A thermodynamic description of the Al–Mo–Si system

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 36 (2012) 100–109

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A thermodynamic description of the Al–Mo–Si system Cuiping Guo a,b , Changrong Li a , Patrick J. Masset b,c , Zhenmin Du a,∗ a

Department of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, PR China

b

Freiberg University of Mining and Technology, Centre for Innovation Competence Virtuhcon, Fuchsmühlenweg 9, D-09596 Freiberg, Germany

c

ATZ Entwicklungszentrum, An der Maxhutte 1, D-92237, Sulzbach-Rosenberg, Germany

article

info

Article history: Received 12 August 2011 Received in revised form 6 December 2011 Accepted 8 December 2011 Available online 2 January 2012 Keywords: Al–Mo–Si system Silicides Thermodynamic properties CALPHAD technique

abstract The thermodynamic reassessment of the Al–Mo–Si system was performed using the CALPHAD technique. The solution phases (liquid, bcc, fcc and diamond) were modeled as a substitutional solution. The compounds AlMo3 in the Al–Mo system and Mo3 Si in the Mo–Si system had the same A15 crystal structure, and were treated as one phase and described by a two-sublattice model (Al, Mo, Si)(Al, Mo)3 . The compound Mo5 Si3 with D8m crystal structure was treated as the formula Mo0.5 (Mo, Si)0.125 (Al, Mo, Si)0.375 in the Al–Mo–Si system. Other compounds, Al63 Mo37 , Al8 Mo3 , Al3 Mo, Al4 Mo, Al17 Mo4 , Al22 Mo5 , Al12 Mo and Al5 Mo in the Al–Mo system, MoSi2 in the Mo–Si system, and ternary compounds C40 and C54 were treated line compounds (Al, Si)m Mon in the Al–Mo–Si system. Based on the published experimental isothermal sections and the liquidus surface projection, the Al–Mo–Si system was re-optimized, and a set of self-consistent thermodynamic parameters was obtained. © 2011 Elsevier Ltd. All rights reserved.

1. Introduction The development of advanced high-temperature structural materials for heat engines poses a great challenge for metallic materials. The compound MoSi2 , with high melting point, excellent oxidation resistance at high temperature, high thermal conductivity and a relatively low density, holds the promise to be enabling materials for a host of important elevated temperature industrial applications [1]. However, its application fields are greatly limited because of its poor low temperature oxidation at around 800 K and low ductility below 1273 K [2] as well as its poor strength and creep resistance above 1573 K [3]. It was also found that the addition of aluminum can make aluminum to substitute silicon and promote the formation of Mo(Al, Si)2 , which resulted in an improvement of the mechanical and oxidation properties of MoSi2 [1,4–9]. Knowledge of thermodynamics and phase diagrams is extremely useful in the field of materials research and process control, especially for the development of the complex alloys. The Al–Mo–Si phase diagram was ever assessed by Costa e Silva [10] and Liu et al. [11]. However, the Al–Mo [12,13] and Al–Mo–Si phase diagrams [5,14,15] were re-determined after the assessment of Costa e Silva [10] and Liu et al. [11], and there were great

∗

Corresponding author. Tel.: +86 10 6233 3772; fax: +86 10 6233 3772. E-mail address: [email protected] (Z. Du).

0364-5916/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.calphad.2011.12.003

differences between the new experimental data and the experiments used in Refs. [10,11]. In the present work, the Al–Mo–Si system was re-optimized using the CALPHAD technique on the basis of the new experimental data [5,14,15]. 2. Literature information 2.1. Al–Si system The Al–Si system was optimized by Dörner et al. [16], Chakraborti and Lukas [17] and Gröbner et al. [18]. Gröbner et al. [18] optimized the Al–Si system on the basis of the latest thermodynamic function of pure elements compiled by Dinsdale [19], and the parameters of from Ref. [18] have been used in the present assessment. Fig. 1 presents the calculated Al–Si phase diagram. 2.2. Al–Mo system The Al–Mo system was optimized by many researchers [20–23]. Du et al. [22] and Cupid et al. [23] optimized the Al–Mo system on the basis of the new experimental data of Schuster and Ipser [12] and Eumann et al. [13]. Good agreement was obtained between the calculated phase diagram [22] and the experimental data [12,13], and the thermodynamic parameters from Ref. [22] have been used in the present calculation. The calculated Al–Mo phase diagram is shown in Fig. 2.

C. Guo et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 36 (2012) 100–109

Fig. 1. Calculated Al–Si phase diagram using the thermodynamic parameters of Ref. [18].

