Thermodynamic assessment of the V–Zn system supported by key experiments and first-principles calculations

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 34 (2010) 75–80

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Thermodynamic assessment of the V–Zn system supported by key experiments and first-principles calculations Keke Chang a , Yong Du a,b,∗ , Weihua Sun a , Honghui Xu a,b , LiangCai Zhou a a

State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan, 410083, PR China

b

Science Center for Phase Diagrams & Materials Design and Manufacture, Central South University, Changsha, Hunan, 410083, PR China

article

info

Article history: Received 8 October 2009 Received in revised form 10 December 2009 Accepted 12 December 2009 Available online 24 December 2009 Keywords: V–Zn system Phase diagram Thermodynamic modeling First-principles calculations

abstract The V–Zn system was investigated by a combination of CALPHAD modeling with key experiments and first-principles calculations. Based on a critical literature review, one diffusion couple and nine alloys were designed to reinvestigate the stabilities of the phases reported in the literature. The samples were annealed and cooled under different conditions, followed by examination with X-ray diffraction and scanning electron microscopy with energy-dispersive X-ray spectrometry. Four phases ((V), (Zn), VZn3 and V4 Zn5 ) were confirmed to exist in the phase diagram, while VZn16 and V3 Zn were not observed. By means of first-principles calculations, the enthalpies of formation for VZn3 and V4 Zn5 were computed to be −4.55 kJ mol-atoms−1 and −4.58 kJ mol-atoms−1 , respectively. A set of self-consistent thermodynamic parameters for this system was obtained by considering the reliable experimental phase diagram data and the enthalpies of formation acquired from first-principles calculations. The calculated V–Zn phase diagram agrees well with the experimental data. © 2009 Elsevier Ltd. All rights reserved.

1. Introduction Zn and V are useful elements in various coatings. Zinc coatings can protect V-based alloys from oxidation at high temperatures [1]. The hot dip Zn–Ni–V (Ecozinc) coating is shown to be more resistant to bending tests compared with a conventional hot dip galvanized coating without V [2]. Also, the addition of V increases the corrosion resistance of a Zn–Fe alloy coating in strong acid solution [3]. For the design and development of Zn-based coatings with high performance, information on the phase equilibria and thermodynamic properties of the V–Zn system is of great importance. The V–Zn phase diagram has been assessed by Smith [4,5], who pointed out that further experimental work was needed to check the stabilities of the reported compounds. Up to now, no thermodynamic data are available in the literature and no thermodynamic modeling has been performed for this system. Thus, the present work aims to (1) reinvestigate the stabilities of the reported phases by key experiments; (2) obtain the enthalpies of formation for the compounds from first-principles calculations in order to provide a reliable energy basis for the thermodynamic modeling; and

∗ Corresponding author at: State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan, 410083, PR China. Tel.: +86 731 88836213; fax: +86 731 88710855. E-mail address: [email protected] (Y. Du). 0364-5916/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.calphad.2009.12.003

(3) provide a set of self-consistent thermodynamic parameters for this system using the CALPHAD approach. 2. Evaluation of phase diagram information in the literature In order to facilitate reading, the crystal structure data of all the phases reported in the literature [6–10] are listed in Table 1. The major contribution to the V–Zn phase diagram was due to Chasanov et al. [7,8], who used X-ray diffraction (XRD), metallographic observations, and chemical and thermal analyses to investigate the phase equilibria. As shown in Table 2, two compounds (V4 Zn5 and VZn3 ) and three invariant reactions associated with these two compounds were reported. In addition, the mutual solid solubilities between V and Zn were found to be negligible. Since the starting materials were of high purity (99.86 wt% V and 99.99 wt% Zn) and the reported stable phases were confirmed by the present experimental results, as shown later, their data [7] were used in the thermodynamic modeling. In addition to V4 Zn5 and VZn3 , Piotrowski [9] found a compound, VZn16 , and Savitskii et al. [11] reported another compound, V3 Zn. However, as assessed by Smith [4,5], V3 Zn was either a metastable or most likely impurity-stabilized phase. VZn16 could not be detected at a cooling rate exceeding 1 ◦ C/min [9]. According to the present experimental results, which will be discussed below, VZn16 and V3 Zn were not observed. Consequently, these two compounds were not considered in the present modeling.

