Thermodynamic assessments of the V–Ge and V–Pt systems

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Intermetallics 16 (2008) 544e549 www.elsevier.com/locate/intermet

Thermodynamic assessments of the VeGe and VePt systems C.P. Wang, A.Q. Zheng, X.J. Liu* Department of Materials Science and Engineering, College of Materials, and Research Center of Materials Design and Applications, Xiamen University, Xiamen 361005, PR China Received 2 November 2007; received in revised form 8 December 2007; accepted 14 January 2008 Available online 6 March 2008

Abstract The VeGe and VePt binary systems have been thermodynamically assessed by using the CALPHAD (Calculation of Phase Diagrams) approach on the basis of the experimental data including the thermodynamic properties and phase equilibria. Gibbs free energies of the solution phases (liquid, fcc, bcc and diamond) were modeled by the subregular solution model with the RedlicheKister formula, and those of the intermetallic compounds (V3Ge, V5Ge3, V11Ge8, V17Ge31, PtV3, PtV, Pt2V and Pt3V) in these two binary systems were described by the sublattice model. A proper set of thermodynamic parameters has been derived for describing the Gibbs free energies of each phase in the VeGe and VePt systems. An agreement between the calculated results and experimental data is obtained. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: A. Intermetallics, miscellaneous; B. Thermodynamic and thermochemical properties; E. Phase diagram, prediction

1. Introduction In recent years CoeV based alloys are considered to be important potential materials in applications of high density recording media [1], because there exists the phase separation consisting of the ferromagnetic phase (fccferro or hcpferro) and paramagnetic phase (fccpara or hcppara) induced by magnetic transformation in the Co-rich corner [2e4], which is similar to the phase separation in the CoeCr system [5]. In order to develop the CoeV based alloys for application of new magnetic materials, the additions of other alloy elements are necessary to improve the properties of magnetic recording media materials [6]. The CALPHAD method is an important tool for designing new CoeV based alloys because it can significantly decrease cost and time during development of materials and provide a clear guideline for material design [7]. As a result, it is of great essence to establish the thermodynamic database for the CoeV based alloys containing alloying elements. Because additions of Ge and Pt to the CoeV alloy may significantly

affect the characteristic of the phase separation, the thermodynamic assessments of the CoeVeGe and CoeVePt ternary systems are important. In the present study, as a part of assessment in the two ternary systems, the thermodynamic calculations of the VeGe and VePt systems are carried out by means of the CALPHAD method based on the available experimental data. 2. Thermodynamic models The information about stable solid phases and the used models in the VeGe and VePt systems is listed in Table 1. 2.1. Solution phases In the VeGe and VePt binary systems, Gibbs free energies of the liquid, fcc, bcc and diamond phases are described by the subregular solution model, as follows: X X 0 f Gfm ¼ Gi xi þ RT xi ln xi þ DE Gfm ; ð1Þ i¼Me;V

* Corresponding author. Tel.: þ86 592 2187888. E-mail address: [email protected] (X.J. Liu). 0966-9795/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.intermet.2008.01.002

i¼Me;V

where 0 Gfi is the Gibbs free energy of the pure component i in the respective reference state with the f phase, which is taken

C.P. Wang et al. / Intermetallics 16 (2008) 544e549 Table 1 The stable solid phases and the used models in the VeGe and VePt systems System Phase

Strukturbericht Prototype designation

Modeling phase

Used models

VeGe

(V) V3Ge V5Ge3 V5Ge3a V11Ge8 V17Ge31 (Ge)

A2 A15 D8m D88 e e A4

bcc (V)0.75(Ge)0.25 (V)0.625(Ge)0.375 (V)0.625(Ge)0.375 (V)0.579(Ge)0.421 (V)0.354(Ge)0.646 Diamond

SSM SM SM SM SM SM SSM

(V) PtV3 PtV Pt2V Pt3V (Pt)

A2 A15 B19 e D022 A1

bcc (Pt,V)0.25(Pt,V)0.75 (Pt,V)0.5(Pt,V)0.5 (Pt,V)0.667(Pt,V)0.333 (Pt,V)0.75(Pt,V)0.25 fcc

