Thermodynamic evaluation of the phase equilibria and glass-forming ability of the Al–Co–Gd system

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 52 (2016) 57–65

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Thermodynamic evaluation of the phase equilibria and glass-forming ability of the Al–Co–Gd system X. Li a, L.B. Liu a, Y. Jiang b, G.X. Huang a, X. Wang a, Y.R. Jiang a, J.S. Liang a, L.G. Zhang a,n, X. Shi a a b

School of Materials Science and Engineering, Central South University, Changsha 410083, China Hunan Farsoon High-Technology Co., Ltd., Changsha 410205, China

art ic l e i nf o

a b s t r a c t

Article history: Received 19 December 2014 Received in revised form 26 November 2015 Accepted 27 November 2015 Available online 7 December 2015

The Al–Co–Gd system was thermodynamically assessed by means of the CALPHAD (CALculation of PHAse Diagrams) method. The substitutional model was adopted to describe the thermodynamic functions of solution phases and sublattice models were used to describe the intermetallic phases in the ternary system. A set of self-consistent thermodynamic parameters was obtained. Furthermore, by using Turnbull Gibbs free energy empirical equations, the driving forces for crystallization of the primary crystalline phases from the undercooled liquid alloys were calculated. Combining thermodynamic data with Davies– Uhlmann kinetic formulas, the time–temperature–transformation (TTT) curves were obtained. By comparing critical cooling rates calculated from the TTT curves, the glass-forming ability of seven Al–Co–Gd alloys was evaluated. The results agree with the experimental data, which suggests that the combined thermodynamic and kinetic approach may be an efficient way for the evaluation of glass-forming ability. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Al–Co–Gd Phase diagram CALPHAD TTT curves Glass forming ability

1. Introduction The study of amorphous alloys has attracted much attention in recent years due to their high strength and excellent magnetic properties. Scholars have proposed many criteria for predicting the glass-forming ability (GFA) of metallic materials [1–3]. Although these criteria have generally deduced reasonable parameters for evaluating GFA, they all have their own limitations. Saunders and Miodownik [4] have successfully predicted the glass-forming range in some binary and ternary metallic alloys by using combined thermodynamic and kinetic calculation. Ge et al. [5] evaluated the GFA of nine Cu–Zr alloys and thirteen Cu–Zr–Ti alloys using the Davies–Uhlmann kinetic equations. In their studies [4– 5], thermodynamic parameters were obtained from thermodynamic models and kinetic values such as free energy barrier for nucleation were used in kinetic formation. In this study, the combined thermodynamic and kinetic method would be used to predict GFA of the Al–Co–Gd alloys. In the Al–Co–Gd system, the constituent binary phase diagrams of Al–Co [6], Al–Gd [7] and Co–Gd [8] have been well evaluated. In order to model the devitrification kinetics of Al–Co–Gd amorphous alloys, a self-consistent thermodynamic database for the ternary system by the CALPHAD approach [9] was developed in this work. n

Corresponding author. E-mail address: [email protected] (L.G. Zhang).

http://dx.doi.org/10.1016/j.calphad.2015.11.002 0364-5916/& 2015 Elsevier Ltd. All rights reserved.

Furthermore, the GFA of seven Al–Co–Gd alloys were compared by calculating critical cooling rates from the TTT curves.

2. Literature review 2.1. Binary system Stein et al. [6] reassessed the binary system with new data acquired from their experiment. Bo et al. [7] reassessed the Al–Gd system using a substitutional solution model for the liquid phase. Liu et al. [8] optimized the Co–Gd binary system. These three binary thermodynamic descriptions were adopted in present work. 2.2. The Al–Co–Gd ternary system Wan et at. [10] measured the Gd–Co–Al vertical section (Al0.5Co0.5–Gd (atomic fraction)) of this system. As reported by MSIT ternary evaluation Program [11], there are five ternary compounds i.e., τ1-Gd2CoAl11, τ2-Gd2Co3Al9, τ3-GdCo5
xAlx, τ4-GdCo2
xAlx and τ5-Gd(Co,Al)1.5 in this system. However, only one compound τ4-GdCo2
xAlx–(GdCo0.74Al1.26) was confirmed by Zhou et al. [12] in the isothermal section at 1173 K. Compounds τ4-GdCo2
xAlx–(GdCo0.74Al1.26) and (Gd2Co2Al) were confirmed by Gu et al. [13] in the isothermal section at 773 K. According to the result reported by Gu et al. [13], Co5Gd should appear in the 773 K