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K. Chang et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 34 (2010) 75–80

Table 1 Crystal structure data on the phases in the V–Zn system. Phase

Structure type

Pearson symbol

Lattice parameter (Å)

Space group

a 0.30271 0.30300 0.26646 0.26680 0.89100 0.89100 0.88720 0.38480 0.38490 0.38230

V

W

¯ cI2, Im3m

(Zn)

Mg

hP2, P63 /mmc

V4 Zn5

–

tI18, I4/mmm

VZn3

AuCu3

¯ cP2, Pm3m

a

Reference c

0.49641 0.50158 0.32270 0.32200 0.31960

[6] This worka [6] This worka [7,8] [9] This worka [7] [10] This worka

First-principles calculations.

Table 2 Comparison between the calculated and measured invariant equilibria in the V–Zn system. Equilibrium L + (V) ↔ V4 Zn5 L + V4 Zn5 ↔ VZn3 L ↔ VZn3 + (Zn)

Measured [7] T (◦ C)

xLZn (at.%Zn)

Calculated (This work) T (◦ C) xLZn (at.%Zn)

670 623 417.3

99.04 99.15 99.828

670 623 418.7

99.03 99.15 99.823

3. Experimental procedure In the present experiment, one Zn/V diffusion couple and nine alloys were designed to reinvestigate the phase stabilities of the phases reported in the literature, in particular for VZn16 and V3 Zn. Table 3 lists the nominal compositions of the alloys and the cooling conditions. The Zn/V diffusion couple was prepared via the following steps. A piece of V rod (99.8 wt% purity, Alfa Aesar, USA) and a pure Zn piece (99.999 wt% purity, Zhuzhou Smelting Plant, PR China) were put in an alumina crucible, which was then encapsulated in an evacuated quartz tube. The quartz capsule was annealed at 500 ◦ C for 1 h in an L4514-type diffusion furnace (Qingdao Instrument & Equipment Co. Ltd., China) and a cylindrical diffusion couple was then formed, as shown in Fig. 1. Subsequently, the quartz capsule was annealed at 400 ◦ C for 16 h and quenched in cold water. The quenched diffusion couple was mounted carefully to reveal the exact vertical interfaces. After standard metallographic preparation, the diffusion couple was examined by using optical microscopy (OM) (Leica DMLP, Leica GmbH, Wetzlar, Germany) and scanning electron microscopy with energy dispersive X-ray spectrometry (SEM/EDX) (JSM-6360LV, JEOL). The alloys were prepared by a powder metallurgical method. V powder (99.5 wt% purity, Alfa Aesar, USA) and Zn powder (99.99 wt% purity, Tianjin Guangfu Fine Chemical Research Institute) were used as starting materials. After being milled for 4 h, the powder mixtures were dried and compacted into small tablets of about 4 g for each alloy. The samples were put in alumina crucibles, which were then encapsulated in quartz tubes. The quartz capsules were annealed at 600 ◦ C for 10 days in an L4514-type diffusion furnace.

