightcorner box.
b(Hf,Ti,Si) dentrite and Hf(Ti)2Si þ b(Hf,Ti,Si) eutectic agree with experimental observation very well.
which the Hf2Si peritectic dendrite forms until the liquid composition reaches the eutectic valley of Hf(Ti)2Si þ b(Hf, Ti,Si). The liquid composition then follows this eutectic valley to form the Hf(Ti)2Si þ b(Hf,Ti,Si) eutectic until it reaches invariant reaction II1 from which the eutectic of (Hf,Ti)5Si3 þ b(Hf,Ti,Si) starts to solidify. The experimental observation of b(Hf,Ti,Si) dendrites, Hf(Ti)2Si peritectic, b(Hf,Ti,Si) þ Hf(Ti)2Si eutectic, and b(Hf,Ti,Si) þ (Hf, Ti)5Si3 eutectic, is close to the Scheil simulation, which suggests that the solidification conditions in the DS experiments [12] are indeed closely represented by the assumptions of the Scheil model.
4.3.2. Hfe30Tie25Si in the Hf-rich (Hf,Ti)5Si3 primary phase regime Fig. 10 shows the simulation along with the experimental observation for the Hfe30Tie25Si alloy. The simulation shows that the solidification path begins with the primary solidification of (Hf,Ti)5Si3, then the liquid composition transverses the L þ (Hf,Ti)5Si3 / Hf(Ti)2Si peritectic ridge and moves into the primary solidification region of Hf2Si in
1440
2000 Hf-10Ti-16Si Hf(Ti)2Si dendrite β(Hf,Ti,Si)+Hf(Ti)2Si eutectic β(Hf,Ti,Si)+(Hf,Ti)5Si3 eutectic
1800
Hf-60Ti-10Si β(Hf,Ti,Si) dendrite β(Hf,Ti,Si)+(Hf,Ti)5Si3 eutectic 1410
Temperature_Celsius
Temperature_Celsius
1900
L->Hf(Ti)2Si 1700 L->β(Hf,Ti,Si)+Hf(Ti)2Si
1600
1500
L->β(Hf,Ti,Si)
1380 L->β(Hf,Ti,Si)+(Hf,Ti)5Si3
1350
1400
L->β(Hf,Ti,Si)+(Hf,Ti)5Si3 1320
1300 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Fraction of Solid Fig. 11. Comparison between the calculated solidification path of the Hfe 10Tie16Si alloy and the experimental observations [12] shown in the rightcorner box.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Fraction of Solid Fig. 13. Comparison between the calculated solidification path of the Hfe 60Tie10Si alloy and the experimental observations [12] shown in the rightcorner box.
Y. Yang et al. / Intermetallics 15 (2007) 168e176
4.3.3. Hfe10Tie16Si in the (Hf,Ti)2Si primary phase regime Fig. 11 shows the comparison between the simulated solidification path and experimental observation for the Hfe10Tie 16Si alloy. The simulated solidification path predicts the primary solidification phase to be Hf(Ti)2Si, followed by the eutectic reaction of L / b(Hf,Ti,Si) þ Hf(Ti)2Si. After that, the (Hf,Ti)5Si3 þ b(Hf,Ti,Si) eutectic solidifies from the liquid. The primary Hf(Ti)2Si phase and the b(Hf,Ti,Si) þ Hf (Ti)2Si eutectic agree very well with experimental observation. But the (Hf,Ti)5Si3 þ b(Hf,Ti,Si) eutectic was not reported in literature [12] probably due to its small volume fraction (<1%). 4.3.4. Hfe60Tie25Si in the Ti-rich (Hf,Ti)5Si3 primary phase regime Fig. 12 shows the comparison between the simulated solidification path and experimental observation for the Hfe60Tie 25Si alloy. The simulated results show two-stage solidification L / (Hf,Ti)5Si3, followed by L / b(Hf,Ti,Si) þ (Hf,Ti)5Si3. Due to the high Ti content, the solidification path of this alloy, or other alloys, in this region do not go through the invariant reaction II1. 4.3.5. Hfe60Tie10Si in the Ti-rich b(Hf,Ti,Si) primary phase regime The comparison between the simulated solidification path and the experimental observation for the Hfe60Tie10Si alloy is shown in Fig. 13. Again, two-stage solidification, i.e. L / b(Hf,Ti,Si) followed by L / b(Hf,Ti,Si) þ (Hf,Ti)5Si3 is predicted by the simulation. The solidification path from this region does not experience the invariant reaction II1 due to the high Ti content. The phases predicted by the solidification simulation are in good agreement with those observed experimentally in the as-cast microstructures. The present study of simple solidification simulations indicates that thermodynamic modeling can not only obtain a set of self-consistent thermodynamic parameters that can describe and predict the Hfe TieSi phase diagram, but it can also give very useful guidance for component casting. The good agreement between the results of the calculations and the majority of experimental data, for both the phase diagrams and the solidification paths, suggests that the present thermodynamic description is accurate for the transition metal-rich region of the HfeTieSi system. There are some residual uncertainties in the Si-rich corner of the ternary system due to the lack of experimental data. However, for design and processing of high temperature Nb-silicide based composites, the transition metal-rich portion of the diagram is more relevant. 5. Conclusions The present paper provides a thermodynamic description of the HfeTieSi system using the CALPHAD technique. From this thermodynamic description, isothermal sections of
175
HfeTieSi at 1000, 1350 and 1600 C were calculated. The calculated phase equilibria at 1350 C confirmed the existence of a three-phase region b(Hf,Ti,Si) þ (Hf,Ti)5Si3 þ Hf(Ti)2Si, and three two-phase regions b(Hf,Ti,Si) þ (Hf,Ti)5Si3, b(Hf,Ti,Si) þ Hf(Ti)2Si, and a(Hf,Ti,Si) þ Hf(Ti)2Si, as were observed from experimental work. The calculation also suggests that the solubility of Ti in Hf2Si increases with temperature. The calculated liquidus projection confirmed the existence of the invariant reaction L þ Hf(Ti)2Si / (Hf,Ti)5 Si3 þ b(Hf,Ti,Si). The experimentally determined Ti concentration of the liquid at this invariant reaction is between 42 and 50 at%, while the Si concentration of this liquid is between 9 and 10 at%. The Si concentration of the liquid at this invariant reaction is more precisely determined by the experiment. The calculated temperature and liquid composition are 1430 C and Hfe51Tie9.9Si, respectively. They are in good agreement with the measured temperature 1420 20 C and the estimated liquid composition Hfe 50Tie9.5Si. This study also carried out solidification simulation using the Scheil and lever-rule models. Comparisons between the calculated and experimental results suggest that the DS microstructure is closer to the Scheil simulation. Five primary solidification regions, i.e. Hf-rich b(Hf,Ti,Si), Hf(Ti)2Si-rich, Hf-rich (Hf,Ti)5Si3, Ti-rich (Hf,Ti)5Si3, and Ti-rich b(Hf,Ti,Si) primary solidification regimes were predicted from simulation. These predictions agree very well with experimental observation. Acknowledgements The authors would like to thank D.J. Dalpe for the directional solidification. The authors would also like to thank Dr. D.A. Wark of R.P.I. for the EMPA measurements.
