Scripta Materialia 55 (2006) 1027–1030

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Glass-forming ability and fragility ofRE55Al25Co20 (RE = Ce, Pr, Nd, Sm, Gd) alloys

Jing Guo,a Xiufang Bian,a,* Qingge Meng,b Yan Zhao,a Shenghai Wang,a

Caidong Wanga and Taibao Lia

aThe Key Laboratory of Liquid Structure and Heredity of Materials, Ministry of Education, Shandong University, Jinan 250061, ChinabSchool of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200030, China

Received 3 July 2006; revised 3 August 2006; accepted 4 August 2006Available online 15 September 2006

The glass-forming ability (GFA) of RE55Al25Co20 (RE = Ce, Pr, Nd, Sm, Gd) alloys ranks as follows: Ce55Al25Co20 <Pr55Al25Co20 and Nd55Al25Co20 < Sm55Al25Co20 and Gd55Al25Co20. Only Sm55Al25Co20 and Gd55Al25Co20 alloys show whollyamorphous structures when the alloys are cast into rods up to 2 mm in diameter. A comparison study shows that the Sm55Al25Co20

alloy exhibits the smaller difference in Gibbs free energy (DG1�x(Tg)) and the stronger fragility, which are consistent with the higherGFA for this alloy.� 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Metallic glasses; Fragility; Difference in the Gibbs free energy

Some rare-earth (RE)-based metallic alloys are cur-rently under widespread investigation due to their goodglass-forming abilities (GFA) and their significance inapplications as functional materials [1–4]. RE-based al-loys like La–Al–Ni, La–Al–Cu and some Nd-based al-loys can form amorphous rods with diameters up to6 mm [5–7]. Therefore, it is of interest to further studythe GFA of RE-based alloys. In our previous study[8], the Sm55Al25Co20 alloy has been demonstrated topossess a high GFA; it can be cast into uniformly glassyrod up to at least 4 mm in diameter. In this report, otherRE-based alloys are studied with the composition ofRE55Al25Co20.

Among the classifications of strong–fragile character-istics of glass-forming liquids, the most useful one wasproposed by Angell [9], where the fragility of a liquidis defined by the deviation of the viscosity’s temperaturedependence from Arrhenius behavior. Angell [9,10] ob-served that around the glass transition region, the tem-perature dependence of viscosity (g) of some strongglass-forming liquids like SiO2 and GeO2 approximatelyfits the Arrhenius equation (logg versus 1/T plot is lin-

1359-6462/$ - see front matter � 2006 Acta Materialia Inc. Published by Eldoi:10.1016/j.scriptamat.2006.08.021

* Corresponding author. Tel.: +86 531 88392748; fax: +86 53188395011; e-mail addresses: gjcp1980@hotmail.com; xfbian@sdu.edu.cn

ear), however, for the fragile liquids like iron phosphate[11], the temperature dependence of viscosity is typicallynon-Arrhenius and the logg versus 1/T plots for theseliquids deviate from linearity. Actually, the temperaturedependence of viscosity is determined by the value ofDHg/Tg, (where DHg is the activation energy for viscousflow) [12]. Some researchers [12–14] have reported thatfor most glass-forming liquids, the activation energyfor the glass transition (DHg) has a similar value to theactivation energy of viscous flow (DHg) within the glasstransition region. DHg is therefore substituted for DHg

to determine the strong–fragile characters of glass-form-ing liquids. DHg can be determined by the dependenceof Tg on the heating rate, which can be derived from dif-ferential scanning calorimetry (DSC) measurements. Bythis approach, the strong–fragile characters of glass-forming liquids can be easily established without viscos-ity measurements.

In this paper, the glass-forming abilities of RE55Al25-Co20 (RE = Ce, Pr, Nd, Sm, Gd) alloys are investigated.Further, the difference in the Gibbs free energy betweenthe liquid and crystalline states at the glass transitiontemperature and the fragility of the Sm55Al25Co20 andGd55Al25Co20 glass-forming alloys will also be studied.

The ingots of RE55Al25Co20 (Ce, Pr, Nd, Sm, Gd)were prepared by arc-melting pure Al, Co and industri-ally pure Ce, Pr, Nd, Sm and Gd in a Ti-gettered argon

sevier Ltd. All rights reserved.