Subsequently, alloys 4–9 were quenched in water and the furnace was slowly cooled down to 400 ◦ C at rate of 0.8 ◦ C/min. Alloys 1–3 were annealed at 400 ◦ C for 30 days and then cooled under different conditions, in order to investigate whether VZn16 could be formed under different cooling rates. The phase identification was performed by using Cu Kα radiation on a Rigaku D-max/2550 VB+ X-ray diffractometer at 40 kV and 300 mA (Rigaku Corporation, Tokyo, Japan). The compositions of the phases were measured by SEM/EDX. 4. Enthalpies of formation computed via the first-principles method Since there are no experimental enthalpies of formation for VZn3 and V4 Zn5 , first-principles calculations were employed to provide these data. The first-principles calculations within the generalized gradient approximation (GGA) based on the Perdew– Burke–Ernzerhof (PBE) approach [12], as implemented in Vienna ab initio simulation package (VASP) [13], were carried out to evaluate the enthalpies of formation for both VZn3 and V4 Zn5 . The valence electrons were explicitly treated by projector augmented plane-wave (PAW) potentials [14]. The atoms were relaxed toward equilibrium until the Hellmann–Feynman forces were less than 10−2 eV Å−1 . A plane-wave cutoff energy of 400 eV and an energy convergence criterion of 10−5 eV for electronic structure self-consistency were used in the calculations. Brillouin zone integrations were performed using the Monkhorst–Pack k-point meshes scheme [15], and the total energy differences were converged to within 0.1 kJ mol-atoms−1 . Both the unit cell sizes and the ionic coordinates were fully relaxed to find the stable state. The enthalpy of formation ∆Hf (Vx Zny ) at 0 K is expressed by the following equation:

∆Hf (Vx Zny ) = E (Vx Zny ) − [xV E (V) + xZn E (Zn)] (1) where E (Vx Zny ), E (V) and E (Zn) denote the total energies of Vx Zny , V and Zn at 0 K, respectively. xi (i = V or Zn) is the atomic fraction of the component. The reference states at 0 K are Bcc_A2 and Hcp_Zn for V and Zn, respectively. The calculated enthalpies of formation for VZn3 and V4 Zn5 are −4.55 and −4.58 kJ mol-atoms−1 , respectively. These first-principles generated data were used in the present modeling.

Table 3 Summary of the experimental results on the V–Zn alloys. Alloy no.

Composition (at.% Zn)

Annealing temperature (◦ C)

Phases

Cooling condition

1 2 3 4 5 6 7 8 9

94.12 94.12 94.12 90 50 90 60 50 90

400 400 400 550 550 600 600 600 650

(Zn), VZn3 (Zn), VZn3 (Zn), VZn3 (Zn), VZn3 (V), V4 Zn5 (Zn), VZn3 VZn3 , V4 Zn5 (V), V4 Zn5 (Zn), V4 Zn5

Quenched in water Cooled in air Cooled with furnace Quenched in water Quenched in water Quenched in water Quenched in water Quenched in water Quenched in water

K. Chang et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 34 (2010) 75–80

77

Fig. 1. Schematic diagram to show the preparation of the Zn/V diffusion couple.

5. Thermodynamic models ϕ

ϕ

The Gibbs energy function o Gi (T ) = Gi (T ) − HiSER for element i (i = V, Zn) in the phase ϕ (ϕ = liquid, (V) or (Zn)) is expressed by the following equation: o

ϕ

Gi (T ) = a + b · T + c · T · ln T + d · T 2 + e · T −1 + f · T 3

+ g · T 7 + h · T −9

(2)

where HiSER

is the molar enthalpy of the element i at 298.15 K and 1 bar in its standard element reference (SER) state, and T is the absolute temperature. In the present modeling, the Gibbs energies for pure elements were taken from the compilation by Dinsdale [16]. The solution phase ϕ (ϕ = liquid, (V) or (Zn)) is described by the Redlich–Kister polynomial [17]: ϕ

ϕ

Gϕm − H SER = xV · o GV + xZn · o GZn + R · T (xV · ln xV + xZn · ln xZn )

+ xV · xZn [a0 + b0 · T + (xV − xZn )(a1 + b1 · T ) + (xV − xZn )2 · (a2 + b2 · T ) + · · ·]

Fig. 2. The Zn/V diffusion couple annealed at 400 ◦ C for 16 h.