References [1] Subramanian PR, Mendiratta MG, Dimiduk DM, Stucke M. Mater Sci Eng 1997;A239e240:1. [2] Subramanian PR, Mendiratta MG, Dimiduk DM. Mater Res Soc Symp Proc 1994;322:491. [3] Bewlay BP, Jackson MR, Lipsitt HA. Metall Mater Trans A 1996;27A:3801. [4] Jackson MR, Bewlay BP, Rowe RG, Skelly DW, Lipsitt HA. J Met 1996; 48:39. [5] Bewlay BP, Briant CL, Davis AW, Jackson MR. Mater Res Soc Symp Proc 2001;646:N2.7.1. [6] Bewlay BP, Briant CL, Sylven ET, Jackson MR, Xiao G. Mater Res Soc Symp Proc 2001;646:N2.6.1. [7] Bewlay BP, Whiting PW, Davis AW, Briant CL. Mater Res Soc Symp Proc 1999;552:KK6.11.1. [8] Bewlay BP, Grylls RJ, Fraser HL. Mater Res Soc Symp Proc 1999;552: KK5.27.1. [9] Yan XY, Chang YA, Yang Y, Xie FY, Chen SL, Zhang F, et al. Intermetallics 2001;9(6):535. [10] Liang H, Chang YA. Intermetallics 1999;7:561. [11] Yang Y, Chang YA, Zhao J-C, Bewlay BP. Intermetallics 2003;11(5): 407e15. [12] Bewlay BP, Jackson MR, Yang Y, Chang YA. Acta Mater, submitted for publication.
176 [13] [14] [15] [16] [17]
Y. Yang et al. / Intermetallics 15 (2007) 168e176 Bewlay BP, Yang Y, Chang YA. Z Metallkd, submitted for publication. Seifert H, Lukas HL, Petzow G. Z Metallkd 1996;87(1):2e13. Bittermann H, Rogl P. J Phase Equilib 1997;18(1):24e47. Redlich O, Kister AT. Indus Eng Chem 1948;40:345. Hillert M, Staffansson LI. Acta Chem Scand 1970;24:3618.
[18] Sundman B, Jansson B, Anderson JO. Calphad 1985;9:153. [19] Pandat 5.0-Phase Diagram Calculation Software for Multicomponent Systems, Computherm LLC, 437S, Yellowstone Dr., Suite 217, Madison, WI 53719; 2005. [20] Scheil E. Z Metallkd 1942;34:70.
Thermodynamic modeling of the HfeTieSi ternary system Y. Yang a,*, B.P. Bewlay b, Y.A. Chang c a CompuTherm LLC, 437 S. Yellowstone Drive, Madison, WI 53719, USA General Electric Company, GE Global Research Center, 1 Research Circle, Niskayuna, NY 12309, USA c Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA b
Received 14 February 2006; accepted 8 May 2006 Available online 19 June 2006
Abstract A thermodynamic description of the HfeTieSi system was developed using the phenomenological or Calphad approach, based on the critically assessed binary thermodynamic descriptions and experimental data of ternary phase equilibria. The parameters of all ternary phases were optimized using experimentally measured solid-state phase equilibria at 1350 C, melting temperatures of selected alloys, and primary solidification information for metal-rich HfeTieSi alloys. Comparisons between the calculated results and the experimental measurements show that the present modeling can satisfactorily describe the experimental information for the metal-rich region of the HfeTieSi ternary phase diagram for Si concentrations of up to 40 at%. The experimentally identified transition reaction L þ Hf(Ti)2Si / (Hf,Ti)5Si3 þ b(Hf,Ti,Si) at the metal-rich end of the ternary phase diagram is confirmed by this calculation. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: A. Intermetallics, miscellaneous; A. Silicides, various; B. Phase diagrams; B. Thermodynamic and thermochemical properties; E. Phase diagram, prediction
1. Introduction Nb-silicide based in situ composites have been investigated extensively [1e3] for applications as structural materials at temperatures of up to 1200 C. Ti and Hf are added to these composites to improve room temperature fracture toughness and high temperature oxidation resistance [2,4]. Recently, Bewlay et al. [5e8] reported that the creep rate at high temperatures increases significantly when the Nb:(Hf þ Ti) atomic ratio is reduced below w1.5. In order to improve the design of new engineering materials and understand the relationship between microstructure and properties, it is essential to have accurate knowledge of the phase equilibria of the NbeTie HfeSi quaternary system, especially in the metal-rich region. Obtaining such knowledge exclusively from experiments is cumbersome and expensive. Thermodynamic modeling of
* Corresponding author. Fax: þ1 608 262 8353. E-mail address: [email protected] (Y. Yang). 0966-9795/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.intermet.2006.05.002
multi-component systems using the phenomenological or Calphad approach has been shown to be a very efficient tool in this regard [9]. A prerequisite to develop the thermodynamic description of the NbeTieHfeSi system is to obtain thermodynamic descriptions of its four constituent ternary systems. In previous studies, we had developed thermodynamic descriptions of the NbeTieSi [10] and NbeHfeSi [11] systems. The objective of the present study is to develop a thermodyamic description for the metal-rich region of the HfeTieSi system, which will be used to build the thermodynamic database of the NbeTieHfeSi system. 2. Literature data for the HfeTieSi system There is almost no experimental data on phase equilibria for the HfeTieSi ternary system. Recently, Bewlay et al. [12,13] experimentally investigated the partial HfeTieSi liquidus projection (for Si concentrations between 0 and 40 at%) close to the HfeTi binary side, and the solid-state phase equilibria at 1350 C for metal-rich HfeTieSi alloys.