SSM SM SM SM SM SSM

VePt

W Cr3Si W5Si3 Mn5Si3 Cr11Ge8 e C (diamond) W Cr3Si AuCd MoPt2 Al3Ti Cu

Note: SSM e subregular solution model; SM e sublattice model. a Stabilized by interstitial impurities.

from the SGTE pure element database [8]; Me means the element Ge or Pt; xi denotes the molar fraction of the component i; R is the gas constant; T is the absolute temperature; and DE Gfm is the excess Gibbs free energy, which is expressed by the RedlicheKister polynomial [9] as: DE Gfm ¼ xMe xV

n X

i f LMe;V ðxMe

 xV Þi ;

545

two-sublattice model (Pt,V)p (Pt,V)q. The molar Gibbs free energies are given by the following equations: Gfm ¼ yIPt yIIPt 0 GfPt:Pt þ yIPt yIIV 0 GfPt:V þ yIV yIIPt 0 GfV:Pt þ yIV yIIV 0 GfV:V     þ pRT yIPt ln yIPt þ yIV ln yIV þ qRT yIIPt ln yIIPt þ yIIV ln yIIV " X f X f  n n n þ yIPt yIV yIIPt LPt;V:Pt yIPt  yIV þyIIV LPt;V:V n¼0



yIPt  yIV

n

n¼0

#

" þ yIIPt yIIV yIPt

X

n f LPt:Pt;V



yIIPt  yIIV

n

n¼0

þyIV

X

n f LV:Pt;V



yIIPt

n  yIIV

# ð5Þ

;

n¼0

where 0 GfPt:Pt , 0 GfPt:V , 0 GfV:Pt and 0 GfV:V correspond to the Gibbs free energies of pure Pt, PtpVq, PtqVp and pure V in the f phase, respectively; yIi and yIIi are the site fractions of f element i (i ¼ Pt, V) in sublattice I and II; Lf i,j:k and Lk:i,j are the iej interaction parameters in the sublattices I and II when the sublattices II and I are occupied by component k, respectively. 3. Experimental information

ð2Þ

3.1. The VeGe system

ð3Þ

The VeGe system consisted of two solution phases (bcc and diamond) and four intermediate phases (V3Ge, V5Ge3, V11Ge8, V17Ge31). The phase diagram in the VeGe system was originally proposed by Svechnikov et al. [10] and Savitskii et al. [11]. The intermediate phases were investigated by several researchers [12e16], however, different conclusions for the congruent melting of the V3Ge compound were

i¼0

where i LfMe;V is the binary interaction parameter, the coefficients of a and b are evaluated on the basis of available experimental data.

2100

2.2. Stoichiometric intermetallic compounds

0 SER 0 0 0 D0 Gff ¼ 0 Gfm  s0 GSER V  t GGe ¼ a þ b T þ c T ln T;

ð4Þ

where D0 Gff represents the Gibbs free energy of formation of the stoichiometric phase referred to the standard element reference (SER) state of the component elements; the parameters a0 , b0 , and c0 are optimized in the present work.

1900

1920°C L

~4.5 1760°C

1700

Temperature, °C

The intermetallic compounds V3Ge, V5Ge3, V11Ge8 and V17Ge31 in the VeGe binary system are treated as stoichiometric phases. The Gibbs free energy per mole of formula unit (V)s (Ge)t can be written as:

1965±35°C 1910°C

1500 1300

(V)

1100 960°C 900

930°C

700

V17Ge31

¼ a þ bT;

V3Ge

i f LMe;V

V5Ge3 V11Ge8

with

938.3°C ~98

(Ge)

500

2.3. Intermediate phases with solubility 300

In the VePt binary system, the solubility of the four intermediate compounds (PtV3, PtV, Pt2V and Pt3V) is considered and their Gibbs free energies are modeled by the

V

20

40

60

80

Ge

Ge, at. % Fig. 1. The phase diagram of the VeGe system reviewed by Smith [19].