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X. Li et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 52 (2016) 57–65

isothermal section of Al–Co–Gd system. However, judging from the Co–Gd binary system [8], there is no Co5Gd forming at 773 K. Zhu et al. [14] believed that the Co5Gd phase would decompose into Co7Gd2 and Co17Gd2 phases at about 1078 K, and below that temperature, the Co5Gd should not exist in an equilibrium state. One of the reasons that Co5Gd phase existed at 773 K in the work reported by Gu et al. [13] possibly lies in insufficient annealing time. In this work, experiments were carried out accordingly to verify the existence of Co5Gd phase. Amorphous Al–Co–Gd alloys became well known to the public because of their high thermal stability and magnetic properties. In 2007, Chen et al. [15] investigated this ternary system in a composition ranging from 50 to 70 wt% Gd and from 5 to 40 wt% Al by copper mold casting and obtained bulk glass alloy cylinders with a maximum diameter of 5 mm. A number of experimental investigations on phase equilibria or crystal structures of phases of this system had been reported [16–18], and the isothermal sections at 1173 K and 773 K [12–13] were reported as mentioned above.

is taken from the Science Group Thermodata Europe (SGTE) Pure Elements Database [19]; R is gas constant; T is the temperature in K; exG φ is the excess Gibbs energy formulated with the Redlich– Kister polynomial [20]: ex

Gφ = xAl x Co

N

φ ∑ j = 0,1, … (xAl −x Co ) j (j) LAl,Co +xAl x Gd

N

∑

φ (xAl −x Gd ) j (j) LAl,Gd +x Co x Gd

j = 0,1, … N

φ φ +xAl x Co x Gd LAl,Co,Gd ∑ j = 0,1, … (x Co −x Gd ) j (j) L Co,Gd

Here,

φ , LAl,Co

φ LAl,Gd

and

φ L Co,Gd

(2)

are the interaction parameters

between elements Al and Co, Al and Gd, Co and Gd, respectively. These parameters are cited from Stein et al. [6], Bo et al. [7] and Liu φ et al. [8], separately. LAl,Co,Gd is the ternary interaction parameter. The general form of the interaction parameters of Lφ is showed as follows:

Lφ = a + bT + cT ln T dT2 + eT 3 + fT−1

Only the first two or three terms are optimized according to the temperature dependence on the experimental data.

3. Experimental information Al blocks (99.99 wt%), Co blocks (99.99 wt%), Gd blocks (99.99 wt%) were used as starting materials. The weight of each sample is 4 g, and their compositions are listed in Table 1. To avoid oxidation, the sample was prepared under the protection of argon atmosphere by arc melting with a non-consumable tungsten electrode on a water-cooled copper plate. To ensure homogeneity, the sample was re-melted for four times. The weight loss of the sample was less than 1 wt%. Then the samples were sealed in evacuated quartz tubes and annealed at 773 K for 150 days. After quenching, the annealed samples and the as-cast samples were measured by scanning electron microscopy (SEM) (FEI Quanta 200). In order to get more accurate data, the samples were measured by electron probe microanalysis (EPMA) (JEOL JXA-8230) with a 15 kV voltage and 10 nA current. Pure elements Al, Co, Gd were provided as standards to revise the measurements.