Table 1. The DHmix, Sr/kB and the structure of RE55Al25Co20

(RE = Ce, Pr, Nd, Sm, Gd) alloys

Alloys DHmix (kJ/mol) Sr/kB Structure

Ce55Al25Co20 �32.62 0.67 cPr55Al25Co20 �33.50 0.63 a + cNd55Al25Co20 �33.50 0.62 a + cSm55Al25Co20 �34.38 0.59 aGd55Al25Co20 �34.93 0.58 a

In the structure column ‘‘a’’ represents amorphous phase and ‘‘c’’represents crystalline phase.

1028 J. Guo et al. / Scripta Materialia 55 (2006) 1027–1030

atmosphere. The purity of RE is about 99.5 wt.%, whichis much lower than that of other base elements of bulkmetallic glasses (BMGs). To ensure homogeneity ofthe samples, the ingots were repeatedly melted, at leastfive times. By using an induction-heating coil, the ingotswere melted in a quartz tube and were injected into acopper mold under the pressure of high-purity argonto get cylindrical rods up to 2 mm in diameter and60 mm in length. The structure of the transverse crosssections of cast rods was ascertained by X-ray diffrac-tion (XRD) with the use of a D/Max-rB diffractometerand Cu Ka radiation and the scattering angle (2h) rangeis 10�–80�. Calorimetric measurements were performedin a Netzsch DSC 404C at different heating rates. Thedetailed measurement processes to obtain the specificheat capacity were given by Bush et al. [15].

Figure 1 shows the XRD patterns of the transversecross sections of the cast rods of RE55Al25Co20

(RE = Ce, Pr, Nd, Sm, Gd) with diameters of 2 mm.The XRD pattern of Ce55Al25Co20 alloy reveals manycrystallization peaks, which indicates its cast structureis mostly crystalline. For RE55Al25Co20 (RE = Pr,Nd), there are some crystalline peaks on the diffuse peakindicating that the rod samples are a mixture of amor-phous and crystalline phases. However, for RE55Al25-Co20 (RE = Sm, Gd), the typical XRD pattern of anamorphous structure without Bragg peaks denotes thehomogeneous amorphous structures for these two al-loys. As a result, it can be deduced that the GFA ofthe samples ranks from low to high as follows: Ce55Al25-Co20 < Pr55Al25Co20 and Nd55Al25Co20 < Sm55Al25Co20

and Gd55Al25Co20.Inoue [16] proposed three empirical rules in search of

new bulk amorphous alloys: (1) multi-component sys-tems consisting of more than three elements; (2) signifi-cant difference in atomic sizes with the size ratios aboveabout 12% among the three main constituent elements;and (3) negative heats of mixing among the three mainconstituent elements. The parameters of mismatchentropy normalized by the Boltzmann constant (Sr/kB)and mixing enthalpy (DHmix) correspond to the secondand the third terms of the above empirical rules, respec-tively. In general, both the large Sr/kB and negativeDHmix are believed to favor the stability of the amor-phous structure and the formation of BMGs [17]. Basedon Miedema’s model of regular solution [18,19] and thesolution of the Perkus–Yevik integral equation [20], val-ues of DHmix and Sr/kB for RE55Al25Co20 (RE = Ce, Pr,

Figure 1. XRD patterns of RE55Al25Co20 (RE = Ce, Pr, Nd, Sm, Gd)cylinder rods with the diameter of 2 mm.

Nd, Sm, Gd) alloys are calculated and listed in Table 1.With increasing atomic number, the absolute value ofDHmix increases and Sr/kB decreases, and the GFA isenhanced. As a result, for RE55Al25Co20 (RE = Ce, Pr,Nd, Sm, Gd) alloys, DHmix has a good correlation withthe GFA, but Sr/kB does not.

Among the samples of RE55Al25Co20 (RE = Ce, Pr,Nd, Sm, Gd) with the diameter of 2 mm, only theSm55Al25Co20 and Gd55Al25Co20 alloys can be cast intowholly amorphous rods, so the GFA and the fragility ofthese two alloys are further investigated.