C.P. Wang et al. / Intermetallics 16 (2008) 544e549

546 2100 1910°C

1900

L

~34 ~37

1769.0°C

~43

(V) PtV3 1500

~1500°C ~45 ~48

~33 1300

~1410°C

1100

PtV

(Pt)

~1100°C~71.5 ~1015°C

~980°C 51.5 65.5 61 ~68 Pt2V

900

~74 Pt3V

Temperature,°C

1700

~1805°C ~73

~1720°C

~1800°C ~12 ~18

Standard enthalpies of formation of the four intermediate phases in the VeGe system were calculated by Smith [19] based on the EMF (Electromotive Force) data reported by Eremenko et al. [20,21], and the entropies of formation at 298 K were also evaluated by Smith [19]. Kleppa and Jung [22] reported an experimental data for the standard enthalpy of formation of the V5Ge3 compound by high-temperature calorimetry, and estimated the standard enthalpies of formation for the other three phases (V3Ge, V11Ge8 and V17Ge31) from the value of the V5Ge3 compound. More recently, Zarembo et al. [23] studied the vaporization thermodynamics in the V-rich portion by means of KEMS (Knudsen Effusion Mass Spectrometry) and derived the standard enthalpies of formation of all the four intermediate compounds in the VeGe system.

~970°C

700 V

20

40

60

80

Pt

Pt, at. % Fig. 2. The phase diagram of the VePt system reviewed by Smith [26].

Table 3 Optimized thermodynamic parameters of the VePt system Parameters in each phase (J/mol) Liquid phase: (Pt,V) 0 Liq LPt;V ¼ 70; 800  19:78T 1 Liq LPt;V ¼ 90; 700 þ 16:54T

obtained due to the different experiments, as follows: Svechnikov et al. [10]: 1910  C; Savitskii et al. [11]: 1590  C; Zagryazhskii and Kuz’menko [17]: 1900e2000  C; and Waterstrat [18]: 1920  10  C. Savitskii et al. [11] presented the peritectic reaction (L þ V5Ge3 4 V11Ge8) at 1575  10  C, this reaction temperature is lower than the corresponding temperature reported by Svechnikov et al. [10]. Based on the above experimental information, Smith [19] reviewed the phase diagram of the VeGe system, with slight changes in compositions and temperatures, as shown in Fig. 1, in which the liquidus temperatures with dashed line are still tentative. Table 2 Optimized thermodynamic parameters of the VeGe system Parameters in each phase (J/mol) Liquid phase: (Ge,V) 0 Liq LGe;V ¼ 125; 377 þ 19:223T 1 Liq LGe;V ¼ þ101; 606  35:95T 2 Liq LGe;V ¼ þ51; 100  15:645T 3 Liq LGe;V ¼ 65; 500 þ 18:52T bcc phase: (Ge,V) 0 bcc LGe;V ¼ 92; 064 þ 18:982T 1 bcc LGe;V ¼ þ62; 000  18T Diamond phase: (Ge,V) 0 Diam LGe;V ¼ 10; 000 V3Ge compound: (V)0.75(Ge)0.25 0 Diam GVf 3 Ge  0:750 Gbcc ¼ 35; 591 þ 12:14T  1:493T ln T V  0:25 GGe

0

V5Ge3 compound: (V)0.625(Ge)0.375 0 Diam GVf 5 Ge3  0:6250 Gbcc ¼ 45; 952 þ 23:7T  2:99T ln T V  0:375 GGe

0

V11Ge8 compound: (V)0.579(Ge)0.421 0 V11 Ge8 0 Diam Gf  0:5790 Gbcc ¼ 46; 511 þ 1:755T V  0:421 GGe V17Ge31 compound: (V)0.354(Ge)0.646 0 V17 Ge31 0 Diam Gf  0:3540 Gbcc ¼ 32; 407 þ 3:946T V  0:646 GGe