Y. Yang et al. / Intermetallics 15 (2007) 168e176
The alloys in Refs. [12,13] were prepared using the cold crucible directional solidification technique. Heat treatment was conducted at 1350 C for 100 h. Electron probe microanalysis (EPMA) was used to measure the phase compositions, while X-ray diffraction (XRD) and electron backscatter diffraction (EBSD) were used for crystal structure identification. The alloy melt temperatures were measured using a two wavelength optical pyrometer. The pyrometer was calibrated against both the melting temperature of 99.9% pure Ti (1670 C) and the temperature of the HfeHf2Si eutectic (1830 C) [12]. Fig. 1 shows the partial liquidus projection of the HfeTie Si system close to the HfeTi binary for Si concentrations between 0 and 40 at% proposed by Bewlay et al. [12], together with the experimentally investigated alloy compositions. The phases present in these as-cast alloys and the melting temperature of these alloys are listed in Table 2. The alloy compositions throughout this article are given in atomic percent. There are three primary solidification phases in this portion of liquidus projection: (Hf,Ti)5Si3, Hf(Ti)2Si and b(Hf,Ti,Si). The Ti5Si3 and Hf5Si3 both have hP16 crystal structures and are referred to as (Hf,Ti)5Si3. The Hf2Si with Ti in solid solution is referred to as Hf(Ti)2Si, and b(Hf,Ti,Si) refers to the ternary solid solution based on bcc structure. The denotation of the phase names is explained in Table 1, which also lists the crystal structures in terms of the Pearson symbols and thermodynamic models used. A eutectic groove extends from the L / b(Hf,Si) þ Hf2Si in the HfeSi binary (denoted by e1) to the L / Ti5Si3 þ b(Ti,Si) in the TieSi binary (denoted by e2). Because of the different binary eutectic reactions there is a change in the nature of the liquidus surface, and the eutectic groove, with decreasing Hf and increasing Ti concentration. The phase transition corresponding to the change on the eutectic groove involves four phases, i.e. liquid, b(Hf,Ti,Si), Hf(Ti)2Si and (Hf,Ti)5Si3. Based on microstructural evidence, Bewlay et al. [12] determined that this phase transition is a type II reaction of the form L þ (Hf,Ti)2Si / (Hf,Ti)5Si3 þ b(Hf,Ti,Si), and it occurred at a composition of approximately Hfe50Tie9.5Si. The temperature of this invariant reaction was measured to be 1420 20 C [12]. 40 at% Si
Hf5Si3 Hf2Si
Ti5Si3 3
0.3
0.2
2 (Hf,Ti)2Si
0.1
1 0.0
4 1
(Hf,Ti)5Si3
0.1
0.2
5
(Hf,Ti,Si) 0.3
0.4
0.5
0.6
0.7
0.8
0.9
Hf
1.0
Ti Hf-rich (Hf,Ti,Si)
Ti-rich (Hf,Ti,Si)
Hf-rich (Hf,Ti)5Si3
Hf(Ti)2Si
Ti-rich (Hf,Ti)5Si3
Fig. 1. Experimentally determined liquidus projection of the metal-rich end of the HfeTieSi ternary system [12]. Symbols represent the alloy compositions. The different symbols denote the different primary solidification phases, as shown in the key to the figure.
169
Table 1 Solid phases in the HfeTieSi system Phase symbol
Thermodynamic model
Crystal structure
Phase description
b(Hf,Ti,Si)
(Hf,Ti,Si)1(Va)3
cI2
a(Hf,Ti,Si)
(Hf,Ti,Si)1(Va)0.5
hP2
(Si) Hf(Ti)2Si
(Si) (Hf,Ti)2Si
cF8 tI12
(Hf,Ti)Si
(Hf,Ti)Si
oP8
Hf3Si2
Hf3Si2
tP10
(Hf,Ti)5Si3
(Hf,Ti)5Si3
hP16
(Hf,Ti)5Si4
(Hf,Ti)5Si4
tP36
HfSi2 Ti3Si TiSi2
HfSi2 Ti3Si TiSi2
oC12 tP32
Ternary solid solution based on bcc Ternary solid solution based on hcp Silicon Solid solution based on Hf2Si Solid solution based on HfSi and NbSi Binary compound Hf3Si2 Solid solution based on Hf5Si3 and Ti5Si3 Solid solution based on Hf5Si4 and Ti5Si4 Binary compound HfSi2 Binary compound Ti3Si Binary compound TiSi2
The solid-state phase equilibria of selected HfeTieSi alloys heat treated at 1350 C for 100 h reported by Bewlay et al. [13] are listed in Table 2. Four phases were observed in these samples, and they were b(Hf,Ti,Si), (Hf,Ti)5Si3, Hf(Ti)2Si, and a(Hf,Ti,Si). One three-phase equilibria region b(Hf,Ti,Si) þ (Hf,Ti)5Si3 þ Hf(Ti)2Si, and three two-phase regions b(Hf,Ti,Si) þ (Hf,Ti)5Si3, b(Hf,Ti,Si) þ Hf(Ti)2Si and a(Hf,Ti,Si) þ Hf(Ti)2Si were observed. The EPMA measurements of the three-phase equilibria b(Hf,Ti,Si) þ (Hf,Ti)5 Si3 þ Hf(Ti)2Si suggest that the maximum solubility of Ti in Hf2Si is 9.8 at% at 1350 C [12]. 