101

Ramberg and Worrell [5] determined the partial phase relationship among Mo5 Si3 , Mo(Al, Si)2 and MoSi2 in the isothermal section at 1873 K, which is consistent with the phase relationship in the Al-poor part reported in Ref. [11]. Arvanitis [14] confirmed that C54 was an equilibrium phase during the investigation of the solidification microstructures and phase selection in the Al–Mo–Si alloys. Recently, Ponweiser et al. [15] reinvestigated phase equilibria at 873 and 1673 K as well as the reaction scheme and the liquidus surface projection using optical microscopy, powder X-ray diffraction (XRD), differential thermal analysis (DTA), electron probe microanalysis (EPMA) and scanning electron microscopy (SEM). Compared to the assessment work of Ref. [11], Ponweiser et al. [15] measured the new isothermal section at 873 K, modified the phase relationship among C40, C54, Al8 Mo3 and liquid in the isothermal section at 1673 K, determined the temperature of invariant reactions in the liquidus surface projection, and constructed the reaction scheme. The enthalpies of transformation of MoSi2 –C11b to C40 at 1110 and 0 K was measured by Frankwicz and Perepezko [34] and calculated by some researchers [35,36] using the first principle calculation, respectively. The enthalpies of formation of the hypothetical compounds MoAl2 –C11b , MoAl2 –C40, Mo5 Al3 –D8m were predicted using Miedema’s model [37]. 3. Thermodynamic model The Gibbs energy functions for the unary phases of elements Al, Mo and Si are taken from the SGTE (Scientific Group Thermodata Europe) database of pure elements compiled by Dinsdale [19] and are listed in Table 1. 3.1. Solution phases In the Al–Mo–Si system, there are four solution phases: liquid, bcc, diamond, and fcc. Their molar Gibbs energies are described by the following expression: φ

φ

φ

Gφm (T ) = xAl GAl (T ) + xMo GMo (T ) + xSi GSi (T )

+ RT (xAl ln xAl + xMo ln xMo + xSi ln xSi ) + E Gφm

(1)

where xAl , xMo and xSi are the mole fractions of the pure elements Al, φ Mo and Si, respectively; E Gm is the excess Gibbs energy, expressed by the Redlich–Kister polynomial, E

Gφm = xAl xMo

j φ LAl,Mo



(xAl − xMo )j

j

+ xMo xSi

Fig. 2. Calculated Al–Mo phase diagram using the thermodynamic parameters of Ref. [22].



j φ LMo,Si

(xMo − xSi )j

j

+ xAl xSi

2.3. Mo–Si system



j φ LAl,Si

φ

(xAl − xSi )j + xAl xMo xSi LAl,Mo,Si

(2)

j

The Mo–Si system was optimized by Costa e Silver [10], Liu et al. [11], Vahlas et al. [24], Kaufman [25] and Geng et al. [26]. Compared with the optimized results of Liu et al. [11], the calculated temperature and phases composition in the invariant reactions in Geng et al. [26] were more consistent with the experimental data of Schlesinger et al. [27]. But the miscibility gap in liquid in Ref. [26] occurs at about 3800 K. 2.4. Al–Mo–Si system Based on the literature [10,28–33] up to the year 2000, the Al–Mo–Si phase diagram was reviewed and optimized by Liu et al. [11]. They assessed four isothermal sections at 1273, 1673, 1823 and 1873 K and predicted liquidus surface projection, in which two ternary compounds C40 and C54 were included.

φ

φ

φ

where j LAl,Mo , j LMo,Si and j LAl,Si are the interaction parameters between elements Al and Mo, Mo and Si, and Al and Si, respectively, φ and are taken from the corresponding binary system. LAl,Mo,Si is the ternary interaction parameter expressed as: φ

φ

φ

φ

LAl,Mo,Si = xAl 0 LAl,Mo,Si + xMo 1 LAl,Mo,Si + xSi 2 LAl,Mo,Si

(3)

j φ

where LAl,Mo,Si = aj + bj T , aj and bj are the parameters to be optimized in this work. 3.2. Intermetallic compounds AlMo3 and Mo3 Si AlMo3 in the Al–Mo system and Mo3 Si in the Mo–Si system have the same A15 crystal structure, and form a complete series of solid solutions in the Al–Mo–Si system [15]. In the present work,

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C. Guo et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 36 (2012) 100–109

Table 1 Thermodynamic parameters in the Al–Mo–Si system.a Phase

liquid

Thermodynamic parameters

Ref.

GHSERAl = 298–700 K −7976.15 + 137.093038T − 24.3671976T ln(T ) − 0.001884662T 2 − 8.77664 × 10−7 T 3 + 74092T −1 700–933 K −11276.24 + 223.048446T − 38.5844296T ln(T ) + 0.018531982T 2 − 5.764227 × 10−6 T 3 + 74092T −1 933–2900 K −11278.378 + 188.684153T − 31.748192T ln(T ) − 1.230524 × 1028 T −9

[19]

GHSERMo = 130–2896 K −7746.302 + 131.9197T − 23.56414T ln(T ) − 0.003443396T 2 + 5.66283 × 10−7 T 3 + 65812T −1 − 1.30927 × 10−10 T 4 2896–5000 K −30556.41 + 283.559746T − 42.63829T ln(T ) − 4.849315 × 1033 T −9

[19]

GHSERSi = 298–1687 K −8162.609 + 137.236859T − 22.8317533T ln(T ) − 0.001912904T 2 − 3.552 × 10−9 T 3 + 176667T −1 1687–3600 K −9457.642 + 167.281367T − 27.196T ln(T ) − 4.20369 × 1030 T −9