fcc phase: (Pt,V) ¼ 13; 186 þ 1:08T ¼ 48; 733  0:838T

0 fcc LPt;V 1 fcc LPt;V

bcc phase: (Pt,V) ¼ 69; 500  4:6T ¼ þ20; 000  9:8T ¼ þ8000  2:5T

0 bcc LPt;V 1 bcc LPt;V 2 bcc LPt;V

PtV3 phase: (Pt,V)0.25(Pt,V)0.75 0 PtV3 GPt:Pt  0 Gfcc Pt ¼ þ2030 0 PtV3 0 bcc GV:Pt  0:750 Gfcc Pt  0:25 GV ¼ þ11; 500 þ 1:19T 0 PtV3 0 bcc GPt:V  0:250 Gfcc  0:75 GV ¼ 20; 500  1:19T Pt 0 PtV3 GV:V  0 Gbcc V ¼ þ2525 0 PtV3 LPt:Pt;V ¼ 51; 000  1:091T 0 PtV3 0 PtV3 3 LV:Pt;V ¼ 0 LPtV Pt;V:Pt ¼ LPt;V:V ¼ 0 PtV phase: (Pt,V)0.5(Pt,V)0.5 0 PtV GPt:Pt  0 Gfcc Pt ¼ þ1500 0 PtV 0 bcc GV:Pt  0:50 Gfcc Pt  0:5 GV ¼ 36; 550  0:458T 0 PtV 0 bcc GPt:V  0:50 Gfcc  0:5 GV ¼ þ36; 550 þ 0:458T Pt 0 PtV 0 bcc GV:V  GV ¼ þ3000 0 PtV LV:Pt;V ¼ þ9700 0 PtV 0 PtV LPt:Pt;V ¼ 0 LPtV Pt;V:Pt ¼ LPt;V:V ¼ 0 Pt2V phase: (Pt,V)0.667(Pt,V)0.333 0 Pt2 V GPt:Pt  0 Gfcc Pt ¼ þ500 0 Pt2 V 0 bcc GV:Pt  0:3330 Gfcc Pt  0:667 GV ¼ þ38; 100  0:73T 0 Pt2 V 0 bcc GPt:V  0:6670 Gfcc Pt  0:333 GV ¼ 37; 605 þ 0:73T 0 Pt2 V GV:V  0 Gbcc ¼ 0 V 0 Pt2 V LPt:Pt;V ¼ þ2000  10T Pt V 0 0 Pt2 V 2 2V LV:Pt;V ¼ 0 LPt Pt;V:Pt ¼ LPt;V:V ¼ 0 Pt3V phase: (Pt,V)0.75(Pt,V)0.25 0 Pt3 V GPt:Pt  0 Gfcc Pt ¼ þ10; 500  0:5T 0 Pt3 V 0 bcc GV:Pt  0:250 Gfcc Pt  0:75 GV ¼ þ21; 730 þ 1:443T 0 Pt3 V 0 bcc GPt:V  0:750 Gfcc  0:25 GV ¼ 30; 785  1:443T Pt 0 Pt3 V GV:V  0 Gbcc ¼ þ15; 000 V 0 Pt3 V LPt:Pt;V ¼ 20; 800 þ 2:687T 0 Pt3 V LPt;V:V ¼ 74; 800 þ 19:609T 1 Pt3 V LPt;V:V ¼ 30; 800 þ 24:934T 0 Pt3 V 3V LV:Pt;V ¼ 0 LPt Pt;V:Pt ¼ 0

C.P. Wang et al. / Intermetallics 16 (2008) 544e549 0

Ref. [10] Ref. [11] Phase boundary Ref. [17] Single phase Ref. [18] Two phases

Ref. [21]

1763°C 1601°C

Temperature, °C

1500

950

900 85

L

V17Ge31+L V17Ge31+(Ge) 90

95

100

(V) 1200 959°C 900

V17Ge31

V11Ge8+L

Ref. [23]

-15 -20 -25 -30

V5Ge3 V11Ge8

Temperature,°C

1800

1000

Ref. [22]

-10

V3Ge

Standard Enthalpy of Formation, kJ/mol

-5

2100 Liquid

547

-35 -40

928°C

V17Ge31

600

V5Ge3 V11Ge8

V3Ge

-45 (Ge)

-50

20

40

60

40

60

80

Ge

Ge, at. %

300 V

20

V

80

Fig. 4. The calculated standard enthalpies of formation in the VeGe system compared with experimental data [21e23].