(3)

SER , R is in which H SER is the abbreviation of xV · HVSER + xZn · HZn the gas constant, and xV and xZn are the mole fractions of V and Zn, respectively. The coefficients aj and bj (j = 0, 1, 2) are to be optimized. V4 Zn5 and VZn3 are modeled as stoichiometric phases. The Gibbs energy of each compound Vx Zny is given by the following expression: o

GVxZny m

− xV ·

HVSER

− xZn ·

SER HZn

= A + B · T + xV o GBCC_A2 + xZn o GHCP_ZN V Zn

(4)

in which A and B are to be evaluated. The gas phase is described as an ideal gas mixture of the species V and Zn, and its Gibbs energy per mol of species in the gas is given by the following expression: Ggas − H SER =

X

gas

yi [Gi

− HiSER + R · T · ln(yi )]

+ R · T · ln(0.98692 · P /bar )

(5)

gas

where yi is the mole fraction of species i, Gi − HiSER the Gibbs energy of species i, and P the pressure. The Gibbs energy functions for the individual gas species are taken from Ref. [18]. 6. Results and discussion The microstructure of the Zn/V diffusion couple annealed at 400 ◦ C for 16 h is shown in Fig. 2. According to EDX examination, four phases ((Zn), VZn3 , V4 Zn5 and (V)) are formed after interdiffusion. The experimental observations based on the diffusion couple indicate no existence of VZn16 and V3 Zn which were reported by Piotrowski [9] and Savitskii et al. [11]. Table 3 lists the nominal compositions of the alloys, the annealing temperatures, and the phases identified by XRD and SEM/EDX under different cooling conditions. It can be clearly seen that the existence of V4 Zn5 and VZn3 was confirmed while VZn16 and V3 Zn were not observed. The backscattered electron (BSE) image and XRD pattern of the representative alloys are presented in Figs. 3

78

K. Chang et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 34 (2010) 75–80

a

a

Alloy 3: V5.88Zn94.12 40000 (Zn)

VZn3

Intensity (CPS)

30000

20000

10000

0 20

30

40

50

60

70

80

90

2θ

b

b 35000

Alloy 9: V10.0Zn90.0 (Zn)

30000

V4Zn5

Intensity (CPS)

25000 35000 30000

20000

25000 43.0

43.1

43.2

15000

43.3 3500 2500

10000

1500 86.2

86.4

86.6

5000 0 20

Fig. 3. (a) The BSE image of alloy 3 (V5.88 Zn94.12 ) cooled at a rate of 0.8 ◦ C/min; (b) The BSE image of alloy 9 (V10.0 Zn90.0 ) annealed at 650 ◦ C.

and 4, respectively. The experimental results from the alloys are consistent with those from the diffusion couple. Both Figs. 3a and 4a indicate that VZn3 and (Zn) are in equilibrium rather than VZn3 and VZn16 . The present experiments indicate that VZn16 could not be formed under either a fast cooling rate (water quenching) or a slow cooling rate (furnace cooling). The SEM/EDX examination of alloys 4, 6 and 9 yields the solubilities of V in liquid (Zn) to be 0.0051 at.%, 0.0069 at.% and 0.0095 at.% at 550, 600 and 650 ◦ C, respectively. These data are in accordance with those from Chasanov et al. [7]. As a result, the present experimental data were also used in the thermodynamic modeling. Evaluation of the model parameters was performed by the optimization program PARROT [19], which works by minimizing the square sum of the differences between measured and calculated values. The step-by-step optimization procedure described by Du et al. [20] was utilized in the present assessment. The reliable experimental data [7], the present experimental values, and the enthalpies of formation for the compounds via first-principles calculations were employed in the optimization. The optimization began with the liquid phase. The experimental liquidus in the Zn-rich side [7] was first considered. Then VZn3 and V4 Zn5 were introduced in the modeling one by one. The A parameters for these two compounds were determined by the enthalpies of formation computed via first-principles calculations, and the B parameters were adjusted to describe the liquidus and invariant reactions. Finally, one regular parameter was employed for each of the (V) and (Zn) phases in order to account for the solubility data. The optimized thermodynamic parameters are listed in Table 4. The V–Zn phase diagram calculated using the present set of thermodynamic parameters is shown in Fig. 5a. The calculated and measured invariant equilibria [7] are compared in Table 2. It can be