[19]

Model (Al, Mo, Si)1 G(liquid, Al) = 298–700 K +GHSERAl + 11005.029 − 11.841867T + 7.9337 × 10−20 T 7 700–933 K +GHSERAl + 11005.03 − 11.841867T + 7.9337 × 10−20 T 7 933–2900 K −795.996 + 177.430178T − 31.748192T ln(T ) G(liquid, Mo) = 130–2986 K +34085.045 + 117.224788T − 23.56414T ln(T ) − 0.003443396T 2 + 5.66283 × 10−7 T 3 + 65812T −1 −1.30927 × 10−10 T 4 + 4.24519 × 10−22 T 7 2986–5000 K +3538.963 + 271.6697T − 42.63829T ln(T ) G(liquid, Si) = 298–1687 K +42533.751 + 107.13742T − 22.8317533T ln(T ) − .001912904T 2 − 3.552 × 10−9 T 3 + 176667T −1 + 2.09307 × 10−21 T 7 1687–3600 K +40370.523 + 137.722298T − 27.196T ln(T ) 0 liq. LAl,Si = −11340.1 − 1.2339T 1 liq. LAl,Si 2 liq. LAl,Si 0 liq. LMo,Si 1 liq. LMo,Si 2 liq. LMo,Si 3 liq. LMo,Si 0 liq. LAl,Mo 1 liq. LAl,Mo 2 liq. LAl,Mo 0 liq. LAl,Mo,Si 1 liq. LAl,Mo,Si 2 liq. LAl,Mo,Si

= −3530.9 + 1.3599T = +2265.4 = −158013.3 + 12.0000T = +20000.0 − 15.0150T = +39026.3 + 5.1567T = −2461.9 + 5.5087T = −96235.7 + 20.9416T = −4384.1 + 12.3636T = −25091.6 = −133821.6 = +236641.0 = −268078.8

bcc

diamond

fcc

Model (Al, Mo, Si)1 (Va)3 G(bcc, Al : Va; 0) = 298–700 K +2106.85 + 132.280038T − 24.3671976T ln(T ) − 1.884662 × 10−3 T 2 − 0.877664 × 10−6 T 3 + 74092T −1 700–933 K −1193.24 + 218.235446T − 38.5844296T ln(T ) + 18.531982 × 10−3 T 2 − 5.764227 × 10−6 T 3 + 74092T −1 933–2900 K −1195.378 + 183.871153T − 31.748192T ln(T ) − 1230.524 × 1025 T −9 G(bcc, Mo : Va; 0) = +GHSERMo G(bcc, Si : Va; 0) = 298–1687 K +38837.391 + 114.736859T − 22.8317533T ln(T ) − 0.001912904T 2 − 3.552 × 10−9 T 3 + 176667T −1 1687–3600 K +37542.358 + 144.781367T − 27.196T ln(T ) − 4.20369 × 1030 T −9 0 bcc LMo,Si = −103304.7 + 16.0464T 0 bcc LAl,Mo = −75938.8 + 10.8187T 1 bcc. LAl,Mo = −44502.8 + 21.6488T 2 bcc LAl,Mo = −22927.1 0 bcc LAl,Mo,Si = 0 1 bcc LAl,Mo,Si = −150000.0 2 bcc LAl,Mo,Si = 0 Model (Al, Mo, Si)1 G(diamond, Al; 0) = 298–700 K −7976.15 + 167.093038T − 24.3671976T ln(T ) − 0.001884662T 2 − 8.77664 × 10−7 T 3 + 74092T −1 700–933 K −11276.24 + 253.048446T − 38.5844296T ln(T ) + 0.018531982T 2 − 5.764227 × 10−6 T 3 + 74092T −1 933–2900 K −11278.378 + 218.684153T − 31.748192T ln(T ) − 1.230524 × 1028 T −9 G(diamond, Mo; 0) = GHSERMo + 5000.0 G(diamond, Si; 0) = GHSERSi 0 diamond LAl,Si = +113246.2 − 47.5551T Model (Al, Mo, Si)1 (Va)1 G(fcc, Al : Va; 0) = +GHSERAl G(fcc, Mo : Va; 0) = 298–2896 K +7453.698 + 132.5497T − 23.56414T ln(T ) − 0.003443396T 2 + 5.66283 × 10−7 T 3 + 65812T −1 − 1.30927 × 10−10 T 4 2896–5000 K −15356.41 + 284.189746T − 42.63829T ln(T ) − 4.849315 × 1033 T −9

[19]

[19] [19] [18] [18] [18] [26] [26] This work This work [22] [22] [22] This work This work This work

[19]

[19] [19]

[26] [22] [22] [22] This work This work This work

[19]

This work [19] [18]

[19] [19]

C. Guo et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 36 (2012) 100–109

103

Table 1 (continued) Phase

Al12 Mo

Thermodynamic parameters

Ref.