Ge

Ge, at. % Fig. 3. The calculated phase diagram of the VeGe system compared with experimental data [10,11,17,18].

an excess vacancy concentration for nucleation of the ordered phase. However, the Pt8V phase was still not considered in the present work because the phase stability of the Pt8V phase is unknown. The standard enthalpies of formation of the Pt3V and Pt2V compounds were studied using direct synthesis calorimetry by Guo and Kleppa [28].

3.2. The VePt system The VePt system consisted of two solution phases (bcc and fcc) and four stable intermetallic compounds (PtV3, PtV, Pt2V and Pt3V) with finite homogeneity ranges. The phase diagram of the VePt system was mainly investigated by Waterstrat [24] based on metallography, X-ray diffraction and electron microprobe. Schryvers and Amelinckx [25] reported that the Pt8V compound was found to be an ordered structure below 810  C. Later, Smith [26] reviewed the phase diagram of the VePt system, as shown in Fig. 2, in which the Pt8V phase was not included, because it was uncertain whether Pt8V is an equilibrium phase or not. Recently Nxumalo and Lang [27] reported that the stable Pt8V-ordered phase exists below 810  C, but the ordering kinetics was very sluggish, requiring

4. Optimization The optimization of the thermodynamic parameters was carried out using the PARROT module in Thermo-Calc software [29]. This software allows the introduction of a great variety of experimental data in the evaluation. The program operates by minimizing the square of the sum of errors between the calculated values and experimental data. A statistical weight assigned to each experimental data according to its compatibility with the other ones was changed by trial and error during the assessment.

Table 4 Special points of the VeGe system Reaction

Reaction type

Experimental data, Ref. [19] Composition, at.% Ge

L 4 (V) L 4 V3Ge þ (V) L 4 V3Ge L 4 V5Ge3 þ V3Ge L 4 V5Ge3 L þ V5Ge3 4 V11Ge8 L þ V11Ge8 4 V17Ge31 L 4 (Ge) þ V17Ge31 L 4 (Ge)

Melting Eutectic Congruent melting Eutectic Congruent melting Peritectic Peritectic Eutectic Melting

0 w16 25 e 37.5 e w95 w100 100

0 w25 25 w37.5 37.5 w37.5 42.1 w98 100

Calculated results 

w4.5 25 42.1 64.6 64.6

Temperature, C

Composition, at.% Ge

1910 1760 1920 w1800? 1930e2000 w1600? 960 930 937

0 13.3 25 30.1 37.5 54.1 96.1 100 100

0 25 25 37.5 37.5 37.5 42.1 97.2 100

Temperature,  C 4.7

25 42.1 64.6 64.6

1910 1763 1920 1891 1962 1601 959 928 937

C.P. Wang et al. / Intermetallics 16 (2008) 544e549

548

2800

2400

-1

Temperature,°C

V5Ge3

900 Pt2V 60

65

70

75

80

85

Liquid 1804°C

(V) (Pt)

-3

1200

-4

800

1416°C

978°C PtV

Pt2V

PtV3 -5

Pt3V

1000

1720°C 1600

(Pt)

972°C 1100

800

1803°C

2000

-2

1200

Ref. [24] [One phase] [Two phases] [Melting Began on Heating] [Melting Completed] [Phase Boundary]

Temperature,°C

V11Ge8

V3Ge

Entropy of Formation, kJ/mol

0

V17Ge31

1

Pt3V

400 V

20

60

40

80

Ge

V

Ge, at. %

20

40

60

80

Pt

Pt, at. %

Fig. 5. The calculated entropies of formation in the VeGe system at 298 K compared with the values evaluated by Smith [19].

Fig. 6. The calculated phase diagram of the VePt system together with experimental data from Waterstrat [24].

All optimized parameters in the VeGe and VePt systems are listed in Tables 2 and 3, respectively.

the invariant reactions in the VeGe system compared with the available experimental data are listed in Table 4. The calculated standard enthalpies of the four intermetallic compounds in the VeGe system together with the experimental data are shown in Fig. 4. And the calculated entropies of formation at 298 K compared with the values evaluated by Smith [19] are shown in Fig. 5, where the reference states of pure elements of V and Ge are bcc and diamond phases, respectively.