The substitutional solution model is adopted to describe all the solution phases, i.e., liquid, fcc, bcc and hcp. The molar Gibbs energy can be expressed as follows:

xi 0Giφ + RT

i = Al,Co,Gd

∑

xi ln(xi )+ ex G φ

i = Al,Co,Gd

′ 0GAl:Gd +yCo ′ 0GCo:Gd + RT yAl ′ ln yAl ′ +yCo ′ ln yCo ′ G (Al,Co)x Gdy = yAl

(

′ y′Co +yAl

(∑

j = 0,1, …

j

(

′ −yCo ′ LAl,Co:Gd yAl

))

)

j

(4)

2Gd As for Al2Gd phase, where GAl:Gd has the same value as G Al Al:Gd , and GCo:Gd represents Gibbs energy of Co2Gd with Al2Gd structure, which is formulated as:

(5)

Table 1 Constituent phases and compositions of alloys. Nominal Composition (at%) Al

Co

Gd

1# 2# 3#

6 1 6

80 76 80

14 23 14

4#

1

76

23

Heattreatment

Phase determination

As-cast As-cast 773 K, 150 d 773 K, 150 d

Co5Gdþ Co17Gd2 Co5Gdþ Co3Gd þCo7Gd2 þ Co2Gd Co5Gdþ Co17Gd2 Co5Gdþ Co3Gd þCo7Gd2

Co5Gd Co17Gd2 Co2Gd same value as GCo:Gd or GCo:Gd or GCo:Gd and GAl:Gd represents Gibbs energy of Al5Gd with Co5Gd structure or Al17Gd2 with Co17Gd2 structure or Al5Gd with Co5Gd structure, which can be expressed as:

Fcc Hcp GAl:Gd = x0GAl + y 0GGd + C + DT

(6)

(1)

where xi is mole fraction of component i (i ¼Al, Co, Gd), and 0Giφ is the molar Gibbs energy of pure element i in the φ phase, which

Alloy (no.)

The Al2Gd, Co5Gd, Co17Gd2 and Co2Gd phases are modeled as (Al,Co)xGdy since they have a homogeneity region in the Al–Co–Gd system according to the literature [12]. Their Gibbs energies can be expressed as:

As for Co5Gd, Co17Gd2 and Co2Gd phases, where GCo:Gd has the

4.1. Solution phases

∑

4.2. Binary intermetallic phases

Hcp Hcp GCo:Gd=x0GCo +y 0GGd + A + BT

4. Thermodynamic models

Gφ =

(3)

where A, B, C and D are the parameters to be optimized in this work.

4.3. Ternary intermetallic phases In the Al–Co–Gd ternary system, stoichiometric phase Gd2Co2Al is modeled as GdxCoyAlz. It is treated as θ in the work. The Gibbs energy can be expressed as Fcc Hcp Hcp GGd:Co:Al = x0GGd + y 0GCo + z0GAl + E + FT

(7)

where E and F are the parameters to be optimized in this work. For GdCo0.74Al1.26, it is molded as Gd(Co,Al)2, and it is treated as δ in the study. The Gibbs energy can be expressed in the same way:

X. Li et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 52 (2016) 57–65

Fig. 1. The calculated three binary systems: (a) Al–Co system, (b) Al–Gd system, (c) Co–Gd system.

Fig. 2. The BSE images of Al–Co–Gd alloys. (a) Alloy #1 (6 at% Al–80 at% Co–14 at% Gd); (b) alloy #2 (1 at% Al–76 at% Co–23 at% Gd).

59

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Table 2 Thermodynamic parameters of the Al–Co–Gd ternary system optimized in this work. Phase

Thermodynamic parameters

Al2Gd:(Al,Gd,Co)2(Al,Gd,Co)1

Al2Gd=15,000+30G Hcp GCo:Co Co Al2Gd=30,000+0GFcc+30G Hcp GCo:Al Co Al Al2Gd=30,000+20GFcc+10G Hcp GAl:Co Co Al

Al2Gd = − 45,000+5T +20G Hcp+0G Hcp GCo:Gd Co Gd Al2Gd =− 35,000.1+8.001T + 0G Hcp+20G Hcp GGd:Co Co Gd