The DSC curves of the Sm55Al25Co20 and Gd55Al25-Co20 BMGs at the heating rate of 20 K/min are shownin Figure 2. A single and narrow endothermic peak ofmelting is observed for the two alloys, indicating thatthe composition of the alloys is typically close to a deepeutectic point. The glass transition begins at 589 K and alarge supercooled liquid region of 66 K (DT = Tx � Tg,where Tx is the onset crystallization temperature, andTg is the glass transition temperature) is obtained forthe Gd55Al25Co20 BMG. The Tx, the melting tempera-ture Tm and the liquidus temperature Tl were deter-mined to be 655, 942, and 971 K, respectively. Thereduced glass transition temperature Trg(Trg = Tg/Tl)and the value c = Tx/(Tg + Tl), which are two importantparameters in determining the GFA of an alloy, are 0.61and 0.42, respectively. Compared with the Gd55Al25Co20

BMG, Sm55Al25Co20 exhibits relatively low Tg (556 K),Tx (625 K), Tm (861 K), Tl (889 K) values but large DTx

(69 K), Trg (0.63) and c (0.43), which illustrates betterGFA of the Sm55Al25Co20 alloy. The characteristic tem-peratures and other important parameters used in eval-uating the GFA of the alloys are listed in Table 2.

The thermal stability for the BMGs can be comparedby examining the activation energy of crystallizationemploying the Kissinger method [21]. The DSC heating

Figure 2. DSC traces of (a) Gd55Al25Co20 and (b) Sm55Al25Co20 bulkmetallic glasses at a heating rate of 20 K/min.

Table 4. The glass transition temperature Tg, the activation enthalpyfor glass transition DHg and the fragility parameter m forSm55Al25Co20 and Gd55Al25Co20 alloys

Alloy DHg (kJ/mol) Tg (K) m

Gd55Al25Co20 362.4 589 74Sm55Al25Co20 187.7 556 40.6

Table 2. Parameters describing the thermal stability and glass forming ability of Sm55Al25Co20 and Gd55Al25Co20

Alloys Tg (K) Tx (K) DTx (K) Tm (K) Tl (K) Trg c = Tx/(Tg + Tl)

Sm55Al25Co20 556 625 69 861 889 0.63 0.43Gd55Al25Co20 589 655 66 942 971 0.61 0.42

J. Guo et al. / Scripta Materialia 55 (2006) 1027–1030 1029

rates are 5, 10, 20 and 40 K/min, respectively. Accordingto Eq. (1):

AR

T 2¼ exp � Ex

kBT p

� �; ð1Þ

where A is a temperature-independent constant, R is theheating rate during the DSC scan, Tp is the peak temper-ature of crystallization transformation and kB is theBoltzmann constant, the activation energy for the crys-tallization of an amorphous phase, Ex, can be obtained.Based on the data shown in Table 3, the Kissinger plotsfor the Gd55Al25Co20 and Sm55Al25Co20 BMGs aredetermined, as shown in Figure 3. The activation ener-gies of crystallization were calculated to be 356.6 and315 kJ/mol for the Gd55Al25Co20 and Sm55Al25Co20

BMGs, respectively. The larger activation energy ofGd55Al25Co20 indicates higher thermal stability againstcrystallization than Sm55Al25Co20.

There are several approaches to quantifying the‘fragility strength’ [22,23], among which the fragilityparameter, m, is often used. The value of the ‘fragilityparameter’ is calculated by using Eq. (2) [24]:

m ¼ DH g

RT g;20

; ð2Þ

where DHg is the activation enthalpy for the glass tran-sition and R is the gas constant. Tg,20 is the glass transi-tion temperature at a scanning rate of 20 K/min by

Table 3. The glass transition temperature Tg and the peak temperatureof crystallization transformation Tp at different heating rates forGd55Al25Co20 and Sm55Al25Co20 BMGs

Heating rates (K/min) Gd55Al25Co20 Sm55Al25Co20

Tg (K) Tp (K) Tg (K) Tp (K)

5 578 647 537 61810 584 654 546 62320 589 665 556 63140 594 678 563 640

Figure 3. Kissinger plots for (a) Gd55Al25Co20 and (b) Sm55Al25Co20

BMGs.