30

40

50

60

70

80

90

2θ Fig. 4. (a) XRD pattern of alloy 3 (V5.88 Zn94.12 ) cooled at a rate of 0.8 ◦ C/min; (b) XRD pattern of alloy 9 (V10.0 Zn90.0 ) annealed at 650 ◦ C.

Table 4 Summary of the thermodynamic parameters in the V–Zn system. Liquid: Model (V, Zn)1 0 L LV,Zn = −23 173.4 + 51.08T (V): Model (V, Zn)1 (Va)3 = 45 000

0 BCC_A2 LV,Zn

(Zn): Model (V, Zn)1 (Va)0.5 = 32 000

0 HCP_ZN LV,Zn

V4 Zn5 : V4/9 Zn5/9 GV4Zn5 − (4/9)o GBCC_A2 − (5/9)o GHCP_ZN = −4573.74 + 3.221T m V Zn

o

VZn3 : V0.25 Zn0.75 o VZn3 Gm − 0.25◦ GBCC_A2 − 0.75◦ GHCP_ZN = −4549.92 + 2.927T V Zn Gas: Model (V, Zn) o gas GV = R · T · ln(0.98692 · P ) + GASV (T ) o

gas

GZn = R · T · ln(0.98692 · P ) + GASZN (T )

In J mol-atoms−1 , with temperature (T ) in Kelvin and pressure (P) in bar. The Gibbs energies for the pure elements are from the SGTE compilation [16], and the Gibbs energies for gas species are from [18].

seen that the present modeling can account for the measured invariant reaction temperatures [7] within ±2 K. As shown in Fig. 5b and c, the calculated V–Zn phase diagram agrees well with the experimental data from [7] and the present work. Fig. 6 presents the calculated V–Zn phase diagram including the gas phase. According to the calculation, there is one invariant reaction: Gas + (V) ↔ Liquid at 920.6 ◦ C.

K. Chang et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 34 (2010) 75–80

a

800

4000

750

3500

Gas

3561.8 L

L+(V)

700

79

3000

650

Temperature, 0C

Temperature, 0C

670 623 600 550

V4Zn5

(V)

VZn3

2500

Gas+Liquid

2000

1910.2

1500

Gas+(V)

500 1000

920.6 Liquid+(V)

450 418.7 400

0 V

b

0.2

0.4 0.6 Mole fraction Zn

0.8

419.5 (Zn) 1.0 Zn

500

V4Zn5

19.5

418.7

(Zn)

VZn3

0

800 Chasanov et al. 1963

0.2

0.4 0.6 Mole fraction Zn

0.8

1.0 Zn

Fig. 6. Calculated V–Zn phase diagram including the gas phase.

This work – Phase compositions from EDX results This work – Nominal compositions of key alloys

L

700 L + (V)

0

650 600

-0.5

CALPHAD calculation

-1.0

First-principles calculation

-1.5

550 V4Zn5

(V)

ΔHf, KJ/mol-atoms

Temperature, 0C

623 (V) 0 V

750

919.7

670

VZn3

500 450 400

0 V

0.2

0.4 0.6 Mole fraction Zn

(Zn) 1.0 Zn

0.8

-2.0 -2.5 -3.0 -3.5 V4Zn5

VZn3

-4.0

c

800 750

Temperature, 0C

700

-4.5 Chasanov et al. 1963 This work

650

-5.0 L

L+(V)

0 V

0.2

0.4 0.6 Mole fraction Zn

0.8

1.0 Zn

430

L+V4Zn5

Fig. 7. Enthalpies of formation at 298.15 K according to the present calculations.