G(fcc, Si : Va; 0) = 298–1687 K +42837.391 + 115.436859T − 22.8317533T ln(T ) − 0.001912904T 2 − 3.552 × 10−9 T 3 + 176667T −1 1687–3600 K +41542.358 + 145.481367T − 27.196T ln(T ) − 4.20369 × 1030 T −9 0 fcc LAl,Si = −3143.8 + 0.3930T 0 fcc LAl,Mo = −85300.0 + 20.4000T 1 fcc LAl,Mo = −10000.0

[19]

Model (Al, Si)12 Mo Al

Mo

GAl12 :Mo = 12GHSERAl + GHSERMo − 146766.8 + 23.1256T Al Mo GSi:12 Mo 0 Al12 Mo LAl,Si:Mo 1 Al12 Mo LAl,Si:Mo

MoSi

= GMo:Si2 + 10GHSERSi + 65000.0 = +313473.3 = −325095.9

Al5 Mo

Al Mo

Al Mo

MoSi

GSi:5Mo = GMo:Si2 + 3GHSERSi + 30000.0 0 Al5 Mo LAl,Si:Mo 1 Al5 Mo LAl,Si:Mo

Al

Mo5

Al Mo5 GSi:22 Mo 0 Al22 Mo5 LAl,Si:Mo

Al

Mo4

Al Mo4 GSi:17 Mo 0 Al17 Mo4 LAl,Si:Mo

= +20077.8 = −18885.4

This work

= 22GHSERAl + 5GHSERMo − 723273.3 + 132.3154T MoSi = 5GMo:Si2 + 12GHSERSi + 135000.0 = +517922.1 = 17GHSERAl + 4GHSERMo − 578455.4 + 107.4145T MoSi = 4GMo:Si2 + 9GHSERSi + 105000.0 = +100000.0

Al Mo

Al Mo

0 Al4 Mo LAl,Si:Mo 1 Al4 Mo LAl,Si:Mo

MoSi

= +301099.8 + 51.4065T = −426674.9

Al Mo

Al Mo

MoSi

GSi:3Mo = GMo:Si2 + GHSERSi + 20000.0 0 Al3 Mo LAl,Si:Mo

= +40000.0

This work

[22] This work This work This work

[22] This work

Model (Al, Si)8 Mo3 Al Mo

Al Mo

MoSi

0 Al8 Mo3 LAl,Si:Mo 1 Al8 Mo3 LAl,Si:Mo

= +41377.6 = +93321.6

GSi:8Mo 3 = 3GMo:Si2 + 2GHSERSi + 55000.0

Al

Mo37

Al

Mo37

GSi:63 Mo

[22] This work This work This work

Model (Al, Si)63 Mo37 GAl63 :Mo

Mo5 Si3

[22] This work

This work

GAl8:Mo 3 = 8GHSERAl + 3GHSERMo − 432556.9 + 99.1737T

A15

This work

Model (Al, Si)3 Mo GAl3:Mo = 3GHSERAl + GHSERMo − 143196.7 + 30.6912T

Al63 Mo37

[22] This work

Model (Al, Si)4 Mo GSi:4Mo = GMo:Si2 + 2GHSERSi + 25000.0

Al8 Mo3

[22] This work This work

GAl4:Mo = 4GHSERAl + GHSERMo − 138851.8 + 23.1120T

Al3 Mo

This work

Model (Al, Si)17 Mo4 GAl17 :Mo

Al4 Mo

This work

Model (Al, Si)22 Mo5 GAl22 :Mo

Al17 Mo4

[22] This work

Model (Al, Si)5 Mo GAl5:Mo = 5GHSERAl + GHSERMo − 144819.3 + 25.4357T

Al22 Mo5

[18] [22] [22]

[22]

= 63GHSERAl + 37GHSERMo − 1638310.2 − 403.7604T = 63GHSERSi + 37GHSERMo + 500000.0

Model (Al, Mo, Si)(Al, Mo)3 GAl5 Al:Al = 4GHSERAl + 20000.0 GAl5 Mo:Al = GHSERMo + 3GHSERAl + 135830.9 − 2.0081T GAl5 Al:Mo = GHSERAl + 3GHSERMo − 95830.9 + 2.0081T GAl5 Mo:Mo = 4GHSERMo + 20000.0 GAl5 Si:Al = GHSERSi + 3GHSERAl + 20000.0 GAl5 Si:Mo = GHSERSi + 3GHSERMo − 117023.4 − 5.2030T 0 Al5 LAl,Mo:Al = 0 LAl5 Al,Mo:Mo = +11628.1 0 Al5 LAl:Al,Mo = 0 LAl5 Mo:Al,Mo = +52100.0 0 Al5 LMo,Si:Mo = +200000.0 0 Al5 LAl,Si:Mo = −60000.0 + 27.0000T