0 Al2Gd LAl,Co:Gd

Co2Gd: (Co,Al)2Gd1

0 Co2Gd GAl:Gd =− 0 Co2Gd L Co,Al:Gd = 1 Co2Gd L Co,Al:Gd

Co5Gd: (Co,Al)5Gd1

(

=− 64,999.998

Fcc+20G Hcp + 170GAl Gd

=− 50,000.001

Theta (θ): Gd2Co2Al

0 θ GGd:Co:Al

Fcc+20G Hcp+20G Hcp =− 204,325+25T + 0GAl Co Gd

Delta (δ): (Co,Al)2Gd1

Hcp 0 Hcp 0 θ GGd:Co =− 45,852.9+18.864T + 20GCo + GGd 0 δ 0 Hcp Fcc GGd:Al =− 60,000+5.001T + GGd +20GAl 0 δ GGd:Al,Co =− 300,000

= − 99,999.999

Co3Gd4: (Co,Al)3Gd4

0 Co3Gd4 GAl:Gd =− 56,431.998+28.917T 0 Co3Gd4 L Co,Al:Gd = − 306,432

CoGd3: (Co,Al)1Gd3

0 CoGd3 GAl:Gd =− 10,065+6.516T 0 CoGd3 GAl,Co:Gd =− 100,065

)

⎛ j ′ yCo ′ ⎜⎜ ∑ LAl,Co:Gd yAl ′ −yCo ′ + yAl ⎝ j = 0,1, …

Fcc+0G Hcp + 50GAl Gd

1 Co17Gd2 L Co,Al:Gd

δ δ ′ GAl2Gd ′ GCo2Gd G(δAl,Co) 2Gd1 =yAl +yCo

(

− 189,999.9+8.001T

=− 9999.9

0 Co17Gd2 GAl:Gd =− 329,999.6+60.002T 0 Co17Gd2 L Co,Al:Gd = − 143,199.9+7.999T

1 δ GGd:Al,Co

′ ln yAl ′ +yCo ′ ln yCo ′ + RT yAl

Fcc+0G Hcp 83,000.1+9.99T + 20GAl Gd

0 Co5Gd GAl:Gd =− 153,000+12T 0 Co5Gd L Co,Al:Gd =+ 312,000+6T

1 Co5Gd L Co,Al:Gd

Co17Gd2: (Co,Al)17Gd2

=− 104,000.1+0.999T

⎞

) j⎟⎟ ⎠

(8)

δ δ δ where GAl2Gd and LAl,Co:Gd are to be evaluated in the preGCo2Gd sent work.

Fcc+40G Hcp + 30GAl Gd

Fcc+30G Hcp + 0GAl Gd

In this equation, t (s) implies the time needed to form a crystalline phase of a volume fraction X, k is Boltzmann's constant, R is the gas constant, α0 is the atomic diameter (m), Nv is the number of atoms per unit volume and T is the transformation temperature (K). η is the viscosity of the supercooled melts. It can be expressed by the Doolittle formulation based on the relative free volume fT as the following [22]:

η = A exp (B/fT )

(10)

where 5. Kinetic formulations

fT = C exp

A combined thermodynamic and kinetic treatment with the Davies–Uhlmann formulations was presented to evaluate the glass-forming ability [21].

A, B and C are constants. EH represents the hole formation energy. Here, EH could be estimated by the following equation [22]: EH =(13.83Tg − 1400)×4.184 . Supposing that fT =0.05 and η=1012 Pa⋅s at Tg , and setting B = 1, then values of A and C can be calculated [22]. Furthermore, crystallization temperatures Tx can replace Tg when Tg data cannot be obtained. f Represents the fraction of sites on the interface, it could be

t=

⎫1/4 ⎪ exp ΔG*/kT 9.3η ⎧ α09 X ⎨ ⎬ kT ⎩ f 3 Nv ⎡⎣ 1−exp (−ΔG m/RT ) ⎤⎦3 ⎪ ⎭

(

)

⎪

(9)

(

− EH / RT )

(11)

X. Li et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 52 (2016) 57–65

61

Fig. 3. Measured isothermal sections of the Al–Co–Gd ternary system at 1173 K (a) and 773 K (b), respectively [11,12].