425

600

L

L+VZn3 420

550

415

L+VZn3

410 0.996

500 450

7. Summary

VZn3+(Zn)

0.998

1.00

VZn3+(Zn) (Zn)

400 0.95 V

0.96

0.97 0.98 Mole fraction Zn

0.99

1.00 Zn

Fig. 5. (a) Calculated V–Zn phase diagram according to the present modeling; (b) calculated V–Zn phase diagram with the experimental data from [7] and the present work; (c) enlarged phase diagram with the experimental data from [7] and the present work.

Fig. 7 presents the calculated enthalpies of formation from CALPHAD modeling compared with those from the first-principles method. The good agreement demonstrates that first-principles calculations can provide reliable ‘‘experimental data’’ when the experimental data are not available.

• The phase diagram data for the V–Zn system were reviewed. One Zn/V diffusion couple and nine alloys were used to detect the phase stabilities of the compounds. It is found that VZn16 and V3 Zn do not exist in the stable phase diagram. • The enthalpies of formation for VZn3 and V4 Zn5 were calculated from first-principles calculations in order to supplement the thermodynamic modeling. By optimizing the reliable experimental data and the enthalpies of formation acquired from first-principles calculations, a set of self-consistent thermodynamic parameters for the V–Zn system was obtained. The calculated phase diagram agrees well with the experimental data. Acknowledgements Financial support from the National Natural Science Foundation of China (Grant Nos. 50831007, 50721003, 50425103) is greatly

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acknowledged. Many thanks are given to Dr. Xiaogang Lu from Thermo-Calc Software AB of Sweden for helpful discussions. In addition, the authors acknowledge the donation of a Leica DMLP microscope from Alexander von Humboldt Foundation of Germany. Appendix. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.calphad.2009.12.003. References [1] W.D. Klopp, C.A. Krier, Def. Met. Inf. Cent. Memo. 88 (1961). [2] C. Alonso, J. Fullea, F.J. Recio, M. Sanchez, R. Soldado, M. Bernal, P. Tierra, International Galvanizing Conference, 2006, 21st 10/1–10/8. [3] C. Cao, D. Lu, Cailiao Baohu 40 (8) (2007) 12–14. [4] J.F. Smith, J. Alloy Ph. Diagr. 5 (2) (1989) 136–141.

[5] J.F. Smith, Binary Alloy Phase Diagrams. Vol. 3, 2nd ed., Materials Information Soc., Materials Park, Ohio, 1990. [6] P. Villars, L.D. Calvert, Pearson’s Handbook of Crystallographic Data for Intermetallic Phases, 2nd ed., ASM International, Materials Park, OH, 1991. [7] M.G. Chasanov, R. Schablaske, P.D. Hunt, B. Tani, Trans. AIME 227 (1963) 485–488. [8] R. Schablaske, B. Tani, M. Homa, R. Larsen, USAEC Rep. ANL-6687, 1963, pp. 84–85. [9] W. Piotrowski, Hutnik 32 (1965) 135–142. [10] Z. Wendorff, W. Piotrowski, Hutnik 31 (1964) 246–249. [11] E.M. Savitskii, V.V. Varon, Yu.V. Efimov, Dokl. Akad. Nauk SSSR 171 (1966) 331–332. [12] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. L 77 (1996) 3865–3868. [13] G. Kresse, J. Furthmueler, Phys. Rev. B 54 (1996) 11169–11186. [14] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758–1775. [15] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188–5192. [16] A.T. Dinsdale, CALPHAD 15 (1991) 317–425. [17] O. Redlich, A.T. Kister, Indust. Eng. Chem. 40 (1948) 345–348. [18] SGTE substance database, Thermo-calc Company, Sweden, 2008. [19] B. Sundman, B. Jansson, J.O. Andersson, CALPHAD 9 (1985) 153–190. [20] Y. Du, R. Schmid-Fetzer, H. Ohtani, Z. Metallkd. 88 (1997) 545–556.