This work This work

[22] [22] [22] [22] This work [26] [22] [22] This work This work

Model Mo0.5 (Mo, Si)0.125 (Al, Mo, Si)0.375 Mo Si

GMo5:Mo3:Al = Mo Si

31 Al5 G 21 Al:Mo

+

4 Al8 Mo3 G 21 Al:Mo

+ 5000.0

GMo5:Si:3Al = 0.375GHSERAl + 0.5GHSERMo + 0.125GHSERSi + 10000.0 Mo Si

GMo5:Mo3:Mo = GHSERMo + 25434.5 + 0.5439T Mo Si

GMo5:Si:3Mo = 0.875GHSERMo + 0.125GHSERSi + 17425.8 + 1.0128T Mo Si

GMo5:Mo3:Si = 0.625GHSERMo + 0.375GHSERSi − 38980.0 − 3.5536T Mo Si

GMo5:Si:3Si = 0.5GHSERMo + 0.5GHSERSi − 25000.0 + 2.0000T 0 Mo5 Si3 LMo:Mo,Si:Al 0 Mo5 Si3 LMo:Mo:Mo,Si

Mo Si

Mo Si

= 0 LMo5:Mo3,Si:Mo = 0 LMo5:Mo3,Si:Si = −14000.0 − 11.0000T Mo Si = 0 LMo5:Si:3Mo,Si = −29000.0 + 13.1599T

This work This work [26] [26] [26] [26] [26] [26] (continued on next page)

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C. Guo et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 36 (2012) 100–109

Table 1 (continued) Phase

Thermodynamic parameters 0 Mo5 Si3 LMo:Mo:Al,Si 1 Mo5 Si3 LMo:Mo:Al,Si

= =

0 Mo5 Si3 LMo:Si:Al,Si 1 Mo5 Si3 LMo:Si:Al,Si

Ref.

= −5000.0 = +6000.0

This work This work

Model (Al, Si)2 Mo

MoSi2

MoSi

GSi:Mo2 = 2GHSERSi + GHSERMo − 114762.8 − 12.8821T

MoSi GAl:Mo2 0 MoSi2 LAl,Si:Mo 1 MoSi2 LAl,Si:Mo

=

This work

5 Al8 Mo3 G 21 Al:Mo

2 Al5 + 21 GAl:Mo + 52118.2 = −50000.0 = +100000.0

This work This work This work

Model (Al, Si)2 Mo

C40

MoSi

2 GC40 Si:Mo = GSi:Mo + 3300.0 5 Al8 Mo3 2 Al5 GC40 Al:Mo = 21 GAl:Mo + 21 GAl:Mo + 45583.5 0 C40 LAl,Si:Mo = −188552.1 + 22.1039T 1 C40 LAl,Si:Mo = +5754.8 + 26.1722T

This work This work This work This work

Model (Al, Si)2 Mo

C54

MoSi

2 GC54 Si:Mo = GSi:Mo + 2500.0

This work

Al Mo

5 2 Al5 8 3 GC54 Al:Mo = 21 GAl:Mo + 21 GAl:Mo + 15335.2 0 C54 LAl,Si:Mo = −101026.3 + 7.4496T 1 C54 LAl,Si:Mo = +70467.2 − 19.6436T a

This work This work This work

In J mol−1 of the formula units.

these two phases were treated as one phase and described by a two-sublattice model [38,39]A15-(Al%, Mo, Si%) (Al, Mo%)3 with Al, Mo and Si in the first sublattice and Al and Mo in the second one, where % indicates the major constituent on each sublattice, on basis of the models of binary compounds AlMo3 and Mo3 Si. The Gibbs energy per mole of formula unit A15 is expressed as follows: GAl5 m

=

′

′′

yAl yAl GAl5 Al:Al

+

′

′′

yAl yMo GAl5 Al:Mo

+

′

′′

yMo yAl GAl5 Mo:Al

′ ′′ Al5 ′ ′′ Al5 + y′Mo y′′Mo GAl5 Mo:Mo + ySi yAl GSi:Al + ySi yMo GSi:Mo

+ RT (y′Al ln y′Al + y′Mo ln y′Mo + y′Si ln y′Si ) + 3RT (y′′Al ln y′′Al + y′′Mo ln y′′Mo )  j Al5 + y′Al y′′Al y′′Mo LAl:Al,Mo (y′′Al − y′′Mo )j  j Al5 + y′Mo y′′Al y′′Mo LMo:Al,Mo (y′′Al − y′′Mo )j  j Al5 + y′Si y′′Al y′′Mo LSi:Al,Mo (y′′Al − y′′Mo )j   ′′ j Al5 + yAl y′Al y′Mo LAl,Mo:Al (y′Al − y′Mo )j + y′Mo y′Si + y′Al y′Si





j Al5 LMo,Si:Al

j Al5 LAl,Si:Al

+ y′Al y′Si





j Al5 LMo,Si:Mo

j Al5 LAl,Si:Mo

Considering the influence of vacancy defects or the substitution of anti-bond atoms, the compound Mo5 Si3 is described as Mo0.5 (Mo%, Si)0.125 (Mo, Si%)0.375 in the binary Mo–Si system [26]. As shown in literature [15], the solubility of Al in Mo5 Si3 is about 13 at.% Al, while the Mo content in Mo5 Si3 remains a constant with increasing Al content. Accordingly, the compound Mo5 Si3 in the Al–Mo–Si system is treated as the formula Mo0.5 (Mo%, Si)0.125 (Al, Mo, Si%)0.375 . The Gibbs energy per mole of formula unit Mo5 Si3 is expressed as follows:

Mo Si

Mo Si

Mo Si

Mo Si

′′ ′′′ 5 3 5 3 + y′′Mo y′′′ Si GMo:Mo:Si + ySi yAl GMo:Si:Al ′′ ′′′ 5 3 5 3 + y′′Si y′′′ Mo GMo:Si:Mo + ySi ySi GMo:Si:Si

+ 0.125RT (y′′Mo ln y′′Mo + y′′Si ln y′′Si )



  j Al5 + y′′Mo y′Al y′Mo LAl,Mo:Mo (y′Al − y′Mo )j + y′Mo y′Si

3.3. Intermetallic compounds Mo5 Si3

Mo5 Si3 ′′ ′′′ Mo5 Si3 5 Si3 GMo = y′′Mo y′′′ m Al GMo:Mo:Al + yMo yMo GMo:Mo:Mo

(y′Mo − y′Si )j

(y′Al − y′Si )j + y′Al y′Mo y′Si LAl5 Al,Mo,Si:Al

parameters between the elements Al and Mo, Mo and Si, and Al and Si in the first sublattice and Al and Mo in the second one, respectively.

(y′Mo − y′Si )j

 (y′Al − y′Si )j + y′Al y′Mo y′Si LAl5 (4) Al,Mo,Si:Mo

where y′∗ and y′′∗ are the site fractions of Al, Mo and Si in the first and Al and Mo in the second sublattices, respectively; GAl5 ∗:∗ represents the Gibbs energies of the compound AlMo3 when the first and second sublattices are occupied by only one element, which are related to the enthalpies of pure structures of elements, fcc for Al, bcc for Mo and diamond for Si in their SER state; j Al5 j Al5 j Al5 LAl,Mo:∗ , j LAl5 Mo,Si:∗ , LAl,Si:∗ and L∗:Al,Mo represent the jth interaction

′′′ ′′′ ′′′ ′′′ ′′′ + 0.375RT (y′′′ Al ln yAl + yMo ln yMo + ySi ln ySi )   Mo Si ′′′ j ′′′ j + y′′Mo y′′′ LMo5:Mo3:Al,Mo (y′′′ Al yMo Al − yMo )  Mo Si ′′′ j ′′′ j + y′′′ LMo5:Mo3:Mo,Si (y′′′ Mo ySi Mo − ySi )   Mo Si ′′′ j ′′′ j + y′′′ LMo:5Mo3:Al,Si (y′′′ Al ySi Al − ySi )   Mo Si ′′′ j ′′′ j + y′′Si y′′′ LMo:5Si:3Al,Mo (y′′′ Al yMo Al − yMo )  Mo Si ′′′ j ′′′ j + y′′′ LMo:5Si:3Mo,Si (y′′′ Mo ySi Mo − ySi )   Mo Si ′′′ j ′′′ j + y′′′ LMo:5Si:3Al,Si (y′′′ Al ySi Al − ySi )  Mo Si ′′ ′′ j + y′′′ LMo5:Mo3,Si:Al (y′′Mo − y′′Si )j Al yMo ySi  Mo Si ′′ ′′ j + y′′′ LMo5:Mo3,Si:Mo (y′′Mo − y′′Si )j Mo yMo ySi  Mo Si ′′ ′′ j + y′′′ LMo:5Mo3,Si:Si (y′′Mo − y′′Si )j . Si yMo ySi

(5)

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105

Table 2 Invariant reactions related to liquid in the Al–Mo–Si system. Reaction

Present work

liq. + C40 + MoSi2 liq. + C40 + Mo5 Si3 liq. + C40 → Mo5 Si3 + MoSi2 liq. + Mo5 Si3 + C40 → C54 liq. + A15 → AlMo + Mo5 Si3 liq. + Al63 Mo37 → Al8 Mo3 + AlMo liq. + AlMo → Al8 Mo3 + Mo5 Si3 liq. + Mo5 Si3 → Al8 Mo3 + C54 liq. + C54 → Al8 Mo3 + C40 liq. + MoSi2 → diamond + C40 liq. + Al8 Mo3 + C40 → Al4 Mo liq. + Al8 Mo3 → Al4 Mo + Al3 Mo liq. + Al4 Mo + Al17 Mo4 → Al5 Mo liq. + Al17 Mo4 → Al22 Mo5 + Al5 Mo liq. + Al4 Mo → C40 + Al5 Mo liq. + Al5 Mo + C40 → Al12 Mo liq. + Al12 Mo → fcc + C40 liq. → diamond + fcc + C40

Ref. [15]

Type

T (K)

x(Al)

x(Mo)

x(Si)

T (K)

C1 C2 U1 P1 U2 U3 U4 U5 U6 U7 P2 U8 P3 U9 U10 P4 U11 E1

2271 2196 2174 1902 1829 1780 1771 1771 1676 1638 1491 1481 1151 1149 1097 991 899 850