Fig. 4. The calculated isothermal section of the Al–Co–Gd system at 1173 K (a) and 773 K(b), respectively.

expressed as follows [23]:

f = 0. 2 (Tm − T )/ Tm

(12)

ΔG* is the free energy barrier for the nucleation of a spherical nucleus. It is expressed as:

G* =

16π 3 2 (σm /∆ Gm ) 3N

The crystal nected energy

(13)

term N is Avogadro's number. σm represents the liquid/ interfacial energy per molar surface area, which is conwith ∆Hfm on account of the relationship between bond values across the interface [24] and can be expressed as:

σm = αHmf

(14)

α was evaluated to be about 0.41 according to Saunders and Miodownik [4].

In this work, the temperature related ΔGm was approximated by Turnbull equation [25]:

∆G m =

∆Hmf(Tm − T ) Tm

(15)

ΔG* can be calculated by inserting the value of and into Eq. (13). Values X=10−6 suggested by Uhlmann [23], α0 ¼0.28  10
9 m and Nv =5×1028 atoms/m3 proposed by Saunders and Miodownik [4] are adopted in this work. On the one hand, information for quantitative determination of these values is absent. On the other hand, the effect of the slight changes in the latter two on the calculated critical cooling rates is less than one order of magnitude [26]. The critical cooling rates can be calculated by the following:

Rc =

Tm − Tn tn

(16)

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X. Li et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 52 (2016) 57–65

Tn and tn refer to the temperature and time at the nose of the TTT curves, respectively.Fig. 1

6. Results and discussion 6.1. Experimental results Constituent phases and compositions of the annealed alloys are listed in Table 1. Fig. 2 shows the back-scattered electronic (BSE) image of the annealed alloys. After annealing at 773 K for 150 days, a two phase region (Co17Gd2 þCo5Gd) and a three phase region (Co5Gd þCo7Gd2 þCo3Gd) were obtained. As it shown in Fig. 2, Co5Gd phase can be observed in both two alloys, we believe that Co5Gd phase is the stable phase in this temperature (773 K), and the samples have reached the equilibrium states. 6.2. Thermodynamic modeling of the Al–Co–Gd ternary system Fig. 5. The calculated vertical section along Al0.5Co0.5–Gd (atomic fraction)of the Al–Co–Gd system compared with experimental data.

Fig. 6. Calculated liquidus projection of the Al–Co–Gd ternary system. Table 3 The calculated invariant reactions and temperatures of the Al–Co–Gd system. Type

Reaction

T(K)

E1 U1 E2 E3 E4 U2 P1 U3 U4 U5 U6 U7 U8 U9 U10 U11 U12 U13 E5 U14 E6 E7

Liquid-BCC_B2þ Co17Gd2 þFCC_A1 Liquid þ Co17Gd2-Co5Gdþ BCC_B2 Liquid-Delta þ BCC_B2 þAl2Gd Liquid-Co5Gdþ Deltaþ Co2Gd Liquid-Co5Gdþ Deltaþ Bcc_B2 Liquid þ Co7Gd2-Co5Gdþ Co3Gd Liquid þ Deltaþ Co2Gd-Theta Liquid þ Co5Gd-Co2Gd þCo3Gd Liquid þ BCC_B2þ Al3Co-Al5Co2 Liquid þ Al5Co2- Al3Coþ Al2Gd Liquid þ Al2Gd-Al3Coþ Al3Gd Liquid þ Al3Co-Al3Gdþ Al13Co4 Liquid þ AlGd-Al2Gd þAl2Gd3 Liquid þ Al2Gd-Deltaþ Al2Gd3 Liquid þ Al13Co4-Al3Gd þAl9Co2 Liquid þ Al2Gd3-Deltaþ AlGd2 Liquid þ HCP_A3-CoGd3 þ Theta Liquid þ Delta-Theta þ AlGd2 Liquid-AlGd2 þ Thetaþ HCP_A3 Liquid þ Theta-CoGd3 þCo2Gd Liquid-Co2Gdþ Co3Gd4 þ CoGd3 Liquid-Al3Gdþ Al9Co2 þ FCC_A1

1620.25 1606.58 1573.64 1571.88 1547.8 1543.88 1533.39 1518.05 1360.91 1330.12 1319.02 1271.06 1191.44 1168.85 1160.75 1115.3 1044.52 1026.45 994.67 934.54 911.96 905.97