3. Thermodynamic modeling of the HfeTieSi system All three constituent binaries of the HfeTieSi system have been thermodynamically modeled. In the present modeling, the thermodynamic parameters of the HfeSi, TieSi, and HfeTi binary systems are taken from Yan et al. [11], Seifert et al. [14] and Bittermann and Rogl [15], respectively. The calculated HfeTi, HfeSi, and TieSi binary phase diagrams are shown in Figs. 2e4, respectively. Neither experimental nor calculated thermodynamic property data for the HfeTieSi ternary system were found in literature. Therefore, the current modeling is based on the experimental information of the liquidus projection and the solid-state phase equilibria discussed in Section 2. The thermodynamic description of the Si-rich region is obtained through extrapolation, again due to lack of experimental data. There are two types of ternary solid solution phases: one is based on the structures of the terminal solid solutions, such as the b(Hf,Ti,Si) phase based on the bcc structure of Hf or Ti, and a(Hf,Ti,Si) based on the hcp structure of Hf or Ti. The second type of solid solution is based on intermetallic compounds such as (Hf,Ti)5Si3 and Hf(Ti)2Si phases. The Gibbs free energy of the first type of ternary solutions is described by the RedlicheKister polynomial [16],
Y. Yang et al. / Intermetallics 15 (2007) 168e176
170
Table 2 Comparison between the calculated and experimental melting temperature and constituent phases in samples Compositions
Tm ( C)
Constituent phases in as-cast samples
Constituent phases in annealed samples at 1350 C
1710 1644
b(Hf,Ti,Si) þ Hf(Ti)2Si b(Hf,Ti,Si) þ Hf(Ti)2Si þ (Hf,Ti)5Si3(<1%)a,b b(Hf,Ti,Si) þ Hf(Ti)2Si b(Hf,Ti,Si) þ Hf(Ti)2Si þ (Hf,Ti)5Si3(<1%) b(Hf,Ti,Si) þ Hf(Ti)2Si b(Hf,Ti,Si) þ Hf(Ti)2Si þ (Hf,Ti)5Si3(1.1%)
a(Hf,Ti,Si) þ Hf(Ti)2Si a(Hf,Ti,Si) þ Hf(Ti)2Si a(Hf,Ti,Si) þ Hf(Ti)2Si a(Hf,Ti,Si) þ Hf(Ti)2Si b(Hf,Ti,Si) þ Hf(Ti)2Si þ a(Hf,Ti,Si) b(Hf,Ti,Si) þ Hf(Ti)2Si þ a(Hf,Ti,Si)
Hf(Ti)2Si þ b(Hf,Ti,Si) b(Hf,Ti,Si) þ Hf(Ti)2Si þ (Hf,Ti)5Si3(4%) Hf(Ti)2Si þ b(Hf,Ti,Si) Hf(Ti)2Si þ b(Hf,Ti,Si) þ (Hf,Ti)5Si3(<1%) Hf(Ti)2Si þ b(Hf,Ti,Si) b(Hf,Ti,Si) þ Hf(Ti)2Si þ (Hf,Ti)5Si3(2%) Hf(Ti)2Si þ b(Hf,Ti,Si) b(Hf,Ti,Si) þ Hf(Ti)2Si þ (Hf,Ti)5Si3(6%) Hf(Ti)2Si þ b(Hf,Ti,Si) þ (Hf,Ti)5Si3 Hf(Ti)2Si þ b(Hf,Ti,Si) þ (Hf,Ti)5Si3 Hf(Ti)2Si þ b(Hf,Ti,Si) þ (Hf,Ti)5Si3 Hf(Ti)2Si þ b(Hf,Ti,Si) þ (Hf,Ti)5Si3 b(Hf,Si) þ Hf2Si Hf2Si þ b(Hf,Si)
Hf(Ti)2Si þ b(Hf,Ti,Si) Hf(Ti)2Si þ b(Hf,Ti,Si)
Group 1 Hfe10Tie10Si Hfe10Tie5Si Hfe20Tie5Si Group 2 Hfe30Tie10Si Hfe10Tie16Si
1530 1507 1720 1708
Hfe20Tie16Si Hfe30Tie16Si Hfe40Tie9Si Hfe42Tie10Si
1420 1430 1415 1430
Hfe12Si Hfe20Si Group 3 Hfe50Tie9.5Si
1420 1412
Hfe30Tie25Si Group 4 Hfe60Tie25Si
a b
1340 1382
b(Hf,Ti,Si) þ (Hf,Ti)5Si3 b(Hf,Ti,Si) þ (Hf,Ti)5Si3
b(Hf,Ti,Si) þ (Hf,Ti)5Si3 b(Hf,Ti,Si) þ (Hf,Ti)5Si3 b(Ti) þ Ti5Si3 (Hf,Ti)5Si3 þ b(Hf,Ti,Si) b(Hf,Ti,Si) þ (Hf,Ti)5Si3
(Hf,Ti)5Si3 þ b(Hf,Ti,Si) b(Hf,Ti,Si) þ (Hf,Ti)5Si3
Italic font denotes the calculated results and normal font the experimental results. The number denotes the calculated mole fraction of the phase.
G4m ¼xTi 0 G4Ti þ xHf 0 G4Hf þ xSi 0 G4Si þ RT xTi ln xTi þ xHf ln xHf þ xSi ln xSi þ ex G4m
L4Hf;Ti;Si ¼ xTi L4Ti þ xHf L4Hf þ xSi L4Si
G4m ¼ xTi xSi L4Ti;Si þ xHf xSi L4Hf;Si þ xTi xHf L4Hf;Ti þ xTi xHf xSi L4Hf;Ti;Si
ð3Þ
ð1Þ
where xTi , xHf and xSi are the mole fractions of Ti, Hf and Si, respectively. 0 G4Ti , 0 G4Hf and 0 G4Si are the 4 phase molar Gibbs energies of element Ti, Hf and Si, respectively. ex G4m is the excess Gibbs energy term of 4 phase. It is expressed by the following equation: ex
(Hf,Ti)5Si3 þ Hf(Ti)2Si þ b(Hf,Ti,Si) (Hf,Ti)5Si3 þ Hf(Ti)2Si þ b(Hf,Ti,Si)
(Hf,Ti)5Si3 þ b(Hf,Ti,Si) (Hf,Ti)5Si3 þ b(Hf,Ti,Si)
Group 5 Hfe85Tie5Si Tie13.5Si Hfe60Tie10Si
Hf5Si3 þ b(Hf,Ti,Si) b(Hf,Ti,Si) þ (Hf,Ti)5Si3 þ Hf(Ti)2Si(2%) (Hf,Ti)5Si3 þ Hf(Ti)2Si þ b(Hf,Ti,Si) (Hf,Ti)5Si3 þ Hf(Ti)2Si þ b(Hf,Ti,Si)
ð2Þ
the parameters denoted by L4Hf;Si, L4Ti;Si and L4Hf;Ti are the interaction parameters from the HfeSi, TieSi and HfeTi binaries, respectively. L4Hf;Ti;Si is the ternary interaction parameter, which is usually expressed by the following equation:
L4Hf , L4Ti and L4Si make the major contributions to the liquidus surfaces in Hf-rich, Ti-rich and Si-rich corners of the HfeTie Si system, respectively. The compound energy formalism developed by Hillert and Staffansson [17] was used to describe the second type of ternary solid solutions with a form of (Hf,Ti)p(Si)q. The Gibbs free energy of such phases for one mole of atoms can be described by the following equation: G4ðHf;TiÞ
p Siq
p ¼yITi 0 G4Ti:Si þ yIHf 0 G4Hf:Si þ pþq RT yITi ln yITi þ yIHf ln yIHf þ yITi yIHf L4Hf;Ti:Si ð4Þ
in which yITi and yIHf are the site fractions of Ti and Hf on the first sublattice, respectively. 0 G4Ti:Si and 0 G4Hf:Si are the Gibbs
Y. Yang et al. / Intermetallics 15 (2007) 168e176 2500
2400
2100
2040
171
L
0.48,1929
900
L
0.61,1570 0.667,1488
960
TiSi2
0.15, 1328
TiSi
0.86,1330
1320
Ti5Si4
(Hf,Ti)
1300
1680
Ti5Si3
1700
Ti3Si
Temperature (ºC)
Temperature (ºC)
0.375,2127
(Si)
(Hf,Ti)
500 0
0.1
0.2
0.3
Hf
0.4
0.5
0.6
0.7
0.8
0.9
Mole fraction of Ti
1
Ti
600 0
0.1
0.2
0.3
Ti
0.4
0.5
0.6
0.7
0.8
0.9
Mole fraction of Si
1
Si
Fig. 2. The HfeTi phase diagram calculated in the present study. The thermodynamic description is taken from Ref. [15].