5. Calculated results and discussion 5.1. The VeGe system The calculated VeGe phase diagram compared with the experimental data is presented in Fig. 3. The calculated results are in reasonable agreement with the experimental data. However, the calculated temperature of the eutectic reaction (L 4 V5Ge3 þ V3Ge) is 1891  C, which is slightly higher than 1800  C proposed by Smith [19] who also pointed out that this is an evaluated value. Due to the limited experimental data, the calculated results are considered to be acceptable. All

5.2. The VePt system The calculated phase diagram of the VePt system is shown in Fig. 6 together with experimental data from Waterstrat [24]. A general agreement is obtained between the calculated results and the experimental data. All deviations of temperatures and

Table 5 Calculated and experimental invariant equilibria in the VePt system Reaction

Reaction type

Experimental data, Ref. [26] Composition, at.% Pt

L 4 (V) L þ (V) 4 PtV3 L 4 (Pt) þ PtV3 (Pt) 4 PtV þ PtV3 (Pt) 4 PtV (Pt) 4 Pt2V þ PtV (Pt) 4 Pt2V (Pt) 4 Pt3V þ Pt2V (Pt) 4 Pt3V L 4 (Pt) L 4 (Pt)

Fusion Peritectic Eutectic Eutectoid Congruent melting Eutectoid Congruent melting Eutectoid Congruent melting Azeotropic melting Fusion

0 w31? w37 w45 50 w61 66.7 w71.5 75 w73 100

0 w12 w43 w48 50 w65.5 66.7 w74 75 w73 100

Calculated results 

Temperature, C w18 w34 w33 w51.5 w68

1910 1800  10 1720  10 w1410 1500  10 980  10 1100  5 970  10 1015  5 1805  10 1769

Temperature,  C

Composition, at.% Pt 0 21.4 39.7 44.1 49.4 61.0 67.3 72.7 75 73.8 100

0 10.6 43.5 48.1 49.4 66.5 67.3 74.5 75 73.8 100

19.4 32.7 32.5 50.0 68.2

1910 1803 1720 1416 1501 978 1100 972 1012 1804 1769

C.P. Wang et al. / Intermetallics 16 (2008) 544e549

Acknowledgements

0

This work was jointly supported by the National Natural Science Foundation of China (Nos. 50571084, 50425101), the Ministry of Science and Technology, PR China (2004CCA04200), the Ministry of Education, PR China (Nos. 105100, 20050384003, and 707037), Fujian Provincial Department of Science and Technology (Grant Nos. 2005HZ1015, 2002I018), and Xiamen Bureau of Science and Technology (Grant No. 02Z20055016).

-5 -10 -15 -20

Pt2V

-25 PtV

Standard Enthalpy of Formation, kJ/mol

549

-30

References

PtV3 -35 Pt3V -40 -45 V

20

40

60

80

Pt

Pt, at. % Fig. 7. The calculated standard enthalpies of formation of the Pt3V and Pt2V phases compared with experimental data [28].

composition values are compatible by considering the accuracy of available data, except for the invariant reaction (L þ (V) 4 PtV3) in the V-rich side, the peritectic composition of which reported by Waterstrat was difficult to reproduce [24]. Thus, the calculated results are considered to be acceptable because of the low accuracy of the related experimental data. All the calculated invariant reactions compared with the experimental data are listed in Table 5. The calculated standard enthalpies of formation of the four intermetallic compounds (PtV3, PtV, Pt2V and Pt3V) in the VePt system are shown in Fig. 7, compared with the experimental data reported by Guo and Kleppa [28] by direct synthesis calorimetry, where the reference states of pure elements of V and Pt are bcc and fcc phases, respectively. 6. Summary The phase diagrams and thermodynamic properties in the VeGe and VePt binary systems were evaluated by combining the thermodynamic models with the available experimental data in the literatures. A consistent set of thermodynamic parameters has been obtained for each phase in the VeGe and VePt binary systems, and a reasonable agreement is obtained between the calculated results and experimental data.

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