The Al–Co–Gd system was optimized by the PARROT module in the Thermo-Calc software package [27,28]. Pandat software [29] was applied to check the database. All the parameters acquired in this work are listed in Table 2. The isothermal sections of the phase diagrams of Al–Co–Gd ternary system measured by Zhou et al. [12] and Gu et al. [13] are shown in Fig. 3(a) and (b), respectively. The calculated isothermal sections at 1173 K and 773 K are shown in Fig. 4(a) and (b), respectively. Fig. 5 presents a comparison of the calculated vertical section along Al0.5Co0.5–Gd (atomic fraction) and corresponding experimental data [10]. The calculated phase relationship in Al– Co–Gd system qualitatively agrees with the experimental results [12,13]. The differences between the experimental and calculated isothermal sections lie in the phase relationship in the Gd-rich region. The experimental results at 773 K demonstrated that there are several two phase regions between Co3Gd and Al–Gd compounds in the Gd-rich corner while our calculated result is different. we found that it was very difficult to fit the result of Gu et al. [13] in our optimization, such two-phase regions were not available even after suspending the ternary compounds. And two samples were also selected to confirm these phase relations. However, with the same methods the samples failed and changed to be powder completely due to the oxidation of the element Gd. Therefore, the phase information in the Gd-poor region was considered as more weight. Hence, our calculation is reasonable and further experimental verification is still needed. The calculated solid solubilities of Al in GdCo0.74Al1.26 and Co2Gd are about 26–38 and 0–17 at% Al, compared with 30–45 and 0–15 at% Al in the literature at 1173 K [12]. The solid solubilities range of Co in Al2Gd is about 0–15.7 at% Co compared with 0– 16 at% Co from Zhou et al. [12]. The maximum solid solubility of Al in Co17Gd2 and Co5Gd extend to 13 and 17 at% Al, compared with 17 and 25 at% Al [12]. The calculated solid solubilities of Al in GdCo0.74Al1.26 and Co2Gd are 29–33 at% and 0–11.5 at% Al, compared with 30–44 and 0–14 at% Al in the literature at 773 K [13]. The solid solubilities of Co in Al2Gd is about 0–15.8 at% Co compared with 0–12 at% Co from Ref. [13]. The maximum solid solubilities of Al in Co17Gd2 and Co5Gd extends to 7 and 8 at% Al, compared with 15 and 24 at% Al in the literature [13]. Fig. 6 shows the liquidus projection of the Al–Co–Gd system. In order to verify the projection, further experimental data are needed. The calculated invariant reactions and temperatures are summarized in Table 3. 6.3. As-cast microstructure and solidification path To verify the reliability of the thermodynamic modeling,

X. Li et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 52 (2016) 57–65

63

Fig. 7. (a) BSE image of the as-cast alloy #1 (6 at% Al–80 at% Co–14 at% Gd) produced in this work labeled with identified phases; (b) Simulated solidification path for the alloy under scheil condition; (c) BSE image of the as-cast alloy #2 (1 at% Al–76 at% Co–23 at% Gd) produced in this work labeled with identified phases; (d) Simulated solidification path for the alloy under scheil condition. Table 4 Alloy compositions, glass transition temperatures, crystallization temperaturesmelting temperatures, critical thicknesses and calculated critical cooling rates of Al–Co–Gd alloys. Alloys

Gd55Co30Al15 Gd60Co35Al5 Gd60Co30Al10 Gd60Co25Al15 Gd60Co20Al20 Gd60Co15Al25 Gd65Co20Al15

Exp [15]

Rc (K/s)

Tg (K)

Tx (K)

Tm (K)

Dmax (mm)

576 557 569 572 580 586 565

607 587 610 617 625 638 598

942 935 948 928 946 953 926

2 1 2 5 2.5 3 2.5

3.07  103 8.18  103 5.90  103 2.17  103 3.12  103 2.38  103 1.09  104

Scheil–Gulliver model [30] was applied to simulate the process of non-equilibrium solidification of the as-cast alloys as illustrated in Fig. 7. The microstructure of as-cast alloy #1 (6Al–80Co–14Gd) is illustrated in Fig. 7(a), with two phases exist in the alloy: dark gray Co17Gd2, light gray Co5Gd.The calculated solidification path of this alloy is shown in Fig. 7(b). According to the calculated results,

Fig. 8. The calculated TTT curves of seven Al–Co–Gd alloys by combined thermodynamic and kinetic method.