Fig. 4. The TieSi phase diagram calculated in the present study. The thermodynamic description is taken from Ref. [14].
energies of the compounds TipSiq and HfpSiq with the structure of 4. L4Hf;Ti:Si represents the interaction between Hf and Ti in the first sublattice with only Si present in the second sublattice. It is expressed as the following equation:
treated as binary compounds due to the lack of solubility data of Hf in Ti3Si and TiSi2, and Ti in HfSi2 and Hf3Si2. The optimization was performed in the parrot module of Thermo-Calc [18], and Pandat [19] was used to calculate the phase diagrams and solidification paths. The optimization procedure begins with solid-state phase equilibria at 1350 C, and then it proceeds to the liquidus surface. The optimized parameters in this study are listed in Table 3.
L4Hf;Ti;Si ¼ 0 L4Hf;Ti:Si þ yIHf yITi 1 L4Hf;Ti:Si
ð5Þ
In the present modeling, the Gibbs energies of b(Hf,Si,Ti), a(Hf,Si,Ti) and liquid were described by Eq. (1). Hf5Si3 and Ti5Si3 are treated as one phase denoted by (Hf,Ti)5Si3 due to their similar crystal structures. Similarly, Hf5Si4 and Ti5Si4 are denoted by (Hf,Ti)5Si4, and HfSi and TiSi by (Hf,Ti)Si. The Gibbs free energies of Hf(Ti)2Si, (Hf,Ti)5Si3, (Hf,Ti)5Si4 are described by Eq. (4). Ti3Si, TiSi2, HfSi2, and Hf3Si2 are 2600 0.4, 2466 0.30, 2354
Hf5Si3 Hf5Si4
0
0.1
0.2
0.3
0.4
0.5
Table 2 lists the good agreement between the calculated and experimentally observed constituent phases in those samples annealed at 1350 C. The calculated 1350 C isothermal section is shown in Fig. 5, together with the experimentally investigated alloy compositions, and the compositions of the phases in these alloys. The experimentally measured three-phase and two-phase equilibria are reasonably well described by this calculation. The calculated maximum solubility of Ti in Hf(Ti)2Si at 1350 C is 10.0%, which agrees very well with the EPMA measurement of 9.8%. In addition to the 1350 C isothermal section, we also calculated isothermal sections at 1000 and 1600 C, as shown in Figs. 6 and 7, respectively. The 1000 C isotherm displays a similar phase relationship to Table 3 The optimized parameters in the study for the HfeTieSi system
0.89, 1329
(Si)
1000
Hf
4.1. Isothermal sections at 1350, 1000 and 1600 C
0.76, 1539
HfSi2
Hf3Si2
0.12,1824
Hf2Si
1400
0.58, 2147
HfSi
β(Hf,Si)
1800
0.21, 2092
α(Hf,Si)
Temperature (ºC)
2200
L
0.51, 2320
4. Results and discussion
0.6
Mole fraction of Si
0.7
0.8
0.9
1
Si
Fig. 3. The HfeSi phase diagram calculated in the present study. The thermodynamic description is taken from Ref. [11].
Phase symbol
Thermodynamic model
Model parameters (J/mol)
b(Hf,Ti,Si) Liquid
(Hf,Ti,Si)1(Va)3 (Hf,Ti,Si)
Hf(Ti)2Si (Hf,Ti)5Si3
(Hf,Ti)0.667Si0.333 (Hf,Ti)5Si3
L0Hf;Si;Ti:Va ¼ L2Hf;Si;Ti:Va ¼ 236 445 L0Hf;Si;Ti ¼ L2Hf;Si;Ti ¼ 80 986 L1Hf;Si;Ti ¼ 31 387 L0Hf;Ti:Si ¼ 161 575 þ 30 T L0Hf;Ti:Si ¼ 370 706 þ 178 T L1Hf;Ti:Si ¼ 274 336 þ 140 T
Y. Yang et al. / Intermetallics 15 (2007) 168e176
172 Si
Phasecomposition Alloy composition
Liq
Liq
Si of
TiSi2
tio n
Si of
HfSi2
0.4
Mo
(Hf,Ti)Si (Hf,Ti)5Si4
Hf3Si2
0.6
le fra c
0.6
tio n le fra c
Si
0.8
0.8
Mo
1
T=1600ºC
1
T=1350ºC
(Hf,Ti)Si (Hf,Ti)5Si4
0.4
(Hf,Ti)5Si3
Hf3Si2 Hf(Ti)2Si
(Hf,Ti)5Si3
Hf(Ti)2Si
0.2
0.2 Liq
0
Liq 0
0
α(Hf,Ti,Si)
0.2
0.4
Hf
0.6
0.8 β(Hf,Ti,Si) 1
Mole fraction of Ti
Ti
Fig. 5. Comparison between the calculated isothermal section and the experimental measurements at 1350 C [13]. The solid circles refer to bulk alloy compositions, and the solid squares refer to phase compositions.