0.0401 0.0805 0.0129 0.5190 0.5815 0.6253 0.6107 0.6112 0.7911 0.0946 0.8834 0.9190 0.9837 0.9851 0.9680 0.9734 0.9440 0.8789

0.3370 0.4331 0.4438 0.3353 0.3662 0.3395 0.3411 0.3391 0.1484 0.0463 0.0758 0.0650 0.0110 0.0107 0.0082 0.0026 0.0004 0.0002

0.6229 0.4864 0.5433 0.1457 0.0523 0.0352 0.0482 0.0497 0.0605 0.8591 0.0408 0.0160 0.0053 0.0042 0.0238 0.0240 0.0556 0.1209

2173∼2273 >2190 2190 1892 – – 1780 1780 1491∼1780 <1673 1491 – 1097∼1104 1104∼1119 1097 991 905 847

3.4. Other intermetallic compounds Other compounds Al63 Mo37 , Al8 Mo3 , Al3 Mo, Al4 Mo, Al17 Mo4 , Al22 Mo5 , Al12 Mo and Al5 Mo in the Al–Mo system, MoSi2 in the Mo–Si system, and ternary compounds C40 and C54 were treated as line compounds and were modeled using a two-sublattice model [38,39](Al, Si)m Mon in the Al–Mo–Si ternary system. The Gibbs energy per mole of formula is expressed as follows: φ

φ

Gφm = yAl GAl:Mo + ySi GSi:Mo + mRT (yAl ln yAl + ySi ln ySi )

+ yAl ySi



j φ LAl,Si:Mo

(yAl − ySi )j .

(6)

j

4. Assessment procedure The thermodynamic parameters for the Al–Mo–Si system were optimized on the basis of the experimental information available [5,14,15,29–33]. During the process of optimization, the experimental data from Refs. [14,15] was given a larger weight. A general rule for selection of the adjustable parameters is that only coefficients determined by the experimental values should be adjusted [40]. The optimization was carried out by means of the optimization module PARROT of the thermodynamic software Thermo-Calc [41], which can handle various kinds of experimental data. The thermodynamic parameters of the Al–Si system [18] and of the Al–Mo system [22] were adopted in the present work, and the calculated Al–Si and Al–Mo phase diagrams are shown in Figs. 1 and 2. liq. For the Mo–Si system, the thermodynamic parameters 2 LMo,Si liq.

MoSi

and 3 LMo,Si in liquid and GSi:Mo2 in MoSi2 were revised in order to avoid the artificial miscibility gap of liquid below 6000 K. And the calculated Mo–Si phase diagram was presented in Fig. 3. The thermodynamic descriptions of liquid, bcc, diamond and fcc in the Al–Mo–Si system were obtained by combining the corresponding Gibbs energy functions from the assessments of binary systems using Muggianu interpolation for excess terms [42]. liq. liq. In the present assessment, the coefficients 0 LAl,Mo,Si , 1 LAl,Mo,Si and 2 liq. LAl,Mo,Si

were optimized on the basis of the phase relationship related to liquid at 1673 K and the liquidus surface projection determined by Ponweiser et al. [15]. The coefficient 1 Lbcc Al,Mo,Si was optimized according to the primary crystallization surface of bcc measured by Arvanitis [14] and Ponweiser et al. [15]. For all compounds, the thermodynamic parameters were optimized according to the experimental data [5,14,15,29–33]. Taking C40 as an example, the assessment procedure will be

Fig. 3. Calculated Mo–Si phase diagram using the thermodynamic parameters optimized by Geng et al. [26] and the modified parameters of liquid and MoSi2 in the present work and comparison with the calculated results [11,26].

introduced. In Eq. (6), the parameters to be optimized are GC40 Si:Mo , C40 C40 j C40 GC40 and L . The parameters G and G in Eq. (6) are Al:Mo Al,Si:Mo Si:Mo Al:Mo described as MoSi

2 GC40 Si:Mo = GSi:Mo + a 5 Al8 Mo3 2 AlMo3 GC40 GAl:Mo + G + b. Al:Mo = 21 21 Al:Mo

(7) (8)

In order to make C40 unstable in the Mo–Si system and the Al–Mo system, the value of ‘‘a’’ and ‘‘b’’ must be positive. GC40 Si:Mo , j C40 GC40 Al:Mo and LAl,Si:Mo are optimized in the present work according to the experimental data of Arvanitis [14] and Ponweiser et al. [15]. 5. Results and calculations The thermodynamic parameters of the Al–Mo–Si system obtained in the present work are shown in Table 1. The predicted invariant equilibria related to the liquid phase in the Al–Mo–Si system are listed in Table 2. As shown in Table 2, the main differences are the invariant reaction temperatures in the invariant

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Fig. 4. Calculated isothermal section of the Al–Mo–Si system at 873 K using the present thermodynamic description in comparison with the experimental data from Ref. [15]. The reversed triangle represents the sample annealed at 823 K, which consists of fcc, C40 and diamond.