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Co17Gd2 primarily precipitates from the liquid phase, followed by the reaction of Liquid-Co17Gd2 þ Co5Gd and Liquid-Co5Gd, and ended with the reaction of Liquid-Co5Gd þ Co7Gd2. However, there is no Co7Gd2 phase in the sample, which is possibly due to the low content of this phase, as the calculated mole fraction of Co7Gd2 is less than 1% in the alloy. The microstructure of as-cast alloy #2 (1Al–76Co–23Gd) is illustrated in Fig. 7(c), with four phases in the alloy: dark gray Co5Gd, gray Co7Gd2, light gray Co3Gd, white gray Co2Gd. Fig. 7 (d) shows the solidification path. According to the calculated results, Co5Gd primarily precipitates from liquid phase. Subsequently, Co7Gd2is formed by the following reactions, Liquid þCo5Gd-Co7Gd2 and Liquid-Co7Gd2. Similarly, Co3Gd comes from the following two reactions, Liquid þ Co7Gd2-Co3Gd and Liquid-Co3Gd. Then a eutectic reaction, Liquid-Co3Gd þCo2Gd will take place. This simulation result is in consistence with the observations as shown in Fig. 7(c). 6.4. Explanation on the glass-forming ability In this work, the GFA of seven alloys for Al–Co–Gd ternary system were evaluated by using the experimental data of Chen et al. [15], including the glass transition temperature Tg, the crystallization temperature Tx and melting temperature Tm by differential scanning calorimetry, as summarized in Table 4. The values of ∆Hfm were calculated from the Thermo-Calc software and ∆Gm were evaluated by Eq. (15) in this work. Fig. 8 shows the TTT curves of seven Al–Co–Gd alloys, calculated from Eq. (9).The critical cooling rates of seven alloys were obtained from Eq. (16). For Gd60Co25Al15, the calculated critical cooling rate is 2.17  103 K/s, which is the lowest rate among those of seven alloys, which agrees with the result reported by Chen et al. [15], in which Gd60Co25Al15 have the best glass-forming composition among these alloys. Furthermore, Gd60Co15Al25 has the second GFA which were also in good agreement with the reported work [15]. In the meantime, in order to check GFA with the additions of Al in Co–Gd alloys, two alloys (binary eutectic composition, Gd63.4Co35.6 and ternary eutectic composition, Gd64.1Co35.8Al0.1) are calculated and the critical cooling rate are 5.55  103 K/s and 2.81  103 K/s respectively. Therefore we can conclude that the addition of Al into Co–Gd alloys can improve the GFA of these alloys. These results indicate that the calculation in this work is consistent with experimental data (Table 4).

7. Conclusion The thermodynamic database was obtained through CALPHAD method to study the solidification path of a typical Al–Co–Gd alloy, which verified the reliability of the thermodynamic description of the system of the present work with a combination of thermodynamic and kinetic approaches. The time–temperature–transformation (TTT) curves and the corresponding critical cooling rates of seven alloys were also obtained, which were consistent with the experimental results in the relative GFA for Al–Co–Gd ternary system.

Prime novelty statement

(1) All authors have participated sufficiently in this work to take public responsibility for it. (2) All authors have reviewed the final version of the manuscript and approve it for publication. (3) Neither this manuscript nor one with substantially similar

content under our authorship has been published or is being considered for publication elsewhere.

Acknowledgments The authors would like to express gratitude to the financial support of the National Natural Science Foundation of China (Grant nos. 51371200, 51501229) and Fundamental Research Funds for the Central Universities, Central South University (No. 502044009). This work also supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry (No. 413060011) and State Key Laboratory of Powder Metallurgy, Central South University, Changsha, China.

Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.calphad.2015.11.002.

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