that at 1350 C. The solubility of Ti in Hf(Ti)2Si at 1000 C is 11.3%, and it is slightly higher than that at 1350 C. The solubility of Ti in Hf(Ti)2Si at 1600 C is calculated to be 8.7%. The calculated results at these three temperatures (1600, 1350 and 1000 C) suggest that the solubility of Ti in Hf(Ti)2Si decreases with temperature. The major difference between 1350 and 1000 C isotherms is that b(Hf,Ti,Si) and (Hf,Ti)5Si3 of the three-phase equilibria b(Hf,Ti,Si) þ (Hf,Ti)5Si3 þ Hf (Ti)2Si contain more Ti at 1000 C. The 1600 C isotherm is above the transition temperature of the reaction L þ H f(Ti)2Si / (Hf,Ti)5Si3 þ b(Hf,Ti,Si) at 1430 C. Therefore, the two three-phase equilibria of L þ b(Hf,Ti,Si) þ Hf(Ti)2Si 1
T= 1000ºC
Si
Mo le
fra ctio no
fS
i
0.8
HfSi2
TiSi2
0.6 (Hf,Ti)Si (Hf,Ti)5Si4
Hf3Si2 0.4
(Hf,Ti)5Si3
Hf(Ti)2Si Ti3Si
0.2
0
0 α(Hf,Ti,Si) 0.2
Hf
0.4
0.6
Mole fraction of Ti
0.8 β(Hf,Ti,Si) 1
Ti
Fig. 6. The HfeTieSi isothermal section at 1000 C calculated in the present study.
0 α(Hf,Ti,Si) 0.2
Hf
0.4
0.6
Mole fraction of Ti
0.8 β(Hf,Ti,Si) 1
Ti
Fig. 7. The HfeTieSi isothermal section at 1600 C calculated in the present study.
and L þ Hf(Ti)2Si þ (Hf,Ti)5Si3 are calculated to exist in the 1600 C isothermal section, instead of b(Hf,Ti,Si) þ (Hf,Ti)5Si3 þ Hf(Ti)2Si and L þ b(Hf,Ti,Si) þ (Hf,Ti)5Si3. Further experimental data are required to validate the calculated isotherms at 1000 and 1600 C. 4.2. Liquidus projection The calculated liquidus projection is shown in Fig. 8, together with alloy compositions investigated by Bewlay et al. [12]. It shows three primary phase regimes: (Hf,Ti)5Si3, Hf(Ti)2Si and b(Hf,Ti,Si) in the metal-rich region for Si concentrations from 0 to 40%. The symbols in this figure refer to the experimentally investigated alloy compositions from the five groups in Table 2. Details on the definition of these five groups will be discussed in Section 4.3. The calculated primary phases of solidification according to the Scheil model are in accord with the experimentally observed results. The observed type II invariant reaction L þ Hf(Ti)2Si / (Hf,Ti)5Si3 þ b(Hf,Ti,Si) is confirmed by the calculation. The calculated temperature of this reaction (1430 C) is in accordance with the experimental measurement (w1420 C). The liquid composition of this invariant reaction was determined through microstructure analysis of selected as-cast alloys [12]. The Ti concentration of the liquid at this invariant reaction is between 42 and 50 at%, while the Si concentration is between 9 and 10 at%. The Si concentration of the liquid at this invariant reaction is determined more precisely than the Ti concentration. The calculated liquid composition of this reaction Hfe51Tie 9.9Si is in good agreement with the composition Hfe50Tie 9.5Si [12] within experimental error. The current thermodynamic modeling also takes the melting temperature measurements [12] of the alloys into consideration. During the thermodynamic modeling, we found that the measured melting temperatures of those alloys with
Y. Yang et al. / Intermetallics 15 (2007) 168e176
(Si) HfSi2
0.8
TiSi2
Calculation Hf-rich (Hf,Ti,Si) Hf(Ti)2Si Hf-rich(Hf,Ti)5Si3 Ti-rich(Hf,Ti)5Si3 Ti-rich (Hf,Ti,Si)
(Hf,Ti)Si
(Hf,Ti)5Si4 0.4
Hf 3 Si 2
Mo
le fra c
tio n
of
Si
0.6
(Hf,Ti)5Si3 0.2
(Hf,Ti)2Si (Hf,Ti,Si) 0.0 0
Hf
0.2
0.4
0.6
Mole fraction of Ti
0.8
1
solidification regimes are Hf-rich b(Hf,Ti,Si), Hf(Ti)2Si-rich, Hf-rich (Hf,Ti)5Si3, Ti-rich (Hf,Ti)5Si3, and Ti-rich b(Hf,Ti,Si) primary solidification regions. Five representative alloy compositions with one alloy from each group were selected for simulations. Solidification path simulations were performed using the Scheil [20] and lever-rule models. The Scheil model assumes no diffusion in the solid and thermodynamic equilibrium is maintained at liquidesolid interface only. The leverrule model assumes complete mixing in the solid, and the total solid and liquid are in thermodynamic equilibrium. Both models require thermodynamic information only and are integrated into the solidification simulation module of Pandat [19]. These two models represent two extreme cases of solidification. The simulation results show that the solidification microstructure in the DS experiments is closer to that predicted by the Scheil model. Therefore, comparisons between predicted phases by the Scheil solidification simulations and the observed phases in as-cast alloys are given in this paper, as shown in Figs. 9e13.
Ti
Fig. 8. The calculated liquidus projection of the HfeTieSi system compared with experimental data. Symbols represent the alloy compositions. The different symbols denote the different primary solidification phases, as shown in the key to the figure.