DSC. The value of DHg is calculated from Eq. (1)[13,25]. According to the values Tg and DHg (Table 3),m is calculated to be 74 for the Gd55Al25Co20 BMGand 40.6 for the Sm55Al25Co20 BMG. The smaller fragil-ity parameter for the Sm55Al25Co20 alloy indicates it is astronger glass former than the Gd55Al25Co20 alloy (seeTable 4).

As investigated by Busch et al. [26], the glass formerswith low critical cooling rates have smaller Gibbs freeenergy difference (DG1�x(T)) than the glass formers withhigh critical cooling rates. This means that the drivingforce for crystallization decreases with increasingGFA. Therefore, the value of the Gibbs free energy dif-ference at the glass transition temperature DG1�x(Tg) isvery important. A smaller value of DG1�x(Tg) generallyfavors bulk glass formation [27,28].

The difference in the Gibbs free energy between theliquid and crystalline states is given by Eq. (3) [27,28]:

DGl�xðT Þ ¼ DH f �Z T m

TDCl�x

p ðT ÞdT� �

� T DSf �Z T m

T

DCl�xp ðT ÞT

dT

" #; ð3Þ

where DCl�xp is the difference in the specific heat capacity

of the liquid and the crystalline states. By using theapproximation, Thompson et al. gave the followingequation to calculate the Gibbs free energy betweenthe liquid and crystalline states [29–31]:

DGl�xðT Þ ¼ DH fDTT m

2TT m þ T

� �; ð4Þ

where DHf is the heat of fusion; DT is the difference be-tween Tm and T. DHf is obtained by the integral of thespecific heat capacity at fusion peak on DSC curve, asshown in Figure 4. According to Eq. (4), DGl�x(Tg) ofSm55Al25Co20 and Gd55Al25Co20 alloys are obtained(Table 5), which are close to the values of Pr-based alloys[31]. Compared with the Gd55Al25Co20 alloy, the smallerDG1�x(Tg) for the Sm55Al25Co20 alloy indicates a higherGFA. That is in agreement with the results of the varioustemperature parameters used in estimating the GFA ofBMGs.

After investigating the GFA of the RE55Al25Co20

(RE = Ce, Pr, Nd, Sm, Gd) alloys, we have drawn thefollowing conclusions:

Figure 4. The heat of fusion obtained by the integral of the specificheat capacity at fusion peak. (a) Gd55Al25Co20 alloy; (b) Sm55Al25Co20

alloy.

Table 5. The glass transition temperature Tg, the melting temperatureTm, the difference between Tm and Tg (DT), the heat of fusion DHf andthe Gibbs free energy difference DG1�x(Tg) at Tg with a heating rate of20 K/min

Alloys Tg

(K)Tm

(K)DT

(K)DHf

(kJ/mol)DG1�x(Tg)(kJ/mol)

Gd55Al25Co20 589 942 353 8.8 2.6Sm55Al25Co20 556 861 305 7.8 2.1

1030 J. Guo et al. / Scripta Materialia 55 (2006) 1027–1030

(1) The GFAs of the RE55Al25Co20 (RE = Ce, Pr, Nd,Sm, Gd) alloys rank from low to high as follows:Ce55Al25Co20 < Pr55Al25Co20 and Nd55Al25-Co20 < Sm55Al25Co20 and Gd55Al25Co20. Whenthe samples were cast into rods up to 2 mm in diam-eter, only Sm55Al25Co20 and Gd55Al25Co20 samplesexhibited wholly amorphous structures.

(2) Compared with the Gd55Al25Co20 alloy,Sm55Al25Co20 exhibited a better GFA and lowerthermal stability against crystallization accordingto the parameters describing the GFA and the ther-mal stability.

(3) Using the data for the glass transition activationenthalpy DHg and the glass transition temperature,the fragility parameter, m, were determined to be 74and 40.6 for the Gd55Al25Co20 and Sm55Al25Co20

BMGs, respectively.(4) The smaller DG1�x(Tg) of the Sm55Al25Co20 alloy

indicated a higher GFA than that of theGd55Al25Co20 alloy.

We thank Dr. Z. Liu for helpful suggestions on thepaper and acknowledge the support of the NationalNatural Science Foundation of China (No. 50231040),

Shandong Natural Science Foundation of China(Z2004F02) and Specialized Research Fund for the Doc-toral Program of Higher Education (No. 20050422024).

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