Fig. 5. Calculated isothermal section of the Al–Mo–Si system at 1273 K using the present thermodynamic description in comparison with the experimental data from Ref. [10].

reactions P3 , liq. + Al4 Mo + Al17 Mo4 → Al5 Mo at 1150 K and U9 , liq. + Al17 Mo4 → Al22 Mo5 + Al5 Mo at 1148 K. In the Table 4 of Ref. [15], the above invariant reactions were recommended as liq.+ Al17 Mo4 → Al5 Mo + Al4 Mo and liq.+ Al22 Mo5 → Al17 Mo4 + Al5 Mo at 1097 ∼ 1104 and 1104 ∼ 1119 K, respectively. However, as shown in Fig. 7 in Ref. [15], these two invariant reactions were not determined experimentally. The calculated temperatures in the invariant reactions U1 , U5 , U6 , U7 , U10 , U11 , P1 , P2 , P4 , E1 , C1 and C2 are in good agreement with the experiments [15]. Table 3 summarizes the calculated enthalpies of formation of hypothetical compounds using the present thermodynamic parameters. The results are compared with the Miedema’s estimations [37] and the calculated values of Liu et al. [11]. The enthalpies of formation of MoAl2 –C11b , MoAl2 –C40 and Mo5 Al3 –D8m [15] are well reproduced in the present work. The calculated enthalpy of transformation of MoSi2 –C11b to C40, the experimental data at 1100 K [34] and the calculated value using the first principle [35,36] at 0 K are listed in Table 4. As shown in Table 4, the calculated value in this work agrees well with the results of Refs. [34–36].

Fig. 6. Calculated isothermal section of the Al–Mo–Si system at 1673 K using the present thermodynamic description in comparison with the experimental data from Refs. [14,15].

Fig. 7. Calculated isothermal section of the Al–Mo–Si system at 1823 K using the present thermodynamic description in comparison with the experimental data from Ref. [31].

Figs. 4–8, are calculated isothermal sections of the Al–Mo–Si system at 873, 1273, 1673, 1823 and 1873 K, respectively. The calculated phase diagrams well reproduce the experimental phase relationship, and satisfactory agreement was obtained between the calculated phase diagrams and the experimental data [5,14,15,29–33]. In Fig. 4, the reversed triangle represents the sample which was annealed at 823 K [15]. After annealing at 823 K, the sample consisted of three phases, fcc, C40 and diamond. The reason why the sample was annealed at 823 K is to avoid the equilibrium with liquid, which will occur at 873 K. Compared with the experimental isothermal section at 1673 K [15], there is an extra three-phase region liquid + MoSi2 + diamond in Fig. 6, which is reasonable according to the Mo–Si phase diagram. Fig. 9a represents the calculated projection of the liquidus surfaces of the Al–Mo–Si system using the present thermodynamic description. Figs. 9b and 9c are an enlarged section of Fig. 9a. The liquidus valleys separate the different fields of primary crystallization and are indicated by solid lines; arrows are directing towards the lower temperature. Compared with the experimental

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107

Table 3 Calculated enthalpies of formation hypothetical compounds. Hypothetical compounds

MoAl2 –C11b MoAl2 –C40 Mo5 Al3 –D8m

Enthalpy of formation, kJ/mol of atoms This work

Miedemia’s estimations [37]

Calculated value in Ref. [11]

−20.0 −22.2 −23.0

−20 −20 −22

−19 −21 −7.3

Table 4 Transformation enthalpy of MoSi2 –C11b to C40. Transformation enthalpy, kJ/mol of atoms This work

Experimental data at 1100 K, [34]

Calculation by first principle at 0 K, [35,36]

−1.1

−0.9

< −1.9

Fig. 8. Calculated isothermal section of the Al–Mo–Si system at 1873 K using the present thermodynamic description in comparison with the experimental data from Refs. [5,14].

Fig. 9b. Enlarged section of Fig. 9a.

Fig. 9c. Enlarged section of Fig. 9a. Fig. 9a. Predicted liquidus surfaces of the Al–Mo–Si system using the present thermodynamic description and comparison with the experimental data [14,15].

data [14,15], the primary crystallization surfaces of most phases were well reproduced in the present work. The reaction scheme related to liquid is shown in Fig. 10. Compared with the reaction scheme constructed by Ponweiser et al. [15], the main difference is the reaction scheme related

to the invariant reactions P3 and U9 mentioned before. Further experimental work is needed in order to determine the reactions. 6. Conclusions The phase relations and thermodynamic properties in the Al–Mo–Si system were critically optimized on the basis of the

108

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Fig. 10. Calculated reaction scheme related to liquid in the Al–Mo–Si system.

experimental information available in the literature. A set of self-consistent thermodynamic parameters describing the Gibbs energy of individual phases in the Al–Mo–Si system as a function

of composition and temperature was obtained. With the present optimized parameters, one can make various thermodynamic calculations of practical interest.

C. Guo et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 36 (2012) 100–109

Acknowledgments This work was supported by National Natural Science Foundation of China (NSFC) (Grant Nos. 50971027, 50934011) and the National Doctorate Fund of the State Education Ministry of China (No. 20090006120029).

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