a wide freezing range cannot be reconciled with those with a narrow freezing range and with the temperature of the transition reaction II1. This suggests that the method used by Bewlay et al. [12] in measuring the melting points of alloys, with wide freezing ranges, may have large uncertainties. Accordingly, the measured melting points for these alloys were not included in Table 2. Table 2 also compares the phases observed in the as-cast microstructure and the phases predicted by the Scheil solidification simulation. The calculation suggests that the (Hf,Ti)5Si3 phase should be present in the solidification microstructure of all these alloys, but it was only observed experimentally in some of them. This may be due to the small volume fraction of (Hf,Ti)5Si3. In general, the comparisons in Table 2 show reasonable agreement between the calculated results and experimental measurements. Three other invariant reactions are identified using the thermodynamic calculation. They are L þ (Hf,Ti)5Si3 / Hf3Si2 þ (Hf,Ti)5Si4, L þ (Hf,Ti) / HfSi2 þ TiSi2 and L / HfSi2 þ TiSi2 þ (Si). These reactions are calculated based on the extrapolated thermodynamic descriptions of relevant phases. While the calculated compositions and temperatures may deviate from the actual values, the topological features of these three reactions are considered to be correct. The currently calculated phase diagram can therefore serve as a design tool to efficiently select critical alloy compositions for further experimental investigation of these three reactions. 4.3. Solidification path simulation
4.3.1. Hfe10Tie5Si in the Hf-rich b(Hf,Ti,Si) primary phase regime Fig. 9 shows the simulated solidification sequence along with the experimental observation (shown in the right-corner box) for the Hfe10Tie5Si alloy located in the Hf-rich b(Hf,Ti,Si) primary phase regime. The calculated solidification sequences show that the first phase to solidify is b(Hf,Ti,Si), then the liquid composition follows the L / Hf(Ti)2Si þ b(Hf,Ti,Si) eutectic valley until it reaches the invariant reaction of L þ Hf(Ti)2Si / (Hf,Ti)5Si3 þ b(Hf,Ti,Si). Then the liquid continues to solidify by following the eutectic valley of L / (Hf,Ti)5Si3 þ b(Hf,Ti,Si). The final point of the Scheil simulation is the L / Ti5Si3 þ b(Ti,Si) binary eutectic reaction. The mole fraction of the (Hf,Ti)5Si3 þ b(Hf,Ti,Si) eutectic is calculated to be very small (<1%). The simulated 2100 Hf-10Ti-5Si β(Hf,Ti,Si) dendrite
2000
β(Hf,Ti,Si)+Hf(Ti)2Si eutectic 1900
Temperature_Celsius
Si 1
Liquidus projection
173
L->β(Hf,Ti,Si)
1800 1700
L->β(Hf,Ti,Si)+Hf(Ti)2Si 1600 1500 1400 L->β(Hf,Ti,Si)+(Hf,Ti)5Si3 1300 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Fraction of Solid
As-cast microstructures of a series of alloys from the five groups corresponding to the five regimes on the liquidus surface have been analyzed by Bewlay et al. [12]. These five
Fig. 9. Comparison between the calculated solidification path of the Hfe 10Tie5Si alloy and the experimental observations [12] shown in the rightcorner box.
Y. Yang et al. / Intermetallics 15 (2007) 168e176
174
2000
2200
Temperature_Celsius
2000 1900
1900
Hf(Ti)2Si peritectic β(Hf,Ti,Si)+Hf(Ti)2Si eutectic β(Hf,Ti,Si)+(Hf,Ti)5Si3 eutectic
1800
Temperature_Celsius
2100
Hf-30Ti-25Si (Hf,Ti)5Si3 dendrite
L->(Hf,Ti)5Si3
1800 1700 1600 1500
L->Hf(Ti)2Si
1400
L->β(Hf,Ti,Si)+Hf(Ti)2Si
Hf-60Ti-25Si (Hf,Ti)5Si3 dendrite β(Hf,Ti,Si)+(Hf,Ti)5Si3 eutectic
1700 L->(Hf,Ti)5Si3
1600
1500 L->β(Hf,Ti,Si)+(Hf,Ti)5Si3
1400 L->β(Hf,Ti,Si)+(Hf,Ti)5Si3
1300 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1300
1
0
0.1
0.2
0.3
Fraction of Solid
0.4
0.5
0.6
0.7
0.8
0.9
1
Fraction of Solid
Fig. 10. Comparison between the calculated solidification path of the Hfe 30Tie25Si alloy and the experimental observations [12] shown in the rightcorner box.
Fig. 12. Comparison between the calculated solidification path of the Hfe 60Tie25Si alloy and the experimental observations [12] shown in the rightcorner box.
b(Hf,Ti,Si) dentrite and Hf(Ti)2Si þ b(Hf,Ti,Si) eutectic agree with experimental observation very well.
which the Hf2Si peritectic dendrite forms until the liquid composition reaches the eutectic valley of Hf(Ti)2Si þ b(Hf, Ti,Si). The liquid composition then follows this eutectic valley to form the Hf(Ti)2Si þ b(Hf,Ti,Si) eutectic until it reaches invariant reaction II1 from which the eutectic of (Hf,Ti)5Si3 þ b(Hf,Ti,Si) starts to solidify. The experimental observation of b(Hf,Ti,Si) dendrites, Hf(Ti)2Si peritectic, b(Hf,Ti,Si) þ Hf(Ti)2Si eutectic, and b(Hf,Ti,Si) þ (Hf, Ti)5Si3 eutectic, is close to the Scheil simulation, which suggests that the solidification conditions in the DS experiments [12] are indeed closely represented by the assumptions of the Scheil model.
4.3.2. Hfe30Tie25Si in the Hf-rich (Hf,Ti)5Si3 primary phase regime Fig. 10 shows the simulation along with the experimental observation for the Hfe30Tie25Si alloy. The simulation shows that the solidification path begins with the primary solidification of (Hf,Ti)5Si3, then the liquid composition transverses the L þ (Hf,Ti)5Si3 / Hf(Ti)2Si peritectic ridge and moves into the primary solidification region of Hf2Si in
1440
2000 Hf-10Ti-16Si Hf(Ti)2Si dendrite β(Hf,Ti,Si)+Hf(Ti)2Si eutectic β(Hf,Ti,Si)+(Hf,Ti)5Si3 eutectic
1800
Hf-60Ti-10Si β(Hf,Ti,Si) dendrite β(Hf,Ti,Si)+(Hf,Ti)5Si3 eutectic 1410
Temperature_Celsius
Temperature_Celsius
1900
L->Hf(Ti)2Si 1700 L->β(Hf,Ti,Si)+Hf(Ti)2Si
1600
1500
L->β(Hf,Ti,Si)
1380 L->β(Hf,Ti,Si)+(Hf,Ti)5Si3
1350
1400
L->β(Hf,Ti,Si)+(Hf,Ti)5Si3 1320
1300 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Fraction of Solid Fig. 11. Comparison between the calculated solidification path of the Hfe 10Tie16Si alloy and the experimental observations [12] shown in the rightcorner box.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Fraction of Solid Fig. 13. Comparison between the calculated solidification path of the Hfe 60Tie10Si alloy and the experimental observations [12] shown in the rightcorner box.
Y. Yang et al. / Intermetallics 15 (2007) 168e176
4.3.3. Hfe10Tie16Si in the (Hf,Ti)2Si primary phase regime Fig. 11 shows the comparison between the simulated solidification path and experimental observation for the Hfe10Tie 16Si alloy. The simulated solidification path predicts the primary solidification phase to be Hf(Ti)2Si, followed by the eutectic reaction of L / b(Hf,Ti,Si) þ Hf(Ti)2Si. After that, the (Hf,Ti)5Si3 þ b(Hf,Ti,Si) eutectic solidifies from the liquid. The primary Hf(Ti)2Si phase and the b(Hf,Ti,Si) þ Hf (Ti)2Si eutectic agree very well with experimental observation. But the (Hf,Ti)5Si3 þ b(Hf,Ti,Si) eutectic was not reported in literature [12] probably due to its small volume fraction (<1%). 4.3.4. Hfe60Tie25Si in the Ti-rich (Hf,Ti)5Si3 primary phase regime Fig. 12 shows the comparison between the simulated solidification path and experimental observation for the Hfe60Tie 25Si alloy. The simulated results show two-stage solidification L / (Hf,Ti)5Si3, followed by L / b(Hf,Ti,Si) þ (Hf,Ti)5Si3. Due to the high Ti content, the solidification path of this alloy, or other alloys, in this region do not go through the invariant reaction II1. 4.3.5. Hfe60Tie10Si in the Ti-rich b(Hf,Ti,Si) primary phase regime The comparison between the simulated solidification path and the experimental observation for the Hfe60Tie10Si alloy is shown in Fig. 13. Again, two-stage solidification, i.e. L / b(Hf,Ti,Si) followed by L / b(Hf,Ti,Si) þ (Hf,Ti)5Si3 is predicted by the simulation. The solidification path from this region does not experience the invariant reaction II1 due to the high Ti content. The phases predicted by the solidification simulation are in good agreement with those observed experimentally in the as-cast microstructures. The present study of simple solidification simulations indicates that thermodynamic modeling can not only obtain a set of self-consistent thermodynamic parameters that can describe and predict the Hfe TieSi phase diagram, but it can also give very useful guidance for component casting. The good agreement between the results of the calculations and the majority of experimental data, for both the phase diagrams and the solidification paths, suggests that the present thermodynamic description is accurate for the transition metal-rich region of the HfeTieSi system. There are some residual uncertainties in the Si-rich corner of the ternary system due to the lack of experimental data. However, for design and processing of high temperature Nb-silicide based composites, the transition metal-rich portion of the diagram is more relevant. 5. Conclusions The present paper provides a thermodynamic description of the HfeTieSi system using the CALPHAD technique. From this thermodynamic description, isothermal sections of
175
HfeTieSi at 1000, 1350 and 1600 C were calculated. The calculated phase equilibria at 1350 C confirmed the existence of a three-phase region b(Hf,Ti,Si) þ (Hf,Ti)5Si3 þ Hf(Ti)2Si, and three two-phase regions b(Hf,Ti,Si) þ (Hf,Ti)5Si3, b(Hf,Ti,Si) þ Hf(Ti)2Si, and a(Hf,Ti,Si) þ Hf(Ti)2Si, as were observed from experimental work. The calculation also suggests that the solubility of Ti in Hf2Si increases with temperature. The calculated liquidus projection confirmed the existence of the invariant reaction L þ Hf(Ti)2Si / (Hf,Ti)5 Si3 þ b(Hf,Ti,Si). The experimentally determined Ti concentration of the liquid at this invariant reaction is between 42 and 50 at%, while the Si concentration of this liquid is between 9 and 10 at%. The Si concentration of the liquid at this invariant reaction is more precisely determined by the experiment. The calculated temperature and liquid composition are 1430 C and Hfe51Tie9.9Si, respectively. They are in good agreement with the measured temperature 1420 20 C and the estimated liquid composition Hfe 50Tie9.5Si. This study also carried out solidification simulation using the Scheil and lever-rule models. Comparisons between the calculated and experimental results suggest that the DS microstructure is closer to the Scheil simulation. Five primary solidification regions, i.e. Hf-rich b(Hf,Ti,Si), Hf(Ti)2Si-rich, Hf-rich (Hf,Ti)5Si3, Ti-rich (Hf,Ti)5Si3, and Ti-rich b(Hf,Ti,Si) primary solidification regimes were predicted from simulation. These predictions agree very well with experimental observation. Acknowledgements The authors would like to thank D.J. Dalpe for the directional solidification. The authors would also like to thank Dr. D.A. Wark of R.P.I. for the EMPA measurements.
References [1] Subramanian PR, Mendiratta MG, Dimiduk DM, Stucke M. Mater Sci Eng 1997;A239e240:1. [2] Subramanian PR, Mendiratta MG, Dimiduk DM. Mater Res Soc Symp Proc 1994;322:491. [3] Bewlay BP, Jackson MR, Lipsitt HA. Metall Mater Trans A 1996;27A:3801. [4] Jackson MR, Bewlay BP, Rowe RG, Skelly DW, Lipsitt HA. J Met 1996; 48:39. [5] Bewlay BP, Briant CL, Davis AW, Jackson MR. Mater Res Soc Symp Proc 2001;646:N2.7.1. [6] Bewlay BP, Briant CL, Sylven ET, Jackson MR, Xiao G. Mater Res Soc Symp Proc 2001;646:N2.6.1. [7] Bewlay BP, Whiting PW, Davis AW, Briant CL. Mater Res Soc Symp Proc 1999;552:KK6.11.1. [8] Bewlay BP, Grylls RJ, Fraser HL. Mater Res Soc Symp Proc 1999;552: KK5.27.1. [9] Yan XY, Chang YA, Yang Y, Xie FY, Chen SL, Zhang F, et al. Intermetallics 2001;9(6):535. [10] Liang H, Chang YA. Intermetallics 1999;7:561. [11] Yang Y, Chang YA, Zhao J-C, Bewlay BP. Intermetallics 2003;11(5): 407e15. [12] Bewlay BP, Jackson MR, Yang Y, Chang YA. Acta Mater, submitted for publication.
176 [13] [14] [15] [16] [17]
Y. Yang et al. / Intermetallics 15 (2007) 168e176 Bewlay BP, Yang Y, Chang YA. Z Metallkd, submitted for publication. Seifert H, Lukas HL, Petzow G. Z Metallkd 1996;87(1):2e13. Bittermann H, Rogl P. J Phase Equilib 1997;18(1):24e47. Redlich O, Kister AT. Indus Eng Chem 1948;40:345. Hillert M, Staffansson LI. Acta Chem Scand 1970;24:3618.
[18] Sundman B, Jansson B, Anderson JO. Calphad 1985;9:153. [19] Pandat 5.0-Phase Diagram Calculation Software for Multicomponent Systems, Computherm LLC, 437S, Yellowstone Dr., Suite 217, Madison, WI 53719; 2005. [20] Scheil E. Z Metallkd 1942;34:70.